Cooperative game of electricity retailers in China's spot electricity market

Energy 145 (2018) 152e170

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Cooperative game of electricity retailers in China's spot electricity market Xu Peng*, Xiaoma Tao School of Economics and Management, Tongji University, 1239 Siping Road, Shanghai 200092, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 May 2017 Received in revised form 20 December 2017 Accepted 23 December 2017 Available online 28 December 2017

Chinese electricity market has undergone twice reforms since 2002. However, the current electricity market is still partially irrational in electricity pricing mechanism. Furthermore, the utilization of renewable energy is inefficient in western regions. From the perspective of market participants, electricity retailers are new entrants in deregulated electricity market. In this spot electricity market, they are faced with various challenges and opportunities. Thus, this paper introduces an inter-regional power transaction model based on bottom-up modeling. There are mainly three parts in this paper: ⑴ It examines the existing problems and achievements in the twice reforms, and introduces the participants of cooperative game in a spot market. ⑵It proposes an inter-regional electricity transaction model to illustrate the new pricing mechanism. ⑶ Based on cooperative game theory, it quantifies how costs, electricity prices and benefits affect the behavior of retailers in a spot market with some reasonable economic assumptions. What is novel about this research is that the proposed transaction model analyzes electricity retailers' behaviors in a spot market. The cooperative game model improves electricity retailer's competitiveness in a spot market, and is of great theoretical and practical significance for the reform and development of China's electricity market. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Deregulated market Electricity retailers Cooperative game Inter-regional transaction

1. Introduction Electricity industries are naturally monopolistic industries all over the world. With the advantage of natural monopoly, the power industry reaps a good deal of benefits [1]. However, it also resulted in the lower operating efficiency, making power companies less competitive in market. A significant restructuring process for power industry has been initiated in many countries since the 1990s [2,3]. In order to enhance operational efficiency and break up monopoly on electricity market, twice important power system reforms have been carried out in China since the 20th century. The first power industry reform was launched by the Chinese government in 2002 to weaken monopoly interests and liberalize power industry. Power System Reform Plan (No.5 Document) was issued, marking the first round of power industry reform. As a result of this reform, the vertical integration power corporation (State Power Corporation, SPC) was divided into two parts: power generation enterprises and power grids enterprises [4]. To be

* Corresponding author. E-mail address: [email protected] (X. Peng). https://doi.org/10.1016/j.energy.2017.12.122 0360-5442/© 2018 Elsevier Ltd. All rights reserved.

specific, Big Five power generation companies-China Huaneng Group(CHG), China Power Investment Corporation(CPIC), China Datang Corporation(CDC), China Guodian Corporation(CGC), China Huadian Corporation(CHC)-and two power grid companies-State Grid Corporation of China (SGCC) and China Southern Power Grid (CSG) are established accordingly (See Fig. 1) [3e5]. The original State Power Corporation (SPC), which is not only a state-owned enterprise (SOE) but also a government sector, has been liberalized on the generation side in electricity market [6]. A competitive market is set up on the generation side to improve the operational efficiency. Besides, two auxiliary services companies were separated from power grid companies and then restructured as China Energy Engineering Corporation (CEEC) and Power Construction Corporation of China (PCCC) in 2011 [7]. It seems that the No.5 action brought a positive influence by introducing a competitive market on the generation side [8]. However, the few participants (Big 5 power generation companies and two power grid companies) resulted in unfair competition phenomena in the regulated market. As a result, expected results are not achieved through the first electricity market reform in 2002. Many administrative measures are released by the National Energy Board (NEB), National Development and Reform Commission(NDRC) and State Electricity

X. Peng, X. Tao / Energy 145 (2018) 152e170

Nomenclature

Pn Sn

TD TN DN TTPP REPP RE Qci Ii Ui Fi Qsi Ci Ca Pa

c j q

Iij PðVi Þ TðVi Þ

Transmission and distribution companies Transmission networks Distribution networks Traditional thermal power plants Renewable energy power plants Renewable energy Electricity consumption in province i Installed capacity in province i Available utilization hour in province i Electricity net flow in province i Electricity supply in province i Electricity supply cost in province i Allowable cost of TD companies Allowable profit of TD companies Electricity price tax rate Total line loss rate from province a to b Line loss rate between province i and j Bernoulli distribution variable P label T label

C loss

Line loss cost

Ptspot Pton

Spot price in an electricity market. On-grid price.

