Junkai Hu

Junkai Hu, Li Xia

Efficiency and reliability are both crucial for energy management, especially in multi-microgrid systems (MMSs) integrating intermittent and distributed renewable energy sources. This study investigates an economic and reliable energy management problem in MMSs under a distributed scheme, where each microgrid independently updates its energy management policy in a decentralized manner to optimize the long-term system performance collaboratively. We introduce the mean and variance of the exchange power between the MMS and the main grid as indicators for the economic performance and reliability of the system. Accordingly, we formulate the energy management problem as a mean-variance team stochastic game (MV-TSG), where conventional methods based on the maximization of expected cumulative rewards are unsuitable for variance metrics. To solve MV-TSGs, we propose a fully distributed independent policy gradient algorithm, with rigorous convergence analysis, for scenarios with known model parameters. For large-scale scenarios with unknown model parameters, we further develop a deep reinforcement learning algorithm based on independent policy gradients, enabling data-driven policy optimization. Numerical experiments in two scenarios validate the effectiveness of the proposed methods. Our approaches fully leverage the distributed computational capabilities of MMSs and achieve a well-balanced trade-off between economic performance and operational reliability.

Junkai Hu, Li Xia

We study a long-run mean-variance team stochastic game (MV-TSG), where each agent shares a common mean-variance objective for the system and takes actions independently to maximize it. MV-TSG has two main challenges. First, the variance metric is neither additive nor Markovian in a dynamic setting. Second, simultaneous policy updates of all agents lead to a non-stationary environment for each individual agent. Both challenges make dynamic programming inapplicable. In this paper, we study MV-TSGs from the perspective of sensitivity-based optimization. The performance difference and performance derivative formulas for joint policies are derived, which provide optimization information for MV-TSGs. We prove the existence of a deterministic Nash policy for this problem. Subsequently, we propose a Mean-Variance Multi-Agent Policy Iteration (MV-MAPI) algorithm with a sequential update scheme, where individual agent policies are updated one by one in a given order. We prove that the MV-MAPI algorithm converges to a first-order stationary point of the objective function. By analyzing the local geometry of stationary points, we derive specific conditions for stationary points to be (local) Nash equilibria, and further, strict local optima. To solve large-scale MV-TSGs in scenarios with unknown environmental parameters, we extend the idea of trust region methods to MV-MAPI and develop a multi-agent reinforcement learning algorithm named Mean-Variance Multi-Agent Trust Region Policy Optimization (MV-MATRPO). We derive a performance lower bound for each update of joint policies. Finally, numerical experiments on energy management in multiple microgrid systems are conducted.