Including complementarity constraints in energy storage system (ESS) models in optimization problems ensure an optimal solution will not produce a physically unrealizable control strategy where there is simultaneous charging and discharging. However, the current approaches to impose complementarity constraints require the use of non-convex optimization methods. In this paper, we propose a convex relaxation for a common ESS model that has terms for both charging and discharging based on a penalty reformulation for use in a model predictive control (MPC) based optimal power flow (DC OPF) problem. In this approach, the complementarity constraints are omitted and a penalty term is added to the optimization objective function. For the DC OPF problem, we provide analysis for the conditions under which the convex relaxation of the complementarity constraint ensures that a solution with simultaneous ESS charging and discharging operation is suboptimal. Simulation results demonstrating ESS behavior with and without the penalty reformulation are provided for an MPC-based DC OPF problem on multiple IEEE test systems.

中文翻译：

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DC OPF中具有互补约束的并网储能系统模型的凸松弛

在优化问题中包括能量存储系统（ESS）模型中的互补性约束，可确保最佳解决方案不会在同时充放电的情况下产生物理上无法实现的控制策略。但是，当前施加互补性约束的方法需要使用非凸优化方法。在本文中，我们提出了一种基于罚函数重整的，具有充放电条件的通用ESS模型的凸松弛，用于基于模型预测控制（MPC）的最佳潮流（DC OPF）问题。在这种方法中，省略了互补性约束，并将惩罚项添加到了优化目标函数。对于DC OPF问题，我们对互补约束的凸松弛条件进行了分析，以确保同时进行ESS充放电操作的解决方案不是最优的。针对在多个IEEE测试系统上基于MPC的DC OPF问题，提供了演示有无罚则重构的ESS行为的仿真结果。