Projected gradient descent on Riemannian manifolds with applications to online power system optimization

Hauswirth, Adrian; Bolognani, Saverio; Hug, Gabriela; Dörfler, Florian

doi:10.1109/allerton.2016.7852234

Cited by 75 publications

(61 citation statements)

References 15 publications

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“…Instead, we need only its Jacobian with respect to the decision variable u (which still depends π and w). In [4], [7], the authors show promising results for various optimal power flow problems where algorithms similar to Algorithm 1 reach near-optimal solutions, reject time-varying disturbances despite not using the exact Jacobian; these robustness properties are precisely the well-known advantages of feedback over feedforward control. In this work, we study robustness for the simplest approximation of the Jacobian i.e.,…”

Section: A the Standard Approach: Feedforward Optimizationmentioning

confidence: 97%

“…Traditionally, the optimal operation of such large scale engineering systems is done via frequent re-optimization based on complex models and disturbance forecasts. Recently, however, much simpler online (or feedback-based) optimization methods have been proposed for constrained engineering systems with tremendous success in applications ranging from communication networks [1] to power systems [2]- [7] to transportation [8].…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we focus on a simple first-order online approximate gradient descent, similar to those proposed in [4], [7]. The novel contributions of the work are that we • characterize the equilibria of the feedback interconnection of the physical system and the online optimization scheme using methods from the literature on variational inequalities [11] and monotone operators [12]; • propose a framework, based on classical robust control theory [13]- [16] that allows us to systematically test the robustness properties of the online algorithm by guaranteeing robust stability with respect to a large class of uncertain physical systems; • validate our results both on an academic example and a case study of a power distribution system, for which the proposed methods allows us to verify robust stability for a wide range of realistic operating conditions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Towards robustness guarantees for feedback-based optimization

Colombino

Simpson-Porco

Bernstein

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Feedback-based online optimization algorithms have gained traction in recent years because of their simple implementation, their ability to reject disturbances in real time, and their increased robustness to model mismatch. While the robustness properties have been observed both in simulation and experimental results, the theoretical analysis in the literature is mostly limited to nominal conditions. In this work, we propose a framework to systematically assess the robust stability of feedback-based online optimization algorithms. We leverage tools from monotone operator theory, variational inequalities and classical robust control to obtain tractable numerical tests that guarantee robust convergence properties of online algorithms in feedback with a physical system, even in the presence of disturbances and model uncertainty. The results are illustrated via an academic example and a case study of a power distribution system.

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Section: A the Standard Approach: Feedforward Optimizationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Towards robustness guarantees for feedback-based optimization

Colombino

Simpson-Porco

Bernstein

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…To achieve this fast optimization process, we can use an early stopping optimization or the recent work on projected gradient online optimization methods for the OPF problem in [4], [5]. Moreover, this fast optimization allows to avoid outdated setpoints and thus suboptimal solutions as remarked in [4].…”

Section: B Power Flow Approximationmentioning

confidence: 99%

Stochastic Optimal Power Flow in Distribution Grids under Uncertainty from State Estimation

Picallo

Anta

Schutter

2018

2018 IEEE Conference on Decision and Control (CDC)

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The increasing amount of controllable generation and consumption in distribution grids poses a severe challenge in keeping voltage values within admissible ranges. Existing approaches have considered different optimal power flow formulations to regulate distributed generation and other controllable elements. Nevertheless, distribution grids are characterized by an insufficient number of sensors, and state estimation algorithms are required to monitor the grid status. We consider in this paper the combined problem of optimal power flow under state estimation, where the estimation uncertainty results into stochastic constraints for the voltage magnitude levels instead of deterministic ones. To solve the given problem efficiently and to bypass the lack of load measurements, we use a linear approximation of the power flow equations. Moreover, we derive a transformation of the stochastic constraints to make them tractable without being too conservative. A case study shows the success of our approach at keeping voltage within limits, and also shows how ignoring the uncertainty in the estimation can lead to voltage level violations.

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“…These facts are particularly useful in the context of feedback-based optimization which has recently garnered a lot of interest for applications such as the real-time control and optimization of power systems [8], communication networks [9], and other infrastructure systems. Feedback-based optimization aims at designing feedback controllers that can steer a (stable) physical system to a steady state that solves a well-defined, but partially unknown, constrained optimization problem, for instance by designing feedback controllers to implement gradient [10]- [12] or saddle-point flows [13]- [15] as a closed-loop behavior.…”

Section: Introductionmentioning

confidence: 99%

On the Differentiability of Projected Trajectories and the Robust Convergence of Non-Convex Anti-Windup Gradient Flows

Hauswirth

Dörfler

Teel

2020

IEEE Control Syst. Lett.

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This paper concerns a new class of discontinuous dynamical systems for constrained optimization. These dynamics are particularly suited to solve nonlinear, non-convex problems in closed-loop with a physical system. Such approaches using feedback controllers that emulate optimization algorithms have recently been proposed for the autonomous optimization of power systems and other infrastructures. In this paper, we consider feedback gradient flows that exploit physical input saturation with the help of anti-windup control to enforce constraints. We prove semi-global convergence of "projected" trajectories to firstorder optimal points, i.e., of the trajectories obtained from a pointwise projection onto the feasible set. In the process, we establish properties of the directional derivative of the projection map for non-convex, prox-regular sets.

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Projected gradient descent on Riemannian manifolds with applications to online power system optimization

Cited by 75 publications

References 15 publications

Towards robustness guarantees for feedback-based optimization

Towards robustness guarantees for feedback-based optimization

Stochastic Optimal Power Flow in Distribution Grids under Uncertainty from State Estimation

On the Differentiability of Projected Trajectories and the Robust Convergence of Non-Convex Anti-Windup Gradient Flows

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