The power flow is usually formulated by nonlinear equations and may present multiple solutions. However, most of these solutions do not represent a practical situation but are mathematical findings. Remarkably, in unbalanced multiphase systems with impedance-grounded loads, a phenomenon can occur where two or more solutions may especially show practical significance. These solutions are called operationally-stable solutions (solutions which for a given loading level the nodal voltages, currents, and losses are feasible) and may be obtained in Distribution Systems (DS). In this paper, some relevant aspects regarding the multiple solutions in unbalanced grounded systems are explored: (i) the development of a simple analytical model considering the feeder and loads to analyze the multiple solutions generically; (ii) a direct procedure for initializing neutral voltages to find possible operationally-stable solutions or reduce the number of iterations to achieve convergence; (iii) a study on multiple solutions using the continuation power flow to analyze their behavior and verify their impacts on DS. The proposed assumptions have been confirmed with numerical experiments over IEEE 123, Simple NEV, and IEEE 8500 test feeders.

中文翻译：

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在不平衡阻抗接地系统中评估多个运行稳定的潮流解决方案：初始化过程和分析

潮流通常由非线性方程式来表示，并且可以提出多种解决方案。但是，这些解决方案中的大多数并不代表实际情况，而是数学上的发现。值得注意的是，在带有阻抗接地负载的不平衡多相系统中，可能会出现一种现象，其中两个或多个解决方案可能特别具有实际意义。这些解决方案称为操作稳定解决方案（对于给定的负载水平，节点电压，电流和损耗可行的解决方案），可以在配电系统（DS）中获得。在本文中，探讨了不平衡接地系统中多种解决方案的一些相关方面：（i）考虑馈线和负载的简单分析模型的开发，以通用方式分析多种解决方案；（ii）初始化中性电压的直接程序，以找到可能的操作稳定的解决方案，或减少迭代次数以实现收敛；（iii）使用持续潮流对多种解决方案进行研究，以分析其行为并验证其对DS的影响。提议的假设已通过IEEE 123，Simple NEV和IEEE 8500测试馈线上的数值实验得到了证实。