Wind power effects and price elasticity of demand for the ... · 2.1 Daily share of traded electricity on Elspot Market, as ratio of total consumption 2012-2014 26 2.2 Relationship

Wind power effects and price elasticity of

demand for the Nordic Electricity Markets

PhD dissertation

Ioana Daniela Neamtu

<

Aarhus BSS, Aarhus University

Department of Economics and Business Economics

2016

CONTENTS

Contents ii

List of Figures v

List of Tables vii

Preface x

Summary xiii

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Danish Summary xvi

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

1 Fundamentals of the Nordic Electricity Markets 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 The Nord Pool market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Short History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

The production mix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 The Elspot market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 The Elbas market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 The balancing market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6 The ancillary services market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.7 The retail market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.9 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2 Demand and Supply Management for the wholesale Electricity market 23

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 The Elspot Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Electricity Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Electricity Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

ii

CONTENTS iii

2.5 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

The demand side variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

The supply side variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Empirical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

The estimation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Preliminary tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

The demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

The supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.8 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.9 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3 Wind Power effects for Price Level and Volatility for the Wholesale Electricity market 56

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2 The Danish Electricity market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Modeling price levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Modeling the volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

The GARCH model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

The EGARCH model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Final model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 Data and descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Wind power penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Congestion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Electricity prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

The regime-switching model with constant variance . . . . . . . . . . . . . . . . . . 69

The regime-switching model with non-constant variance . . . . . . . . . . . . . . . . 71

Price levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Price volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.7 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4 Wind Power Effects in the Real-time Balancing Market 85

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.3 The regulating market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

CONTENTS iv

4.4 Data and variables description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

The regulating price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

The regulating power and the state of the market . . . . . . . . . . . . . . . . . . . . . 92

Wind power forecast errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.5 Model and estimation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Quantile regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Models for the regulating price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Hour 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Hour 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Hour 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.7 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.8 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.9 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

LIST OF FIGURES

1.1 Description of electricity markets in Denmark and Nordic countries . . . . . . . . . . . 3

1.2 Net Power Generation Mix on Nord Pool in 2013 and 2015, by production source . . . . 6

1.3 Total cost function, for different types of electricity producers . . . . . . . . . . . . . . . 7

1.4 Average retail price decomposition for households, in Denmark, 2010-2015 . . . . . . . 15

1.5 Share of the Elspot electricity price of the retail price (including VAT and other taxes),

for West and East Denmark, 2006-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.6 Average monthly price for electricity (øre/kWh) for households, by type of contract, in

Denmark, 2014-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.7 Percentage of consumers changing suppliers, by type of consumption and overall, in

Denmark, 2003-20014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.1 Daily share of traded electricity on Elspot Market, as ratio of total consumption 2012-2014 26

2.2 Relationship between demand and temperature at hour 11 on Elspot Market, 2012-2014 31

2.3 Daily variations of demand on the Elspot Market, at hour 11, 2012-2014 . . . . . . . . . 32

2.4 Electricity price formation on Nord Pool market . . . . . . . . . . . . . . . . . . . . . . . 33

2.5 Daily variations of the Elspot system price, 2012-2014 . . . . . . . . . . . . . . . . . . . . 33

2.6 Percentage change of quantity demanded at a 1% increase in Elspot system prices,

2012-2014, base specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 Interconnections between the bidding areas on the Elpost Market . . . . . . . . . . . . . 60

3.2 Relationship between wind power penetration (%) and daily Elspot area prices

(DKK/MWh) in West Denmark, for hour 12, during congested and non-congested

regimes, 2012-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.3 Average daily Elspot area prices (DKK/MWh) in West Denmark, during congested and

non-congested periods, per hour, 2012-2015 . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.4 Box plot for daily Elspot area prices (DKK/MWh) in West Denmark, per hour, 2012-2015 68

3.5 Total number of hours with negative Elspot area prices in West Denmark, per hour,

2012-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.6 Change in the daily Elspot area price, for West Denmark at hour 12 and 00, 2012-2015 . 71

3.7 Graphical representations of the effects of wind power penetration on price variance in

West Denmark, during congested and non-congested periods (presented in Table 3.3) 75

3.8 Total forecasted consumption in Elspot market, during congested and non-congested

periods, 2012-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

v

List of Figures vi

4.1 Box-plot for the regulating price in West Denmark (DKK), by hour, during up and down

regulating states, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.2 Daily variation of regulating prices, during up and down-regulating states, in West

Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.3 Average daily regulating quantities (MWh), during up and down regulating states, in

West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.4 Average daily rate of occurrence (%) for the regulating states in West Denmark, by hour,

2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.5 Average daily wind power forecasting errors (MWh),in West Denmark, by hour, 2012-

2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.6 Relationship between wind power forecasting errors and regulating price, hours 3 and

11, in West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.7 Quantile regression, model fit, equation (4.10), hour 3, West Denmark, 2012-2014 . . . 102

4.8 Quantile regression, model fit, equation (4.10), hour 9, West Denmark, 2012-2014 . . . 104

4.9 Quantile regression, model fit, equation (4.10), hour 18, West Denmark, 2012-2014 . . 107

4.10 The wind power forecasting error effects on the regulating price, during up and down-

regulation, when demand (D) or supply (S) shifts up or down . . . . . . . . . . . . . . . 108

4.11 Empirical distribution of daily regulating price, by state of the market, hour 3, West

Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112


Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112


Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.14 Average daily regulating price, by type of wind power forecasting errors, during the up-

regulating state, West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.15 Average daily regulating price, by type of wind power forecasting errors, during down-

regulating state, West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.16 Quantile regression, model fit, equation (4.9), for hour 3, West Denmark, 2012-2014 . . 125

4.17 Quantile regression, model fit, equation (4.9), for hour 9, West Denmark, 2012-2014 . . 125

4.18 Quantile regression, model fit, equation (4.9), for hour 18, West Denmark, 2012-2014 . 125

4.19 Coefficient estimates for equation (4.10), for hour 3, West Denmark, 2012-2014 . . . . . 127

4.20 Coefficient estimates for equation (4.10), for hour 9, West Denmark, 2012-2014 . . . . . 128

4.21 Coefficient estimates for equation (4.10), for hour 18, West Denmark, 2012-2014 . . . . 129

LIST OF TABLES

1.1 Shares of annual consumption and production for Nordic and Baltic countries, per

country, 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Net power production mix, as share of total net production(%), for Nordic and Baltic

countries, per country, 2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Fixed and variable costs of electricity included in the retail price, per electricity

participants, in Denmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.4 Short definitions of concepts used in this chapter . . . . . . . . . . . . . . . . . . . . . . 22

2.1 Description of daily Elspot system price, per hour, 2012-204 . . . . . . . . . . . . . . . . 30

2.2 Price elasticity of demand, per hour, several specifications . . . . . . . . . . . . . . . . . 38

2.3 Effects of the wind power production on the Elspot system price, per hour . . . . . . . . 39

2.4 Data definition and sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.5 Descriptive statistics of the daily Elspot system price (DKK/MWh), per hour, 2012-2014 44

2.6 Descriptive statistics of the daily Elspot equilibrium quantity (MWh), per hour, 2012-2014 45

2.7 Descriptive statistics of the daily total available capacity (GWh) on the Elspot market,

per hour, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.8 Descriptive statistics of the daily weighted average temperature for the Elspot market,

per hour (Celsius), 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.9 Descriptive statistics of the daily weighted average wind chill factor, for the Elspot

market, per hour, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.10 Descriptive statistics of the daily aggregated wind power production (MWh) on Elspot

market, per hour, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.11 Hour-invariant variables, daily, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.12 Results for seasonality effects for each hour of the day, based on F-tests . . . . . . . . . 50

2.13 Augmented Dickey-Fuller test for price and quantity . . . . . . . . . . . . . . . . . . . . . 51

2.14 Coefficients for the base model, for the demand equation . . . . . . . . . . . . . . . . . . 52

2.15 Coefficients for the demand when price lags(1 and 7) are included in the model . . . . 53

2.16 Coeficients of the base model, for the supply equation . . . . . . . . . . . . . . . . . . . . 54

2.17 Test for overidentification for each hour of the day . . . . . . . . . . . . . . . . . . . . . . 55

3.1 Marginal effects of wind power penetration for the Elspot area price in West Denmark,

for the single regime and the regime-switching model (congestion and

non-congestion), assuming constant-variance, per hour . . . . . . . . . . . . . . . . . . 70

vii

List of Tables viii

3.2 Marginal effects of wind power penetration for the daily Elspot area price in West

Denmark, for the single-regime and regime-switching

model(congetion/non-congestion), with non-constant variance, per hour . . . . . . . . 73

3.3 Effects of wind power penetration for the daily Elspot area price variance in West

Denmark, under the single-regime and the regime-switching

(congestion/non-congestion) model, and different specifications of the conditional

mean(M1, M2, M3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.4 Descriptive statistics of congestion and daily Elspot area prices for West Denmark, per

hour, 2012-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.5 Descriptive statistics of daily wind power penetration in West Denmark and Elspot

Market, per hour, 2012-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.6 Specification for each hour of the day in West Denmark . . . . . . . . . . . . . . . . . . . 83

3.7 Akaike Information Criterion (AIC) for different model specifications in the conditional

mean (equation (3.2)), for wind power penetration . . . . . . . . . . . . . . . . . . . . . . 84

4.1 Summary for the use of regulating power in Denmark . . . . . . . . . . . . . . . . . . . . 88

4.2 Pricing scheme for the regulating market, by state of the market and type of regulation

power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.3 Descriptive statistics of important variables, hour 3, West Denmark, 2012-2014 . . . . . 99

4.4 Coefficient estimates for equation (4.9), hour 3, West Denmark, 2012-2014 . . . . . . . 100

4.5 Effects of positive versus negative wind power forecasting errors (WPFE), during up-

and down-regulation, hour 3, West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . 101

4.6 Descriptive statistics of important variables, hour 9, West Denmark, 2012-2014 . . . . . 102


4.8 Effects of positive versus negative wind power forecasting errors (WPFE), during up-

and down-regulation, hour 9, West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . 104

4.9 Descriptive statistics of important variables, hour 18, West Denmark, 2012-2014 . . . . 105


4.11 Effects of positive versus negative wind power forecasting errors (WPFE), during up and

down-regulation, hour 18, West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . 106

4.12 Descriptive statistics for the daily net regulating volumes, by state of the market and

hour, West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.13 Descriptive statistics for the daily regulating prices, by state of the market and hour,

West Denmark, 2012-2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.14 Seasonality tests for the daily regulating price, per hour, West Denmark, 2012-2014 . . 117

4.15 Unit-root tests for regulating prices, by hour, West Denmark, 2012-2014 . . . . . . . . . 118


4.17 Wind power forecasting errors (WPFE) for the cond. quantiles of regulating prices,

during up and down regulation, different specifications, hour 3 . . . . . . . . . . . . . . 120

List of Tables ix


4.19 Wind power forecasting errors (WPFE) for the cond. quantiles of regulating prices,

during up and down regulation, different specifications, hour 9 . . . . . . . . . . . . . . 122

4.20 Coefficient estimates for equation (4.10), hour 18, West Denmark, 2012-2014 . . . . . . 123

4.21 Effects of positive versus negative wind power forecasting errors (WPFE) for the cond.

quantiles of regulating prices, during up and down regulation, different specifications,

hour 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

PREFACE

This Ph.D dissertation was written in the period January 2013 and February 2016, as part of my

graduate studies at the Department of Economics and Business, at Aarhus University and during

my visit at the Department of Economics, at Melbourne University. The work presented has been

done in support of package 3.2. of the EDGE (Efficient Distribution of Green Energy) project,

developed in collaboration with the Department of Automation and Control from Aalborg

University and partially supported by the Danish Council for Strategic Research, within the

Programme Sustainable Energy and Environment. I am grateful to all of these institutions for

hosting me and providing an outstanding research environment and generous financial support

for participation to courses and conferences.

Many people deserve my gratitude. First and foremost, I would like to thank my supervisor,

Henning Bunzel, for his support and great advice; for always having his door opened for

questions and discussions and always having an emergency plan, when everything seemed to

collapse. I am very grateful for your gentile support and all the freedom I had during these three

years. Likewise, I would like to thank Kirsten Stentoft for her invaluable, administrative help

during this time and excellent proof-reading of the chapters of this thesis. Second, I would like to

thank Mariola Pytlikova, for being a great supervisor during my master’s thesis and sharing her

wisdom beyond her job requirements and for encouraging me follow a Ph.D at the Department.

Likewise, I would like to thank Niels Westergaard Nielsen for being a great boss during my

research-assistant position. I have learned so much during this time. It was an amazing and

inspiring experience, for which I would also like to thank all the people down at Frichshuset.

I would like to extend my gratitude to Christopher Skeels and Kevin Staub for making my visit

at Melbourne University possible and a very nice experience. Likewise, I want to thank Matt and

all the Ph.D students in room 305, for making me feel at home on the other side of the world.

Moreover, I would like to thank Rafal Wisniewski and all the people involved in the EDGE project

for creating a relaxed, creative and productive atmosphere during our project meetings and for all

their comments and suggestions during the project.

I am also grateful to have been a part of the Department of Economics and Business at Aarhus

University and be surround by great professionals and wonderful people who always have a good

advice regarding research and life. I am thankful to all my “lunch-buddies” for relaxing chats

during stressful days and to all those who worked hard for creating and maintaining an

entertaining social life for the Ph.D students. Likewise, I would like to thank Girum, for being a

great friend and an excellent office-mate.

Last but not least, I would like to thank my friends for their support and encouragement during

x

PREFACE xi

the good times and more importantly, during the dark times. Also, I want to thank Alex, for his love

and support during the beginning of this Ph.D and Peter for helping me get through the writing

process; for his constant encouragement, love and understanding. You both have helped me so

much, in so many different ways. But above all, I would like to thank my parents and my family,

for all their wonderful advice, continuous support and unconditional love.

Ioana Neamtu

Aarhus, February 2016

PREFACE xii

Updated Preface

The predefense took place on April 12, 2016. I am very grateful to the members of the assessment

committee Rafał Weron (Wrocław University of Technology), Frits Møller Andersen (DTU,

Denmark) and Svend Hylleberg (Aarhus University and CREATES) for their careful reading of my

dissertation and their constructive comments and suggestions. Many of the suggestions have

been incorporated in the current version of the dissertation while others remain for future

research.

Ioana Neamtu

Aarhus, August 2016

SUMMARY

This thesis is comprised of four self-contained chapters related to the electricity market(s) in

Danish and Nordic countries. They present empirical investigations of the hot-topics

surrounding electricity market research today, with a focus on wind power effects on the Danish

electricity system, for the day-ahead market and the regulating market.

The first chapter of the thesis, entitled Fundamentals of the Nordic Electricity Markets, offers

an overview of the Nordic electricity markets and points to the main research directions related to

the Nordic electricity markets. It introduces the reader to the functionality of the Nordic

electricity system, its main characteristics and unique features. Based on current literature, the

pluses and minuses of the current market design are being discussed in order to better

understand the limitations and possible drawbacks of the Nordic market design as well as why it

is considered one of the most efficient systems in the world. This chapter offers a description of

the markets where physical electricity is traded (the day-ahead market, the hour-ahead market,

the balancing market, the ancillary services market and the Danish retail electricity market), the

main participants in these markets and their roles, and it answers questions regarding the

existence of market power, the efficiency of the marginal auction system, the possibility of

arbitrage on the regulating market and the competitiveness of the retail market.

Chapter two of the thesis, Demand and Supply Management for the wholesale Electricity

Market, investigates the existence of demand side response on the Nordic day-ahead, wholesale

electricity market. The day-ahead market for Nordic countries is a spot market where consumers

and producers bid for the purchase and sale of electricity power, respectively, up to 12 hours

before the delivery hour. Therefore, the demand response of the aggregators for consumption in

the day-ahead market is investigated, by estimating the price elasticity of demand for each hour

of the day, through a system of simultaneous equations. It is assumed that aggregators on this

market have the most potential for flexibility.

The structural model proposes a demand function with constant elasticity that controls for

weather conditions and a supply function that accounts for the different production technologies

of the Nordic countries. The model follows the methodology proposed by Huisman et al. (2007).

Each hour of the day is treated as a separate daily time-series, but the model still accounts for

unobserved correlations between the hours, by not imposing restrictions on the covariance

matrix of the errors. A supply and demand equilibrium model is then defined for each hour and

the model is estimated simultaneously for the 48 resulting equations, using the generalized

method of moments introduced by Hansen (1982). Small and statistically significant price

elasticities of demand are found, which are different for day and night-time hours.

xiii

SUMMARY xiv

Chapter three, Wind Power effects for Price Level and Volatility for the Wholesale Electricity

market, focuses on the supply side of the day-ahead electricity market for Nordic countries. It

investigates the wind power penetration effects of the prices of electricity, for levels and volatility,

for each hour of the day, for West Denmark. The model proposed accounts for the congestion

constraints that appear in the Nordic electricity market and assumes that the fluctuations of wind

power production affects both the levels and the volatility of the prices. These effects are

investigated through a GARCH-regime-switching model with observed states. It uses the wind

power penetration levels for the Elspot market, during non-congested periods and the wind

power penetration levels for West Denmark, during congested periods. Congestion is defined as

the situation in which the price of the Elspot market is different than the price for West Denmark.

It is found that wind power penetration reduces the levels of prices for all hours of the day and the

volatility of prices during the day-time hours (similarly to Jonsson et al.(2010)). It was also found

that the reduction in price levels during congested hours are lower than during non-congested

periods and that price volatility increases during night-time hours for congested periods, while

no effects are found during non-congested periods for night-time hours.

In chapter four, Wind Power Effects in the Real-time Balancing Market, the effects of wind

power forecasting errors for the levels of the prices from the balancing (or regulating) market are

investigated, in West Denmark. This market is a 45 minutes ahead market, that opens after the

closing of the day-ahead electricity market, where the Transmission System Operator buys or sells

the electricity needed to keep the electricity system in balance. The assumption underlying this

chapter is that higher wind power penetration levels lead to higher wind power forecasting errors

and a higher need for balancing on the regulating market, thus affecting the regulating prices. To

test this assumption a variable for wind power forecasting errors is defined as the difference

between forecasted wind power production from the Elspot and actual wind power production

from the Elspot market. The effects of positive and negative wind power forecasting errors are

investigated by using a regime switching model with three observed states, similar to the one

proposed by Skytte(1999), for several quantiles of the distribution of the regulating price. It is

found that positive wind power forecasting errors reduce the conditional quantiles of the

down-regulating price, but it increases the conditional quantiles of the up-regulating price,

during the night-time hour investigated. During day-time hours, positive wind power forecasting

errors have a positive effect on the conditional quantiles of the down-regulating price and no

statistically significant effect for the conditional quantiles of the up-regulating price. Moreover,

negative wind power forecasting errors have a positive effect on the conditional quantiles of the

down-regulating prices during the night-time hour investigated, but a negative effect during the

day-time hours. During the up-regulating state, the negative wind power forecasting errors have

no significant effect during night-time hours, but a negative effect on the conditional quantiles of

the price distribution, during the down-regulating state.

SUMMARY xv

Bibliography

Hansen, L. P. (1982). Large Sample Properties of Generalized Method of Moments Estimators.

Econometrica: Journal of the Econometric Society, 1029–1054.

Huisman, R., C. Huurman, and R. Mahieu (2007). Hourly electricity prices in day-ahead markets.

Energy Economics 29(2), 240–248.

Jonsson, T., P. Pinson, and H. Madsen (2010). On the market impact of wind energy forecasts.


Skytte, K. (1999). The regulating power market on the Nordic power exchange Nord Pool: an

econometric analysis. Energy Economics 21(4), 295–308.

DANISH SUMMARY

Afhandlingen består af fire selvstændige kapitler relateret til elektricitetsmarkederne i Danmark

og de andre nordiske lande. Der fremlægges empiriske undersøgelser af aktuelle problemer

relateret til forskningen af elektricitetsmarkederne i dag. Fokus er på vindkrafteffekterne på det

danske elektricitetssystem, fra næste-dags-marked til det regulerende marked.

Afhandlingens første kapitel, Fundamentals of the Nordic Electricity Markets, giver et overblik

over de nordiske elektricitetsmarkeder og opremser de væsentligste forskningsemner i relation til

de nordiske elektricitetsmarkeder. Det introducerer læseren til det nordiske elektricitetssystems

funktionalitet og hovedkarakteristika. Baseret på den tilgængelige litteratur diskuteres plusser og

minusser ved det nuværende markedsdesign for bedre at forstå begrænsningerne og mulige

mangler ved det nordiske markedsdesign, og hvorfor det alligevel betragtes som et af de mest

effektive systemer i verdenen. Kapitlet giver en beskrivelse af de markeder, hvor fysisk elektricitet

handles (næstedagsmarked, real-tids-markedet(regulerende markedet) afregningsmarked,

reserve markedet og det danske detail marked). Der gives også en beskrivelse af hovedaktørerne

på disse markeder og deres roller, og det besvarer spørgsmå lom mulighederne for at påvirke

priser, effektiviteten af et marginal auktionssystem, muligheden for arbitrage på real-tids

markedet og konkurrencen på detailmarkedet.

Afhandlingens andet kapitel, Demand and Supply Management for the wholesale Electricity

Market, undersøger mulighederne for at påvirke efterpørgslen på det nordiske

næste-dagsmarked. Næste-dags-markedet for de nordiske lande er et spotmarked, hvor

forbrugere og producenter byder på hhv. køb og salg af elektricitet, op til 12 timer før levering.

Derfor undersøges efterspørgelseselasticiteten for detailhandlere på næste-dags-markedet ved at

estimere efterspørgsel priselasticitet for hver time af dagen ved hjælp af et system af simultane

ligninger. Det forudsættes, at storforbugere og detailhandlere på dette marked har det største

potentiale for fleksibilitet. Den strukturelle model understøtter en efterspørgselsfunktion med

konstant elastitictet, som kontrollerer for vejrforhold, og en udbudsfunktion, som forklarer

forskellige produktionsteknologier i de nordiske lande. Modellen følger Huisman et. (2007). Hver

time på dagen behandles som en daglig, selvstændig tidsserie, men modellen tillader

uobserverede korrelationer mellem hver times fejlled ved ikke at lægge restriktioner på

kovariansmatricen. Derefter defineres en udbuds- og efterspørgsels ligevægtsmodel for hver

time, og modellen estimeres simultant for de 48 resulterende ligninger ved hjælp af generalized

method of moments introduceret af Hansen (1982). Der findes små og statistisk signifikante

efterspørgselspriselasticiteter, som er forskellige for dag- og nattetimer.

Kapitel 3, Wind Power Effects for Price Level and Volatility for the Wholesale Electricity Market,

xvi

DANISH SUMMARY xvii

fokuserer på udbudssiden af næstedagselektricitetsmarkedet for de nordiske lande. Virkningerne

af vindkraftens penetration på middelværdi og volatilitet af priserne på elektricitet undersøges for

hver time på dagen for Vestdanmark. Den foreslåede model tager hensyn til de

kapacitetssbegrænsninger, som kan opstå på det nordiske elektricitetsmarked, og antager at

svingninger i vindkraftproduktionen påvirker både prisens niveau og volatilitet. Disse virkninger

undersøges ved hjælp af en GARCH regimeskifte model med observerede tilstande. Den

anvender vindkraft penetration niveauer for ELSPOT markedet i ikke-kapacitetsbegrænsede

perioder og vindkraft penetration niveauer for Vestdanmark i kapacitetsbegrænsede perioder.

Kapacitetsbegrænsning defineres som den situation, hvor prisen på Elspot markedet er forskellig

fra prisen for Vestdanmark. Det ses, at vindkraft penetration reducerer prisniveauerne for alle

timer på dagen og volatiliteten i priser i dagtimerne (se Jonsson et al. (2010)). Det ses også, at

prisreduktionerne i timer med kapacitetsbegrænsning er lavere end prisreduktionerne i

ikke-kapacitetsbegrænsede perioder, og at prisvolatliteten stiger i nattetimerne i

kapacitetsbegrænsede perioder, medens der ikke findes virkninger i ikke-kapacitetsbegrænsede

perioder for nattetimerne.

I kapitel fire, Wind Power Effects in the real-time Balancing Market, undersøges virkningerne

af vindkraft-forudsigelsesfejl på prisniveauerne for det balancerende marked i Vestdanmark. Der

refereres også til dette marked som det regulerende marked. Markedet lukker 45 minutter før

leveringen ifølge kontrakter indgået på næste-dags-elektricitetesmarked. På dette marked køber

og sælger Transmission System Operator den elektricitet, der er nødvendig for at holde

elektricitetssystemet i balance. Den antagelse, der ligger til grund for dette kapitel, er, at højere

vindkraft penetration fører til højere forudsigelsesfejl for produceret elektricitet, og derfor højere

behov for korrektioner på det regulerende marked, og hermed påvirkninger af

elektricitetspriserne. For at teste denne antagelse konstrueres en variabel for

vindkraftforudsigelsesfejl, defineret som differencen mellem forudsagt vindkraftproduktion og

aktuel vindkraftproduktion på ELSPOT markedet. Virkningerne af positive og negative

vindkraftforudsigelsesfejl undersøges ved hjælp af en regimeskifte model med tre observerede

tilstande som foreslået af Skytte (1999) for flere kvantiler af fordelingen af den regulerende pris.

Det ses, at positiv vindkraft forudsigelsesfejl reducerer de betingede kvantiler i den

ned-regulerende pris, men øger de betingede kvantiler i den op-regulerende pris i løbet af de

undersøgte nattetimer. I dagtimerne har de postive vindkraftforudsigelsesfejl en positiv effekt på

de betingede kvantiler i den ned-regulerende pris. Endvidere har negative

vindkraftforudsigelsesfejl en positiv effekt på de betingede kvantiler i de ned-regulerende priser i

de undersøgte nattetimer, men en negativ effekt i løbet af dagtimerne. I den op-regulerende

tilstand har de negative vindkraftforudsigelsesfejl ingen signifikant effekt i løbet af nattetimerne,

men en negativ effekt på de betingede kvantiler i prisfordelingen i den ned-regulerende tilstand.

DANISH SUMMARY xviii

Bibliography

Hansen, L. P. (1982). Large Sample Properties of Generalized Method of Moments Estimators.








CH

AP

TE

R

1FUNDAMENTALS OF THE NORDIC ELECTRICITY

MARKETS

Ioana Neamtu

Aarhus University

Abstract

This chapter gives an overview of the functionality of electricity markets in the Nordic

countries, with a focus on the Danish markets. It presents a detailed description of the market

design, price mechanism and specific characteristics of each of the spot markets where

electricity is traded on its way from producers to the end-consumer. The chapter also

provides an overview of the Danish retail market, with an emphasis on the price structure of

end-consumers. The efficiency of the wholesale and balancing market is discussed with

examples from the existing literature. The purpose of this chapter is to offer a basic

introduction to anyone interested in the economics of electricity markets in the Nordic

countries.

1

CHAPTER 1. FUNDAMENTALS OF THE NORDIC ELECTRICITY MARKETS 2

1.1 Introduction

Electricity is one of the most important commodities in today’s society. It powers our appliances,our cars and it heats our houses. Indirectly, it allows us to work, connect with people all aroundthe world, fly into space and cook our food. In one word, it is essential to our modern lives.

Net consumption of electricity has been constantly increasing worldwide, from 10395 billion

KWh in 1990 to 19711 billion KWh in 2012. In Denmark, net electricity consumption has been

increasing from 30 to 33 billion kilowatthours, from 1990 to 2012, although in later years it has

been slightly decreasing, mainly due to the increased efficiency of electrical appliances1.

The purpose of this chapter is to give a detailed overview of the functionality of the Danish and

Nordic electricity markets and discuss some of the theoretical implications of the market design

of the Nordic electricity markets. Therefore, it serves as a basic introduction to anyone interested

in the Nordic electricity markets and why they seem to work so well.

To reach our homes and appliances, electricity is traded on several markets, as described in

Figure 1.1, from long-term contracts to spot-markets and retail markets, each with different

players, price formation mechanisms, market design and administrator. The chapter gives an

overview of all these markets for the case of Denmark, which is integrated within the Nordic and

Baltic electricity markets. Therefore, it describes the main actors, price formation mechanisms

and market design of the Nordic countries, focusing only on the Danish case for the

non-integrated markets, such as the retail market.

This structure of markets and division of roles is given by the special characteristics of

electricity such as the need for balance between generation and consumption at all times, the

physical limitations of the power network and the transmission grid, the high costs of storing

electricity as well as the special characteristics of the demand of electricity - such as the ’must be

consumed now’, the low flexibility and the forecasting challenges.

The main actors on the electricity markets are the producers, who can be present on all the

spot markets, depending on their production capacity and ability to start/stop production

quickly; the consumers, who can be divided into retail consumers (small business and

households) who are typically found on the retail market, and the big industrial consumers who

can act on one or all the spot markets, depending on their size and ability to start/stop

consumption on a short notice, as well as their ability to pay possible penalties for imbalances.

Intermediate, but very important, actors are balance responsible parties or demand/supply

aggregators who act on several spot markets, as representatives for smaller

consumers/producers. Also important are the retail suppliers (distributors) of electricity on the

retail markets who sell the electricity bought en-gross on the spot markets to the retail

consumers.

1Latest data available, from U.S Energy Information Administration


Figure 1.1: Description of electricity markets in Denmark and Nordic countries

Note: Each box summaries the closing time for each market, the type of auction (e.g. marginal priceauction), the number of actors for the demand and the supply and the type of actors (Producers,Consumers)

This division of roles between entities on the electricity market is regulated by law in each of

the Nordic countries by a national regulator (e.g. The Danish Energy Regulatory Authority DERA).

These roles have been strictly defined in order to deregulate the electricity market - to allow for

prices to be determined by market mechanisms, promote competition and transform the

vertically integrated companies into separate companies. Other entities on the electricity markets

are the transmission system operators (TSOs), who are independent, national operators, whose

responsibility is to ensure the balance between demand and supply on the transmission grid, at

all times, at a fixed frequency. The TSOs operate only on the reserve capacity and the balancing

markets and do not produce electricity themselves. A role similar to the TSO’s has the DSO

(distribution system operators) who owns the grid and transports electricity, on a

lower-frequency grid, from retail suppliers to retail consumers. Moreover, each market is

operated by an independent market operator whose role is to organize and operate the market

place (e.g. the Nord Pool market operator).

Electrical power can be traded through bilateral contracts between big producers and big

consumers or producers and retail suppliers, up to 7 years before delivery time or directly on the

Elspot (wholesale day-ahead) market. There are two types of bilateral contracts: long-term

contracts and over-the-counter (OTC) contracts. Long-term contracts are private, flexible

contracts, for large quantities of energy and large transaction costs, and over-the-counter (OTC)

contracts are standard, flexible contracts, with low transaction costs, which trade smaller

quantities of energy, with low transaction costs.

In the Nordic countries, more than 80% of the hourly consumed electricity 2 is traded on Elspot

market, the day-ahead electricity market which is part of the Nord Pool market, a common power-

trading market for Nordic and Baltic countries (detailed in Section 1.2).

Since security of supply 3 is very important and forecasts for demand and/or supply a day

2calculated as share of total quantity traded in the total consumption3the quantity of electricity demanded must always be equal with the quantity of electricity supplied


ahead are not very accurate, several other spot markets have been put in place. Up to an hour

before delivery producers and retail suppliers can update the quantity sold or bought on the

Elbas market. On average, 1% of total consumption is traded monthly on this market.4 If demand

does not equal supply, the missing quantity is traded on the regulating market, by the TSO of each

country. This market differs from the Elbas market because the TSO is responsible for buying or

selling regulating power purchased from third parties. The balancing market is used only to repay

producers/consumers who sold electricity to the TSO on the regulating market. Also, if in the

hour of delivery, the frequency of the electricity is not at 50 MHz, ancillary services are activated

automatically on the reserve market, if the quantity needed is very small.

A detailed description of the Nord Pool market and its producers is given in Section 1.2 while

the functionality of Elspot market is provided in Section 1.3 and the Elbas market is described in

Section 1.4. The balancing market is detailed in Section1.5, while Section 1.6 offers an overview

of the ancillary services market. The Danish retail market is described in Section 1.7. The sections

offer a description of the market and an overview of the literature on the topic. The chapter ends

with some concluding remarks.

1.2 The Nord Pool market

Short History

The Nord Pool market is one of the biggest power markets in the world and the biggest in Europe,

with 7 participating countries: Denmark, Finland, Sweden, Norway, Estonia, Latvia and

Lithuania. It is comprised of three markets - the day-ahead market (Elspot) and the intra-day

market (Elbas) - where physical electricity is traded ahead of delivery time, up to an hour ahead,

and a financial market5 (Nasdaq Commodities) - where contracts for electricity power with no

physical delivery are traded up to 6 years ahead. These contracts can be daily, weekly, monthly or

yearly and have, as a reference price, the system price, determined on the Elspot market (see

Section 1.3 for a description of how the system price is determined) and which is used to reduce

the risk of price volatility on physical markets.

The Nord Pool Market was formed in 1995, after the deregulation of the Norwegian electricity

market and started operating as a cross-border trading (day-ahead spot market) after Sweden

joined it. Norway has 5 market areas today and it is responsible for 35% of total production on

Nord Pool, being able to export, on average, 2% of its total production. Sweden currently has 4

different interconnected market areas; it produces the most on Nord Pool market, 38% of total

production and is able to export, annually, 4% of its total production, as shown in Table 1.1.

In 1998, Finland joined the Elspot market with its unique market area, and has, in 2014, an

annual consumption of 20% of total consumption and a production of 16% of total production on

4calculated as share of total quantity traded in the total consumption5This market does not make the object of this chapter and it is, therefore, not described into detail


Nord Pool market. Together with Sweden, it created the Elbas market which started its operations

one year later, in 1999, as a common balancing market for the two countries and it was joined by

Norway in 2007.

Nord Pool market became an integrated Nordic market in 2000, when West Denmark joined

Elspot market. East Denmark joined both Elspot and Elbas markets in 2004. The two Danish

market areas are responsible for an annual consumption of 8.3% of total consumption and an

annual production of 7.7% of total production on Nord Pool Market. Moreover, in 2007, West

Denmark also joined Elbas market. In 2010, Nord Pool market extended towards Estonia, while

Lithuania joined in 2012 and Latvia in 2013.

