Swing dynamics as primal-dual algorithm for optimal load control

In electricity transmission networks, loads can provide flexible, fast responsive, and decentralized sources for frequency regulation and generation-demand balancing, complementary to generation control. We consider an optimal load control (OLC) problem in a transmission network, when a disturbance in generation occurs on an arbitrary subset of the buses. In OLC, the frequency-insensitive loads are reduced (or increased) in real-time in a way that balances the generation shortfall (or surplus), resynchronizes the bus frequencies, and minimizes the aggregate disutility of load control. We propose a frequency-based load control mechanism and show that the swing dynamics of the network, together with the proposed mechanism, act as a decentralized primal-dual algorithm to solve OLC. Simulation shows that the proposed mechanism can resynchronize the bus frequencies, balance demand with generation and achieve the optimum of OLC within several seconds after a disturbance in generation. Through simulation, we also compare the performance of the proposed mechanism with automatic generation control (AGC), and discuss the effect of their incorporation.