Real-time Curative Actions for Power Systems via Online Feedback Optimization

Curative or remedial actions are the set of immediate actions intended to bring the power grid to a safe operating point after a contingency. The effectiveness of these actions is essential to guarantee curative N-1 security. Nowadays, curative actions are derived ahead of time, based on the anticipated future grid state. Due to the shift from steady to volatile energy resources, the grid state will frequently change and the curative actions would need to be pre-planned increasingly often. Furthermore, with the shift from large bulk production to many small decentralized energy sources more devices need to be actuated simultaneously to achieve the same outcome. Instead of pre-planning, we propose to calculate these complex curative actions in real-time after the occurrence of a contingency. We show how the method of Online Feedback Optimization (OFO) is well suited for this task. As a preliminary demonstration of these capabilities, we use an (OFO) controller, that after a fault, reduces the voltage difference over a breaker to enable the operators to reclose it. This test case is inspired by the 2003 Swiss-Italian blackout, which was caused by a relatively minor incident followed by ineffective curative actions. Finally, we identify and discuss some open questions, including closed-loop stability and robustness to model mismatch

Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes

Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This tutorial paper surveys the recent advances in the field as well as provides novel convergence results for primal-dual online algorithms with heterogeneous step sizes for different elements of the gradient. The analysis is performed for quadratic programs and the approach is illustrated on applications for adaptive step-size and model-free online algorithms, in the context of optimal control of modern power systems

Online Feedback Optimization for Subtransmission Grid Control

The increasing electric power consumption and the shift towards renewable energy resources demand for new ways to operate transmission and subtransmission grids. Online Feedback Optimization (OFO) is a feedback control method that enables real-time, constrained, and optimal control of these grids. Such controllers can minimize, e.g., curtailment and losses while satisfying grid constraints like voltage and current limits. We tailor and extend the OFO control method to handle discrete inputs and explain how to design an OFO controller for the subtransmission grid. We present a novel and publicly available benchmark which is of the real French subtransmission grid on which we analyze the proposed controller in terms of robustness against model mismatch, constraint satisfaction, and tracking performance. Overall, we show that OFO controllers can help utilize the grid to its full extent, virtually reinforce it, and operate it optimally and in real-time by using flexibility offered by renewable generators connected to distribution grids

Tutorial on Congestion Control in Multi-Area Transmission Grids via Online Feedback Equilibrium Seeking

Online feedback optimization (OFO) is an emerging control methodology for real-time optimal steady-state control of complex dynamical systems. This tutorial focuses on the application of OFO for the autonomous operation of large-scale transmission grids, with a specific goal of minimizing renewable generation curtailment and losses while satisfying voltage and current limits. When this control methodology is applied to multi-area transmission grids, where each area independently manages its congestion while being dynamically interconnected with the rest of the grid, a non-cooperative game arises. In this context, OFO must be interpreted as an online feedback equilibrium seeking (FES) scheme. Our analysis incorporates technical tools from game theory and monotone operator theory to evaluate the stability and performance of multi-area grid operation. Through numerical simulations, we illustrate the key challenge of this non-cooperative setting: on the one hand, independent multi-area decisions are suboptimal compared to a centralized control scheme; on the other hand, some areas are heavily penalized by the centralized decision, which may discourage participation in the coordination mechanism

Non-Convex Feedback Optimization with Input and Output Constraints

In this letter, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer a physical plant to the solution of a constrained optimization problem without numerically solving the problem. Our controller can be interpreted as a discretization of a continuous-time projected gradient flow. Compared to other schemes used for feedback optimization, such as saddle-point schemes or inexact penalty methods, our control approach combines several desirable properties: it asymptotically enforces constraints on the plant steady-state outputs, and temporary constraint violations can be easily quantified. Our scheme requires only reduced model information in the form of steady-state input-output sensitivities of the plant. Further, global convergence is guaranteed even for non-convex problems. Finally, our controller is straightforward to tune, since the step-size is the only tuning parameter. © 2017 IEEE.ISSN:2475-145

Feedback Optimizing Model Predictive Control with Power Systems Applications

Feedback optimization (FO) is a control paradigm that is gaining popularity for the optimal steady-state operation of complex systems through the use of optimization algorithms in closed-loop control. FO controllers are capable of addressing control objectives beyond simply regulating setpoints and are often used to track solution trajectories of time-varying optimization problems that are not known in advance. Previous research in this area has typically utilized simplified control dynamics, ignored model uncertainties, and has not adequately addressed constraints or transient performance. Additionally, traditional optimal control approaches often require prior knowledge of the desired equilibrium point. In this thesis, we approach the FO problem from an optimal control and model predictive control (MPC) perspective. Specifically, we propose MPC schemes that can steer the steady-state of a linear dynamical system to the solution of a defined static optimization problem without numerically solving the problem or relying on external setpoints. We accomplish this by formulating the cost functional in MPC to embed an optimization algorithm for the steady-state optimization problem, which is driven to convergence by the implicit feedback inherent in MPC. This allows for the system to be driven to an optimal equilibrium point following a disturbance, without explicit knowledge of the disturbance or setpoints, while also achieving improved transient performance. Compared to direct online economic optimization (e.g., economic MPC), our approach offers improved computational efficiency, and robustness to model uncertainty and unmeasured disturbances. Additionally, the algorithms we develop are only slightly more complex than conventional linear tracking MPC, so theoretical guarantees of stability and performance can be readily derived from standard tracking MPC results without additional assumptions. To demonstrate the effectiveness of the proposed MPC schemes, we present several numerical examples and an application to the challenging problem of real-time economic dispatch in load-frequency control of power system networks. The results obtained show that our proposed MPC schemes are indeed feedback optimizing, with good robustness properties and optimal transient performance

Non-convex Feedback Optimization with Input and Output Constraints for Power System Applications

In this thesis, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer the steady state of a physical plant to the solution of a constrained optimization problem without numerically solving the problem. Our controller can be interpreted as a discretization of a continuous-time projected gradient flow and only requires reduced model information in the form of the steady-state input-output sensitivity of the plant. Compared to other schemes used for feedback optimization, such as saddle-point flows or inexact penalty methods, our scheme combines several desirable properties: It asymptotically enforces constraints on the plant outputs, and temporary constraint violations along the trajectory can be easily quantified. Further, as we prove in our main result, global convergence to a minimum is guaranteed even for non-convex problems, and equilibria are feasible regardless of model accuracy. Additionally, our scheme is straightforward to tune, since the step-size is the only tuning parameter. Finally, we numerically verify robustness (in terms of stability) of the closed-loop behavior in the presence of model uncertainty. For the envisioned application in power systems, we use our novel feedback approach to steady-state optimization for time-varying AC power flow optimization. In numerical experiments, we show that our scheme scales nicely for larger power system setups and exhibits robustness with respect to time-varying generation limits, unobserved demand variations, and a possible model mismatch