A study on propagation depth restriction for improving the observability of electrical networks

Abstract The problem of achieving full observability in electrical networks with a limited number of measurement devices is commonly addressed using power domination theory. For path and cycle graph structures, a single Phasor Measurement Unit (PMU) is theoretically sufficient to observe all network vertices. Despite this advantage, dependence on a single PMU reduces system reliability, as unexpected device failures can result in a significant loss of observability. To address this issue, the present study focuses on enhancing observability by restricting the propagation depth to two, denoted by $$\gamma_{P(\le 2)}(G)$$ . In this article, we introduce the concept of restricted propagation depth–based power domination. A comparative analysis is made between the standard graphs with and without restricting the propagation distance. We also discuss its impact on the different IEEE bus systems such as IEEE-9, IEEE-14, IEEE-30, IEEE-39, IEEE-57, IEEE-78, IEEE-118 and IEEE-300. The results indicate that monitoring a vertex at least twice is more advantageous than the restricted power-dominating measures $$\gamma_{P(\le 2)}(G)$$ , highlighting the potential for increased efficiency in graph observability.