Ability and limitations of optimization models for computing

Ability and limitations of optimization models for computing the equilibrium in competitive energy markets Kris Poncelet, Steffen Kaminski, Erik Delarue

Motivation • Deregulation of energy markets → introduction of competitive markets • Decisions (investment and operational) made by private companies → no central authority apparent for maximizing total welfare • Optimization models are limited calculating the competitive market equilibrium → equilibrium modelling approaches gain popularity 2 TME

When can an equilibrium problem be cast into an optimization problem? * Ø Inherent assumption Ø Mathematical conditions 3 * We restrict our work to imperfect energy markets in which no agent behaves strategically TME

Limitations of optimization models (1) for a generation company: CQ Cost minimization problem Linking constraint: 4 Market Exogen. Cost/values (dual) Constr. TME

Limitations of optimization models (2) • CQ Cost minimization problem • 5 Market Exogen. Cost/values (dual) Constr. TME

Limitations of optimization models (3) • • A paid-as-cleared market is implicitly formed around every linking constraints 6 TME

Inherent Assumptions made in optimization models 1. Endogenously determined prices apply to all (agents’) variables contributing to the linking constraint 2. Endogenously determined market prices do not directly influence the values of variables not appearing in the corresponding linking constraint 3. All agents have the same valuation of the revenues or costs related to the participation in a certain market formed around a linking constraint 4. the decision space of each agent is not dependent on the endogenously determined market prices 7 TME

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Derivation of necessary conditions • 9 TME

Conditions for assuring equality between optimization and equilibrium problems • 10 TME

Methodology: Determining the existence of an optimization problem equivalent to the equilibrium problem 1. Formulate the objective function of all agents involved 11 2. Formulate linking constraints 3. Check whether the inherent assumptions 1 -3 hold / check whether Condition 1 holds 4. Formulate Agents’ constraints 5. Check whether inherent assumption 4 / check whether Condition 2 holds TME

Example problems restricted to equilibrium modelling: Net metering Consumer: Generation Company: Linking constraint: 12 Inherent Assumption 1: Endogenously determined prices apply to all (agents’) variables contributing to the linking constraint TME

13 Questions? Contact: Kris Poncelet: kris. poncelet@kuleuven. be Steffen Kaminski: steffen. kaminski@kuleuven. be Erik Delarue: erik. delarue@kuleuven. be TME