Optimizing Inertia Estimation in Virtual Synchronous Generators With MMC-Based Proportional Integral and Model Predictive Control Strategies

The increasing integration of renewable energy sources influences the power grid, resulting in a reduction in the traditional inertia supplied by synchronous generators. Significant frequency deviations are caused by power fluctuations, which are affected by the grid’s stability due to the reduction of inertia and damping. To address this problem, the idea of a Virtual Synchronous Generator (VSG) was created to simulate the fundamental features of a synchronous generator, including damping and inertia. This study proposes the use of a Proportional-Integral (PI) controller and Model Predictive Control (MPC) for the computation of the inertia in a Virtual Synchronous Generator (VSG) controller. Power and frequency responses are balanced by the PI controller, which employs a control law that is derived from the cross-error between power variations and system frequency droop. The MPC method establishes an optimal output trajectory that minimizes input costs associated with inertia and damping factors, effectively balancing power and frequency responses. Fluctuations in power output result in frequency variations between 49.754 Hz and 50.0267 Hz. In steady-state conditions, the frequency oscillates around the nominal value with an amplitude of 0.042 Hz and stabilizes within 150 milliseconds. When reactive power output changes, these oscillations increase to 0.069 Hz after half a second VSG-PI reducing the peak frequency to 50.180 Hz and VSG-MPC to 50.177 Hz. The minimum frequency is reduced to 49.833 Hz for VSG-PI and 49.842 Hz and 49.844 Hz for VSG-MPC. During steady-state, VSG-PI and VSG-MPC exhibit frequency oscillations of 0.035 Hz and 0.024 Hz, respectively, with stabilization times of 150 ms and 80 ms. Reactive power output changes cause these oscillations to increase to 0.060 Hz for VSG-PI and 0.023 Hz for VSG-MPC. VSG-MPC shows similar peak frequency and stabilization time to VSG-PI but outperforms other methods by further reducing the minimum frequency. The rate of change of frequency (RoCoF) is 2.096 Hz/s for VSG-PI and 2.692 Hz/s for VSG-MPC.