Online Distributed Generalized Nash Equilibrium Seeking of Energy Sharing Markets in Distribution Networks

With the proliferation of distributed generations and energy storage systems, traditional passive consumers in the distribution network have been gradually evolving into “prosumers”, who can both produce and consume energy. To alleviate the energy surplus and shortage problem, energy sharing between prosumers is advocated. This paper investigates an online distributed method to seek the generalized Nash equilibrium (GNE) of the energy sharing market. We first formulate the energy sharing problem as a multi-period generalized Nash game (GNG), which has been proven to have a unique variational GNE (v-GNE) with the same multiplier. Then, the GNG is transformed into an equivalent optimization problem based on the variational inequality, which is further divided into multiple single-period problems under the Lyapunov optimization framework. An online distributed algorithm is introduced to solve the Lyapunov drift problems and consequently seek the v-GNE in a time-varying environment. We prove that the expected performance gap is bounded compared to the deterministic offline v-GNE with perfect uncertainty information, while all the constraints across the entire horizon are maintained. Finally, numerical results with 33 and 123 prosumers validate the performance of the algorithm.