1 Systems Analysis Advisory Committee (SAAC) Thursday, February 27, 2003 Michael Schilmoeller John Fazio

1

Systems Analysis Advisory Committee (SAAC)

Thursday, February 27, 2003Michael Schilmoeller

John Fazio

Northwest Power Planning Council

2

Agenda

• Approval of the Feb 7 meeting minutes

• Incentives for new generation

• Detailed assumptions around renewables and distributed generation (from the December SAAC)

• More discussion of statistics


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Agenda






4

Agenda






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Incentives for New Generation

• The purpose of this discussion is....– To explore what risk-constrained least-cost

planning has to say about supply adequacy– To propose some approaches to supply

adequacy that rely on these concepts


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• The events of 2000-2001 have led many to ask whether the industry should return to planning criteria that guarantee a level of reliability

• Some believe we may return to a period of volatility, high prices and short supplies in a few years if further resource development is put on hold

Simulation Scenarios for the Western Electricity Market -A Discussion Paper for the California Energy Commission Workshop on Alternative Market Structures for California, Prof. Andrew Ford, Washington State University. Available at: http://www.wsu.edu/~forda/FordCECPaper.pdf


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Some options for addressing resource adequacy include:

Provide some form of capacity payment to provide an incentive for a greater level of investment in generation. Such a mechanism requires some entity of sufficient scope to implement the payment and recover the costs.

Empower some entity to construct resources to ensure maintenance of a particular capacity margin.


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Other options are:Establish a regulatory requirement on load serving

entities to maintain a certain capacity margin.

Do nothing and let the mechanisms for hedging the risk of volatility develop. The premiums paid for such mechanisms can support the development of resources to guarantee supply and, as a consequence, moderate volatility.


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• FERC has proposed reserve margin requirements in their Standard Market Design

• California is proposing reserve margin requirements (MD02) for load-serving entities


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Problems with centralized administration• Who makes capacity payments? To which parties?

Who pays?– Experience with capacity markets in the East has not been

encouraging

– After the unit is complete, does all of the output belong to the party constructing the unit?

– Is all capacity “equal?” Would all capacity receive the same payment?


11


Problems with centralized administration• Who would build for the PNW?

– The PNW is still paying for the WPPSS mistakes– Would put the regional authority in the role of a “super

utility”

• How would it be enforced?– Enforcing physical curtailment on a distribution utility’s

franchise customers is feasible, though absent some overarching entity like an RTO, it would be difficult; enforcing it in a retail access environment, even with an RTO would be quite difficult.


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There are also significant wealth transfer issues• If California requires in-state load-serving

entities to build reserves, they are guaranteeing lower power prices for entities outside California.

• Parties that don’t have to meet such requirements voluntarily will probably save money by not doing so


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Among the biggest difficulties with a reserve margin planning criterion is it is “yesterday’s solution” and does not address the general issue of risk.

• The 2000-2001 energy crisis was a problem primarily of over-reliance on wholesale power markets and unexpected prices in those markets. It had its roots in poor resource adequacy.

• Tomorrow’s problem may or may not be.


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An Example

A load-serving entity is required to meet a reserve margin criterion. What is the least-cost solution? A combustion turbine.

Is the load-serving entity better insulated from risk than it was before?


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An Example

Load requirement in a typical month: 752 MWa,

On-peak electricity prices average $60.00/MWh ($30-$134); off-peak average prices $55.00 ($30-$100)

Gas price, averages $4.00/MMBTU with daily prices between $1.50/MMBTU and $11/MMBTU (lognormally distributed 100% volatility)


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An Example

Combined Cycle, 8000 BTU/kWh, $100/kWyr real-levelized capital + FOM + fixed gas transportation + other fixed cost

Wind generators 3 MW, $160/kWyr real-levelized capital + FOM + other fixed

cost, 33% capacity factor.


