Optimization of Active Power Supply in an Electrical Distribution System Through the Optimal Integration of Renewable Energy Sources

The sustained growth of electricity demand and the global transition toward low-carbon energy systems have intensified the need for efficient, flexible, and reliable operation of electrical distribution networks. In this context, the coordinated integration of distributed renewable energy resources and demand-side flexibility has emerged as a key strategy to improve technical performance and economic efficiency. This work proposes an integrated optimization framework for active power supply in a radial, distribution-like network through the optimal siting and sizing of photovoltaic (PV) units and wind turbines (WTs), combined with a real-time pricing (RTP)-based demand-side response (DSR) program. The problem is formulated using the branch-flow (DistFlow) model, which explicitly represents voltage drops, branch power flows, and thermal limits in radial feeders. A multiobjective function is defined to jointly minimize annual operating costs, active power losses, and voltage deviations, subject to network operating constraints and inverter capability limits. Uncertainty associated with solar irradiance, wind speed, ambient temperature, load demand, and electricity prices is captured through probabilistic modeling and scenario-based analysis. To solve the resulting nonlinear and constrained optimization problem, an Improved Whale Optimization Algorithm (I-WaOA) is employed. The proposed algorithm enhances the classical Whale Optimization Algorithm by incorporating diversification and feasibility-oriented mechanisms, including Cauchy mutation, Fitness–Distance Balance (FDB), quasi-oppositional-based learning (QOBL), and quadratic penalty functions for constraint handling. These features promote robust convergence toward admissible solutions under stochastic operating conditions. The methodology is validated on a large-scale radialized network derived from the IEEE 118-bus benchmark, enabling a DistFlow-consistent assessment of technical and economic performance under realistic operating scenarios. The results demonstrate that the coordinated integration of PV, WT, and RTP-driven demand response leads to a reduction in feeder losses, an improvement in voltage profiles, and an enhanced voltage stability margin, as quantified through standard voltage deviation and fast voltage stability indices. Overall, the proposed framework provides a practical and scalable tool for supporting planning and operational decisions in modern power distribution networks with high renewable penetration and demand flexibility.