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Advanced techniques of power system restoration and practical applications in transmission grids

ELECTRIC POWER SYSTEMS RESEARCH 2020年第0期182卷 106238-000页

作者： Sharma, Dhruv Lin, Chenxi Luo, Xiaochuan Wu, Di Thulasiraman, Krishnaiya Jiang, John N. VIT Bhopal Univ Bhopal India Eleon Energy Austin TX USA ISO New England Holyoke MA USA North Dakota State Univ Fargo ND USA Univ Oklahoma Norman OK 73019 USA

Optimal restoration of a real-time power system following a disruption is a complex process. In view of that and with increase in frequency and severity of power system outages across the US and their impact on consumers and utilities, North American Electric Reliability Corporation elevated the standard of compliance for power system restoration. While several utilities have proposed solutions addressing the elevated standards based on dynamic programming, they could not address the issues for large-scale power systems and real-time operations including those using steady-state and transient analysis due to the curses of dimensionality. In this paper, we introduce a restoration process based on approximate dynamic programming integrated with solution space reduction methodology. The main theoretical foundations of the methodology and key algorithms used in this restoration process include the knowledge of power system engineering, complex network science, concepts of graph theory, and dynamic programming in operation research. We first use the proposed method to demonstrate an optimal restoration process on the IEEE 118-bus test system and then on a 2000-bus synthetic test system. This method addresses the concerns related to the curses of dimensionality and simplifies the solution space and thus can be applied to various complex real-time operation settings.

关键词： Power system restoration approximate dynamic programming Solution space reduction

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approximate dynamic programming for dynamic capacity allocation with multiple priority levels

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IIE TRANSACTIONS 2011年第2期43卷 129-142页

作者： Erdelyi, Alexander Topaloglu, Huseyin Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14853 USA

This article considers a quite general dynamic capacity allocation problem. There is a fixed amount of daily processing capacity. On each day, jobs of different priorities arrive randomly and a decision has to made about which jobs should be scheduled on which days. Waiting jobs incur a holding cost that is a function of their priority levels. The objective is to minimize the total expected cost over a finite planning horizon. The problem is formulated as a dynamic program, but this formulation is computationally difficult as it involves a high-dimensional state vector. To address this difficulty, an approximate dynamic programming approach is used that decomposes the dynamic programming formulation by the different days in the planning horizon to construct separable approximations to the value functions. Value function approximations are used for two purposes. First, it is shown that the value function approximations can be used to obtain a lower bound on the optimal total expected cost. Second, the value function approximations can be used to make the job scheduling decisions over time. Computational experiments indicate that the job scheduling decisions made by the proposed approach perform significantly better than a variety of benchmark strategies.

关键词： approximate dynamic programming capacity allocation scheduling

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Robust Control of Unknown Observable Nonlinear Systems Solved as a Zero-Sum Game

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IEEE ACCESS 2020年 8卷 214153-214165页

作者： Radac, Mircea-Bogdan Lala, Timotei Politehn Univ Timisoara Dept Automat & Appl Informat Timisoara 300223 Romania

An optimal robust control solution for general nonlinear systems with unknown but observable dynamics is advanced here. The underlying Hamilton-Jacobi-Isaacs (HJI) equation of the corresponding zero-sum two-player game (ZS-TP-G) is learned using a Q-learning-based approach employing only input-output system measurements, assuming system observability. An equivalent virtual state-space model is built from the system's input-output samples and it is shown that controlling the former implies controlling the latter. Since the existence of a saddle-point solution to the ZS-TP-G is assumed unverifiable, the solution is derived in terms of upper-optimal and lower-optimal controllers. The learning convergence is theoretically ensured while practical implementation is performed using neural networks that provide scalability to the control problem dimension and automatic feature selection. The learning strategy is checked on an active suspension system, a good candidate for the robust control problem with respect to road profile disturbance rejection.

关键词： Mathematical model Robust control Games Optimal control Linear systems Game theory Roads Active suspension system approximate dynamic programming neural networks optimal control reinforcement learning state feedback zero-sum two-player games

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Output feedback adaptive dynamic programming for linear differential zero-sum games

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AUTOMATICA 2020年 122卷 109272-109272页

作者： Rizvi, Syed Ali Asad Lin, Zongli Brown, Charles L. Univ Virginia Charles L Brown Dept Elect & Comp Engn POB 400743 Charlottesville VA 22904 USA

