## Load frequency control of a dynamic interconnected power system using generalised Hopfield neural network based self-adaptive PID controller

A novel generalised Hopfield neural network (GHNN) based self-adaptive proportional–integral–derivative (PID) controller for load frequency control (LFC) is designed for a two-area interconnected power system with nonlinearities of generator rate constraint and governor dead band. The control problem is conceptualised as an optimisation problem with an objective function as an area control error in terms of the PID controller parameters. The differential equations governing the behaviour of the GHNN were solved to obtain the controller parameters *K* _{p}, *K* _{i} and *K* _{d}. To test the feasibility and robustness of the proposed controller, the system is tested in the presence of randomness in load demands, imprecisely modelled system dynamics, nonlinearities in the system model and uncertainties in the system parameter variations. The proposed method is simulated using Matlab R2014b/Simulink and the results obtained have shown that the propounded controller performance is superior to the integral, PID and fuzzy-based proportional–integral controllers. In addition, the Lyapunov stability analysis of the overall closed-loop system was carried out and the controller is implemented in real-time digital simulator run in hardware-in-the-loop to validate the effectiveness of the proposed method. Furthermore, the proposed controller is applied to the three-area power system to test its adaptability.