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A Model Predictive Control Based Distributed Coordination of Multi-microgrids in Energy Internet

Zhang Yan Zhang Tao Wang Rui Liu Yajie Guo Bo

张彦, 张涛, 王锐, 刘亚杰, . 基于模型预测控制的含多微电网的能源互联网分布式协同优化. 自动化学报, 2017, 43(8): 1443-1456. doi: 10.16383/j.aas.2017.e150300
引用本文: 张彦, 张涛, 王锐, 刘亚杰, . 基于模型预测控制的含多微电网的能源互联网分布式协同优化. 自动化学报, 2017, 43(8): 1443-1456. doi: 10.16383/j.aas.2017.e150300
Zhang Yan, Zhang Tao, Wang Rui, Liu Yajie, Guo Bo. A Model Predictive Control Based Distributed Coordination of Multi-microgrids in Energy Internet. ACTA AUTOMATICA SINICA, 2017, 43(8): 1443-1456. doi: 10.16383/j.aas.2017.e150300
Citation: Zhang Yan, Zhang Tao, Wang Rui, Liu Yajie, Guo Bo. A Model Predictive Control Based Distributed Coordination of Multi-microgrids in Energy Internet. ACTA AUTOMATICA SINICA, 2017, 43(8): 1443-1456. doi: 10.16383/j.aas.2017.e150300

基于模型预测控制的含多微电网的能源互联网分布式协同优化

doi: 10.16383/j.aas.2017.e150300

A Model Predictive Control Based Distributed Coordination of Multi-microgrids in Energy Internet

More Information
    Author Bio:

    Tao Zhang received the B.S., M.S., PhD degree from the National University of Defense Technology (NUDT), China, in 1998, 2001, and 2004, respectively.He is currently a Professor at the College of Information System and Management, the NUDT.His main research areas include multi-criteria decision making, optimal scheduling, data mining and optimization methods on energy internet network.E-mail:zhangtao@nudt.edu.cn

    Rui Wang received the B.S.degree from the National University of Defense Technology (NUDT), China, in 2008, and the Ph.D.degree from the University of She-eld, U.K in 2013.He is currently a Lecturer at the NUDT.His main research areas include evolutionary computation, multi-objective optimization, machine learning, optimization methods on energy internet network.He wins the Operational Research Society Ph.D.prize Runners-up for the best Ph.D.dissertation 2016.E-mail:ruiwangnudt@gmail.com

    Yajie Liu a Ph.D.and an Associate Professor in National University of Defense Technology.He was a visiting scholar at the Mechanical and Industrial Engineering Department of the University of Toronto from September 2008 to October 2009.His research interests include stochastic and robust optimization methods in energy management systems of microgird.E-mail:energy net@sohu.com

    Bo Guo received the B.S.degree in Mathematics from Huazhong Institute of Technology, the M.S.degree in system engineering from NUDT and the Ph.D.degree in engineering management from Tokyo University of Science.Currently, he is the academic leader of Group of Management Science and Engineering, the principal of National Level Teaching Team in System Engineering and Management, a member of National Educational Guidance Committee for the Postgraduate of Engineering Management, and an assessor of International Project Management Professional.His research interests include system reliability, maintenance, supportability and safety.He has received 8 provincial-level scientiflc and technological progress awards and 3 provincial-level teaching progress awards.He has published over 80 papers and 4 books including "Analysis of System Reliability" and "Project Risk Management".E-mail:guobo@nudt.edu.cn

    Corresponding author: Yan Zhang received the B.S.degree from the Sichuan University (SCU), China, in 2010, and the Ph.D.degree from the National University of Defense Technology (NUDT), China in 2016.He is currently a Lecturer at the Science and Technology on Ship Integrated Power System Technology Laboratory, Naval University of Engineering.His main research areas include model predictive control, energy management and optimization, optimization methods on microgrid and energy internet.Corresponding author of this paper. E-mail:zy331214534@126.com
  • 摘要: 研究了预测不确定性条件下含多个微电网的能源互联网分布式协同调度策略.各微电网都拥有多种智能负荷,如功率可调负荷、可调度负荷和关键负荷;部分微电网含有分布式电源,如微型燃气轮机、风电机组、光伏发电系统等;且部分微电网还拥有储能设备,如电池储能系统.每个微电网都可当做一个独立的实体,拥有自己的运行目标,这些运行目标可表示成混合整数规划模型.提出了基于并行分布式优化的博弈模型以较小的信息通信量协调各微电网带有竞争性的运行目标.在此基础上,引入模型预测控制(MPC)机制以降低能源互联网中风、光等可再生能源输出、负荷需求及电价波动的不确定性产生的不利影响.算例证明了本文所提方法的可行性和有效性.
    Recommended by Associate Editor Haibo He
  • Fig.  1  Schematic of an EI.

