WSEAS Transactions on Power Systems
Print ISSN: 1790-5060, E-ISSN: 2224-350X
Volume 21, 2026
Optimal Reactive Power Dispatch with Voltage-Dependent Loads using an
Enhanced Butterfly Optimization Algorithm
Authors: ,
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Abstract: 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.
Keywords:
Optimal Reactive Power Dispatch (ORPD), Exponential Load Model, Voltage-Dependent Loads, Enhanced Butterfly Optimization Algorithm (EBOA), Metaheuristics, Power Loss Minimization, Voltage Stability, IEEE 30-Bus System
Pages: 82-92
DOI: 10.37394/232016.2026.21.8