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An Example

Least-cost hourly deterministic solution: Rely on the market ($27M)


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An Example

Least-cost probabilistic solution: 2000 trials with Crystal Ball, 57 percent uncertainty in gas and power market prices. Rely on the market, $38 M. Optimum solution: 383 MW of CCCT ($36 M)


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An Example

Least-cost probabilistic solution with risk constraint: 2000 trials with Crystal Ball , 57 percent uncertainty in gas and power market prices. Optimum solution: 500 MW of CCCT and 417 MW of wind generation -- 22 percent reserve margin ($48 M)

– CVAR of cost exceeding $ 55 M constrained to $2M


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An Example


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An Example


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An Example


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An Example

Built-in capability to examine the relationship of cost to risk


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An Example

Efficient Frontier

Relationship between risk constraint and cost


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An Example

Implications to Incentives for Generation

• Risk constraints provide more general protection– The choice of wind provides a hedge against gas

price and emission tax excursion

• Risk constraints monetize the insurance premium


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An Example

Implications to Incentives for Generation

• Issue of wealth transfer is moot– Participants are protecting their self-interests

• Drivers and home owners are required to carry insurance to protect others or society– Who is protected by “insurance” carried by a load-

serving entity? What are the externalities?


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Conclusions

• Those responsible for rate stability should use risk-constrained least-cost planning to protect their constituents

• Such analysis is feasible• Discussion should turn to the extent to which there are

externalities associated with high retail rates, such as social harm

• To the extent there are social externalities, some kind of enforcement would probably be necessary.– Insurance is expensive. There are reasons why there are laws requiring drivers to have insurance.


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Agenda






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Some Specific Renewablesand Distributed Generation Tech

• Wind

• Solar

• Microturbines

• Diesel engines

• Fuel cells


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Wind

• Wind– 20 year service life– $1030/kW all-in construction cost ($160/kWyr real

levelized)– Development: 24 months; construction 12 months– 6 month “mothball” period; indefinite self life (greater

planning flexibility)– 30% capacity factor, non-dispatchable (less operating

flexibility)– some penalty for shaping (on- vs off-peak power prices?)

Northwest Power Planning Council, New Resource Characterization for the Fifth Power Plan, Wind Power Plants, August 27, 2002


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Wind

• Wind risk attributes– Fuel price and emission tax mitigation

– Greater planning flexibility• Development and construction annual cash flow:

2%/98%

• Primary decision criteria?

• Favorable mothball characteristics, such as extended site licensing

– Higher forced outage rate


32

Solar

• Central Station Solar-Thermal– 30 year service life

– $1250/kW-$3500/kW all-in construction cost, use $2000/kW

– Development: 24 months; construction 12 months

– 6 month “mothball” period; indefinite self life (greater planning flexibility)

– 25% capacity factor, non-dispatchable (less operating flexibility)

– some penalty for shaping (on- vs off-peak power prices?)


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Solar

• Flat panel, roof-top solar– 20 year service life– $4500/kW all-in construction cost– Development and construction < 12 months– little “mothball” cost; indefinite self life– 21% capacity factor, non-dispatchable– some penalty for shaping (on- vs off-peak power

prices?)


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Solar

• Potential– Limited potential in PNW, due to reduced

insolation and mismatch with PNW loads• Insolation rate is about half that of central California,

for example

– Primary areas of application will be remote load


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Solar

• Risk attributes– Fuel price and emission tax mitigation– Greater planning flexibility

• Development and construction annual cash flow:2%/98%

• Primary decision criteria?• Favorable mothball characteristics, such as extended site licensing

– Higher forced outage rate– Located closer to thermal and power load centers


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Reciprocating Engines

• Diesel Engines– 20 year service life– $1100/kW– Development: 12 months; construction 12 months– Heat rate: 11,100 BTU/kWh– 6 month “mothball” period– 90% availability factor– Greater waste heat use potential


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Fuel Cell

• Phosphoric acid– 20 year service life– $1900/kW– Development and construction, < 12 months– Heat rate: 9,480 BTU/kWh– 90% availability factor– Greater waste heat use potential


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Microturbines

• Microturbines (100 kW) – 20 year service life– $500 to $1,400/kW– Development and construction, < 12 months– Heat rate: 14,500 – 18,000 BTU/kWh– 90% availability factor– Greater waste heat use potential


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Fueled, Distributed Generation

• Risk attributes– No fuel price and emission tax risk mitigation; probably

larger risks– Greater planning flexibility

• Development and construction annual cash flow:2%/98%

• Primary decision criteria?• Decidedly unfavorable mothballing attributes (more stringent

envrionmental controls)

– Good operating flexibility– Located closer to thermal and power load centers (less

transmission congestion risk)


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Renewables andDistributed Generation

• Conclusions– Wind and solar have similar risk mitigation

attributes and their risk-mitigation attributes can probably be assessed the same way

– Fuel-based distributed generation technologies have risk mitigation attributes distinct from those of wind and solar, but similar among themselves. Distribution technologies can also probably be assessed together.