Table 1.1: Shares of annual consumption and production for Nordic and Baltic countries, percountry, 2014

Denmark Finland Norway Sweden Estonia Latvia LithuaniaConsumption 8.4% 20.6% 31.4% 33.4% 2.0% 1.8% 2.4%

Production 7.7% 16.2% 35.3% 37.5% 2.7% 0.0% 0.7%

Source: Nord Pool Spot

The production mix

The Nord Pool market is characterized by a mix of producers with different production sources,

depending on the endowments and political ambitions of each participating country. Norway

relies mainly on hydro-power (95% of net production), Sweden and Finland rely on a

combination of hydro power (47% and 26% , respectively) and nuclear power (34%, each), as well

as renewable resources (16% and 19%, respectively). Denmark relies on conventional thermal

power (38%), of which coal (26%) and gas (12%) and renewable resources (62%). Estonia and

Lithuania rely mostly on thermal power (84% and 53%, respectively) and renewable resources

(15% and 23%, respectively), as presented in Table 1.2.

Table 1.2: Net power production mix, as share of total net production(%), for Nordic and Balticcountries, per country, 2015

Country Hydro Nuclear Fossil Fuels Wind Power BiomassDenmark 0.1 0 38 51 9

Estonia 0.3 0 84 7 8Finland 26 34 20 3 16

Lithuania 22 0 53 15 8Latvia 43 0 40 3 7

Norway 96 0 2 2 0Sweden 48 34 2 10 6

Source: ENTSO-E (European Network of Transmission System Operators for Electricity)


The overall mix of production sources on Nord Pool is described in Figure 1.2. In 2015, 57% of

all net generation has been hydro-production, while renewable resources such as wind, biomass

and solar summed to 15% of the net generation. More importantly, the share of renewable energy

has been increasing (by 3 percentage points) from 2013 to 2015, while the share of nuclear and

fossil fuels has declined, in accordance with the political ambitions of the Nordic countries of

moving towards green energy. From the 10% of the fossil fuels used, 4% of total production comes

from gas, 3.5% from hard coal, mainly from Denmark and Finland. This particular distribution of

the production mix is mainly driven by the endowments of each country on Nord Pool and its

corresponding consumption needs, but also by the production costs associated with each

production source.

Figure 1.2: Net Power Generation Mix on Nord Pool in 2013 and 2015, by production source

Source: ENTSO-E

Production costs can be divided into start-up costs and per-unit (variable) costs (Elmaghraby

(1999)). In general, the higher the start-up costs, the lower the per-unit costs and vice-versa.

Therefore, maximum production is a decreasing function of its variable cost and an increasing

function of its start-up costs, as described in Figure 1.3.

Based on the costs of production and running-time (availability), electricity producers can be

divided into three categories: (Denton (1998)):

- base-load producers who have relatively high start-up costs, but low marginal costs ( hydro,

nuclear, and coal-fired plants);

- peak-load producers who have a very low start-up cost and a high marginal cost (gas

turbines);

- intermediate producers.

The activation of production will depend on the quantity needed to be produced on the

market. Therefore, the high penetration of hydro is due to its availability (high installed capacity)

as well as the low marginal cost of production which allows it to cover most of the demand, while

the relatively low penetration of wind power is mostly the result of low installed capacity and

wind unavailability and not high marginal production costs, as in the case of gas plants.


Figure 1.3: Total cost function, for different types of electricity producers

Source: Elmaghraby, 1999Note: Electricity producers can be divided into base-load, intermediate load and peak-loadproducers, based on the type of demand(load) that they serve

1.3 The Elspot market

The Elspot market is the world’s biggest spot market for electricity with 358 members from Nordic

and Baltic countries, corresponding to 15 local market areas. This is a day-ahead, auction-based

market, where participants can submit bids for buying and selling electricity from 14 days before

and up to 1 day before the day of delivery. The market is closed at 12 am, the day before delivery

and prices are determined by the market operator by 1 pm, the day before the delivery day. Each

participating country is divided into one or more interconnected market areas, also known as

bidding areas. Between two bidding areas there is a maximum available transmission capacity,

which is determined daily, for each hour, by the Nord Pool market operator and it is made

publicly available before the day of delivery.

Participants on this market bid only for electricity and do not need to bid separately for the

availability of transmission capacity. Therefore, the bidding prices for electricity include both

production and transmission costs, which makes Elspot an implicit capacity auction. (Nord Pool

Spot)

The price on this market is determined hourly, based on the principle of social surplus

maximization, conditioned on the equilibrium between aggregated supply and demand.

Aggregated demand is constructed in a descending order, from the highest to the lowest buying

price, while the aggregated supply is constructed starting from the lowest selling bid to the

highest one, creating what is known as a merit order. The equilibrium price, found at the

intersection of the two curves, is known as the system price and it represents the price of the most

expensive unit needed to meet demand in a given hour. This is an uniform, marginal price

auction, where all activated producers receive the market price, irrespective of their (lower)

bidding price, while all the buyers on the market pay this price, irrespective of their (higher)

bidding price.


This uniform auction system is considered to be efficient because it allows for profit margins

for the efficient production units that will earn more than the marginal cost at which they were

willing to sell (Nielsen et al. (2011)). Moreover, Rassenti et al. (2003) show that this type of auction

leads to lower electricity prices than a pay-as-bid auction (where each winning bidder is paid his

own bid price), although it creates a higher price volatility than a discriminatory (pay-as-bid)

auction.

The system price is determined without taking into consideration any transmission capacity

limits between market areas and it is used as the reference price for trading and clearing of

financial contracts, on Nasdaq Commodities. When transmission capacity is lower than the

needed quantity in an area, capacity congestion occurs. If congestion appears at the system price,

area prices are determined. These are the settlement prices for physical delivery for sellers and

buyers on the Elspot market. In practice, when constraints appear between two market areas, a

new demand and supply curve is formed in each market area and a quantity equal to the

congested quantity is added as a price independent bid for the supply or demand, depending on

the needs of the market (extra supply in the high-price area and extra-demand in the low-price

area). Therefore, electricity will flow from the lower price areas to the higher price areas and

efficient allocation will be achieved. The area price is determined on the same principle as the

system price described above. Holmberg and Lazarczyk (2012) suggest that this pricing

mechanism encourages more producers to bid at a marginal price, compared to the case of nodal

pricing (where producers supplying electricity at one node of the grid are paid the same price

while producers connected to another node of the grid are paid a different price) but also that

zonal (area) pricing (where producers connected to different nodes within a zone/ market area

are paid the same price) is less sensitive to price shocks than nodal pricing. Nonetheless, they do

not exclude the possibility of inefficient dispatch in the case of zonal pricing, when allowing for

uncertainty of demand or uncertainty regarding the output of the competition.

Although the area pricing system is considered a simplified version of the nodal pricing system,

Stoft (1997) shows that the zonal pricing approach does not efficiently account for costs at the

nodes within one area, because it assigns the same price at all nodes within the area, regardless of

individual transmission costs. Moreover, Björndal and Jörnsten (2001) and Glachant and Pignon

(2005) show that determining the optimal bidding area (such that social welfare is maximized) is

not trivial because there might be more than one solution to the problem of grouping nodes into

the ’right’ areas. Björndal et al. (2003) also suggest that TSOs may not have incentives to maximize

social welfare in markets with zonal pricing,

Also, Hogan (1999) and Harvey and Hogan (2000) suggest that area pricing cannot prevent

producers from exerting market power, compared to the nodal pricing system. Empirical studies

regarding market power, as summarized by Fridolfsson and Tangerås (2009), show that there are

no signs of market power in the Nordic wholesale market, at the system level, although they

conclude that some producers do take advantage of transmission constraints to increase profits


(Steen (2003), Johnsen (2004), Tangerås and Mauritzen (2014))).

There are different types of members in the Elspot market: the direct participant, who trades

on his own behalf and who can be a producer, an industrial consumer or a retail supplier and the

trading and clearing representative, who buys electricity from a producer and sells it to a retail

supplier or buys electricity from a retail supplier and sells it to another supplier. Participants can

bid only in the areas where their production or consumption is physically located, but trade

between areas is done freely, as permitted by capacity constraints (Newberry, 2006).

There are three types of bids on the Elspot market: single hour bid, block bid and flexible bid.

A bid must contain the bidding area , the volume (MWh), the hour(s) and the price(s)6.

The single hour bids are the most common bids on Elspot and must contain the quantities

corresponding to the lower and upper ceiling prices imposed by Nord Pool before each auction,

currently set at -200 and +3000 euros, respectively. A bidder can submit only one single hour bid

for the same delivery hour and he can choose between a price dependent and a price independent

bid. Price dependent bids can be submitted in the form of a 64 step functions, which are linearly

interpolated by the market operator to create the aggregated demand and supply curves. The step

functions must be increasing in price for the sale bids and decreasing for buying bids, thus forming

an increasing aggregated supply and decreasing aggregated demand function, respectively. On the

other hand, independent price bids contain only the quantity and the delivery hour, irrespective

of the hour price (Nord Pool Spot, Market Setup(2013)).

The block bids must be submitted for a minimum of 3 consecutive hours and include the

delivery hours, volumes per hour and the price for the entire block. The hours and volumes

mentioned under these bids are not divisible. These bids will be accepted and included in the

demand/supply curve only if the price of the block is higher/lower than the average area price in

the market. There are three types of bidding blocks: simple blocks, linked blocks and convertible

blocks.

Linked bids can be activated under the condition that the acceptance of one bidding block

implies the acceptance of one or more of the linked blocks submitted by the same participant. The

relationship between blocks is established by the bidder through priority levels. The priority levels

and the maximum number of linked blocks are set by Nord Pool Spot, one day before the auction.

Convertible block bids can be activated as separate hourly bids if the block cannot be activated

and if the maximum system price for the bidded period is included within one or several hours of

the block bid. If a block bid can be converted, individual hour prices must be added to the bid.

The flexible bids can be submitted only for sales bids and include the quantity to be sold and

the price, without a delivery hour. The time length for these bids is one hour only and they can

be activated only after ordinary (single hour) bids and block bids are accepted. Moreover, they are

included in the area with the highest area price (lower than the specified bid price), in order to

maximize social welfare (Elspot Market Regulations (2011)) .

6Different bidding types require different price specifications


Integrating all these bids into a maximization problem for determining the system price can

be tricky, but Elmaghraby et al. (1999) suggest that simple hourly bids can be modeled as “vertical

auctions”, where the aggregated demand is partitioned into hourly markets, while block bids can

be modeled as “horizontal auctions”, where aggregated demand is “sliced” horizontally based on

duration. They show that block bids allow for higher efficiency than simple bids, in a multi-auction

setting.

Vertical auctions are optimal for flexible suppliers, who have low start-up costs (peak-load

producers), while horizontal auctions are optimal for base-load producers (who can produce

electricity for long time periods and have high start-up costs that must be recovered) Wilson

(1998).

1.4 The Elbas market

This is the intra-day market, where actors can submit bids for sale and purchase, up to 5 minutes

before the delivery hour for Belgium and the Netherlands, 30 minutes before delivery for

Germany, 1 hour for Denmark, Sweden and Finland and Estonia and 2 hours before delivery for

Norway (Elbas User Guide(2012)). Currently, there are 112 members trading on this market, from

8 countries (Norway, Sweden, Finland, Denmark, Estonia, Germany, Belgium and the

Netherlands) bidding within different market areas. Every day the TSOs allocate transmission

capacity for Elbas trading.

The purpose of this market is to correct for any production/consumption deviations that

appear close to delivery time, after Elspot market is closed. This is not a very liquid market.

The bids submitted here are similar to bids on Elspot. They must contain the hour (period) of

delivery, volume and price. Bidders can use hourly bids or block bids using the “all or nothing”

rule. Hence, on Elbas, actors enter into hourly contracts, where the price is set on a first-came

first served basis, meaning that both producers and suppliers can see the list of available bids for

sell/buy of electricity and can simply choose the one they are willing to accept. Therefore this is a

continuous market, where transactions begin at 2 pm the day before the day of delivery and close

shortly before the hour of delivery (as explained above).

1.5 The balancing market

The balancing market also known as the regulating market, is a 45 minutes ahead market where

the TSO buys and sells the electricity needed in order to keep the balance between the demand and

supply. This is a common market for all Nordic countries (Norway, Sweden, Finland and Denmark)

and it can be divided into the regulating market, which is used to determine the price for electricity

imbalances, and the balancing settlement done the day after delivery, where the TSO charges the

entities responsible for the imbalances.


There are two types of bids on this market: the upward-regulating bids which require increased

production or reduced consumption, and downward-regulating bids which require a reduction of

production or an increase in consumption. Each bid must specify the volume, the price and the

hour of operation. These values can be changed up to 45 minutes before the delivery hour if the

bid has not been accepted earlier by the TSO (EnergiNet.dk, Regulation C2).

The Elspot area price for the delivery hour is the reference price for the regulating market,

being the minimum bidding price for upward-regulating bids and the maximum bidding price for

downward-regulating.

Up-regulating bids act as the supply-side and give the price the actors require in order to start

production or reduce consumption, while down-regulating bids act as demand-side and show the

price actors are willing to pay to reduce production or increase consumption.

To determine the price on this market, the TSO uses a marginal price auction system, sorting all

bids within the hour by type and price (increasing prices for up-regulating and decreasing prices

for down-regulating power) and activating the bids with the lowest prices first. The price of the last

activated bid will be the hour price for the entire Nordic market if there is no congestion. For a bid

to be considered as price-defining, it must be activated for at least 10 consecutive minutes. If the

player has been active for less than 10 minutes he is paid as he bid. Also, if specifically agreed with

Energinet.dk or under special circumstances (special bid activation that does not respect the bid

order), players can receive a different price than the market price.

In the case of capacity restrictions between bidding areas, the price in the congested areas will

be the price of the last active bid before the formation of the congestion or capacity limitation. If

there is a need for both up- and down-regulation power within an hour but the aggregated

volume is for upward regulation, then the price for up-regulation will be the marginal market

price while the price for down-regulating will be “pay-as-bid”. Similarly, if within an hour, the

aggregated volume in the Nordic market is for down-regulation, the price of downward regulation

will be the common marginal market price while the price for upward regulation will be the

pay-as-bid price. In cases of congestion, the affected and unaffected areas may have different

regulation states and prices. (EnergiNet.dk).

The day after delivery day, the TSO charges or credits market participants for their imbalances

according to the regulating price. The imbalances caused by production and consumption are

calculated differently and priced according to different price mechanisms. For production

imbalances a two-price model is used while for consumption and trade imbalances the one price

model is used.

If the imbalance of a producer has the same direction as the total imbalance on the market

(thus increasing total imbalance), the producer is charged at the regulating market price; if the

producer’s imbalance has the opposite direction than the total imbalance (thus reducing total

imbalance), the producer is charged the Elspot market price of the area. In the hours with no

active regulation, imbalances still appear for individual players in the market and the price


charged in this case is the area spot market price. For consumption, imbalances will be priced at

the regulating market (area) price, irrespective of the direction of the imbalance.

This complex price formation mechanism of the regulating market has been designed to

discourage arbitrage and, as concluded by Klaeboe et al. (2013) based on different forecasting

models for the regulating prices, this market is efficient, because it is impossible to predict them

before the closing time of the day-ahead market, in the case of Norway. Nonetheless, Vandezande

et al. (2010) point out that this two-price system encourages market participants to buy

unneeded electricity on the day-ahead market to hedge against the higher up-regulating prices

and thus increasing the prices on the wholesale market and having negative effects on the supply,

leading to inefficiencies in extreme cases. Nevertheless, having a one-price scheme for

consumption, as it happens in Denmark, reduces the negative effects of the two-system price.

Also using Norway as a case study, Ravnaas et al. (2010) show that, in the case of a wind farm,

the 2-price system for imbalances does not allow for arbitrage, compared to the 1-price system,

and it also incentivizes wind producers to bid very close to expected production with small

deviations given by the skewness of the balancing market price distribution and the wind forecast

error deviations. On the other hand, Boomsma et al. (2013) test the profitability of coordinating

bids in the balancing and spot market for hydro and thermal generators in the Nordic market and

conclude that although it is profitable to hold off bidding in the day-ahead market for the

balancing market, the gains are very small, being offset by the risk of not being dispatched in the

balancing market. Nevertheless, increasing the price difference between the day-ahead and the

balancing market results in higher gains for the generators, suggesting that in the future the

incentive for potential new entrants in the balancing market will increase, as the necessity for

regulating power will increase, due to the integration of wind power within the market.

1.6 The ancillary services market

Unlike Elspot and Elbas markets, the ancillary services market, also known as the reserve capacity

market, is not a common market for all Nordic countries. Therefore, we focus only on the case of

Denmark. There are two different reserve capacity markets for each of the two Danish electricity

regions. These are spot markets or contractual obligations managed by the TSO of Denmark, for

both West and East Denmark. Although both are managed by EnergiNet.dk, each area follows a

different acquisition mechanism for capacity reserves. Ancillary services are divided into

frequency controlled reserves, secondary reserves (load frequency control) and manual reserves.

In West Denmark, primary and secondary reserves are used, while in East Denmark only

frequency controlled reserves are used. Manual reserves are bought by the TSO for both East and

West Denmark only to ensure that there is available capacity to regulate the market in case of an

outage or imbalances.

The activation of ancillary services can be done automatically (for frequency controlled


reserves and load frequency control) or manually by the TSO. Participants on this market are

being paid for their availability (capacity reserves) and not for actual delivery. If activated, the

energy delivered is treated as an imbalance and priced according to the rules of the balancing

market. The ancillary services described below can only be provided by balance responsible

parties or very large producers and consumers with balancing obligation (EnergiNet.dk, (2011).

Frequency controlled reserves are activated automatically within 30 seconds in West Denmark

and 150 seconds in East Denmark, in order to keep frequency between 49.9 and 50.1 Hz. Upward or

downward capacity reserves are bought by the TSO on separate daily auctions, one day ahead the

delivery day in West Denmark and one and two day(s) ahead of the delivery day in East Denmark.

In West Denmark, bids consist of a 4 hours (“all-or-nothing”) block, with a unique price for

the block and variable volumes of available capacity for each hour in the block. Bids must be

submitted before 3 pm the day before delivery day and the accepted bidders are notified by 3.30

pm of the same day. Upwards and downwards regulating bids are sorted by price and the

cheapest bids are chosen first. The price of the last unit activated is the price of the auction and it

is offered to all winning bidders, regardless of their initial bidding price (uniform marginal price

auction system).

In East Denmark, frequency controlled reserves are auctioned together with the TSO of Sweden

for both East Denmark and Sweden areas on two consecutive markets: a 2 days ahead market and

a one day ahead market. The bids can be single hour bids or block bids of maximum 6 hours (for

the 2 days ahead auction) and single hour bids or block bids of maximum 3 hours for the 1 day

ahead auction. The bids for the first auction must be placed before 3 pm of the auction day and the

winning actors are announced by the TSO within an hour. The bids in the second auction must be

placed before 7 pm the day of the auction and the winning actors are announced within an hour.

The bids from East Denmark and Sweden are pulled together and sorted by price, the cheapest

bid being activated first. Each winning bidder is offered his own bidding price (pay-as-bid auction

system).

Secondary reserves (Load Frequency Control) are employed only in West Denmark in cases of

major frequency disturbance in order to restore frequency at 50.00 Hz and release the primary

frequency control that has been previously employed. The TSO buys secondary reserves monthly

through individual negotiations with bidders, after analyzing the bids containing volumes, prices

and availability periods within the month. These represent payments for capacity availability. If

the reserves are actually used (energy is produced/consumed), actors receive an extra payment

depending on the type of the regulating power. The price for up-regulation will be the day-ahead

market price+100 DKK/MWh, which should be higher than the price on the balancing market for

up-regulating power, and the price for down-regulation is the day-ahead market price-100

DKK/MWh, which should not exceed the price for down-regulating power on the balancing

market.

Manual reserves can be up or down regulating capacity reserves activated by EnergiNet.dk.


These reserves are bought under 5 year contracts for East Denmark and auctioned daily, the day

before the operation day for West Denmark. At 9 am the day before the operation day,

EnergiNet.dk provides the needed reserve capacity for the next day and uses a marginal price

auction system where the actors offer hourly bids with the volumes and prices for the available

capacity that they can provide. At 9.30 am, no more bids are accepted and the bids already made

become binding. At 10.00 am, after sorting by price, EnergiNet.dk chooses the cheapest bids and

notifies the corresponding actors who must provide a subsequent bid stating the activation of the

entire capacity available for the price offered by EnergiNet.dk, after receiving the notification.

Manual reserves are activated through the balancing market, where winning bidders on this

market must submit bids for the physical delivery of energy (EnergiNet.dk, (2011)).

1.7 The retail market

The retail market is the market where end-consumers (households and small and medium sized

companies) buy electricity for their day-to-day activity from retail suppliers as well as the right to

use the electrical grid, from the grid companies. In general, the price on this market is a monthly

price because most consumers are risk-averse and prefer an average monthly price rather than a

variable daily or hourly electricity price, but also because it covers not only the cost of produced

electricity but also the transport on the grid and balancing costs. In Denmark, prices, tariffs and

fees charged by the electricity suppliers and grid companies on the retail electricity market are

regulated by the Ministry of Climate, Energy and Building Affairs and supervised by the Danish

Energy Regulatory Authority (DERA) as well as other organizations from the energy industry,

overseen by DERA.

The suppliers of electricity on this market can be categorized into universal suppliers and

’regular’ suppliers. The distinction between the two appeared when the retail market has been

deregulated and more suppliers could enter the market (regular suppliers). The universal

supplier is a regular supplier with an extra attribution of being the default supplier in a certain

region, if consumers do not exercise their right to choose an electricity supplier. A universal

supplier is highly regulated by DERA with respect to the maximum price that they are allowed to

charge for electricity and for balancing and administrative activities. DERA also ensures that the

price charged by the universal supplier for commercial and non-commercial customers is similar

to the market price and that no customers are being discriminated against (based on location, for

example). (El Supply Act, chapter 10)

The price charged by the grid companies is also regulated, such that it covers the costs of an

efficient operation and limits the revenue of the grid companies. (Electricity Supply Act (2012))

The efficiency requirements (equivalent to total cost reductions) and the revenue caps for these

companies are imposed by DERA. The current revenue cap is calculated at the level from 2004 (in

real terms) and it is increasing yearly with the rate of depreciation of capital. It also allows for new


investments (i.e. expansion of the grid) and can be changed if the costs of maintaining the grids

have accelerated compared to 2004. The law also provides a definition for new investments and

the corresponding price increases. For any unexpected increases in costs or maintenance, DERA

can allow for increases in revenue caps.

In Denmark, the retail electricity price is roughly 5 times higher than the electricity price from

the Elspot market because, apart from the wholesale price, consumers pay taxes, PSO (public

obligations tax) and VAT, grid connection fees and subscriptions to the grid and to retail

suppliers. Figure 1.4 shows the evolution of each component across time, from 2010 to 2015.

According to the DERA report (2012), in 2012 the increase in the final retail price was due to a 6%

increase in the grid payment and an 11% increase in taxes and PSO, which made the 18%

decrease in the wholesale electricity price (energy price) imperceptible to the final customer. The

increase in the grid payments is attributed to price-adjusted revenue-caps, higher exploitation of

revenue caps by grid companies and new investments to the grid.

Figure 1.4: Average retail price decomposition for households, in Denmark, 2010-2015

Source: DERA report, 2012

The retail price for electricity reflects the prices of each of the markets and the costs of the

participants on each market, as described in Table 1.3. As shown in Figure 1.4, the biggest part of

the price for the end-consumer (63%) covers taxes and PSO as well as the VAT tax, and only 37% of

total payment represents actual costs of production. According to DERA Report (2012), from the

“pure electricity price” (Elspot market and retail subscription) that is included in the retail’s market

electricity price, 90% goes to the producers from the Elspot market and only 10% of it goes to the

retail supplier. Nonetheless, the structure of the price depends also on the type of consumer.

Both the electricity supplier and the grid companies perceive a monthly subscription,

irrespective of consumption, covering their fixed costs for customer administration and metering

(meter equipment, billing, emergency services). Apart from the payments they receive for


Table 1.3: Fixed and variable costs of electricity included in the retail price, per electricityparticipants, in Denmark

Retail Supplier Grid company EnergiNet.dk The StateSubscription Subscription System tariff Other Taxes

Electricity Price Distribution tariff Grid tariff VATTransmission tariff PSO

operating the transmission and distribution of electricity, the grid companies also collect all

payments for the state and EnergiNet.dk on their behalf.

Consumers must support a share of the costs of EnergiNet.dk, proportional with their

consumption. These costs cover the security of supply (payments for reserve capacity, balancing

and regulating costs) and all the costs for the transmission grid and international connections.

Also, the end-consumers are paying a proportionate share of total consumption for research and

development and sustaining the environmental-friendly electricity production through the

public obligation tax (PSO). The PSO is changed annually or quarterly and it is determined

individually by each grid company. (EnerigNet.dk- Regulation A) Other taxes paid by the

customers are the electricity tax, the electricity distribution tax and the electricity saving tax (Tax

on Electricity Act, no. 310/2011)

As defined by DERA, end-consumers can be divided into households with an annual

consumption of 4000 kWh, small firms, with an annual consumption of 10000 kWh, and big

consumers with an annual consumption of 50 millions kWh, shown in Figure 1.5.

In 2015, households in Denmark have a share of the Elsopt electricity price of 20% of the total

retail electricity price in East Denmark and 21% in West Denmark, with a maximum of 31% in West

Denmark and 28% in East Denmark. Small firms have the Elspot market price as a share of 51%

from the retail price in West Denmark and 48% in East Denmark, on average, having a maximum

share of 68% in West and 61% in East Denmark, respectively. Similarly, big consumers have a real-

time price share of up to 73% in both West and East Denmark, and an average share of 55% in both

Danish regions.

Figure 1.5: Share of the Elspot electricity price of the retail price (including VAT and other taxes),for West and East Denmark, 2006-2015

Source: DERA


The differences in the share of Elspot prices of the total retail price between different types of

consumers (shown in Figure 1.5) is a result of the difference in grid tariffs and monthly

subscriptions charged for the different consumer categories. Grid tariffs and monthly

subscriptions are higher for households and they are reduced proportional with higher

consumption. Moreover, the retail price for households includes VAT, which is another reason

why the share of the Elspot price of the retail price is so low for households, compared to the

other types of consumers.

From 2003, retail consumers are able to choose variable price contracts from different

suppliers. Figure 1.6 shows the average monthly price for different types of contracts, offered to

households with an annual consumption of 4000 kWh. The variable price contract has a variable

price which can change daily or monthly over the delivery period. As expected, these contracts

have a higher per month price for the autumn and winter months (when demand for electricity is

generally higher) but lower prices for the summer months, compared with the fixed-price

contracts, where the monthly price is considered fixed during the contract period, usually 3, 6 or

12 months. Contracts under 6 months are offered only for fixed-price contracts and they are the

cheapest because they do not include a risk-premium for longer-term contracts, as in the case of

fixed-long term contracts. The last type of product is a climate-friendly contract which is

generally more expensive than others because it electricity comes from energy sources that

reduce carbon-dioxide emissions or from renewable resources only. Figure 1.6 shows that, for

both East and West Denmark, fixed price contracts under 6 months represent the best alternative

for consumers, while alternating between a fixed-term contract and a variable price contract may

depend on the household consumption during the year. Even though variable price contracts are

a better alternative for the summer months, the extra-consumption in the winter when these

prices are higher might make this alternative more expensive than fixed-price contracts, overall,

for the entire year.


Figure 1.6: Average monthly price for electricity (øre/kWh) for households, by type of contract, inDenmark, 2014-2015

Source: DERANote: Prices include average monthly retail subscription, but not grid tariffs, taxes, PSO, etc; Fixedprice contracts include fixed price contracts, under 6 months as well

While search costs are greatly reduced by the existence of a common, free, database

(elpristavlen.dk) where all available contracts and prices for different consumption groups are

publicly available, subscription taxes and changing of supplier every 3 to 6 months might make

the possibility of changing supplier unattractive for most customers. Data from Danske Energi

shows that there is little interest in changing supplier, especially from households. Figure 1.7

shows that on average, only 3.1% of households and small companies (with a consumption below

100 000 MWh/year) change supplier each year, since the policy has been implemented.

Figure 1.7: Percentage of consumers changing suppliers, by type of consumption and overall, inDenmark, 2003-20014

Source: Danske EnergiNote: Data by consumer type unavailable for 2013 and 2014 cannot be divided .


On the other hand, large consumers have a higher rate of changing suppliers, of 48% in 2003

and declining to 13.5% in 2012. The low rate of change of suppliers for small consumers can be

explained by the low price differentials of products given by local suppliers. This can be explained

by the non-differentiability of electricity, market structure as well as the fact that the final retail

price, seen by retail consumers, includes transportation costs, connection fee and different taxes

(as described above).

1.8 Conclusion

In this chapter, the functionality of the electricity markets in the Nordic countries is presented,

with a focus on the rules and regulations of the Danish electricity market, which is integrated in

the Nordic electricity markets. All spot markets that trade electricity are described, from the day-

ahead electricity market, to the intra-day, hour-ahaed market and the real-time balancing market

and the ancillary services market and up to the retail electricity market in Denmark. The market

structure, price mechanism and participants on each of these markets are presented along with

the advantages and disadvantages of the market structure and the price mechanism as described

in the literature, for the wholesale day-ahead market and the balancing market.

The uniform marginal price auction system implemented for the Elspot day-ahead market is

efficient (Nielsen at el.(2011)) and leads to lower system price with relatively higher volatility than

a pay-as-bid auction market (Rassenti et al. (2003)). Also, no evidence of market power at the

system level could be found (Fridolfsson and Tangerås (2009)) but the transmission constraints

and the area pricing system might encourage some regional market power (Steen (2003), Johnsen

(2004), Tangerås and Mauritzen (2014)). Furthermore, several papers rise concerns regarding the

optimality of area pricing as opposed to nodal pricing, which is considered to allow for strategic

bidding (Hogan (1999) and Harvey and Hogan (2000)).

The structure of the balancing market with a two-price system for the producers defers

arbitrage between the day-ahead and the regulating market ( Ravnaas et al. (2010)). Moreover,

forecasts of the balancing prices before the closure of the Elspot market are impossible (Klaeboe

et al.(2013)). This strengthens the belief of an efficient market design of the Nordic electricity

market.

Further research should be focusing on the optimality of the intra-day, hour ahead market,

balancing and reserve capacity market as well as the possibility of arbitrage on these markets. It is

shown that efforts are made for exposing end-consumers on the retail market to the real-time,

day-ahead electricity price, but this is difficult given the existing structure of the electricity system

and the natural monopoly that comes with it. Nevertheless, exposing consumers to the different

components of their electricity price seems to encourage them to take advantage of the

deregulated and competitive retail market, although the percentage of consumers changing

supplier is still very low.


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1.10 Appendix

Table 1.4 presents a short description of the main concepts related to the electricity markets.

Table 1.4: Short definitions of concepts used in this chapter

DefinitionNodal pricing Pricing scheme where all producers within a region are charged

differently, depending on the costs associated with the nodes of thegrid to which they are connected to

Zonal pricing Pricing scheme where all producers within a certain (predetermined)area are paid/charged the same price, irrespective of different costsassociated with the nodes of the grid

Pay-as-bid auction Type of auction where all the winning bidders are paid their biddingprice

Marginal-price auction Type of auction where all the winning bidders are paid the same price,the price of the highest winning price

System price Price determined on the day-ahead market at the intersection ofdemand and supply when all areas are considered and no capacityrestrictions between areas are taken into account

Area price Price determined on the market, when congestions appear andelectricity cannot flow freely between different areas

Transmission SystemOperator (TSO)

Independent operator, regulated by the state, responsible formaintaining the balance on the market

Producer Company responsible for producing electricityIndustrial consumer Company with very high individual electricity consumption (per

year)Aggregated retail consumer Company buying electricity on the day-ahead market or bilateral

contracts and delivers it to small companies and households on theretail market

Balance resposable party Company held responsible by the TSO for the production orconsumption imbalances produced during the day

Elspot market wholesale, day-ahead market for the sale and procurment ofelectricity for Nordic and Baltic countries

Elbas market Continous, hour-ahead market for the sale and procurment ofelectricity for Nordic and Baltic countries

Balancing market 45 minutes ahead market for the procurment and sale of electricityfor Nordic countries used by the TSO to prevent imbalances of thesystem

Ancillary services market Day-ahead market for the procurment of available capaicty for thedelivery hour used by the TSO to keep the frequency of the gridconstant

CH

AP

TE

R

2DEMAND AND SUPPLY MANAGEMENT FOR THE

WHOLESALE ELECTRICITY MARKET

Ioana Neamtu

Aarhus University

Abstract

This chapter investigates the potential for demand-side management for the system price

in the Nordic electricity market and the price effects of introducing wind-power into the

system. The model proposed accounts for the micro-structure of the Nordic electricity market

by modeling each hour individually, and for the relationship between the hours within a day,

through a system of simultaneous equations. This flexibility allows us to explore the

differences between peak and shoulder demand hours. Results show potential for demand

response management, as indicated by the price elasticity of demand as well as a small but

statistically significant decrease in price, given by the wind power penetration. Moreover, our

study shows that these effects are stronger during night-time and shoulder hours, compared

to day-time and peak hours.

23

CHAPTER 2. DEMAND AND SUPPLY MANAGEMENT FOR THE WHOLESALE ELECTRICITYMARKET 24

2.1 Introduction

More and more integration of wind power production (9% in total production on Nord Pool) and

solar energy into the electricity market pose the threat to the reliability of supply, due to the

variability and low (medium term) predictability of wind speed and sun exposure. Therefore,

maintaining the balance of the system becomes more challenging and, potentially, more

expensive. A cheaper way of dealing with the reliability of electricity of supply is manageable

demand. The new paradigm of electricity systems focuses in developing demand response

programs for retail and industrial consumers of electricity

Different demand response programs have been proposed in the literature (Borestain et al.