QtPP

Amount of power procured from power plants

d U rij

Cqcong ;t

153

T C pp

Probability of n customers in a queuing system Cumulative service rate Service intensity Set of scenarios Scenario q Set of periods Generation cost of power plant (￥/kW.h)

Qtspot

Amounts of the procured power in a spot market.

qRT t

Qti

Amounts of the procured power in a real-time market. Selling price to customers Residential electricity price. Industrial electricity price. Commercial electricity price. Real-time price in an electricity market. Proportional parameter Proportional parameter Amount of power selling to customer i

CqTD ;t

Transmission and distribution tariff (Grid access fee/

SPt SP re SP in SP co pRT t

a b

network tariff) gf

Cq M Mre Min Mco N S v Shi PFITs

Congestion cost

Pr: Occurring probability Pr:ðcongÞ Probability of congestion l Arrival rate in queuing system m Service rate in queuing system

Government funds Set of consumers:M ¼ fMin ; Mre ; Mco g Set of residential customers Set of industrial customers Set of commercial customers Set of players Subset of N Characteristic function Shapley value to player i Fit-in tariff of renewable energy

Power industry in China 2002-2015

Power grid companies

State Grid Corporation of China

Auxiliary service companies

Generation companies

China Southern Power Grid

Huaneng Group

State Power Investment Corporation

Datang Corporation

Guodian Corporation

Huadian Corporation

Energy Engineering Corporation

Power Construction Corporation

Fig. 1. Participants in China's electricity market during 2002e2015.

Regulatory Commission(SERC)(before 2013) to regulate the operation of electricity market. Thus, electricity market is still completely controlled by the Chinese government [9]. Both on-grid price and transmission and distribution price are decided by National Development and Reform Committee (NDRC). The monopoly pricing mechanism has invisibly increased the cost of users, thus hindering the development of electricity market [10]. Besides, home users (not including large users) do not have the right to negotiate with power plants and power grid corporations, which leads to low operational efficiency and high cost in the end [5,11]. It still needs to increase the competitive capacity of participants in electricity market. In electricity market, there are several regular patterns for ensuring the soft landing of electricity market reforms [2,12].

Initially, competition mechanism was just introduced to the generation side of vertical integration, for the establishment of the single buyer mode. Subsequently, the competition mechanism was applied to the downstream industry, and developed the electrical wholesale market. In the end, it was introduced to the sell side, for setting up the retail competition mode [4]. This step-by-step process ensured a smooth transition from a vertical integration to a competitive electricity market [13,14]. Electricity market reform in China is similar to these liberalized processes [15]. Prior to 2002, China's power system was operated with a vertical integration mode, meaning that there was only one company to control all processes from the generation side to the sell side. After the first round of electricity market reform, the principle of competition was introduced to the generation side [16]. The power

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X. Peng, X. Tao / Energy 145 (2018) 152e170