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Agenda






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Stats – Gas and Electric Prices

• Objectives– Analytically Descriptive– Results Useful For Portfolio Modeling– Plausible Answers to Specific

Questions– Revelation


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Some Basic Concepts

• Time Series– Discrete Measurements– Indexed On The Integers– Possibly Extend – unobserved - Into

The Distant Past– Example: Henry Hub


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More Basic Concepts – HH Example

• Henry HubHt for t = 1, 2, … , 2739t = 1 for June 21, 1995t = 2739 for December 19, 2002

• Notation– t = 0 for June 20, 1995– t = -11 for June 9, 1995– t = 2900 for May 29, 2003


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Dependence

• Two random variables are independent if the likelihood of a particular value of one variable is unaffected by knowing the value of the other.

• The equivalence of correlation and dependence is not general


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Example – Bivariate Lognormal

Bivariate Lognormal Sample, Perfect DependencePearson Product-Moment Correlation = .89

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500

Associated Normal Parameters: mu = 4.5, sigma = .8

As

so

cia

ted

No

rma

l Pa

ram

ete

rs:

mu

= 5

, sig

ma

= .3

• Perfect dependence does not guarantee correlation = 1

• Be careful about correlation and dependence


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Example – N(0,1) AndAbs(N(0,1))

100 Samples From Perfectly Dependent N(0,1) and |x|Correlation In This Sample is -0.0827

0

0.5

1

1.5

2

2.5

3

-3 -2 -1 0 1 2 3

Normal (0,1)

De

pe

nd

en

t C

au

ch

y


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Gas Prices – Henry Hub And Sumas

• Daily Prices

• Weekends Spanned With Linear Interpolation


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Gas Prices ExampleHenry Hub And Sumas

Two Gas Price Series

0

5

10

15

20

25

30

35

40

45

Jun-95 Jun-96 Jun-97 Jun-98 Jun-99 Jun-00 Jun-01 Jun-02

Delivery Date

$/m

mb

tu

Henry Hub

NW Sumas


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0

1

10

100


Delivery Date

$/m

mb

tu

Henry Hub

NW Sumas


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Henry Hub

Su

mas


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Sampled Hubs

•Nine Hubs•Henry Hub

•Kern River

•Malin

•Malin 400

•Malin 401

•NOVA (AECO)

•NOVA (Field)

•Stanfield

•Sumas

•Combine to Six•Henry Hub

•Kern River

•Malin

•NOVA

•Stanfield

•Sumas


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Gas Graph – Six Hubs

0

1

10

100

Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03

Delivery Date

$/m

mb

tu

Henry HubKERN RIVER/OPAL PLANTMalinNOVANW StanfieldNW Sumas


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Bivariate Gas Graphs0

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Henry Hub

Kern

Malin

Nova

Stanfield

Sumas

Kern Malin Nova Stanfield


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Bivariate Gas Graphs Observations

• Most show decidedly “non-linear” behavior• Some non-linearity is in the form of “flanges”• Some seems “curvilinear”• A few are very linear – e.g. Stanfield vs Sumas• Some show prices usually higher for one hub• Most show distinct regions, rather than a continuous

smooth pattern• Hypothesis: discrete temporal phenomena drive the

observed patterns – probably transitory transmission constraints, dramatic temperature differences, etc.


