Análise modal da estabilidade de tensão em sistemas trifásicos desequilibrados com geração distribuida

Abstract

This work addresses the problem of voltage stability in electric power distribution systems, focusing on the application of static modal analysis. Traditionally, this methodology is applied to systems modeled under the assumption of three-phase balance, which simplifies the calculations but neglects the operational reality of distribution networks, often subject to significant load and generation unbalances. In this context, the present study proposes the application of static modal analysis explicitly considering unbalanced three-phase conditions, enabling a more accurate assessment of bus vulnerability and voltage stability margins under asymmetric operating scenarios. The methodology was developed based on the solution of the power flow in polar coordinates and the analysis of the reduced Jacobian matrix, allowing the identification of critical eigenvalues and the classification of the buses most susceptible to voltage collapse through participation factors. Additionally, the impact of distributed generation (DG) insertion on the stability and security margins of unbalanced distribution systems was investigated, constituting the main contribution of this work. The proposed methodology was computationally implemented and tested on the IEEE 4-bus, IEEE 13-bus, and IEEE 14-bus systems. The results demonstrate that static modal analysis applied to unbalanced three-phase systems provides diagnoses that are substantially more representative of real system operation when compared with equivalent single-phase models. Furthermore, it was observed that the integration of DG can act as a strategic resource for enhancing voltage stability, being particularly beneficial in unbalanced systems when the generated power is carefully distributed among the phases. In this context, allocating DG to the most heavily loaded phases contributes to compensating system imbalances, resulting in increased loading margins and reduced vulnerability of critical buses.