Optimal Sizing and Placement of Distributed Generation Based on Adaptive Manta Ray Foraging Optimization

doi:10.16183/j.cnki.jsjtu.2021.397

Abstract

Abstract:

In this paper, an optimal sizing and placement model for distributed generation (DG) is established, which includes active power losses, voltage profile, pollution emission, DG costs, and meteorological conditions. Since optimizing placement and sizing are discrete and continuous variables respectively, the model established is a highly nonlinear complex one with discrete optimization variables. Therefore, the adaptive manta ray foraging optimization (AMRFO) algorithm is applied to obtain the optimal Pareto front, which has a rich and diverse search mechanism, individual updating mechanism, and advanced Pareto solution selection mechanism. For this model, a better solution of high quality can be obtained. In order to avoid the influence of subjective setting of weight coefficient, the ideal point method based on Mahalanobis distance is used to make Pareto front decision. Finally, the simulation based on the IEEE 33, 69-bus distribution network and the IEEE 33, 69-bus distribution network in isolated network operation are implemented. The results show that compared with the traditional multi-objective intelligent optimization algorithm, AMRFO algorithm can obtain a more widely distributed and uniform Pareto front. While considering the economy, the optimized distribution network voltage profile and active power losses can be significantly improved.

Key words: distribution network, distributed generation (DG), optimal sizing and placement, adaptive manta ray foraging optimization (AMRFO) algorithm

CLC Number:

TM76

YANG Bo, YU Lei, WANG Junting, SHU Hongchun, CAO Pulin, YU Tao. Optimal Sizing and Placement of Distributed Generation Based on Adaptive Manta Ray Foraging Optimization[J]. Journal of Shanghai Jiao Tong University, 2021, 55(12): 1673-1688.

