Dynamics-aware Continuous-time Economic Dispatch: A Solution for Optimal Frequency Regulation

This paper outlines a continuous-time economic dispatch (CTED) problem that intrinsically embeds dynamic constraints arising from the electromechanical behavior of synchronous generators and enables near-to-real-time optimal scheduling of generation. In its original form, the CTED problem is infinite-dimensional, however, we present a linear-programming reformulation that offers computational burden comparable to traditional economic dispatch. The resulting optimal dispatch trajectories are continuously differentiable and induce only small-signal variations in automatic generation control signals. In addition to yielding better system frequency response, this improves economic efficiency since the dispatch cost is better aligned with the actual cost of operating the system. We demonstrate the economic advantages and dynamic-performance improvements of the proposed method with time-domain simulations for a detailed differential algebraic equation model of an illustrative power network

Sorta Solving the OPF by Not Solving the OPF: DAE Control Theory and the Price of Realtime Regulation

This paper presents a new approach to solve or approximate the AC optimal power flow (ACOPF). By eliminating the need to solve the ACOPF every few minutes, the paper showcases how a realtime feedback controller can be utilized in lieu of ACOPF and its variants. By \textit{(i)} forming the grid dynamics as a system of differential algebraic equations (DAE) that naturally encode the non-convex OPF power flow constraints, \textit{(ii)} utilizing advanced DAE-Lyapunov theory, and \textit{(iii)} designing a feedback controller that captures realtime uncertainty while being uncertainty-unaware, the presented approach demonstrates promises of obtaining solutions that are close to the OPF ones without needing to solve the OPF. The proposed controller responds in realtime to deviations in renewables generation and loads, guaranteeing transient stability, while always yielding feasible solutions of the ACOPF with no constraint violations. As the studied approach herein indeed yields slightly more expensive realtime generator controls, the corresponding price of realtime control and regulation is examined. Cost-comparisons with the traditional ACOPF are also showcased -- all via case studies on standard power networks

Load and Renewable-Following Control of Linearization-Free Differential Algebraic Equation Power System Models

Electromechanical transients in power networks are mostly caused by mismatch between power consumption and production, causing generators to deviate from the nominal frequency. To that end, feedback control algorithms have been designed to perform frequency and load/renewables-following control. In particular, the literature addressed a plethora of grid- and frequency-control challenges with a focus on linearized, differential equation models whereby algebraic constraints (i.e., power flows) are eliminated. This is in contrast with the more realistic nonlinear differential algebraic equation (NDAE) models. Yet, as grids are increasingly pushed to their limits via intermittent renewables and varying loads, their physical states risk escaping operating regions due to either a poor prediction or sudden changes in renewables or demands -- deeming a feedback controller based on a linearization point virtually unusable. In lieu of linearized differential equation models, the objective of this paper is to design a simple, purely decentralized, linearization-free, feedback control law for NDAE models of power networks. The objective of such controller is to primarily stabilize frequency oscillations after a large, unknown disturbance in renewables or loads. Although the controller design involves advanced NDAE system theory, the controller itself is as simple as a decentralized proportional or linear quadratic regulator in its implementation. Case studies demonstrate that the proposed controller is able to stabilize dynamic and algebraic states under significant disturbances.Comment: 13 pages, 6 figures, 2 table

Power system intelligent operation knowledge learning model based on reinforcement learning and data-driven

With the expansion of power grid scale and the deepening of component coupling, the operation behavior of power system becomes more and more complex, and the traditional function decoupling dispatching architecture is not available anymore. Firstly, this paper studies the corresponding relationship between reinforcement learning method and power system dispatching decision problem, and constructs the artificial intelligent dispatching knowledge learning model of power system based on reinforcement learning (AIDLM). Then, a data-driven intelligent dispatching knowledge learning method is proposed, and interpretable dispatching decision knowledge is obtained. Finally, a knowledge efficiency evaluation indexes is proposed and used to guide the extraction of original acquired knowledge. The intelligent economic dispatching problem of a regional power grid is analyzed. The results show that the AIDLM method can intelligently give the dispatching strategy of power generation according to the time series changing load, which effectively reduces the cost of power generation in the grid. The method proposed in this paper can make up for the shortcomings of traditional dispatching methods and provide strong support for modern power system dispatching

Non-Convex Phase Retrieval Algorithms and Performance Analysis

University of Minnesota Ph.D. dissertation. April 2018. Major: Electrical Engineering. Advisor: Georgios Giannakis. 1 computer file (PDF); ix, 149 pages.High-dimensional signal estimation plays a fundamental role in various science and engineering applications, including optical and medical imaging, wireless communications, and power system monitoring. The ability to devise solution procedures that maintain high computational and statistical efficiency will facilitate increasing the resolution and speed of lensless imaging, identifying artifacts in products intended for military or national security, as well as protecting critical infrastructure including the smart power grid. This thesis contributes in both theory and methods to the fundamental problem of phase retrieval of high-dimensional (sparse) signals from magnitude-only measurements. Our vision is to leverage exciting advances in non-convex optimization and statistical learning to devise algorithmic tools that are simple, scalable, and easy-to-implement, while being computationally and statistically (near-)optimal. Phase retrieval is approached from a non-convex optimization perspective. To gain statistical and computational efficiency, the magnitude data (instead of the intensities) are fitted based on the least-squares or maximum likelihood criterion, which leads to optimization models that trade off smoothness for ‘low-order’ non-convexity. To solve the resultant challenging nonconvex and non-smooth optimization, the present thesis introduces a two-stage algorithmic framework, that is termed amplitude flow. The amplitude flows start with a careful initialization, which is subsequently refined by a sequence of regularized gradient-type iterations. Both stages are lightweight, and they scale well with problem dimensions. Due to the highly non-convex landscape, judicious gradient regularization techniques such as trimming (i.e., truncation) and iterative reweighting are devised to boost the exact phase recovery performance. It is shown that successive iterates of the amplitude flows provably converge to the global optimum at a geometric rate, corroborating their efficiency in terms of computational, storage, and data resources. The amplitude flows are also demonstrated to be stable vis-a-vis additive noise. Sparsity plays a instrumental role in many scientific fields - what has led to the upsurge of research referred to as compressive sampling. In diverse applications, the signal is naturally sparse or admits a sparse representation after some known and deterministic linear transformation. This thesis also accounts for phase retrieval of sparse signals, by putting forth sparsity-cognizant amplitude flow variants. Although analysis, comparisons, and corroborating tests focus on non-convex phase retrieval in this thesis, a succinct overview of other areas is provided to highlight the universality of the novel algorithmic framework to a number of intriguing future research directions