    Fig.  2  Data of the EI system needed in this paper.

    Fig.  3  Operation schedules of the EI system for the DMPC approach.

    Fig.  4  Operation schedules of the EI system for DDA approach.

    Fig.  5  Actual generation of the utility company with DDA approach and DMPC approach.

    Fig.  6  Convergence of the distributed optimization algorithm with different step-size coefficients.

    A. Index
    $t$ time index
    $i$ microgrid index
    $k$ iteration step index
    $a$ index of schedulable appliances in microgrid $i$
    B. Constants
    $M$ set of microgrids in the EI system ( $i\in M$ )
    $T$ number of periods for the control horizon ( $t\in T$ )
    $N$ a preset iteration coefficient used for accelerating the convergence speed
    $A_{i, s}$ set of schedulable appliances in microgrid $i$ ( $a\in A$ )
    $\Delta t$ time interval of each period (h)
    $P_{i, l}^{\rm max}, P_{i, O}^{\rm max}$ the rated power that can be purchased/sold from/to the utility for microgrid $i$ (kW)
    $E_{i, E}^{\rm max}, E_{i, E}^{\rm min}$ the maximum, minimum available energy level of the ESD unit in microgrid $i$ (kWh)
    $E_{i, E}^{\rm init}$ the initial energy level of ESD unit in microgrid $i$ (kWh)
    $P_{i, Ec}^{\rm max}, P_{i, Ec}^{\rm min}$ the maximum, minimum charging power of the ESD unit in microgrid $i$ (kW)
    $P_{i, Ed}^{\rm max}, P_{i, Ed}^{\rm min}$ the maximum, minimum discharging power of the ESD unit in microgrid $i$ (kW)
    $\eta_{i, Ed}, \eta_{i, Ec}$ discharging, charging efficiency of the ESD unit in microgrid $i$ (%)
    $\varepsilon_{i, E}$ self-discharging rate of the ESD unit in microgrid $i$ (kWh/h)
    $c_{i, E}^{\rm O \ M}$ operation and maintenance cost of the ESD unit in microgrid $i$ ($)
    $c_{i, E}^{\rm switch}$ status switch cost of the ESD unit in microgrid $ i $ ($)
    $P_{i, \rm DDG}^{\rm max}, P_{i, \rm DDG}^{\rm min}$ the maximum, minimum allowed power output of the DDG unit in microgrid $i$ (kW)
    $T_{i, \rm DDG}^{\rm down}, T_{i, \rm DDG}^{\rm up}$ the minimum down, operation time of the DDG unit in microgrid $i$ (h)
    $c_{i, \rm DDG}^{\rm down}, c_{i, \rm DDG}^{\rm up}$ shut-down, start-up cost of the DDG unit in microgrid $i$ ($)
    $R_{i, \rm DDG}$ the maximum ramp down/up power rate of the DDG unit in microgrid $i$ (kW)
    $c_{i, \rm DDG}^{1}, c_{i, \rm DDG}^{2}$ cost coefficients of the DDG unit in microgrid $i$ ( $$/\rm{kW^2}, $/\rm{kW}$ )
    $\alpha 1, \alpha 2$ cost coefficients of the utility generator ( $$/\rm{kW^2}, $/\rm{kW)}$
    $l_{i, a}^{\rm min}, l_{i, a}^{\rm max}$ the minimum, maximum load demand of appliance a for microgrid $i$ (kW)
    $l_{i, B}^{\rm max}$ rated capacity of the critical loads in microgrid $i$ (kW)
    $P_{i, PV}^{\rm max}$ rated power capacity of the PV plant in microgrid $i$ (kW)
    $P_{i, \rm wind}^{\rm max}$ rated power capacity of the wind farm in microgrid $i$ (kW)
    $T_{i, a}^{\rm start}, T_{i, a}^{\rm end}$ start time, deadline of appliance a for microgrid $i$ (h)
    $E_{i, a}$ total energy demand of the appliance a for microgrid $i$ (kWh)
    $D_{i}$ spinning reserve ratio for microgrid $i$ (%)
    $\xi_{1}, \xi_{2}, \xi_{3}, \xi_{4}$ preset stopping criteria for the distribution optimization algorithm
    $\theta_{i, F}^{\rm max}$ the maximum curtailment ratio of flexible loads in microgrid $i$ (%)
    $c_{i, F}^{\rm curt}$ penalty cost coefficient for curtailing flexible loads in microgrid $i$
    $P_{u}^{\rm max}, P_{u}^{\rm min}$ the maximum, minimum power limit of the utility generator (kW)
    C. Parameters
    $P_{i, \rm wind}(t)$ power output of the wind turbines in microgrid $i$ at time $t$ (kW)
    $P_{i, PV}(t)$ power output of the PV plant in microgrid $i$ at time $t$ (kW)
    $l_{i, B}(t)$ demand of the critical loads in microgrid $i$ at time $t$ (kW)
    $l_{i, F}(t)$ demand of the flexible loads in microgrid $i$ at time $t$ (kW)
    $p_u(t)$ base electricity price for the utility company ($/kWh)
    $p_{i, b}(t), p_{i, s}(t)$ buying, selling electricity price for microgrid $i$ at time $t$ ($)
    $p_{i, b}(t), p_{i, s}(t)$ buying, selling price coefficient
    D. Variables
    $P_{i, l}(t), P_{i, O}(t)$ power imported/exported from/to the utility for microgrid $i$ at time $t$ (kW)
    $\delta_{i, l}(t), \delta_{i, O}(t)$ purchasing, selling power status for microgrid $i$ at time $t$ (0/1)
    $P_{i, Ec}(t), P_{i, Ed}(t)$ charging, discharging power rate of the ESD unit for microgrid $i$ at time $t$ (kW)
    $\delta_{i, Ec}(t), \delta_{i, Ed}(t)$ charging, discharging status of the ESD unit for microgrid $i$ at time $t$ (0/1)
    $E_{i, E}(t)$ energy level of the ESD unit for microgrid $i$ at time $t$ (kWh)
    $P_{i, \rm DDG}(t)$ power output of the DDG unit for microgrid $i$ at time $t$ (kWh)
    $\delta_{i, \rm DDG}(t)$ operation status of the DDG unit for microgrid $i$ at time $t$ (0/1)
    $\theta_{i, F}(t)$ curtailment ratio of the flexible loads for microgrid $i$ at time $t$ (%)
    $l_{i, a}(t)$ load demand of appliance a for microgrid $i$ at time $t$ (kW)
    下载: 导出CSV

