0 导语

传统微电网调度策略（如模型预测控制等）过于依赖随机变量的预测精度，且对系统历史数据未充分利用。为此，本文提出了一种基于分段线性ADP的微电网调度策略，并进一步提出了一种新型分段线性函数更新策略以提高算法收敛速度。敬请关注本期推荐。

Stochastic Optimization of Economic Dispatch for Microgrid Based on Approximate

Dynamic Programming

Hang Shuai, Jiakun Fang, Xiaomeng Ai, Yufei Tang, Jinyu Wen, and Haibo He

期刊名字：IEEE Transactions on Smart Grid

Abstract/Highlight

This paper proposes an approximate dynamic programming (ADP)-based approach for the economic dispatch (ED) of microgrid with distributed generations. The time-variant renewable generation, electricity price, and the power demand are considered as stochastic variables in this paper. An ADP based ED (ADPED) algorithm is proposed to optimally operate the microgrid under these uncertainties. To deal with the uncertainties, Monte Carlo method is adopted to sample the training scenarios to give empirical knowledge to ADPED. The piecewise linear function (PLF) approximation with improved slope updating strategy is employed for the proposed method. With sufficient information extracted from these scenarios and embedded in the PLF function, the proposed ADPED algorithm can not only be used in day-ahead scheduling but also the intra-day optimization process. The algorithm can make full use of historical prediction error distribution to reduce the influence of inaccurate forecast on the system operation. Numerical simulations demonstrate the effectiveness of the proposed approach. The near-optimal decision obtained by ADPED is very close to the global optimality. And it can be adaptive to both day-ahead and intra-day operation under uncertainty.

1 研究背景

微电网是实现分布式可再生能源高效利用的重要方式。微电网的日前及日内优化调度技术对提高系统运行的经济性和安全性至关重要。现有的微电网调度方法过于依赖可再生能源、电价及负荷等预测信息的精度，且对系统历史数据未充分利用。此外，微电网日内在线调度目前大多采用模型预测控制（MPC），其根据日内滚动更新的超短期预测信息，实时滚动优化系统决策。但是，基于MPC的在线调度策略难以保证决策的全局最优性。

2 论文所解决的问题及意义

围绕微电网随机优化问题，建立了考虑线性化网络潮流约束的微电网随机优化模型，并将该优化模型转化为马尔科夫决策过程（Markov decision process），在此基础上提出了基于改进分段线性ADP算法的在线优化策略，为微电网的日前及日内调度提供了新方法。

3 论文重点内容

1）微电网随机优化模型

微电网中的电源可以分为可调度电源和不可调度电源。可调度电源包含小型燃气发电机（gas generator, GG）、燃料电池（fuel cell, FC）、储能设备等；不可调度电源包括风机（wind turbine, WT）、光伏电池板（photovoltaic panel, PV）等。图1为微电网的结构示意图。微电网在线优化的目标函数是最小化优化周期T 内系统的运行费用，包括常规机组的燃料费用、常规机组的运行维护费用、微电网向大电网的购电费用，以及弃风/光/负荷费用。微电网运行约束包括网络潮流约束、机组出力上下限约束、机组爬坡速率约束、弃风/光/负荷功率约束、微电网与外部电网功率交换上下限约束、电池充放电功率上下限约束、电池充放电状态约束、电池荷电状态平衡约束，电池剩余电量约束、网络节点电压幅值和相角约束、线路传输功率约束。

图1 微电网结构示意图

2）分段线性ADP算法

根据贝尔曼最优性原理，多时段优化问题可按时段分解为多个单时段优化问题，而每一时段的最优决策通过求解贝尔曼方程获得。但由于实际优化问题中的状态空间、决策空间过大带来的“维数灾”问题以及系统中存在随机性，使得求解贝尔曼方程极为耗时甚至不可解。为此，近似动态规划（ADP）通过采用近似值函数逐步迭代逼近真实值函数来避免“维数灾”难题。本研究采用分段线性函数近似真实值函数，如图2所示。

传统分段线性ADP算法的收敛速度相对较慢。本文认识到分段线性函数斜率的物理含义为储能所储存电量的边际效应，进而提出了一种改进的分段线性函数斜率更新策略，从而明显加快了分段线性ADP算法的收敛速度。

图2 分段线性值函数示意图

3）基于分段线性ADP的微电网在线调度策略

图3所示为基于分段线性ADP的微电网日前及日内在线调度策略示意图。首先，根据日前预测的光伏、风电、电价及负荷曲线，以及日前预测误差的分布信息，通过蒙特卡洛抽样产生诸多场景；其次，采用生成的训练场景训练ADP算法直至收敛，并计算微电网日前运行费用的期望值；最后，根据训练得到的分段线性函数以及微电网实时状态信息逐时段求解贝尔曼方程获得日内在线调度决策。

图3 基于分段线性ADP的微电网日前及日内在线调度策略

Conclusion

This paper proposes an ADPED algorithm for the stochastic optimization of the microgrid. A modified value function update strategy is included in the proposed method.