plants had to compete with each other and sell the power to the power grid companies, namely single buyer mode. Besides, the reform about the direct power-purchase for the large user has lasted over 14 years (since 2002). The direct power-purchase for the large user has been implemented since 2005. Chinese government launched another round of electricity market reform in 2015, with the issuing of Several Opinions on Further Deepening the Reform of Electric Power System (No.9 Document). After the second reform, distribution market and retail market were also introduced to the existing electricity market. More participants were introduced into this market, and the competition mechanism was further applied to the sell side. Market-oriented measures were taken to regulate the participants in this electricity market. With the introduction of competition mechanism, generation efficiency has been improved considerably [11,17]. According to the No.9 Document, the electricity retailers consist of at least six kinds of bodies, including high-tech industrial center and economic development zone, social capital, distributed generation system (DGS), public service sectors and energy service company (ESC), generation corporations and grid company (GC). The electricity retail market (ERM) has been successfully implemented in many countries, such as Australia, America, England, Norway, and so on [18,19]. With more electricity retailers actively involved in retail competition market, the gap between retail market and consumers can be bridged [20]. Electricity retailers have the advantages of large members, flexible operation and independent right in supplying electricity [19]. Electricity consumers had the freedom to easily switch between different retail electricity providers. Therefore, in a deregulated electricity market, this business mode (electricity retailer mechanism) is likely to be accepted by customers [21]. Fig. 2 shows four basic types of retailers, who are summarized based on ownership relationship, including TN-owned (transmission networks) retailers, DN-owned (distribution networks) retailers, PP-owned (power plants) retailers and independent retailers. These ownership relationships mean that retailers will form different cooperative game structures based on their converging interests and goals [22,23]. The interdependence in cooperative game arises from largely diverging interest game structures. The cooperation (alliance) between electricity retailers and other participants can effectively reduce the cost by sharing the real-time information and improving the production efficiency in a spot market. Besides, direct power trading (DPT) policy is adopted to solve the distorted pricing issue. The electricity price is determined by direct negotiations between power plants and large users (See Fig. 2). In a spot market, the consumption equilibrium should be achieved by real-time transactions. The uncertainty of purchase prices and demand load can be resolved by a scenario generation method. Another uncertainty about retailers is associated with the selling price in a smart grid. In order to deal with these uncertain problems, Sayyad proposes the real-time pricing (RTP) mechanism and time-of-use pricing (TOU) mechanism in its model [24]. The rest of this paper is structured as follows. Section 2 introduces the status and issues of energy resources in China. A logical linkage of building trans-regional power transmission corridors is also established in this part. Section 3 presents participants' behaviors in a retail electricity market, and proposes an inter-regional power transaction model from the perspective of bottom-up modeling and two reasonable economic assumptions. Cooperative game theory and Shapley value solution are explained in the last part of this section. Section 4 refers to the empirical analysis of a cooperative game in China's electricity market. Section 5 makes some conclusions about the restructured electricity market.

2. Status and issues of China's energy The total energy consumption in China has increased quickly since 1980. Coal plays an important part in China's energy consumption, accounting for 62% of primary energy consumption in 2016(See Fig. 3). The thermal power generation accounted for 71.6% of the total power generation in 2016, due to the special energy endowment in China [25]. Fighting against climate change and carbon emissions are the common goals for countries around the world. As the largest consumer of primary energy, China has the obligation to achieve this target [26]. Since 2000, renewable energy has developed rapidly in China (See Fig. 4). The installed capacity of renewable energy increased significantly in the last decade [20]. The generation proportion went up by more than 10% in China during 2004e2016. However, the output of renewable energy power and distributed generation (DG) is variable or even random, making it difficult to be integrated into the power grid [27]. Up to now, large-scale renewable energy power and distributed generation have not been integrated into the power grid, which becomes a bottleneck for its further development. Because of the stochastic and intermittent output of renewable electric power, the amount of unutilized renewable energy can hardly be calculated [20,28]. The available utilization hour is defined as the total power generation dividing by total installed capacity in province i. The national average utilization hour is shown in Fig. 5. It gives a specific comparative analysis of the available utilization hours of several powers in different provinces based on Eq. (1).

Ui ¼

Qsi Ii

(1)

where Qsi is the electricity generation in province i (kW.h); Ii is the installed capacity in province i (kW); Ui is the available utilization hour in province i (hour). To better analyze the available utilization hours in different provinces, the comparison is based on regional level. After 2002, China's power grid was further regrouped into six big regional power grids, including Northwest Power Grid (NWPG), Central China Power Grid (CCPG), East China Power Grid (ECPG), North China Power Grid (NCPG), Northeast Power Grid (NEPG) and China Southern Power Grid (CSPG) (See Fig. 5). The utilization hours of hydropower in Northwest Power Grid, Central China Power Grid and China Southern Power Grid are higher than those of other power grids. However, it is worth noting that the comprehensive available utilization hours of China's power generation have dropped down since 2008. The utilization hours of wind power are low in Northwest Power Grid and Northeast Power Grid, while the utilization hours of solar power are lower in Central China Power Grid than others (See Fig. 5). As shown in Fig. 5, Northwest Power Grid has affluent renewable energy, like hydropower and solar power. However, the power demand in Northwest Power Grid is in low level. On the contrary, the power demand in East China Power Grid and North China Power Grid is relatively high, namely, “Reverse Distributed Problem”. As a result, the power generated from renewable energy in the northwest region has to be transmitted to eastern regions. Another problem also arises from this transmission process. With controllable output of coal-fired power plant and flexible dispatching process, limited power transmission channel and imperfect pricing mechanism of renewable electricity, the power dispatch center would dispatch the power generated from coal-fired power plants rather than from renewable energy power plants. This phenomenon leads to the serious “Priority Dispatched Problem” in China's power sector, namely, “wind power curtailment” and/or “solar

X. Peng, X. Tao / Energy 145 (2018) 152e170

155

Fig. 2. Simplified electricity market participants in China.

