Incidence Matrix based Method for $N-1$ Contingency Parallel Analysis of Main Transformers in Distribution Networks

$N -1$ security is an important criterion for the development and planning of distribution networks. The existing $N-1$ contingency analysis methods of distribution networks are primarily based on the unit of components, and the faults of each component are analyzed and verified one by one. The calculation process of these methods is complicated, and the positioning effect of the weak links needed for distribution network planning is insufficient. For this reason, this paper proposes a method of $N-1$ contingency parallel analysis for main transformers based on the incidence matrix. First, the main transformer incidence matrix is established, and the load transfer process is classified into three types, according to different transfer modes, and the contact matrices are then established respectively. Second, considering the capacity constraint of main transformers and tie-lines, the corresponding capacity matrices are established. The maximum transfer capability (MTC) of the distribution network in the case of each main transformer fault is calculated by contact matrices and capacity matrices, and the $N-1$ contingency analysis result is obtained by comparing MTC with the load that needs transferring. Meanwhile, the transfer margin of the main transformers and tie-lines after transferring can be obtained in the process of $N-1$ contingency analysis, so as to find any weak links. An example is given to verify the correctness and effectiveness of the proposed method. In this paper, the $N-1$ contingency analysis results of all main transformers in the distribution network are expressed analytically through matrices operations, and the weak links can then be intuitively identified. The cumbersome operation of checking each component is avoided, and the computational efficiency is improved.