Formation of the Z-form of equations of steady-state modes of energy systems’ complex electric networks

Dauren Akhmetbayev ,Arman Akhmetbayev,Assemgul Zhantlessova

doi:10.1051/e3sconf/20185802021

Dauren Akhmetbayev , Arman Akhmetbayev + Show 1 more

Open Access

https://doi.org/10.1051/e3sconf/20185802021

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Abstract

This paper describes the state of the methodological problem of calculating steady-state modes of energy systems’ complex electric networks. It also describes the topological method of forming the Z-form of equations of steady-state modes of complex electric networks. The analytical dependence of the node impedance matrix with the matrix of the nodal currents distribution coefficients is established. The matrix of infeed coefficients is determined during the initial data preparation. An analytical approach for determining infeed coefficients topological essence is considered. A simplified method for calculating the driving current distribution coefficients is proposed based on all possible graph trees of a complex electric network. An algorithm for forming infeed coefficients matrix in the environment is developed. A technique for obtaining real solutions of the steady-state mode equations is developed. Steady-state modes direct formation significantly reduces the amount of work performed, increases the visibility of the calculation algorithms performance, and ensures fast and reliable iteration convergence. Increases the level of automation and efficiency of the calculations performed.

Highlights

Methodological problems of analysing the electric power system modes are associated with the need to perform a large amount of work on the steady-state modes calculation [1, 2]
Steady-state modes equations are written in various forms and are nonlinear, which can be solved only by iterative methods [3,4,5]
The conducted studies [9,10,11] have shown that the difficulties of obtaining real solutions in the steady-state modes calculation can be considerably overcome if we start with inverted form of nodal equations

Summary

Introduction

Methodological problems of analysing the electric power system modes are associated with the need to perform a large amount of work on the steady-state modes calculation [1, 2]. Steady-state modes equations are written in various forms and are nonlinear, which can be solved only by iterative methods [3,4,5]. The conducted studies [9,10,11] have shown that the difficulties of obtaining real solutions in the steady-state modes calculation can be considerably overcome if we start with inverted form of nodal equations. The resulting equation (4) is a solution of the equation of nodal voltages and allows us to write the equality in the following form: Z=Ct Zb C=Y-1. The problem of forming an inverted form of nodal equations can be reduced to determining the infeed coefficients matrix

Infeed coefficients matrix and network topology

Formation of Z-form of nodal voltages

Steady-state mode calculations

Conclusions