Proportion of coal

Proportion of thermal power

80%

85% 83%

75% Proportion of coal(%)

79% 70%

77% 75% 73%

65%

71% 69%

60%

67%

Proportion of thermal power(%)

81%

65%

55% 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Year

Fig. 3. Coal consumption and thermal power generation proportion in China during 1980e2016. Note: a The data is collected from National Bureau of Statistical of China (NBSC).

power curtailment”. The recent report of National Energy Board (NEB) revealed the list of provinces with a high unutilized rate of renewable energy, shown in Table 1. It can be seen that Gansu, Xinjiang, Ningxia, Jilin and Inner Mongolia have a high unutilized rate of renewable energy. Most of the power plants are thermal plants in China, which have obvious market force to affect electricity price in a deregulated electricity market. It is another reason for the low utilized rate of

renewable energy. Electricity balance equation in province i is defined as follows.

Qci  Qsi ¼ Fi

(2)

where Q ci is the electricity consumption in province i; Qsi is the electricity supply in province i, and Fi is the electricity net flow in province i.

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X. Peng, X. Tao / Energy 145 (2018) 152e170

25000

Renewable energy types

Consumption

104tce

20000

15000

10000

5000

0

Year Fig. 4. Renewable energy consumption during 2004e2016. Note: a The data is collected from BP Statistical Review of World Energy 2017.

Hydropower

Wind power

Solar power

Thermal power

Nuclear power

7000

3500

6000

3000

5000

2500

4000

2000

3000

1500

Northwest Power Grid

East China Power Grid

North China Power Grid

Northeast Power Grid

Yunnan

Guizhou

Hainan

Guangxi

Guangdong

Jilin

Heilongjiang

Liaoning

Inner Mongolia

Shandong

Hebei

Shanxi

Beijing

Tianjing

National average

Anhui

Fujian

Jiangsu

Zhejiang

Sichuan

Central China Power Grid

Shanghai

Chongqing

Hubei

Hunan

Henan

Jiangxi

Ningxia

0

Xinjiang

1000 Qinghai

500 Gansu

2000

Shaanxi

1000

Available utilization hours

8000

4000

Tibet

Average utilization hours

4500

0

China Southern Power Grid

Regional power grid Fig. 5. Average utilization hours of several powers in different provinces in 2014. Note: a Meng Xi Power Grid belongs to Inner Mongolia Power Grid, which is an independent power enterprise. Meng Dong Power Grid belongs to Northeast Power Grid. The average utilization hour of Inner Mongolia Power Grid is regarded as the average of Meng Dong and Meng Xi in this paper. b The data is collected from China Electric Power Yearbook 2015.

China's electricity load shows serious imbalance between electricity supply and demand among different power grids. If Fi > 0, province i is a net inflow power province. Conversely, province i is a net outflow power province. As shown in Fig. 6, East China Power Grid and North China Power Grid are net inflow power grids. The rest regional power grids are net outflow power grids in 2015. The inter-regional transaction is an important measure to balance regional electricity load and satisfy the electricity demand and supply in different provinces. Furthermore, inter-regional electricity transaction can effectively promote the utilization of renewable energy in renewable energy-abundant areas (See Figs. 5 and 6). In renewable energy-abundant area, local government should encourage consumers to use renewable energy as much as possible. With the new electricity market reform, retailers play a

dominant role in power transactions, which would help maximize social welfare and reduce operation cost. In the end, Fig. 7 summarizes the logical linkage of China's energy issue. Inter-provincial reverse energy distribution usually leads to unbalanced power supply and demand in China. The priority dispatched problem and limited power transmission channel result in low utilization hours of renewable energy (high unutilized rate of RE). Thus, it's important to construct a trans-regional (provincial) electricity transmission grid and coordinate regional energy development. 3. Methodology China's electricity market has been undergoing the change of

X. Peng, X. Tao / Energy 145 (2018) 152e170

157

Table 1 Unutilized renewable energy in China during 2015e2016. Provinces

Gansu Xinjiang Jilin Heilongjiang Inner Mongolia Ningxia Hebei Liaoning Yunnan Shanxi Qinghai

