Distributed Continuous-time Optimal Power Flow

In this paper, we propose a distributed continuous-time optimal power flow (OPF) model, with DC power flow constraints, for a multi-area transmission network. The model exploits the unique properties of variational optimization, function space representation, and the alternating direction method of multipliers (ADMM) to enable continuous-time power exchange between adjacent areas. More specifically, the centralized multi-area OPF is formulated as a variational optimization problem with continuous-time load and decision variables (power generation, voltage phase angles, line/tieline power flows), which is then converted to a conventional optimization problem by projecting the load and decision trajectories into the Bernstein function space, and is decomposed to function space-based OPF sub-problems of individual areas using ADMM. The numerical results of implementing the proposed model on a synthesized three-area network indicate convergence to the centralized continuous-time OPF solution and showcase computational efficiency and the efficient sharing of ramping resources among areas.