Figures/Tables 21

Fig.1

Fig.2

Fig.3

Tab.1

Fig.4

Fig.5

Fig.6

Fig.7

Tab.2

Tab.3

Tab.4

Fig.8

Fig.9

Fig.10

Tab.5

Tab.6

Tab.7

Fig.11

Fig.12

Fig.13

Fig.14

References 26

[1]	YANG B, YU T, SHU H C, et al. Adaptive fractional-order PID control of PMSG-based wind energy conversion system for MPPT using linear observers[J]. International Transactions on Electrical Energy Systems, 2019, 29(1):2697.
[2]	孙立明, 杨博. 蓄电池/超导混合储能系统非线性鲁棒分数阶控制[J]. 电力系统保护与控制, 2020, 48(22):76-83.
	SUN Liming, YANG Bo. Nonlinear robust fractional-order control of battery/SMES hybrid energy storage systems[J]. Power System Protection and Control, 2020, 48(22):76-83.
[3]	YANG B, WANG J T, CHEN Y X, et al. Optimal sizing and placement of energy storage system in power grids: A state-of-the-art one-stop handbook[J]. Journal of Energy Storage, 2020, 32:101814.
[4]	付学谦, 陈皓勇, 刘国特, 等. 分布式电源电能质量综合评估方法[J]. 中国电机工程学报, 2014, 34(25):4270-4276.
	FU Xueqian, CHEN Haoyong, LIU Guote, et al. Power quality comprehensive evaluation method for distributed generation[J]. Proceedings of the Chinese Society for Electrical Engineering, 2014, 34(25):4270-4276.
[5]	薛帅, 高厚磊, 郭一飞, 等. 大规模海上风电场的双层分布式有功控制[J]. 电力系统保护与控制, 2021, 49(3):1-9.
	XUE Shuai, GAO Houlei, GUO Yifei, et al. Bi-level distributed active power control for a large-scale wind farm[J]. Power System Protection and Control, 2021, 49(3):1-9.
[6]	沈鑫, 曹敏. 分布式电源并网对于配电网的影响研究[J]. 电工技术学报, 2015, 30(S1):346-351.
	SHEN Xin, CAO Min. Research on the influence of distributed power grid for distribution network[J]. Transactions of China Electrotechnical Society, 2015, 30(S1):346-351.
[7]	曲绍杰, 王绍然, 刘明波, 等. 基于互补内点法的多目标静态电压稳定约束无功规划[J]. 电力系统保护与控制, 2010, 38(23):49-54.
	QU Shaojie, WANG Shaoran, LIU Mingbo, et al. Static voltage stability constrained multi-objective reactive power planning based on complementary interior point method[J]. Power System Protection and Control, 2010, 38(23):49-54.
[8]	YANG B, YU L, CHEN Y X, et al. Modelling, applications, and evaluations of optimal sizing and placement of distributed generations: A critical state-of-the-art survey[J]. International Journal of Energy Research, 2021, 45(3):3615-3642. doi: 10.1002/er.v45.3 URL
[9]	ABU-MOUTI F S, EL-HAWARY M E. Optimal distributed generation allocation and sizing in distribution systems via artificial bee colony algorithm[J]. IEEE Transactions on Power Delivery, 2011, 26(4):2090-2101. doi: 10.1109/TPWRD.2011.2158246 URL
[10]	QUADRI I A, BHOWMICK S, JOSHI D. A hybrid teaching-learning-based optimization technique for optimal DG sizing and placement in radial distribution systems[J]. Soft Computing, 2019, 23(20):9899-9917. doi: 10.1007/s00500-018-3544-8 URL
[11]	李珂, 邰能灵, 张沈习, 等. 考虑相关性的分布式电源多目标规划方法[J]. 电力系统自动化, 2017, 41(9):51-57.
	LI Ke, TAI Nengling, ZHANG Shenxi, et al. Multi-objective planning method of distributed generators considering correlations[J]. Automation of Electric Power Systems, 2017, 41(9):51-57.
[12]	任洪伟, 韩丛英, 裴玮, 等. 基于多目标优化模型的分布式电源选址方案研究[J]. 电力系统保护与控制, 2013, 41(24):64-69.
	REN Hongwei, HAN Congying, PEI Wei, et al. Research on distributed generation locating based on multi-objective optimization model[J]. Power System Protection and Control, 2013, 41(24):64-69.
[13]	KEFAYAT M, LASHKAR ARA A, NABAVI NIAKI S A. A hybrid of ant colony optimization and artificial bee colony algorithm for probabilistic optimal placement and sizing of distributed energy resources[J]. Energy Conversion and Management, 2015, 92:149-161. doi: 10.1016/j.enconman.2014.12.037 URL
[14]	徐俊杰. 元启发式优化算法: 理论阐释与应用[M]. 合肥: 中国科学技术大学出版社, 2015.
	XU Junjie. Theoretical interpretation and application: Meta-heuristic optimization algorithm[M]. Hefei: University of Science and Technology of China Press, 2015.
[15]	徐迅, 陈楷, 龙禹, 等. 考虑环境成本和时序特性的微网多类型分布式电源选址定容规划[J]. 电网技术, 2013, 37(4):914-921.
	XU Xun, CHEN Kai, LONG Yu, et al. Optimal site selection and capacity determination of multi-types of distributed generation in microgrid considering environment cost and timing characteristics[J]. Power System Technology, 2013, 37(4):914-921.
[16]	DOAGOU-MOJARRAD H, GHAREHPETIAN G B, RASTEGAR H, et al. Optimal placement and sizing of DG (distributed generation) units in distribution networks by novel hybrid evolutionary algorithm[J]. Energy, 2013, 54:129-138. doi: 10.1016/j.energy.2013.01.043 URL
[17]	UGRANLı F, KARATEPE E. Multiple-distributed generation planning under load uncertainty and different penetration levels[J]. International Journal of Electrical Power & Energy Systems, 2013, 46:132-144. doi: 10.1016/j.ijepes.2012.10.043 URL
[18]	吴小刚, 刘宗歧, 田立亭, 等. 基于改进多目标粒子群算法的配电网储能选址定容[J]. 电网技术, 2014, 38(12):3405-3411.
	WU Xiaogang, LIU Zongqi, TIAN Liting, et al. Energy storage device locating and sizing for distribution network based on improved multi-objective particle swarm optimizer[J]. Power System Technology, 2014, 38(12):3405-3411.
[19]	ZHAO W G, ZHANG Z X, WANG L Y. Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications[J]. Engineering Applications of Artificial Intelligence, 2020, 87:103300.
[20]	杨蕾, 吴琛, 黄伟, 等. 含高比例风光新能源电网的多目标无功优化算法[J]. 电力建设, 2020, 41(7):100-109.
	YANG Lei, WU Chen, HUANG Wei, et al. Pareto-based multi-objective reactive power optimization for power grid with high-penetration wind and solar renewable energies[J]. Electric Power Construction, 2020, 41(7):100-109.
[21]	YANEZ-BORJAS J J, MACHORRO-LOPEZ J M, CAMARENA-MARTINEZ D, et al. A new damage index based on statistical features, PCA, and mahalanobis distance for detecting and locating cables loss in a cable-stayed bridge[J]. International Journal of Structural Stability and Dynamics, 2021, 21(9):2150127.
[22]	刘煌煌, 雷金勇, 蔡润庆, 等. 基于SVM-MOPSO混合智能算法的配电网分布式电源规划[J]. 电力系统保护与控制, 2014, 42(10):46-54.
	LIU Huanghuang, LEI Jinyong, CAI Runqing, et al. Distributed generation planning in distribution network based on hybrid intelligent algorithm by SVM-MOPSO[J]. Power System Protection and Control, 2014, 42(10):46-54.
[23]	GOSWAMI S K, BASU S K. A new algorithm for the reconfiguration of distribution feeders for loss minimization[J]. IEEE Transactions on Power Delivery, 1992, 7(3):1484-1491. doi: 10.1109/61.141868 URL
[24]	李亮, 唐巍, 白牧可, 等. 考虑时序特性的多目标分布式电源选址定容规划[J]. 电力系统自动化, 2013, 37(3):58-63.
	LI Liang, TANG Wei, BAI Muke, et al. Multi-objective locating and sizing of distributed generators based on time-sequence characteristics[J]. Automation of Electric Power Systems, 2013, 37(3):58-63.
[25]	王丽萍, 邱飞岳. 复杂多目标问题的优化方法及应用[M]. 北京: 科学出版社, 2018.
	WANG Liping, QIU Feiyue. Complex multi-objective optimization and it’s applications[M]. Beijing: Science Press, 2018.
[26]	胡旺, YEN Gary G, 张鑫. 基于Pareto熵的多目标粒子群优化算法[J]. 软件学报, 2014, 25(5):1025-1050.
	HU Wang, YEN Gary G, ZHANG Xin. Multiobjective particle swarm optimization based on Pareto entropy[J]. Journal of Software, 2014, 25(5):1025-1050.

