Assessing the Structural Vulnerability of PMU Placement Based on Complex Network Theory

State estimation is considered the core functionality of the Wide Area Measurement System (WAMS). During state estimation, phasor measurement units (PMUs) measure raw and noisy data from the electrical buses to extract creditable state for each bus. Since the reliability and efficiency of the smart grid's energy flow depend on the PMU measurements, it is important to assess the impact of PMU placement and their communication links on the overall resilience of the WAMS network. In this paper we define the structural vulnerability of system states, as a metric to assess the effect of attacks or failures of PMUs, based on the underlying topology of the WAMS. To do this, cyber dependency is represented as a dependency graph, which is then analyzed using eigenvector centrality. The deviation of structural vulnerability from ideal case of WAMS is also define as a metric to evaluate the whole WAMS structural vulnerability. Simulation results demonstrate that the proposed method effectively identifies the structural vulnerabilities of system states, revealing that states monitored by multiple PMUs exhibit significantly lower vulnerability compared to those observed by a single PMU. This highlights the critical importance of optimal PMU placement in enhancing the resilience of WAMS.