Steven Low, Caltech, US
Title: Swing Dynamics as Primal-Dual Algorithm for Optimal Load Control

Abstract:
Consider a network of power generators and loads connected by transmission lines. Generator dynamics is governed by the swing equations that describe how bus frequencies change in response to supply-demand imbalance in the network according to Newton's second law. In equilibrium, all bus frequencies are synchronized and mechanical power is in balance with electric power at each bus. Given a disturbance in generation at an arbitrary subset of the generator buses, how should loads be controlled in real-time to (i) balance the generation shortfall (or suplus), (ii) resynchronize the bus frequencies, and (iii) minimize the aggregate disutility of load control?

We formulate this as an optimal load control problem and prove that these objectives can be achieved by having the loads adapt based only on frequency deviations measured at their local buses. These local frequency deviations turn out to convey exactly the right information about global power imbalance for the loads themselves to make local decisions using their own marginal cost functions that turn out to be globally optimal. This allows a completely decentralized solution without the need for explicit communication among the buses. Moreover, our load control coupled with the system dynamics of swing equations and branch power flows serve as a distributed primal-dual algorithm to solve the dual of the optimal load control problem, where frequency deviations emerge as the Lagrange multipliers that measure the cost of power imbalance and the branch power flows emerge as a measure of the cost of frequency asynchronism.