Grid-aware Stochastic Game modeling of residential electric flexibility under incentives

Abstract

We consider a community of households owning electrical assets that can be operated as flexible loads, such as an electric vehicle, a heat pump with thermal storage and a stationary battery. Automated agents are tasked with the management of flexibility under a variable time-of-use tariff with the goal of maximizing final user utility. A population of homogeneous automated agents with similar interests, managing flexibilities of the same nature, runs the risk of stressing the grid through excessively synchronized actions, and this interaction among the agents has to be taken into account. We model this environment as a Stochastic Game, developing a formulation of the state and action spaces and obtaining the transition probability matrix. The probabilities involved are fitted on real or realistic synthetic data. Leveraging the particular structure of the problem, we propose a two-step solution method similar to policy iteration, that proves capable of producing sensible solutions. Finally, we provide an example of flexibility steering through the modulation of the time-of-use tariff, investigating the effectiveness of the incentive depending on its entity and the model parameters that characterize punishment for overcoordination and user satisfaction, and we illustrate how the tool could be employed in a real Energy Community.