Dynamic economic dispatch of multi-area wind-solar-thermal power systems with fractional order comprehensive learning differential evolution

The significance of multi-area dynamic economic dispatch (MADED) is amplified by the integration of wind and solar energy sources which introduces considerable fluctuations. In this work, a MADED model incorporating wind and solar energy is developed. Weibull and lognormal distributions are employed to characterize their uncertainty, respectively. The over/underestimation technique is then employed to model the uncertainty. To resolve the model, an enhanced variant named FORCL-LSHADE by incorporating refined comprehensive learning (RCL) strategy, fractional order mutation, RCL-based crossover, and RCL-based parameter tuning is presented. FORCL-LSHADE overcomes the premature convergence issues of LSHADE while preserving robust convergence and maintaining population diversity. Comparative results across two MADED systems and a practical system in China, considering scenarios with and without wind and solar, demonstrate that FORCL-LSHADE offers a significant competitive advantage over other algorithms. It achieves cost reductions of 214.64$, 59394.55$, and 2657.10$ in Case (i), and 228.38$, 57045.64$, and 2993.28$ in Case (ii). It also exhibits faster convergence, reaching final solutions at 10 %, 22.5 %, and 70 % of function evaluations in Case (i), and 10 %, 20 %, and 70 % in Case (ii). Its standard deviation is only 4.25 %, 36.87 %, and 44.99 % of LSHADE's in Case (i), and 3.91 %, 34.43 %, and 36.81 % in Case (ii).