Invited Session Fri.2.MA 550

Friday, 13:15 - 14:45 h, Room: MA 550

Cluster 18: Optimization in energy systems [...]

Stochastic equilibria in energy markets I


Chair: Daniel Ralph and Andreas Ehrenmann



Friday, 13:15 - 13:40 h, Room: MA 550, Talk 1

Golbon Zakeri
Models for large consumer peak shaving and the impact on line pricing

Coauthors: Andy Philpott, Michael Todd


We will present a mathematical programming model for a price responsive
electricity user with an option to self generate. We will discuss the properties of this model and time permitting use it in a Stackelberg game where a lines company setting its tariffs is the leader and the user is a follower.



Friday, 13:45 - 14:10 h, Room: MA 550, Talk 2

Gauthier de Maere
Modelling market liquidity in restructured power systems by stochastic Nash and generalized Nash equilibrium

Coauthor: Yves Smeers


The volatility of electricity prices makes its financial derivatives important instruments for asset managers. Even if the volume of derivative contracts traded on Power Exchanges has been growing since the inception of the restructuring of the sector, the liquidity of electricity markets can drastically differ depending on the situation. We analyze the situation by formulating a spatial stochastic equilibrium model of the restructured power sector with a financial market consisting of futures and financial transmission rights. We prove the existence of an equilibrium in a liquid market when the players optimize convex risk measures and show that the futures prices obey a risk neutral valuation property. We then turn to illiquidity and use a definition based on the limitation of transaction volumes. This changes the model into a Generalized Nash equilibrium (GNE) implying that several equilibrium may exist. The non arbitrage property is lost in the illiquid case. Those two features are signs of a badly functioning market. The formalism also allows one to model a market applying bid/ask spreads. Eventually we illustrate these different ideas on a six node example.



Friday, 14:15 - 14:40 h, Room: MA 550, Talk 3

Andreas Ehrenmann
Risk adjusted discounting

Coauthor: Yves Smeers


Capacity expansion models in the power sector were among the first applications of operations research to the industry. We introduce stochastic equilibrium versions of these models that we believe provide a relevant context for looking at the current very risky market where the power industry invests and operates. We then look at the insertion of risk related investment practices that developed with the new environment and may not be easy to accommodate in an optimization context.
Specifically, we consider the use of plant specific discount rates due to different risk exposure.
In a first step we introduce an iterative approach that facilitates the use of exogenously given discount rates within an capacity expansion model. This corresponds to the industry practice of assigning specific hurdle rates.
As a second step we allow for discount rates being set endogenously in the equilibrium model by including stochastic discount rates in the equilibrium model. This approach is compatible with the standard CAPM from finance as long as all agents use the same (market induced) stochastic discount rate. We close with a numerical illustration.


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