Online Feedback Optimization leverages properties of optimization algorithms to develop controllers for systems with limited model availability, which is often the case in process control. The interplay between the parameters of the chosen optimization algorithm, as well as lack of direct connection to the characteristics of the underlying process make their tuning challenging. We propose a method for adaptive tuning of Online Feedback Optimization controllers based on scaled projected gradient descent by using sensitivity of the desired objective to the parameters of the algorithm. The proposed adaptive tuning method limits the operator-tunable parameters to scalar values that represent how much the control inputs and the objective can change between iterations without requiring either additional information about the controlled system or repeated experiments. Numerical studies on a gas lift and a continuously-stirred tank reactor processes confirm that our adaptive scheme improves closed-loop performance of Online Feedback optimization compared to standard manual tuning methods.

The increasing electric power consumption and the shift toward renewable energy resources demand for new ways to operate transmission and subtransmission grids. Online Feedback Optimization (OFO) is a feedback real-time control method that can be employed to enable optimal operation of these grids. Such controllers can maximize grid efficiency (e.g., minimizing curtailment) while satisfying grid constraints like voltage and current limits. The OFO control method is tailored and extended to handle discrete inputs and it is explained how to design an OFO controller for the subtransmission grid. A novel benchmark is presented and published that corresponds to the real French subtransmission grid on which the proposed controller is analyzed in terms of robustness against model mismatch, constraint satisfaction, and tracking performance. It is shown 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 the flexibility offered by renewable generators connected to distribution grids.

The coordination of a large number of flexibility providing units across various grid layers requires innovative control concepts. This is needed, e.g., to allow active distribution systems to provide ancillary services for the transmission system. A cascaded control structure based on Online Feedback Optimization (OFO) can be used to meet flexibility requests at the point of common coupling by tracking an active power set point at the point of common coupling. This paper investigates the practical influence of the parameterization of the individual controllers on the performance of the hierarchical flexibility provision in three case studies. One case study includes a two-level controller cascade acting on one medium and two low voltage grids, and the other one includes a three-level cascade acting on low to high voltage levels. The results show that the behavior of one controller is highly dependent on the choice of control parameters of the other controllers in the cascade. Additionally, the choice of parametrization has a significant impact on the accuracy and speed of flexibility provision. A third case study investigates the effects of model mismatch and measurement noise on the appropriate selection of parameters. Overall, careful tuning enables the efficient vertical coordination of flexibility providing units with a cascaded structure based on OFO.

When high amounts of active power are injected into power distribution grids, the overall power flow is limited because voltages reach their upper acceptable limits. Volt/var control aims to raise this power flow limit without physically reinforcing the grid but by controlling the voltage using reactive power. We use real consumption and generation data on a low-voltage CIGR & Eacute; grid model and an experiment on a real distribution grid feeder to analyze how different volt/var methods can enhance the grid. We show that local droop control enhances the grid but underutilizes the reactive power resources. We discuss how this inefficiency can be partly reduced by fine-tuning the droop curves through data-driven techniques but illustrate that inherent trade-off persist for any local control method. We finally demonstrate that coordinated control methods can track the optimal solution and enhance the grid to its full potential if grid-wide communication is available. Our numerical study over a whole year of real data suggests that coordinated volt/var control can enable another 10.4% of maximum active power injections compared to droop control. In a small-scale real-life experiment, coordinated control enhanced the grid by the same amount.

Online Feedback Optimization (OFO) controllers steer a system to its optimal operating point by treating optimization algorithms as auxiliary dynamic systems. Implementation of OFO controllers requires setting the parameters of the optimization algorithm that allows reaching convergence, posing a challenge because the convergence of the optimization algorithm is often decoupled from the performance of the controlled system. OFO controllers are also typically designed to ensure steady-state tracking by fixing the sampling time to be longer than the time constants of the system. In this paper, we first quantify the impact of OFO parameters and the sampling time on the tracking error and number of oscillations of the controlled system, showing that adjusting them without waiting for steady state allows good tracking. We then propose a tuning method for the sampling time of the OFO controller together with the parameters to allow tracking fast trajectories while reducing oscillations. We validate the proposed tuning approach in a pressure controller in a centrifugal compressor, tracking trajectories faster than the time needed to reach the steady state by the compressor. The results of the validation confirm that simultaneous tuning of the sampling time and the parameters of OFO yields up to 87% times better tracking performance than manual tuning based on steady state.

