Voltage Collapse Stabilization in Star DC Networks

Voltage collapse is a type of blackout-inducing dynamic instability that occurs when the power demand exceeds the maximum power that can be transferred through the network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficiencies as it prevents operators to fully utilize the network resources and does not account for unprescribed events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization. More precisely, for a DC star network, we formulate the problem of voltage stability as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We show that such a system can be interpreted as a game, where each player (load) seeks to myopically maximize their utility using a gradient-based response. Using this framework, we show that voltage collapse is the unique Nash Equilibrium of the induced game and is caused by the lack of cooperation between loads. Finally, we propose a Voltage Collapse Stabilizer (VCS) controller that uses (flexible) loads that are willing to cooperate and provides a fair allocation of the curtailed demand. Our solution stabilizes voltage collapse even in the presence of non-cooperative loads. Numerical simulations validate several features of our controllers.