Some IIT Operations Research Models for Electricity Markets · PDF fileSome IIT Operations Research Models for Electricity Markets ... – Equivalent quadratic problem ... Some IIT

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

Some IIT Operations Research Models for Electricity Markets

INSTITUTO DE INVESTIGACIÓN TECNOLÓGICA

Andrés Ramoshttp://www.iit.upcomillas.es/~aramos/

[email protected]

2IIT Electricity Market Models – Andrés RamosSeptember 2008

Content

� Model development at IIT• More detailed description of some specific models• Brief description of some models


History• Last 10 years (1998 begins the Spanish electricity market)• Development teams were split and isolated by confidentiality

reasons• This resulted in a rich use of OR techniques

– Mathematical programming (LP, MIP, NLP, MCP, SP, Benders decomposition, Lagrangian Relaxation)

– Simulation (Probabilistic Simulation, Business Dynamics)– Other (Fuzzy)

• “Commercial” grade models used in the Spanish or any other large-scale electric system


Electricity Produced by Company in Mainland Spain

• Source: OMEL (www.omel.es)


Electricity Distributed by Company in Mainland Spain

• Year 2006: 231461 GWh

• Source: CNE (www.cne.es)


Generation Planning Functions

Functions

Scope

Traditional operation functions

New market functions

Short termMedium termLong term

• Fuel management• Annual reservoir and seasonal pumped storage management- Water value assessment

• Investments- Installation- Repowering

• Maintenance• Energy management- Nuclear cycle- Hyperannual reservoirs

• Start-up and shut-down of thermal units

• Pumped storage operation

• Economic dispatch

• Market bids:- Energy

- Power reserve

- Other ancillary services

• Objectives:- Market share

- Price

• Budget planning • Future market bids

• Risk management • Long term contracts:

- Fuel acquisition- Electricity selling


Iberdrola Endesa Unión Fenosa Gas Natural

E.ON España (antes Viesgo) Red Eléctrica Others

Back Office Long Term Operation Planning

BEST MORSE

Market Equilibrium MOES MPO VALORE MARAPE PLAMER PREMED

Hydro Subsystem MHE

Simulador EXLA

Renewable sources MEMPHIS

Transmission Network SIMUPLUS StarNet SECA

Back Office Medium Term Operation Planning Reliability Indices FLOP

Front Office Short Term Offer Strategies and Operation Planning MAFO SGO GRIMEL

General Perspective of Electricity Market Models


Content

• Model development at IIT� More detailed description of some specific models

� MOES Stochastic� MHE� Simulador� MAFO

• Brief description of some models


Hierarchy of Operation Planning ModelsST AR T

E ND

Sto chastic M arke tEqu ilib r ium Mode lS tocha stic M arke tEq u ilib r iu m Mode l

Hyd ro the rm a lCoo rdina tion M ode l

H yd ro the rm a lC oo rdin a tion M o de l

Stochastic S im ula tion Mode l

Stoch as tic S im ulation Mod e l

M onth l y hyd ro basin and the rm a l p lant p roduction

W eekly hyd ro un it p roduction

D a il y h yd ro un it p roduction

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O ffering Strateg ies

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MOES Stochastic• Purpose

– Medium-term generation operation– Market equilibrium model– Conjectural variations approach– Implicit elasticity of residual demand function

• Main characteristics– Market equilibrium model based on the complementarity problem (MCP)

• References– J. Cabero, Á. Baíllo, S. Cerisola, M. Ventosa, A. García, F. Perán, G. Relaño, "A Medium-

Term Integrated Risk Management Model for a Hydrothermal Generation Company," IEEE Transactions on Power Systems. vol. 20, no. 3, pp. 1379-1388, August 2005

– J. Cabero, Á. Baíllo, S. Cerisola, M. Ventosa, "Application of benders decomposition to an equilibrium problem," Proceedings of the 15th PSCC, Power Systems Computing Conference. Liege, Belgium, 22-26 Agosto 2005

– M. Ventosa, A. Baíllo, A. Ramos, M. Rivier Electricity Market Modeling Trends Energy Policy Vol. 33 (7) pp. 897-913 May 2005

– A. García-Alcalde, M. Ventosa, M. Rivier, A. Ramos, G. Relaño Fitting Electricity Market Models. A Conjectural Variations Approach 14th Power Systems Computation Conference (PSCC '02) Seville, Spain June 2002

– M. Rivier, M. Ventosa, A. Ramos, F. Martínez-Córcoles and A. Chiarri A Generation Operation Planning Model in Deregulated Electricity Markets based on the ComplementarityProblem in book Complementarity: Applications, Algorithms and Extensions KluwerAcademic Publishers. Dordrecht, The Netherlands. pp. 273-295. 2001


Optimization problem statement

( )max

0

0

e e

e

j

e

k

z x

h

g

=

≤

( )max

0

0

e e

e

j

e

k

z x

h

g

=

≤

( )max

0

0

e e

e

j

e

k

z x

h

g

=

≤

Electricity Market

Price-m(x)=0

Optimization problemFor company 1

( )1 1

1

1

max

0

0

j

k

z x

h

g

=

≤

Optimization problemFor company A

Optimization problemFor company a

( )max

0

0

a a

a

j

a

k

z x

h

g

=

≤

( )max

0

0

A A

A

j

A

k

z x

h

g

=

≤


Problem statement for each company

( )max

0

0

e e

e

j

e

k

z x

h

g

=

≤

( )max

0

0

e e

e

j

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k

z x

h

g

=

≤

( )max

0

0

e e

e

j

e

k

z x

h

g

=

≤

Electricity Market

Price-m(x)=0

Optimization problem

For company 1

( )1 1

1

1

max

0

0

j

k

z x

h

g

=

≤

Optimization problemFor company A

Optimization problemFor company a

( )max

0

0

a a

a

j

a

k

z x

h

g

=

≤

( )max

0

0

A A

A

j

A

k

z x

h

g

=

≤

Objective Function

Maximization of:

Company profit for the problem scope

• Other revenues• CTC’s

• Long term contracts...