(2002); Albadi et al.(2008); Borestain (2009), Walawalkar et al. (2010)) and they can be classified

into two main categories: incentive based demand response programs and price based programs.

The first category includes direct load control and the interruptible/curtailment load programs,

direct bidding of demand in the spot markets, emergency demand response or capacity reserves,

where consumers are offered a payment or price reductions to decrease their consumption with

no or very short notice or provide capacity reserves. The second category includes different

pricing schemes, such as time-of-use, critical-peak, extreme-day, where consumers are charged

differently during different hours of the day, with higher tariffs corresponding to consumption

during peak-consumption hours and lower tariffs during off-peak hours or real-time pricing,

where consumers are exposed to the selling price on the wholesale market, Elspot.

As such, investigating the effectiveness of these programs translates into investigating price

elasticity of demand for industrial and retail consumers. Accurate estimates of consumer response

are important for both producers and retail suppliers of electricity as well as policy-makers and

energy-systems modelers.

Many researchers investigate the demand-response of electricity consumers, using theoretical

and empirical methods. Great attention has been paid to price elasticities and income elasticities

of demand and the factors that influence demand for residential users (Espey et al.(2004), Reiss

and White (2005), Madlener et al.(2010); Ito(2012); Labandeira et al. (2012); ). The research in

this direction has been concentrated on short, medium or long term price elasticities and has

employed a vast array of models, from panel data models to time-series models using both linear

and non-linear specifications.

This chapter uses a structural model to analyze the price dynamics of the Nordic electricity

market. The model is implemented for the Elspot market, which is characterized by a mixture of

electricity sources (wind, hydro, thermal, nuclear). 12 to 36 hours ahead, aggregated consumers

and producers both bid on the market the price and quantity they desire, forming the supply and

demand curve for each hour of the day. At the intersection of the two, when physical constraints

of the electricity system are not considered, the system (equilibrium) price is determined. The

novelty of this chapter is integrating wind production within the structural models for the


electricity market as well as investigating price elasticities of hourly demand in a system of

equations, allowing for hourly correlations between demand and supply.

This chapter investigates a couple of issues related to the wholesale electricity market in Nord

Pool. Empirically, it investigates the hourly (real-time) price elasticity of demand for aggregated

consumers, under the assumption that demand-response programs, if efficient, will be easier to

observe at an aggregate level. The ability of retail suppliers (considered here as aggregators for

retail consumers) and big industrial consumers to bid in the wholesale day-ahead market, makes

this a perfect case-study. Moreover, the effects of wind power production on the electricity price

is analyzed and a measure of price elasticity of cost is offered. This is important because it allows

policy makers and consumers to better forecast price changes, assuming the demand for

electricity will increase.

Modeling hourly observations as individual variables as opposed to a continuous time series

is motivated by the bidding system on Elspot, as described in Section 2.2. Section 2.3 offers an

overview of electricity price modeling and Section 2.4 describes the structural model used in this

chapter. Section 2.5 presents the data and empirical model, while Section 2.6 presents the results.

Concluding remarks can be found in Section 2.7.

2.2 The Elspot Market

The Nord Pool market is the world’s biggest wholesale spot market for the physical trading of

electricity, with 358 traders, from Nordic and Baltic countries (Norway, Sweden, Finland,

Denmark,Estonia, Latvia and Lithuania). The spot market is not a mandatory electricity market,

but its importance has increased since its opening in 1995 and it now trades over 75% of the

electricity is consumed daily in the Nordic and Baltic countries. It has been created as an

alternative to the balancing market, allowing participants involved in bilateral trading 1 to adjust

their imbalances (quantities and prices) very close to delivery time. Figure 2.1 offers a picture of

the evolution of the market share of electricity traded daily at Nord Pool, as a fraction of total

consumption, from 2012 to 2014. To participate in this market, there is a minimum amount of

energy that must be bidded, therefore most participants in the market are aggregators for

producers and/or consumers.

1Bilateral contracts for electricity are made up to several years in advance


Figure 2.1: Daily share of traded electricity on Elspot Market, as ratio of total consumption 2012-2014

The market is organized as a double auction, where participants can submit bids2 for buying

and selling electricity up to 12 hours ahead of the delivery time. Bids for the day ahead are made

simultaneously for each hour, before the closing time of the market, at 12 am. Thus, the a-priori

information available to the bidders is the same for all the hours of the day and cannot be

updated based on information from the previous hour, as it is assumed when hourly time series

are used. Moreover, this is an implicit capacity auction, meaning that bidding prices include both

production costs and transmission (capacity) costs. The available capacity (maximum amount of

electricity that can be transmitted through the physical system) is determined hourly by the

system operator.

The price is determined hourly, at the intersection of the supply and demand curve (which

maximizes social welfare), without taking into account any physical restrictions of the power grid

and it is called the system price. This is a marginal price, where the price of the last unit needed

to meet demand determines the market price, received by all winning bidders, regardless of their

own bidding price. This is the price at which all financial contracts are settled and the market price

when no congestion occurs. If congestion occurs on the transmission between areas, area prices

are determined for the congested area and the area price is different from the system price.

2.3 Literature review

The following section offers an overview of time-series models used in the literature for modeling

hourly electricity prices as independent time series, from parsimonious models to structural

models and simultaneous equation models, with the intent of offering a brief overview of the

base models, on which the model presented in Section 2.4 is build. For a thorough review of

electricity price modeling and forecasting, see Weron (2014).

2Bids represent 64 step functions of price and quantity


We use a structural model to analyze the demand and supply on the day-ahead market for

electricity, simultaneously, for each hour of the day. The idea of modeling each hour separately

was introduced by Ramanathan, Engle, Granger et al.(1997), to forecast electricity demand and

supported by Huisman et al.(2007), which modeled electricity prices using a seemingly unrelated

regression model and noticed that prices do behave differently across the day and by Fezzi and

Bunn (2006), which used a dynamic, asymmetric, structural, vector error-correction model to

estimate hourly demand and supply for electricity prices to investigate, among others, the price

elasticity of demand. They find that the demand is almost inelastic,but responds to past

disequilibrium in the supply function. In their structural model, they allowed for economic

activity (including dummies for holidays and daily dummies) and weather conditions for the

demand side. They modeled supply by a composite of power functions and included the price of

fuel and the capacity constraints. To account for these intra-day fluctuations in the supply, they

modeled each hour of the day individually.

Karakatsani and Bunn (2008) also modeled half-hour prices as separate daily time-series and

included forecasted demand, demand slope and demand curvature to account for the balancing

needs, demand volatility (over a 7 days interval), excess generation capacity as a measure of supply,

scarcity (as a ratio between excess capacity and demand) and lagged prices as a measure of the

learning capabilities of the bidders and the average daily price from the previous day. They also

include price volatility (for the past 7 days) and a measure of ‘spread’ between the balancing prices

for up and down regulation as a measure of unhedgeable risk exposure. They also accounted for

daily trends and seasonality.

Huisman et. al. (2013) employ a structural model for hourly electricity prices, using data from

the Nord Pool Spot market. They obtain indirect evidence of the effect of renewable resources on

electricity prices, but restrict their analysis only to hydro-power (by including water reservoir

levels in the supply function). They do not use the equilibrium quantity directly, instead they

proxy demand by estimated expected consumption, without explicitly allowing for price elasticity

of demand. Their supply function is based on a model of Buzoianu (2005) and they allow it to vary

based on the reservoir levels available for the Nord Pool market.

2.4 The Model

This section presents the proposed hourly, simultaneous, structural equilibrium model. The

equations for demand and supply used to model each hour of the day are presented in the

following.


Electricity Demand

Due to the structure of electricity markets in general, the literature on price elasticity of electricity

demand is divided into two main categories - the retail price elasticity and the industrial price

elasticity, which are estimated using a single-equation framework. To the best of our knowledge,

Lijesen (2007) is the only other paper investigating the price elasticity of demand for the

wholesale spot market for the Netherlands, using the two stage least square (2SLS) estimation

method in a single-equation framework. It also offers an overview of other models for price

elasticity of demand found in the literature and the corresponding values of estimated, for the

interested reader.

The demand of electricity is derived from a Cobb-Dougles utility function, assuming electricity

is an independent good, and assuming a constant elasticity of demand, similarly to Fezzi and Bunn

(2006):

Q = A ·pα0 (2.1)

where Q represents total quantity demanded, p represents the price of electricity,α0 represents the

price elasticity of demand and At is a time-varying factor affecting the slope and curvature of the

demand, depending on variables such as weather conditions, daily business activities, holidays,

etc. Variables such as household income are not included in the model, since they are assumed

constant at an hourly level.

A = f (tempetur e, wi nd chi l l ,d ay,hol i d ay,month) (2.2)

Electricity Supply

The aggregated supply function for the electricity market is determined by improving on the model

introduced by Porter (1983). The cost function of an individual firm is defined as:

T Ci = Fi +ai qci (2.3)

where Fi represents the firm-specific costs, qi is the quantity of the firm and ai represents a firm

specific cost shifter. Each producer wants to maximize his profit, which can be defined as:

πi = p ·qi −TCi = p ·qi −Fi −ai qci (2.4)

Therefore, the first order condition for profit maximization is:

∂πi

∂qi= p −MCi = 0 (2.5)

where p represents the price of electricity, Q represents the total quantity produced and c is a

measure of elasticity of variable costs. A condition for equilibrium to exist is c > 1, therefore c −1


must be positive. (Porter(1983)) Aggregating over the entire market and assuming perfect

competition (p = MC ), the following form for the electricity supply is obtained:

p =∑i

MCi = D ·Qc−1 (2.6)

where D represents the market aggregation term, which gives the curvature and the slope of the

supply function and it depends on ai (the firm specific cost shifter is assumed to depend on the

type of production). Therefore, it is assumed that:

D = f (Qwi nd ,rw ater , pcoal ,cap) (2.7)

where Qwi nd is the wind production, rw ater is the level of water reservoirs, and pcoal is the price

of coal and cap is the maximum quantity that can be distributed within the system. Since the

marginal price of wind is virtually zero, the only effect wind has on the electricity price is through

the quantity produced. The more wind-production in the system, the lower the price of electricity

should be. Similarly, reservoir levels of hydro-power are a good proxy for the marginal cost of

production, since lower levels of water make the producers bid strategically and willing to

produce at a higher cost. When high levels of water are present in the reservoirs, the producers

are willing to produce more, at a lower price, hence, decreasing the marginal cost of production.

(Huisman et al. (2013)) Coal prices are introduced to account for the marginal cost of production

of coal plants while available capacity is introduced to account for the price on available capacity

that is implicitly paid by producers when bidding on Elspot. Other factors such as wages can

affect the cost function of the firms, but since this is not a labor intensive industry, wages are not

included in this analysis.(Hjalmarsson (2000))

2.5 Data description

The data used in this chapter comes from Nord Pool and the Danish Energy Agency as well as the

Weather Underground website, from 01.01.2012 to 15.05.2014, giving 861 daily observations, for

each hour of the day, summing up to 20566 observations.

The data is collected mostly on an hourly basis as well as a daily basis, if hourly values were

not available. For both demand and supply equations we use the hourly equilibrium quantity for

the aggregated quantity and the hourly system price for the equilibrium price, provided by Nord

Pool Spot. Data on weather conditions (temperature, wind speed) is downloaded from Weather

Underground, a website that has cost-free historical weather values for most countries in the

world. The data used for the supply equation has been collected from the Nord Pool Spot Market

website, except for the coal price data, which has been provided by the Danish Energy Agency

website. Descriptive statistics for all variables can be found in the Appendix.


A preliminary analysis of the time series properties of electricity prices confirms the hypothesis

that they differ within a day and it also suggests the existence of peak and shoulder hours. Table

2.1 shows the results.

Table 2.1: Description of daily Elspot system price, per hour, 2012-204

Skewness -1 0-1 1-2 2-5Hours: 22-07 13-16 11,12,17,21 8-10, 18-20

Kurtosis 3-6 7-10 11-15 20-50Hours: 22-07 13-16 11,12,17 8-10,18-21Type sholder-hours relatively normal hours peak-hours

Very high, positive skewness indicates fatter/longer tails of the distribution to the right,

meaning higher prices, compared to the mean, while high positive kurtosis indicates a peaked

distribution (higher peaked and fatter tails). Based on these results, night-time hours, from 10 pm

to 7 am can be considered shoulder hours, while the morning hours 08 am to 10 am and evening

hours, 6 pm to 9 pm can be considered peak hours.

The analysis also shows that prices exhibit quarterly and seasonally patterns for all hours,

except for the peak-hours, which do not exhibit the quarterly pattern. Also, daily patterns have

been noticed for most hours of the day3.

The demand side variables

Weather related variables such as temperature, temperature-humidity index, wind-chill index

have been used in the literature to explain the variation seen in the demand for electricity

(Feinberg and Genethliou (2005)). Temperature above or bellow a certain base comfort level will

generate an increase in demand. High wind speed reduces perceived temperatures, making it feel

colder and thus reducing demand for electricity. Illumination, rain and snow fall can also affect

the perceived temperature and thus demand for electricity, but these are considered secondary

effects that will not be included in the model.

Temperature and demand have a well-documented U shape relationship, for the US market.

(Cottet and Smith (2003), Engle et al. (1986) and Al-Zayer and Al-Ibrahim(1996)). However, on

average, Nordic countries present a different relationship between temperature and demand of

electricity as shown in Figure 2.2, because of the lower maximum temperatures during summer

time, which do not require the use of cooling devices.

3see Table 2.12 in Appendix


Figure 2.2: Relationship between demand and temperature at hour 11 on Elspot Market, 2012-2014

The data used for weather variations is realized temperature for all countries active in Elspot,

which has been collected on an hourly basis and has been aggregated for the entire region, as a

weighted average for each big city in each of the regions included in the model. The weights have

been constructed as the consumption share of each country in the total consumption in the Elspot

market, following the formula:

av g _tempt ,h =∑i

ct ,h,i∑i

ct ,h,iTa t ,h,i (2.8)

where ct ,h,i represents the total electricity consumption in country i , in day t and hour h and Ta is

the air temperature in the capital city of country i .

Another weather-related variable particularly interesting for Nordic countries which has been

previously used to model electricity demand (Feinberg and Genethliou (2005)) is the wind-chill

index. It can be interpreted as the temperature felt by individuals and is most relevant in the

winter, when temperatures are low and wind is high. The formula used for calculating this index

was introduced in 2001 by the Ministry of Environment in Canada and it is widely used by

meteorologists (NWS, 2001)4.

wi nd_chi l l = 13.12+0.6215Ta −11.37V 0.16 −11.37V 0.16 +0.3965TaV 0.16 (2.9)

where Ta is the air temperature (in F ) and V represents wind speed (m/s). The wind chill

variable has been calculated for each capital city of the countries in the Elspot market, for each

hour of the day and each day of the dataset5. The aggregated index for the market is calculated

similarly to the temperature data, as described in equation (2.8).

The data used in this chapter comes from Nord Pool. The hourly equilibrium quantity is used

as a measure for demand/supply quantity and the hourly system price is used for the equilibrium

4Source: National Weather Service- National Oceanic and Atmospheric Administration5The indices t and h indicating the day and the hour have been left out for ease of read


price. Data on weather conditions is downloaded from Weather Underground, a website that has

cost-free historical temperature and wind data for all Nordic regions.

Other variables included in the model are dummy variables for each day of the week, as well

as a dummy accounting for legal holidays in each of the countries included in the model. As it can

be seen in Figure 2.3, demand in weekends is lower than the demand during week days, and this

behavior is consistent over the summer and winter time.

Figure 2.3: Daily variations of demand on the Elspot Market, at hour 11, 2012-2014

The supply side variables

The electricity supply curve is highly influenced by the costs of production, which depend on the

type of resources used for production. Norway relies mainly on hydro-power, Sweden and

Finland rely on a combination of hydro-power, nuclear power, Denmark relies on conventional

thermal power and more and more wind power, while Estonia and Lithuania rely mostly on

thermal power. The cheapest source of production is wind, with virtually zero marginal cost of

production, followed by hydro-power and coal, as shown in Figure 2.4.


Figure 2.4: Electricity price formation on Nord Pool market

Source: Nielsen et al. (2011)

The supply’s equation variables include wind power production, water reserves,price of coal,

available capacity, as well as the total quantity traded on Elspot. Water reserves is a variable

available on a weekly basis, therefore it has been linearly interpolated to daily observations. The

price of coal is also available only on a daily basis and used as such in the model.

Similarly to the demand equation, dummy variables for week days and holidays have been

included to account for different patterns in the price behavior. Preliminary tests as well as simple

data analysis show that prices are lower for weekend than week days, for most hours of the day, as

shown in Figure 2.5.

Figure 2.5: Daily variations of the Elspot system price, 2012-2014


Empirical model

Formalizing the model previously described, it can written as follows:

yDth =αyS

th +βX Dth +εD

th (2.10)

ySth =αyD

th +βX Sth +εS

th (2.11)

where the superscripts D and S indicate the type of equation (demand or supply), t indicates the

time (daily observations) and h indicates the hour of the day (h = 1,24). y represents the

endogenous variable (total equilibrium quantity (yD ) and hourly price (yS) both in logarithmic

form) and X is a vector of explanatory variables specific to the demand or supply equations, as

described in Section 2.4. More specifically, the model is divided into 2 groups of 24 equations, one

for each hour of the day.

This model is designed to follow the structure of the bidding system on the day-ahead market

at Nord Pool. The simultaneous system of equations for demand and supply for each hour

acknowledges that prices and quantities are determined simultaneously. The system of equations

for each hour of the day allows us to model the correlations between each hour. Producers and

consumers think in terms of daily intervals when deciding to sell/ buy electricity for the day

ahead which creates a high correlation between the demand equations each hour and the supply

equations for each hour, respectively. Moreover, daily dummies are included in the model but

monthly and yearly dummies have been excluded from the model in order to capture the

relationship between temperature and demand.

The model to be estimated is:

l og (Qth) =βD0h +α0h · log pth +α1h · tempth +α2h ·w_chi l l th +

7∑i=1α3i h ·di +εD

th (2.12)

l og (pth) =βS0h + (ch −1) · log (Qth)+β1hQwi nd

th +β3hrth +β4h pcoal +β5hcap +εSth (2.13)

where Q represents the aggregated demand, p represents the system price of electricity and

temp represents the temperature, w_chi l l represents the wind chill, based on the formula

described above and di is a dummy for the day of the week and a dummy for holidays. Qwi nd is

the wind power produced, r represents the water reservoir, pcoal is the coal price, cap represents

the available capacity.t indicates time,h represents the hour of the day.ε represent the error term

and D and S stand for demand and supply, respectively.

The estimation method

This section provides a brief description of the challenges posed by estimating the system of

simultaneous equations proposed above.


The identification of simultaneous equations

In the Elspot market prices and quantities are determined simultaneously. Therefore, when

identification is possible, using the ordinary least squares (OLS) estimation method would

produce inconsistent estimates. Moreover, to be able to estimate the model, each equation must

be identified. Since only the equilibrium pair for price and quantity can be observed for each

hour, identification for each pair of demand and supply for each hour can be challenging.

Nonetheless, the existence of the exogenous variables temperature and wind_chill in the demand

equation (2.12) ensures a shift in the demand equation that allows identification of the supply

curve, while the exogenous variables wind production, coal price,water levels and capacity

available in equations (2.11) or (2.13) allow for a shift in the supply equation that allows the

identification of the demand equation, assuming that the demand and supply curves have

different slopes.

Temperature and wind chill are used as instruments for the supply equation and wind

production, coal price,water levels and capacity available as instruments for the demand

equation. Therefore, the necessary order condition is satisfied, with both equations being

over-identified in this specification (under the underlying assumptions that outside temperature

does not affect the supply of electricity and that coal prices, wind production, water levels and

available capacity do not shift the demand for electricity). Also, the rank condition which requires

that at least one of the population coefficients for the instruments of each equation (e.g.

temper atur e and wi nd_chi l l for the supply equation and

wi nd_pr oducti on,coal pr i ce, w ater level s and capaci t y avai l able for the supply

equation) is non-zero is tested and it is satisfied. Therefore, we could proceed to the estimation of

this system of demand and supply equations for each hour via 2SLS.

It can be argued that the wind chill index is not completely exogenous because it is based on

wind speed, which can be correlated

The system of equations for demand and supply

Since we want to estimate the model simultaneously for all hours of the day and allow for

unobserved contemporaneous correlations between the each hour of the day, a system of

seemingly unrelated equations for each hour of the day is constructed and estimated using

feasible generalized least squares (FGLS) for seemingly unrelated regression equations (SUR).

(Zellner (1962))

Under FGLS, it is assumed that there is some correlation between the error terms of each

equation but the explanatory variables in the model are exogenous. Nevertheless, as discussed

above, this is not a valid assumption in this case. Therefore, a system of 48 equations with a

simultaneous model for each hour of the day, as described previously, has been created.

The three stage least squares (3SLS) method was considered because it allows for both


correlations between the equations of the systems and the use of exogenous variables in the

model as instruments for the entire system. However, this method does not allow for the use of

different instruments for different equations in the system.

Our specification requires the use of different instruments for different equations. For

example, the temperature in hour 4 cannot be treated as an instrument for the supply equation of

hour 10 because it is not a reasonable assumption. Therefore, we have used the general method

of moments (GMM) estimation (Hansen(1982)) for our system of equations. This is a very general

estimation method that does not require distributional assumptions or cross-equations

restrictions within the system of equations. Also, no cross-equation restrictions on the

variance-covariance matrix of errors are needed. For the case of linear models, this method can

be reduced to 3SLS (when all the exogenous regressors in the system are used as instrumental

variables for each endogenous explanatory variable) and SUR when exogeneity of all variables in

the system is assumed. (Hayashi (2000))

Since none of these assumptions hold for the system of equations presented here, we use the

general case for estimating this model, the generalized method of moments.

2.6 Results

This section presents the results of the estimation for the system of equations described in Section

2.4 as well as the results of the preliminary tests performed. Different specifications have been

used. First of all, a single hour system of equations (demand and supply for each hour estimated

individually) specification has been estimated. Second of all, a system of equations for all hours,

for demand and supply is estimated. Thirdly, a lagged value of the system price in introduced in

the supply equation, as an extra-robustness check and a final specification includes the system

price for the previous day and the previous week. Results for all these specifications are included

presented separately for the demand and supply equation.

Preliminary tests

Before estimating the empirical model, a series of tests has been performed to determine the

statistical validity of the models, for both quantity and price. Different unit-root tests exist and, as

it has been clearly determined in the literature, they are very sensitive to the data generating

process. As proved by Ng and Perron (2001) , the Dicky-Fuller test is even more sensitive to loss of

power and size distortions if the data exhibits AR(1) coefficients close to 1 and large negative

MA(1) coefficients. Preliminary analysis shows that, for the case of detrened and deseasonalized

log prices, these properties are observed. Therefore, the Dickey Fuller test based on GLS detrened

series has been chosen, using the modified AIC lag-selection criterion, as it is superior to all other

selection methods.(Ng and Perron (2001)) The same procedure has been used for the equilibrium


quantity because it also exhibits negative MA(1) coefficients and close to 1 AR(1) coefficients.

Both the Dickey-Fuller6 and the Phillip-Perron tests reject the unit root hypothesis for both prices

and quantities. Therefore, both time series are treated as stationary.

The demand

To determine the effects of a change in prices on the quantity demanded, several specifications

have been tested, using both single hour system of equations as well as the entire system of

equations. The results are presented in Table 2.2. As it can be noticed, all specifications indicate a

negative and statistically significant relationship between prices and quantities, in accordance

with the theoretical model. The size of this relationship is very small under the full specification,

where the lagged values of prices, for the previous day and the previous week are included. Lag

prices account for learning effects of the producers, in the supply equation. Under this

assumption, we observe a demand response in the consumer side of only 5%, at best, when

prices double in size.

On the other hand, not accounting for lagged prices, gives a higher response from the demand

side, of 22% at best, when prices double in value. Regardless of the specification, it is obvious from

the results, that some hours have a better response to price modifications than others. Figure 2.6

graphs the average demand response, to help visualize the differences between each hour.

Figure 2.6: Percentage change of quantity demanded at a 1% increase in Elspot system prices,2012-2014, base specification

During office hours (8am-4 pm), demand is very inflexible. The only hours that might allow

some flexibility are the night hours, from 22.00 to 07.00 and the hours immediately before and after

office hours when individuals are probably traveling to/from work and firms are not active. These

results are consistent with other estimates of short-term price elasticity of demand, as summarized

by Lijesen (2007).

6Results of the tests are presented in Table 2.13 in the Appendix


Table 2.2: Price elasticity of demand, per hour, several specifications

Single-hour system Base model Price lag1 Price lag 1 and 7Coeff. (Std. dev.) Coeff. (Std. dev.) Coeff. (Std. dev.) Coeff. (Std. dev.)

Hour 1 -0.20 (0.040) -0.182 (0.012) -0.048 (0.004) -0.049 (0.003)Hour 2 -0.20 (0.037) -0.185 (0.011) -0.036 (0.004) -0.038 (0.003)Hour 3 -0.20 (0.033) -0.180 (0.011) -0.031 (0.004) -0.033 (0.003)Hour 4 -0.22 (0.032) -0.184 (0.011) -0.024 (0.004) -0.024 (0.003)Hour 5 -0.25 (0.040) -0.203 (0.013) -0.023 (0.004) -0.022 (0.004)Hour 6 -0.31 (0.048) -0.240 (0.015) -0.025 (0.004) -0.023 (0.004)Hour 7 -0.30 (0.049) -0.213 (0.015) -0.017 (0.005) -0.014 (0.004)Hour 8 -0.18 (0.039) -0.164 (0.014) -0.011 (0.004) -0.011 (0.003)Hour 9 -0.09 (0.029) -0.101 (0.012) -0.017 (0.004) -0.018 (0.003)Hour 10 -0.08 (0.027) -0.108 (0.011) -0.021 (0.004) -0.023 (0.003)Hour 11 -0.08 (0.026) -0.108 (0.010) -0.022 (0.004) -0.024 (0.003)Hour 12 -0.08 (0.024) -0.116 (0.009) -0.024 (0.004) -0.025 (0.003)Hour 13 -0.08 (0.023) -0.115 (0.009) -0.022 (0.004) -0.024 (0.003)Hour 14 -0.08 (0.025) -0.107 (0.009) -0.022 (0.004) -0.023 (0.003)Hour 15 -0.09 (0.024) -0.112 (0.009) -0.020 (0.004) -0.021 (0.003)Hour 16 -0.13 (0.026) -0.142 (0.010) -0.022 (0.004) -0.023 (0.003)Hour 17 -0.17 (0.031) -0.195 (0.013) -0.027 (0.004) -0.027 (0.003)Hour 18 -0.18 (0.033) -0.221 (0.013) -0.029 (0.004) -0.029 (0.003)Hour 19 -0.16 (0.029) -0.182 (0.012) -0.025 (0.004) -0.025 (0.004)Hour 20 -0.14 (0.027) -0.130 (0.012) -0.013 (0.004) -0.013 (0.003)Hour 21 -0.12 (0.030) -0.101 (0.011) -0.006 (0.004) -0.007 (0.003)Hour 22 -0.14 (0.032) -0.130 (0.011) -0.014 (0.004) -0.015 (0.003)Hour 23 -0.17 (0.035) -0.160 (0.011) -0.031 (0.004) -0.032 (0.003)Hour 24 -0.18 (0.034) -0.183 (0.011) -0.051 (0.005) -0.052 (0.004)Includes also daily holiday dummies as well as temperature.All coefficients statistically significant at 1%

Results also indicate that demand depends on the outside temperature, such that the increase

of temperature by 1 degree will reduce the demand by 1.9%, on average7. Several other

specifications have been tested, for example including wind chill into the model to control for

weather conditions in the demand equation or including wind speed instead of wind power in

the supply function, with similar results for the price elasticity of demand. Post-estimation tests

reveal that the set of instruments used are adequate at a system and single-equation8 level

(underidentification, weak identification and overidentification tests exhibit satisfactory results).

Moreover, since high autocorrelation and heteroskedasticity is a problem, the Bartlett kernel

estimator has been used. The selection of the lags has been done using the Newey-West

methodology.

7see Table 2.14 in the Appendix for the results8see Table 2.17 in the Appendix for the results


The supply

The estimated effects of wind on the prices of electricity are reported in Table 2.3. Results for the

entire specification can be found in Table 2.16 in the Appendix. Although the effect is very small,

there is a strong evidence that wind power reduces the prices of electricity. This effect is consistent

across specifications although it is reduced when the model allows for a learning mechanism from

the firms (by introducing lagged values of prices in the model). Adding these terms does increase

the goodness of fit of the model, although it does not completely account for the autocorrelation

observed in the error term of previous models.

Table 2.3: Effects of the wind power production on the Elspot system price, per hour

Single hour eq. Base model Price lag 1 Price lag 1 and 7Coef. (Std. err.) Coef. (Std. err.) Coef. (Std. err.) Coef. (Std. err.)

Hour 1 -0.34 (0.09) -0.43 (0.04) -0.29 (0.01) -0.30 (0.01)Hour 2 -0.43 (0.10) -0.53 (0.04) -0.35 (0.01) -0.37 (0.01)Hour 3 -0.53 (0.11) -0.60 (0.04) -0.41 (0.01) -0.43 (0.01)Hour 4 -0.49 (0.11) -0.61 (0.04) -0.44 (0.01) -0.47 (0.01)Hour 5 -0.41 (0.10) -0.56 (0.04) -0.43 (0.01) -0.46 (0.01)Hour 6 -0.35 (0.09) -0.45 (0.04) -0.38 (0.01) -0.40 (0.01)Hour 7 -0.27 (0.08) -0.39 (0.04) -0.35 (0.01) -0.37 (0.01)Hour 8 -0.39 (0.08) -0.58 (0.04) -0.39 (0.01) -0.43 (0.01)Hour 9 -0.49 (0.09) -0.64 (0.04) -0.41 (0.01) -0.46 (0.01)Hour 10 -0.43 (0.07) -0.54 (0.04) -0.33 (0.01) -0.37 (0.01)Hour 11 -0.41 (0.07) -0.48 (0.04) -0.30 (0.01) -0.32 (0.01)Hour 12 -0.38 (0.07) -0.44 (0.04) -0.27 (0.01) -0.30 (0.01)Hour 13 -0.39 (0.07) -0.42 (0.03) -0.26 (0.01) -0.28 (0.01)Hour 14 -0.38 (0.07) -0.41 (0.03) -0.25 (0.01) -0.28 (0.01)Hour 15 -0.36 (0.07) -0.40 (0.03) -0.24 (0.01) -0.27 (0.01)Hour 16 -0.35 (0.07) -0.43 (0.04) -0.25 (0.01) -0.27 (0.01)Hour 17 -0.38 (0.08) -0.47 (0.04) -0.29 (0.01) -0.31 (0.01)Hour 18 -0.44 (0.09) -0.57 (0.04) -0.33 (0.01) -0.35 (0.01)Hour 19 -0.38 (0.08) -0.55 (0.04) -0.36 (0.01) -0.38 (0.01)Hour 20 -0.27 (0.08) -0.41 (0.04) -0.29 (0.01) -0.31 (0.01)Hour 21 -0.25 (0.08) -0.32 (0.03) -0.24 (0.01) -0.25 (0.01)Hour 22 -0.23 (0.08) -0.28 (0.03) -0.22 (0.00) -0.22 (0.00)Hour 23 -0.22 (0.08) -0.27 (0.04) -0.22 (0.00) -0.22 (0.00)Hour 24 -0.27 (0.09) -0.34 (0.04) -0.25 (0.01) -0.25 (0.01)Includes also daily holiday dummies as well as all exogeneous variables described in Section 2.4All coefficients statistically significant at 1%.All values have been multiplied with 104 for ease of presentation

As expected, integration of wind power into the system leads to lower hourly prices, with very

small but significant decreases, varying during the hours of the day. The results are robust to

different specifications. Furthermore, it must be mentioned that the base model has the expected

results, as predicted by economic theory. For example, an increase in power production from

wind of 100 MWh will lead to a decrease in price from 27% to 65%, ceteris-paribus, as indicated

by the base model. The decrease observed in the effects of wind power production, when lagged

values of the price is included into the equation is attributed to the omitted variable bias. Because


the economic model used does not require its presence, it has been omitted from the

base-model. Nonetheless, the positive and statistically significant coefficient obtained by it’s

introduction, proves it’s usefulness. Including the lagged values accounts for unobserved

characteristics of the market and as well as learning effects. Lagged prices are correlated both

with the price in the current period, but also with the wind power penetration, thus creating a

negative bias and affecting the estimated coefficient of wind power penetration. Furthermore, the

increase of the water levels reserves also reduces the electricity prices, while the coal price has

little to no effect on the prices of electricity. Also, the elasticity of variable cost is positive,

indicating that the market is in equilibrium, as suggested by Porter(1983).

2.7 Conclusions

In light of the environmental-friendly aspirations of increased fossil-fuel independence, reduced

greenhouse-gas emissions and increased energy efficiency in Europe by 2020 and complete

independence of fossil-fuels by 2050 in Denmark, the question of flexible demand is more

pressing than ever.

This chapter investigates the hourly price elasticity of demand for the wholesale electricity

market for the Nord Pool Market and the effects of wind power for the system price. A structural

model for aggregated demand and supply for electricity is used, for each hour of the day and

estimated simultaneously. Previous research, as well as preliminary analysis of the data supports

the validity of this model, showing that different hours of the day have distinct patterns.

GMM estimation for the system of equations is used, because it makes the least distributional

assumptions on the data and it models the covariance structure between the hours of the day. We

find small price elasticities of demand, for most of the hours of the day (when we account for

learning effects of bidders), with peak hours being the least flexible and the night hours (or

shoulder hours) having the most flexibility. These findings underline the need for different

instruments for managing the demand of electricity, customized for each hour of the day, in order

to achieve the best results. They show that there is a potential for demand management, even for

peak hours. Also, it shows that, allowing some of the clients to see real-time prices (as they do in

Norway) increases demand response, but this effect is most likely offset by the large majority of

clients that do not use real-time pricing schemes in countries such as Denmark (where these

schemes are very slowly implemented). It also gives the indication that peak hour programs do

not increase demand flexibility too much, compared to the flexibility that exists now during night

hours.

