## Invited Session Fri.3.MA 549

#### Friday, 15:15 - 16:45 h, Room: MA 549

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

### Stochastic equilibria in energy markets II

**Chair: Daniel Ralph**

**Friday, 15:15 - 15:40 h, Room: MA 549, Talk 1**

**Juan Pablo Luna**

Finding equilibrium prices for energy markets with clearing conditions

**Coauthors: Claudia Sagastizábal, Mikhail Solodov**

**Abstract:**

Energy markets often involve a large number of agents, responsible for production, transportation, storing, or consumption of items such as generated power, distributed energy, stored gas.

We analyze an equilibrium model for a market whose agents seek to maximize profits by selling items through a network at a price determined by market clearing.

This type of market can be modelled as a large complementarity problem, obtained by gathering the agents profit-maximization conditions together with the market-clearing relation.

We consider an alternative model formulated as a generalized Nash equilibrium problem, with agents seeking to minimize costs instead of maximizing profits. Interestingly, this alternative formulation turns out to be equivalent to the more common complementarity model mentioned above. At the same time, it reduces substantially the size of the variational problem and is amenable to decomposition schemes, thus making it possible to consider more realistic situations dealing, for example, with uncertainty and risk for large gas or power networks.

**Friday, 15:45 - 16:10 h, Room: MA 549, Talk 2**

**Ozge Ozdemir**

Generation capacity investments in electricity markets: Perfect competition

**Coauthors: Gul Gurkan, Yves Smeers**

**Abstract:**

We focus on perfectly competitive electricity markets with alternative resource adequacy mechanisms: with VOLL pricing, additional capacity market, and operating-reserve pricing.We model each firm's problem as a two-stage problem where generation capacities are installed in the first stage and generation takes place in future spot market at the second stage.When future spot market conditions are not known in advance (i.e., uncertain demand), we have a stochastic equilibrium model. We assess the extent to which these stochastic equilibrium models can be cast into a two-stage stochastic program. In case of all the market mechanisms except operating- reserve pricing, an equilibrium point can be found by solving a two-stage stochastic program.This provides the prevalence of stochastic programming for solving stochastic equilibrium models.For operating-reserve pricing, while the formulation of an equivalent stochastic optimization problem is possible when operating reserves are based on observed demand, this simplicity is lost when operating-reserves are based on installed capacities.We illustrate how all these models can be numerically tackled by using the framework of sample path method.

**Friday, 16:15 - 16:40 h, Room: MA 549, Talk 3**

**Daniel Ralph**

Risk averse long term capacity equilibria: An optimization formulation extending MARKAL

**Coauthor: Yves Smeers**

**Abstract:**

Linear Programming (LP) and other optimization models are standard & useful for long term capacity equilibria, eg, MARKAL for energy capacity equilibria. Such models:

\begin{compactitem}[-]

assume Perfect competition

can handle uncertainty via risk neutral valuation, ie, expectation with respect to given probability density.

\end{compactitem}

Our main result is that risk aversion can be included in LP/optimization models for long term capacity equilibria:

\begin{compactitem}[-]

assuming Perfect competition

where valuation of uncertain assets is modelled by Coherent Risk Measures

by using financial securities which are traded in a Complete Risk Market

\end{compactitem}