Modern power systems have become increasingly complex, making the detailed modeling and analysis of large-scale networks computationally demanding and often impractical. Therefore, network reduction techniques are essential for representing a smaller area of interest while preserving the electrical behavior of the complete system. For electromagnetic transient (EMT) studies, such as load rejection analysis, reduced networks are commonly derived using classical methods like Kron reduction under maximum power transfer conditions. However, this approach can lead to discrepancies in load flow and short-circuit levels between the reduced and complete systems. In addition, Kron reduction may introduce negative resistances in the reduced-order model, compromising system stability by producing non-passive equivalents and potentially causing unrealistic or numerically unstable EMT simulations. To address these limitations, this paper proposes an optimization-based approach, termed PSO-OPF-Kron, which integrates Optimal Power Flow (OPF) with the Particle Swarm Optimization (PSO) algorithm to refine the equivalent network parameters. The method optimally determines power injections, bus voltages, transformer tap settings, and impedances to align the reduced model with the full system’s operating point and short-circuit levels. Validation on the IEEE 39-bus system demonstrates that the proposed method significantly improves accuracy and numerical stability, ensuring reliable EMT simulations for load rejection studies.

This paper proposes a methodology for the day-ahead operational planning of isolated microgrids equipped with renewable distributed generation based on solar photovoltaic and wind generation systems, energy storage systems, and diesel generation as backup power sources. As one of the main contributions of this paper, the proposed methodology is based on optimal power flow (OPF), considering cost minimization as the objective function that combines probabilistic costs of the renewable distributed generation systems with the determinist cost associated with the degradation of the battery bank. In addition, the cost of fuel consumption associated with the diesel generator is also considered. The costs associated with the renewable distributed generation are modeled by probability density functions, where a reserve cost for overestimation and a penalty cost for underestimation of the output power from these renewable sources are adopted. Hence, the proposed OPF avoids the over/underestimation of the available day-ahead solar and wind generations. The differential evolution optimization technique was used to solve the proposed OPF formulation and to obtain a minimum cost of operation considering the deterministic load profile for the operation of the microgrid under study. The proposed formulation was tested for different solar photovoltaic and wind generation scenarios in a microgrid in Lençóis Island, Brazil, another important contribution of the paper. The obtained results showed that the considered microgrid's day-ahead planning is sensitive to climatic conditions that impact the generation scenario and minimize long-term operating costs.