Computational Framework for Zbus Matrix Construction in Power Systems Based on Case-Based Algorithms
DOI:
https://doi.org/10.61467/2007.1558.2027.v18i1.1453Keywords:
Electric Power System, Zbus, admittance, transmission line, matrix, inductive reactance, resistance, algorithm, Sistema eléctrico de potencia, reactancia inductivaAbstract
The analysis of Electric Power Systems requires computational tools capable of handling admittance and impedance matrices accurately and efficiently. This work presents the development and implementation of MATLAB software for the construction of Ybus and Zbus matrices using the Zbus building algorithm together with Kron reduction. The proposed methodology applies the four fundamental cases of impedance matrix expansion, allowing the electrical network topology to be updated without performing complete matrix inversion processes, which helps reduce computational effort and improve processing efficiency.
The software also includes matrix visualization and topological representation functions for the analysis of symmetrical and asymmetrical electrical networks. In addition, a comparative analysis was performed between the proposed implementation and conventional matrix inversion methods in order to evaluate their computational performance during matrix construction and reduction. To validate the methodology, the algorithm was tested on a five-bus power system, verifying the correct formation and reduction of the matrices. The obtained results show that the implementation provides an efficient and practical tool for matrix processing in applications such as load flow analysis, fault studies, and stability analysis in Electric Power Systems.
Spanish-language metadata / Metadatos en español
Título en español:
Marco computacional para la construcción de la matriz Zbus en sistemas eléctricos de potencia mediante algoritmos basados en casos
Resumen:
El análisis de sistemas eléctricos de potencia requiere herramientas computacionales capaces de manejar matrices de admitancia e impedancia con precisión y eficiencia. Este trabajo presenta el desarrollo y la implementación de un software en MATLAB para la construcción de las matrices Ybus y Zbus mediante el algoritmo de construcción de Zbus junto con la reducción de Kron. La metodología propuesta aplica los cuatro casos fundamentales de expansión de la matriz de impedancias, lo que permite actualizar la topología de la red eléctrica sin realizar procesos completos de inversión matricial, contribuyendo así a reducir el esfuerzo computacional y mejorar la eficiencia del procesamiento.
El software también incluye funciones de visualización de matrices y representación topológica para el análisis de redes eléctricas simétricas y asimétricas. Además, se realizó un análisis comparativo entre la implementación propuesta y los métodos convencionales de inversión matricial con el fin de evaluar su rendimiento computacional durante la construcción y reducción de las matrices. Para validar la metodología, el algoritmo se probó en un sistema eléctrico de potencia de cinco barras, verificándose la correcta formación y reducción de las matrices.
Los resultados obtenidos muestran que la implementación proporciona una herramienta eficiente y práctica para el procesamiento matricial en aplicaciones como el análisis de flujo de carga, los estudios de fallas y el análisis de estabilidad en sistemas eléctricos de potencia.
Palabras Claves:
Sistema eléctrico de potencia, Zbus, admitancia, línea de transmisión, matriz, reactancia inductiva, resistencia, algoritmo.
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