Robust $\mathbb {H}_{\infty }$Based Virtual Synchronous Generators for low Inertial Microgrids Considering High Penetration of Renewable Energy

Fossil-based generators are phasing out in favor of Renewable-Based Sources (RESs), impacting the generation mix and causing low inertia levels. In this regard, this paper presents a static output feedback <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> based virtual synchronous generator to regulate the frequency of low inertial microgrids dominated by inertia-less (RESs). The control strategy addresses the uncertainty of power system inertia, stochasticity of RESs, and demand volatility. Also, the proposed static <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> replaces the dynamic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> control that normally entails complexity and impracticality. Previous development on dynamic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> control, which entails complexity and impracticality, is replaced by a simple and static <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> counterpart that achieves the same control objectives, offering seamless implementation and minimal computational burden. Using Lyapunov theories and Linear Matrix Inequalities, the dynamics of the microgrids are transformed into a set of uncertain polytopic systems. A convex optimization model is developed to tune the controller that optimizes microgrid operation over the entire uncertain region. A multi-step verification method on a realistic testbed comprising conventional and RES-based units showcases the robustness of the control design against extreme grid disruptions and multiple RES injections. Conducting a Real-Time simulation with RTDS technologies to validate the control design concludes the paper.