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Download Graph Theory and Voltage Stability Analysis In Radial Distribution
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Graph Theory and Voltage Stability Analysis In Radial Distribution Systems Ahmed R. Abul'Wafa Ain Shams University Egypt [email protected] Tel./Fax 22639022 Aboul’Fotouh El’Garably El’Shorouk Academy Egypt [email protected] 01004881722 Wael A.Fatah Mohamed El’Shorouk Academy Egypt [email protected] 01061326336 ABSTRACT A graph-based method is reported in this paper to identify nodes that are on the verge of voltage collapse of radial distribution networks. The voltage stability index is derived from the bi-quadratic equation which is generally used for the voltage calculation of distribution load flow algorithms. The proposed method based on network graphical information allows power flow equations formulation in matrix form to satisfy the need of distribution automation. A directed graph, of an N-node radial network is represented by a sparse matrix of an N-by-N matrix. Paths from the reference node to any node (downstream nodes for each node including the node itself) are detected by traversing the directed graph in depth-first search form. A connection matrix (𝑩𝑵) is constructed based on the discovered paths. The proposed method uses 𝑩𝑵 for dynamic building of a symmetric upper triangular Bus-Injection to Branch-Current matrix (𝑩𝑰𝑩𝑪) and a Branch-Current to Bus-Voltage matrix (𝑩𝑪𝑩𝑽) of the system. The authors present a detailed analysis of effects of different load models on voltage computation and voltage stability.The results of the applications of the proposed methodology to a set of networks taken from the literature on the topic along with conclusion are presented.
