Stability analysis of volt-VAr control in linear distribution networks

While increasing integration of renewable energy is effective for combatting climate change, it faces challenges like voltage fluctuation. Volt-VAr control allows inverter-based devices to counteract voltage issues. The optimal methodology for determining stable decentralized Volt- VAr control policies is unclear. In this study, stability of a distribution grid is analyzed using Lyapunov and eigenvalue methods. The exact set of stable control policies for any linearized radial distribution grid is found using eigenvalues. Due to computational complexity, an inner approximation with minimal voltage deviation loss is implemented, creating an efficient design tool for inverter control that allows stable integration of clean energy.