We study a multiperiod optimal power flow (OPF) problem in unbalanced three-phase radial distribution networks with batteries. To address this problem, we first take the resistance-line battery model that treats lossy batteries by adding resistive lines and virtual buses. Then, we derive a linearization for the power flow equations, called generalized three-phase simplified DistFlow, which accounts for shunt elements. Also, it is exact at a freely chosen point while having globally good performance. Using it, we extend the heuristic iterative OPF algorithm, CoDistFlow, to unbalanced three-phase networks. At convergence, three-phase CoDistFlow gives a solution that satisfies the exact nonlinear power-flow equations and the exact security constraints. To theoretically guarantee the convergence of three-phase CoDistFlow, we develop the forced convergent three-phase CoDistFlow. Moreover, we show how to adapt the three-phase CoDistFlow to solve a scenario-based OPF in the presence of uncertainties, whereas other existing OPF solution methods may not offer this possibility. Finally, we perform evaluations on the IEEE 123-bus test feeder and comparisons with Ipopt.

中文翻译：

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储能三相径向配电网络最优潮流的求解。

我们研究了带有电池的不平衡三相径向配电网中的多周期最优潮流（OPF）问题。为了解决这个问题，我们首先采用电阻线电池模型，该模型通过添加电阻线和虚拟总线来处理有损电池。然后，我们导出了潮流方程的线性化，称为广义三相简化DistFlow，它考虑了分流元件。而且，它在自由选择的时间点上具有精确性，同时具有全局良好的性能。使用它，我们将启发式迭代OPF算法CoDistFlow扩展到不平衡的三相网络。收敛时，三相CoDistFlow提供的解决方案可以满足精确的非线性潮流方程和精确的安全约束。为了从理论上保证三相CoDistFlow的收敛，我们开发了强制收敛的三相CoDistFlow。此外，我们展示了如何在不确定性的情况下使三相CoDistFlow适应基于场景的OPF，而其他现有的OPF解决方案可能无法提供这种可能性。最后，我们在IEEE 123总线测试馈线上进行评估，并与Ipopt进行比较。