Optimal Placement of Phasor Measurement Units to Monitor Center of Inertia Frequency

Efficient monitoring of center of inertia (COI) frequency is critical for maintaining system frequency stability. Numerous studies have demonstrated the possibility of monitoring COI frequency through phasor measurement units (PMUs) placed at system buses. However, the question of where to place the PMUs is rarely addressed. In this letter, the optimal placement of PMUs, especially when limited devices are available, is investigated. The formula governing the linear relationship between the COI frequency and few bus frequencies is firstly derived. In order to evaluate the monitoring accuracy for different numbers and locations of PMUs, a L2 norm-based performance metric is proposed. Further, the closed-form solution of linear coefficients corresponding to a certain PMU placement is deduced to minimize the performance metric. The optimal placement is finally determined by selecting the best performance metric among different placement combinations. The proposed method ensures that the complete dynamics of COI frequency can be monitored accurately with few PMUs deployed at system buses, which is tested in the IEEE 39 bus system.