Power flow solution using a novel generalized linear Hopfield network based on Moore–Penrose pseudoinverse

Abstract

This paper proposes a novel generalized linear Hopfield neural network-based power flow analysis technique using Moore–Penrose Inverse (MPI) to solve the nonlinear power flow equations (PFEs). The Hopfield neural network (HNN) with linear activation function augmented by a feed forward layer is used to compute the MPI. In this work, the inverse of Jacobian matrix in solving the PFEs is determined by including feed forward network along with feedback network. The developed power flow technique is coded in MATLAB, and its effectiveness is tested on well-conditioned IEEE bus systems (9-bus, 14-bus, 30-bus, and 118-bus), naturally ill-conditioned systems (11-bus and 13-bus), and real-time Malaysian 87-bus system. The results of voltage magnitude and phase angle obtained are compared with standard Newton–Raphson method in case of well-conditioned system. Further, the sensitivity analysis of this approach is carried out against change in initial conditions, line outage, and increase in power generation to validate its robustness. The computational cost of convergence time is compared with well-known power flow techniques of Modified HNN, fourth-order Runge–Kutta (RK4), Iwamoto, and Euler method. The convergence of solution obtained from proposed technique is ensured by Lyapunov notion of stability.