• Price equation

• Interperiod• Fuel management• Hydro reservoir scheduling

• Intraperiod• Weekly pumping • Operational constraints

Technical constraints

Restricciones del Mercado

Subject to:


Practical difficulties• Good theoretical statement• However, no solver available to solve such

mathematical problem:– Several optimization problems tied by price variable

• Look for another equivalent mathematical problem– With the same solution values– Numerically solvable

• Several alternatives– Complementarity problem [Ventosa, Hobbs]– Equivalent quadratic problem [Barquín, Hobbs]


Optimality conditions of company problem

max za (x)

Subject to:

hja (x) = 0 ⊥λj

a

gka (x) ≤ 0 ⊥µk

a

( ), ,a a a a a a

j j k k

j k

x z h gλ µ λ µ= + ⋅ + ⋅∑ ∑L

Lagrange Function

( )

( )

, , 0

, , 0

0 0 0

aa

x a

aa a

ja

j

a a a a

k k k k

xx

x h

g g

λ

λ µ

λ µλ

µ µ

∂∇ = =∂

∂∇ = = =∂

⋅ = ≤ ≤

LL

LL

KKT Optimality

Conditions


( )

( )

, , 0

, , 0

0 0 0

aa

x a

aa a

ja

j

a a a a

k k k k

xx

x h

g g

λ

λ µ

λ µλ

µ µ

∂∇ = =∂

∂∇ = = =∂

⋅ = ≤ ≤

LL

LL

Mixed complementarity problem

• Set of system of equations plus a complementarity problem

• Generalization of complementarityproblem

System of Equations

Complementarity

Problem


Electricity Market

Deterministic equivalent complementarity problem

Price-m(y)=0

Optimality conditions of company 1

Optimality conditionsof company A

Optimality conditionsof company a

( )

( )

11

1

11 1

1

1 1 1 1

, , 0

, , 0

0 0 0

x

j

j

k k k k

xx

x h

g g

λ

λ µ

λ µλ

µ µ

∂∇ = =∂

∂∇ = = =∂

⋅ = ≤ ≤

LL

LL

( )

( )

, , 0

, , 0

0 0 0

aa

x a

aa a

ja

j

a a a a

k k k k

xx

x h

g g

λ

λ µ

λ µλ

µ µ

∂∇ = =∂

∂∇ = = =∂

⋅ = ≤ ≤

LL

LaL

( )

( )

, , 0

, , 0

0 0 0

AA

x A

AA A

jA

j

A A A A

k k k k

xx

x h

g g

λ

λ µ

λ µλ

µ µ

∂∇ = =∂

∂∇ = = =∂

⋅ = ≤ ≤

LL

LL


• This approach is a Cournot model with conjectural variations• Decision variable of each company is total output bid into the

market• In the Cournot model, the optimal output of a company considers

a fixed output from competitors• However, in conjectural variation approach reaction from

competitors is taken into account when the company decides its optimal output

Conjectural variation approach


• For each agent a different conjectural variation is set

• Therefore, sensitivity of spot price with respect to company output is different from the slope of the inverse demand function

Conjectural variation approach

( ),1 1a

a a

a a

s qV

q qα α

−− ∂ ∂= − ⋅ + = − ⋅ +

∂ ∂

( )0 a as S q qα −= − ⋅ +

,aaV−


Stochastic optimization problem without risk• Simultaneous agents’ stochastic optimization problems with

price equation

Optimization problem of company a

0 at t t t

a

α= − ⋅∑s S q

( )1max

subject to:

Operation constraints

E ΠΠΠΠ

Optimization problem of company A

Optimization problem of company 1

( )max

subject to:


aE ΠΠΠΠ ( )max

subject to:


AE ΠΠΠΠ


Stochastic equilibrium problem without risk

Optimality conditions of company a

0 at t t t

a

α= − ⋅∑s S q

1 1

0


Complementarity conditions

i jt t

∂ ∂= =∂ ∂L L

q q

Optimality conditions of company A


A

0



A

i jt t

∂ ∂= =∂ ∂L L

q q

0



a a

i jt t

∂ ∂= =∂ ∂L L

q q


Stochastic optimization problem with risk

AΠ

0 at t t t

a

α= − ⋅∑s S q ( ),l t t l= Ef s s

AΠ1Π aΠ

( )1max

subject to:


E ΠΠΠΠ ( )max

subject to:


aE ΠΠΠΠ ( )max

subject to:


AE ΠΠΠΠ

Optimization problem of company a

Optimization problem of company A

Optimization problem of company 1


Forward price of electricity

• Risk is limited to a certain value• Forward and expected spot price relation:

( ),l t l tf = E s

l t

, ,sc l tf

( ),sc l tE s


Futures modeling– Futures’ revenues

– Contract gains and losses computed at maturity

– Transaction costs associated to contracts computed when signed. Piecewise linear approximated

, ,t l t t kl k

l t k t< >

= −∑ ∑ΠΠΠΠ r c

( ) ( ), , , ,s b

l t l t t l t l t= − ⋅ −r f s t t

( ), , ,s b

t k m t k t k mC C′≥ ⋅ +c t + t

f forward prices spot pricets forward salestb forward purchases

C‘ Fixed costC Variable cost

Π Futures’ profitsr Gains/lossesc Transaction cots


Risk constraint• Risk modeling: CVaR

– For a discrete distribution function

( )1VaR α–

1 – α

Π

( )f Π

( )1CVaR α–

( ) ( ) 11 1

1sc sc

sc

CVaR VaR P zα αα

− − − ⋅ ⋅− ∑Π ΠΠ ΠΠ ΠΠ Π=

( )1 0sc sc scz VaR zα≥ − − Π ≥ΠΠΠΠ

Π Profitz Negative values of ΠP Probabilityα Confidence level

scz


Stochastic equilibrium problem with risk

0 at t t t

a

α= − ⋅∑s S q ( ),l t t l= Ef s s

AΠ1Π aΠ

Optimality conditions of company a

1 1

0



i jt t

∂ ∂= =∂ ∂L L

q q

Optimality conditions of company A


A

0



A

i jt t

∂ ∂= =∂ ∂L L

q q

0



a a

i jt t

∂ ∂= =∂ ∂L L

q q


Content






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Keys to success• According to [Labadie, 2004] “the keys to success in

implementation of reservoir system optimization models are:– (1) improving the levels of trust by more interactive of decision

makers in system development;– (2) better “packaging” of these systems; and– (3) improved linkage with simulation models which operators more

readily accept”.


