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Frontiers of Engineering Management

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Front. Eng    2021, Vol. 8 Issue (2) : 271-283    https://doi.org/10.1007/s42524-019-0083-7
RESEARCH ARTICLE
Benefit-based cost allocation for residentially distributed photovoltaic systems in China: A cooperative game theory approach
Xi LUO1(), Xiaojun LIU2, Yanfeng LIU1, Jiaping LIU3, Yaxing WANG1
1. School of Building Services Science and Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China
2. School of Management, Xi’an University of Architecture and Technology, Xi’an 710055, China
3. School of Architecture, Xi’an University of Architecture and Technology, Xi’an 710055, China
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Abstract

Distributed photovoltaic (PV) systems have constantly been the key to achieve a low-carbon economy in China. However, the development of Chinese distributed PV systems has failed to meet expectations because of their irrational profit and cost allocations. In this study, the methodology for calculating the levelized cost of energy (LCOE) for PV is thoroughly discussed to address this issue. A mixed-integer linear programming model is built to determine the optimal system operation strategy with a benefit analysis. An externality-corrected mathematical model based on Shapley value is established to allocate the cost of distributed PV systems in 15 Chinese cities between the government, utility grid and residents. Results show that (i) an inverse relationship exists between the LCOEs and solar radiation levels; (ii) the government and residents gain extra benefits from the utility grid through net metering policies, and the utility grid should be the highly subsidized participant; (iii) the percentage of cost assigned to the utility grid and government should increase with the expansion of battery bank to weaken the impact of demand response on increasing theoretical subsidies; and (iv) apart from the LCOE, the local residential electricity prices remarkably impact the subsidy calculation results.
Keywords solar photovoltaic      cost allocation      cooperative game theory      Shapley value      mixed-integer linear programming      levelized cost of energy     
Corresponding Author(s): Xi LUO   
Just Accepted Date: 19 December 2019   Online First Date: 13 March 2020    Issue Date: 25 March 2021
 Cite this article:   
Xi LUO,Xiaojun LIU,Yanfeng LIU, et al. Benefit-based cost allocation for residentially distributed photovoltaic systems in China: A cooperative game theory approach[J]. Front. Eng, 2021, 8(2): 271-283.
 URL:  
https://academic.hep.com.cn/fem/EN/10.1007/s42524-019-0083-7
https://academic.hep.com.cn/fem/EN/Y2021/V8/I2/271
City Minimum living standard
(yuan/month)
Baoji 495
Beijing 710
Changsha 450
Chengdu 450
Chongqing 375
Guiyang 477.5
Hangzhou 660
Harbin 510
Hefei 510
Kunming 502.5
Lanzhou 451
Mang’ai 373
Nancheng 465
Shanghai 790
Wuhan 580
Tab.1  Minimum living standards of 15 Chinese cities
Fig.1  Possible coalitions.
