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. Note to Practitioners—In a distribution network with massive prosumers, energy sharing with the main grid and among prosumers is inevitable. With the existence of energy storage systems (ESSs), the energy sharing problem is usually formulated as a multi-period GNG with time-coupling constraints, which needs to be solved online due to the integration of volatile renewable generations. However, the existing online distributed GNE seeking algorithm is usually designed for a single-period problem, which is not applicable to the multi-period GNG. In this paper, we first formulate the energy sharing market as a multi-period GNG, and transform it into an equivalent optimization problem. Then, the online solving algorithm is proposed to solve the equivalent problem under the Lyapunov optimization framework. In this way, the multi-period GNG is finally solved online. Simulations on the IEEE 33-bus benchmark show that the accuracy can be guaranteed in a time-varying environment compared with offline method using full information. Results with the IEEE 123-bus system further validate the scalability of our approach. Besides the application in power systems, our approach is also applicable to other scenarios modeled as multi-period GNGs.