A large number of iterations and oscillation are those of the major concern in solving the economic load dispatch problem using the Hopfield neural network. This paper develops two different methods, which are the slope adjustment and bias adjustment methods, in order to speed up the convergence of the Hopfield neural network system. Algorithms of economic load dispatch for piecewise quadratic cost functions using the Hopfield neural network have been developed for the two approaches. The results are compared with those of a numerical approach and the traditional Hopfield neural network approach. To guarantee and for faster convergence, adaptive learning rates are also developed by using energy functions and applied to the slope and bias adjustment methods. The results of the traditional, fured learning rate, and adaptive learning rate methods are compared in economic load dispatch problem.

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This paper proposes a novel structure of a power system stabilizer (PSS) to improve the stability of synchronous generators (SGs) in microgrids. Microgrids are relatively vulnerable in terms of stability due to their small size and low inertia. The rotational inertia and voltage support of SGs are highly suitable for getting over the vulnerabilities of microgrids, but there exist weaknesses in low-frequency oscillations (LFOs) and limitations of synchronization due to electromagnetic characteristics. Therefore, we study how to accommodate the features of microgrids in the PSS of SGs and further enhance present advantages. The PSS proposed in this paper not only damps out LFOs by conventional lead-lag compensation but also provides additional damping torque according to the magnitude of the perturbation using a synchronous impedance characteristic (SIC). The proposed Lyapunov energy-function-based control strategy can also increase the synchronizing power of the SG to improve transient stability. For performance verification, we use parameters obtained by the particle swarm optimization (PSO) algorithm to compare the existing PSS with the proposed one and analyze them. The effect of the proposed micro-power system stabilizer (µPSS) is analyzed through frequency response analysis, and finally, small-signal stability analysis and the performance of transient stability are verified by time-domain simulation (TDS) on MATLAB/Simulink.

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