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This paper aims to find the minimum possible number of phasor measurement units (PMUs) to achieve maximum and complete observability of the power system and improve the redundancy of measurements, in normal cases (with and without zero injection bus [ZIB]), and then in conditions of a single PMU failure and outage of a single line.

An efficient approach operates adequately and provides the optimal solutions for the PMUs placement problem. The finest function of optimal PMUs placement (OPP) should be mathematically devised as a problem, and via that, the aim of the OPP problem is to identify the buses of the power system to place the PMU devices to ensure full observability of the system. In this paper, the grey wolf optimizer (GWO) is used for training multi-layer perceptrons (MLPs), which is known as Grey Wolf Optimizer (GWO) based Neural Network (“GW-NN”) to place the PMUs in power grids optimally.

Following extensive simulation tests with MATLAB/Simulink, the results obtained for the placement of PMUs provide system measurements with less or at most the same number of PMUs, but with a greater degree of observability than other approaches.

The efficiency of the suggested method is tested on the IEEE 14-bus, 24-bus, New England 39-bus and Algerian 114-bus systems.

This paper proposes a new method for placing PMUs in the power grids as a multi-objective to reduce the cost and improve the observability of these grids in normal and faulty cases.