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Pool strategy of an electricity producer with endogenous formation of clearing prices Antonio J. Conejo, Carlos Ruiz University of Castilla-La Mancha, Spain, 2011 Contents Background and Aim Approach Model Features Model

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Pool strategy of an electricity producer with endogenous formation of clearing prices

Antonio J. Conejo, Carlos Ruiz University of Castilla-La Mancha, Spain, 2011

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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Formulation

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Formulation

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Background and Aim

  • Comparatively large number of generating units
  • Units distributed throughout the power network

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Strategic power producer

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Background and Aim

  • Cleared once a day, one-day ahead and on a

hourly basis

  • DC representation of the network including first

and second Kirchhoff laws

  • Hourly Locational Marginal Prices (LMPs)

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Pool-based electricity market

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Background and Aim

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Pool-based electricity market Strategic power producer

Best offering strategy to maximize profit

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Background and Aim

  • Considering the market: MPEC

formulation

  • Considering the real-world: Stochastic

formulation

  • Stochastic MPEC!

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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Formulation

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Approach

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Social Welfare Maximization (Market Clearing)

Profit Maximization

Upper-Level Lower-Level

Bilevel model:

subject to

LMPs Offering curve Dual Variables

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Approach

  • Bilevel model: Optimization problem

constrained by other optimization problem (OPcOP)!

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OPcOP

11

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Approach

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Profit Maximization

Upper-Level

MPEC:

LMPs

KKT Conditions

Offering curve

subject to

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MPEC

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MPEC

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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Structure

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Features

1) Strategic offering for a producer in a pool with endogenous formation of LMPs. 2) Uncertainty of demand bids and rival production

  • ffers.

3) MPEC approach under multi-period, network- constrained pool clearing. 4) MPEC transformed into an equivalent MILP.

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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Formulation

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Deterministic Model

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Upper-Level → Profit Maximization:

Costs - Revenues Ramping Limits Price = Balance dual variable

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Deterministic Model

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Upper-Level → Profit Maximization:

Dual variable

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Deterministic Model

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Lower-Level → Market Clearing

Maximize Social Welfare Power Balance

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Deterministic Model

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Lower-Level → Market Clearing

Price

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Deterministic Model

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Production / Demand Power Limits Transmission Capacity Limits Angle Limits

Lower-Level → Market Clearing

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Deterministic Model

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Lower-Level → Market Clearing

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Deterministic Model

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Lower-Level → Market Clearing → KKT conditions

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Deterministic Model

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Lower-Level → Market Clearing → KKT conditions

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Deterministic Model

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KKT Lower-Level

MPEC model

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Deterministic Model

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The MPEC includes the following non-linearities: 1) The complementarity conditions ( ). 2) The term in the objective function.

Linearizations

   b a

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Deterministic Model

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 

1 , ) 1 (           u M u b uM a b a b a

M Large enough constant (but not too large)

Linearizations → Complementarity Conditions

Fortuny-Amat transformation

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Deterministic Model

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Based on the strong duality theorem and some of the KKT equalities

Linearizations → Term:

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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Formulation

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Stochastic Model

  • Consumers’ bids
  • Rival producers’ offers

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Uncertainty incorporated using a set of scenarios modeling different realizations of:

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Pairs of production quantities ( ) and market prices ( ).

Stochastic Model

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Deterministic model for each scenario

tn Building of the optimal offering curve

S tib

P 

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Stochastic Model

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Optimal

  • ffering

curve

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Stochastic Model

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To ensure that the final offering curves are increasing in price some additional constraints are needed: These constraints link the individual problems increasing the computational complexity of the model.

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Stochastic Model Math Structure

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Stochastic Model Math Structure

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Stochastic Model Math Structure

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  • 1. Direct solution: CPLEX, XPRESS
  • 2. Decomposition procedures (Lagrangian Relaxation)
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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Formulation

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Examples

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Six-bus test system→ electricity network

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Examples

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Six-bus test system→ demand curve

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Examples

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Six-bus test system→ generating units

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Examples

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The maximum power flow through lines 2-4, 3-6 and 4-6 are 269.62, 229.44 and 39.6933 MW respectively

Six-bus test system→ uncongested network results

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Examples

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Six-bus test system→ uncongested network results

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Examples

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Capacity of line 3-6 limited to 230 MW:

Six-bus test system→ congested network results

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Examples

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Capacity of line 3-6 limited to 230 MW:

Six-bus test system→ congested network results

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Examples

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Capacity of line 4-6 limited to 39 MW:

Six-bus test system→ congested network results

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Examples

  • Uncongested network case
  • 8 equally probable scenarios
  • They differ on the rival producer offers ( ) and
  • n the consumer bids ( )
  • Selected to obtain a wide range of prices

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Six-bus test system→ stochastic model

D tdk

O tjb

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Examples

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Six-bus test system→ stochastic model results

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Examples

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Six-bus test system→ stochastic model results

Offering curves for strategic generator 1

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Examples

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Six-bus test system→ stochastic model results

Offering curves for strategic generator 1

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Examples

  • 24 Nodes
  • 8 strategic units
  • 24 non-strategic

units

  • 17 consumers
  • 24 hours

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IEEE One Area Reliability Test System

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Examples

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IEEE One Area Reliability Test System → Results

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Examples

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IEEE One Area Reliability Test System → Results

Marginal cost offer Strategic offer

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Examples

  • Model solved using CPLEX 11.0.1 under GAMS on a

Sun Fire X4600 M2 with 4 processors at 2.60 GHz and 32 GB of RAM.

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Model 6-bus uncongested 6-bus congested 6-bus stochastic IEEE RTS CPU Time [s] 2.91 5.82 204.77 449.33

Computational issues

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Contents

  • Background and Aim
  • Approach
  • Model Features
  • Model Formulation

– Deterministic – Stochastic

  • Examples
  • Conclusions

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Conclusions

  • Procedure to derive strategic offers for a power

producer in a network constrained pool market.

– LMPs are endogenously generated: MPEC approach. – Uncertainty is taken into account. – Resulting MILP problem.

  • Exercising market power results in higher profit and

lower production.

  • Network congestion can be used to further increase

profit.

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Thanks for your attention!

http://www.uclm.es/area/gsee/web/antonio.htm

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Appendix A Computational Issues

  • Model has been solved using CPLEX 11.0.1 under GAMS on a

Sun Fire X4600 M2 with 4 processors at 2.60 GHz and 32 GB

  • f RAM.
  • The computational times are highly dependent on the values
  • f the linearization constants M.

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Model 6-bus uncongested 6-bus congested 6-bus stochastic IEEE RTS CPU Time [s] 2.91 5.82 204.77 449.33

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Appendix A Computational Issues

  • 1. Solve a (single-level) market clearing considering that

all the producers offer at marginal cost.

  • 2. Obtain the marginal value of each relevant constraint.
  • 3. Compute the value of each relevant constant as:

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  100

1 value variable dual    M

Heuristic to determine the value of M:

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Appendix B Stochastic model

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Appendix B Stochastic model

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Appendix B Stochastic model

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