The Nash Equilibrium (NE) estimation in bidding games of electricity markets is the key concern of both generation companies (GENCOs) for bidding strategy optimization and the Independent System Operator (ISO) for market surveillance. However, existing methods for NE estimation in emerging modern electricity markets (FEM) are inaccurate and inefficient because the priori knowledge of bidding strategies before any environment changes, such as load demand variations, network congestion, and modifications of market design, is not fully utilized. In this paper, a Bayes-adaptive Markov Decision Process in FEM (BAMDP-FEM) is therefore developed to model the GENCOs' bidding strategy optimization considering the priori knowledge. A novel Multi-Agent Generative Adversarial Imitation Learning algorithm (MAGAIL-FEM) is then proposed to enable GENCOs to learn simultaneously from priori knowledge and interactions with changing environments. The obtained NE is a Bayesian Nash Equilibrium (BNE) with priori knowledge transferred from the previous environment. In the case study, the superiority of this proposed algorithm in terms of convergence speed compared with conventional methods is verified. It is concluded that the optimal bidding strategies in the obtained BNE can always lead to more profits than NE due to the effective learning from the priori knowledge. Also, BNE is more accurate and consistent with situations in real-world markets.

翻译：电力市场竞价博弈中的纳什均衡（NE）估计是发电企业（GENCOs）优化报价策略和独立系统运营商（ISO）实施市场监控的关键问题。然而，现有方法在估计新兴现代电力市场（FEM）的纳什均衡时存在精度低、效率差的问题，其根本原因在于未能充分利用环境变化（如负荷需求波动、网络阻塞及市场设计调整）前已有的报价策略先验知识。为此，本文首先构建了面向FEM的贝叶斯自适应马尔可夫决策过程（BAMDP-FEM），以建模考虑先验知识的发电企业报价策略优化过程。进而提出一种新的多智能体生成对抗模仿学习算法（MAGAIL-FEM），使发电企业能同步从先验知识和与动态环境的交互中进行学习。所获得的均衡解为贝叶斯纳什均衡（BNE），其中蕴含了从先前环境迁移而来的先验知识。算例分析验证了该算法相较于传统方法在收敛速度方面的优越性。研究表明：由于有效学习了先验知识，在所得BNE下的最优报价策略总能获得高于NE的收益。此外，BNE比NE更精确且更符合真实市场运行场景。