Distributed Plug-and-Play Robust <i>L</i> _∞ Voltage Control for Islanded Microgrids

This paper proposes a distributed Plug-and-Play robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\infty }$ </tex-math></inline-formula> control scheme for islanded microgrids composed of multiple interconnected Distributed Generation Units (DGUs). Firstly, the robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\infty }$ </tex-math></inline-formula> performance is well defined to consider the influence of external inputs and the electrical couplings among interconnected DGUs in a robust framework. Secondly, a distributed robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\infty }$ </tex-math></inline-formula> Plug-and-Play control scheme is carefully constructed to regulate the voltage at the Point of Common Coupling (PCC) of each DGU while ensuring the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\infty }$ </tex-math></inline-formula> stability of overall microgrids, real-time tracking of PCC voltage and Plug-and-Play functionality can be implemented simultaneously. The advantages of proposed Plug-and-Play functionality is that, when plugging a DGU it only requires redesigning the controllers of itself and its neighbors DGU, when unplugging a DGU it no longer requires redesigning any controllers. Then, a series of robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{\infty }$ </tex-math></inline-formula> Plug-and-Play stable conditions in Linear Matrix Inequalities (LMIs) are derived to guarantee the whole stability of the studied system. Finally, two simulation examples of islanded microgrids are used to demonstrate the effectiveness of the proposed method.