Delay-Dependent $ H_{\infty }$ Robust Frequency Control in Microgrids: Coordination of Secondary Frequency Control and Virtual Inertia Control

The time delay, disturbances, and parameters uncertainties brought by open communication networks and renewable energy source threaten the stable operation of the frequency control system (FCS) in microgrids (MGs). Plus, the low inertia of MGs exacerbates frequency fluctuations. In this article, the codesign of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> robust controllers for secondary frequency control (SFC) and virtual inertia control (VIC) in the delay-dependent FCS of MG is presented. First, the FCS of MG considering the VIC under the influence of the time delay is established. Second, based on Lyapunov stability theory, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> performance analysis method is proposed for the FCS of MG with the time-varying delay. Then, with robust performance index as the design condition, the grey wolf optimizer is used to carry out the codesign of the SFC and VIC. Finally, the simulation test proves that the proposed control strategy can effectively codesign the SFC and VIC. The designed robust controllers can effectively deal with the problems of low inertia, time delay, disturbance, and parameters uncertainty in MG frequency control.