It is also found that wind power integration does reduce prices of electricity, although the effect

is quite small and this behavior is consistent during the day. A thorough investigation of the effects

of wind power on the electricity prices in the Nordic countries is the focus of following chapter.


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2.9 Appendix

Data description

This section of the Appendix offers several tables presenting the descriptive statistics and

description of the data used in this chapter. Table 2.4 offers a detailed description of the variables

used in this chapter, the data source and the transformations done to the data, while Tables 2.5

-2.11 shows information regarding the mean, standard deviation and minimum/maximum

values for the same variables.

Table 2.4: Data definition and sourcesData Transformation Data source DefinitionSystem price Log-transformed Nord Pool Spot Equilibrium price for the day-ahead marketQuantity Log-transformed Nord Pool Spot Equilibrium quantity for the day-ahead market

SUPPLY VARIABLES

Wind Power - Nord Pool Spot Actual wind power production, per countryAvailable capacity Sum available capacities between all areas Nord Pool Spot Available capacity on an interconnection between two areasWater reserves Linear interpolation of the total sum of weekly water levels Nord Pool Spot Total available reservoir levels on Nord PoolCoal price - Danish Energy Agency Price of coal

DEMAND VARIABLES

Temperature Weighed average of temperature in capital cities of each country Weather Underground Historical temperature data, for each capital cityTemperature weights Share of total final consumption own computationConsumption Total consumption per country and as sum for all countries Nord Pool Spot Consumption of electricity, per bidding areaWind Chill Based on wind speed and temperature data Weather Underground Historical temperature data, for each capital city


Table 2.5: Descriptive statistics of the daily Elspot system price (DKK/MWh), per hour, 2012-2014

Price N Mean St. Dev. Min Max

Hour 00 861 196 47 42 335Hour 01 861 189 48 30 325Hour 02 858 185 49 26 319Hour 03 861 183 51 25 319hour 04 861 186 52 18 321Hour 05 861 195 51 11 334Hour 06 861 208 56 9 416Hour 07 861 233 97 37 1283Hour 08 861 245 113 51 1365Hour 09 861 239 88 53 1276Hour 10 861 234 70 57 690Hour 11 861 230 66 56 754Hour 12 861 226 61 55 645Hour 13 861 222 60 53 642Hour 14 861 220 60 51 641Hour 15 861 220 61 51 677Hour 16 861 224 71 51 777Hour 17 861 236 103 51 1443Hour 18 861 234 87 52 1347Hour 19 861 226 68 51 1090Hour 20 861 219 56 49 872Hour 21 861 214 49 48 465Hour 22 861 209 47 49 345Hour 23 861 199 46 39 331


Table 2.6: Descriptive statistics of the daily Elspot equilibrium quantity (MWh), per hour, 2012-2014

Equilibrium quantity No. obs Mean St. Dev. Min MaxHour 00 861 33211 5152 24519 47579Hour 01 861 32172 5152 23643 45584Hour 02 858 31705 5166 23027 44887Hour 03 861 31636 5298 22559 44960Hour 04 861 32058 5554 22212 45886Hour 05 861 33650 6129 22345 50219Hour 06 861 36992 7172 22960 55355Hour 07 861 40148 7883 23918 59148Hour 08 861 41336 7574 25119 59459Hour 09 861 41683 7110 26309 59475Hour 10 861 41764 6854 27110 58829Hour 11 861 41577 6695 27508 58685Hour 12 861 41067 6642 27396 58346Hour 13 861 40650 6734 27112 58142Hour 14 861 40384 6902 26922 58593Hour 15 861 40405 7185 26864 58804Hour 16 861 40751 7529 26967 59249Hour 17 861 41491 7752 27295 59712Hour 18 861 41703 7528 27383 58861Hour 19 861 41335 7144 27578 58504Hour 20 861 40310 6558 26824 56607Hour 21 861 39105 6017 26361 54943Hour 22 861 37591 5481 26265 52605Hour 23 861 35339 5156 25695 49326


Table 2.7: Descriptive statistics of the daily total available capacity (GWh) on the Elspot market,per hour, 2012-2014

Available capacity N Mean St. Dev. Min MaxHour 00 861 43729 2554 33450 49186Hour 01 861 43742 2549 33450 49186Hour 02 861 43769 2569 33450 49186Hour 03 861 43829 2595 33338 49186Hour 04 861 43934 2618 33200 49186Hour 05 861 44142 2810 29510 49386Hour 06 861 44221 2840 33495 49351Hour 07 861 44258 2838 33395 49486Hour 08 861 44305 2866 33395 49486Hour 09 861 44334 2876 33395 49486Hour 10 861 44334 2879 33395 49486Hour 11 861 44337 2878 33395 49486Hour 12 861 44332 2869 33395 49486Hour 13 861 44327 2879 33395 49486Hour 14 861 44371 2862 33395 49486Hour 15 861 44446 2835 33395 49486Hour 16 861 44626 2793 33395 49486Hour 17 861 44722 2778 33395 49486Hour 18 861 44756 2754 33395 49586Hour 19 861 44745 2741 33395 49586Hour 20 861 44709 2711 33495 49786Hour 21 861 44604 2629 33888 49786Hour 22 861 44436 2584 33888 49786Hour 23 861 43848 2548 33450 49186


Table 2.8: Descriptive statistics of the daily weighted average temperature for the Elspot market,per hour (Celsius), 2012-2014

Temperature N Mean St. Dev. Min MaxHour 00 861 4 7 −18 18Hour 01 861 4 7 −20 17Hour 02 861 3 7 −20 17Hour 03 861 3 7 −20 17Hour 04 861 3 7 −20 17Hour 05 861 3 8 −21 18Hour 06 861 4 8 −19 18Hour 07 861 5 8 −20 20Hour 08 861 5 8 −20 21Hour 09 861 6 8 −18 22Hour 10 861 7 8 −16 23Hour 11 861 7 8 −15 24Hour 12 861 8 9 −14 24Hour 13 861 8 9 −14 25Hour 14 861 8 9 −14 25Hour 15 861 8 9 −15 26Hour 16 861 8 9 −16. 26Hour 17 861 7 9 −16 25Hour 18 861 7 9 −17 25Hour 19 861 6 9 −17 24Hour 20 861 6 8 −19 23Hour 21 861 5 8 −19 20Hour 22 861 5 8 −19 19Hour 23 861 4 8 −17 18


Table 2.9: Descriptive statistics of the daily weighted average wind chill factor, for the Elspotmarket, per hour, 2012-2014

Wind chill N Mean St. Dev. Min MaxHour 00 861 2 9 - 23 19Hour 01 861 1 9 - 24 18Hour 02 861 1 9 - 24 18Hour 03 861 1 8 - 23 17Hour 04 861 1 9 - 24 18Hour 05 861 1 9 - 25 18Hour 06 861 1 9 - 24 18Hour 07 861 2 10 - 24 20Hour 08 861 3 10 - 25 22Hour 09 861 4 10 - 22 24Hour 10 861 4 10 - 21 25Hour 11 861 5 10 - 20 25Hour 12 861 5 10 - 20 25Hour 13 861 6 10 - 19 26Hour 14 861 6 10 - 19 27Hour 15 861 6 10 - 19 27Hour 16 861 6 11 - 20 27Hour 17 861 5 11 - 20 27Hour 18 861 5 10 - 25 27Hour 19 861 4 10 - 26 25Hour 20 861 3 10 - 21 24Hour 21 861 3 9 - 22 21Hour 22 861 2 9 - 23 19Hour 23 861 2 9 - 23 18


Table 2.10: Descriptive statistics of the daily aggregated wind power production (MWh) on Elspotmarket, per hour, 2012-2014

Wind Production N Mean St. Dev. Min MaxHour 00 861 1346 1016 34 4519Hour 01 861 1334 1012 0 4436Hour 02 861 1330 1008 32 4469Hour 03 861 1324 1008 41 4513Hour 04 861 1325 1013 35 4555Hour 05 861 1325 1024 35 4571Hour 06 861 1327 1039 31 4632Hour 07 861 1345 1059 24 4682Hour 08 861 1380 1079 22 4672Hour 09 861 1427 1100 33 4603Hour 10 861 1475 1118 31 4579Hour 11 861 1509 1126 30 4578Hour 12 861 1530 1123 28 4598Hour 13 861 1533 1110 40 4616Hour 14 861 1530 1098 60 4676Hour 15 861 1519 1086 56 4728Hour 16 861 1506 1079 53 4669Hour 17 861 1479 1073 41 4633Hour 18 861 1443 1069 35 4674Hour 19 861 1409 1066 32 4683Hour 20 861 1396 1062 38 4770Hour 21 861 1389 1055 55 4814Hour 22 861 1377 1041 53 4825Hour 23 861 1357 1029 0 4766

Table 2.11: Hour-invariant variables, daily, 2012-2014

N Mean St. Dev. Min Max

holiday 861 0.046 0.211 0 1monday 861 0.143 0.350 0 1tuesday 861 0.14 0.35 0 1wednesday 861 0.143 0.35 0 1thursday 861 0.143 0.35 0 1friday 861 0.143 0.35 0 1saturday 861 0.143 0.35 0 1sunday 861 0.143 0.35 0 1coal (dkk) 861 80 10 66 105water (GWh) 857 74160 22714 28689 109601


Preliminary analysis

This section of the Appendix presents preliminary analysis of the data. Table 2.12 presents the

summary of the seasonality effects present for each hour of the day.

Table 2.12: Results for seasonality effects for each hour of the day, based on F-tests

Trend Day Holiday Month YearHour 00 Yes No No Yes YesHour 01 Yes No No Yes YesHour 02 No Yes No Yes YesHour 03 Yes No No Yes YesHour 04 Yes Yes No Yes YesHour 05 Yes Yes No Yes YesHour 06 Yes Yes No Yes YesHour 07 Yes Yes Yes Yes YesHour 08 Yes Yes Yes Yes YesHour 09 Yes Yes Yes Yes YesHour 10 Yes Yes No Yes YesHour 11 Yes Yes No Yes YesHour 12 Yes Yes No Yes YesHour 13 Yes Yes No Yes YesHour 14 No Yes No Yes YesHour 15 No Yes No Yes YesHour 16 No Yes No Yes YesHour 17 Yes Yes No Yes YesHour 18 Yes Yes No Yes YesHour 19 Yes Yes No Yes YesHour 20 Yes Yes No Yes YesHour 21 Yes Yes No Yes YesHour 22 Yes No No Yes YesHour 23 Yes No No Yes Yes


Table 2.13 presents the number of optimal lags chosen using the MAIC criterion developed by

Ng and Perron (2001), as well as the level at which the null hypothesis of unit root can be rejected,

at each level.

Table 2.13: Augmented Dickey-Fuller test for price and quantity

Price Quanity(A) (B) (C) (A) (B) (C)

Hour 00 2*** 2*** 2*** 7*** 7*** 7***Hour 01 17** 17*** 17*** 5*** 13*** 5***Hour 02 17** 17*** 17*** 6*** 13*** 6***Hour 03 12*** 5*** 12*** 5*** 13*** 5***Hour 04 13*** 13*** 13*** 5*** 13*** 5***Hour 05 7*** 7*** 7*** 5*** 5*** 5***Hour 06 7*** 7*** 7*** 5*** 5*** 5***Hour 07 17*** 17*** 17*** 6*** 6*** 6***Hour 08 17*** 17*** 17*** 6*** 6*** 6***Hour 09 16** 16** 17*** 6*** 20*** 6***Hour 10 16** 16** 16*** 20*** 20** 20***Hour 11 16** 16** 16*** 20** 20* 20**Hour 12 17** 17** 17*** 20** 20* 20**Hour 13 17** 17** 17*** 20*** 20** 20***Hour 14 7*** 7*** 17*** 5*** 20*** 20***Hour 15 7*** 7*** 7*** 20*** 20** 20***Hour 16 7*** 7*** 7*** 20** 20** 20**Hour 17 16*** 16*** 16*** 20** 20** 20**Hour 18 5*** 5*** 5*** 20** 20* 20**Hour 19 5*** 5*** 5*** 20** 20* 20**Hour 20 3*** 3*** 3*** 20* 13* 18**Hour 21 1** 1** 1*** 6*** 6* 6**Hour 22 1** 1** 1*** 6*** 6* 6**Hour 23 1*** 1** 1*** 5*** 6* 5**

(A): Deseasonalized(B): Deseasonalized and detrended, I(0) around a trend(C): Deseasonalized, I(0) around a trendStatistically significant at*** 1%, **5%, *10%


Final results

This section presents the full specifications for the demand and supply equations, for each hour

of the day, as described in the chapter.

Tables 2.14 and 2.16 present the results for the base model, presented in Section 2.4 for the

demand and supply, respectively, while Table 2.15 presents the results for an alternative

specification, where the supply equation includes lags for electricity prices (lag 1 and 7). The

results in the case of the supply equations have not been reported, as the introduction of lags

does not significantly change the results from the base model.

Table 2.14: Coefficients for the base model, for the demand equation

Price Temperature Temp2̂Coef. (Std. err.) Coef. (Std. err.) Coef. (Std. err.)

Hour 1 -0.18 (0.01) -0.02 (0.0004) 0.00000 (0.00002)Hour 2 -0.18 (0.01) -0.02 (0.0004) -0.0001 (0.00002)Hour 3 -0.18 (0.01) -0.02 (0.0003) -0.0002 (0.00002)Hour 4 -0.18 (0.01) -0.03 (0.0004) -0.0002 (0.00003)Hour 5 -0.20 (0.01) -0.03 (0.0004) -0.0003 (0.00003)Hour 6 -0.24 (0.01) -0.03 (0.0004) -0.0004 (0.00003)Hour 7 -0.21 (0.01) -0.02 (0.0004) -0.0003 (0.00003)Hour 8 -0.16 (0.01) -0.02 (0.0005) -0.0001 (0.00002)Hour 9 -0.10 (0.01) -0.02 (0.0005) 0.0000 (0.00002)Hour 10 -0.11 (0.01) -0.02 (0.0004) 0.0001 (0.00002)Hour 11 -0.11 (0.01) -0.02 (0.0003) 0.0001 (0.00002)Hour 12 -0.12 (0.01) -0.02 (0.0003) 0.0002 (0.00002)Hour 13 -0.12 (0.01) -0.02 (0.0003) 0.0002 (0.00002)Hour 14 -0.11 (0.01) -0.02 (0.0003) 0.0002 (0.00002)Hour 15 -0.11 (0.01) -0.02 (0.0003) 0.0002 (0.00002)Hour 16 -0.14 (0.01) -0.02 (0.0003) 0.0002 (0.00002)Hour 17 -0.19 (0.01) -0.03 (0.0004) 0.0003 (0.00002)Hour 18 -0.22 (0.01) -0.03 (0.0006) 0.0003 (0.00002)Hour 19 -0.18 (0.01) -0.03 (0.0005) 0.0002 (0.00002)Hour 20 -0.13 (0.01) -0.02 (0.0004) 0.00006 (0.00002)Hour 21 -0.10 (0.01) -0.02 (0.0003) -0.00001 (0.00002)Hour 22 -0.13 (0.01) -0.02 (0.0003) -0.00002 (0.00002)Hour 23 -0.16 (0.01) -0.02 (0.0003) 0.00005 (0.00002)Hour 24 -0.18 (0.01 -0.02 (0.0003) 0.00000 (0.00002)


Table 2.15: Coefficients for the demand when price lags(1 and 7) are included in the model

Price Temperature Temp2

Coef. (Std. err.) Coef. (Std. err.) Coef. (Std. err.)Hour 1 -0.05 (0.003) -0.02 (0.0002) -0.00002 (0.00001)Hour 2 -0.04 (0.003) -0.02 (0.0002) -0.00011 (0.00001)Hour 3 -0.03 (0.003) -0.02 (0.0002) -0.00015 (0.00002)Hour 4 -0.02 (0.003) -0.02 (0.0002) -0.0002 (0.00002)Hour 5 -0.02 (0.004) -0.02 (0.0002) -0.0002 (0.00002)Hour 6 -0.02 (0.003) -0.02 (0.0002) -0.0003 (0.00002)Hour 7 -0.01 (0.004) -0.02 (0.0002) -0.0002 (0.00001)Hour 8 -0.01 (0.003) -0.02 (0.0002) -0.0002 (0.00001)Hour 9 -0.02 (0.003) -0.02 (0.0002) -0.00009 (0.00001)Hour 10 -0.02 (0.003) -0.02 (0.0002) 0.00000 (0.00001)Hour 11 -0.02 (0.003) -0.02 (0.0002) 0.00006 (0.00001)Hour 12 -0.02 (0.003) -0.02 (0.0002) 0.0001 (0.00001)Hour 13 -0.02 (0.003) -0.02 (0.0002) 0.0002 (0.00001)Hour 14 -0.02 (0.003) -0.02 (0.0002) 0.0002 (0.00001)Hour 15 -0.02 (0.003) -0.02 (0.0002) 0.0002 (0.00001)Hour 16 -0.02 (0.003) -0.022 (0.0002) 0.0002 (0.00001)Hour 17 -0.03 (0.003) -0.02 (0.0002) 0.0001 (0.00001)Hour 18 -0.03 (0.003) -0.02 (0.0002) 0.00009 (0.00001)Hour 19 -0.02 (0.003) -0.02 (0.0002) 0.00005 (0.00001)Hour 20 -0.01 (0.003) -0.02 (0.0002) 0.00000 (0.00001)Hour 21 -0.01 (0.003) -0.02 (0.0001) -0.00004 (0.00001)Hour 22 -0.011 (0.003) -0.02 (0.0001) -0.00004 (0.00001)Hour 23 -0.03 (0.003) -0.02 (0.0001) 0.00002 (0.00001)Hour 24 -0.05 (0.003) -0.02 (0.0002) -0.00001 (0.00001)


Table 2.16: Coeficients of the base model, for the supply equation

Quantity Capacity* 10-̂4 WL* 10-̂4 Coal*10-̂4Coeff. (Std. dev.) Coeff. (Std. dev.) Coeff. (Std. dev.) Coeff. (Std. dev.)

Hour 00 1.3 (0.06) -0.5 (0.03) -0.02 (0.002) -0.001 (0.001)Hour 01 1.5 (0.08) -0.6 (0.11) -0.02 (0.003) -0.001 (0.002)Hour 02 1.6 (0.06) -0.6 (0.03) -0.02 (0.002) -0.001 (0.001)Hour 03 1.7 (0.06) -0.6 (0.03) -0.02 (0.002) -0.001 (0.001)Hour 04 1.7 (0.06) -0.6 (0.03) -0.02 (0.002) -0.001 (0.001)Hour 05 1.5 (0.06) -0.5 (0.03) -0.02 (0.002) -0.002 (0.001)Hour 06 1.4 (0.05) -0.5 (0.03) -0.02 (0.002) -0.001 (0.001)Hour 07 1.6 (0.05) -0.5 (0.03) -0.03 (0.002) 0.002 (0.001)Hour 08 1.7 (0.05) -0.5 (0.03) -0.03 (0.002) 0.003 (0.001)Hour 09 1.6 (0.05) -0.5 (0.03) -0.03 (0.002) 0.002 (0.001)Hour 10 1.5 (0.06) -0.5 (0.03) -0.03 (0.002) 0.001 (0.001)Hour 11 1.4 (0.05) -0.5 (0.02) -0.03 (0.003) 0.001 (0.001)Hour 12 1.4 (0.05) -0.5 (0.02) -0.03 (0.002) 0.000 (0.001)Hour 13 1.4 (0.06) -0.5 (0.04) -0.03 (0.002) 0.000 (0.001)Hour 14 1.5 (0.06) -0.5 (0.03) -0.03 (0.004) -0.001 (0.001)Hour 15 1.5 (0.05) -0.5 (0.03) -0.03 (0.002) -0.001 (0.001)Hour 16 1.5 (0.05) -0.5 (0.03) -0.03 (0.002) -0.001 (0.001)Hour 17 1.6 (0.05) -0.5 (0.03) -0.03 (0.002) 0.001 (0.001)Hour 18 1.5 (0.05) -0.5 (0.03) -0.03 (0.002) 0.001 (0.001)Hour 19 1.3 (0.05) -0.5 (0.02) -0.03 (0.002) 0.000 (0.001)Hour 20 1.2 (0.05) -0.5 (0.02) -0.03 (0.002) -0.001 (0.001)Hour 21 1.2 (0.05) -0.5 (0.02) -0.03 (0.002) -0.001 (0.001)Hour 22 1.2 (0.06) -0.5 (0.03) -0.03 (0.002) -0.001 (0.001)Hour 23 1.3 (0.06) -0.6 (0.03) -0.03 (0.002) -0.001 (0.001)


Table 2.17 presents the results for the over-identification test of Hansen’s (1982) J statistic χ2

test is reported for the instrumental variables used in the case of the single-hour estimation, for

each hour of the day.

Table 2.17: Test for overidentification for each hour of the day

Hour χ2(11) P-value1 11.5411 0.39912 11.6644 0.38943 11.7211 0.3854 12.3797 0.33585 13.3749 0.26956 12.267 0.34397 14.8061 0.19158 15.4039 0.16479 16.9005 0.1109

10 18.4131 0.072511 18.5368 0.069912 19.44 0.053613 19.0987 0.059314 19.4905 0.052815 18.9532 0.061916 18.9145 0.062617 18.8007 0.064818 18.3117 0.074619 15.6267 0.155620 15.3851 0.165521 15.9354 0.143522 16.305 0.130223 14.96 0.184324 15.517 0.16

CH

AP

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R

3WIND POWER EFFECTS FOR PRICE LEVEL AND

VOLATILITY FOR THE WHOLESALE

ELECTRICITY MARKET

Ioana Neamtu

Aarhus University

Abstract

In this chapter we investigate the effects of wind power penetration on the wholesale’s

electricity prices in West Denmark, for the level and the variance of prices, at an hourly level,

during congested and non-congested periods. Denmark’s electricity market is divided into

two different areas, which are part of Nord Pool, a wholesale’s electricity market for Nordic

and Baltic countries. A common price is determined for all countries, as long as no congestion

occurs. When congestion occurs, each region determines its own price, which may differ from

the common (system) price. We model this behavior explicitly by using a regime switching

model, with observed states, for the congested and non-congested periods, for each hour of

the day. Also, we use an GARCH model for the states of the model to account for the

time-varying variance of the electricity prices, which we assume can be affected by the levels

of wind power penetration. We find that wind power penetration reduces the levels of

electricity prices for each hour of the day, during the congested and the non-congested

periods. We also find that the effect on price volatility differs between peak and off peak

hours, contributing on its increase during night-time hours and to its decrease during some

day-time hours. We also observe higher price reduction during non-congested period than

during congested periods, across all hours of the day, indicating positive effect of belonging to

the Nord Pool market, for West Denmark.

56

CHAPTER 3. WIND POWER EFFECTS FOR PRICE LEVEL AND VOLATILITY FOR THEWHOLESALE ELECTRICITY MARKET 57

3.1 Introduction

In the context of integrating of more wind power production within the electricity grid and having

in mind the Danish policy of reaching 100% renewable energy within the Danish consumption

by 2050, the question of how electricity prices are affected by the wind power penetration is very

important for both producers and distributors of electricity. Price levels and price fluctuations are

important issues when discussing investment opportunities in the transmission and distribution

grid but also for risk management analysis for both suppliers and distributors of electricity. The

question of how wind power penetration affects electricity prices is very important not only for

wind producers themselves, but also for traditional (non-renewable) producers, who need to make

strategic investment decisions regarding the operation of their plants. Since the Danish electricity

market is part of the Nord Pool market, participants on the Danish market must consider the wind

power penetration effects from both Danish and international producers and also consider how

these effects might be affected by the transmission constraints of the grid.

In this chapter we are quantifying the effects of the wind power penetration on the Elspot area

price in West Denmark, during congested and non-congested periods, for each hour of the day.

We define congestion as the event when the system price differs from the area price. We define

the system price as the common price on the Elspot market, determined based on the aggregated

supply and demand from all bidding areas, without taking into account any capacity constraints

between the areas, while the area price is the price determined for each area if the capacity on the

interconnections between bidding areas in the Elspot market is exceeded. In the non-congested

periods, the area price is actually the system price - therefore allowing us to analyze the effect of

wind power penetration on the system price, while analyzing the area price during congested

periods. We assume that the area price is determined by the local consumption and the local

(wind) production, while the system price is determined by the aggregated consumption and

production from all the bidding areas within the Elspot market. Hence, we are able to determine

the effects of wind power penetration on electricity prices, both at the market level and the area

level.

By investigating the effects of wind power penetration for the electricity price during

congested and non-congested periods, we can determine the full extent of the gains from wind

power production for Danish producers during congested periods and for the Nordic producers

during non-congested periods. The model proposed allows us to quantify the gains of being part

of the Elspot market for the Danish market participants.

To quantify these effects, we use a regime-switching model, with two states, one for

congestion and one for non-congestion and we investigate the wind power effects on price levels

and its variance, during each state. We assume that wind power penetration has a strong effect on

price volatility and we use a GARCH specification for the variance of the electricity prices to test

this hypothesis. We focus our attention on price levels (as opposed to a logarithmic


transformation of the prices) because we want to allow for the negative prices observed on the

market and also because we believe that a logarithmic transformation would reduce the variance

of the prices and not allow for a good measure of the wind power penetration effects on the price

volatility. We define volatility of prices as the variance of electricity prices, after correcting for the

effects of wind power penetration, water level reservoirs and seasonal, daily and yearly patterns.

We focus our attention on the Elspot area price effects of wind power penetration in West

Denmark, while accounting for the fact that it is part of the Nord Pool market.

We use daily times series, for each hour of the day to closely follow the structure of the Danish

electricity market, where producers and consumers make bids for electricity 12 hours ahead of

delivery time. Therefore, they have a limited set of available information about prices, quantities

and wind power production a day before the day of delivery and no information that they can use

the hour before delivery. This idea was introduced in the literature by Ramanathan et al. (1997)

for the demand of electricity and, thereafter, implemented to model prices of electricity by several

authors (Huisman et al. (2007; 2013) Raviv et al (2013),Varaat and Varaat (2014)).

We find that increasing the level of wind power penetration by 1 percentage point reduces

the Elspot area prices by 0.6 to 1.9 DKK/MWh during congested periods. During non-congested

periods, the reduction of the Elspot area price varies between 0.7 and 3 DKK/MWh. Moreover, we

find that wind power penetration increases price volatility during night time hours for congested

periods, while decreasing the volatility during day-time hours for both regimes.

Regime-switching models for electricity prices have been expanding in the literature and they

can be categorized into 4 categories- observable vs. non-observable transition probabilities

(Haldrup and Nielsen (2006, 2010) vs. Janczura and Wenon (2010)) and constant versus

time-varying transition probabilities (Haldrup and Nielsen (2006) vs. Sapio(2015)).

Also, GARCH models for electricity price volatility have been developed, but the definition of

volatility may vary within each paper, while the best GARCH specification has not yet been found,

as it may vary, depending on the particularities of the electricity market under investigation.

(Thomas and Mitchell (2005), Worthington et al.(2005), Koopman et al. (2007), Escribano et al.

(2011))

We contribute to the existing literature first by quantifying the wind power penetration effects

on the levels of electricity prices for West Denmark, for each hour of the day and by allowing

congestion to play a significant role in shaping these effects and second, by using a

regime-switching GARCH specification for electricity prices, with observed states, for the Danish

market.

Analyzing the volatility effects of wind power production has recently received more attention

in the literature, but there are still very few studies which have quantified these effects. A few

examples are Mauritzen (2010), who assesses the impact of wind power production on the

volatility of the system price and area prices in Nord Pool Market and West and East Denmark,

respectively, for daily, weekly and monthly price averages. He uses a distributional lagged model


(an auto-regressive moving average with exogenous variables (ARMAX(p,q)) model) for the

variability of wind and defines daily volatility of prices as the standard deviation of the hourly

prices from the daily average. He concludes that wind power decreases short term volatility, but it

increases it over longer time periods.

Jonsson et al. (2010) look at the effects of wind power forecasts on the average area prices of

electricity and its distribution in West Denmark, using a non-parametric approach and data from

2002-2006. They conclude that the average price is decreased when more wind power is expected

in a given hour. They introduce the notion of wind power penetration, as the ratio between wind

power and total consumption and note that this is the best measure for the effects of wind power

on prices.

Ketterer (2014) uses a GARCH model to assess the effects of wind power on the average daily

electricity price and volatility of electricity prices in Germany. They find that prices are reduced by

the increase of wind power but the volatility of electricity prices is also increased.

None of these studies allow for the possibility of regime switching in the levels or the volatility

of the prices. They do not consider possible congestion effects. It has been shown that allowing

for regime switching in the behavior of electricity prices improves the fit of the model and the

forecasting (e.g.: Janczura and Weron (2010), Haldrup and Nielsen (2006)). One of the few papers

currently making use of a regime-switching model for analyzing wind-effects on electricity prices

is Sapio (2015) who proposes a regime-switching model with observed probabilities, based on the

specific functionality of the Italian electricity market. They consider two regimes, based on

congestion. The switch between the two regimes is easily observed and given by the non-zero

difference between the system and area price (as first suggested by Haldrup and Nielsen (2006)).

A short description of the Danish electricity market is given in Section 3.2. Sections 3.3 and 3.4

present the model, estimation method and data while Section 3.5 and 3.6 present the results and

concluding remarks.

3.2 The Danish Electricity market

The Danish electricity market is divided into two market regions (West and the East), which are

part of the Nord Pool market. The Nord Pool market includes several markets, but in this chapter

we are focusing only on the Elspot market, the wholesale day-ahead electricity market. This is a

double marginal price auction where both producers and consumers bid for the price they are

willing to pay for a certain amount of electricity. There are seven countries which participate in

this market - Finland, Sweden, Norway, Denmark, Estonia, Lithuania and Latvia. Each country is

divided into several bidding areas (or market regions), as described in Figure 3.1. Not all areas

are connected directly; for example, Denmark is connected only with Sweden and Norway. The

maximum amount of electricity which can be transported between each region is called available

capacity. The amount of available capacity for each interconnection is determined each day by


the Nord Pool operator. When the amount of available capacity between two regions is exceeded,

congestion occurs, due to transmission constraints.

Figure 3.1: Interconnections between the bidding areas on the Elpost Market

Note: The numbers associated with each country indicate the different bidding areas, within thecountry (e.g. Norway has 5 different bidding areas)

The price formed on the Elspot market is named the system price and it is determined

simultaneously for all bidding regions at the intersection of the aggregated demand and supply,

without taking into consideration any physical restrictions between the bidding areas. After

determining this price, the transmission constraints between regions are taken into account. If

the quantity required from one region to another exceeds the maximum capacity available, area

prices are calculated and electricity flows from the lower price areas to the higher price areas, to

increase economic efficiency. When there is no congestion, the area price is the same as the

system price. Nevertheless, capacity congestion is very frequent for the Nordic market. In

Denmark, the congestion average per day is 89.9% for West Denmark and 89.6% for East

Denmark. The area price is the price that participants pay for the electricity traded on the Elspot

market and it is binding after the closing-time of the market.

3.3 The model

The behavior of electricity prices has been extensively studied in the literature and many different

models have been proposed. In this chapter, we consider a regime-switching model, with two

observed states, in which a state is determined by the existence of congestion. We assume that

the high oscillations observed for the Elspot area prices are affected, among other things, by

congestion. Our regime-switching variable is observed from the data and is defined as the

non-zero difference between the Elspot system price and the Elspot area price, for West

Denmark. Furthermore, we assume a non-constant variance for each of the two regimes and we

test this assumption. We assume that daily Elspot area prices are stochastic processes, defined as:


ph,t =µh,Sh,t +ah,Sh,t . (3.1)

where ph,t represents the daily Elspot area price, in hour h,µh,Sh,t represents the conditional mean

of ph,t , defined as µh,t = E [ph,t |Ih,t−1] and ah,Sh,t = ph,t −µh,Sh,t represents the conditional error

term, defined as ah,Sh,t = σh,Sh,t · εh,t . σ2h,t = V ar [ph,t |Ih,t−1] = E [(ph,t −µh,t )2|Ih,t−1] represents

the conditional variance of ph,t and εh,t is an independent and identically distributed random

variables, εh,t v I I D(0,1). Sh,t represents the state of the system (congested or not congested) in

hour h of day t and Ih,t−1 represents the information set available to the bidders for hour h, the

day before delivery.

The models used for the conditional mean and the conditional variance as well as the full

model and the estimation method are described in the following subsections.

Modeling price levels

Since we are investigating the effects of wind power penetration for the price levels and the price

variance, several assumptions have been made. First, we assume a non-linear relationship

between wind power penetration and electricity prices during congested and non-congested

regimes, as observed in Figure 3.2. This assumption is tested by fitting a first, second and third

order polynomial of wind power penetration onto the Elspot area prices. Second, we assume that

having more wind power penetration in the system will reduce electricity prices and third, we

assume that in periods of congestion, the reduction in prices will be lower than in periods of

non-congestion.

Figure 3.2: Relationship between wind power penetration (%) and daily Elspot area prices(DKK/MWh) in West Denmark, for hour 12, during congested and non-congested regimes, 2012-2015


We also assume that lagged values of prices affect the current price and we allow for the

possibility that the weekly average prices of the neighboring hours also affect the current price.

We use the following model for the price level:

E [ph,t |I h,t−1] =α0h +βh Xh,t ,Sh,t +lh∑

i=1θi h ·ph,t−i +γhD t +δh Mt +ρh

7∑j=1

ph−1,t− j +λh

7∑j=1

ph+1,t− j

(3.2)

where ph,t is the daily Elspot area price, D t represents a vector of dummy variables for each

day of the week and Mt represents a vector of monthly dummies. Xh,t ,Sh,t is a vector of explanatory

variables, which depend on the state of the system (described in equation (3.3)). t represents the

day and h represents the hour of the day. Ih,t−1 represents the information set available at time

t −1, for hour h.7∑

j=1ph−1,t− j and

7∑j=1

ph+1,t− j represent the average of the daily Elspot area price from the

previous week, for the two neighboring hours (h −1 and h +1) of the hour investigated (h).

