Teager Energy Operator as a Metric to Evaluate Local Synchronization of Power System Devices

TL;DR

This work addresses the challenge of assessing local synchronization in power systems with growing inverter-based resources. It introduces Synchronization Energy (SE), a metric based on the Teager Energy Operator applied to the complex power, leveraging the complex-frequency framework to capture coupled voltage and current dynamics. The key contribution is the analytic expression $\psi_c(\bar{s})=\left(2\left(\omega_v-\omega_\imath\right)^2 + \frac{\psi(v)}{v^2} + \frac{\psi(\imath)}{\imath^2}\right)|\bar{s}|^2$ and the local synchronization condition $\psi_c(\bar{s}) \to 0$, along with extensive case studies across SMIB, Kundur two-area, IEEE 14-bus, and grid-following IBR systems. The findings show SE effectively reflects how inertia, damping, reactance, and controller gains shape local synchronization and system strength, offering a practical tool for stability assessment and control design in modern power networks.

Abstract

This paper introduces a novel formulation to evaluate the local synchronization of power system devices, namely Synchronization Energy (SE). The formulation is derived based on the complex frequency concept and the Teager Energy Operator applied to the complex power. This formulation offers valuable insights into the relationship between complex frequency of voltage and current of the device and its stationary operating. Based on this relationship we derive the conditions for a novel definition of local synchronization of power system devices. Through various case studies, the paper demonstrates how SE can effectively assess local synchronization under diverse operating conditions.

Figures (22)

• Figure 1: Scheme of the synchronous reference frame PLL.
• Figure 2: Single line diagram of a SMIB system.
• Figure 3: SMIB system --- Active and reactive powers injected at bus 1 for two values of inertia.
• Figure 4: SMIB system --- Comparison of SEs at bus 1 for two values of inertia.
• Figure 5: SMIB system --- Active and reactive powers injected at bus 1 for two values of inertia and $D = 5$.