Decomposition coordinating method for the solution of a multi-area power system dynamic optimisation problem incorporating distributed generation sources.

This research investigates the optimal coordination of wind and thermal power generation in single- and multi-area systems using advanced economic dispatch formulations and optimization methods. A comprehensive literature review was conducted to examine existing problem formulations, methodologies, and algorithms applied to hybrid power systems, including wind-thermal, wind-diesel, wind-PV, and hydrothermal configurations.The study first develops a rigorous mathematical formulation for the wind-thermal economic emission dispatch (WEED) problem in a single-area power system, explicitly incorporating operational constraints and emission considerations. The formulation is then extended to a multi-area wind-thermal economic dispatch (WTED) problem, where inter-area power exchange and tie-line constraints are modelled to reflect realistic interconnected grid conditions.Two optimization techniques are developed and implemented: the Lagrange multiplier method, representing a conventional analytical approach, and the Particle Swarm Optimization (PSO) method, representing a modern metaheuristic algorithm. Both methods are applied to the single-area and multi-area WTED problems. To facilitate computational analysis, MATLAB-based software is developed for each approach, including a decomposition-based framework for the multi-area case to enhance scalability and solution efficiency.The developed methods are tested on standard IEEE benchmark systems, and the obtained results are compared with existing solutions reported in the literature. The comparative analysis demonstrates the accuracy, robustness, and computational efficiency of the proposed approaches. The findings provide valuable insights into optimizing hybrid wind-thermal power systems, advancing sustainable, economically efficient power generation strategies.