Photovoltaic Inverter Controllers Seeking AC Optimal Power Flow Solutions

Abstract

Abstract-This paper considers future distribution networks featuring inverter-interfaced photovoltaic (PV) systems, and addresses the synthesis of feedback controllers that seek real-and reactive-power inverter setpoints corresponding to AC optimal power flow (OPF) solutions. The objective is to bridge the temporal gap between long-term system optimization and realtime inverter control, and enable seamless PV-owner participation without compromising system efficiency and stability. The design of the controllers is grounded on a dual ǫ-subgradient method, and semidefinite programming relaxations are advocated to bypass the non-convexity of AC OPF formulations. Global convergence of inverter output powers is analytically established for diminishing stepsize rules for cases where: i) computational limits dictate asynchronous updates of the controller signals, and ii) inverter reference inputs may be updated at a faster rate than the power-output settling time.Index Terms-Distribution systems, photovoltaic inverter control, distributed optimization and control; optimal power flow.

Convergence of Limited Communication Gradient Methods

“…These methods are typically based on communicating gradient information from a set of source nodes to users, which then solve a simple local subproblem. The procedure can be performed using i) one-way communication where the source nodes estimate the gradient using available information [7], [13], [14] or ii) two-way communication where users and sources coordinate to evaluate the gradient. We investigate the performance of such methods using one-way communication where the number of bits per coordination step are limited.…”

“…There, a distributed solution approach is achieved by solving the dual problem using gradient methods as given in Equations (2) and (3). The dual gradient ∇(f (x(t)) can often be measured over the course of the algorithm, as it is the constraint violation in the primal problem, given dual variable x(t) (see, e.g., [7], [13], [14]). To perform the gradient update in Equations (2) and (3) the gradient or gradient direction must be communicated, as illustrated in the following examples.…”

“…A point x is an optimal solution to optimization Problem (1) if and only if (13) [or (14)] hold with = 0. The Type-1 optimality condition is a generalization of the optimality condition 3 This assumption is only needed in this section.…”

“…(14)] can be achieved for any > 0 in a finite number of iterations. However, unlike for the Type-1 optimality condition, we could not provide an explicit step-size choice or a bound on the number of iterations needed to achieve the > 0 accuracy.…”

Stability of Dynamic Feedback optimization with Applications to Power Systems

“…1 to provide fast grid operation in order to accommodate fluctuating renewable energy sources, and to yield increased efficiency, safety, and robustness of the system trajectories, even in the presence of a substantial model mismatch. For example, feedback optimization has been proposed to drive the state of the power grid to the solution of an AC optimal power flow (OPF) program [3] while enforcing operational limits (either as soft constraints [4] or hard ones [5], [6]) and even in the case of time-varying problem parameters [7], [8].…”