This paper addresses the problem of finding optimal output feedback strategies for solving linear differential zero-sum games using a model-free approach based on adaptive dynamic programming (ADP). In contrast to their discrete-time counterparts, differential games involve continuous-time dynamics and existing ADP approaches to their solutions require access to full measurement of the internal state. This difficulty is due to the fact that direct translation of the discrete-time output feedback ADP results requires derivatives of the input and output measurements, which is generally prohibitive in practice. This work aims to overcome this difficulty and presents a new embedded filtering based observer approach towards designing output feedback ADP algorithms for solving the differential zero-sum game problem. Two output feedback ADP algorithms based respectively on policy iteration and value iteration are developed. The proposed scheme is completely online in nature and works without requiring information of the system dynamics. In addition, this work also addresses the excitation bias problem encountered in output feedback ADP methods, which typically requires a discounting factor for its mitigation. We show that the proposed scheme is bias-free, and therefore, does not require a discounting factor. It is shown that the proposed algorithms converge to the solution obtained by solving the game algebraic Riccati equation. Two numerical examples are demonstrated to validate the proposed scheme. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Adaptive dynamic programming approximate dynamic programming Zero-sum games Output feedback

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Train trajectory optimization for improved on-time arrival under parametric uncertainty

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2020年 119卷 102680-102680页

作者： Wang, Pengling Trivella, Alessio Goverde, Rob M. P. Corman, Francesco Swiss Fed Inst Technol IVT Inst Transport Planning & Syst Zurich Switzerland Delft Univ Technol Dept Transport & Planning Delft Netherlands

In this paper we study the problem of computing train trajectories in an uncertain environment in which the values of some system parameters are difficult to determine. Specifically, we consider uncertainty in traction force and train resistance, and their impact on travel time and energy consumption. Our ultimate goal is to be able to control trains such that they will arrive on-time, i.e. within the planned running time, regardless of uncertain factors affecting their dynamic or kinematic performance. We formulate the problem as a Markov decision process and solve it using a novel numerical approach which combines: (i) an off-line approximate dynamic programming (ADP) method to learn the energy and time costs over iterations, and (ii) an on-line search process to determine energy-efficient driving strategies that respect the real-time time windows, more in general expressed as train path envelope constraints. To evaluate the performance of our approach, we conducted a numerical study using real-life railway infrastructure and train data. Compared to a set of benchmark driving strategies, the trajectories from our ADP-based method reduce the probability of delayed arrival, and at the same time are able to better use the available running time for energy saving. Our results show that accounting for uncertainty is relevant when computing train trajectories and that our ADP-based method can handle this uncertainty effectively.

关键词： Train trajectory optimization Parametric uncertainty approximate dynamic programming

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approximate dynamic programming for an inventory problem: Empirical comparison

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COMPUTERS & INDUSTRIAL ENGINEERING 2011年第4期60卷 719-743页

作者： Katanyukul, Tatpong Duff, William S. Chong, Edwin K. P. Colorado State Univ Coll Engn Dept Mech Engn Ft Collins CO 80523 USA Colorado State Univ Coll Engn Elect & Comp Engn Dept Ft Collins CO 80523 USA

This study investigates the application of learning-based and simulation-based approximate dynamic programming (ADP) approaches to an inventory problem under the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Specifically, we explore the robustness of a learning-based ADP method, Sarsa, with a GARCH(1,1) demand model, and provide empirical comparison between Sarsa and two simulation-based ADP methods: Rollout and Hindsight Optimization (HO). Our findings assuage a concern regarding the effect of GARCH(1,1) latent state variables on learning-based ADP and provide practical strategies to design an appropriate ADP method for inventory problems. In addition, we expose a relationship between ADP parameters and conservative behavior. Our empirical results are based on a variety of problem settings, including demand correlations, demand variances, and cost structures. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： approximate dynamic programming Inventory control Reinforcement learning Simulation Heterogeneity AR(1)/GARCH(1,1)

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approximate dynamic programming for Optimal Stationary Control with Control-Dependent Noise

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2011年第12期22卷 2392-2398页

作者： Jiang, Yu Jiang, Zhong-Ping NYU Polytech Inst Dept Elect & Comp Engn Brooklyn NY 11201 USA Beijing Univ Coll Engn Beijing 100214 Peoples R China

This brief studies the stochastic optimal control problem via reinforcement learning and approximate/adaptive dynamic programming (ADP). A policy iteration algorithm is derived in the presence of both additive and multiplicative noise using Ito calculus. The expectation of the approximated cost matrix is guaranteed to converge to the solution of some algebraic Riccati equation that gives rise to the optimal cost value. Moreover, the covariance of the approximated cost matrix can be reduced by increasing the length of time interval between two consecutive iterations. Finally, a numerical example is given to illustrate the efficiency of the proposed ADP methodology.