S v(S)
{∅} 0
{utility grid} Ee- LCOE
{governments} kUEg- LCOE
{residents} kUpB- LCOE
{utility grid, governments} Ee + Eg- LCOE
{utility grid, residents} Ee + Er- LCOE
{governments, residents} kU(Eg + pB) - LCOE
{utility grid, governments, residents} Ee + Eg + Er- LCOE
Tab.2  Characteristic functions for each coalition
S ve(S)
{∅} 0
{utility grid} Eg + Er
{governments} kU(Ee + pB)
{residents} kU(Ee + Eg)
{utility grid, governments} Er
{utility grid, residents} Eg
{governments, residents} kUEe
{utility grid, governments, residents} 0
Tab.3  Characteristic functions for each coalition in the externality distribution
Component Characteristics Value
Solar module (CS6X-320P) Nominal efficiency 16.82%
Maximum power 319.72 W
Maximum power voltage 36.8 V
Maximum power current 8.7 A
Open circuit voltage 45.3 V
Short circuit current 9.3 A
Module area 1.90 m2
Material Multi-C-Si
Inverter (SB6000US-12 240 V) CEC weighted efficiency 95.64%
Maximum AC power 6000 W
Maximum DC power 6282 W
Nominal AC voltage 240 V
Nominal DC voltage 310 V
Maximum DC voltage 480 V
Maximum MPPT DC voltage 480 V
Minimum MPPT DC voltage 100 V
Battery (single unit) Nominal capacity 2 kWh
Charge efficiency 75%
Discharge efficiency 75%
Minimum SOC 5%
Maximum SOC 95%
Minimum charge power 0.5 kW
Maximum charge power 2 kW
Minimum discharge power 0.5 kW
Maximum discharge power 2 kW
Tab.4  Technical specifications of critical components
City Level of solar resources LLCOE without battery bank (yuan/kWh) LCOE with battery bank
(yuan/kWh)
2 kWh 4 kWh 6 kWh 8 kWh 10 kWh
Baoji III 0.5874 0.6285 0.6697 0.7108 0.7520 0.7931
Beijing II 0.5241 0.5609 0.5976 0.6343 0.6710 0.7077
Changsha III 0.6858 0.7349 0.7830 0.8311 0.8792 0.9273
Chengdu II 0.7311 0.7823 0.8335 0.8847 0.9359 0.9871
Chongqing III 0.7578 0.8108 0.8639 0.9170 0.9701 1.0231
Guiyang III 0.7415 0.7934 0.8453 0.8972 0.9492 1.0011
Hangzhou III 0.6548 0.7007 0.7465 0.7924 0.8383 0.8841
Harbin II 0.5249 0.5617 0.5984 0.6352 0.6719 0.7087
Hefei III 0.6324 0.6767 0.7209 0.7652 0.8095 0.8538
Kunming II 0.5485 0.5870 0.6254 0.6638 0.7022 0.7406
Lanzhou II 0.5186 0.5550 0.5913 0.6276 0.6639 0.7003
Mang’ai I 0.4327 0.4631 0.4934 0.5237 0.5540 0.5843
Nancheng III 0.6448 0.6900 0.7352 0.7803 0.8255 0.8707
Shanghai III 0.6341 0.6785 0.7229 0.7673 0.8117 0.8561
Wuhan III 0.6239 0.6676 0.7113 0.7550 0.7987 0.8424
Tab.5  LCOEs of distributed PV systems in 15 Chinese cities
City Electricity price*
(yuan/kWh)		 Feed-in tariff
(yuan/kWh)
Baoji 0.7983 0.3545
Beijing 0.7883 0.3598
Changsha 0.8880 0.4500
Chengdu 0.6224 0.4012
Chongqing 0.8200 0.3964
Guiyang 0.7556 0.3515
Hangzhou 0.8380 0.4153
Harbin 0.8100 0.3740
Hefei 0.8653 0.3844
Kunming 0.8000 0.3358
Lanzhou 0.8100 0.3078
Mang’ai 0.6771 0.3247
Nancheng 0.9000 0.4143
Shanghai 0.9170 0.4155
Wuhan 0.8580 0.4161
Tab.6  Electricity prices and feed-in tariffs of 15 Chinese cities
Fig.2  Impact of the demand response on load profiles.
Fig.3  Impact of the addition of a battery bank on load profiles: System output (a) without a battery bank; (b) with a 2 kWh battery bank; (c) with a 4 kWh battery bank; (d) with a 6 kWh battery bank; (e) with an 8 kWh battery bank; (f) with a 10 kWh battery bank.