Unutilized wind power(108 kW h)

Unutilized rate

Unutilized solar power(108 kW h)

Unutilized rate

2015

2016

2015

2016

2015

2016

2015

2016

82 70 27 19 91 13 19 12 3 3

104 137 29 20 124 19

39% 32% 32% 21% 18% 13% 10% 10% 3% 2%

43% 38% 30% 19% 21% 13%

26 18

26 31

31% 26%

30% 32%

3

4

7%

7%

19

13%

2

3%

Note: a The data is collected from national renewable energy power development monitoring and evaluation report.

Consumption balance

Net inflow

Electricity balance(108kW.h)

1500 1000 500 0 -500 -1000

Northwest Power Grid Net outflow

Central China Power Grid East China Power Grid North China Power Grid Northeast Power Grid Regional grid

Total line loss

Guangdong

Total SCPG

Hainan

Guangxi

Yunnan

Guizhou

Liaoning

Total NEPG

Jilin

Heilongjiang

Inner Mongolia

Hebei

Total NCPG

Beijing

Shandong

Shanxi

Tianjing

Jiangsu

Total ECPG

Zhejiang

Shanghai

Anhui

Fujian

Henan

Total CCPG

Hunan

Chongqing

Hubei

Jiangxi

Sichuan

Total NWPG

Tibet

Qinghai

Gansu

Ningxia

Shaanxi

Xinjiang

-1500

China Southern Power Grid

Fig. 6. Electricity consumption balance in different provinces in 2015. Note: a The data is collected from National Bureau of Statistical of China (NBSC). b Meng Xi Power Grid belongs to Inner Mongolia Power Grid, which is an independent power enterprise. Meng Dong Power Grid belongs to Northeast Power Grid.

major restructures since 2015. Competition mechanism will be introduced to the monopolistic electricity markets in the near future. Power generation corporations, electricity retailers, transmission companies, and distribution companies are allowed to buy and resell electric power in a deregulated electricity market. The present electricity market is no longer a monopoly utility, but far more from a perfect market due to asymmetric information among stakeholders [29]. In this restructured market, electricity retailers play an important role in retail competition. In the context of a cooperative game theory, electricity retailers' behaviors are displayed by the next sections. 3.1. Behavior in retail market The behaviors of four participants, including electricity retailers, power generation corporations, transmission companies and distribution companies, are formulated by the transaction model in a spot market. 3.1.1. Electricity retailer After the second reform in 2015, the retail market was established to provide various selections of services for consumers.

Retailers procure the power from spot electricity market and resell the procured power to their customers [30]. Retailers have the specific real-time consuming information of their customers, while others cannot accurately forecast their load demand due to information asymmetry [31,32]. It can be seen that the output of renewable energy is variable or even random in a short time, thus this paper proposes a spot trading mechanism to deal with the problem [33]. Consumers purchase power at a flexible price (spot price or real-time price), which is offered by electricity retailers. On the one hand, retailers can maximize their profit by obtaining regional price differences [34,35]. On the other hand, PP-owned retailers and independent retailers have to pay the network tariff to TD companies. Compared with PP-owned and/or independent retailers, TN-owned and DNowned retailers have a lower operational cost due to the network tariff [36]. Assuming that the REPP-owned retailer is a price taker in a spot market, REPP-owned retailers will have little influence. The income of REPP-owned retailers is determined by spot (real-time) selling price, bidding price and the amount of sales in a spot market. If the bidding price is lower than the local spot price, the REPP-owned retailers may require TD companies to transmit the power from

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Cooperative game of electricity retailer

Unbalanced power supply and demand

High unutilized rate of RE (Abandoned renewable energy)

Trading mechanism reform

Pricing mechanism reform

Trans-regional (provincial) electricity transmission

Low utilization hours of renewable energy (RE)

Reverse energy distributed problem

Priority dispatched problem

Limited power transmission channel

Fig. 7. Logical linkage of China's energy issues.

