Adaptive Inertia for a Virtual Synchronous Machine Using an LQR Controller Applicable to a High-Voltage DC Terminal

Abstract

Synchronous machines are a fundamental component of electrical power systems because they not only provide electricity but also inertia and damping to maintain the stability during disturbances. Besides, they allow the system to respond to sudden power changes while the frequency remains within the required limits. However, the growth in the penetration of renewable energies (e.g., solar and wind), and the implementation of power converters has led to less inertia, which may cause potential stability problems. The concept of Virtual Synchronous Machine (VSM) has been introduced to overcome this issue. This consists of emulating the inertia and damping by power converters used to integrate renewable energy sources into the power grid. The VSM must be flexible and stable during power changes, preventing oscillations, and frequency overshoots from increasing during system’s response to disturbances. Recently, the VSM with adaptive inertia has been proposed as a potential solution since it provides inertia to the system according to its requirements, however, the inertia estimation is not a straightforward task, and the optimal balance between the power and frequency response required especial techniques to be guaranteeing.This paper proposes a Linear Quadratic Regulator (LQR) controller to estimated the inertia of the VSM. Since the LQR solves the optimization problem between the power and frequency responses, a fast response and small oscillations are accomplished. To validate the proposed method, a comparison with a VSM with constant inertia is performed. To this end, a 200 MW/200 kV Modular Multilevel Converter (MMC) terminal (commonly used to connect off-shore wind farms with the power grid), with seven sub-modules is used as a power converter.Time-domain simulations have been carried out in the MMC terminal, considering variations in the active and reactive powers in order to show the power and frequency responses using both controllers. Results show that the VSM-LQR controller presents lower frequency oscillations when compare to the traditional approach.