On eigenvalues to the Y-bus matrix

• We investigate and interpret the spectrum of the Y-bus matrix.
• We propose indices to evaluate the Y-bus matrix based on its eigenvalues.
• We present the proposed indices on the Nordic32 system.

The topology of a power system has a profound impact on its reliability. If a power system faces a contingency, for example a loss of a transmission line or a transformer, this contingency might, in worse case, lead to a blackout. Since the Y-bus matrix contains information about the structure, the line impedances, the loading in each bus and is commonly used in power system calculations it can be used to evaluate the topology of the transmission system. This paper reports on the relation between the eigenvalues to the Y-bus matrix and the underlying graph representing the topology of the transmission system. The paper also proposes four different indices’ based on the spectrum to the Y-bus matrix and the corresponding Laplacian matrix to be used to evaluate power system topologies. In addition, this paper will also show how the so called algebraic connectivity and the mean impedance in a graph is related and how the mean impedance can be calculated through the eigenvalues to the Laplacian matrix and the Y-bus matrix. In a numerical example, the indices’ on the Nordic32 system is presented.