A METHODOLOGY FOR MODELING POWER SUPPLY SYSTEMS

Abstract

The article is devoted to the development and testing of a methodology for analytical modeling of power supply systems that include multiple sources and multiple consumers of electricity, located at a distance from each other and connected by power transmission lines. The developed methodology will help designers assess the possibilities of distributing electricity among consumers while calculating the optimal voltages that need to be maintained at the nodes of the power sources, thereby achieving minimal voltage differences between the load nodes. The methodology is tested using a 10-node power supply system, in which the number of energy source nodes and load nodes is equal to 5.

The modeling methodology is based on calculating the parameters of the power supply system using the node potential method, along with Ohm's and Kirchhoff's laws. The calculations utilize the method of complex amplitudes and are carried out according to a proposed iterative algorithm, the flowchart of which is presented in the article. The calculations are performed in the MathCAD environment using the mathematical framework of matrix computations. For this purpose, a conductance matrix and a node current matrix are constructed, and the node potential matrix is calculated in MathCAD. The paper demonstrates how to transit from a three-phase system to a single-phase system, with all calculations performed on a single-phase scheme. To obtain accurate results, formulas are derived for converting the parameters of the three-phase system into single-phase parameters, including the conversion of consumed load powers into complex impedances. The results of the modeling are presented in tabular form and as directed graphs, indicating the potentials of the nodes and the directions of active power flows. The results of modeling two variants of power supply systems are provided. The proposed methodology is recommended for assessing the parameters of power supply systems that include multiple sources of electricity and several load nodes.