We use this model independently, for each hour of the day and we determine the number of

lagged1 prices included in the model (l ) individually for each hour of the day, according to the

Box-Cox methodology. Most hours of the day include the Elspot area price from the previous day

and seven days ago.

βh Xh,,St ,t expands to the following specification, when accounting for congestion:

βh ·Xh,t =β0h xh,t +β1h x2

h,t +β2h x3h,t +β3hWh,t , Sh,t = 0

β0h A xh,At +β1h A x2h,At +β2h A x3

h,At , Sh,t = 1(3.3)

where xh,t represents the wind power penetration for the entire Nordic market and it is defined as

the ratio between forecasted consumption on Elspot and the forecasted wind power production

for the Elspot market (which includes the wind power production from Denmark, Sweden,

Estonia and Latvia). xh,At represents the wind power penetration for West Denmark, defined as

forecasted consumption in West Denmark and forecasted wind power production in West

Denmark. The state variable Sh,t is 0 when there is no congestion and 1 when congestion occurs.

Wt represents the levels of water reservoirs on Nord Pool market. This variable is not included in

the congested regime because West Denmark does not have this endowment.

The last two terms of equation (3.2) represent the average of the Elspot area prices from the

previous seven days, for the hour before (h − 1) and the hour after (h + 1) the hour investigated.

We introduce these variables into the model to account for the correlations that may exist across

hours, under the assumption that neighboring hours affect each other (e.g.: through block bids)

and we also allow for learning effects of the bidders, not only from previous days of the same

hour (ph,t−i ) but also from previous days for the neighboring hours (ph±1,t− j ). The averaging also

1the number of lags selected for each hour is specified in Table 3.6


reduces the unexpected changes in prices within the week that may not be relevant for the present

price of the investigated hour.

Modeling the volatility

In this chapter, volatility is defined as the conditional variance of the prices of electricity. We

assume that the conditional variance is not constant over time and we also assume that the

variation can be caused by congestion and by the integration of more wind power penetration in

the system. We also assume that volatility is different for each hour of the day and that the effects

of congestion and wind power penetration are different, especially for peak and off-peak hours.

Although there are many ways in which we can model volatility (ARCH model, the SV model,

realized volatility) we choose the generalized auto-regressive conditional heteroskedasticity

(GARCH) model, introduced by Bollerslev (1986) and the exponential GARCH model of Nelson

(1991). We assume that prices exhibit asymmetries in volatility (negative/positive shocks of

supply or demand have different effects on volatility), especially for day-time and peak-hours.

The GARCH model

For each ph,t =µh,t +ah,t , we define σ2h,t =V ar [ph,t |Ih,t−1] =V ar [ah,t |Ih,t−1].

We assume that ah,t = σh,t · εh,t and σ2h,t = φoh +

mh∑i=1φi h · a2

h,t−i +sh∑

i=1θi h ·σ2

h,t−i , where {εh,t } is

an independent and identically distributed random variables, εh,t v I I D(0,1), φ0h > 0, φi h ≥ 0,

θi h ≥ 0 andmax(m,s)∑

i=1(θi h +φi h) < 1 (Zivot(2008)). We assume εht follows a t-student distribution.

The latter conditions are the sufficient conditions to guarantee the stationary of the process.

GARCH models allow for the introduction of explanatory variables in the conditional variance.

Since we are testing the wind power penetration effects on electricity prices, we introduce wind

power penetration as an explanatory variable into the conditional variance equation. Therefore,

the model becomes:

σ2h,t = exp(φ0h +λhSh,t xh,t ,Sh,t )+

mh∑i=1φi h ·a2

h,t−i +sh∑

i=1θi h ·σ2

h,t−i , (3.4)

where xh,t ,Sh,t is the wind power penetration at hour h in day t , during congested and

non-congested periods (Sh,t ) and λhSh,t are the parameters of interest, describing the effects of

wind power penetration on the conditional variance (volatility) of the prices, during congested

(λ1h) and non-congested periods (λ0h) for each hour of the day.

The EGARCH model

We assume that some hours of the day are characterized by asymmetric effects of the volatility of

electricity prices and we employ an EGARCH model to be able to capture them.


Therefore, we model the innovations through the following equation:

g (εh,t ) = θhεh,t +γ(|εh,t |−E [|εh,t |]) (3.5)

where both εh,t and |εh,t |−E(|εh,t |) are independent and identically distributed random

variables, following a Student-t distribution, in which case E(|εh,t |) = 2p

vh−2Γ((vh+1)/2)(vh −1)Γ(vh /2) ; where Γ(·)

is the Gamma distribution and vh > 2, the degrees of freedom.

Therefore, we model volatility with an EG ARC H(mh , sh) process through:

ln(σ2h,t ) =α0h +δh,Sh,t xh,t ,Sh,t +

sh∑i=1φi h · g (εht−i )+

mh∑j=1

θi h · ln(σ2h,t− j ) (3.6)

where xh,t ,Sh,t is the wind power penetration at hour h in day t , during congested and

non-congested periods (St ) and δSt are the parameters of interest, describing the effects of wind

power penetration on the log-conditional variance (volatility) of the prices, during congested

(δ1h) and non-congested periods (δ0h).

We test different specifications for the GARCH and EGARCH models and choose the best

model fit for our data, based on the Akaike Information Criterion (AIC) and different tests for the

adequacy of the standard assumptions (stationary)2.

Final model

Elspot area prices prices in West Denmark depend on the physical restrictions (capacity

availability) of the grid. This allows us to model two different regimes for our prices, depending

on the state of the system: congested or non-congested.

Therefore, we estimate the following model for the electricity prices :

ph,t =µ0h,t +a0h,t , Sh,t = 0

µ1h,t +a1h,t , Sh,t = 1(3.7)

where ph,t represents the electricity price, µh,t ,Sh,t represents the level of the price (in equation

(3.2) ) and aSh,t =

σ0h,t ·εh,t , Sh,t = 0

σ1h,t ·εh,t Sh,t = 1represents the error term.

To estimate the effects of wind power penetration and congestion on price volatility, we

estimate one of the following models, depending on the hour of the day:

σ2h,t =

exp(φ0h +λ0h x0h,t )+

mh∑i=1φi h ·a2

h,t−i +sh∑

i= jθi h ·σ2

h,t− j , Sh,t = 0

exp(φ0h +λ1h x1h.t )+mh∑i=1φi h ·a2

h,t−i +sh∑

i= jθi h ·σ2

h,t− j , Sh,t = 1(3.8)

2Table 3.6 in the Appendix presents the specification chosen for each hour of the day


or

ln(σ2h,t ) =

α0h +δ0h x0t +

sh∑i=1φi h · g (εh,t−i )+

mh∑j=1

θi h · l n(σ2h,t− j ), Sh,t = 0

α0h +δ1h x1,t +sh∑

i=1φi h · g (εh,t−i )+

mh∑j=1

θi h · ln(σ2h,t− j ), Sh,t = 1

(3.9)

The estimation method is the conditional maximum likelihood. Conditional maximum

likelihood requires priming values for σ2h,t and ε2

h,t . The likelihood function we use for the

estimation of the model is:

f (ah,1, ..., ah,T |θh) = f (ah.T |Ih,T ) f (ah,T−1|Ih,T−1) · · · · f (ah,m |Ih,m) f (ah,1, ...., ah,m |θh) (3.10)

Assuming a Student-t distribution for εh,t , the probability density function of the innovations

is:

f (εh,t |νh) = Γ((vh +1)/2)

Γ(vh/2)√

(vh −2)π

(1+

ε2h,t

vh −2

)−(vh+1)/2

, vh > 2 (3.11)

Therefore, we get:

f (Ah,m+1,T |θh , Ah,m) =∏Tt=m+1

Γ((vh +1)/2)

Γ(vh/2)√

(vh −2)π

1

σh,t

[1+

a2h,t

vh −2

]−(vh+1)/2

(3.12)

where Ah,m+1,T = ah,m+1, ...., ah,T , Am = ah,1, ..., ah,m and θh represents the set of parameters to

be estimated, for hour h.

The degrees of freedom of the t-distribution can be specified a-priori or it can be estimated

jointly with the other parameters. For our model, we are estimating it within the model. Hence,

our log-likelihood function is:

lnL(Ah,m+1,T |θh , vh , Ah,m) = (T −m) · [lnΓ

(vh +1

2

)− lnΓ

(vh

2

)− 1

2ln((vh −2)π) (3.13)

where

lnL(Am+1,T |θh , Ah,m) =−T∑

t=m+1

[vh +1

2l n

(1+

a2h,t

vh −2

)+ 1

2ln(σ2

h,t )

](3.14)

Since we observe the states of the system and we assume that each state of the model is

determined by different variables, we decided to use an observed-state regime switching GARCH

model, where the volatility differs in each state, but we do not differentiate between low and high

volatility regimes. We estimate σ2h,t recursively, based on equations (3.8) or (3.9), depending on

the hour of the day. Initially, we assume σ2h,t = ε2

h,t and we hold it constant, estimating it as

expected unconditional variance.


3.4 Data and descriptive statistics

The data used in this chapter comes from the Nord Pool website and includes data for West

Denmark and the entire Nordic region. We use data on prices, forecasted consumption,

forecasted wind power production, for the period 01.01.2012 - 25.09.2015. In the following, we

give a short description of the data and the motivation behind using it.

Wind power penetration

We construct wind power penetration as a ratio between forecasted wind power production and

forecasted consumption for West Denmark and the Elspot market. Formally, the wind power

penetration ratio is defined as:

xh,Sh,t ,t =f wh,t ,Sh,t

f ch,t ,Sh,t

(3.15)

where xh,t ,Sh,t is wind power penetration, f wh,Sh,t ,t is forecasted wind power production and

f ch,t ,Sh,t is forecasted consumption at time t , for hour h and state of the market Sh,t .

If there is no congestion on the market (Sh.t = 0) , we use the wind power penetration for the

Elspot market. If there is congestion (Sh.t = 1) on the market, we use the wind power penetration

for the West Denmark.

For the Elspot market, the forecasted wind power production represents the sum of the

forecasted wind power production from Denmark, Sweden and Estonia, the only countries that

rely on wind power production. The forecasted consumption for the Elspot market is defined as

the sum of forecasted consumption of all countries from the Elspot market.

The average hourly wind power penetration in West Denmark is 46.5% , at times reaching

211%, being the region with the highest wind power penetration within the Elspot market, while

the hourly average for the market is of only 4.5%, reaching up to 22%. A full description of

averages per hour for each region can be found in the Appendix, Table 3.5.

Using forecasted consumption and forecasted wind power production has a few advantages.

Apart from creating a parsimonious model, it avoids the simultaneity bias problem that occurs

by using actual consumption and production (since the system operator determines prices and

quantities simultaneously). Furthermore, it allows us to model the system more accurately, since,

at the closing time of the bidding on the Elspot market, this is the information available to the

bidders.

Congestion

We define congestion as the event in which the price for the Elspot area in West Denmark differs

from the Elspot system price, as described in equation (3.16).


Sh,t =1, ph,t , 6= pE ,h,t

0, other wi se(3.16)

where Sh,t is the congestion dummy, ph,t is the Elspot area price at time t in West Denmark,

and pE ,h,t is the Elspot system price.

Congestion occurs, on average, 89% of the time, for West Denmark and it affects the level of

prices in this region3. As illustrated in Figure 3.3, prices differ during congestion and

non-congestion periods, for some hours of the day. During peak hours intervals (5am-11am and

7pm-10pm), prices are higher during congested periods, while during shoulder hours prices are

slightly higher during non-congested periods.

Figure 3.3: Average daily Elspot area prices (DKK/MWh) in West Denmark, during congested andnon-congested periods, per hour, 2012-2015

Electricity prices

Prices in West Denmark vary considerably, from an hourly average of 244 DKK to a maximum of

1492 DKK. Figure 3.4 illustrates the distribution of the Elspot area prices, for each hour of the day,

for West Denmark. Night hours have a skewed distribution to the left, while day-time prices exhibit

a skewness to the right, which is explained by the higher consumption of electricity during day-

time hours, compared to the night time hours. Moreover, the median of prices differs significantly

between night and day hours, which motives the use of different models for each hour of the day.

Prices in West Denmark also exhibit weekly and monthly patterns for each hour of the day. After

eliminating outliers (defined as values above or below 3 ·σ), detrending and deseasonalizing, we

cannot reject the null hypothesis of level stationary (using KPSS test ) for price levels and we reject

the null of unit-root (based on augmented Dickey Fuller test, which is proven to be more efficient

for AR(1) processes (Ng and Perron (2001)).

3Table 3.4 in the Appendix presents a detailed description of the congestion, for each hour of the day.


Figure 3.4: Box plot for daily Elspot area prices (DKK/MWh) in West Denmark, per hour, 2012-2015

There have been 167 hours of negative prices in in our sample, mostly during night-time hours,

as presented in Figure 3.5.

Figure 3.5: Total number of hours with negative Elspot area prices in West Denmark, per hour,2012-2015

Negative prices occur mainly when there is excess production of electricity and producers are

willing to pay to stay operational during a certain hour of the day, specifically during January-

May and December, mostly in December and January (over 40% of negative prices). This happens

because of the very high consumption in these months and high wind power production.

3.5 Results

In this section, we present the results obtained by using the model described in equations (3.7)

and (3.8), including a series of different specifications, to test the robustness of our final model. For

each model, we fit a first, second and third order polynomial function of wind power penetration

for the levels of electricity prices and a first order polynomial for the conditional variance. We

distinguish between congested and non-congested regimes for both the conditional mean and


variance. We also analyze the case of constant versus non-constant variance and the case of a

single regime versus a two regime switching model.

We treat each hour of the day as a separate daily time series and we assume that there is no

contemporaneous correlation between the hours of the day. This is a restrictive assumption and,

to allow for some correlations between the hours within a day, we add, to each hourly equation,

the average for the previous seven days for the neighboring hours, as described in equation (3.2).

For each hour of the day, we determine the best AR(p) structure for the electricity prices,

based on the general test for auto-correlation developed by Cumby-Huizinga (1990, 1992 ) and

implemented by Baum and Schaffer (2013). It allows us to test the hypothesis of auto-correlation

at a specific lag p and it is general enough to allow for endogenous regressors and the presence of

conditional heteroskedastiticy.

In the following we present only the marginal effects of the wind power penetration, for both

levels and variance. We use the levels of the prices because a logarithmic transformation for prices

would reduce the conditional variance and would not allow us to observe the full impact of the

wind power penetration on its variance.

The regime-switching model with constant variance

We begin by analyzing the effects of the wind power penetration on the Elspot area prices, using a

two-state regimes switching model and assuming constant variance within each state of the model

and we test whether the regime-switching alone accounts for the conditional heteroskedasticity

observed in the data.

We also look at the wind power penetration effects on the Elspot area prices assuming no

regime-switching and constant variance. We use three alternative functional specification for

wind power penetration: a linear relationship (specification M1), a second-order polynomial

(specification M2) and third order polynomial (specification M3). Table 3.1 presents the marginal

effects for each of these specifications, for the single-regime case and the two-regimes case

(congetion and non-congestion), with constant variance. The values represent the marginal

effects of wind power penetration on the level of the Elspot area price, when wind power

penetration doubles.

The hourly models with constant variance and a single regime exhibit serial correlation and

conditional heteroskedasticity. Allowing for two-regimes, based on the physical restrictions on the

market improves the serial correlation observed in the error term but it is not enough to account

for the conditional heteroskedasticity.


Table 3.1: Marginal effects of wind power penetration for the Elspot area price in West Denmark,for the single regime and the regime-switching model (congestion and non-congestion), assumingconstant-variance, per hour

Single-regime Congestion Non-congestionβ(M3) β(M2) β(M1) β(M3) β(M2) β(M1) β(M3) β(M2) β(M1)

Hour 0 -57.08*** -43.88*** -46.71*** -68.04** -45.38** -54.67*** -79.33*** -49.05*** -53.41***(3.59) (2.44) (1.96) (10.23) (3.17) (2.081) (29.63) (15.88) (16.83)

Hour 1 -59.34*** -50.38*** -58.07*** -61.31*** -63.53*** -84.17*** -84.83* -64.81* -75.95***(4.67) (3.42) (5.02) (7.59) (3.93) (3.360) (17.09) (12.62) (13.99)

Hour 2 -64.26*** -52.58*** -56.49*** -66.52*** -47.72*** -63.64*** -79.64* -65.58* -75.46***(19.34) (3.65) (4.71) (19.97) (3.81) (5.318) (20.16) (11.32) (12.57)

Hour 3 -61.75*** -56.08*** -60.59*** -63.82*** -55.61*** -67.47*** -73.61* -67.21* -92.77***(4.02) (3.65) (4.62) (18.96) (4.08) (4.698) (23.64) (8.84) (10.21)

Hour 4 -61.22*** -55.9*** -61.43*** -63.23*** -55.11*** -67.28*** -88.25* -78.63* -88.68***(4.06) (3.28) (3.90) (20.36) (3.59) (4.134) (25.78) (12.42) (13.53)

Hour 5 -66.51*** -55.32*** -59.65*** -72.19*** -54.7*** -61.55*** -69* -83.62* -91.85***(3.83) (3.01) (3.27) (4.76) (3.17) (3.369) (33.98) (19.06) (18.94)

Hour 6 -100.93*** -81.09*** -84.63*** -110.44*** -81.39*** -87.02*** -166.27* -157.09* -171.6***(6.51) (4.49) (4.53) (66.9) (4.84) (4.643) (60.67) (20.02) (20.21)

Hour 7 -153.90*** -140.54*** -124.8*** -164.93*** -147.36*** -131.0*** -316.82* -166.61* -162.2***(9.72) (7.05) (5.80) (45.99) (7.6) (5.991) (117.46) (41.22) (42.20)

Hour 8 -169.69*** -157.90*** -130.2*** -180.67*** -165.77*** -135.9*** -462.73* -211.52* -199.4***(11.46) (7.28) (5.44) (57.69) (7.89) (5.504) (167.08) (50.02) (49.84)

Hour 9 -168.83*** -156.67*** -129.1*** -186.6*** -165.63*** -136.7*** -368.2* -241.42* -212.4***(10.53) (7.45) (6.16) (35.66) (8.17) (6.364) (78.91) (25.31) (24.28)

Hour 10 -160.92*** -147.21*** -122.4*** -181.78*** -159.96*** -129.8*** -247.35* -170.64* -162.6***(10.74) (7.56) (6.15) (38.37) (8.51) (6.342) (62.74) (30.63) (31.10)

Hour 11 -152.78*** -136.2*** -109.9*** -174.88*** -144.58*** -114.7*** -245.61* -235.38* -198.4***(10.93) (8.15) (6.35) (36.26) (8.9) (6.482) (67.55) (25.78) (23.78)

Hour 12 -146.06*** -125.23*** -106.3*** -166.24*** -134.76*** -110.7*** -249.43* -173.7* -165.6***(9.62) (6.38) (5.10) (37.64) (7.22) (5.229) (64.68) (37.23) (39.02)

Hour 13 -129.82*** -111.33*** -99.56*** -148.52*** -119.96*** -104.9*** -163.43* -120.8* -121.7***(8.59) (6.47) (5.27) (10.38) (7.19) (5.393) (44.72) (21.51) (27.05)

Hour 14 -119.93*** -103.45*** -130.3*** -132.02*** -107.74*** -100.3*** -237.47* -134.5* -81.27***(7.92) (6.13) (13.89) (24.47) (6.6) (5.391) (37.52) (19.37) (27.06)

Hour 15 -109.89*** -97.35*** -90.84*** -124.1*** -102.06*** -94.92*** -66.6* -118.9* -89.11***(7.36) (5.79) (5.08) (26.19) (6.23) (5.210) (47.77) (18.21) (28.48)

Hour 16 -119.38*** -108.47*** -97.34*** -132.89*** -113.78*** -99.64*** -179.67* -163.01* -171.9***(7.59) (5.81) (4.97) (26.27) (6.17) (5.122) (63.97) (25.41) (26.23)

Hour 17 -172.04*** -69.40*** -121.7*** -188.55*** -158.66*** -124.9*** -316.15* -174.44* -152.6***(11.08) (26.24) (6.58) (43.17) (8.53) (6.711) (99.91) (46.89) (47.53)

Hour 18 -182.66*** -161.72*** -121.8*** -198.78*** -171.35*** -125.6*** -387.27* -223.27* -197.0***(11.48) (9.07) (7.84) (33.47) (9.75) (7.988) (125.11) (49.28) (50.64)

Hour 19 -163.85*** -138.04*** -104.2*** -182.43*** -147.37*** -108.0*** -253.39* -170.84* -147.9***(10.38) (8.24) (7.15) (32.11) (8.91) (7.348) (101.73) (42.93) (41.70)

Hour 20 -128.98*** -104.22*** -79.36*** -153.49*** -118.74*** -85.20*** -199.09* -134.61* -125.0***(10.15) (7.51) (6.78) (28.97) (8.5) (7.323) (48.23) (19.24) (20.42)

Hour 21 -157.16*** -76.98*** -64.15*** -171.06*** -85*** -68.03*** -143.34* -106.39* -101.3***(8.83) (6.00) (5.15) (32.8) (7.02) (5.446) (30.63) (17.01) (17.70)

Hour 22 -73.63*** -52.05*** -47.53*** -91.93*** -56.66*** -50.63*** -86.33* -74.4* -73.78***(9.20) (5.41) (4.66) (30.91) (6.26) (5.379) (25.52) (12.56) (13.22)

Hour 23 -83.99*** -63.62*** -74.99*** -90.65*** -63.21*** -79.69*** -136.73* -89.01* -99.11***(5.24) (5.78) (3.46) (30.05) (4.31) (3.715) (35.34) (15.61) (17.31)

Robust Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

M3 :β(M3) = ∂p∂X A

=β0 +2 ·β1 · x̄A +3 ·β3 x̄2A ; M2 :β(M2) = ∂p

∂X A=β1k +2 ·β2k · x̄A ; M1 :β(M1) = ∂p

∂X A=β1k

where A indicates the regime (or the single regime), k indicates the specification k ∈ {M1, M2, M3} and x̄ is the average wind power penetrationSpecification M3 fits a third order polynomial for wind power penetrationSpecification M2 fits a second order polynomial for wind power penetrationSpecification M1 fits a first order polynomial for wind power penetration

The single regime model shows negative and statistically significant results, indicating a

reduction in the Elspot area price, when wind power penetration increases, although the size of

the increase is underestimated, for all three specifications, compared to the two-states regime

model.


Using a regime-switching model has the benefit of allowing us to evaluate the wind power

penetration effects on prices when congestion occurs. We observe that, for the two-regime

model, under all specifications, the effects of the wind power penetration are higher, both under

the congested and the non-congested period. Moreover, the wind power penetration effects are

lower during the congested periods than under non-congested periods. This suggests that being

part of the Nord-Pool is beneficial for West Denmark, as price reductions during non-congestion

period are higher.

The regime-switching model with non-constant variance

Using Baum and Wiggins (1999)’s module based on Engle (1982)’s LM test for ARCH effects,

volatility was confirmed for each hour of the day. Our tests indicate high conditional

heteroskedasticity and strong serial correlation of the squared residuals for each hour of the day,

so we relax the constant variance specification and we model the conditional variance explicitly,

using a GARCH or EGARCH specification, for each hour, as defined in equations (3.8) and (3.9).

Figure 3.6 shows the changes in prices, from one day to the next, for hour 12 and hour 00.

Figure 3.6: Change in the daily Elspot area price, for West Denmark at hour 12 and 00, 2012-2015

We use the same general test for autocorrelation developed by Cumby-Huizinga (1990, 1992 )

to determine the optimal (E)G ARC H(p, q) specification, based on the squared values of the error

terms, as suggested by Enders (2009). Tests based on Akaike Information Criterion (AIC) have

been performed to determine whether allowing for wind power penetration effects within the

conditional variance equation improves the model fit. The assumption has been confirmed.

Results for the model are presented in the following subsections. We first discuss the level of

prices and then the volatility (defined as the conditional variance of prices).


Price levels

The marginal effects of the fitted third order polynomial (specification M3), second order

polynomial (specification M2) and first order polynomial (specification M1) of the wind power

penetration, for the price levels (as described in equation (3.7)) are presented in Table 3.2, for

West Denmark. Our tests indicate that the third order polynomial is the best fit to our data (see

Table 3.8 in the Appendix).

A few observations can be made based on these results. First, as expected, wind power

penetration lowers the level of electricity prices, in each of the two observed regimes. This is

mainly due to the low (and virtually) zero marginal cost of production for wind producers, which

allows them to always be dispatched first. Second, the effects of wind power penetration on

electricity prices differ substantially for each hour of the day, having similar patterns for each

regime. We observe stronger effects during peak hours (7am-9am;5pm-7pm), when consumption

is high and lower effect during night-time hours and mid-day-time hours, when consumption is

lower.

Third, we notice that accounting for the conditional heteroskedasticity improves our model fit

and reduces the estimated coefficients slightly, for both the congested and non-congested

periods, for most hours of the day. Moreover, estimates of the single-regime case are lower than

the estimates of the two-state model. Furthermore, we estimate that during congested periods a 1

percentage point increase in the wind power penetration in West Denmark decreases prices from

0.6 to 1.9 DKK/MWh, depending on the hour of the day; in periods of non-congestion in the

market, the wind power penetration reduces prices from 0.77 to 4 DKK/MWh, as shown in Table

3.2.

During congested periods, local consumption is higher, which requires the dispatch of more

expensive local electricity producers, leading to higher prices, than in non-congested periods

(when electricity can move freely between areas and the lowest marginal cost producers in the

market can be dispatched). During congested periods, low-cost producers such as hydro

producers, cannot be activated in West Denmark. The local demand must be met with local

production (mainly coal-based generators or gas generators), which leads to higher prices, due to

the higher marginal costs of production. Although the wind power penetration in West Denmark

is the highest among all bidding areas on Nord Pool, the segmentation caused by congestion and

high demand reduces its positive effects on prices, because of merit order supply and the local,

more expensive, coal and gas production.

When congestion is not present, more wind power production can be dispatched freely, along

side with other lower cost production units, which keep prices at a lower level and enhances the

wind power effects for electricity prices.

Moreover, across specifications and hours of the day, water levels during non-congested

periods have been found to have a negative but not significant effect on area prices for West

Denmark. Also, we find a positive relationship between the hourly price and the weekly average


price of neighboring hours, as well as positive correlations with lagged values of prices from the

same hour. This indicates that, if prices the day before (or week before) for the current hour or

neighboring hours have been high, the price today will also be high.

Table 3.2: Marginal effects of wind power penetration for the daily Elspot area price in WestDenmark, for the single-regime and regime-switching model(congetion/non-congestion), withnon-constant variance, per hour

Single regime Congestion No congestionβ(M3) β(M2) β(M1) β(M3) β(M2) β(M1) β(M3) β(M2) β(M1)

Hour 0 -50.68*** -39.48*** -38.48*** -61.52*** -41.28*** -41.42*** -81.81*** -48.84*** -29.61***(3.26) (2.05) (2.06) (8.88) (2.06) (2.35) (11.91) (7.13) (4.24)

Hour 1 -55.83*** -47.65*** -46.39*** -59.09*** -45.11*** -50.83*** -80.28*** -49.32*** -34.86***(4.28) (2.92) (3.00) (5.11) (3.30) (3.27) (15.82) (11.05) (4.22)

Hour 2 -61.84*** -53.03*** -53.24*** -63.88*** -50.53*** -59.63*** -78.99*** -66.93*** -41.72***(4.06) (3.05) (3.18) (23.40) (3.31) (3.57) (20.19) (11.82) (5.09)

Hour 3 -56.65*** -51.78*** -56.46*** -60.81*** -51.84*** -58.00*** -66.78*** -62.10*** -40.01***(4.56) (3.58) (6.17) (21.38) (3.67) (3.91) (22.34) (9.41) (5.56)

Hour 4 -60.18*** -53.72*** -52.78*** -62.9*** -52.61*** -57.55*** -74.6*** -65.55*** -69.95***(4.38) (3.15) (3.29) (22.19) (3.36) (7.24) (26.44) (14.52) (16.24)

Hour 5 -63.30*** -53.63*** -54.66*** -70.26*** -53.84*** -57.17*** -40.35*** -64.73*** -57.25***(4.34) (3.04) (2.93) (5.25) (3.21) (3.09) (33.45) (17.76) (8.55)

Hour 6 -92.55*** -75.74*** -79.57*** -98.82*** -76.73*** -82.95*** -142.85*** -130.53*** -67.43**(5.91) (4.53) (4.11) (67.84) (4.90) (4.43) (64.36) (26.43) (22.35)

Hour 7 -138.57*** -127.16*** -114.1*** -149.55*** -132.54*** -119.3*** -307.75*** -157.44*** -48.25(9.80) (7.17) (5.96) (45.65) (7.81) (6.08) (77.52) (38.99) (38.79)

Hour 8 -169.78*** -155.69*** -126.5*** -184.87*** -165.63*** -132.5*** -395.39*** -199.98*** -28.31(11.53) (7.53) (5.33) (48.45) (8.47) (5.47) (93.30) (47.26) (28.82)

Hour 9 -165.06*** -148.25*** -117.8*** -188.08*** -153.20*** -124.4*** -296.72*** -196.68*** -25.00***(10.69) (8.00) (6.38) (33.25) (9.95) (6.63) (21.11) (37.88) (6.21)

Hour 10 -159.63*** -138.94*** -113.3*** -192.22*** -150.87*** -120.9*** -205.2*** -144.86*** -33.22**(11.87) (8.57) (7.04) (45.36) (9.61) (7.41) (55.33) (33.39) (10.77)

Hour 11 -149.8*** -124.96*** -99.41*** -184.83*** -130.41*** -103.3*** -182.7*** -202.83*** -27.96**(13.07) (8.81) (6.90) (52.62) (9.39) (7.65) (27.45) (30.71) (10.25)

Hour 12 -135.09*** -112.49*** -97.39*** -154.73*** -121.83*** -102.5*** -190.93*** -122.08*** -37.35*(9.47) (6.98) (5.30) (32.11) (7.87) (5.53) (52.54) (33.02) (16.61)

Hour 13 -127.72*** -102.08*** -93.68*** -144.39*** -107.71*** -98.99*** -171.77*** -100.87*** -30.87**(9.21) (6.82) (5.64) (10.57) (7.37) (5.81) (34.89) (17.02) (9.43)

Hour 14 -113.57*** -94.31*** -89.51*** -125.7*** -97.07*** -94.44*** -223.83*** -115*** -44.36***(7.46) (5.91) (5.31) (21.14) (6.31) (5.50) (36.18) (18.55) (7.59)

Hour 15 -100.23*** -84.78*** -81.06*** -112.85*** -84.50*** -82.40*** -100.56*** -94.28*** -38.07***(7.95) (5.76) (5.23) (31.17) (5.98) (5.26) (60.18) (17.68) (7.65)

Hour 16 -103.05*** -92.46*** -83.97*** -115.95*** -97.29*** -86.92*** -171.18*** -145.65*** -60.01**(8.80) (6.51) (5.97) (29.07) (6.88) (6.15) (64.80) (24.20) (21.55)

Hour 17 -148.07*** -125.91*** -100.0*** -163.9*** -132.52*** -101.0*** -300.52*** -141.70*** -47.75*(12.13) (8.12) (6.50) (45.24) (8.89) (6.74) (71.57) (45.66) (21.97)

Hour 18 -161.86*** -138.06*** -96.49*** -175.25*** -143.92*** -97.19*** -228.25*** -144.70*** -41.04**(11.41) (7.60) (6.03) (33.65) (8.18) (6.14) (88.25) (38.54) (12.62)

Hour 19 -142.44*** -117*** -80.35*** -157.59*** -123.21*** -81.55*** -146.98*** -147.31*** -35.83**(12.24) (8.93) (7.71) (37.42) (9.03) (7.45) (44.82) (33.43) (12.64)

Hour 20 -106.92*** -85.04*** -67.27*** -126.23*** -96.26*** -71.37*** -152.38*** -106.70*** -54.72***(10.96) (7.07) (5.58) (27.45) (9.44) (7.14) (37.60) (15.86) (13.96)

Hour 21 -144.09*** -69.30*** -59.27*** -152.62*** -75.04*** -55.21*** -126.73*** -91.39*** -33.12***(7.31) (4.89) (4.50) (24.38) (5.83) (4.74) (27.61) (16.01) (6.15)

Hour 22 -68.87*** -47.76*** -44.44*** -86.85*** -50.51*** -46.86*** -70.65*** -54.71*** -21.71***(8.71) (4.51) (4.56) (32.33) (4.86) (4.83) (17.53) (10.65) (4.32)

Hour 23 -52.96*** -36.92*** -38.37*** -62.48*** -37.29*** -35.44*** -85.18*** -55.05*** -30.69***(4.08) (2.44) (2.54) (24.10) (2.76) (2.66) (16.29) (9.94) (4.41)

Robust Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

M3 :β(M3) = ∂p∂X A

=β0 +2 ·β1 · x̄A +3 ·β3 x̄2A ; M2 :β(M2) = ∂p

∂X A=β1k +2 ·β2k · x̄A ; M1 :β(M1) = ∂p

∂X A=β1k

where A indicates the regime (or the single regime), k indicates the specification k ∈ {M1, M2, M3} and x̄ is the average wind power penetrationSpecification M3 fits a third order polynomial for wind power penetrationSpecification M2 fits a second order polynomial for wind power penetrationSpecification M1 fits a first order polynomial for wind power penetration


Price volatility

Although Jonsson et al.(2010) and Mauritzen (2009) support the hypothesis of decreased price

volatility in the short run, several authors still find evidence for increased volatility (e.g.

Ketterer(2014),Woo et al.(2011)). We show that increased wind power can lead to both increase

and decrease in price volatility.