1) The proposed ADP algorithm outperforms the myopic method and MPC algorithm in the deterministic and stochastic cases. Besides, the optimization error of the pro osed ADP algorithm is less than 0.56% in the case studies.

2) The proposed ADP algorithm has a faster convergence rate than the traditional ADP algorithm.

3) The proposed ADP algorithm can be utilized in both the day-ahead scheduling and the intra-day online optimization. With the empirical knowledge embedded in the well trained ADP, the algorithm does not need the intra-day forecast information of the microgrid when applied in the on-line optimization process.

引文信息

H. Shuai, J. Fang, X. Ai, Y. Tang, J. Wen and H. He, "Stochastic Optimization of Economic Dispatch for Microgrid Based on Approximate Dynamic Programming[J]," IEEE Transactions on Smart Grid, 2019, 10 (3): 2440-2452. doi: 10.1109/TSG.2018.2798039.

（https://ieeexplore.ieee.org/abstract/document/8269410）

作者简介：

Hang Shuai (S’17) ) received the B.Eng. degree from Wuhan Institute of Technology (WIT), China, in 2013, and the Ph.D. degree in electrical engineering from Huazhong University of Science and Technology (HUST), China, in 2019. He was also a visiting student researcher at the University of Rhode Island, Kingston, RI, USA. Currently he is a postdoctoral researcher at the Department of Electrical, Computer, and Biomedical Engineering at the University of Rhode Island.His research interests include power systems operation and economics, stochastic optimization, and machine learning.

Jiakun Fang (S’10–M’13) received the B.Sc. and Ph.D. degrees from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 2007 and 2012, respectively.He was with HUST. He is currently an Assistant Professor with the Department of Energy Technology, Aalborg University, Aalborg, Denmark. His research interests include power system dynamic stability control, power grid complexity analysis, and integrated energy system.

Xiaomeng Ai (M’17) received the B.Eng. degree in mathematics and applied mathematics and the Ph.D. degree in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2008 and 2014, respectively, where he is currently a Research fellow.His research interests include robust optimization theory in power system and renewable energy integration.

Yufei Tang (M’16) received the B.Eng. and M.Sci. degrees from Hohai University, Nanjing, China, in 2008 and 2011, respectively, and the Ph.D. degree in electrical engineering from the Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI, USA, in 2016.He is currently an Assistant Professor with the Department of Electrical, Computer, and Biomedical Engineering, and a Faculty Fellow with the Institute for Sensing and Embedded Network Systems Engineering, Florida Atlantic University, Boca Raton, FL, USA. His research interests include power systems stability and control, smart grid security, computational intelligence, and cyber-physical energy systems.

Jinyu Wen (M’10) received the B.Eng. and Ph.D. degrees from the Huazhong University of Science and Technology (HUST), Wuhan, China, in 1992 and 1998, respectively, both in electrical engineering. He was a visiting student from 1996 to 1997 and a Research Fellow from 2002 to 2003 with the University of Liverpool, U.K., and a Senior Visiting Researcher with the University of Texas at Arlington, USA, in 2010. From 1998 to 2002, he was a Director Engineer with XJ Electric Company Ltd., China. In 2003, he joined HUST, where he is currently a Professor. His current research interests include renewable energy integration, energy storage application, dc grid, and power system operation and control.

Haibo He (SM’11–F’17) received the B.S. and M.S. degrees in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China, in 1999 and 2002, respectively, and the Ph.D. degree in electrical engineering from Ohio University, Athens, OH, USA, in 2006. From 2006 to 2009, he was an Assistant Professor with the Department of Electrical and Computer Engineering, Stevens Institute of Technology. He is currently the Robert Haas Endowed Chair Professor with the Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI, USA. His research interests include adaptive dynamic programming, computational intelligence, machine learning and data mining, and various applications.Prof. He was a recipient of the IEEE International Conference on Communications Best Paper Award in 2014, the IEEE Computational Intelligence Society Outstanding Early Career Award in 2014, the National Science Foundation CAREER Award in 2011, and the Providence Business News “Rising Star Innovator Award” in 2011. He served as the General Chair of the IEEE Symposium Series on Computational Intelligence. He is currently the Editor-in-Chief of the IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS.

期刊简介：IEEE Transactions on Smart Grid，一区期刊，2018年影响因子10.486。期刊主要关注智能电网发电、输电、配电和用电相关的原创理论及应用研究。