Optimal Reactive Power Dispatch with Voltage-Dependent Loads Using an Enhanced Butterfly Optimization Algorithm

This paper presents an Algorithm for solving the Optimal Reactive Power Dispatch problem under exponential load modeling. Traditional formulations assume constant power demands, which neglect the voltagedependent nature of real-world loads. In this work, we incorporate an exponential load model that accurately represents residential, commercial, industrial, and rural consumption patterns. The proposed EBOA combines the standard BOA with crossover mechanisms to improve exploration and exploitation capabilities. The algorithm is tested on the IEEE 30-bus system using both the traditional constant-power model and the proposed exponential load representation. Compared to conventional constant-power modeling, the exponential model reduces active power losses by up to 24.7%, improves voltage deviation by 91.1%, and enhances voltage stability by approximately 38% in the IEEE 30-bus system. These results highlight that incorporating voltage-dependent characteristics leads to more realistic and economically efficient reactive power dispatch solutions.