Application of generalized hopfield neural network for the steady state analysis of self-excited induction generators

Abstract

This study proposes a generalized Hopfield neural network (GHNN) for solving the non-linear equations involved in the steady state analysis of Self-Excited Induction Generators (SEIGs). Unlike other neural network architectures, the generalized Hopfield neural network can convert a non-linear equation solving problem into an optimization problem. Moreover, the weights and bias of GHNN can easily be obtained from the coefficients of the non-linear equations to be solved without additional training dataset. Motivated by its simplicity, faster convergence, and global stability properties, this study proposes a GHNN for solving the non-linear equations involved in the steady state analysis of Self-Excited Induction Generators (SEIGs). Moreover, unlike the heuristic algorithms, this approach does not require the boundary values for the unknown parameters (per unit frequency, magnetizing reactance Xm and core loss resistance Rm) of the SEIG to be given as inputs, for initiating the optimization process and it ensures guaranteed convergence. Symbolic programming technique has been employed to form the non-linear equations required for the analysis, thereby eliminating the lengthy derivations involved. The formulated equations are then used to form an energy function and a set of differential equations describing the dynamic behavior of the Hopfield network is obtained from this function. These equations are then solved until the energy function minimizes to zero to arrive at the unknown parameters of the SEIG. Using the energy function equation, the stability analysis of the proposed network has been carried out according to the Lyapunov’s second method of stability, which assures the convergence of the proposed method leading to the solutions. The proposed method has been found to be more efficient than other conventional optimization techniques, in terms of accuracy, number of iterations required and computation time. Experiments have been conducted on a 3.5 kW, 415 V SEIG and the results are shown to be in close agreement with the values predetermined using GHNN. It is also concluded that wind driven SEIGS, will find increased deployment in hybrid renewable energy sources, being applied in several emerging areas.