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

Zhang Yan; Zhang Tao; Wang Rui; Liu Yajie; Guo Bo

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

张彦^1, ,,
张涛^1,,
王锐^1,,
刘亚杰^1,,
^1,

1.
国防科学技术大学信息系统与管理学院长沙 410073

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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

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

Zhang Yan^{1
, ,},
Zhang Tao^1
,,
Wang Rui^1
,,
Liu Yajie^1
,,
Guo Bo^1
,

1.
College of Information System and Management, National University of Defense Technology, Changsha 410073, China

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

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.
- 能源互联网 /
- 博弈论 /
- 多微电网 /
- 模型预测控制 /
- 并行优化
Abstract: This paper focuses on the development of optimization-based distributed scheduling strategies for the coordination of an energy internet (EI) with multi-microgrids with consideration of forecast uncertainties. All microgrids have flexible loads, schedulable loads and critical loads; some microgrids have distributed generators, such as micro-turbines, wind turbines, photovoltaic panels; besides, a few microgrids have energy storage devices, such as battery storage. Each microgrid is considered as an individual entity and has its individual objective, these objective functions of microgrids are formulated by mixed integer programming (MIP) models. A game theory based parallel distributed optimization algorithm is proposed to coordinate the competitive objectives of the microgrids with only a little information interaction. A model predictive control (MPC) framework which integrates the distributed optimization algorithm is developed to reduce the negative impacts introduced by the uncertainties of the EI. Simulation results show that our method is flexible and efficient.
- Energy internet (EI) /
- game theory /
- model predictive control (MPC) /
- multi-microgrids /
- parallel optimization
Recommended by Associate Editor Haibo He
注释:

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Fig. 1 Schematic of an EI.

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

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

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

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

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

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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)

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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

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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

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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

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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

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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

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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

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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

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