Relationship between the coefficients of a six-terminal network with two input and four output terminals

Abstract

Problem Statement (Relevance): This paper describes one of the possible variants of the quantitative relationship between the coefficients of the B-form equations and the equations of other forms that evaluate the state of a passive six-terminal network with two input and four output terminals. Such six-terminal network can replace devices, elements or parts of electrical circuits or electric power systems. The coefficients of the B-form equations, as well as the coefficients of the A-form equations, can be determined experimentally. In principle, the coefficients of equations of other forms can also be determined experimentally. However, such experiments are usually difficult to set up and conduct. Thus, it seems to be more reasonable to determine these coefficients from the established quantitative relationship with the previously determined coefficients of the B-form. Objectives: To establish a quantitative relationship between the coefficients of the B-form equations describing the state of the six-terminal network with two input and four output terminals and the coefficients of the G-, H-, Y- and Z-form equations describing the state of the same six-terminal network. Methods Applied: Mathematical modelling and some elements of the theory of multi-terminal networks. Originality: The originality of this research lies in the proposed method of establishing a quantitative relationship between the coefficients of the A-form equations and the equations of other forms describing the state of the passive six-terminal network with two input and four output terminals. Findings: This paper examines one of the possible variants of the quantitative relationship between the coefficients of the B-form equations and the coefficients of the G-, H-, Y- and Z-form equations describing the state of the passive six-terminal network with two input and four output terminals. Some mathematical statements are presented which can help establish such relationship. Practical Relevance: If one knows the values of the B-form equation coefficients, the proposed quantitative relationship between the coefficients of various forms of equations will help build equations of other forms and establish various types of dependencies between the input and output characteristics of an electric power unit, which can be replaced with a six-terminal network with two input and four output terminals. This technique can be used to establish a quantitative relationship between the coefficients of the G-, H-, Y- or Z-form equations and the coefficients of equations of other forms describing the state of different modifications of passive six-terminal networks.