Physics-Informed Neural Network for Load Margin Assessment of Power Systems with Optimal Phasor Measurement Unit Placement

The load margin is an important index applied in power systems to inform how much the system load can be increased without causing system instability. The increasing operational uncertainties and evolution of power systems require more accurate tools at the operation center to inform an adequate system load margin. This paper proposes an optimization model to determine the parameters of a Physics-Informed Neural Network (PINN) that will be responsible for predicting the load margin of power systems. The proposed optimization model will also determine an optimal location of Phasor Measurement Units (PMUs) at system buses whose measurements will be inputs to the PINN. Physical knowledge of the power system is inserted in the PINN training stage to improve its generalization capacity. The IEEE 68-bus system and the Brazilian interconnected power system were chosen as the test systems to perform the case studies and evaluations. Three different metaheuristics called the Hiking Optimization Algorithm, Artificial Protozoa Optimizer, and Particle Swarm Optimization were applied and evaluated in the test system. The results achieved demonstrate the benefits of inserting physical knowledge in the PINN training and the optimal selection of PMUs at system buses for load margin prediction.