Data-Driven Modelling and Control for Smart Energy Systems

In the energy systems there are multiple participants that take different actions. For example, some consumers might change their demand given a change in the electricity price, or some gen-erators might offer less power to the grid if they cannot make a profit. This kind of behavior is for-malized in what is known as a game, where each player choses and action from different alterna-tives. Usually, it is considered that players act in a selfish way since they try to maximize their own utility, e.g., the profit, the comfort level, the energy savings, etc. In each game, there is a point where each player will not change their action. I.e., an equilibrium is reached. When the game reaches this state, if a player made a different choice, the utility would deviate from the best one that can be obtained, being it a non-rational choice. On the other hand, the optimal outcome of a game is that set of actions made by players that achieve the best joint utility. Under this optimality point, there is the possibility of players being able to make their utility better by choosing another action. I.e., the optimal and equilibrium setting are not necessarily the same. This is well known in literature and there is a metric named price of anarchy (PoA) to measure it, which can be seen as the inefficiency of the equilibrium respect to the optimal point. Although PoA has been introduced, its characterization for energy systems, and especially power systems, is limited and follows ad-hoc proofs. For this reason, in this PhD is expected to develop a generalized methodology to charac-terize the PoA of energy systems when defied as games.

Once the PoA is characterized, the game theoretic control can be used to generate incentives that modify the utility of each of the players. This enables to control of the equilibrium point, and therefore the possibility to make the equilibrium and the optimal point be the same, or at least, closer one to each other. During the PhD, is expected to develop the adequate control algorithms to make the equilibrium and optimal points be as close as possible, and ideally, the same.