A Feedback-Based Regularized Primal-Dual Gradient Method for Time-Varying Nonconvex Optimization

This paper considers time-varying nonconvex optimization problems, utilized to model optimal operational trajectories of systems governed by possibly nonlinear physical or logical models. Algorithms for tracking a Karush-Kuhn-Tucker point are synthesized, based on a regularized primal-dual gradient method. In particular, the paper proposes a feedback-based primal-dual gradient algorithm, where analytical models for system state or constraints are replaced with actual measurements. When cost and constraint functions are twice continuously differentiable, conditions for the proposed algorithms to have bounded tracking error are derived, and a discussion of their practical implications is provided. Illustrative numerical simulations are presented for an application in power systems

A Feedback-Based Regularized Primal-Dual Gradient Method for Time-Varying Nonconvex Optimization

This paper considers time-varying nonconvex optimization problems, utilized to model optimal operational trajectories of systems governed by possibly nonlinear physical or logical models. Algorithms for tracking a Karush-Kuhn-Tucker point are synthesized, based on a regularized primal-dual gradient method. In particular, the paper proposes a feedback-based primal-dual gradient algorithm, where analytical models for system state or constraints are replaced with actual measurements. When cost and constraint functions are twice continuously differentiable, conditions for the proposed algorithms to have bounded tracking error are derived, and a discussion of their practical implications is provided. Illustrative numerical simulations are presented for an application in power systems

Distributed Algorithm for Time-varying Optimal Power Flow

Future power system applications may require real-time optimization of a large network of distributed energy resources. This has motivated recent development of online algorithms for solving time-varying optimal power flow problems. We have proposed a centralized quasi-Newton algorithm and have derived theoretical guarantees for its tracking performance. In this paper we show how this algorithm can be implemented in a distributed manner by a network of controllable energy resources coordinated by an operator. The proposed distributed implementation now can handle general convex quadratic constraints on power injections, and only requires minimal communication between the operator and local controllers. Simulation shows that the proposed distributed implementation has good performance

Distributed Algorithm for Time-varying Optimal Power Flow

Future power system applications may require real-time optimization of a large network of distributed energy resources. This has motivated recent development of online algorithms for solving time-varying optimal power flow problems. We have proposed a centralized quasi-Newton algorithm and have derived theoretical guarantees for its tracking performance. In this paper we show how this algorithm can be implemented in a distributed manner by a network of controllable energy resources coordinated by an operator. The proposed distributed implementation now can handle general convex quadratic constraints on power injections, and only requires minimal communication between the operator and local controllers. Simulation shows that the proposed distributed implementation has good performance