Topological algorithm for forming nodal stresses of complex networks energy systems

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.

On convergence of nonlinear topological algorithms for calculation of steady modes of electric networks

“…The conducted studies showed that the elements of the matrix of current distribution coefficients of a circuit of arbitrary complexity can be determined based on the natural parameters of the network according to the formula [9]:…”

Simplified topological algorithm for forming a steady mode of electric power system

“…Suppose we know the independent currents in chords 7 and 8. Then, the equivalent driving currents in the nodes, determined according to expression (4), as well as the values of the nodal powers, respectively, will be equal to: The steady state parameters are determined by (8), based on the simplified topological model shown in Fig. 3.…”

“…This led to a significant simplification of the technology of searching for specific trees without defining the 2-trees of a complex network graph. The proposed method significantly reduces the amount of work performed and provides fast and reliable convergence of the steady state [7,8].…”