MHE• Purpose

– Determine the optimal yearly operation of all the thermal and hydro power plants

– Medium term stochastic hydrothermal model for a complex multi-reservoir and multi-cascaded hydro subsystem

• Main characteristics– General reservoir system topology– Cost minimization model– Thermal and hydro units considered individually– Nonlinear water head effects modeled for large reservoirs (NLP Problem)– Stochastic nonlinear optimization problem solved directed by a nonlinear

solver given a close initial solution provided by a linear solver• References

– A. Ramos, S. Cerisola, J. M. Latorre, R. Bellido, A. Perea, and C. P. López A Medium Term Hydrothermal Coordination Model by Stochastic Nonlinear Programming Working paper


Demand• Weekly demand with two load levels (peak and off-peak

each week)

0

10000

20000

30000

40000

1 13 25 37 49 61 73 85 97

Dem

and

[MW

]


Hydro subsystem• Different modeling approach for hydro reservoirs

depending on:– Owner company– Relevance of the reservoir

• Reservoirs belonging to other companies modeled in energy units [GWh]

• Own reservoirs modeled in water units [hm3, m3/s]• Important reservoirs modeled with water head effects• Very diverse hydro subsystem:

– Hydro reservoir volumes from 0.15 to 2433 hm3

– Hydro plant capacities from 1.5 to 934 MW


Scenario tree generation• A multivariate scenario tree is obtained by neural gas

clustering technique that simultaneously takes into account the main stochastic series and their spatial and temporal dependencies.

• Very extreme scenarios can be artificially introduced with a very low probability

• Number of scenarios generated enough for medium term operation planning


Unregulated historical hydro inflows


Natural inflows: scenario tree


Constraints: Generation and load balance

Generation of thermal units

+ Generation of storage hydro units

– Consumption of pumped hydro units

= Demand

Generation of thermal units

+ Generation of storage hydro units

– Consumption of pumped hydro units

= Demand


Constraints: Minimum and maximum operating hours of thermal units

• Introduced to model:– Unavailability of thermal units– Domestic coal subsidies– CO2 Emission allowances– Capacity payments

• They are not separable by period

minimum ≤ Yearly operation hours of each thermal unit for each scenario ≤ maximum

minimum ≤ Yearly operation hours of each thermal unit for each scenario ≤ maximum

minimum ≤ Average yearly operation hours of each thermal unit ≤ maximum

minimum ≤ Average yearly operation hours of each thermal unit ≤ maximum


Constraints: Water balance for large reservoirs

Reservoir volume at the beginning of the period

+ Natural inflows

– Spills from this reservoir

+ Spills from upstream reservoirs

+ Turbined water from upstream storage hydro plants

+ Pumped water from downstream pumped hydro plants

– Turbined and pumped water from this reservoir

= Reservoir volume at the end of the period

Reservoir volume at the beginning of the period

+ Natural inflows

– Spills from this reservoir

+ Spills from upstream reservoirs

+ Turbined water from upstream storage hydro plants

+ Pumped water from downstream pumped hydro plants

– Turbined and pumped water from this reservoir

= Reservoir volume at the end of the period


Constraint: Water head effects• Power generation is the product (nonlinear function) of

the flow and the production function

• Production function PF depends linearly on plant water head

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0 20 40 60 80 100 120

Water head [m]

Pro

duct

ion

func

tion

[MW

/m3/

s]

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0 20 40 60 80 100 120

Water head [m]

Pro

duct

ion

func

tion

[MW

/m3/

s]

P = Q x PFP = Q x PF

PF = α HpPF = α Hp


Constraint: Volume as a function of the head• Reservoir volume depends quadratically (nonlinearly) on

reservoir water head

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100 120

Water head [m]

Vol

ume

[hm

3]

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100 120

Water head [m]

Vol

ume

[hm

3]

V = β + β’ Hr+ β” Hr2V = β + β’ Hr+ β” Hr2


Constraint: Water heads

Water head of the reservoir = forebay height – reference heightWater head of the reservoir = forebay height – reference height

Water head of the plant = forebay height of the reservoir –tailrace height of the plant

Water head of the plant = forebay height of the reservoir –tailrace height of the plant

Tailrace height of the plant = max [forebay height of downstream reservoir, reference tailrace height of the plant]

Tailrace height of the plant = max [forebay height of downstream reservoir, reference tailrace height of the plant]


Constraint: operation limits

Reservoir volumes between limits for each hydro reservoirReservoir volumes between limits for each hydro reservoir

Power operation between limits for each unitPower operation between limits for each unit


Multiobjective function• Thermal plant variable costs

• Penalties introduced in the objective function for softening several additional constraints:

– Final reservoir volumes– Exceeding operating rule curves (minimum and maximum)– Minimum and maximum yearly operation hours of thermal

units


Model results• Results for each period and load block and for each

scenario– Storage hydro, pumped hydro and thermal plant operation– Reservoir management– Basin and river production– Marginal costs

• Byproduct– Optimal water release tables for different stochastic natural

inflows and reservoir volumes (obtained by stochastic nested Benders’ decomposition) used by a lower level stochastic simulation model


Solution algorithm• Algorithm:

– Successive LP– Direct solution by a NLP solver

• Very careful implementation– Natural scaling of variables– Use of simple expressions– Initial values and bounds for all the nonlinear variables computed

from the solution provided by linear solver (CPLEX 10.2 IPM)– Nonlinear solvers

– CONOPT 3.14 [Generalized Reduced Gradient Method]– KNITRO 5.1.0 [Interior-Point or an Active-Set Method]– MINOS 5.51 [Project Lagrangian Algorithm]– IPOPT 3.3 [Primal-Dual Interior Point Filter Line Search

Algorithm]– SNOPT 7.2-4 [Sequential Quadratic Programming Algorithm]


Two-year long case study• Spanish electric system

– 130 thermal units– 3 main basins with 50 hydro reservoirs/plants and 2

pumped storage hydro plants– 12 scenarios


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Simulador• Purpose

– Analyze and test different management strategies of hydro plants– Economic planning of hydro operation:

• Yearly and monthly planning– Update the yearly forecast:

• Operation planning up to the end of the year– Short term detailed operation:

• Detailed operation analysis of floods and droughts, changes in irrigation or recreational activities, etc.

• Main characteristics– Simulation technique– It has been proposed a general simulation method for hydro basins– A three phase method implements the maximize hydro production objective– Object Oriented Programming has been used– A flexible computer application implements this method

• References– J.M. Latorre, S. Cerisola, A. Ramos, R. Bellido, A. Perea Creation of Hydroelectric System

Scheduling by Simulation in the book H. Qudrat-Ullah, J.M. Spector and P. Davidsen (eds.) Complex Decision Making: Theory and Practice pp. 83-96 Springer October 2007 ISBN 9783540736646

– J.M. Latorre, S. Cerisola, A. Ramos, A. Perea, R. Bellido Simulación de cuencas hidráulicasmediante Programación Orientada a Objetos VIII Jornadas Hispano-Lusas de IngenieríaEléctrica Marbella, España Julio 2005


Data representation (i)

• Basin topology is represented by a graph of nodeswhere each node is an element:

• Connections among nodes are physical junctions through the river.

