Measurement-Based Sparsity-Promoting Optimal Control of Line Flows

This paper proposes an optimal strategy for regulating active-power flows in electric power systems based on sparsity-promoting linear-quadratic-Gaussian (LQG) control. The proposed method relies on the mapping of nodal active- and reactive-power injections to line flows, which are obtained via a measurement-based approach. Building on this, we outline a combined sparsity-promoting linear-quadratic regulator and Kalman-filter design. The optimal controller sparsity is identified using the alternating direction method of multipliers, which strikes a balance between feedback controller sparsity and the closed-loop dynamic performance. With this, we optimally dispatch generators and controllable loads to achieve desired line flows while ensuring zero steady-state frequency offset. We demonstrate the utility of the proposed LQG controller via a representative congestion-management application deployed on the New England 10-machine 39-bus test system.