Development of a Non-Convex Economic Load Dispatch Across Small to Very Large-Scale Power Systems Using Improved Sine Cosine Algorithm

• Abdultoyyib A. ALABI

  Author

• Adamu S. ABUBAKAR

  Author

• Patrick U. OKORIE

  Author

• Abdulwahab IBRAHIM

  Author

The Economic Load Dispatch (ELD) problem is fundamental to power system operation, requiring the optimal allocation of generation among committed units to minimize fuel cost while satisfying demand and operational constraints. The incorporation of valve-point loading effects (VPLE) introduces non-convex and multimodal characteristics that can cause conventional and standard metaheuristic optimization methods to become trapped in local optima. This study proposes an Improved Sine Cosine Algorithm (ISCA) for solving non-convex ELD problems with VPLE across small-, medium-, large-, and very large-scale power systems. The novelty of ISCA lies in the integration of three complementary mechanisms into the conventional Sine Cosine Algorithm: (i) an adaptive parameter control strategy that dynamically regulates exploration and exploitation, (ii) a Lévy flight-based search mechanism that improves global exploration and facilitates escape from local optima, and (iii) an enhanced power-balance adjustment strategy that enforces the supply-demand equality constraint with high numerical precision. The proposed algorithm is evaluated on five benchmark systems comprising 3, 13, 40, 80, and 140 generating units, with load demands of 850, 2,520, 10,500, 21,000, and 49,342 MW, respectively. For each test system, 30 independent runs are conducted to evaluate solution quality, convergence behavior, robustness, and constraint satisfaction using best and statistical fuel-cost measures, convergence characteristics, cost distributions, and power-balance errors. ISCA obtained best fuel costs of 8,284.67 USD/h, 21,670.76 USD/h, 90,158.27 USD/h, 182,013.39 USD/h, and 428,106.68 USD/h for the 3-, 13-, 40-, 80-, and 140-unit systems, respectively. The observed standard deviations were as low as 0.01 USD/h for the smaller system and remained below 0.05% of the corresponding total generation cost for the 140-unit system, indicating stable performance across repeated runs. In addition, power-balance errors remained below 10⁻¹³ MW, demonstrating accurate satisfaction of the equality constraint. Comparative analysis across the benchmark systems indicates that the proposed enhancements improve the search capability and solution consistency of the conventional SCA, particularly as problem dimensionality increases. Overall, the results demonstrate that ISCA provides a robust and scalable optimization framework for non-convex ELD with VPLE. However, its computational competitiveness should be assessed alongside solution quality using runtime or function-evaluation measures and statistically validated comparisons with established algorithms.

• 62_Alabi et al. (2026)

Copyright (c) 2026 Abdultoyyib A. ALABI, Adamu S. ABUBAKAR, Patrick U. OKORIE, Abdulwahab IBRAHIM (Author)

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.