DG种类	投资成本/ (美元·kW^-1)	运维成本/ (美元·kW·h^-1)	CO₂/ (kg·kW·h^-1)	SO₂/ (kg·kW·h^-1)	NO_x/ (kg·kW·h^-1)
燃料电池	3500~10000	0.5~1.0	0.502	3.629×10^-6	0.5216
微型燃汽轮机	700~1100	0.5~1.6	3.445	3.629×10^-6	0.1996×10^-3
光伏系统	4500~6000	每年初始投资成本的1%	-	-	-
风力发电机	800~3500	每年初始投资成本的1.5%~2%	-	-	-

节点	年平均风速/ (m·s^-1)	年平均辐射量/ (MJ·m^-2)	节点	年平均风速/ (m·s^-1)	年平均辐射量/ (MJ·m^-2)
1	3.464	0.6179	18	4.437	0.6912
2	2.765	0.3120	19	4.616	0.3916
3	2.315	0.1270	20	4.675	0.5796
4	3.037	0.6776	21	4.893	0.5712
5	4.670	0.6893	22	1.487	0.5941
6	4.016	0.6949	23	4.712	0.6056
7	4.452	0.6991	24	3.967	0.6087
8	2.792	0.6963	25	4.595	0.6195
9	3.359	0.6984	26	3.808	0.6862
10	4.513	0.6752	27	4.156	0.6329
11	2.304	0.6981	28	2.654	0.6812
12	2.882	0.4695	29	2.679	0.6020
13	3.694	0.6262	30	4.458	0.6108
14	2.108	0.6695	31	2.779	0.2820
15	4.566	0.6983	32	3.1125	0.6993
16	3.683	0.7054	33	4.383	0.5712
17	1.333	0.6741