REPPs to local load center [37]. Then the REPP-owned retailers resell the power procured from local TD companies to customers under time-of-use (TOU) price [24 periods during a day] and make a profit after paying a network tariff to TD companies [38]. If power is surplus or in shortage during a unit period, it will be adjusted in a real-time electricity market [27,39]. It is a possible method to increase the utilized rate of renewable energy in Northwest Power Grid and Northeast Power Grid. Retailers make a profit using its ownership with participants in a deregulated electricity market. Moreover, retailers' ownership structure has a significant influence on its revenue in a spot market [22]. Retailers participate in retail market on behalf of consumers [40], and protect them against financial risks and real-time pricing issues in a deregulated electricity market [41]. 3.1.2. Transmission and distribution companies TD companies are responsible for electricity transmission and voltage management. Power is transmitted from power generation companies (power plants) to electricity load centers through transmission network. The distribution networks deliver power to consumers after transformers reduce voltage within the allowable range. Hence, retailers who use the transmission and distribution networks should pay network tariffs to TD companies in exchange [42,43]. The network tariff includes line loss cost, congestion cost, operation cost, maintenance cost and long-term investment cost [44]. With the focus on cooperative game analysis in a spot market, the investment cost, maintenance cost and operation cost of TD companies are ignored. This paper approximately deals with the cost from line losses. The network tariff affects retailers' profit in a deregulated electricity market [45]. The cost of retailers is the revenue of TD companies. Thus, it is rational for TD companies to incorporate network tariff into their decision-making problems [46,47]. 3.2. Inter-regional power transaction model This paper mainly explores the retail competition under

cooperative game in a spot market, and ignores the impact of longterm investment cost on the decision making of retailers. It needs to note that this paper only refers to the short-term decision-making problem. As the PP-owned retailers don't have transmission and/or distribution assets in China, PP-owned retailers have to pay network tariff to TD companies. Compared with PP-own retailers, TN-owned retailers and/or DN-owned retailers have the advantage of low network tariff. Hence, it is reasonable to incorporate network tariff into a retailer model [4,48]. Considering that network tariff has not been widely implemented at national level, this paper proposes approximated algorithms for calculating the cost of TD companies. The cost of inter-regional power dispatch includes two parts: congestion cost and line loss cost [48e51]. Furthermore, line loss cost and congestion cost of TD companies are estimated by Dijkstra algorithm [52,53] and M/M/C/C queuing algorithm [54] respectively. The inter-regional power transaction model in a spot market is established from the perspective of bottom-up modeling. Fig. 8 exhibits participants' power transaction prices in a deregulated electricity market. It can be seen that the four participants are further classified into three sub-systems, including generation system, TD system and retail market. The arrow denotes the direction of capital flow from A to B. As for A, it refers to cost (expense). Contrarily, it denotes the revenue of B. Retailers procure power at the spot/real-time price and then resell it to customers. If electricity imbalance is negative, retailers may buy power at a realtime market to satisfy their needs. In comparison, retailers sell surplus power to TD companies, if electricity imbalance is positive. Retailers' decision-making deals with economic order quantity in a spot market and real-time market. Section 4 explains cooperative game of electricity retailers in a spot market. H.W. examined the impact of regulatory reforms on electricity price in 83 countries in 2010 [55]. According to No.9 Document, electricity price and on-grid price will be deregulated. Home users are able to determine electricity price by direct contracting with electricity retailers. Only transmission and distribution prices and government funds are still decided by National Development and

X. Peng, X. Tao / Energy 145 (2018) 152e170

1.Power plant model

159

1.Generation system

Generation cost

Bidding price On-grid price

Cooperative game in a spot market

Inter-regional power transaction model

2.Transmission and distribution system 2.TD company model TD cost in spot market

Line loss cost(Dijkstra algorithm) Congestion cost(M/M/C/C queuing algorithm)

Spot price

Real-time buying price Real-time selling price

3.Retailer model

3.Retail market Selling price

Customers Fig. 8. Cooperative game and inter-regional power transaction model in a spot market.

Reform Committee (NDRC) [3,10]. With the new network tariff pricing mechanism, the transmission and distribution price consists of allowable cost (including maintenance cost, operation cost and depreciation cost in this paper), allowable profit and tax. In economics, both maintenance cost and operation cost are variable costs, and depreciation cost is fixed cost, as shown in Fig. 9. Moreover, it should be noted that compared with long depreciation period (over 30 years), spot trade period (within 24 h) is short with small proportional cost. Hence, allowable cost could be ignored in this paper. Only line loss cost and congestion cost are considered in the transaction model in a spot market [Trans-regional transmission line loss rate is around 5% in 2013, as shown in Table 2]. In order to establish inter-regional power transaction model, some reasonable assumptions are needed based on No.9 Document in this paper. Assumption 1. All participants in a deregulated electricity market are rational economic men. They make efforts to maximize their profits through electricity transaction in a spot market. Retailers should follow general principles when they make choices in electricity market (See Eq. (3)).

