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

**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.

Talk 1 of the invited session Fri.3.MA 549

**"Stochastic equilibria in energy markets II"** [...]

Cluster 18

**"Optimization in energy systems"** [...]