City Externality to utility grid
(yuan/kWh)		 Externality to government
(yuan/kWh)		 Externality to residents
(yuan/kWh)
Baoji 0.4802 -0.2329 -0.2473
Beijing 0.4744 -0.2380 -0.2363
Changsha 0.5272 -0.2175 -0.3097
Chengdu 0.5099 -0.2227 -0.2873
Chongqing 0.5098 -0.2220 -0.2878
Guiyang 0.4856 -0.2316 -0.2540
Hangzhou 0.5054 -0.2279 -0.2775
Harbin 0.4786 -0.2364 -0.2422
Hefei 0.5020 -0.2261 -0.2759
Kunming 0.4745 -0.2340 -0.2405
Lanzhou 0.4642 -0.2357 -0.2285
Mang’ai 0.4440 -0.2455 -0.1985
Nancheng 0.5166 -0.2213 -0.2954
Shanghai 0.5189 -0.2240 -0.2948
Wuhan 0.5093 -0.2252 -0.2841
Tab.7  Externalities assigned to each participant
City LCOE
(yuan/kWh)		 Utility grid
(yuan/kWh)		 Government
(yuan/kWh)		 Theoretical PBI (yuan/kWh) Residents
(yuan/kWh)
Baoji 0.5874 -0.5879 0.6138 0.0259 0.5615
Beijing 0.5241 -0.6239 0.6096 -0.0143 0.5384
Changsha 0.6858 -0.6128 0.6196 0.0068 0.6790
Chengdu 0.7311 -0.5478 0.6298 0.0820 0.6491
Chongqing 0.7578 -0.5330 0.6354 0.1024 0.6554
Guiyang 0.7415 -0.5051 0.6421 0.1370 0.6045
Hangzhou 0.6548 -0.6067 0.6293 0.0226 0.6322
Harbin 0.5249 -0.6393 0.6117 -0.0276 0.5525
Hefei 0.6324 -0.6006 0.6197 0.0191 0.6133
Kunming 0.5485 -0.5918 0.6037 0.0119 0.5366
Lanzhou 0.5186 -0.5908 0.6009 0.0101 0.5085
Mang’ai 0.4327 -0.6162 0.5889 -0.0273 0.4600
Nancheng 0.6448 -0.6180 0.6173 -0.0007 0.6456
Shanghai 0.6341 -0.6332 0.6222 -0.0110 0.6451
Wuhan 0.6239 -0.6191 0.6149 -0.0042 0.6281
Tab.8  Cost allocation results
Fig.4  Percentage of costs assigned to participants in Beijing with different battery capacities.
City Without battery bank
(yuan/kWh)		 With battery bank (yuan/kWh)
2 kWh 4 kWh 6 kWh 8 kWh 10 kWh
Baoji +0.0053 +0.0030 +0.0006 -0.0019 -0.0044 -0.0056
Beijing +0.0075 +0.0059 +0.0044 +0.0028 +0.0036 +0.0099
Changsha +0.0090 +0.0063 +0.0034 +0.0006 -0.0056 -0.0183
Chengdu +0.0079 +0.0048 +0.0017 -0.0015 -0.0201 -0.0278
Chongqing +0.0071 +0.0037 +0.0002 -0.0031 -0.0263 -0.0291
Guiyang +0.0081 +0.0048 +0.0016 -0.0017 -0.0205 -0.0258
Hangzhou +0.0107 +0.0083 +0.0055 +0.0028 +0.0049 -0.0012
Harbin +0.0081 +0.0065 +0.0047 +0.0029 +0.0088 +0.0152
Hefei +0.0018 -0.0009 -0.0034 -0.0062 -0.0517 -0.0762
Kunming +0.0022 -0.0001 -0.0024 -0.0045 -0.0068 -0.0128
Lanzhou +0.0025 -0.0047 -0.0069 -0.0092 -0.0114 -0.0149
Mang’ai +0.0145 +0.0132 +0.0121 +0.0107 +0.0046 -0.0111
Nancheng +0.0023 -0.0004 -0.0031 -0.0059 -0.0894 -0.0096
Shanghai +0.0013 -0.0016 -0.0048 -0.0076 -0.0068 -0.0084
Wuhan +0.0075 +0.0053 +0.0029 +0.0005 -0.0004 -0.0002
Tab.9  Impact of demand response on theoretical subsidies with different battery bank capacities
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[1] Sameh Al-SHIHABI, Mohammad AlDURGAM. Multi-objective optimization for the multi-mode finance-based project scheduling problem[J]. Front. Eng, 2020, 7(2): 223-237.
[2] Xi Luo,Jia-ping Liu. Economic Analysis of Residential Distributed Solar Photovoltaic[J]. Front. Eng, 2015, 2(2): 125-130.
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