Table 3.3 shows the changes in volatility (defined as the conditional variance of electricity

prices), due to changes in wind power penetration, for West Denmark. We present the results

from the three different specifications of the conditional mean of prices (M3, M2 and M1), but we

keep the same functional form of the wind power penetration in the conditional variance

equation, across all three specifications (equations (3.8) and (3.9)). We also include the results of

the single regime case, in which we control for wind power penetration in both conditional mean

and variance. Different models for volatility have been tested for each hour of the day and the

optimal model has been chosen based on AIC criterion. Moreover, the final specifications have

been tested and the stability conditions for each GARCH specification are met (see Tables 3.6 in

the Appendix for the final specification). Nonetheless, the effects of wind power production have

been robust across different specifications (ARCH, asymmetric-GARCH, power-ARCH,

asymmetric-power-ARCH, EGARCH). We observe different effects of wind power penetration

across the day, but the same pattern accros specifications. The specification of the conditional

mean does not influence the effect of wind power production for the conditional variance of the

prices.

Figure 3.7 illustrates the positive and negative effects of wind power penetration on price

volatility, for each hour of the day, for the congested and non-congested period. During night

hours (11pm to 6am), price volatility increases because there is more wind power penetration

during these hours, for the congested periods. During day and evening hours (7am to 10pm),

price volatility is decreasing, as the percentage of wind power penetration on the market

increases, while during peak-hours (9am, 11am, 6pm) prices exhibit a decrease in volatility in

both regimes.


Figure 3.7: Graphical representations of the effects of wind power penetration on price variance inWest Denmark, during congested and non-congested periods (presented in Table 3.3)

Note: The figure illustrates the effects of a 1% increase in wind power penetration on the conditionalvariance of the Elspot area prices, for West Denmark, for each hour of the day, during the congestedand non-congested regimes.The dark color indicates the statistical significance of the effect, duringthe congested regime while the light color indicates statistical significance during non-cogestedperiods. The lack of color suggest the lack of statistical significance. The size of the change in notillustred. Only the direction of the change is illustrated.

On average, electricity consumption is lower during non-congested periods compared to the

congested periods.4 This leads to the dispatch of relatively cheaper production sources during

non-congested periods, compared to periods of congestion. Therefore, price volatility during

non-congested periods is lower and not affected by the wind power production, because, on

average, the same (lower cost) producers tend to be dispatched. Exceptions from this assumption

are the peak hours during the day (9am-11am, 5am-7am) when higher levels of demand require

the dispatch of relatively more expensive producers, in which case more integration of wind

power production keeps prices relatively lower.

The decrease in volatility during day-time hours can be explained by the high levels of wind

power penetration, which would consistently keep prices at lower levels and would not require the

dispatch of costly power production, therefore making prices less volatile. The observed positive

effect on volatility during night time hours can be explained by the lower demand observed during

night hours and the inflexibility of conventional producers, who cannot stop production easily

if the marginal demand is low. Since demand is already lower during night-times, the increased

production of wind power will only deepen this effect, therefore creating negative and volatile

prices.

4see Figure 3.8 in the Appendix


Table 3.3: Effects of wind power penetration for the daily Elspot area price variance inWest Denmark, under the single-regime and the regime-switching (congestion/non-congestion)model, and different specifications of the conditional mean(M1, M2, M3)

Single regime1 Congestion No congestionM3 M2 M1 M3 M2 M1 M3 M2 M1λ2 λ2 λ2 λ1 λ1 λ1 λ0 λ0 λ0

Hour 0 3.05*** 3.03*** 3.06*** 2.82*** 2.90*** 2.88*** -1.43 0.69 0.26(0.23) (0.22) (0.21) (0.22) (0.22) (0.21) (1.70) (0.92) (0.60)

Hour 1 2.72*** 2.73*** 2.78*** 2.5*** 2.5*** 2.52*** 0.21 0.5 0.461(0.2) (0.19) (0.19) (0.2) (0.20) (0.20) (0.59) (0.56) (0.49)

Hour 2e 1.33*** 1.36*** 1.35*** 1.36*** 1.38*** 1.39*** 0.26 0.25 0.177(0.15) (0.14) (0.14) (0.14) (0.13) (0.13) (0.29) (0.27) (0.26)

Hour 3 2.73*** 2.74*** 2.74*** 2.57*** 2.58*** 2.48*** 1.18** 1.19*** 1.14**(0.19) (0.19) (0.19) (0.20) (0.20) (0.19) (0.36) (0.33) (0.41)

Hour 4 2.63*** 2.62*** 2.56*** 2.54*** 2.53*** 2.51*** 1.01* 1.01* 1.01*(0.19) (0.19) (0.19) (0.21) (0.20) (0.18) (0.47) (0.43) (0.43)

Hour 5 2.34*** 2.34*** 2.35*** 2.38*** 2.33*** 2.36*** 1.5 1.63*** 1.78***(0.22) (0.21) (0.22) (0.25) (0.22) (0.23) (0.77) (0.48) (0.42)

Hour 6 0.19* 2.01*** 1.96*** 1.78*** 1.83*** 1.75*** 1.86* 2.02* 2.26***(0.11) (0.38) (0.40) (0.50) (0.41) (0.41) (0.86) (0.82) (0.66)

Hour 7 -0.07 -0.05 -0.02 -0.28 -0.22 -0.20 -1.76* -1.32 -0.36(0.275) (0.26) (0.29) (0.31) (0.29) (0.31) (0.81) (0.84) (1.10)

Hour 8e -0.14* -0.12 -0.14 -0.22 -0.19 -0.209 -0.63 -0.52 -0.32(0.08) (0.07) (0.08) (0.14) (0.11) (0.13) (0.40) (0.31) (0.40)

Hour 9 -1.01*** -0.95*** -0.98*** -1.41** -1.34*** -1.34*** -9.48*** -9.08*** -8.56***(0.33) (0.32) (0.38) (0.48) (0.39) (0.40) (2.59) (2.16) (1.76)

Hour 10 -0.83*** -0.69*** -0.70** -0.76* -0.76* -0.86** -3.60 -3.10 -2.8(0.31) (0.27) (0.30) (0.34) (0.34) (0.32) (2.67) (2.67) (1.78)

Hour 11 -1.24*** -1.04*** -1.08*** -1.46** -1.11*** -1.25** -11.52*** -9.39* -10.02**(0.45) (0.33) (0.41) (0.48) (0.33) (0.41) (3.29) (4.32) (3.41)

Hour 12 -0.04 -0.03 -0.03 -0.07 -0.05 -0.05 -0.23 -0.21 -0.16(0.04) (0.04) (0.04) (0.05) (0.05) (0.05) (0.20) (0.19) (0.19)

Hour 13 -0.37 -0.08 -0.05 -0.67 -0.20 -0.34 -5.84* -5.11** -6.9(0.50) (0.38) (0.39) (0.65) (0.36) (0.41) (2.54) (1.90) (3.93)

Hour 14e 0.01 0.02 0.025 0.004 0.02 0.02 0.033 0.015 0.014(0.03) (0.03) (0.03) (0.04) (0.04) (0.04) (0.14) (0.15) (0.14)

Hour 15 0.11 0.21 0.27 -0.08 0.07 0.11 -19.83* -16.18 -15.87(0.42) (0.4) (0.36) (0.44) (0.38) (0.35) (7.91) (9.07) (9.03)

Hour 16 -0.23 -0.16 -0.04 -0.15 -0.07 -0.008 -0.77 -0.94 -0.11(0.50) (0.47) (0.39) (0.39) (0.39) (0.37) (0.81) (0.84) (0.67)

Hour 17 -0.83 -0.88 -0.61 -0.91 -0.86 -0.88 -0.78 -0.99 -0.38(0.55) (0.58) (0.52) (0.51) (0.56) (0.59) (0.71) (1.03) (0.87)

Hour 18 -2.73*** -2.53*** -2.15*** -3.01*** -2.8*** -2.5*** -3.15** -3.3** -3.73*(0.643) (0.57) (0.57) (0.75) (0.66) (0.65) (1.01) (1.05) (1.51)

Hour 19 -2.12*** -2.16*** -1.74*** -2.04*** -2.05*** -1.88** -6.47** -6.70*** -8.23***(0.45) (0.54) (0.57) (0.43) (0.52) (0.58) (2.35) (1.89) (2.46)

Hour 20e -0.14 -0.15 -0.07 -0.16 -0.14 -0.04 -0.45 -0.33 0.05(0.12) (0.12) (0.06) (0.41) (0.22) (0.05) (1.90) (0.97) (0.22)

Hour 21 -0.07 -0.07 -0.04 -1.97* -1.97* -1.76 -26.16 -26.16 -25.94(0.09) (0.09) (0.08) (0.87) (0.87) (0.96) (18.92) (18.92) (20.63)

Hour 22e 0.07 0.08 0.09 0.18 0.19 0.19 -1.49*** -1.56** -1.53**(0.11) (0.11) (0.10) (0.12) (0.13) (0.12) (0.41) (0.49) (0.51)

Hour 23 0.8*** 0.88*** 0.88*** 2.70*** 0.19 0.19 -1.14 -1.563** -1.53**(0.23) (0.23) (0.22) (0.48) (0.13) (0.12) (4.28) (0.49) (0.51)

Robust Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1Specification M3 fits a third order polynomial for wind power penetration for the conditional meanSpecification M2 fits a second order polynomial for wind power penetration for the conditional meanSpecification M1 fits a first order polynomial for wind power penetration for the conditional meanThe conditional variance uses a first order polinomial of the wind power penetration in all specificationse : the EGARCH model has been used for this hour (δi is shown instead of λi , i=0,2)

1) σ2h,t = exp(φo +λh,2xh,t )+

m∑i=1

φh,i ·a2h,t−i +

s∑i= j

θh,i ·σ2h,t− j or

e1) ln(σ2h,t ) =αh,2 +δh,2xh,t +

s∑i=1

φh,i · g (εh,t−i )+m∑

j=1θh,i · ln(σ2

h,t− j )

where xh,t is the wind power penetration in West Denmark in hour h, σ2h,t is the conditional variance of the price,

ah,t =σh,t ·εh,t , εh,t v t − student (0,1)


3.6 Concluding remarks

In this chapter, we analyze the wind power penetration effects on the price levels and volatility in

West Denmark, using a regime switching model with observed states and non-constant variance.

We assume that wind power penetration affects electricity prices differently during congested and

non-congested periods, which has been confirmed by our results.

Our regime switching variable is defined as one when the system price on the Elspot market

differs from the area price in West Denmark. When non-congestion occurs we analyze the

response of the system price to the wind power penetration on the entire Nord Pool market, while

in the congested regime we analyze the effects of wind power penetration on Elspot area prices in

West Denmark.

We find that during non-congested periods the prices for electricity are lower and the effects

are stronger than during the congested periods (for morning and after-noon hours). We also find

that the effects differ significantly during the day, between and within each regime, with stronger

effects during peak hours, for both regimes. This leads us to the conclusion that more investments

in available capacity between the bidding areas within Nord Pool are required, in order to fully

benefit from the price reductions given by higher levels of wind power penetration in the market.

Furthermore, we find that wind power penetration has a positive effect on price volatility, for

West Denmark, during night hours and a negative effect during peak and day-time hours. Further

investigations are required to fully understand the differences observed for the volatility prices.

For example, investigating the wind power effects on price volatility in a framework where both

demand and supply are model explicitly.


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3.8 Appendix

Data description

This section of the Appendix offers a few tables with descriptive statistics of the data used in this

chapter. Table 3.4 offers information regarding the mean, standard deviation and

minimum/maximum values for the congestion variable and the Elspot area price in West

Denmark and Table 3.5 presents the descriptive statistics for wind power penetration for West

Denmark and the Elspot market. Figure 3.8 shows the daily average forecasted consumption on

the Elspot market, during the congested and non-congested period.

Table 3.4: Descriptive statistics of congestion and daily Elspot area prices for West Denmark, perhour, 2012-2015

Congestion Elspot area priceMean Std. Dev. Min. Max. Mean Std. Dev. Min Max

Hour 0 0.82 0.38 0 1 197 72 -0.2 339.6Hour 1 0.81 0.40 0 1 186 73 -7.1 330.3Hour 2 0.80 0.40 0 1 178 75 -30.1 330.3Hour 3 0.81 0.39 0 1 175 75 -12.8 335.2Hour 4 0.83 0.37 0 1 178 76 -14.1 343.3Hour 5 0.89 0.31 0 1 191 75 -7.01 349.5Hour 6 0.92 0.27 0 1 226 86 -8.8 431.1Hour 7 0.92 0.27 0 1 271 109 3.6 584.2Hour 8 0.92 0.27 0 1 291 115 44.3 671.8Hour 9 0.92 0.28 0 1 288 102 64.05 579.4

Hour 10 0.91 0.29 0 1 283 98 59.7 565.6Hour 11 0.92 0.28 0 1 278 96 69.8 559.3Hour 12 0.92 0.28 0 1 265 89 61.4 516.8Hour 13 0.92 0.28 0 1 256 89 42.9 487.5Hour 14 0.92 0.28 0 1 250 87 42 484.8Hour 15 0.92 0.26 0 1 247 85 41.5 473.8Hour 16 0.93 0.25 0 1 251 86 50.1 490.3Hour 17 0.94 0.23 0 1 277 100 61.6 616.6Hour 18 0.94 0.25 0 1 287 100 68.1 616.3Hour 19 0.93 0.25 0 1 281 93 66.9 559.5Hour 20 0.89 0.31 0 1 266 83 64.9 502.9Hour 21 0.89 0.31 0 1 252 77 63.75 446.5Hour 22 0.88 0.32 0 1 238 72 57.44 403.2Hour 23 0.88 0.32 0 1 210 70 0.6 342.2

No. obs. 1368


Table 3.5: Descriptive statistics of daily wind power penetration in West Denmark and ElspotMarket, per hour, 2012-2015

West Denmark Elspot MarketMean Std. Dev. Min Max Mean Std. Dev. Min Max

Hour 0 0.55 0.43 0 1.9 0.05 0.04 0 0.22Hour 1 0.57 0.45 0 2.0 0.05 0.04 0 0.22Hour 2 0.58 0.46 0 2.1 0.05 0.04 0 0.22Hour 3 0.58 0.46 0 2.1 0.05 0.04 0 0.22Hour 4 0.57 0.45 0 2.1 0.05 0.04 0 0.22Hour 5 0.54 0.43 0 2.0 0.05 0.04 0 0.21Hour 6 0.48 0.39 0 2.0 0.04 0.03 0 0.19Hour 7 0.42 0.35 0 1.8 0.04 0.03 0 0.18Hour 8 0.40 0.33 0 1.7 0.04 0.03 0 0.18Hour 9 0.40 0.33 0 1.6 0.04 0.03 0 0.18

Hour 10 0.40 0.33 0 1.6 0.04 0.03 0 0.18Hour 11 0.41 0.33 0 1.6 0.04 0.03 0 0.19Hour 12 0.43 0.34 0 1.6 0.04 0.03 0 0.19Hour 13 0.44 0.34 0 1.6 0.04 0.03 0 0.20Hour 14 0.45 0.35 0 1.6 0.04 0.03 0 0.21Hour 15 0.46 0.35 0 1.6 0.04 0.03 0 0.21Hour 16 0.45 0.34 0 1.5 0.04 0.03 0 0.20Hour 17 0.41 0.31 0 1.4 0.04 0.03 0 0.19Hour 18 0.41 0.31 0 1.4 0.04 0.03 0 0.18Hour 19 0.42 0.32 0 1.5 0.04 0.03 0 0.18Hour 20 0.44 0.34 0 1.6 0.04 0.03 0 0.19Hour 21 0.45 0.35 0 1.6 0.04 0.03 0 0.19Hour 22 0.48 0.38 0 1.6 0.04 0.03 0 0.19Hour 23 0.52 0.41 0 1.8 0.05 0.04 0 0.20

No. obs. 1368


Figure 3.8: Total forecasted consumption in Elspot market, during congested and non-congestedperiods, 2012-2015


The Model

This section presents the AR and GARCH specification for each hour of the day and the number of

lags for the Elspot area price, for the model presented in equation (3.2). The model specification

is shown in Table 3.6. Table 3.7 present the Akaike Information Criterion, for each hour of the day,

for different specifications of the conditional mean for the Elspot area prices.

Table 3.6: Specification for each hour of the day in West Denmark

Price lags SpecificationHour 0 1 3 AR(1 2 3)-GARCH(1 6; 1)Hour 1 1 2 AR(1)-GARCH(1 ; 1)Hour 2 1 2 AR(1)-EGARCH(1 ; 1)Hour 3 1 3 AR(1 2 )-GARCH(1 7; 1)Hour 4 1 AR(1 2 7)-GARCH(1 7; 1)Hour 5 1 to 6 8 AR(1 4 7)-GARCH(1 5 7; 1)Hour 6 1 2 6 7 10 AR(1 3 4)-GARCH(1 7; 1)Hour 7 1 AR(1 7)-GARCH(1 2 3 6 7)Hour 8 1 AR(1 2 3)-EGARCH(1 6;1)Hour 9 1 AR(1 7)-ARCH(1 2 3 5 6)Hour 10 0 AR(1 4)-ARCH(12 3 4)Hour 11 1 AR(1 )-GARCH(13 5)Hour 12 0 EGARCH(1;1)Hour 13 1 2 6 7 AR(1 4 5)-ARCH(1 2 4 5)Hour 14 1 2 6 7 AR(1 4 5)-EGARCH(1 2 4 5)Hour 15 1 7 AR(1)-ARCH(1 4 5 6)Hour 16 1 2 4 7 AR(1 )-ARCH(1 4 5 6)Hour 17 1 2 7 AR(1)-ARCH(1 4 7 8)Hour 18 0 AR(1 8)-GARCH(1 5 8)Hour 19 1 2 3 4 6 8 AR(1 7)-ARCH(1 7)Hour 20 1 2 4 AR(1 7)-EGARCH(1 ; 1)Hour 21 1 AR(1 )-GARCH(1; 1)Hour 22 1 to 5 AR(1 3 4 5)-EGARCH(1 ; 1)Hour 23 1 to 5 AR(1 2)-GARCH(1; 1)


Table 3.7: Akaike Information Criterion (AIC) for different model specifications in the conditionalmean (equation (3.2)), for wind power penetration

M3 M2 M1Hour 0 12980.28 13013.49 13250.36Hour 1 12935.53 12950.07 13000.74Hour 2 13049.95 13055.67 13119.46Hour 3 13193.01 13193.53 13249.88Hour 4 13141.97 13144.49 13193.25Hour 5 13147.79 13166.27 13176.84Hour 6 13848.48 13869.17 13988.19Hour 7 14628.28 14634.75 14653.93Hour 8 14924.84 14930.85 14983.99Hour 9 14761.99 14784.66 14827.25Hour 10 14637.02 14654.83 14697.42Hour 11 14574.44 14610.37 14656.7Hour 12 14412.77 14433.47 14458.7Hour 13 14180.94 14216.71 14229.58Hour 14 14178.91 14203.45 14212.9Hour 15 14042.3 14059.25 14064.39Hour 16 14058.74 14065.99 14083.69Hour 17 14409.27 14427.79 14481.67Hour 18 14439.18 14451.29 14556.92Hour 19 14238.68 14252.79 14359.55Hour 20 13836.78 13854.08 13917.7Hour 21 13381.52 13417.24 13444.51Hour 22 13255.63 13295.04 13302.88Hour 23 12720.63 12768.61 12798.18

M3: Third order polynmial specification for wind power penetrationM2: Second order polynmial specification for wind power penetrationM1: First order polynmial specification for wind power penetration

CH

AP

TE

R

4WIND POWER EFFECTS IN THE REAL-TIME

BALANCING MARKET

Ioana Neamtu

Aarhus University

Abstract

This chapter investigates the effects of wind power forecasting errors on the price for the

real-time balancing market. The balancing (regulating) market is a close to real-time market,

where producers and consumers bid for their willingness to increase or decrease production

or consumption in the hour of delivery, up to 45 minutes ahead of the delivery hour. Under

the assumption that more wind power penetration might increase imbalances and therefore

the the regulating prices, the effects of wind power forecasting errors are estimated for the

conditional quantiles of the regulating prices, using a regime-switching model with observed

states; each state corresponds to the state of the market. It is found that positive and negative

wind power forecasting errors have a mixed and complementary effect on the conditional

quantiles of the regulating prices, during the up and down-regulation states, depending on

the relative size between excess demand and supply.

85

CHAPTER 4. WIND POWER EFFECTS IN THE REAL-TIME BALANCING MARKET 86

4.1 Introduction

Many papers analyze the effects of wind power production on the electricity price, for the

wholesale day-ahead market, for different countries, using econometric or simulation-based

approaches (Woo et. al (2013); Ketterer(2014); Sensfuss et al.(2008); Clo et al.(2015); Sapio(2015);

Green and Vasilakos(2010)). Only a handfull of papers analyze the effect of wind power on the

entire electricity system (Albadi and Saadany (2010)), the ancillary market (Makarov et al. (2009)

and references thereon; Holttinen et al.(2011)), the balancing market (Sorknes et al. (2013)), as

well as the retail market (Lund et al. (2013)). These studies show that more wind power

penetration increases the need for reserve capacity, secondary ancillary services and regulating

power (Vandezande et al (2010)), while decreasing the wholesale electricity prices (Jonsen et al,

2010) and the retail consumer prices (Lund et al. (2013)).

To the best of our knowledge, the effects of wind power production on the price of the

regulating market have been investigated only by Sorknes et al.(2013) who show that wind farms

have the potential to decrease the price for down-regulation, when they are allowed to bid in the

regulating market.

Wind power production is very cheap1 but also volatile and difficult to predict for medium

and long-term periods, having the lowest forecast uncertainty 1 to 6 hours before the delivery

hour (Foley (2012)). Wind power forecasts rely heavily on wind-speed forecasts. In fact, 80 % of

the uncertainty of wind power forecasts is generated by the weather forecasting models

(Sorknes(2013)).

The variability of wind power production as well as the forecasting uncertainties create

technical and economic challenges for the security of supply. Therefore, the effects of wind power

production on the electricity system are of interest. These effects can be divided into short-term

effects - associated with the costs and load effects on the spot markets and long-term effects

-associated with planning and investing in the electricity system, especially during peak-hours

(Albadi and Saadany (2010)).

In this chapter, the effects of the aggregated wind power forecasting errors on the price of the

regulating market are empirically investigated for the case of West Denmark, which has a high

wind power penetration level (45%).

The regulating market (or the balancing market) is a spot market which takes place after the

closing of the day-ahead market, where the Transmission System Operator (TSO) buys the

electricity needed to keep the balance between demand and supply, during the hour of operation.

Since the regulating market is the market where excess demand or excess supply are the main

drivers of the price and considering the uncertainties surrounding wind power forecasts, it is

natural to assume that the regulating price is affected by the introduction of wind power

production, through wind power forecasting errors.

1close to zero marginal cost


To investigate the effects of the wind power forecasting errors2 on the regulating prices, a

regime-switching model with observed states is used, corresponding to the three possible states

of the regulating market, as proposed by Skytte (1999). Each hour of the day is considered as a

separate daily time series because of the differences in means and variances between the hours,

but also because the regulating price is based on the Elspot area price, which is determined

hourly (and not directly influenced by the price of the previous hour). Furthermore, the prices

and quantities for two consecutive hours on the regulating market are unknown to the bidders,

since this information is made publicly available two hours after the delivery hour, making this

information unavailable to the market participants when submitting bids for consecutive hours.

We use quantile regressions to determine the effects of positive and negative wind power

forecasting errors for the conditional distributions for up and down-regulating prices. This

technique is more robust than ordinary least squares to the presence of outliers and it allows us to

better understand the distribution of prices and to analyze the effects of wind power forecasting

errors for the extreme values of the regulating prices. We find that positive and negative wind

power forecasting errors influence differently the conditional quantiles of the distribution of the

regulating price. While positive wind power forecasting errors increase the conditional quantiles

of the up-regulating price during the night, it has no statistically significant effect for the day-time

hours analyzed. On the other hand, positive wind power forecasting errors have a negative effect

on the conditional quantiles of the down-regulating price for night time hours, but a positive

effect during the day-time hours analyzed. Similarly, an opposite effect between day-time and

night-time hours is observed for negative forecasting errors, during down-regulation periods. The

effects are contrary to the ones observed for the up-regulating state, which is to be expected,

considering the fact that down-regulation is a mirroring state for up-regulation, from the TSO’s

perspective.

A short literature review of the models used for the regulating market is offered in Section 4.2.

Section 4.3 describes the functionality of the regulating market and Section 4.4 presents the data

and the variables used. The model is detailed in Section 4.5, the results are described in Section

4.6 and concluding remarks are presented in Section 4.7.

4.2 Literature review

Skytte (1999) is the first to empirically analyze the regulating market in Norway. Since then, a few

other papers have looked at the regulating market for Nordic countries. The models proposed can

be divided into two categories -models where the state of the market is modeled explicitly

(Olsson and Soder(2008) and Jaehnert et al. (2010)), or models where the state of the market is

modeled implicitly (Boomsma et al. (2014), Ilieva and Bolksjo (2014), and Brolin and Soder

(2010)). Klaeboe et al. (2013) compare these models and conclude that models where the state of

2defined as the difference between forecasted wind power production and actual wind power production


the market is modeled explicitly perform better than models with implicit state of the market.

Nevertheless, they do conclude that forecasting models for the regulating price a day-ahead do

not perform well and that the volume and price on this market are random. They attribute this

finding to the efficient functioning of the regulating market, which has been designed to handle

unforeseen events/fluctuations.

4.3 The regulating market

In Denmark, electricity can be traded through bilateral contracts or on the Elspot day-ahead

market. Producers and consumers determine the quantity they want to sell or buy, during a

certain period of time at a certain price. The lowest trading interval for electricity is an hour.

Therefore, electricity contracts and electricity bids require the specification of the delivery time

(interval), called the delivery hour. The price and the quantity traded for each hour is agreed

upon ahead of time. Consumers and producers have the chance to adjust this quantity closer to

the delivery hour on the Elspot market, the day before the delivery hour, or on the Elbas market,

one hour before the delivery hour.

There are three situations that can occur during the delivery hour: the market is in balance

(demand and supply are in equilibrium), the market exhibits excess demand (there is a need to

increase production or reduce consumption) or the market exhibits excess supply (there is a need

to decrease production or increase consumption). The responsibility for maintaining the balance

between demand and supply during the delivery hour belongs to the TSO.

The TSO is an intermediate, state-regulated entity that determines the quantity needed to

maintain the balance between production and consumption each hour and buys this quantity

(known as regulating power) from the participants on the regulating market.

Table 4.1 summarizes the situations that can arise during the delivery hour and the type of

regulating power needed in each situation. Up-regulating power is used to reduce demand, while

down-regulating power is used to reduce supply.

Table 4.1: Summary for the use of regulating power in Denmark

Regulating power Demand SupplyUp-regulating Excess DeficitDown-regulating Deficit Excess

The regulating market, also known as the balancing market, is a spot market that opens the day

before the delivery hour and closes 45 minutes before the delivery hour. The electricity auctioned

on this market is activated in real time, within the delivery hour. The purpose of this market is to

correct for the differences that can occur between the electricity traded on the day-ahead market

and the electricity needed during the delivery hour. This is a common market for Nordic countries

(Norway, Sweden, Finland and Denmark), where participants make bids to sell electricity to their


local TSO. Each country is divided into several bidding areas, similar to the bidding areas on the

day-ahead market and each country has their own TSO.

The participants on the regulating market help the TSO maintain balance between

production and consumption and also help determine the price for imbalances. The regulating

market is a marginal-price auction where actors can participate voluntarily3 or they are required

to participate, by the TSO, based on a-priori contracts.

There are two types of bids in this market: up-regulating bids and down-regulating bids. Each

bid must specify the volume4, the price5 and the hour of operation.

The minimum bidding price for up-regulating bids is the Elspot area price during the delivery

hour. It is also the maximum bidding price for down-regulating bids. Up-regulating bids show the

price which the actors require to increase production or reduce consumption, while

down-regulating bids show the price which the actors require to reduce production or increase

consumption. The volume of regulating power is negative for down-regulating bids and positive

for up-regulating bids. The net sum of all activated bids during the delivery hour determines the

state of the market. For each hour, the market can be in one of the following states: up-regulation,

down-regulation or non-regulation. If the net sum of all activated bids is positive, the market is in

an up-regulating state. If the sum of all activated bids is negative, the market is in a

down-regulating states. If the net sum is zero, the market is in a non-regulating state.

The auctions for the up- and down-regulating power are marginal price auctions, where the

bids for both up and down regulation are sorted by price and the bids with lowest prices are

activated first. The price of the regulating market is given by the last bid activated within the

delivery hour, which corresponds to the state of market.

If in a given hour both up and down regulating bids are activated, the bids which correspond

to the state of the market receive the marginal price, while the bids which are different than the

state of the market receive a pay-as-bid price, as summarized in Table 4.2.

Table 4.2: Pricing scheme for the regulating market, by state of the market and type of regulationpower

Up regulation state Down regulation stateUp-regulating price Marginal-price Pay-as-bidDown-regulating price Pay-as-bid Marginal-price

After the delivery day, financial settlements are made for both producers and consumers under

a two price system and a one price system, respectively.

Producers are charged the regulating market price if their imbalance is in the same direction

as the local market imbalance or they are charged the Elspot area price, for imbalances in the

opposite direction to the market imbalance.

3if they are approved by the TSO4which has a minimum of 10 MW and a maximum of 50 MW5which has a maximum threshold at 37 500 DKK for up-regulating bids


Consumers are charged the regulating market price, irrespective of the direction of the

imbalance. If the market was in a no-regulation state, any imbalances are settled according to the

Elspot market price.

The two-price system is used to discourage arbitrage for producers of electricity, but as shown

by Vandezande et al. (2010), this system also can lead market participants to buy extra electricity

on the wholesale market, to hedge against up-regulating prices (higher than the system price by

design) and thus increasing the prices on the wholesale market and having negative effects on

the supply, leading to inefficiencies, in extreme cases. Nevertheless, having a one-price scheme

for consumers, as it happens in Denmark, reduces the negative effects of the two-system price.

(Vandezande (2010))

4.4 Data and variables description

The time series used for this chapter represents daily observations for the period 01.01.2012 to

31.12.2014, for each hour of the day, for West Denmark. The data is extracted from Energinet.dk

and it covers the regulating prices and the net regulating power. The area price for West Denmark,

as well as the actual and forecasted wind power production for this region are extracted from the

NordPool website. This section offers an overview of the regulating prices and quantities, state of

the regulating market and the wind power forecasting errors.

The regulating price

The price on the regulating market depends on the state of the market. If the market is in an up-

regulating state, the regulating price is the marginal price of the last activated up-regulating bid.

If the market is in a down-regulating state, the regulating price is the marginal price of the last

activated down-regulating bid. If the market is in a non-regulating state, the regulating price is the

Elspot area price.

Figure 4.1 shows the distribution of the regulating prices used in this chapter, for up and down

regulating prices, for each hour of the day. It is clear that the two states of the market have very

different distributions.


Figure 4.1: Box-plot for the regulating price in West Denmark (DKK), by hour, during up and downregulating states, 2012-2014

-1,0

00-5

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Different hours of the day have different price distributions, for each of the two states. The

different means and variances observed for each hour and for each state motivates the analysis of

each hour of the day as a separate time series.

Figure 4.2 shows the time series of daily regulating prices for up and down regulation, at 3 am

and 9 pm, to illustrate the differences between the two states of the market and between night

hours and day-time hours.

Figure 4.2: Daily variation of regulating prices, during up and down-regulating states, in WestDenmark, 2012-2014

-500

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Up-regulation Down-regulation

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01jan2012 01jan2013 01jan2014 01jan2015

Up-regulation Down-regulation

Similarly to area prices, regulating prices can be negative and exhibit seasonality. Tests for the

presence of unit-roots have been performed for the deseasonalized price series, using both the

augmented Dickey-Fuller test and the Phillips-Perron test and the null hypothesis of unit root has

been rejected6. Negative prices are common during down-regulation. They show the willingness to

6see Table 4.15 in the Appendix


pay of producers who need to stay active on the market. Producers with high start-up costs, high

ramping costs or technological restrictions7, prefer to pay to be able to produce within a given

hour.

The regulating power and the state of the market

The aggregated quantity traded on the regulating market is determined as the sum of all activated

bids on the market, during the hour of delivery, irrespective of the type of the bid. The sign of the

sum of up and down-regulating bids determines the state of the regulating market and the

regulating price. Positive regulating power indicates an up-regulating state, while a negative

aggregated regulating power indicates a down-regulating state. The state of the market

determines the price of the regulating market, as described in the previous subsection.

Figure 4.3 shows the average aggregated regulating power for up and down regulation in West

Denmark, for each hour of the day. The average up-regulating power is always higher than average

the down-regulating power, suggesting a trend for under-bidding on the Elspot market.

Figure 4.3: Average daily regulating quantities (MWh), during up and down regulating states, inWest Denmark, 2012-2014

Note: The quantity for down-regulation is presented in absolute values, for ease of comparison

To construct the state of the market variable, the area prices in West Denmark is compared to

the regulating price, as shown in equation (4.1). If the Elspot area price is lower than the

regulating price, the market area is up-regulated. Otherwise, if the Elspot area price is higher than

the regulating price, the market area is down-regulated. If the regulating price is equal to the

Elspot area price then the market is in a non-regulation state.

The state of the market variable (Sh,t ) is constructed as follows:

7Ramping costs- costs of adjusting production from one hour to the next


Sh,t =

1, pr eg .h,t > par ea,h,t (up − r eg ual t i on)

0, pr eg .h,t = par ea,h,t (no − r eg ul ati on)

−1, pr eg < par ea (down − r eg ul ati on)

(4.1)

where pr eg represents the regulating price, par ea represents the Elspot area price. h indicates

the hour of the day and t indicates the day.

Figure 4.4 shows that the predominant state of the market is the down-regulation state, for all

hours of the day, varying from 38% to 51%. The need for down-regulation is lowest during evening

and night time hours, when the need for up-regulation increases (31%), compared to day-time

hours (18%).