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Focus on Sumas

• Near and dear to our hearts in the NW

• Mostly a virtual clone of Stanfield

Sumas With Centered 30-Day MA

0

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100

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95

Dec-95

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Dec-99

Jun-

00

Dec-00

Jun-

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Dec-01

Jun-

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Dec-02


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Sumas Raw Autocorrelation

• “True” autocorrelation at some lag is

E{ [ x(t)-E(x(t) ] * [ x(t-lag)-E(x(t-lag)) ] }

– We estimate this and plot as a function of lag = 1, 2, …

Raw Estimated Autocorrelation - ln(Sumas)

0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300

Lag

Au

toc

orr

ela

tio

n


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Sumas Seasonal & Trend Model• The raw Sumas autocorrelation function shows a dull

pattern common to series with trends and/or seasonal patterns

• We suspect both for the Sumas price series• Step 1: use simple stepwise linear regression to fit a

trending/monthly pattern model

Ln(Sumas) = a yt + b + Cmonth(t) + et

where yt is the number of years to the tth value in the time series since January 1, 1995; a, b are unknown constants, as are the C terms, which take on one of twelve values, depending on the month of the tth observation; et is an unknown “error” or “innovation” term, with the {ei} i.i.d.


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Sumas Seasonal & Trend Model

• The monthly terms in the model are fit in a stepwise manner

• Seven monthly terms enter the regression with strongly significant effects

• Five monthly terms are “left behind” and are estimated to be zero.


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Sumas Seasonal & Trend Model

• Estimated Parameter Values– a-hat = 0.177– b-hat = -0.053

– C12 = 0.37

– C7 = -0.26

– C1 = 0.19

– C11 = 0.14

– C8 = -0.17

– C9 = -0.15

– C6 = -0.12


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Sumas Seasonal & Trend ModelBasic De-trending And Seasonal Adjustment

ln(Sumas) and Regression Estimates

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0


Delivery Date

ln(S

um

as $

/mm

btu

)

ln(Sumas)

Estimated ln(Sumas)


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Sumas Seasonal & Trend ModelResiduals

Basic De-trending And Seasonal AdjustmentResiduals

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Jun-95 Jun-96 Jun-97 Jun-98 Jun-99 Jun-00 Jun-01 Jun-02Delivery Date

ln(S

um

as $

/mm

btu

)


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Sumas Seasonal & Trend ModelAutocorrelation for Residuals

Estimated Autocorrelation of ResidualsFrom ln(Sumas) Trend and Seasonal Model

-0.1

0.0

0.1

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0 50 100 150 200 250 300Lag

Au

toc

orr

ela

tio

n

Autocorrelations are still indicating nearly non-stationary behavior. If trending and seasonality is not present, taking first differences usually cuts through this.


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Del1

•Del1 is the first difference operator

•Del1(Xt) = Xt – Xt-1

•First differencing removes a certain kind of non-stationary behavior from a time series that is otherwise without trend or seasonality

•Backward shift operator B(Xt) = Xt-1

•As a polynomial in the backward shift operator B

Del1 (B) = 1 - B


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Sumas Seasonal & Trend ModelAutocorr. for Del1(Residuals)

With approximate .05 confidence bands (pointwise) around series

Autocor of Del1

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 20 40 60 80 100 120 140


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Sumas Seasonal & Trend ModelPartial Autocorr. for Del1(Residuals)

With approximate .05 confidence bands (pointwise) around series

Partial Autocor of Del1

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 20 40 60 80 100 120 140


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Remaining Periodicity? The Cumulative Periodogram

• Periodogram and cumulative periodogram – analogous to spectral density and cumulative spectrum in continuous context

• Cumulative periodogram at a particular frequency is sum of spectral intensity at and below that frequency

• Just sums of appropriate sines and cosines• Domain: frequencies from 1/n to ½ (1 cycle is the entire

length of the series being examined)• Range: normalized so that the periodogram (spectrum)

always integrates to 1. • White noise (i.i.d. normal series) has


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Cumulative Periodogram

• White noise (i.i.d. normal series) has a theoretical cumulative periodogram that lies exactly on the diagonal line running from (0,0) to (.5,1) on the frequency (x) axis vs. intensity (y) axis graph

• Distribution-free confidence limits (lines) can be drawn on the graph for the entire cumulative periodogram

• Based on Kolmogorov-Smirnov statistics• The cumulative periodogram of a residual series

cleanly tests for remaining periodicity indicating that a fitted model is inadequate


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Del1 Cumulative Periodogram

Cumulative Periodogram Del1

0

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0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Frequency