Ci þ ðC a þ P a Þ  ð1 þ dÞ ¼ Cj

(3)

where Ci is power supply cost in province i; Cj is theoretical supply cost when the power is transmitted from province i to province j; C a means the allowable cost and P a means the allowable profit of TD companies. If network tariff charged by TD companies is lower than the local supply cost, retailers will procure more power to improve their profits through electricity transaction. Assumption 2. There is no completely independent power dispatch right. Previously, power dispatch center belonged to power grid companies. They were reluctant to dispatch renewable energy in priority with variable outputs. After the second reform, the main income of TD companies arises from network tariff. Thus, all retailers could require TD companies to transmit amounts of power after paying the network tariff. This indicates that the power dispatch right is no longer independent in a deregulated electricity market.

3.2.1. Line loss cost approximation In recent years, with the rapid expansion of power grids and large-scale development of renewable energy, trans-regional and/ or trans-provincial electricity transmission with ultra-high voltage (UHV) direct-current (DC) and alternating current (AC) technologies promote the integration in the main power grid of renewable energy in western areas, and mitigate power shortage in East China Power Grid and China Southern Power Grid in peak periods. With reverse distribution of energy resources and load centers in China, UHV projects are proposed by SGCC to connect the energy production bases and load centers (See Fig. 10). With the asymmetrical development of regional economy, there is growing gap between power demand and power supply in some provinces. In 2013, the trans-regional electricity trading is up to 2006.2*108 kW h, an increase of 17.1%, as shown in Table 2. The line loss rate of different transmission lines is exhibited in the last column. Fufeng DC (direct current) from Sichuan province to Shanghai is of the highest line loss rate, reaching 6.54% in 2013. Jingsu DC from Sichuan province to Jiangsu province is amounted to 6% (See Table 2). It can be seen that energy resource advantage in western regions is transformed into economic advantage based on trans-regional electricity transmission projects. In 2013, the trans-provincial electricity transmission was up to 8398.5*108 kW h. China Southern Power Grid transmitted 2452.1*108 kW h, ranking first among the six power grids. The line loss rate of different trans-provincial lines is displayed in the last column. The largest line loss rate is in CSPG, reaching 2.7% in 2013(See Table 3). Based on the analysis above, it can be seen that trans-regional transmission line significantly promotes the development of China's power industry, as it mitigates the tense peak load in some areas and improves the operation efficiency and the reliability of power grid. Prior to the second electricity market reform, electricity transmission pricing mechanism was un-transparent and confusing to the public. In order to further deregulate electricity market, it is important to figure out real operational cost of TD companies, and separate the transmission process from retail market. China's power grid is a massive network containing numerous circuits. In order to calculate the cost of TD companies, it needs to analyze the real cost of each circuit by power flow equations. However, it can hardly find out the real cost of trans-regional (provincial) electricity

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X. Peng, X. Tao / Energy 145 (2018) 152e170

Fig. 9. Electricity price structure in China after 2015.

Table 2 Trans-regional transmission line loss in China in 2013. Exporter

Importer

Transmission line (DC or AC)

Voltage grade (kV)

Transformer capacity (104kW)

Line length (km)

Output (108 kW h)

Input (108 kW h)

Line loss rate (%)

Hubei

Jiangsu Shanghai Shanghai Shanghai Guangdong Shanghai Jiangsu Shaanxi Henan Jiangsu Henan Hebei Hebei Shandong

Longzheng(DC) Genan(DC) Yihua(DC) Linfeng(DC) Jiangcheng(DC) Fufeng(DC) Jingsu(DC) Debao(DC) Changnan(AC) Yangcheng(AC) Linbao(DC) Jingjie/Fugu(AC) Gaoling(DC) Yindong(DC)

±500 kV ±500 kV ±500 kV ±500 kV ±500 kV ±800 kV ±800 kV ±500 kV 1000 kV 500 kV ±330 kV 500 kV ±500 kV ±660 kV