Coordinating a high number of flexibility providing units (e.g. to provide ancillary services for the transmission system) across various grid layers requires new control concepts. A flexibility request at a point of common coupling can be met by utilizing a cascaded control structure based on online feedback optimization. In this paper the influence of the parameterization of the individual controllers on the performance of the hierarchical flexibility provision is studied on a three-level test system. The results show a high interdependency between the choice of control parameters of one controller and the behavior of other controllers as well as a significant impact on the accuracy and speed of flexibility provision. With a careful tuning, a cascaded structure based on online feedback optimization can achieve efficient vertical coordination of flexibility providing units.

Distribution grid flexibility is discussed as a possible measure in curative system operation, yielding a need for an efficient and robust coordination mechanism for the joint flexibility provision by individual units to the transmission grid. This paper introduces a method to coordinate distribution grid level flexibility as a fast-responding curative measure based on Online Feedback Optimization. We utilize an optimization algorithm in a closed loop with the distribution grid to dispatch set points for active and reactive power to flexibility providing units. The approach is evaluated in an experimental setup, utilizing assets connected to an exemplary low voltage grid. Online Feedback Optimization is found to be both a viable as well as a highly effective approach to coordinate distributed energy resources in real-time curative system operation.

Utilizing distribution grid flexibility for ancillary services requires the coordination and dispatch of requested active and reactive power to a large number of distributed energy resources in underlying grid layers. This paper presents an approach to hierarchically dispatch flexibility requests based on Online Feedback Optimization (OFO). We implement a framework of individual controllers coordinating actors, contributing to flexibility provision, to track a requested operating point at the interface between grid layers. The framework is evaluated in terms of performance during coordination and possible interaction between individual controllers, both central and distributed. Results show high reliability and robustness of the OFO controllers as well as an efficient dispatch of active and reactive power. Its computational efficiency and capabilities in set point tracking during online grid operation are making OFO a promising approach to the flexibility dispatch problem.

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.

Optimization is an essential part of power grid operation and lately, Online Optimization methods have gained traction. One such method is Online Feedback Optimization (OFO) which uses measurements from the grid as feedback to iteratively change the control inputs until they converge to the solution of the optimization problem. Such algorithms have been applied to many power system problems and experimentally validated in lab setups. This paper implements an OFO controller in a real distribution grid for 24/7 operation using off-the-shelf hardware and software. The proposed control strategy optimizes the reactive power flow at the substation while satisfying voltage constraints. As part of an existing coordination scheme between (sub)transmission grid operator (TSO) and distribution grid operator (DSO), this comes with a financial reward and simultaneously it virtually reinforces the grid by regulating the voltage on the feeder and therefore allowing higher levels of distributed generation/consumption. We present how a distribution grid is retrofitted such that we can use existing inverters, we analyze the controller's interaction with legacy infrastructure, and investigate its overall control behavior. Finally, we demonstrate the successful deployment of an OFO controller in an operational environment which corresponds to Technology Readiness Level (TRL) 7.

Online Feedback Optimization is a method used to steer the operation of a process plant to its optimal operating point without explicitly solving a nonlinear constrained optimization problem. This is achieved by leveraging a linear plant model and feedback from measurements. However the presence of plant-model mismatch leads to suboptimal results when using this approach. Learning the plant-model mismatch enables Online Feedback Optimization to overcome this shortcoming. In this work we present a novel application of Online Feedback Optimization with online model adaptation using Gaussian process regression. We demonstrate our approach with a realistic load sharing problem in a compressor station with parametric and structural plant-model mismatch. We assume imperfect knowledge of the compressor maps and design an Online Feedback Optimization controller that minimizes the compressor station power consumption. In the evaluated scenario, imperfect knowledge of the plant leads to a 5% increase in power consumption compared to the case with perfect knowledge. We demonstrate that Online Feedback Optimization with model adaptation reduces this increase to only 0.8%, closely approximating the case of perfect knowledge of the plant, regardless of the type of mismatch.

—The increasing electric power consumption and the shift towards renewable energy resources demand for new ways to operate transmission grids. We propose a feedback control method called Online Feedback Optimization (OFO) to enable real-time, constrained, and optimal control of the grid. The resulting controllers can minimize e.g., curtailment and losses while satisfying grid constraints, like voltage and current limits. Overall, we present the OFO control method which we extend to handle discrete inputs and tailor to transmission grids, we show a novel benchmark, explain how to design an OFO controller for the transmission grid, and display its performance on the benchmark. Finally, we show that OFO controllers can help utilize the transmission grid to its full extend, virtually reinforce it, and operate it optimally and in real-time while satisfying all grid constraints.

