Game theoretic stochastic energy coordination under a distributed zeroth-order algorithm

Dealing with the effects from uncertainties properly is a key problem in stochastic energy management problems to achieve safe and efficient operation of the system. In this paper, we study the problem of coordinating multi-period electric vehicles charging amidst uncertainty from the embedded renewable generation in a local distribution network under transformer capacity limits. A stochastic generalized game is presented to formulate the underlying electric vehicle coordination problem wherein the cost function of each player is affected by the intermittent renewable energy supply. Existing algorithms for seeking the equilibrium rely on conditions on the form of the cost functions. In our setting, however, stochastic effects are not known in advance which results in an unknown form of the cost functions. We propose a distributed iterative zeroth-order algorithm, which only relies on the observations of costs, to achieve a stochastic generalized Nash equilibrium of the game under the concept of Gaussian smoothing. Under certain mild assumptions, the proposed algorithm is guaranteed to converge to the neighborhood of the stochastic generalized Nash equilibrium. We demonstrate the algorithm for a distribution network energy management problem with 3 heterogeneous subgroups of electric vehicles.