*Supervisors: *Athanasios Papakonstantinou, Pierre Pinson,

* *in* **Energy Analytics & Markets group, Centre for Electric Power and Energy, Department of Electrical Engineering*

**Context**

The deployment of stochastic renewable energy sources (RES) e.g. wind and solar power, has been steadily increasing, bringing significant economic and environmental benefits. As renewable generation approaches grid parity, stochastic producers are asked to participate in electricity markets under the rules applied to conventional producers. Although now they may face regulation costs due to imbalances between their day-ahead market offers and real-time production, they can also employ trading strategies in the day-ahead markets that may offset the cost of imbalances.

There has been an increasing scientific interest in addressing such issues with stochastic optimization methods being the most prevalent. Although such approaches bring significant contributions, they have limitations. First, the stochastic producers rely on knowledge that is unlikely to be available to them, such as complete information of the power system’s attributes and access to the predictive distributions of all other stochastic producers, while assuming that they accurately model real-time production. Second, they assume that only a single producer is strategic and capable of devising an optimal strategy, with the rest following without a reaction. That is, they do not capture the inherent dynamics of participating in a market, with the exception being the formulation of the competition among stochastic producers as an equilibrium program with equilibrium constraint. However, such techniques are computationally demanding with reduced tractability, often too complex to be implemented in real-world real-time basis.

**Objectives**

In this context, the main objective of this MSc project is to analyze the behaviour of stochastic producers in electricity markets focusing on the collective impact of the individual actions.

**Methodology**

We model the interactions among stochastic producers as Minority Game, a class of game-theoretic problems that can be used to study market competition among self-interested agents. In a Minority Game, a population of agents has to decide between options A and B with those belonging on the minority group by the end of the game considered as the winners. Naturally, the fact that those belonging in the minority group derive more benefits is very appealing in financial markets, given that market complexity is summarized under the famous mantra: “Sell when everybody is buying and buy when everybody is selling”. This can have applications in power systems, either to model electricity market interactions or congestion in the grid. In both cases it is possible to

bypass the complexity often associated with electricity markets and grid operation by designing intuitive rules that capture the principle of the Minority Game.

**Expected results**

The expected outcome includes relevant literature review and the formulation and improvement of rules based on well-known game-theoretic problems such as the El Farol Bar problem (EFBP). The developed rules will be evaluated on a test system focusing on several aspects of the market clearing i.e. market prices, congestion in network nodes, scheduled and dispatched energy.

**Prerequisites**

Power system operations, electricity markets, basics of optimization, basics of probability theory, python, gurobi are preferred (or matlab, GAMS).