Nonlinear least squares curve fitting method for measuring virtual inertia and damping in renewable energy grid stability studies

With the increasing penetration of renewable energy sources such as wind and solar, modern power grids face reduced inertia and damping, posing significant challenges to frequency stability and secure operation. Virtual synchronous generator (VSG) technology has emerged as an effective solution, enabling inverter-based resources to emulate synchronous machine dynamics and support grid resilience. However, while existing research primarily focuses on optimizing VSG control strategies, limited attention has been given to accurate measurement of inertia and damping parameters, which are critical for reliable stability assessment and optimized operation. In practical VSG applications, the inertia time constant τ is often used to jointly characterize the system inertia J and damping coefficient D . However, this approach couples the two parameters, making it difficult to identify their individual values. To address this issue, this paper proposes a method based on nonlinear least squares curve fitting to analyze the unit step response of the system under different operating conditions, including both grid-connected and islanded modes, as well as varying damping states. A qualitative method for identifying the J and D parameters using dynamic response indicators is introduced. The practical measurement approach, founded on curve fitting, draws inspiration from the load rejection test commonly used to measure the inertia of synchronous generators, and combines it with a power step test under grid-connected conditions to form a self-verifiable comprehensive measurement method. The effectiveness of the proposed method is validated through multiple simulations and experiments under various parameters and operating scenarios.