Abstract
The paper presents a new topological algorithm for the formation of nodal stresses of complex networks of power systems. The first step of the described algorithm is the search and determination of the values of all possible and specific trees of the graph corresponding to a given network of the power system. The well-known advantage of the topological approach compared to matrix methods, which allows one to obtain the final solution of non-linear equations of the steady state, has led to the development of many methods and corresponding software implementations. The paper provides a comparative analysis of the advantages and disadvantages of these methods. The main computational complexity of these methods is the search for 2 trees for each tree, which are obtained from it by dividing into two parts by removing any branch. A completely new topological approach that does not require finding 2 trees was proposed by one of the authors. The process of this method consists of the following steps: finding all possible graph trees, selecting specific graph trees, calculating the network node voltage. The work offers a unique algorithm for the implementation of these stages, which are implemented and tested at the software level. The result of the execution of the software package is the calculation of the steady state of a complex electric network using the distribution coefficients of the driving currents.
Highlights
The main task of the topological analysis of the electric network is to determine all of its possible trees [1,2,3]
In [5, 6], three methods are realized for finding possible trees of complex electric networks
We present the result of the program for determining all possible trees of a real 220
Summary
The main task of the topological analysis of the electric network is to determine all of its possible trees [1,2,3]. In one method, iteration is carried out along branches, the second - through nodes, and in the third - along contours Another approach is implemented in the theory of structural numbers [7]. The search algorithm for all possible trees of the graph with the calculation of their values. The resulting value of all possible trees is formed as the sum of the weights of the individual trees of the graph. According to this algorithm, a program is compiled that reads the source data from an external file and performs a preliminary check of the correctness of the source data. The number of all possible trees is 85, and they are presented in table 1
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