• Cumulative periodogram clearly wanders outside the .05 confidence limits for a white noise series

• Significant periodicity remains


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Autocorrelation and Partial Autocorrelation

• Heuristically (hand-waving), partial autocorrelation takes out the influence of lower order correlations from the calculation of each succeeding value

• Examining the sample autocorrelation and partial autocorrelation functions suggests possible forms for ARMA models

• ARMA: Autoregressive-moving average


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AR

• Autoregreesive models are in the formXt = a1Xt-1 + a2Xt-2 + … + apXt-p + et

• Autocorrelations of AR models fall off as lag increases, possibly slowly, and possibly with quasi-periodic behavior

• Partial autocorrelations typically cut off after lag p• Certain combinations of parameters in the model lead to

wildly explosive non-stationary behavior• On the boundary between stationary and non-stationary

behavior in the parameter space the time series can behave in a mildly non-stationary way


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MA

• Moving average models are in the formXt = b1et-1 + b2et-2 + … + bpet-q + et

• Partial autocorrelations of MA models fall off as lag increases, possibly slowly, and possibly with quasi-periodic behavior

• Autocorrelations of MA models cut off after lag q• MA models do not exhibit wildly explosive non-

stationary behavior• The term “moving average” is a little misleading

since the coefficients don’t have to add to 1


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ARMA

• Autoregressive - Moving average models combine the features of both AR and MA formulationsXt = a1Xt-1 + a2Xt-2 + … + apXt-p + b1et-1 + b2et-2 + … + bpet-q + et

• Autocorrelations and partial autocorrelations of ARMA models have mixed but relatively distinctive behavior that can help select the appropriate values for p and q, the AR and MA degrees, respectively


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Fitting an ARMA Model to the Del1 Series from the Sumas Model

• Autoregressive - Moving average models combine the features of both AR and MA formulationsXt = a1Xt-1 + a2Xt-2 + … + apXt-p + b1et-1 + b2et-2 + … + bpet-q + et

• Autocorrelations and partial autocorrelations of ARMA models have mixed but relatively distinctive behavior that can help select the appropriate values for p and q, the AR and MA degrees, respectively


75

Fitting an ARMA Model to the Del1 Series from the Sumas Model

• AR parameters– Lag 1 = 0.47– Lag 2 = -0.01– Lag 3 = 0.67– Lag 4 = -0.42

• MA parameters– Lag 1 = -0.33– Lag 2 = -0.09– Lag 3 = -0.63– Lag 4 = 0.24


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ARMA Residuals Autocorrelations

Autocor of ARMA Residuals

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 10 20 30 40 50 60 70 80 90 100


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ARMA Residuals Partial Autocorrelations

Partial Autocor of ARMA Residuals

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 10 20 30 40 50 60 70 80 90 100


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ARMA Residuals Cumulative Periodogram

Cumulative Periodogram Of ARMA Residuals

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Frequency


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Full Model ComparisonFull Model Comparison With Actuals

0.1

1.0

10.0

100.0


Delivery Date

ln(S

um

as $

/mm

btu

)

Sumas

Full Model Estimates


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ARMA Residuals Density

ARMA Residual Density

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

Residual

Re

lati

ve

Lik

elih

oo

d

• Symmetrical but probably not quite normal• Use this distribution to drive the ARMA process for deviations from the ln(Sumas) trended

and seasonal model


81

Next Step

• Similar trending and seasonality treatment for mid-C

• Apply same Del1 and ARMA transformation to mid-C raw residuals

• Examine cross-correlations between the (whitened) gas series and the transformed mid-C series

• Fit appropriate transfer function to the series• Correlation structure for the fitted models can inform

the portfolio model regarding series path construction


82

Next Next Step

• Examine other series• Discrete events

– Capacity shortages– Transmission constraints/congestion– Temperature/load events

• Specific questions/hypotheses


83

Agenda






84

Next Meeting

• March 20, 9:30AM, Council Offices

• Agenda

– More discussion of statistics– Results with Olivia

Documents

1 Systems Analysis Advisory Committee (SAAC) Thursday, February 27, 2003 Michael Schilmoeller John Fazio