Online optimization in closed loop on the power flow manifold

The focus of this paper is the online load flow optimization of power systems in closed loop. In contrast to the conventional approach where an AC OPF solution is computed before being applied to the system, our objective is to design an adaptive feedback controller that steers the system in real time to the optimal operating point without explicitly solving an AC OPF problem. Our approach can be used for example to simultaneously regulate voltages, mitigate line congestion, and optimize operating costs under time-varying conditions. In contrast to related work which is mostly focused on distribution grids, we introduce a modeling approach in terms of manifold optimization that is applicable in general scenarios. For this, we treat the power flow equations as implicit constraints that are naturally enforced and hence give rise to the power flow manifold (PFM). Based on our theoretical results for this type of optimization problems, we propose a discrete-time projected gradient descent scheme on the PFM. In this work, we confirm through a detailed simulation study that the algorithm performs well in a more realistic power system setup and reliably tracks the time-varying optimum of the underlying AC OPF problem.