    Table  Ⅰ  ALGORITHM FOR PARALLEL DISTRIBUTED OPTIMIZATION METHOD FOR EI SYSTEM

    $\textbf{Algorithm 1:}$ for utility at time $t$
    $\textbf{begin}$
       $k$ = 0; ${\%}$ iteration counter
      Obtain the initial $P_{i, I}^k(\tau)$ , $P_{i, O}^k(\tau)$ of each microgrid according to the random generation technique; $\tau\in[t, t+1, \ldots, t+T-1]$
       Calculate utility cost $\Psi_u^k$ according to (29), the retail buying electricity price $p_{i, b}^k(\tau)$ and selling price $p_{i, s}^k(\tau)$ according to (26) and (27), respectively;
       do
       Broadcast updated retail prices to all microgrids;
       Receive the newly updated $P_{i, I}^{k+1}(\tau)$ , $P_{i, O}^{k+1}(\tau)$ simultaneously from all the microgrids according to Algorithm 2 shown in the following; $i\in[1, M]$
       Calculate utility cost $\Psi_u^{k+1}$ , retail electricity price $p_{i, s}^{k+1}(\tau)$ , $p_{i, b}^{k+1}(\tau)$
       $k:=k+1$ ;
       $\textbf{until}$ $||\Psi_u^k\!-\!\Psi_u^{k-1}||\leq \xi_1, ||l^k(\tau)\!-\!l^{k-1}(\tau)||\!\leq\!\xi_2, $
           $|||P_{Ed}^k(\tau)\!-\!P_{Ec}^k(\tau)||- ||P_{Ed}^{k-1}(\tau)-P_{Ec}^{k-1}(\tau)|||\leq\xi_3, $
           $||P_{\rm DDG}^k(\tau)-P_{\rm DDG}^{k-1}(\tau)||\leq\xi_4$
    $\textbf{end}$
    $\textbf{Algorithm 2:}$ for microgrid $i$ at time $t$
    $\textbf{begin}$
       $k$ = 0; ${\%}$ iteration counter
       Initialize $P_{i, I}^k(\tau), P_{i, O}^k(\tau)$ according to the random generation technique;
       Report $P_{i, I}^k(\tau)$ , $P_{i, O}^k(\tau)$ to the EI operator; $\tau\in[t, t+1, \ldots, t+T-1]$
      While
       Update the received retail electricity price $p_{i, s}^k (\tau)$ , $p_{i, b}^k (\tau)$ from the EI operator
       Solve the optimization problem (31) and obtain the newly updated $P_{i, I}^{k+1}(\tau)$ , $P_{i, O}^{k+1}(\tau)$ ;
       Report $P_{i, I}^{k+1}(\tau)$ , $P_{i, O}^{k+1}(\tau)$ to the EI operator;
       $ k:=k+1$ ;
      end
    end
    下载: 导出CSV