Medical drug infusion problems pose a combination of challenges such as nonlinearities from physiological models, model uncertainty due to inter- and intra-patient variability, as well as strict safety specifications. With these challenges in mind, we propose a novel real-time Nonlinear Model Predictive Control (NMPC) scheme based on projected gradient descent iterations. At each iteration, a small number of steps along the gradient of the NMPC cost is taken, generating a suboptimal input which asymptotically converges to the optimal input. We retrieve classical Lyapunov stability guarantees by performing a sufficient number of gradient iterations until fulfilling a stopping criteria. Such a real-time control approach allows for higher sampling rates and faster feedback from the system which is advantageous for the class of highly variable and uncertain drug infusion problems. To demonstrate the controller’s potential, we apply it to hypnosis control in anesthesia of two interacting drugs. The controller successfully regulates hypnosis even under disturbances and uncertainty and fulfils benchmark performance criteria.

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.

In this paper we propose an approach based on an Online Feedback Optimization (OFO) controller with grid input-output sensitivity estimation for real-time grid operation, e.g., at subsecond time scales. The OFO controller uses grid measurements as feedback to update the value of the controllable elements in the grid, and track the solution of a time-varying AC Optimal Power Flow (AC-OPF). Instead of relying on a full grid model, e.g., grid admittance matrix, OFO only requires the steady-state sensitivity relating a change in the controllable inputs, e.g., power injections set-points, to a change in the measured outputs, e.g., voltage magnitudes. Since an inaccurate sensitivity may lead to a model-mismatch and jeopardize the performance, we propose a recursive least-squares estimation that enables OFO to learn the sensitivity from measurements during real-time operation, turning OFO into a model-free approach. We analytically certify the convergence of the proposed OFO with sensitivity estimation, and validate its performance on a simulation using the IEEE 123-bus test feeder, and comparing it against a state-of-the-art OFO with constant sensitivity.

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.

In this paper, we study the stability and convergence of continuous-time Lagrangian saddle flows to solutions of a convex constrained optimization problem. Convergence of these flows is well-known when the underlying saddle function is either strictly convex in the primal or strictly concave in the dual variables. In this paper, we show convergence under non-strict convexity when a simple, unilateral augmentation term is added. For this purpose, we establish a novel, non-trivial characterization of the limit set of saddle-flow trajectories that allows us to preclude limit cycles. With our presentation we try to unify several existing problem formulations as a projected dynamical system that allows projection of both the primal and dual variables, thus complementing results available in the recent literature.

This paper addresses the problem of voltage regulation in a power distribution grid using the reactive power injections of grid-connected power inverters. We first discuss how purely local voltage control schemes cannot regulate the voltages within a desired range under all circumstances and may even yield detrimental control decisions. Communication and, through that, coordination are therefore needed. On the other hand, short-range peer-to-peer communication and knowledge of electric distances between neighbouring controllers are sufficient for this task. We implement such a peer-to-peer controller and test it on a 400~V distribution feeder with asynchronous communication channels, confirming its viability on real-life systems. Finally, we analyze the scalability of this approach with respect to the number of agents on the feeder that participate in the voltage regulation task.

We consider the problem of controlling the voltage of a distribution feeder using the reactive power capabilities of inverters. On a real distribution grid, we compare the local Volt/VAr droop control recommended in recent grid codes, a centralized dispatch based on optimal power flow (OPF) programming, and a feedback optimization (FO) controller that we propose. The local droop control yields suboptimal regulation, as predicted analytically. The OPF-based dispatch strategy requires an accurate grid model and measurement of all loads on the feeder in order to achieve proper voltage regulation. However, in the experiment, the OPF-based strategy violates voltage constraints due to inevitable model mismatch and uncertainties. Our proposed FO controller, on the other hand, satisfies the constraints and does not require load measurements or any grid state estimation. The only needed model knowledge is the sensitivity of the voltages with respect to reactive power, which can be obtained from data. As we show, an approximation of these sensitivities is also sufficient, which makes the approach essentially model-free, easy to tune, compatible with the current sensing and control infrastructure, and remarkably robust to measurement noise. We expect these properties to be fundamental features of FO for power systems and not specific to Volt/VAr regulation or to distribution grids.

The human insulin-glucose metabolism is a time-varying process, which is partly caused by the changing insulin sensitivity of the body. This insulin sensitivity follows a circadian rhythm and its effects should be anticipated by any automated insulin delivery system. This paper presents an extension of our previous work on automated insulin delivery by developing a controller suitable for humans with Type 1 Diabetes Mellitus. Furthermore, we enhance the controller with a new kernel function for the Gaussian Process and deal with noisy measurements, as well as, the noisy training data for the Gaussian Process, arising therefrom. This enables us to move the proposed control algorithm, a combination of Model Predictive Controller and a Gaussian Process, closer towards clinical application. Simulation results on the University of Virginia/Padova FDA-accepted metabolic simulator are presented for a meal schedule with random carbohydrate sizes and random times of carbohydrate uptake to show the performance of the proposed control scheme.