节点	年平均风速/ (m·s^-1)	年平均辐射量/ (MJ·m^-2)	节点	年平均风速/ (m·s^-1)	年平均辐射量/ (MJ·m^-2)
1	2.575	0.8029	36	2.891	0.4583
2	3.270	0.5895	37	3.157	0.5970
3	4.504	0.8487	38	4.112	0.9929
4	2.833	0.2275	39	3.957	0.8437
5	2.241	0.4133	40	2.279	0.4362
6	1.754	0.6670	41	1.404	0.25791
7	3.791	0.7575	42	3.387	0.7879
8	5.066	0.7679	43	5.762	0.9933
9	4.979	0.7717	44	4.437	0.9004
10	5.15	0.7279	45	4.416	0.9204
11	4.154	0.6508	46	2.151	0.5995
12	3.754	0.6141	47	3.191	0.7420
13	3.079	0.5775	48	3.612	0.7454
14	2.658	0.9079	49	2.041	0.6408
15	1.529	0.8395	50	1.670	0.4720
16	1.312	0.4912	51	1.191	0.5133
17	2.312	0.4862	52	3.133	0.5358
18	4.779	0.9379	53	4.804	0.8354
19	4.233	0.6991	54	2.387	0.5945
20	4.070	0.8316	55	1.879	0.2441
21	4.320	0.9141	56	2.766	0.4808
22	2.875	0.8666	57	1.033	0.4033
23	3.225	0.8379	58	0.908	0.1520
24	2.904	0.7133	59	0.883	0.3716
25	2.116	0.5120	60	2.162	0.8954
26	3.066	0.6204	61	2.216	0.5895
27	2.141	0.7229	62	1.066	0.3920
28	1.875	0.33291	63	1.612	0.42166
29	2.608	0.62791	64	1.125	0.66751
30	1.883	0.38254	65	1.358	1.01625
31	0.416	0.19208	66	1.595	0.65666
32	1.937	0.58833	67	2.058	0.64833
33	3.037	0.57666	68	2.225	0.29875
34	4.037	0.68125	69	1.425	0.49208
35	4.287	0.95416

算法	光伏系统							燃料电池			微型燃气轮机				风电机组
算法	#1容量/ kW	#1安装节点		#2容量/ kW		#2安装节点		容量/ kW	安装节点		容量/ kW		安装节点		#1容量/ kW		#1安装节点	#2容量/ kW	#2安装节点
AMRFO	289.79	11		419.74		25		395.14	30		399.55		12		101.39		26	69.38	16
MRFO	317.94	11		347.85		25		303.26	8		399.67		30		60.99		23	212.44	12
NSGA-II	649.20	3		401.55		32		8	16		382.85		9		334.64		31	453.68	22
MOPSO	218.14	16		134.63		15		50.64	18		50.41		6		519.05		25	414.64	21
算法	目标函数适应度值											目标函数权重分配
算法	f₁/kW		f₂(p.u.)		f₃/kg		f₄/美元			f₅(p.u.)		ω_f₁		ω_f₂		ω_f₃		ω_f₄	ω_f₅
AMRFO	2023.26		28.26		5.14×10⁷		8.76×10⁷			0.4837		0.1929		0.2194		0.2144		0.1947	0.1783
MRFO	2167.09		33.98		4.44×10⁷		7.82×10⁷			0.5373		0.1822		0.2244		0.1845		0.2005	0.2082
NSGA-II	4061.87		53.2		2.09×10⁷		4.97×10⁷			0.5685		0.2082		0.1994		0.1875		0.1619	0.2428
MOPSO	27706.8		70.51		6.49×10⁶		1.45×10⁷			0.4251		0.2184		0.2173		0.1823		0.1993	0.1824

算法	光伏系统							燃料电池			微型燃气轮机				风电机组
算法	#1容量/ kW	#1安装节点		#2容量/ kW		#2安装节点		容量/ kW	安装节点		容量/ kW		安装节点		#1容量/ kW		#1安装节点	#2容量/ kW	#2安装节点
AMRFO	78.3	35		298.09		61		398	62		261.23		17		26.27		52	120.94	53
MRFO	416.19	58		370.51		61		385	62		379.23		12		269.88		30	162.38	21
NSGA-II	285.55	44		186.27		61		50.23	23		50.14		63		383.4		31	270.79	66
MOPSO	298.79	11		419.74		25		395	30		399.551		12		101.4		26	69.38	16
算法	目标函数适应度值											目标函数权重分配
算法	f₁/kW		f₂(p.u.)		f₃/kg		f₄/美元			f₅(p.u.)		ω_f₁		ω_f₂		ω_f₃		ω_f₄	ω_f₅
AMRFO	672.49		20.54		4.44×10⁷		7.11×10⁷			0.4278		0.2321		0.1923		0.2043		0.1559	0.2151
MRFO	1664.82		25.22		7.59×10⁷		8.54×10⁷			0.7341		0.2067		0.1886		0.2071		0.2074	0.1899
NSGA-II	3621.59		42.19		6.49×10⁵		1.45×10⁷			0.5912		0.2389		0.1871		0.1586		0.1552	0.2601
MOPSO	1568.83		63.68		5.15×10⁷		8.76×10⁷			0.6246		0.1929		0.2194		0.2144		0.1947	0.1783