• This structure induces the use of– Object Oriented Programming

Natural inflow

Reservoir

Hydro plant


Data representation (ii)• Five types of nodes (objects) are needed:

– Reservoir– Channel– Plant– Inflow point– River junction

• Each node is independently operated although it may require information from other elements


Data representation (iii)

• Reservoir:– Manages the water

• One or more natural inflows• One outflow

– May have associated:• Minimum outflow• Volume curves that guide its operation:

– Minimum/maximum target curves– Lower/upper guiding curves– Avoiding spillage curve

• Minimum and maximum volume• Optimal water release table (input from long term hydrothermal

models)


Data representation (iv)

• Channel:– Doesn’t manage the water– Flow transportation between nodes with a limit


Data representation (v)

• Plant:– Produces electric energy from hydro inflow– Coefficient of efficiency depending linearly on the head– May also pump


Data representation (vi)

• Natural inflow point:– Introduces water into the system– Uses historical or synthetic inflows


Data representation (vii)

• River junction:– Groups elements in a river junction– Limits the maximum joint outflow– Management determined in tho steps:

1. Independent initial decision2. Reduction of it following a priority order up to the maximum flow


Reservoir operation strategies

1. Optimal outflow decision taken from a precalculated optimal water release table depending on:

• Week of the simulated day• Hydrologic index of the basin inflows (type of year)• Volume of the own reservoir• Volume of a reference reservoir

– Table calculated by a long term hydrothermal model– Usually for the main reservoirs of the basin

2. Outflow equals incoming inflow (usually for small reservoirs)

3. Go to minimum target curve (spend as much as possible)

4. Go to maximum target curve (keep water for the future)


Simulation method (I)

• Main objective:– Maximize hydro production following the reservoir

operation strategies– Other objectives:

• Avoid spillage• Satisfaction of minimum outflow (irrigation)

• Proposed method requires three phases:1. Decides the initial management2. Modifies it to avoid spillage and produce minimum

outflows3. Determines the electricity output for previous inflows


Simulation method (II) – Phase 1

• Downstream• Each element is individually operated according to its

own operation and strategies• Additional information is collected:

– In reservoirs• Spillage and non served minimum flow• Additional volume to spend or to keep

– In all the elements:• Accumulates those values for the own element and those

located upstream


Simulation method (III) – Phase 1

Keep

Additional


Simulation method (III) – Phase 2

• Upstream from the end of the basin • Modifies the Phase 1 operation

– To avoid spillage forces the reservoirs to keep water– To serve a minimum flow increases the production of

reservoirs• Splits the changes proportionally to the capacity of

each element with respect to all the remaining elements located upstream


Simulation method (IV) – Phase 3

• Determines the plant output– By using a coefficient of efficiency– Depending on the average water head of the day

• Splits the production between peak and off-peak hours:– As much as possible in peak hours– The rest in off-peak hours


Case study• Application to the Tajus basin belonging to Iberdrola with:

– 9 reservoirs of different sizes– 8 hydro plants– 6 natural inflow points– 27 historical series of daily inflows


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MAFO• Purpose

– Short-term generation operation– Strategic Unit Commitment development of offering strategies– Daily and adjustment markets

• Main characteristics– Decomposition techniques (Benders, Lagrangean relaxation)

• References– A. Baillo, S. Cerisola, J. Fernandez-Lopez, A. Ramos Stochastic Power Generation

Unit Commitment in Electricity Markets: A Novel Formulation and A Comparison of Solution Methods Operations Research (accepted) JCR impact factor 1.234 (2006)

– J.M. Fernandez-Lopez, Á. Baíllo, S. Cerisola, R. Bellido, "Building optimal offer curves for an electricity spot market: a mixed-integer programming approach," Proceedings of the 15th PSCC, Power Systems Computing Conference. Liege, Belgium, 22-26 Agosto 2005

– Á. Baíllo, M. Ventosa, M. Rivier, A. Ramos, "Optimal offering strategies for generation companies operating in electricity spot markets," IEEE Transactions on Power Systems. vol. 19, no. 2, pp. 745-753, May 2004

– A. Baíllo, M. Ventosa, M. Rivier, A. Ramos, G. Relaño Bidding in a Day-Ahead Electricity Market: A Comparison of Decomposition Techniques 14th Power Systems Computation Conference (PSCC '02) Seville, Spain June 2002

– A. Baíllo, M. Ventosa, A. Ramos, M. Rivier, A. Canseco Strategic unit commitment for generation companies in deregulated electricity markets in book The Next Generation of Electric Power Unit Commitment Models Kluwer Academic Publishers Boston, MA, USA pp. 227-248 2001


Curva esperada de demanda residual

0

20

40

60

80

100

120

6000 8000 10000 12000 14000 16000 18000

Energía (MWh)

Pre

cio

(€/M

Wh)

Modeling short term uncertainty: multistage approach

• Generation company doesndoesn’’t knowt know the residual demand residual demand curve for each hour:


Curva esperada de demanda residual

0

20

40

60

80

100

120

6000 8000 10000 12000 14000 16000 18000

Energía (MWh)

Pre

cio

(€/M

Wh)


• Explicit recognition of uncertainty justifies the importance of offering strategies:

Posibles curvas de demanda residual

0

20

40

60

80

100

120

6000 8000 10000 12000 14000 16000 18000

Energía (MWh)

Pre

cio

(€/M

Wh)


Selling offers have to build an increasing curve

Offering curve between two possible realizations of residual demand curve

is irrelevant

Company decisions are reduced to chose selling output for each residual demand


•• Hypothesis:Hypothesis: probability distributionprobability distribution of residualresidual demand demand curve has finitefinite supportsupport:

Number of possible realizations of residual demand curve is finite

Cantidad

Precio

( )1p q

1q 2q

( )2p q

3q

( )3p q


•• Solution in two phases:Solution in two phases:– Stochastic unit commitment

– Optimal offering strategies under uncertainty.•• StructureStructure of these problems.•• Possible decomposition techniques:Possible decomposition techniques:

– Benders.– Lagrangian relaxation.

Solution problem strategy


•• Scope of short term decisionsScope of short term decisions is one weekone week:– Startup and shutdown planning: unit commitmentunit commitment.– Daily hydro scheduling: hydrothermal coordinationhydrothermal coordination.

• This weekly problem can be seen as a sequence of sequence of twotwo--stage stochastic problemsstage stochastic problems, one for each day of the week.