Figure 4.4: Average daily rate of occurrence (%) for the regulating states in West Denmark, by hour,2012-2014

Wind power forecast errors

In this chapter, wind power forecast errors are used to investigate the possible effects of wind

power production on the regulating prices. As such, wind power forecast errors are considered to

be a factor adding up to the total imbalance observed on the market. It is assumed that high

levels of wind power forecast errors will have a strong effect on the prices of the regulating

market. The hypothesis is that high levels of wind power forecasting errors lead to higher

imbalances, thus affecting the regulating price. Moreover, positive and negative forecasting errors

are expected to affect the regulating price differently, depending on the state of the market.

Wind power forecasting errors are defined in equation (4.2) as the difference between

forecasted wind power production and actual wind power production. The forecasted wind

power production is the aggregated wind production registered by Nord Pool the day before the

delivery hour, on the Elspot market. The actual wind power production is the aggregated value

recorded by the Nord Pool, the day after the delivery hour.


w h,t = f wh,t −awh,t (4.2)

where w h,t represents the wind power forecasting errors, f wh,t represents forecasted wind

power and awh,t represents the actual wind power on the regulating market; t denotes the day

and h denotes the hour of the day. Figure 4.5 describes the hourly average wind power forecasting

errors for our sample. It is interesting to notice a pattern of negative wind power forecasting errors,

on average, during night hours and early morning, and positive wind power forecasting error for

mid-day to evening hours.

Figure 4.5: Average daily wind power forecasting errors (MWh),in West Denmark, by hour, 2012-2014

To distinguish between positive and negative wind power forecasting errors, a dummy

variable has been constructed, based on the values of wind power forecasting errors, as described

in equation (4.3):

nh,t =0, i f wh,t ≥ 0

1, i f wh,t < 0(4.3)

where nh,t represents the negative forecasting errors in hour h and day t ; wh,t represents the

wind power forecasting errors at hour h and day t .

It is expected that positive forecasting errors will increase in the regulating price during the

up-regulated state, because higher positive wind power forecasting errors would add up to the

shortage of supply that already exists on the market. Similarly, negative wind power forecasting

errors will increase the price during the down-regulated state, because more available wind power

production for the regulating market would increase the need for down-regulation, thus increasing

the price. Our data8 shows that both the average up and down regulating prices are higher when

wind power forecasting errors are positive, compared to the case when wind power forecasting

errors are negative, during day and evening hours (9 to 23).

8see Figures 4.14 and 4.15 in the Appendix


Figure 4.6 illustrates the relationship between the regulating price and positive and negative

wind power forecasting errors, for both up and down regulating states, for hours 3 am and 11 am.

There seems to be asymmetric effects of positive and negative wind power forecasting errors for

the regulating price for the up- and down-regulating state.

Figure 4.6: Relationship between wind power forecasting errors and regulating price, hours 3 and11, in West Denmark, 2012-2014

-500

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-1000 -500 0 500 1000Wind power forecasting errors (MWh)

Pos Errors, up-regulation Neg Errors,up-regulation Pos Errors, down-regulation Neg Errors,down-regulation

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Pos Errors, up-regulation Neg Errors,up-regulation Pos Errors, down-regulation Neg Errors,down-regulation

Since wind power forecasting errors are defined as the difference between forecasted wind

production and the actual wind production, positive forecasting errors will lead to unexpected

shortages of production in a given day, leading to the need for more up-regulation on the market,

while negative forecasting errors will lead to an excess of supply, creating a need for more down-

regulating power, thus affecting the prices differently, for each state.

4.5 Model and estimation methods

This section describes the models used to identify the effects of wind power forecasting errors on

the regulating price and the underlying assumptions. The models described below can be used

for each hour of the day. For illustration purposes, in this chapter, the focus is only on three

representative hours of the day: hour 3, hour 9 and hour 18. The choice of these hours is not

arbitrary, but rather based on the average9 forecasted wind power penetration (defined as the

ratio between forecasted wind power production and forecasted consumption) on the Elspot

market, for West Denmark.

9The average represents the daily average is defined as the average of daily values within an hour of the day


Quantile regression

As observed from Figure 4.6, up-regulating prices increase both in size and spread, as the values of

the positive wind power forecasting errors increase. Similarly, their spread decreases as the values

for negative forecasting errors increase. This observed variability for the regulating price violates

the assumption of constant variance, which makes the inference of ordinary least square invalid.

Therefore, the quantile regression model introduced by Koenker and Bassett (1978) is considered.

Quantile regression is used to model the distribution of the dependent variable, conditional on

a set of independent variables. It models the relationship between a set of independent predictors

and specific quantiles (or percentiles) of the dependent variable and it determines changes for the

quantiles of the dependent variable, conditioned on different levels of the independent variables.

For any real-valued random variable Y , characterized by the distribution function:

F (y) = P (Y ≤ y) (4.4)

and for any τ ∈ (0,1) , the τ th quantile of Y is defined as:

QY (τ) = F−1(τ) = i n f {y : F (y) ≥ τ} (4.5)

QY (1/2) is the median of Y . The quantile function offers a complete characterization of

variable Y, just as the distribution function.

Defining the regulating prices as:pt = X >t θ+εt , a linear model for the τ th conditional quantile

of pt is then:

Qpt (τ|X t ) = X >t θ(τ)+Qε(τ|X t ) (4.6)

where pt represents the price on the regulating market, X t is the set of independent variables

described in following subsection and εt is an independent and identically distributed error term

and θ(τ) is the vector of coefficients of interest.

Under the assumption that Qε(τ|X t ) = 0 ,

Qpt (τ|X t ) = X tθ(τ). (4.7)

θ(τ) captures, among others, the effects of wind power forecasting errors at the τ-th quantile

of the conditional distribution of the regulating prices. The vector of coefficients can be estimated

by solving the following optimization problem:

minθ

∑pt>X >

t θ

τ|pt −X >t θ|+

∑pt<X >

t θ

(1−τ)|pt −X >t θ| (4.8)

The minimization problem is solved using linear programming, as suggested by Armstrong,

Frome, and Kung (1979).


Quantile regression models the relationship between wind power forecasting errors and the

prices on the regulating market at different points of the conditional distribution of the regulating

prices. It is used to model the 10th, 25th, 50th, 75th and 90th conditional quantiles of the empirical

distribution of the regulating prices, to provide an overall picture of the wind power forecasting

errors on the conditional distribution of the regulating price.

Quantile regression allows for a better understanding of the effects of the covariates on the

conditional distribution of prices but also allows for more robust estimates of the coefficients, in

the presence of outliers (Koenker(2005)).

Models for the regulating price

The effects of wind power forecasting errors on the regulating prices are investigated by extending

the model proposed by Skytte(1999). A regime switching model with observed states is used for

several quantiles of the regulating price (pr eg ). The states of the model correspond to the states of

the regulating market (defined in equation (4.1)):

Qpr eg (τ|Xh,t ) =α0h(τ)+α1h(τ) ·par ea,h,t+

+Iup−r eg (β0h(τ) ·qh,t +β1h(τ) ·par ea,h,t +β2h(τ) ·wh,t )+

+Idown−r eg (γ0h

(τ) ·qh,t +γ1h(τ) ·par ea,h,t +γ2h(τ) ·wh,t )+Qε(τ|Xh,t ) (4.9)

where Xh,t is the set of independent variables, described here: par ea,h,t is the price from the Elspot

market for West Denmark, wh,t represents wind power forecasting errors (as described in equation

(4.2) ) and qh,t represents the production imbalance. Iup−r eg and Idown−r eg are indicator functions

equaling one for up and down regulation, respectively. h shows the hour of the day and t represents

the day.

Equation (4.9) summarizes the full model used to investigate the effect of 1 MWh increase in

wind power forecasting errors for the conditional quantiles of up and down regulating prices.

Parameters β0 and γ0 measure the marginal regulating power prices per unit of regulated power,

as suggested by Skytte (1999), while parameters β1 and γ1 measure the premium for readiness to

activate on the regulating market. The parameters of interest are β2 and γ2 which measure the

effect of wind power forecasting errors for the up-regulating and the down-regulating price,

respectively.

A model with an interaction term has been used to determine the effects of positive and

negative wind power forecasting errors for the regulating price, as described in equation (4.10),

during up- and down-regulating states.


Qpr eg ,h,t (τ|Xh,t ) =α2h(τ)+α3h(τ) ·par ea,h,t+

+Iup−r eg (β3h(τ) ·qh,t +β4h(τ) ·par ea,h,t +β5h(τ) ·nh,t ·wt +β6h(τ) ·wh,t )+

+Idown−r eg (γ3h

(τ) ·qh,t +γ4h(τ) ·par ea,h,t +γ5h(τ) ·nh,t ·wh,t +γ6h(τ) ·wh,t )+Qε(τ|Xh,t ) (4.10)

where pr eg ,h,t represents the regulating price, par ea,h,t is the Elspot area price for West

Denmark, nh,t ·wh,t represents a interaction variable between a dummy variable accounting for

negative forecasting errors (nh,t ) (as defined in equation equation (4.3)) and the wind power

forecasting error variable (wh,t ), while Iup−r eg and Idown−r eg are indicator functions accounting

for the state of the market and qh,t represents the regulating power on the regulating market for

West Denmark. h shows the hour of the day and t represents the day, while X t summarizes all the

independent variable shown in the model.

The parameters of interest in this equation are γ6 and β6, which measure the effects of

positive wind power forecasting errors for the down-regulating and up-regulating state,

respectively and γ5 and β5, which measures the difference between positive and negative wind

power forecasting errors and allows us to test the hypothesis that positive and negative wind

power effects affect prices differently and estimate the size of this difference, for each conditional

quantile of the regulating price.

4.6 Results

In this section the results from the previous models are presented. Only hours 3, 9 and 18 have

been chosen to be analyzed in detail. Therefore, this section will be divided into three

subsections, each describing the effects of wind power forecasting errors on the prices for the

regulating market, for the hours of interest. The quantiles chosen for this analysis are the 10th,

25th, 50th, 75th and 90th. Different specifications for each of the two models presented above

have been estimated: including and excluding outliers in multivariate settings10, including lagged

values of the regulating price during the up and down-regulating states, respectively and

including the contemporaneous value of the previous hours, for up and down-regulating states.

The coefficients of interest have not changed significantly across these specifications11. To

account for the heterogeneity of the error term, robust-standard errors have been calculated,

using the algorithm implemented by Machado et. al. (2015), where the robust covariance matrix

is computed following Chamberlain (1994), Angrist et al. (2006), and Powell (1984). The

10using the BACON algorithm, based on the Mahalanobis distance (as suggested by the Billor, Hadi, and Velleman(2000))

11See Tables 4.17, 4.19 and 4.21 in the Appendix


heteroskedastic-robust errors are lower than the standard errors, which improved the

significance of most wind power forecasting error coefficients. Each of the following subsections

presents a short description of each hour of interest, the reason why they were chosen and the

results of the models described in equations (4.9) and (4.10).

Hour 3

In West Denmark, hour 3 is characterized by the highest average forecasted wind power

penetration, with the lowest average forecasted wind power production and lowest forecasted

consumption. It also has the lowest average price on the Elspot market and the lowest average up

and down-regulating prices. These values can be observed in Table 4.3. Moreover, for hour 3, the

market is more likely to be in a down-regulating state, 37% as opposed to 33%, and it is more

likely to exhibit positive forecasting errors (56%), as opposed to negative errors (44%). As such, on

average, the values of positive wind power forecasting errors is higher than the negative wind

power forecasting errors, in absolute values.

Table 4.3: Descriptive statistics of important variables, hour 3, West Denmark, 2012-2014

Obs. Mean Std. Dev. Min. Max.Forecasted wind power penetration 1095 0.58 0.46 0.02 2.11Forcasted consumption 1095 1686.81 169.25 1210 2315Forecasted wind production 1095 986.30 792.06 23 3472Elspot area price 1095 171.97 95.92 -1491.92 372.18Up-regulating price 1095 207.70 95.02 -1492.14 800.01Down-regulating price 1095 163.75 108.67 -1503.11 372.18Regulating quantity 1095 15.20 96.23 -477.5 545.3Wind power forecasting errors 1095 28.54 182.03 -737 1286Positive Wind power forecasting errors 1095 77.63 131.64 0 1286Negative Wind power forecasting errors 1095 -49.1 90.42 -737 0Up-regulating state, percentage 1095 0.33 0.47 0 1Down-regulating state, percentage 1095 0.37 0.48 0 1Positive forecasting errors, percentage 1095 0.56 0.5 0 1Negative forecasting errors, percentage 1095 0.44 0.5 0 1

The effects of the wind power forecasting errors for the up and down regulating prices (as

described in equation (4.9)) are presented in Table 4.4. The OLS results (with robust errors) are

also included, to show the difference in methods.

As expected, during the non-regulation state, the coefficient for the Elspot area price, is one,

for each conditional quantile of the distribution of the regulating prices. The Elspot area price has

a positive effect on the regulating price, for each quantile, during the up-regulating state. It has a

higher impact at higher conditional quantiles of the regulating prices than at lower quantiles. For

the lowest quantile (Q(10)), the Elspot area price has no effect. During the down-regulating state,

the Elspot area price has a negative effect on the conditional quantiles of the regulating price. The

effects of the Elspot area price are higher, in absolute value, for lower quantiles of the conditional

distribution than for the higher quantiles. These effects are to be interpreted as a premium for

readiness for the actors on the regulating market.


Table 4.4: Coefficient estimates for equation (4.9), hour 3, West Denmark, 2012-2014

OLS Q(10) Q(25) Q(50) Q(75) Q(90)No-regulationElspot area price (α1) 0.936*** 1.000*** 1.000*** 1.000*** 1.000*** 0.706***

(0.04) (0.01) (0.00) (0.00) (0.00) (0.07)Up-regulationRegulating quantity (β0) 0.404*** 0.0965*** 0.128*** 0.232** 0.503*** 0.547***

(0.05) (0.02) (0.02) (0.07) (0.06) (0.11)Elspot area price (β1) -0.0504 0.00641 0.0420*** 0.0620** 0.0966*** 0.120***

(0.04) (0.01) (0.01) (0.02) (0.03) (0.02)WPFE (β2) 0.175*** 0.0260* 0.0479*** 0.0770** 0.118*** 0.132***

(0.04) (0.01) (0.01) (0.03) (0.03) (0.03)Down-regulationRegulating quantity (γ0) 0.512*** 1.238*** 0.666*** 0.224*** 0.156*** 0.164***

(0.12) (0.31) (0.16) (0.03) (0.02) (0.02)Elspot area price (γ1) -0.147*** -0.337*** -0.227*** -0.147*** -0.1000*** -0.0716***

(0.02) (0.03) (0.03) (0.01) (0.01) (0.01)WPFE (γ2) 0.00621 0.00118 0.00748 0.00929 0.0193** 0.0121

(0.02) (0.02) (0.03) (0.01) (0.01) (0.02)N 1095 1095 1095 1095 1095 1095R-sq 0.755 0.623 0.703 0.708 0.714 0.687Robust errors in parentheses; * p<0.05, ** p<0.01, *** p<0.001WPFE: Wind Power Forecasting Errors

The observed negative effect of the Elspot area price on the down-regulating price is due to the

nature of the down-regulating market, where the maximum regulating price is actually the Elspot

area price and the auction quantity is negative, as opposed to the case on the up-regulating market,

where the Elspot area price is the minimum allowed price and the auction quantity is positive.

In the up-regulating state, the regulating quantity has a positive effect for the regulating price,

for each conditional quantile of the distribution. The regulating quantity has a much lower

impact at lower conditional quantiles than at higher conditional quantiles of the regulating price

distribution. In the down-regulating state, the regulating quantity has positive effect on the

conditional quantiles of the distribution of the regulating prices, but the effect is higher for the

lower conditional quantiles than higher conditional quantiles, where the effects are lower. For

both states, the marginal price of an extra unit of regulating power is positive and it is statistically

different across the conditional quantiles of the distribution, for each state, respectively.

Also, we observe that wind power forecasting errors (WPFE) increase the up-regulating prices,

for each of the conditional quantiles of the distribution. Similarly to the regulating quantity, the

impact of the wind power forecasting errors is lower for the lower conditional quantiles of the

distribution of the regulating prices than at higher conditional quantiles. The wind power

forecasting errors seem to have a positive, but statistically insignificant effect on the conditional

quantiles of the distribution of the down-regulating prices.

In the following, we distinguish between positive and negative wind power forecasting errors.

Positive wind power forecasting errors are indicative of a shortage of wind power in the regulating

market (actual wind production< forecasted wind power production) and negative wind power

forecasting errors are indicative of an extra supply of wind power production in the system (actual

wind production>forecasted wind power production). Therefore, Table 4.5 shows the results for a

model where the effects of positive and negative wind power forecasting errors are investigated


separately, as proposed in equation (4.10)12.

Table 4.5: Effects of positive versus negative wind power forecasting errors (WPFE), during up- anddown-regulation, hour 3, West Denmark, 2012-2014

OLS Q(10) Q(25) Q(50) Q(75) Q(90)Up-regulationPositive WPFE (β6) 0.29*** 0.065** 0.088*** 0.16*** 0.35*** 0.7***

(0.06) (0.02) (0.02) (0.04) (0.05) (0.11)Diff. bet. neg. and pos. WPFE (β5) -0.45*** -0.12** -0.12*** -0.23*** -0.49*** -0.97***

(0.09) (0.04) (0.04) (0.05) (0.08) (0.14)Down-regulationPositive WPFE (γ6) -0.13** -0.1** -0.13** -0.09* -0.01 0.001

(0.04) (0.03) (0.04) (0.04) (0.03) (0.01)Diff. bet. neg. and pos. WPFE (γ5) 0.25*** 0.17** 0.27*** 0.15** 0.05 0.03

(0.05) (0.06) (0.06) (0.05) (0.03) (0.02)N 1095 1095 1095 1095 1095 1095R-sq 0.78 0.65 0.72 0.74 0.75 0.67Robust errors in parentheses; * p<0.05, ** p<0.01, *** p<0.001Coefficients estimates for equation (4.10)

The results show that, during the up-regulating state, positive wind power forecasting errors

impact the regulating price stronger for the higher conditional quantiles than the lower

conditional quantiles of the distribution of the regulating price. On the one hand, positive wind

power forecasting errors translate into a deficit in wind power production and having an extra

MWh of wind power deficit increases the up-regulating price unequally across the conditional

distribution, having a stronger effect for the higher quantiles of the conditional distribution. On

the other hand, negative wind power forecasting errors translate into a surplus of wind power

production, therefore contributing to a decrease in the demand deficit and, as such, decreasing

the regulating price, during the up-regulating state. The difference between the effects of positive

and negative wind power forecasting errors is negative and it is stronger for the higher

conditional quantiles of the distribution of the regulating prices than lower conditional quantiles.

As expected, the opposite effects are observed for the down-regulating state. Figure 4.7 shows the

fit of the regression lines for positive and negative wind power forecasting errors, holding all other

covariates fixed at their mean values, for the up-regulating and down-regulating state.

Misspesification tests indicate that the model can be improved for the lower quantiles and show

no problems for quantiles higher than the median. This can also be observed in Figure 4.7, where

in the down-regulating state, there is a slight crossing of the lower quantiles.

12The results of the full model can be found in Table 4.16 in the Appendix


Figure 4.7: Quantile regression, model fit, equation (4.10), hour 3, West Denmark, 2012-2014

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Linear fit of the wind power forecasting errors; all other covariates are held constant, at their averagevalues

Hour 9

In West Denmark, hour 9 is characterized by the minimum average forecasted wind power

penetration, with maximum average forecasted consumption and high average forecasted wind

power production. Moreover, it exhibits the second largest average price for the Elspot market.

The behavior of the Elspot area price is also observed for the up and down regulating price, for

this hour. These values can be observed in Table 4.6. In hour 9 the market is more likely to be in a

down-regulating state (47%) as opposed to the up-regulating state (31%), and it is more likely to

exhibit positive forecasting errors (56%), as opposed to negative errors (43%). As such, on

average, the values of positive wind power forecasting errors is higher than the negative wind

power forecasting error, in absolute values.


Obs Mean Std. Dev. Min MaxForecasted wind power penetration 1095 0.40 0.33 0.01 1.59Forcasted consumption 1095 2636.99 413.36 1636 3614Forecasted wind production 1095 1036.92 835.78 18 3412Elspot area price 1095 299.84 410.00 0.52 14910.8Up-regulating price 1095 361.59 485.48 61.08 14910.8Down-regulating price 1095 266.13 97.79 -199.98 854.86Regulating quantity 1095 -4.58 94.70 -501.4 505.6Wind power forecasting errors 1095 21.19 201.46 -794 1483Positive Wind power forecasting errors 1095 83.81 132.84 0 1483Negative Wind power forecasting errors 1095 -62.62 111.51 -794 0Up-regulating state, percentage 1095 0.31 0.46 0 1Down-regulating state, percentage 1095 0.47 0.50 0 1Positive forecasting errors, percentage 1095 0.56 0.50 0 1Negative forecasting errors, percentage 1095 0.43 0.50 0 1

Table 4.7 presents the results for the model described in equation (4.9), for hour 9. As for hour

3, in the non-regulating state, the only effect observed is that the regulating price is equivalent to

the Elspot area price, for each conditional quantile of the distribution of the regulating price.


Statistically, these values do not differ from 1. In the up-regulating state, on the other hand, the

marginal regulating power prices per unit of regulated power is positive and it is larger for the

upper conditional quantiles of the regulating price than for the lower quantiles, for which it is

actually statistically insignificant. There is also a positive marginal regulating price per unit of

regulating power for the higher conditional quantiles of the down-regulating price, similarly to

the night time hour.



(0.04) (0.05) (0.24) (0.17) (0.02) (0.01)Up-regulationRegulating quantity (β0) 1.257*** 0.029 0.09 0.7*** 1.85** 3.2***

(0.36) (0.04) (0.10) (0.14) (0.58) (0.10)Elspot area price (β1) 0.16** 0.074*** 0.087 0.078** 0.13*** 0.17**

(0.06) (0.01) (0.05) (0.03) (0.03) (0.06)WPFE (β2) 0.026 0.007 -0.004 0.016 0.033 0.026

(0.07) (0.01) (0.02) (0.04) (0.09) (0.09)Down-regulationRegulating quantity (γ0) -0.0984 -0.238 0.108 0.186* 0.162*** 0.159***


(0.03) (0.05) (0.07) (0.05) (0.02) (0.01)WPFE (γ2) 0.032* 0.052 0.024 0.008 0.005 0.001


The premium for readiness in the up-regulating state is positive and it is higher for the higher

conditional quantiles of the regulating price than the lower conditional quantiles. During

down-regulation, the premium for readiness is also observed, and, since the regulating price for

down regulation is actually the opposite of the up-regulating price (having the Elspot area price

as a maximum value, as opposed to the minimum value for the up-regulation) the mirrored

results observed, when compared to the up-regulation state, are the expected ones. The wind

power forecasting errors have no significant effects during the up or down-regulating states.

Nonetheless, separating them into positive and negative wind power forecasting errors offers a

different picture, as shown in Table 4.813.

During the up-regulating state, positive wind power forecasting errors have no statistical

significant effect on the regulating price, except for the last conditional quantile (Q(90)), where it

reduces. Moreover, the negative wind power effects do not seem to reduce the conditional

quantile significantly, compared to the positive forecasting errors. This indicates that, during pick

hours (such as hour 9 where consumption is, on average, very high compared to other hours of

the day), the effects of wind power forecasting errors on the conditional quantiles of the

up-regulating price distribution are negligible.

13The full estimates are reported in Table 4.18, in the Appendix.


Table 4.8: Effects of positive versus negative wind power forecasting errors (WPFE), during up- anddown-regulation, hour 9, West Denmark, 2012-2014

OLS Q(10) Q(25) Q(50) Q(75) Q(90)Up-regulationPositive WPFE (β6) -0.17 -0.01 -0.03 -0.05 -0.01 -0.051***

(0.09) (0.01) (0.04) (0.04) (0.05) (0.01)Diff. bet. neg. and pos. WPFE (β5) 0.710*** 0.04 0.10 0.210* 0.11 0.192*

(0.14) (0.03) (0.10) (0.09) (0.09) (0.08)Down-regulationPositive WPFE (γ6) 0.197*** 0.313*** 0.143*** 0.0817*** 0.03 0.02

(0.04) (0.04) (0.02) (0.02) (0.02) (0.02)Diff. bet. neg and pos. WPFE (γ5) -0.311*** -0.572*** -0.236*** -0.144*** -0.0688* -0.04

(0.07) (0.06) (0.06) (0.03) (0.03) (0.03)N 1095 1095 1095 1095 1095 1095R-sq 0.52 0.36 0.11 0.09 0.11 0.15Robust errors in parentheses; * p<0.05, ** p<0.01, *** p<0.001Coefficient estimates for equation (4.10)

On the other hand, during the down-regulating state, positive wind power forecasting errors

have a positive effect on the lower conditional quantiles and the median, showing that having an

unforecastable aggregated deficit14 in wind power production , increases the regulating prices.

This effect is stronger for the lower conditional quantiles than for higher quantiles. Similarly,

negative wind power forecasting errors reduce regulating prices and the difference between

positive and negative forecasting errors are statistically significant. Graphically, the results are

illustrated in Figure 4.8, which shows the linear fit between the regulating price and the wind

power forecasting errors, using the model described in equation (4.10), where all other covariates

are held constant, at their average values.


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14forecasted wind production> actual wind power production


Hour 18

Hour 18, in West Denmark distinguishes itself from the other two hours of the day by having, on

average, higher volumes of negative wind power forecasting errors, in absolute values, than

positive forecasting errors, as well as a higher percentage of negative forecasting errors compared

to positive wind power forecasting errors. This leads to a negative average of wind power

forecasting errors, as described in Table 4.9. It is also the lowest average value from all the hours

of the day (as it is described also in Figure 4.5). This hour is representative for hours 11-19, which

exhibit average negative wind power forecasting errors. It also has one of the highest average

Elspot area price and one of the lowest average forecasted wind power penetration levels, given

by a very high average forecasted consumption and low average forecasted wind power

production.


Obs Mean Std. Dev. Min MaxForecasted wind power penetration 1095 0.41 0.31 0.01 1.40Forcasted consumption 1095 2612 370 1719 3589Forecasted wind production 1095 1067 823 30 3410Elspot area price 1095 290 117 44 1561Up-regulating price 1095 350 183 64 1775Down-regulating price 1095 277 103 -50 1263Regulating quantity 1095 9 95 -305 504Wind power forecasting errors 1095 -28 219 -872 818Positive Wind power forecasting errors 1095 67 124 0 818Negative Wind power forecasting errors 1095 -95 141 -872 0Up-regulating state, percentage 1095 0.35 0.48 0 1Down-regulating state, percentage 1095 0.41 0.49 0 1Positive forecasting errors, percentage 1095 0.45 0.50 0 1Negative forecasting errors, percentage 1095 0.55 0.50 0 1

Table 4.10 presents the results of the model in equation (4.9). As expected, in the

non-regulating state, the Elspot area price accounts for the value of the regulating price, the same

as for the other hours presented before. Similar to hour 9, in hour 18, Elspot area price and

quantity have the expected signs over the conditional quantiles of the price distribution for both

up and down-regulating prices. The effects of wind power forecasting errors are statistically

insignificant.




(0.07) (0.01) (0.01) (0.01) (0.01) (0.01)Up-regulationRegulating quantity (β0) 0.873*** 0.0700** 0.132*** 0.451*** 1.002*** 2.228***

(0.17) (0.02) (0.03) (0.11) (0.09) (0.08)Elspot area price (β1) 0.150*** 0.0143 0.0468*** 0.0884*** 0.177*** 0.204***

(0.04) (0.01) (0.01) (0.02) (0.02) (0.05)WPFE (β2) -0.00203 0.0118 0.0145 0.0081 0.02 0.0299

(0.04) (0.01) (0.01) (0.01) (0.03) (0.07)Down-regulationRegulating quantity (γ0) 0.106* 0.108 0.161*** 0.186*** 0.197*** 0.172***


(0.03) (0.04) (0.03) (0.01) (0.01) (0.01)WPFE (γ2) -0.014 -0.015 -0.031 0.0008 -0.001 -0.001


Table 4.11 presents the effects of positive and negative wind power forecasting errors, for the

regulating price, as described in equation (4.10)15.

Interestingly enough, in hour 18, the effects of positive and negative wind power forecasting

errors are consistent with the results found for hour 9, for the up-regulating state and the down-

regulating state, but in opposition with the results of hour 3, for both up and down-regulating

states.

During the up-regulating state, positive wind power forecasting errors have a statistically

insignificant effect on the conditional quantiles of the regulating price distribution. The

difference between positive and negative effects of wind power forecasting errors is also

statistically insignificant for the investigated conditional quantiles, with the exception of the 10th

quantile.

Table 4.11: Effects of positive versus negative wind power forecasting errors (WPFE), during upand down-regulation, hour 18, West Denmark, 2012-2014

OLS Q(10) Q(25) Q(50) Q(75) Q(90)Up-regulationPositive WPFE (β6) -0.1 0.024* 0.02 -0.01 -0.01 -0.02

(0.07) (0.01) (0.01) (0.05) (0.08) (0.04)Diff. bet. neg. and pos. WPFE (β5) 0.3** -0.039* -0.02 0.03 0.06 0.05

(0.11) (0.02) (0.02) (0.07) (0.10) (0.06)Down-regulationPositive WPFE (γ6) 0.17*** 0.21*** 0.14*** 0.061*** 0.059*** 0.038***

(0.04) (0.03) (0.02) (0.02) (0.01) (0.01)Diff. bet. neg. and pos. WPFE (γ5) -0.25*** -0.32*** -0.21*** -0.09*** -0.08*** -0.05***

(0.06) (0.04) (0.04) (0.02) (0.01) (0.01)N 1095 1095 1095 1095 1095 1095R-sq 0.68 0.56 0.58 0.62 0.65 0.59Robust errors in parentheses; * p<0.05, ** p<0.01, *** p<0.001Coefficient estimates for equation (4.10)

15The coefficients for the full models can be found in Table 4.20 in the Appendix.


During down-regulation, the price for regulation increases for each conditional quantile of

the distribution, due to the increase of positive wind power forecasting errors. Moreover, the

conditional quantiles of prices for down-regulation decrease if the aggregated volume of negative

wind power forecasting errors increases. The effects between positive and negative aggregated

wind power forecasting errors are statistically different. This effect is also observed for hour 9.

Figure 4.9 presents the model fit for the results presented in Table 4.11, where the other covariates

have been set to their average values. The fit for the up-regulating state could be improved,

although from the different specifications tested, the fit did not improve considerably. On the

other hand, the model fit for the down-regulating state is much better.


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ice

in h

our

18 (

DK

K)

-600 -400 -200 0 200 400Wind power forecasting errors, down-regulation (MWh)



The model presented above assumes that the wind power forecasting errors are not large

enough to determine the state of the market, which is determined by exogenous factors such as

production malfunctions, bidding strategies, wrong consumption forecasts,etc. As such, we

investigate the effects of an extra MWh of wind power forecasting errors into the system which is

already in one of the two state - up-regulation or down-regulation.

As shown in Figure 4.10, depending on the movement of demand and supply curve, the change

of the regulating price will depend on the size of the change in demand, relative to the change in

supply. The expected demand and supply curves (D0, S0) meet at point O(p0,Q0).

There are two cases presented here - when demand is below expectation (D1), which is the

case of down-regulation and when the demand is higher than expected (D2), corresponding to the

up-regulation state.

In the first case, when the demand line shifts to the left, the supply can be either below

expectation (S1 or S2) or above expectation (S3 or S4). If demand is below expectation and supply

is above expectation, the new price will always be lower than the expected price ( the region

below p0).

If the supply is also below expectations (the forecasted production is higher than actual

production - positive wind power forecasting errors), the change in price can vary, making it


possible to have an increase in price (point A) or a decrease in price (point B).

Similarly, in the second case, when demand is above expectation, shifting to the right (D2), if

the supply is below expectation, the change in price will be positive (the region above p0), while

in the case of higher demand and higher supply, the change in price depends on the shifts of the

demand and supply curves. As illustrated in Figure 4.10, the price can be above the original price

(point C) or below it (point D).

Figure 4.10: The wind power forecasting error effects on the regulating price, during up and down-regulation, when demand (D) or supply (S) shifts up or down

This is also the behavior observed for the hours investigated here. During down-regulation,

positive wind power forecasting errors lead to an increase in the regulating price for day-time

hours 9 and 18, while leading to a decrease in the regulating price during hour 3. Similarly,

negative wind power effects reduce the regulating price during day-time hours. At the same time,

the negative wind power forecasting errors represent an excess in supply, which, if added to the

supply excess already existing on the market, would increase the regulating price, as the model

suggests.

4.7 Concluding remarks

The introduction of wind power production into the Danish electricity market has challenged the

functionality of the system which was designed to support less variable production sources, such

as coal and gas plants. Nonetheless, the existence of spot markets, such as the day-ahead market

and the regulating market made the integration of wind power production into the system feasible.

In this chapter, the economic effects of wind power integration for the regulating market have

been investigated, under the assumption that more wind power production might lead to higher


wind power forecasting errors which would increase the need for regulation and therefore, the

price. A variable for wind power forecasting errors has been constructed, as the difference between

the aggregated forecasted wind power production (from Elspot market) and the aggregated actual

wind power production, observed the day of delivery. Moreover, wind power forecasting errors

have been separated into positive and negative errors, because positive wind power forecasting

errors generates a shortage of supply, while negative wind power forecasting errors generates a

surplus in demand. Depending on the overall state of the market - having a excess demand or

excess supply, the effects of these errors differ significantly.

Using a quantile regression framework, it has been found that the effects of wind power

forecasting errors on the conditional distribution of regulating prices are opposed, during

day-time hours and night time hours. They depend on the relative size of the excess or shortage of

demand to the shortage or excess of supply and on the type of the wind power forecasting errors.

Positive wind power forecasting errors reduce the conditional quantiles of the down-regulating

price distribution during night-time hours, while they increase the conditional quantiles of the

down-regulating price distribution for day-time hours. Positive wind power forecasting errors also

increase the conditional quantiles of the up-regulating price distribution during night-time hours.