关键词： approximate dynamic programming control-dependent noise optimal stationary control stochastic systems

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Valuing portfolios of interdependent real options using influence diagrams and simulation-and-regression: A multi-stage stochastic integer programming approach

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COMPUTERS & OPERATIONS RESEARCH 2020年 115卷 104505-000页

作者： Maier, Sebastian Polak, John W. Gann, David M. Imperial Coll London Dept Civil & Environm Engn London SW7 2AZ England Imperial Coll London Grantham Inst Climate Change & Environm London SW7 2AZ England Imperial Coll London Ctr Transport Studies London SW7 2AZ England Imperial Coll London Urban Syst Lab London SW7 2AZ England Imperial Coll London Imperial Coll Business Sch London SW7 2AZ England

Although real options generally occur within portfolios, most valuation approaches based on either option pricing or decision analysis alone focus on single well-defined options. In this paper we present a new approach for modelling and approximating the value of portfolios of interdependent real options using both influence diagrams and simulation-and-regression. The key feature of this approach is that it translates the interdependencies between real options into a set of constraints and then directly models the dynamics of all underlying uncertainties using (Markovian) stochastic processes. These are then integrated in a portfolio optimisation problem which is formulated as a multi-stage stochastic integer program. Applying a simulation and parametric regression approach to approximate the value of this optimisation problem, we present a transparent valuation algorithm that explicitly takes into account vector-valued exercise decisions and the state variable's multidimensional resource component. The approach is therefore applicable to a wide range of complex investment projects with both inherent interdependent flexibilities and many underlying uncertainties. The approach is illustrated by evaluating a complex natural resource investment that features both a large portfolio of interdependent real options and four stochastic factors. We analyse the way in which the approximated value of the portfolio and its individual options are affected by the initial copper price as well as by the degrees of production cost and copper price uncertainty. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Real options portfolio Influence diagram Simulation-and-regression approximate dynamic programming Natural resource investment

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Reinforcement-Learning-based Optimization for Day-ahead Flexibility Extraction in Battery Pools ⁎

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IFAC-PapersOnLine 2020年第2期53卷 13351-13358页

作者： Georgios C. Chasparis Christian Lettner Software Competence Center Hagenberg GmbH Softwarepark 21 4232 Hagenberg Austria

We address the problem of trading energy flexibility, derived from pools of residential Photovoltaic and battery-storage systems, to the Day-ahead electricity market. By flexibility, we imply any additional energy that can be stored to or withdrawn from the participating batteries/households at a given time during the next day. The optimization variables include the selection/activation of a subset of participating batteries and the amount of flexibility that should be extracted. Furthermore, the optimization objective corresponds to the expected forecast revenues that can be generated by trading this flexibility to the Day-ahead electricity market. Given the high computationally complexity of a full scale optimization in the case of a large number of participating batteries, we propose a reinforcement-learning-based methodology, which admits linear complexity with the number of participating batteries. The proposed methodology advances prior work with respect to the integration of a large number of batteries. Furthermore, it extends prior work of the authors with respect to providing analytical performance guarantees in comparison with the baseline/nominal operation of the battery. Finally, we compare through simulations the performance of the proposed method with a Linear-programming-based optimization that provides the exact optimum.

关键词： Control of renewable energy resources Smart grids approximate dynamic programming Day-ahead spot electricity market

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approximate dynamic programming with state aggregation applied to UAV perimeter patrol

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2011年第12期21卷 1396-1409页

作者： Krishnamoorthy, K. Pachter, M. Darbha, S. Chandler, P. USAF Control Design & Anal Branch Res Lab RBCA Wright Patterson AFB OH 45433 USA USAF Inst Technol Dept Elect Engn Wright Patterson AFB OH 45433 USA Texas A&M Univ Dept Mech Engn College Stn TX 77843 USA

One encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for large-scale controlled Markov chains. In this paper, we provide a reward-based aggregation method to construct suboptimal policies for a perimeter surveillance control problem which gives rise to a large scale Markov chain. The novelty of this approach lies in circumventing the need for value iteration over the entire state space. Instead, the state space is partitioned and the value function is approximated by a constant over each partition. We associate a meta-state with each partition, where the transition probabilities between these meta-states are known. The state aggregation approach results in a significant reduction in the computational burden and lends itself to value iteration over the aggregated state-space. We provide bounds to assess the quality of the approximation and give numerical results that support the proposed methodology. Published 2011. This article is a US Government work and is in the public domain in the USA.

关键词： controlled Markov chain perimeter patrol approximate dynamic programming state aggregation

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