    Table  Ⅱ  POWER LIMITS OF MICROGRIDS AND INDEPENDENT USER

    PV plant Wind farm PCC node Critical load
    Microgrid 1 400 192 1200 672
    Microgrid 2 400 0 800 496
    Microgrid 3 0 240 800 560
    Independent user 0 0 1500 800
    下载: 导出CSV

    Table  Ⅲ  PARAMETER OF SCHEDULABLE LOADS

    Power demand
    (kW)
    Operation interval
    (h)
    Time window
    (h)
    Duration
    (h)
    Task 1 22 15-21 6 2
    Task 2 28 14-23 9 4
    Task 3 45 8-18 10 6
    Task 4 37.5 6-24 18 8
    Task 5 12 2-22 20 12
    Task 6 60 8-22 14 7
    Task 7 75 6-24 18 9
    下载: 导出CSV

    Table  Ⅳ  PARAMETER OF ESDS

    Max charge/ discharge power Min charge/ discharge power O & M cost Switch cost Max energy level Charge / discharge efficiency
    Microgrid 1 160 5 0.05 0.06 320 0.95
    Microgrid 2 140 8 0.05 0.05 300 0.95
    Microgrid 3 120 6 0.05 0.07 260 0.95
    下载: 导出CSV

    Table  Ⅴ  PARAMETER OF CONTROLLABLE GENERATORS

    Max power Min power Ramp rate Min up/down time Startup/shut down cost Cost coefficients
    Microgrid 2 150 5 100 2/2 1.2/1.2 0.0042/0.32
    Utility 4500 50 - - - 0.00048/0.28
    下载: 导出CSV

    Table  Ⅵ  SCHEDULING COSTS AND THE TOTAL COSTS FOR BOTH DMPC APPROACH AND DDA APPROACH

    Cost (×105$) Microgrid
    1
    Microgrid
    2
    Microgrid
    3
    Microgrid
    4
    Scheduling cost with no optimization 0.6661 0.6721 0.6716 1.1479
    Scheduling cost with DDA 0.6316 0.5741 0.6376 1.0982
    Scheduling cost with DMPC 0.6484 0.5867 0.6537 1.0993
    Total cost with no optimization 0.6764 0.6831 0.6856 1.1619
    Total cost with DDA 0.6574 0.6016 0.6717 1.1338
    Total cost with DMPC 0.6502 0.5878 0.6555 1.1005
    下载: 导出CSV

    Table  Ⅶ  SCHEDULING COSTS AND TOTAL COSTS FOR DMPC APPROACH WITHOUT SOME DISPATCHABLE ELEMENTS

    Cost (×105$) Microgrid
    1
    Microgrid
    2
    Microgrid
    3
    Microgrid
    4
    Scheduling cost without ESDs 0.6522 0.5920 0.6617 1.1186
    Total cost without ESDs 0.6536 0.5929 0.6631 1.1201
    Scheduling cost without ESDs and DDG 0.6800 0.6961 0.6846 1.1617
    Total cost without ESDs and DDG 0.6788 0.6951 0.6831 1.1605
    下载: 导出CSV
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出版历程
  • 收稿日期:  2015-11-02
  • 录用日期:  2016-05-25
  • 刊出日期:  2017-08-20

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