Economic dispatch (ED) is one of the most important problems in terms of energy planning, management, and operation in power systems. This study presents a snow ablation optimizer (SAO) algorithm developed with the fuzzy-based fitness–distance balance (FFDB) method for solving ED problems in small-, medium- and large-scale electric power systems and determining the optimal operating values of fossil fuel thermal generation units. The FFDB-based SAO algorithm (FFDBSAO) controls early convergence problems through balancing exploration–exploitation and improves the solving of high-dimensional optimization problems. In the light of extensive experimental studies conducted on CEC2020, CEC2022, and classical benchmark test functions, the FFDBSAO2 algorithm has shown superior performance against its competitors. Wilcoxon and Friedman’s statistical analysis results confirm the performance and efficiency of the algorithm. Moreover, the proposed algorithm significantly reduces total fuel cost by optimizing fossil fuel thermal generation units. According to the results, the scalability and robustness of the algorithm make it a valuable tool for solving large-scale optimization problems in the planning of electric power systems.

In this study, firstly, the balance between the exploration and exploitation capabilities of the weighted mean of vectors (INFO) algorithm was developed using the fitness–distance balance (FDB) method. Then, the FDB-INFO algorithm was developed with a hyper-heuristic method to create the beginning optimal population by using Linear Population Reduction Success History-based Adaptive Differential Evolution (LSHADE) and a novel Hyper-FDB-INFO algorithm was presented. Finally, the developed Hyper-FDB-INFO algorithm was applied to solve the optimal placement and sizing of FACTS devices for the optimal power flow (OPF) problem incorporating wind energy sources. Moreover, determining the placement and sizing of FACTS devices is an additional problem to minimize the total cost of generation and reducing the power losses of the power system. The experimental results showed that the Hyper-FDB-INFO algorithm is a more effective solver than the SHADE-SF, INFO, FDB-INFO and Hyper-INFO algorithms for wind power and FACTS devices integrating the OPF problem.

Generators used in multi-machine power systems are very affected by transient situations such as malfunctions and line breaks. In transient situations, the system becomes unstable, and oscillations increase. In particular, order modeling of synchronous generators effectively eliminates transient stability situations. To analyze this in the best way, a small signal stability analysis is performed. This study was carried out in the MATLAB-based Power Systems Analysis Program (PSAT), using the 2nd-order and 5th-order models of the synchronous generator for small signal stability analysis in a 3-machine 9-bus power system. While the 2nd-order model is used as the traditional model in synchronous generators, the 5th-order model has been developed as a dynamic order model. Especially in the 5th-order model, it was developed based on a sub-temporal model for better damping of the system. In the comparisons made in both order models, the real and imaginary values and participation factors are shown in figures, while the eigenvalues, damping percentage, frequency, dominant values, and operating modes are presented in tables. By using both order models in the synchronous generator, the number of eigenvalues of the system was determined. The results obtained showed that the 5th-order model gave better results in small signal stability analysis.