Improved Runge–Kutta Optimizer for Energy-Efficient Operation of Active Distribution Systems with EVs and BESS

This paper introduces the Improved Runge–Kutta algorithm (IRUN), an enhanced optimization framework that addresses the limitations of the standard RUN method. By integrating success-history adaptation, an external archive, and linear population reduction, IRUN achieves a more effective exploration–exploitation balance, leading to faster and more stable convergence. Evaluations on twenty-three unimodal, multimodal, and composite benchmark functions confirm that IRUN consistently outperforms RUN, achieving markedly lower median errors, narrower interquartile ranges, and more reliable convergence trajectories. In a real-world 136-bus distribution system, IRUN reduces active and reactive power losses by 1.6%, lowers maximum and daily utility energy consumption by 5.9% and 2.5%, and produces smoother, more coordinated charging behavior for distributed BESS units. Voltage-quality indicators—including minimum/maximum voltages and total voltage deviation—demonstrate improved regulation and enhanced system stability, while convergence time is reduced by 16.3%, reinforcing IRUN’s suitability for real-time operational environments. Overall, the combined benchmark and distribution-system results establish IRUN as a robust, accurate, and computationally efficient optimization strategy for next-generation smart distribution networks.