On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems

TL;DR

This paper investigates the fundamental properties of the compound nodal admittance matrix in unbalanced polyphase power systems, establishing conditions for its rank and implications for network reduction and hybrid parameter existence.

Contribution

It provides the first comprehensive theoretical analysis of the compound nodal admittance matrix for unbalanced polyphase grids, extending previous work on balanced systems.

Findings

Conditions for the rank of the admittance matrix are derived.

Implications for Kron reduction feasibility are discussed.

Theoretical foundation for power system analysis applications is established.

Abstract

Most techniques for power system analysis model the grid by exact electrical circuits. For instance, in power flow study, state estimation, and voltage stability assessment, the use of admittance parameters (i.e., the nodal admittance matrix) and hybrid parameters is common. Moreover, network reduction techniques (e.g., Kron reduction) are often applied to decrease the size of large grid models (i.e., with hundreds or thousands of state variables), thereby alleviating the computational burden. However, researchers normally disregard the fact that the applicability of these methods is not generally guaranteed. In reality, the nodal admittance must satisfy certain properties in order for hybrid parameters to exist and Kron reduction to be feasible. Recently, this problem was solved for the particular cases of monophase and balanced triphase grids. This paper investigates the general case of unbalanced polyphase grids. Firstly, conditions determining the rank of the so-called compound nodal admittance matrix and its diagonal subblocks are deduced from the characteristics of the electrical components and the network graph. Secondly, the implications of these findings concerning the feasibility of Kron reduction and the existence of hybrid parameters are discussed. In this regard, this paper provides a rigorous theoretical foundation for various applications in power system analysis