Self-excited induction generators (SEIGs) are extensively used in isolated micro-hydro and wind energy systems due to their rugged construction, low maintenance, and inherent short-circuit protection. However, the determination of optimal excitation capacitance remains a challenging nonlinear problem. The capacitor value directly governs voltage buildup, steady-state regulation, operating frequency, and power quality under varying speed and load conditions. This paper proposes a hybrid Grey Wolf Optimizer-Differential Evolution (GWO-DE) algorithm for optimal capacitor value calculation in three-phase SEIGs. The capacitor selection is formulated as a constrained single-objective optimization problem. Three design criteria (voltage-regulation quality, operating-speed range, and capacitor cost) are combined a priori through a fixed weighted-sum scalarization, based on the steady-state per-phase equivalent circuit incorporating core losses and a fifth-order polynomial magnetizing characteristic. An adaptive switching parameter transitions the search from GWO-dominant exploration to DE-dominant exploitation, while an elite archive and stagnation-triggered reinitialization prevent premature convergence. The proposed GWO-DE is benchmarked against PSO, standard GWO, GA, and Nelder-Mead across 24 operating conditions spanning six speed levels and four load levels. All reported optimization metrics are obtained from 30 independent runs. Results demonstrate that GWO-DE achieves 3.07× better mean fitness than PSO, 15.18× better than standard GWO, and 22.92× better than GA, with 38.7% faster convergence than PSO. The optimized capacitor maintains terminal voltage within ±5% of rated value up to 85% load, with voltage THD compliant with IEEE 519 limits. Experimental validation on a 3.7 kW laboratory SEIG prototype using a Fluke 435-II power quality analyzer confirms the predictions with an average error of 2.32%. A capacitor value contour map across the speed-load space is provided as a practical design tool for field installations.
Jadhav et al. (Tue,) studied this question.