First problem: weekly stochastic multistage planning


First problem: weekly stochastic multistage planning

Ofertas para el mercado diario

Casación mercado

diario

Distribución de probabilidad discreta del mercado diario

Ofertas para el mercado de ajustes

Casación mercado ajustes

Resultado esperado para el mercado de ajustes

Programa de generación

Día 1


Casación mercado

diario






Día 2


Casación mercado

diario






Día 7



Casación mercado

diario






Día 1


Casación mercado

diario






Día 2


Casación mercado

diario






Día 7

First problem: detail for each day of the week


Casación mercado

diario






Día 2


Casación mercado

diario






Día 2


Second problem: two-stage problem of offering strategies


Casación del mercado diario

Distribución de probabilidad discreta para el mercado diario


Casación del mercado de

ajustes




Solution technique:Benders decomposition

Subproblem: Adjustment market (resource) and generation planning

Marginal costs associated to

offers.

Daily market offers

Master problem: Daily market.

Decide offers: quantities and prices.


Content

• Model development at IIT• More detailed description of some specific models

� Brief description of some models


BEST• Purpose

– Assessment of investments in generation assets and other strategic decisions • Main characteristics

– Long-term scope (20-30 years)– System-dynamics based simulation (Business Dynamics)– Includes a detailed representation of agents’ market behavior based on

endogenously-computed conjectured price variation– Includes a detailed representation of decisions evaluation based on Merton-Black-

Scholes theory • References

– E. Centeno, J. Barquín, A. López-Peña, J.J. Sánchez, "Effects of gas-production constraints on generation expansion," 16th Power Systems Computation Conference - PSCC 08. Glasgow, Scotland, 14-18 Julio 2008

– J.J. Sánchez, J. Barquín, E. Centeno, "Fighting market power by auctioning generation: A system dynamics approach," INFORMS Annual Meeting 2007. Seattle, USA, 4-7 Noviembre2007

– J.J. Sánchez, J. Barquín, E. Centeno, A. López-Peña, "System dynamics models for generation expansion planning in a competitive framework: Oligopoly and market power representation," Twenty-Fifth International System Dynamics Conference. Boston, Massachusetts, USA, 29 Julio-2 Agosto 2007


BEST

AVAILABLEPOWER PLANTS

ELECTRICITYPRICE

POWERPRODUCTION

PRICEFORECASTING

POWERPRODUCTIONFORECASTING

NEW POWERPLANTS

DEMAND

Building

ForecastingDecision

Market

• Overall structure


MORSE (+EQUITEC)• Purpose

– MORSE: Simplified model of the electricity Spanish sector, for strategic long term analysis (regulatory policies, agent structure evolution, technological improvements, etc.)

• Main characteristics– Set of excel modules for conventional calculations, data input and output, and

reporting– Includes EQUITEC, which is a quadratic optimization GAMS module to solve the

equilibrium market, with the following features:• Generation is aggregated at a technology level: less details allows for more complex

complementary algorithms, such as multiple scenario evaluation for statistic results, iterative conjecture determination, etc.

• Conjectural variation Cournot market model• Algorithm for robust conjecture determination assuming robustness against demand

scenarios and linear behaviors around the equilibrium point.

– Long term purposes– Additional goal optimization module for relevant input determination (such as

tariffs for zero deficit)


MORSE (+EQUITEC) architecture

Liberalized clients energy, for agents and distrib zones

Agents: conjectures,

power, technologies,

contracts, etc.

Sector final

balance

Other incomes

(coogeneration,

transmission, distrib,

international

exchanges, …)

Sector balance

Clients

Load

Insular

compensation

Peninsular s.

Non dispatched

energies (hydrau, coogen, internation

exchanges, ….)

Generation(technologies)

load levels demand

EQUITEC

(GAMS)

Regulated business

(trams, distrib)

Fuels

Lib clients energy for agent, distrib

Sector incomes, from

lib. and tarifs clients

Prod. cost for each

technology

Insular syst.

Total energy and energy profile

Energy for load levels Technologies data: fuel

costs, availability, etc.

Peninsular s.

Insular syst.

Prices, productions,

incomes, costs, margins

Market results, prods, prices,

incomes, costs, etc

% liberalized clients for

agents and zones

network loads

Total load,

profiles, load

levels

Extra cost for

regulatory

purposes

Peninsular s.

Insular syst.

Data for ancilllary and

security of supply incomes

estimation

Macro variables (brent, Api2, etc.)

Insular syst.

Peninsular s.

Contracts for hedging

Peninsular s.

Insular syst.

Tolls, tarifs

Contracts

Peninsular s.

Insular syst.

Energy prices and

energy contract prices

Total

ancilllary and

security of supply

prices

Transmission and

distribution data

Excel optimaser for

Input data coherence

%’s lib

% lib for

agents,

zones


• Iterative conjecture determination – equivalent to slopes bidding curves determination– Klemperer based method is being used with linear bidding curves– Equilibrium is solved for two different demand scenarios – Slopes bidding curves are iteratively adjusted until convergence to

the final slopes

MORSE: EQUITEC conjecture determination

( ) ( )( ) ( ) { }

( ) ( ) { }∑

∑

∈∀=

∈∀⋅+=

≠E

e

e

e

ee

e

ee

DP

ePPCM

21

21

'

'

,

,,1

εεεεε

εεεεα

εελ

Equilibrium equations for both demand scenarios

( ) ( )( ) ( ) e

PP eee ∀

−−

=12

12

ελελεεα

Iterative adjustment of bidding slopes0,eα

0,eα

D

( )1εD

( )2εD

( )11ελ( )

12ελ

( )11εeP

( )12εeP

Energy

Price

1,eα

Aggregated supply function at iteration 1


Valore• Purpose

– Oligolopolistic electricity markets simulation

• Main characteristics– Based on quadratic optimization– Medium-term

• Detailed physical assets modeling• Stochastic optimization (i.e. water inflows)• Network constraints (explicit and implicit transmission auctions)

• References– J. Barquín, M. Vázquez, Cournot Equilibrium Calculation in Power Networks: An

Optimization Approach With Price Response Computation, IEEE Trans. on Power Systems, 23, no. 2, 317-326, May, 2008

– J. Barquín, E. Centeno, J. Reneses , Stochastic Market Equilibrium Model For Generation Planning, Probability in the Engineering and Informational Sciences, 19, 533-546, August, 2005


Valore Deterministic equilibrium

• In equilibrium, for each company (utility) u, marginal cost and marginal revenue must be equal

• The theory is explained in the single period case, but it is straightforward to generalize it to include inter-temporal constraints (as in the example case).

u uMC MR=


Valore Deterministic equilibrium

• Marginal revenue has two components:– 1 additional MW-h earns the market price .– But because of the greater production, market price decreases

an amount . The price fall impacts on all the energy sold in the market, that we assume to be the total generation.

