An LMI Based Stability Margin Analysis for Active PV Power Control of Distribution Networks with Time-Invariant Delays

High penetration of photovoltaic (PV) generators can lead to voltage issues in distribution networks. Various approaches including the real power control through PV inverters have been proposed to address voltage issues. However, among different control strategies, communication delays are inevitably involved and they need to be carefully considered in the control loop. Those delays can significantly deteriorate the system performance with undesired voltage quality, and may also cause system instability. In this paper, according to the inverter based active power control strategy, a linearized state space model with communication delay is presented. A delay dependent stability criterion using linear matrix inequality (LMI) approach is used to rigorously obtain the delay margins based on different system parameters. The method can handle multiple PVs in the distribution network as well.