There is a knowledge gap about the development of optimal coordination of microgrids, which considers all N-1 contingencies by using the smart selection of standard relay characteristics. This paper tries to fill such a knowledge gap by contributing to introduce a novel method to optimize the coordination of microgrids’ directional overcurrent relays (DOCRs), which smartly selects the time-current characteristic of relays and considers all system topologies. Achieving an optimal protection scheme of microgrids without any selectivity constraint under various topologies is the main purpose of this research. The proposed objective function of total operating time of DOCRs under various system topologies is linearized as the TDSs. The hybrid heuristic-linear programming algorithms (HHLPAs) are used to solve the mixed-integer non-linear programming (MINLP) problem. The decrease in the number of heuristic algorithm’s decision variables improves the performance of the proposed HHLPAs. The soft computing-based comparison of the hybrid genetic algorithm-linear programming (GA-LP) and the hybrid particle swarm optimization-linear programming (PSO-LP) is another contribution of this paper. About 80% decrease in the DOCRs’ operating time has been achieved by applying the proposed smart selection of standard relay characteristics (normally inverse, very inverse, and extremely inverse) in comparison to use of just normally inverse curve based on existing methods. The satisfaction of coordination constraints of optimum relay settings is validated based on the DIgSILENT protection simulations.

关于微电网优化协调的发展存在知识鸿沟，它通过使用标准继电器特性的智能选择来考虑所有N-1偶然性。本文试图通过引入一种新颖的方法来优化微电网的定向过电流继电器（DOCR）的协调性，从而填补这一知识空白，该方法巧妙地选择了继电器的时电流特性并考虑了所有系统拓扑。本研究的主要目的是在各种拓扑下实现无选择性约束的微电网最优保护方案。所建议的各种系统拓扑下DOCR的总运行时间的目标函数被线性化为TDS。混合启发式线性规划算法（HHLPA）用于解决混合整数非线性规划（MINLP）问题。启发式算法决策变量数量的减少提高了所提出的HHLPA的性能。混合遗传算法-线性规划（GA-LP）和混合粒子群优化-线性规划（PSO-LP）的基于软计算的比较是本文的另一项贡献。与基于现有方法的正常反曲线相比，通过采用建议的标准继电器特性（正常反，非常反和极反）智能选择，可以减少DOCR的工作时间约80％。