λ

uθ

u uuR PM λ θ= −

Conjectural Response


Valore Deterministic equilibrium• All together

0

0

u

u

u

u

u

uu P

MRMC

DD

P D

MR θλα

λ== −

= −

=∑


Valore Deterministic equilibrium• It is easy to check that previous equations are just the

optimality conditions of problem

– Demand utility:

– Effective cost:

( )( ) ( ),

.

min

s.t :

uu

u

u

u

u

P DUP

P D

C D

λ

−

=

∑

∑

( )2

0

0

1

2D

DD DU

α

= −

( ) ( ) 2

2u uu

uu uC P PCP

θ= +

Price is the multiplier


Fuzzy Valore

• Purpose– Proposing an electricity market model based on the conjectural-price-

response equilibrium when uncertainty of RDC is modeled using the possibility theory

• Main characteristics– Compute robust Cournot equilibrium by using possibilistic VAR for

medium term analysis– Determine possibility distributions of main outputs (prices and incomes)– Novel variational inequalities (VI) algorithms with global and proved

convergence that iteratively solve quadratic programming (QP) models• References

– F.A. Campos, J. Villar, J. Barquín, J. Reneses, “Variational inequalities for solving possibilistic risk-averse electricity market equilibrium," IET Gener. Transm. Distrib.vol. 2, no. 5, pp. 632-645, Sep 2008

– F.A. Campos, J. Villar, J. Barquín, J. Ruipérez, "Robust mixed strategies in fuzzy non-cooperative Nash games," Engineering Optimization. vol. 40, no. 5, pp. 459-474, May 2008

– F.A. Campos, J. Villar, J. Barquín, "Application of possibility theory to robust Cournot equilibriums in electricity market," Probability in the Engineering and Informational Sciences. vol. 19, no. 4, pp. 519-531, October 2005


Fuzzy Valore Possible RDC and uncertainty reduction

1

0

( )eµπ

(pe,λe)

pe

λe

Price

Power

10

( )eλπ

Posible RDC for each agent

λ(Pe,µµµµe)=λe+µµµµe·(pe-Pe)

µµµµ1e µµµµ2

e µµµµ3e

Slope µµµµe

µµµµ4e

Possibility

Possibility 1

UncertaintyUncertainty reductionreductionusingusing possibilisticpossibilistic VARVAR

Price

Power

(De,λe)EquilibriumEquilibriumconditionsconditions

( ) ( )

( )D

PD

ePPCM

E

e

e

eeeeee

λλ

αλµαλ

=

=

∀⋅+=

∑=1

00 ,,

SlopeSlope expectedexpectedRDC:RDC:

notnot constantconstant !!!!!!

ExpectedExpected RDC: RDC: PercentilPercentil


Fuzzy Valore Equilibrium resolution

Proposed resolution:

““VI algorithm that solve at each iteration an approximated VI proVI algorithm that solve at each iteration an approximated VI problem and a blem and a additional projection oneadditional projection one””

• The approximated VI problem is solved with a QP similar to Valore:

• The projection problem is also solved with a QP:

( ) ( ){ }PPPPMinArgPkTk

XP

k −−=∈

+1

( ) ( )

PDas

PPDUPPCaMin

T

kE

e

e

k

eeXPD

1..

2,,

2

1

0,

=

−⋅+−∑=∈

αα

PenalizationPenalizationDemandDemand utilityutilityAmpliatedAmpliated CostsCosts


Fuzzy Valore Possibility distributions of Incomes

Average and variance of incomes

5

7

9

11

13

15

17

19

21

Ene Feb Mar Abr May Jun Jul Ago Sep Oct Nov Dic

Monh

Inco

mes

(M€)

Possibilitic

Deterministic

Lesser variance withpossibilistic approach:RobustRobust EquilibriumEquilibrium

Main results:


EXLA• Purpose

– Optimal planning of hydroelectric reservoirs in the mid-term• Main characteristics

– Deterministic & stochastic approach– Profit-based & demand-based– LP in a iterative under-relaxed process, MILP or QPC– Mid-term: weekly periods, with load blocks.– Very detailed representation of hydro systems peculiarities– Used by Endesa to manage their reservoirs in the Spanish system.

• References– R. Moraga, J. García-González, E. Parrilla, S. Nogales, "Modeling a nonlinear

water transfer between two reservoirs in a midterm hydroelectric scheduling tool," Water Resources Research. vol. 43, no. 4-W04499, pp. 1-11, April 2007

– J. García-González, R. Moraga, S. Nogales, A. Saiz-Chicharro, "Gestión óptima de los embalses en el medio-largo plazo bajo la perspectiva," Anales de Mecánica y Electricidad. vol. LXXXII, no. IV, pp. 18-27, July 2005


Resultados agregados� producción de cada UGH� evolución de las reservas

Resultados detallados� producciones por central� caudales turbinados por central� caudales vertidos� políticas de desembalse� evolución de cotas� identificación de riesgo de vertidos, etc...

Emb-Camarasa

Cen-Camarasa

Cen-Talarn

Emb-Talarn

Cen-Terradets

Emb-Rialb

Cen-Rialb

Cen-Gavet

Cen-Lorenzo

Cen-Termens

Cen-Balaguer

Cen-Lleida

Emb-Presaler

Emb-Seros

Cen-Seros

Emb-Terradets

Emb-Oliana

Cen-Oliana

TalarnTalarnD

Gavet

Terradets

Camarasa

Olinana

Rialb

Urgell

LorenzoAux_Urgell

Cu_Com

Termens

Fontanet

Nog

Seros

Emb-Camarasa

Cen-Camarasa

Cen-Terradets

Emb-Rialb

Cen-Rialb

Cen-Gavet

Cen-Lorenzo

Emb-Terradets

Emb-Oliana

Cen-Oliana

Terradets

Camarasa

Olinana

Rialb

Urgell

LorenzoAux_Urgell

Cu_Com

Datos físicos [Hm3],[m3/s]

� topología de los subsistemas� caudales de aportaciones� servidumbres� curvas de garantía� consignas de cotas de los embalses� datos estáticos de emb. y cen., etc...

Modelo equivalente [MWh],[MW]� producible� potencia fluyente� reservas máximas y mínimas� reservas iniciales� energías máximas y mínimas, etc...

Modelo de coordinación

hidrotérmica de medio plazo

EXLA


SGO: Intelligent Electricity Market Information System • Purpose

– Electricity market set of tools for strategic market analysis and optimal bids generation, applied to the Spanish Electricity Market.

