In this paper, we consider microgrids that interconnect prosumers with distributed energy resources and dynamic loads. Prosumers are connected through the microgrid to trade energy and gain profit while respecting the network constraints. We establish a local energy market by defining a competitive equilibrium which balances energy and satisfies voltage constraints within the microgrid for all time. Using duality theory, we prove that under some convexity assumptions, a competitive equilibrium is equivalent to a social welfare maximization solution. Additionally, we show that a competitive equilibrium is equivalent to a Nash equilibrium of a standard game. In general, the energy price for each prosumer is different, leading to the concept of locational prices. We investigate a case under which all prosumers have the same locational prices. Additionally, we show that under some assumptions on the resource supply and network topology, locational prices decay to zero after a period of time, implying the available supply will be more than the demand required to stabilize the system. Finally, two numerical examples are provided to validate the results, one of which is a direct application of our results on electric vehicle charging control.

翻译：在本文中，我们研究了互连产消者、分布式能源资源和动态负载的微电网。产消者通过微电网连接以交易能源并获取利润，同时需满足网络约束。我们通过定义一种竞争均衡来建立本地能源市场，该均衡能在所有时刻平衡微电网内的能源并满足电压约束。利用对偶理论，我们证明在特定凸性假设下，竞争均衡等价于社会福利最大化解。此外，我们证明竞争均衡等价于标准博弈中的纳什均衡。通常情况下，每个产消者的能源价格不同，由此引出位置电价的概念。我们研究了所有产消者具有相同位置电价的情况，并证明在资源供给与网络拓扑结构的特定假设下，位置电价在一段时间后衰减至零，表明可用供给将超过系统稳定所需的需求。最后，通过两个数值算例验证了结果，其中一个算例是本文结论在电动汽车充电控制中的直接应用。