power system state estimation through optimal pmu placement and neural network using whale algorithm

The efficient operation and planning along with security of power systems have always occupied an important position. the power system becomes increasingly complex due to the rapidly growth in energy demand. such a system requires a real-time approach to monitoring and control. therefore, state estimation (se) tools are necessary, especially for nonlinear power grids. most of network applications use the real-time data provided by the state estimator. therefore, an optimal performance of state estimation output is the ultimate concern for the system operator. this need is particularly more in focus today due to deregulated and congested systems and smart grid initiatives. the output of the state estimator nearly represents a true state of the system. the present paper, describes the general framework of state estimation in power networks. also, in the present study linear state estimation method accompanied by optimal placement for phasor measurement unit (pmu) for complete observability and artificial neural network (ann) trained by whale optimization algorithm (woa) is employed. the trained model can be used to estimate voltage magnitudes and phase angles as power system states. the proposed method increases accuracy and execution speed while the complication in the formulation will be reduced considerably. a seasonal load profile is considered to measure the accuracy of the state estimation and make the simulation more realistic. finally, the minimum estimation error will be shown for ieee 14 and 30 buses benchmark.