• Main characteristics– First versions running for Endesa since 2000, it includes:

• Oracle Database• Market analysis tools for past bids competitors analysis using data

mining techniques (Matlab)• Generation resources determination tools based on linear and heuristic

optimization techniques (C, Gams)• Optimal bidding strategies: competitors patterns, scenarios

generations, optimal bidding strategies determination, genetic algorithms (C, Matlab, Excel)

• Reporting tools (Excel)– Short term, day ahead


SGO architecture

SGO-BDORACLE

SGO-BDORACLE

SGO-DataSGO-Data

Thermal unitsre-dispatch

Thermal unitsre-dispatch

Hidraulic unitsre-dispatch

Hidraulic unitsre-dispatch

Pumping unitsre-dispatch

Pumping unitsre-dispatch

Data Files

SGO-Market-1SGO-Market-1



SGO-LoaderSGO-Loader

DLL-LOADDLL-LOAD

SGO-AutoloaderSGO-Autoloader

SGO-ReportsSGO-Reports

SGO-AnalysisSGO-Analysis

OPTIMIZER

...

SGO-ExpertSGO-Expert


SGO-Analysis example

Day

s

Hours

0 5 10 150

20

40

60

80

100

120

140

Precio (Pta/kW)

Ba

nda

NO

RM

ALI

ZA

DA

(%

)

Curv as de of erta de reserv a secundaria de la competencia de Endesa

0 5 10 150

20

40

60

80

100

120

140

Precio (Pta/kW)

Ba

nda

NO

RM

ALI

ZA

DA

(%

)

Curv as de of erta de reserv a secundaria de la competencia de Endesa


SGO: Intelligent Electricity Market Information System

• References– J. Villar, A. Muñoz, E.F. Sánchez-Úbeda, A. Mateo, M. Casado, F.A. Campos, J.

Maté, E. Centeno, S. Rubio, J.J. Marcos, R. González, "SGO: Management information system for strategic bidding in electrical markets," IEEE Power Tech. Conference, POM6-394. Porto, Portugal, September 2001

– E.F. Sánchez-Úbeda, A. Muñoz, J. Villar, "Minería y visualización de datos del mercado eléctrico español," Inteligencia Artificial - Revista Iberoamericana de Inteligencia Artificial . vol. 10, no. 29, pp. 79-88, May 2006

– A. Mateo, E.F. Sánchez-Úbeda, A. Muñoz, J. Villar, A. Saiz-Chicharro, J.T. Abarca, E. Losada, "Strategic bidding under uncertainty using genetic algorithms," PMAPS2000: 6th International Conference on Probabilistic Methods Applied to Power Systems. Funchal, Madeira, Portugal, September 25-28, 2000

– J. García-González, A. Muñoz, F.A. Campos, J. Villar, "Connecting the intraday energy and reserve markets by an optimal redispatch," IEEE Transactions on Power Systems. vol. 22, no. 4, pp. 2220-2231, November 2007

– E. Centeno, B. Vitoriano, F.A. Campos, A. Muñoz, J. Villar, E.F. Sánchez-Úbeda, "A goal programming model for rescheduling of generation power in deregulated markets," Annals of Operations Research. vol. 120, no. , pp. 45-57, April 2003


MARAPE• Purpose

– Risk identification, analysis and management– Risk and rate-of-return measures– Medium-term contracting decisions

• Main characteristics– Strategic Probabilistic Simulation– ELDC convolution– Time series, GARCH

• References– C. Batlle, J. Barquín, "A strategic production costing model for electricity market

price analysis," IEEE Transactions on Power Systems. vol. 20, no. 1, pp. 67-74, February 2005

– C. Batlle, J. Barquín, "Fuel prices scenario generation based on a multivariate GARCH model for risk analysis in a wholesale electricity market," International Journal of Electrical Power & Energy Systems. vol. 26, no. 4, pp. 273-280, May 2004


PLAMER• Purpose

– Compute medium term market prices and agents’ output applying liberalized market equilibrium conditions

– Evaluate the impact of incorporating new bidding units– Analyze electricity market regulatory changes

• Main characteristics– Model with quadratic objective function, linear constraints, binary variables.– Minimum load of bidding units– Different scenarios of fuel prices– Hydro reserves management by agent– Pumped storage units– CO2 emission costs– Medium term scope (2 years)– Results disaggregated by weeks, periods and load levels

• References– López de Haro, S., Sánchez Martín, P., de la Hoz Ardiz, J.E.. y Fernández Caro, J.,

“Estimating conjectural variations for electricity market model”, European Journal of Operations Research, Vol. 181, Issue 3, 16, Septiembre 2007, Pages 1322-1338


GRIMEL• Purpose

– Strategic bidding model that optimizes the electrical resources (energy and ancillary services) of a generation company

• Main characteristics– Short term stochastic optimization model (MIP)– The same model is used to obtain the optimal bid for the daily energy

market, secondary reserve and intradaily markets in Spain– Used in the Spanish electricity market by a medium size generation

company– The strategy of the rest of the agents is modeled by the residual demand

curve• Forecasted using decision trees

– High degree of modeling in the units• For instance, models each physical unit of a pumping generator and is

able to obtain simultaneously its sell and buy bid• References

– A. Ugedo, E. Lobato, A. Franco, L. Rouco, “Strategic bidding in Sequential Electricity Markets”, IEE Generation, Transmission and Distribution, Julio, vol. 153 (4), pp. 431-442, 2006

– A. Ugedo, E. Lobato, A. Franco, L. Rouco, J. Fernández-Caro, J. de-Benito, J. Chofre, J.de la Hoz “Stochastic Model of Residual Demand Curves with Decision Trees”. 2003 PES General Meeting, Toronto, Canada, 2003.