Negative wind-power forecasting errors increase the conditional quantiles of down-regulating

price distribution for night-time hours, while decreasing the conditional quantiles of the

up-regulating price distribution for night-time hours and the conditional quantiles of the

down-regulating price distribution for day-time hours.

This chapter sheds some light on the question of wind power effects on the regulating market,

through the investigation of the effects of wind power forecasting errors on the conditional

distribution on regulating prices, for up and down regulating states and proves that positive and

negative wind power forecasting errors have different and opposite effects for day-time and

night-time hours. It also shows the importance of analyzing each hour of the day as a different

time-series and it shows that, although opposite effects do occur due to the difference in the

structure of supply and demand during day and night time hours, the premium for readiness

does exist for both day and night hours and that the marginal price for the regulating quantity per

unit of regulating power is different for up and down-regulating state and it varies across the

hours of the day.

Although some effects of wind power forecasting errors can be observed, these are not

substantial, suggesting that the existing structure of the electricity markets in Denmark is very

good at handling high levels of wind power integration.


4.8 Bibliography

Albadi, M. and E. El-Saadany (2010). Overview of wind power intermittency impacts on power

systems. Electric Power Systems Research 80(6), 627–632.

Armstrong, R. D., E. L. Frome, and D. Kung (1979). A revised simplex algorithm for the absolute

deviation curve fitting problem. Communications in Statistics-Simulation and Computation 8(2),

175–190.

Boomsma, T. K., N. Juul, and S.-E. Fleten (2014). Bidding in sequential electricity markets: The

Nordic case. European Journal of Operational Research 238(3), 797–809.

Brolin, M. O. and L. Soder (2010). Modeling Swedish real-time balancing power prices using

nonlinear time series models. In Probabilistic Methods Applied to Power Systems (PMAPS), 2010

IEEE 11th International Conference on, pp. 358–363. IEEE.

Clò, S., A. Cataldi, and P. Zoppoli (2015). The merit-order effect in the Italian power market: The

impact of solar and wind generation on national wholesale electricity prices. Energy Policy 77,

79–88.

Foley, A. M., P. G. Leahy, A. Marvuglia, and E. J. McKeogh (2012). Current methods and advances

in forecasting of wind power generation. Renewable Energy 37(1), 1 – 8.

Green, R. and N. Vasilakos (2010). Market behaviour with large amounts of intermittent

generation. Energy Policy 38(7), 3211–3220.

Holttinen, H., P. Meibom, A. Orths, B. Lange, M. O’Malley, J. O. Tande, A. Estanqueiro, E. Gomez,

L. Söder, G. Strbac, et al. (2011). Impacts of large amounts of wind power on design and operation

of power systems, results of IEA collaboration. Wind Energy 14(2), 179–192.

Ilieva, I. and T. F. Bolkesjo (2014). An econometric analysis of the regulation power market at the

Nordic power exchange. Energy Procedia 58, 58–64.



Ketterer, J. C. (2014). The impact of wind power generation on the electricity price in Germany.

Energy Economics 44, 270–280.

Klaeboe, G., A. L. Eriksrud, and S.-E. Fleten (2013, October). Benchmarking time series based

forecasting models for electricity balancing market prices. Working Papers 2013-006, The George

Washington University, Department of Economics, Research Program on Forecasting.

Koenker, R. (2005). Quantile regression. Number 38. Cambridge university press.


Koenker, R. and G. Bassett Jr (1978). Regression quantiles. Econometrica: journal of the

Econometric Society, 33–50.

Lund, H., F. Hvelplund, P. A. Østergaard, B. Möller, B. V. Mathiesen, P. Karnøe, A. N. Andersen, P. E.

Morthorst, K. Karlsson, M. Münster, et al. (2013). System and market integration of wind power

in Denmark. Energy Strategy Reviews 1(3), 143–156.

Makarov, Y. V., C. Loutan, J. Ma, and P. De Mello (2009). Operational impacts of wind generation

on California power systems. Power Systems, IEEE Transactions on 24(2), 1039–1050.

Sapio, A. (2015). The Impact of Renewables on Electricity Prices and Congestion in a Regime

Switching Model: Evidence from the Italian Grid. In Stochastic Models, Statistics and Their

Applications, pp. 441–451. Springer.

Sensfuss, F., M. Ragwitz, and M. Genoese (2008). The merit-order effect: A detailed analysis of

the price effect of renewable electricity generation on spot market prices in Germany. Energy

policy 36(8), 3086–3094.



Sorknæs, P., A. N. Andersen, J. Tang, and S. Strøm (2013). Market integration of wind power in

electricity system balancing. Energy Strategy Reviews 1(3), 174–180.

Vandezande, L., L. Meeus, R. Belmans, M. Saguan, and J.-M. Glachant (2010). Well-functioning

balancing markets: A prerequisite for wind power integration. Energy Policy 38(7), 3146–3154.

Woo, C.-K., J. Zarnikau, J. Kadish, I. Horowitz, J. Wang, and A. Olson (2013). The impact of wind

generation on wholesale electricity prices in the hydro-rich Pacific Northwest. Power Systems,

IEEE Transactions on 28(4), 4245–4253.


4.9 Appendix

Descriptive statistics

This section of the Appendix presents the distribution of the regulating prices, for the up and

down-regulating states, for the hours investigated in this chapter. Figure 4.11 shows the

distribution of regulating prices for hour 3, in West Denmark, Figure 4.12 presents the

distribution of the regulating price for hour 9 and Figure 4.13 shows the distribution of the

regulating prices for hour 18, in West Denmark.

Figure 4.11: Empirical distribution of daily regulating price, by state of the market, hour 3, WestDenmark, 2012-2014

0.0

02.0

04.0

06.0

08R

egul

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3(D

KK

), d

own-

regu

latio

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-600 -400 -200 0 200 400regp5

0.0

02.0

04.0

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08R

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), u

p-re

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tion

0 200 400 600 800regp5


05.

0e-0

4.0

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015

.002

.002

5R

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9 (D

KK

), u

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0 1000 2000 3000 4000regp11

0.0

02.0

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KK

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-200 0 200 400regp11



0.0

01.0

02.0

03.0

04R

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K),

up-

regu

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0 500 1000 1500 2000regp20

0.0

02.0

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08R

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dow

n-re

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tion

-100 0 100 200 300 400regp20

Figures 4.14 and 4.15 compare the average up-regulating prices and down-regulating prices,

respectively, for each hour of the day, for the case of positive and negative wind power forecasting

errors. Wind power forecasting errors are defined as the difference between forecasted wind power

production and actual wind power production, from the Elspot market. With the exception of a

few night hours (hours 00 to 06 for the down regulating state and hours 00-08), regulating price are

significantly higher when positive wind power forecasting errors are on the market, compared to

the negative wind power forecasting errors.

Figure 4.14: Average daily regulating price, by type of wind power forecasting errors, during theup-regulating state, West Denmark, 2012-2014


Figure 4.15: Average daily regulating price, by type of wind power forecasting errors, during down-regulating state, West Denmark, 2012-2014

Tables 4.13 and 4.12 present the descriptive statistics for the regulating power and regulating

prices, for each hour of the day, during the up and down-regulating state.

Tables 4.14 and 4.15 present the seasonality tests and the unit-root tests performed for each

hour of the day for the regulating prices in West Denmark.


Table 4.12: Descriptive statistics for the daily net regulating volumes, by state of the market andhour, West Denmark, 2012-2014

Down -regulation Up -regulationObs Mean Std Dev Min Max Obs Mean Std Dev Min Max

Hour 0 411 -20.0 60.7 -153.7 275.5 306 75.5 69.7 -42.8 295.9Hour 1 408 -19.9 66.7 -186.6 332.8 313 88.3 80.9 -20.9 320.2Hour 2 436 -27.6 65.0 -227.1 365.0 336 95.0 89.7 -10.5 365.9Hour 3 435 -33.2 66.9 -237.0 303.3 322 94.4 86.7 -8.4 324.2Hour 4 441 -37.8 65.0 -245.6 274.2 303 86.3 82.9 -39.7 309.8Hour 5 484 -38.5 65.4 -239.9 274.2 239 79.4 78.8 -20.6 271.8Hour 6 520 -40.1 65.7 -251.4 233.3 183 59.0 64.6 -29.3 235.0Hour 7 482 -41.4 66.5 -244.5 200.0 274 60.4 64.1 -25.6 240.6Hour 8 514 -38.1 74.3 -260.4 285.3 297 82.3 81.0 -33.6 363.1Hour 9 550 -46.2 74.6 -263.1 315.8 285 69.1 71.8 -46.8 305.9Hour 10 534 -44.2 76.5 -262.5 296.3 289 77.0 75.5 -58.8 329.8Hour 11 499 -41.8 79.6 -294.4 330.5 309 84.3 78.0 -10.8 327.9Hour 12 497 -40.3 88.5 -354.3 327.0 315 79.7 79.0 -12.9 335.6Hour 13 522 -41.8 87.5 -346.0 272.6 298 78.3 76.2 -10.2 310.3Hour 14 554 -44.6 86.3 -384.8 244.6 271 77.1 77.9 -16.8 312.9Hour 15 573 -45.2 80.4 -333.5 248.1 266 77.1 79.8 -31.4 300.0Hour 16 579 -43.1 77.9 -305.9 296.0 279 69.6 72.5 -25.2 298.8Hour 17 572 -43.4 78.0 -298.0 288.3 272 73.7 73.7 0.0 290.9Hour 18 503 -35.8 74.3 -248.0 302.6 318 83.0 77.5 -20.2 303.0Hour 19 499 -33.6 76.3 -242.5 283.6 313 80.9 74.5 -18.9 288.5Hour 20 495 -22.5 71.8 -213.3 289.7 311 70.6 73.2 -41.8 287.3Hour 21 490 -23.2 69.8 -217.5 272.4 298 70.6 68.2 -28.9 277.7Hour 22 449 -21.4 66.1 -197.1 273.3 326 73.0 74.8 -19.8 290.9Hour 23 419 -20.5 62.6 -185.8 292.1 307 77.7 82.3 -5.0 326.3


Table 4.13: Descriptive statistics for the daily regulating prices, by state of the market and hour,West Denmark, 2012-2014

Down-regulation Up-regulationVariable Obs Mean Std. Dev. Min Obs Mean Std Dev Min MaxHour 0 411 183.3 60.0 -50.0 309.4 307 252.1 53.6 50.0 425.7Hour 1 411 168.7 67.1 -74.6 321.3 313 246.9 51.6 50.0 390.5Hour 2 439 161.7 70.5 -90.0 309.4 336 242.0 48.4 52.1 372.7Hour 3 438 151.6 78.1 -268.5 321.3 321 242.7 48.3 50.0 375.4Hour 4 449 150.6 75.4 -99.0 326.2 303 245.1 51.0 40.0 375.5Hour 5 489 163.9 69.3 0.0 330.6 239 252.1 53.2 50.0 392.2Hour 6 525 186.7 72.0 -50.0 410.7 183 293.3 87.0 1.0 500.0Hour 7 486 206.3 79.9 0.0 520.9 275 400.9 174.7 84.9 1400.0Hour 8 518 223.1 73.6 20.1 555.7 297 452.9 266.5 109.3 1656.0Hour 9 553 228.3 65.7 30.0 488.7 285 407.6 182.3 111.6 1250.0Hour 10 537 232.0 63.8 20.0 458.7 288 389.6 165.0 160.0 1119.5Hour 11 503 227.5 66.2 32.0 461.7 307 398.7 191.4 178.8 1491.5Hour 12 501 217.7 70.2 0.0 462.4 312 364.1 125.7 119.0 800.0Hour 13 525 210.7 75.5 0.0 458.2 294 357.0 132.4 109.4 1000.0Hour 14 555 206.1 77.8 -100.0 394.0 268 338.7 114.6 88.1 800.0Hour 15 575 206.7 75.0 -90.0 456.4 263 337.9 108.9 88.1 744.0Hour 16 580 208.3 70.4 -50.0 416.1 277 338.4 115.4 93.7 800.0Hour 17 576 222.7 65.9 22.3 550.0 270 383.3 172.3 95.2 1400.0Hour 18 508 233.8 61.9 75.0 578.0 316 400.2 178.7 115.3 1300.0Hour 19 502 232.8 62.9 52.8 486.3 310 388.4 155.4 115.4 1001.0Hour 20 496 229.8 57.6 40.2 445.0 312 372.6 147.8 88.8 1000.0Hour 21 490 222.8 55.7 25.1 413.1 297 344.7 119.1 79.6 800.0Hour 22 452 217.0 54.5 26.4 403.8 326 327.8 115.3 78.8 800.0Hour 23 424 198.2 57.0 0.0 342.5 309 281.9 76.8 59.5 700.0


Table 4.14: Seasonality tests for the daily regulating price, per hour, West Denmark, 2012-2014

Daily effects Yearly effects Holiday effectsHour 0 F(6,331)=1.66 F(2,331)=6.35 F(1,331)=2.45

Prob>F=0.13 Prob>F=0.002 Prob>F=0.11Hour 1 F(6,324)=3.11 F(2,324)=8.65 F(1,324)=3.96





Prob>F=0 Prob>F=0.0029 Prob>F=0.00Hour 6 F(6,340)=19.47 F(2,340)=20.52 F(1,340)=22.11

Prob>F=0 Prob>F=0 Prob>F=0Hour 7 F(6,290)=42.17 F(2,290)=5.63 F(1,290)=28.92

Prob>F=0 Prob>F=0.004 Prob>F=0Hour 8 F(6,233)=34.78 F(2,233)=3.56 F(1,233)=33.9












Prob>F=0 Prob>F=0.9029 Prob>F=0.09Hour 20 F(6,244)=7.49 F(2,244)=2.68 F(1,244)=10




Prob>F=0.02 Prob>F=0.01 Prob>F=0.2646


Table 4.15: Unit-root tests for regulating prices, by hour, West Denmark, 2012-2014

KPSS :Critical values Dickey-Fuller:Critical valueCalc 10% 5% 1% Lags Calc 1% 5% 10% Lags

Hour 0 0.236 0.347 0.463 0.739 21 -2.1 -2.58 -1.947 -1.627 -7Hour 1 0.161 0.347 0.463 0.739 20 -3.123 -2.58 -1.948 -1.627 -7Hour 2 0.174 0.347 0.463 0.739 21 -2.856 -2.58 -1.947 -1.627 7Hour 3 0.209 0.347 0.463 0.739 21 -2.491 -2.58 -1.947 -1.627 6Hour 4 0.218 0.347 0.463 0.739 13 -2.969 -2.58 -1.954 -1.633 6Hour 5 0.294 0.347 0.463 0.739 21 -2.169 -2.58 -1.947 -1.627 6Hour 6 0.299 0.347 0.463 0.739 21 -1.76 -2.58 -1.947 -1.627 7Hour 7 0.125 0.347 0.463 0.739 18 -2.085 -2.58 -1.95 -1.629 7Hour 8 0.0959 0.347 0.463 0.739 21 -1.865 -2.58 -1.947 -1.627 8Hour 9 0.14 0.347 0.463 0.739 18 -4.016 -2.58 -1.95 -1.629 4Hour 10 0.0932 0.347 0.463 0.739 15 -7.281 -2.58 -1.952 -1.631 1Hour 11 0.0833 0.347 0.463 0.739 15 -7.251 -2.58 -1.952 -1.631 1Hour 12 0.113 0.347 0.463 0.739 21 -2.427 -2.58 -1.947 -1.627 7Hour 13 0.0817 0.347 0.463 0.739 18 -5.287 -2.58 -1.95 -1.629 1Hour 14 0.0745 0.347 0.463 0.739 13 -7.261 -2.58 -1.954 -1.633 1Hour 15 0.0633 0.347 0.463 0.739 7 -9.715 -2.58 -1.959 -1.638 1Hour 16 0.111 0.347 0.463 0.739 21 -4.513 -2.58 -1.947 -1.627 1Hour 17 0.0717 0.347 0.463 0.739 8 -9.593 -2.58 -1.958 -1.637 1Hour 18 0.0366 0.347 0.463 0.739 13 -6.837 -2.58 -1.954 -1.633 2Hour 19 0.0925 0.347 0.463 0.739 19 -6.38 -2.58 -1.949 -1.628 2Hour 20 0.1 0.347 0.463 0.739 18 -6.043 -2.58 -1.95 -1.629 1Hour 21 0.156 0.347 0.463 0.739 19 -4.439 -2.58 -1.949 -1.628 4Hour 22 0.14 0.347 0.463 0.739 9 -8.566 -2.58 -1.957 -1.636 1Hour 23 0.135 0.347 0.463 0.739 20 -4.251 -2.58 -1.948 -1.627 4


Results

This section of the Appendix present graphical and numerical representations of the models

described in equation (4.9) and (4.10) and the coefficient estimates, for hour 3, 9 and 18, during

the up and down-regulating states.

Tables 4.16, 4.18 and 4.20 present the coefficient results for equation (4.10), for hours 3, 9 and

18, respectively and Tables 4.17, 4.19 and 4.21 present only the coefficients of interest, for different

specifications of the model presented in equation (4.10).



(0.03) (0.01) (0.00) (0.00) (0.00) (0.01)Up-regulationRegulation Quantity (β3) 0.35*** 0.1*** 0.12*** 0.21*** 0.38*** 0.49***

(0.04) (0.02) (0.03) (0.02) (0.06) (0.04)Elspot area price (β4) -0.11* -0.02 0.02 0.03 0.01 0.04

(0.05) (0.02) (0.02) (0.02) (0.02) (0.03)WPFE (β6) 0.288*** 0.0648** 0.0869*** 0.156*** 0.345*** 0.697***

(0.06) (0.02) (0.02) (0.04) (0.05) (0.11)Diff bet pos and neg WPFE (β5) -0.45*** -0.12** -0.12*** -0.23*** -0.49*** -0.97***

(0.09) (0.04) (0.04) (0.05) (0.08) (0.14)Down-regulationRegulation Quantity (γ3) 0.481*** 1.205** 0.375*** 0.218*** 0.155*** 0.132***

(0.11) (0.38) (0.03) (0.04) (0.02) (0.02)Elspot area price (γ4) -0.09** -0.29*** -0.18*** -0.11*** -0.094*** -0.062***

(0.03) (0.04) (0.03) (0.01) (0.01) (0.01)Positive WPFE (γ6) -0.135** -0.102** -0.133** -0.0907* -0.01 0.00

(0.04) (0.03) (0.04) (0.04) (0.03) (0.01)Diff bet pos and neg WPFE (γ5) 0.254*** 0.174** 0.270*** 0.150** 0.05 0.03

(0.05) (0.06) (0.06) (0.05) (0.03) (0.02)N 1095 1095 1095 1095 1095 1095R-sq 0.78 0.65 0.72 0.74 0.75 0.67Robust errors in parentheses; * p<0.05, ** p<0.01, *** p<0.001WPFE: Wind power forecasting errors


Table 4.17: Wind power forecasting errors (WPFE) for the cond. quantiles of regulating prices,during up and down regulation, different specifications, hour 3

OLS Q(10) Q(25) Q(50) Q(75) Q(90)Up-regulation

(1) 0.288*** 0.0648** 0.0869*** 0.156*** 0.345*** 0.702***(0.06) (0.02) (0.02) (0.04) (0.05) (0.11)

(2) 0.287*** 0.0659** 0.0792*** 0.165*** 0.340*** 0.681***Positive WPFE (β6) (0.05) (0.02) (0.01) (0.05) (0.05) (0.14)

(3) 0.288*** 0.0648** 0.0869*** 0.156*** 0.345*** 0.697***(0.06) (0.02) (0.02) (0.04) (0.05) (0.11)

(4) 0.287*** 0.0659** 0.0792*** 0.165*** 0.340*** 0.663***(0.06) (0.02) (0.01) (0.05) (0.05) (0.17)

(1) -0.449*** -0.116** -0.121** -0.233*** -0.493*** -0.980***(0.09) (0.04) (0.04) (0.05) (0.08) (0.14)

(2) -0.450*** -0.117** -0.124*** -0.241*** -0.478*** -0.968***Diff bet Neg and Pos WPFE (β5) (0.09) (0.04) (0.03) (0.07) (0.10) (0.17)

(3) -0.449*** -0.116** -0.121*** -0.233*** -0.493*** -0.980***(0.09) (0.04) (0.04) (0.05) (0.08) (0.14)

(4) -0.449*** -0.117** -0.124*** -0.241*** -0.478*** -0.934***(0.09) (0.04) (0.03) (0.07) (0.10) (0.21)

Down-regulation(1) -0.134** -0.102** -0.130** -0.0906* -0.00918 0.000825

(0.04) (0.03) (0.04) (0.04) (0.03) (0.02)(2) -0.137*** -0.102** -0.133** -0.0907* -0.0092 0.00258

Positive WPFE (γ6) (0.04) (0.03) (0.04) (0.04) (0.03) (0.01)(3) -0.133** -0.102** -0.133** -0.0907* -0.0092 0.00232

(0.04) (0.03) (0.04) (0.04) (0.03) (0.01)(4) -0.133** -0.102** -0.133** -0.0907* -0.0092 -0.00731

(0.04) (0.03) (0.04) (0.04) (0.03) (0.03)

(1) 0.249*** 0.172* 0.249** 0.149** 0.0452 0.0312(0.06) (0.07) (0.08) (0.05) (0.03) (0.03)

(2) 0.259*** 0.174** 0.270*** 0.150** 0.05 0.03Diff bet Neg and Pos WPFE (γ5) (0.06) (0.06) (0.06) (0.05) (0.03) (0.02)

(3) 0.252*** 0.174** 0.270*** 0.150** 0.05 0.03(0.05) (0.06) (0.06) (0.05) (0.03) (0.02)

(4) 0.252*** 0.174** 0.270*** 0.150** 0.0453 0.0393(0.05) (0.06) (0.06) (0.05) (0.03) (0.03)

Robust standard errors in parantheses; *p<0.05, **p<0.01, ***p<0.001Spec.(1): Equation (4.10) includes lagged values of the regulating price pr egh,t−1Spec.(2): Equation (4.10) includes of the regulating price pr egh−1,tSpec.(3): Equation (4.10) includes a squared term for the regulating powerSpec.(4): Equation (4.10) includes a dummy that accounts for the outliers determined using the BACON algorithmpr eg : regulating price, h: hour of the day t




(0.04) (0.02) (0.16) (0.12) (0.02) (0.01)Up-regulationRegulation Quantity (β3) 1.361*** 0.06 0.153* 0.724*** 1.880*** 3.138***

(0.36) (0.03) (0.06) (0.11) (0.55) (0.10)Elspot area price (β4) 0.251*** 0.0615*** 0.09 0.117*** 0.146*** 0.248**

(0.06) (0.01) (0.05) (0.03) (0.04) (0.09)Positive WPFE (β6) -0.17 -0.01 -0.03 -0.05 -0.01 -0.0510***

(0.09) (0.01) (0.04) (0.04) (0.05) (0.01)Diff bet pos and neg WPFE (β5) 0.710*** 0.04 0.10 0.210* 0.11 0.192*

(0.14) (0.03) (0.10) (0.09) (0.09) (0.08)Down-regulationRegulation Quantity (γ3) -0.02 -0.08 0.14 0.188*** 0.161*** 0.150***


(0.04) (0.02) (0.04) (0.02) (0.02) (0.01)Positive WPFE (γ6) 0.197*** 0.313*** 0.143*** 0.0817*** 0.03 0.02

(0.04) (0.04) (0.02) (0.02) (0.02) (0.02)Diff bet pos and neg WPFE (γ5) -0.311*** -0.572*** -0.236*** -0.144*** -0.0688* -0.04

(0.07) (0.06) (0.06) (0.03) (0.03) (0.03)N 1095 1095 1095 1095 1095 1095R-sq 0.52 0.36 0.11 0.09 0.11 0.15Robust errors in parentheses; * p<0.05, ** p<0.01, *** p<0.001WPFE: Wind power forecasting errors


Table 4.19: Wind power forecasting errors (WPFE) for the cond. quantiles of regulating prices,during up and down regulation, different specifications, hour 9


(1) -0.167 -0.00793 -0.0278 -0.0492 -0.00575 -0.0510***(0.09) (0.01) (0.04) (0.03) (0.06) (0.01)

(2) -0.151 -0.0221 -0.0279 -0.0465 -0.0529 -0.0508**Positive WPFE (β6) (0.09) (0.02) (0.04) (0.04) (0.10) (0.02)

(3) -0.163 -0.016 -0.034 -0.0528 -0.00821 -0.0574***(0.09) (0.02) (0.05) (0.04) (0.05) (0.01)

(4) 0.287*** 0.0131 -0.00738 -0.0464 -0.0504 0.0438**(0.09) (0.01) (0.01) (0.04) (0.07) (0.01)

(1) 0.695*** 0.0278 0.088 0.207* 0.0997 0.192*(0.14) (0.03) (0.10) (0.09) (0.10) (0.08)

(2) 0.582*** 0.06 0.10 0.159* 0.17 0.11Diff bet Neg and Pos WPFE (β5) (0.16) (0.04) (0.13) (0.08) (0.16) (0.08)

(3) 0.695*** 0.06 0.10 0.216* 0.11 0.206*(0.14) (0.03) (0.13) (0.11) (0.10) (0.08)

(4) 0.695*** -0.117** -0.124*** -0.241*** -0.478*** -0.934***(0.14) (0.04) (0.03) (0.07) (0.10) (0.21)

Down-regulation(1) 0.198*** 0.302*** 0.144*** 0.0819*** 0.0348 0.0238

(0.04) (0.04) (0.02) (0.02) (0.02) (0.02)(2) 0.159*** 0.294*** 0.145*** 0.0813*** 0.0274* 0.0232

Positive WPFE (γ6) (0.03) (0.03) (0.03) (0.02) (0.01) (0.02)(3) 0.193*** 0.299*** 0.146*** 0.0800*** 0.0308 0.0274

(0.04) (0.03) (0.02) (0.02) (0.02) (0.03)(4) 0.193*** 0.145*** 0.132*** 0.0815*** 0.0315 0.023

(0.04) (0.03) (0.03) (0.02) (0.02) (0.02)

(1) -0.312*** -0.550*** -0.239*** -0.144*** -0.0705* -0.0446(0.07) (0.07) (0.06) (0.03) (0.03) (0.03)

(2) -0.253*** -0.509*** -0.239*** -0.145*** -0.0586* (0.04)Diff bet Neg and Pos WPFE (γ5) (0.05) (0.06) (0.04) (0.03) (0.03) (0.03)

(3) -0.318*** -0.524*** -0.241*** -0.142*** -0.0651* (0.04)(0.07) (0.06) (0.05) (0.03) (0.03) (0.03)

(4) -0.318*** -0.249*** -0.243*** -0.143*** -0.0656 -0.0438(0.07) (0.05) (0.04) (0.03) (0.03) (0.03)




OLS Q(10) Q(25) Q(50) Q(75) Q(90)No-regulationElspot area price (α5) 0.956*** 1.000*** 1.000*** 1.000*** 1.000*** 1***

(0.06) (0.01) (0.01) (0.01) (0.01) (0.01)Up-regulationRegulation Quantity (β3) 0.9*** 0.077*** 0.13*** 0.45*** 1.03*** 2.25***

(0.17) (0.02) (0.03) (0.14) (0.20) (0.05)Elspot area price (β4) 0.196*** 0.0001 0.04*** 0.1** 0.18*** 0.21***

(0.05) (0.01) (0.01) (0.04) (0.03) (0.05)Positive WPFE (β6) -0.10 0.0240* 0.02 -0.01 -0.01 -0.02

(0.07) (0.01) (0.01) (0.05) (0.08) (0.04)Diff bet pos and neg WPFE (β5) 0.296** -0.0393* -0.02 0.03 0.06 0.05

(0.11) (0.02) (0.02) (0.07) (0.10) (0.06)Down-regulationRegulation Quantity (γ3) 0.133** 0.08 0.170*** 0.206*** 0.175*** 0.144***


(0.04) (0.04) (0.03) (0.01) (0.01) (0.01)Positive WPFE (γ6) 0.170*** 0.2*** 0.14*** 0.06*** 0.06*** 0.04***

(0.04) (0.03) (0.02) (0.02) (0.01) (0.01)Diff bet pos and neg WPFE (γ5) -0.25*** -0.32*** -0.2*** -0.09*** -0.08*** -0.05***



Table 4.21: Effects of positive versus negative wind power forecasting errors (WPFE) for the cond.quantiles of regulating prices, during up and down regulation, different specifications, hour 18


(1) -0.102 0.0240* 0.0228 -0.015 -0.0133 -0.0199(0.07) (0.01) (0.01) (0.05) (0.08) (0.04)

(2) -0.094 0.0218* 0.0163 -0.0153 -0.0106 0.0136Positive WPFE (β6) (0.07) (0.01) (0.01) (0.02) (0.11) (0.04)

(3) -0.107 0.0240* 0.0228 -0.0134 0.00909 -0.0185(0.07) (0.01) (0.01) (0.05) (0.04) (0.04)

(4) 0.287*** 0.0218* 0.0134 -0.0193 -0.0216 0.0289(0.07) (0.01) (0.01) (0.03) (0.11) (0.07)

(1) 0.295** -0.0393* -0.0246 0.0356 0.064 0.0546(0.11) (0.02) (0.02) (0.07) (0.10) (0.06)

(2) 0.308** (0.03) (0.00) 0.05 0.08 0.12Diff bet Neg and Pos WPFE (β5) (0.11) (0.02) (0.02) (0.05) (0.13) (0.07)

(3) 0.303** -0.0393* (0.02) 0.03 0.04 0.05(0.11) (0.02) (0.02) (0.07) (0.05) (0.06)

(4) 0.303** -0.117** -0.124*** -0.241*** -0.478*** -0.934***(0.11) (0.04) (0.03) (0.07) (0.10) (0.21)

Down-regulation(1) 0.169*** 0.212*** 0.138*** 0.0612*** 0.0590*** 0.0380***

(0.04) (0.03) (0.02) (0.02) (0.01) (0.01)(2) 0.162*** 0.212*** 0.138*** 0.0612*** 0.0590*** 0.0386***

Positive WPFE (γ6) (0.04) (0.03) (0.02) (0.02) (0.01) (0.01)(3) 0.170*** 0.212*** 0.138*** 0.0612*** 0.0590*** 0.0380***

(0.04) (0.03) (0.02) (0.02) (0.01) (0.01)(4) 0.170*** 0.114 0.136*** 0.0612*** 0.0590*** 0.0380***

(0.04) (0.14) (0.02) (0.02) (0.01) (0.01)

(1) -0.250*** -0.322*** -0.198*** -0.093*** -0.079*** -0.055***(0.06) (0.05) (0.04) (0.02) (0.01) (0.01)

(2) -0.236*** -0.322*** -0.198*** -0.0935*** -0.0795*** -0.0553***Diff bet Neg and Pos WPFE (γ5) (0.05) (0.04) (0.04) (0.02) (0.01) (0.01)

(3) -0.250*** -0.322*** -0.198*** -0.0935*** -0.0795*** -0.0550***(0.06) (0.04) (0.04) (0.02) (0.01) (0.01)

(4) -0.250*** -0.182 -0.193*** -0.0935*** -0.0795*** -0.0550***(0.06) (0.16) (0.03) (0.02) (0.01) (0.01)


Figures 4.16, 4.17 and 4.18 present the linear fit of wind power forecasting errors for the

regulating prices, during up and down-regulating states, where all the other covariates of the

model in equation (4.9) have been set to their average values.


Figure 4.16: Quantile regression, model fit, equation (4.9), for hour 3, West Denmark, 2012-2014

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Figures 4.19-4.21 present the graphical representation of the coefficients for equation 4.10, for

each conditional quantile of the distribution of the regulating prices.

Results show that, during the up-regulating state, the marginal price per unit of regulating

power has a positive effect on the conditional quantiles of the reuglating price. For the lower

conditional quantiles of the regulating price, the effect is weaker than for the upper conditional

quantiles. This indicates that, in days with low electricity prices, the marginal price per unit of

regulating power is also lower than in days with high electricity prices.

In days when the regulating price is low (and the Elspot area price is low), producers with

relatively lower marginal costs are active on both markets. When high marginal cost producers

are active on the Elspot market, the regulating price is also higher and the marginal price per unit

of regulating power is higher as well. The effect of one extra unit of regulating power needed on

the market dependes on the type producers that are able to be active on the market. If

low-margnial cost producers are active, the effect of one extra unit of regulating power will be

lower than in the case when high-marginal producers are active. The same argument can be

made for the premium of readiness, received by the producers on the regulating market.

The effects of positive wind power production are also stronger for higher conditional

quantiles of the regulating price distribution, for both up and down regulating state. In days with

low electricity prices, low marginal-cost producers are active on the Elspot and the regulating

market. Therefore, the marginal cost on extra unit of regulating power needed will be lower in

low-price days than in days with very high electricity prices. Thus, the effect of an extra unit of

wind power forecasting error is lower in days with low regulating price than in days with high

electricty prices.


Figure 4.19: Coefficient estimates for equation (4.10), for hour 3, West Denmark, 2012-2014

The gray area around the coeffiecent function represent confidence intervals of the estimates, at95%.The thick dotted line represents the OLS estimates of the coefficient and thin dotted lines show theconfidence intervals for the OLS estimates, at a 95%.The overlap of the confidence intervals for OLS and Quantile regression estimates indicates that thequantile regression estimates are not statistically different than the OLS estimate.Coefficient interpretation:Elspot area price(DKK): Effect of the Elspot area price during non-regulation.Regulating quantity(MWh), during Up (Down) Reg.: Marginal price per unit of regulating power.Elspot area price(DKK), during Up (Down) Reg.: Marginal price per unit of regulating power.Pos WPFE, during Up(Down)Reg(MWh): Change in the regulating price when positive wind powerforecasting errors increase by 1 MWhNeg-Pos WPFE, during Up(Down)Reg(MWh): The difference between the change in price, given bya 1 MWh increase in negative forecasting errors and the change in price given by 1 MWh increasein positive wind power forecasting errors.







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SCHOOL OF BUSINESS AND SOCIAL SCIENCES www.econ.au.dk

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Wind power effects and price elasticity of demand for the ... · 2.1 Daily share of traded electricity on Elspot Market, as ratio of total consumption 2012-2014 26 2.2 Relationship