GRIMEL• Overview

Thermal units

Hydro units

Pump storage units

Market data Strategic parameters

Residual demand curves’ estimationExplanatory variables

STOCHASTIC

OPTIMIZATION

Market

bid curves

construccion


GRIMEL• Modes of operation

– MD: obtains the strategy and bid curve for daily market– BS: obtains the strategy and bid curve for secondary reserve, taking

into account results of the previous daily energy market– MI: obtains the strategy and bid curve for each intradaily market,

taking into account results of previous energy markets and secondary reserve market

– The same model is valid for each market


GRIMEL

THE SAME MODEL IS VALID FOR ALL MARKETSTHE SAME MODEL IS VALID FOR ALL MARKETS

MDMD

M

O

D

E

( )1 1

1 1md mi 1

md mi mi

g ,h ,scmig ,h ,esc ,esc g ,h ,s g ,h ,scmicmdqt qt qt dt= + −

,

max

, , ,, _0 g h g g hg h sc hbs POPs ve qtb≤ ≤ ⋅ −δ

, ,

min

, ,, _0 gg h scb hs g hh gPOb Pe qtb v≤ ≤ − ⋅δ

Decision

variable to

obtain bid

in actual

market

BSBS

MIMI

Decision

variable of

future

markets

Parameters

known

( )1 1

md mi 1 1 1

md mi mi

g ,h ,esc ,esc g ,hg ,h ,scmd ,scmi g ,h ,scmiqt qt dtqt= + −

,

max

, , ,, _0 g h g g hg h sc hbs POPs ve qtb≤ ≤ ⋅ −δ

, ,

min

, ,, _0 gg h scb hs g hh gPOb Pe qtb v≤ ≤ − ⋅δ

( )1 1

md mi 1 1 1

md mi mi

g ,h ,esc ,esc g ,hg ,h ,scmd ,scmi g ,h ,scmiqt qt dtqt= + −

max

, ,, , , _0 g h scbs g h g h g hbs POP ve qt≤ ≤ ⋅ −δ

min

, ,,, ,_0 gg h sc hbs g h g hbb POPve qt≤ ≤ − ⋅δ


GRIMEL

Modo de estrategia de oferta:

• Modo MD• Modo BS• Modo MIx

Definición de índices y parámetros

Carga de índices

Carga de parámetrosValidación de parámetros

Modelo de mercado

Modelo del parque generador

Ejecución del modo seleccionado

Identificación variables holgura

Alarmas parámetros

Alarmas infactibilidades

Generación salidas con resultados

Módulo de construcción de ofertas según el formato requerido por el mercado

Fijar variables según resultados reales de mercados anteriores

Modelo térmico

Modelo hidráulico

Modelo bombeo

PROGRAMMING STRUCTURE OF THE ORIGINAL MODELPROGRAMMING STRUCTURE OF THE ORIGINAL MODEL

Model

Adaptation to each

mode and solver

Infeasibility

detectionResults

Bids adapted to the required format


MEMPHIS• Purpose

– Determine the impact of a large scale penetration of renewable energy sources in the electric system operation

• Main characteristics– Chronological simulation

• References– A. Ramos, L. Olmos, J. M. Latorre, I. Pérez-Arriaga Modeling

Medium Term Hydroelectric System Penetration with Large-scale Penetration of Intermittent Generation XIV Congreso Latino IberoAmericano de Investigación de Operaciones (CLAIO 2008) Cartagena de Indias, Colombia September 2008


SIMUPLUS• Purpose

– Evaluation of potential network investments in regulated and liberalized electric markets

– Analysis of additional investments by sensitivities– Study the security of supply due to failures in generation or transmission elements

• Main characteristics– Medium and long term– Linear optimization– Simulation of availability of generation or transmission elements – Simulation of agents’ bids– Hydro scheduling in regulated markets– Scenarios for hydro inflows and fuel prices– Transmission network DC load flow with ohmic losses– N-1 preventive security criterion– Long term scope– Disaggregation by weeks, periods and load levels


SIMUPLUS• References

Sánchez-Martín, P., Ramos, A. y Alonso, J.F., “Probabilistic Midterm

Transmission Planning in a Liberalized Market”, IEEE Transactions on

Power Systems, Vol. 20, nº 4, Noviembre 2005, pp. 2135-2142


PREMED• Purpose

– Forecast marginal costs and electricity prices in the mid-term• Main characteristics

– PreMed is an hybrid model that combines two different approaches: fundamental and quantitative.

• Fundamental: cost-based dispatch model (LP) used to obtain the theoretical marginal cost in a perfect competition situation and the theoretical optimal schedule of the system. It is also used to estimate future marginal cost s(input for the quantitative model in the forecasting)

• Quantitative: the difference between historic prices and obtained marginal cost (markup) is adjusted by means of statistical techniques (multivariate regression, time series and Neural Networks).

• References– J. García-González, J. Barquín Gil, P. Dueñas, “A hybrid approach for modeling

electricity price series in the medium-term.” 16th Power Systems Computation Conference (PSCC'08) Glasgow, Scotland, July 14-18, 2008.

PreMed


... 2008-09

Estimation of historical marginal

costs

Market simulation(optimization)

Market simulation(optimization)

Estimation of future marginal costs and productions

Statistical analysis(regression + time seris +NN)

Historical data

Prices

Hypothesis about demand, fuel costs, hydro inflows, …

2004 2007


StarNet• Purpose

– Determines the system operation variables that minimize variablecosts for a defined time scope. It determines the unit commitment binary variables and furthermore the unit output and power flow through the network.

– Short and medium-term generation operation– Nodal prices, nodal factors.

• Main characteristics– Generalized unit commitment– Hydro scheduling– Transmission network DC load flow with losses

• References– M. Rey, A. Ramos, P. Sánchez Martín, F. Martínez Córcoles, V. Martín

Corrochano Modelado de las pérdidas óhmicas de transporte en modelosde explotación generación/red a medio plazo V Jornadas Hispano-Lusasde Ingeniería Eléctrica 2: 885-891 Salamanca, España Julio 1997

– http://www.iit.upcomillas.es/~aramos/starnet.htm


SECA• Purpose

– Evaluation of capacity bids for exchange between areas– Price determination for transmission capacity auctions for different time

scopes– Hydrothermal multiarea dispatch with transmission network

• Main characteristics– Mixed integer linear model– Hydro scheduling– Scenarios for hydro inflows and fuel prices– Minimum load of thermal units– Pumped hydro units– Transmission network DC load flow– Medium term scope with disaggregation in months and load levels

• References– P. Sánchez, A. Campos Marginalistic Bidding for Cross Border Transmission

Capacity XIV Congreso Latino Ibero Americano de Investigación de Operaciones(CLAIO 2008) Cartagena de Indias, Colombia September 2008


FLOP• Purpose

– Compute reliability indexes:• Expected Energy Non Served (EENS)• Loss Of Load Probability (LOLP)

– Determine firm capacity of any unit.• Main characteristics

– Probabilistic simulation– ELDC convolution– Excel based

• Reference– http://www.iit.upcomillas.es/~aramos/flop.htm

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

Some IIT Operations Research Models for Electricity Markets

INSTITUTO DE INVESTIGACIÓN TECNOLÓGICA

Andrés Ramoshttp://www.iit.upcomillas.es/~aramos/

[email protected]

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Some IIT Operations Research Models for Electricity Markets · PDF fileSome IIT Operations Research Models for Electricity Markets ... – Equivalent quadratic problem ... Some IIT