300 120 300 300 300 640 720 300 500 300 111 360 300 400 4951

860 1109 1049 978 941 1891 2090 534 639 508 95 439 204 1333 12739

112.6 36.3 102 55.5 126.7 320.4 224.6 131.9 81.8 166.5 65.5 207.3 181.8 284.3 2097.2

107 34.6 96.5 52.7 120.3 299.5 211.2 128.1 81.2 160.7 64.8 202.5 178.8 268.3 2006.2

4.94% 4.91% 5.34% 5.13% 5.03% 6.54% 6.00% 2.93% 0.70% 3.49% 1.11% 2.34% 1.63% 5.61% 4.34%

Sichuan

Shanxi Shaanxi Liaoning Ningxia Total

Note: a The data is collected from National Energy Board.

transmission processes in a spot market. Trans-regional or provincial transmission (distribution) networks are too complex to figure out the real cost of transmission processes in a spot market. In the

context of policy evaluation, we just calculate imputed cost of transmission processes, which is an intermediate cost. A new method is proposed in this paper to estimate the intermediate cost

X. Peng, X. Tao / Energy 145 (2018) 152e170

161

Fig. 10. Trans-regional transmission networks.

Table 3 Trans-provincial transmission line loss in China in 2013. Line length (km) Output (108 kW h) Input (108 kW h) Line loss rate (%)

National power grid Regional power grids Amount of transmission lines Grid to grid lines Point to grid lines Total lines SGCC

CSPG Total

NCPG NEPG NWPG ECPG CCPG CSPG

17 23 58 23 19 50 190

10 3 0 0 0 16 29

27 26 58 23 19 66 219

5188 5873 9862 2651 3290 16391 43255

1730.7 852.9 916.9 1871.4 638.9 2520.1 8530.9

1706.6 838 909.3 1858.7 633.8 2452.1 8398.5

1.39% 1.75% 0.83% 0.68% 0.80% 2.70% 1.55%

Note: a The data is collected from National Energy Board.

of trans-regional electricity transmission processes in a macro (national) level. Although the micro factors of power network are ignored, this method can specifically reveal the cost structures from the generation side to consumption side based on rational economic Assumption 1 and 2. In order to get more profits [lower cost] in transmission process, economic power dispatch (EPD) is adopted by TD companies in electricity market. Dijkstra algorithm is recognized as one of the best algorithms to solve the classical shortest path problem (SPP) [56]when all weight data are positive in graph theory. In a given network, this algorithm can be used to find the path with the lowest cost [shortest path] between origin node and destination node [57]. Dijkstra model is adopted here to search for a possible electricity transmission path from origin node [power plant location] to destination node [retailer location or large user location] across China. Dijkstra algorithm can be applied to find out the shortest path between one load center and another center [58]. The complicated transmission and distribution lines between any two neighboring provinces are simplified as one line for possible calculation. A total of 34 provinces are regrouped into 28 electricity

load centers, with Beijing, Tianjin and Hebei provinces in a load center, and Jiangsu and Shanghai in another load center. It's worth noting that Hainan, Hong Kong, Macao and Taiwan provinces are not included in the simplified network. The lines between any two neighboring provinces represent the simplified transmission and/ or distribution lines. Each load center represents a node. The 28 electricity load centers, namely 28 nodes, are shown in Fig. 11. Furthermore, an additional line will be integrated into transmission network if two provinces are connected by UHV lines. For example, V17 and V24 are connected by UHV lines (See Fig. 11). The line loss cost C loss is defined as follows.


 C loss ¼ P spot  P on $Q pp $U

(4)

where U is the minimum total line loss rate from province a to province b. In order to calculate the line loss cost C loss , it needs to firstly figure out the minimum total line loss rate U. 3.2.1.1. Shortest path problem. The concept of Dijkstra algorithm is based on searching process, which starts from the original point

162

X. Peng, X. Tao / Energy 145 (2018) 152e170

V16 Heilongjiang

V15 Jilin V14 Liaoning Xinjiang

V1

V5

Hebei,Beijing & Tianjing

Inner Mongolia

V13

V4 Gansu

Shanxi

Ningxia

Shandong

Qinghai

V21

V20

V11

Jiangsu &Shanghai

Henan

Shaanxi

V12

V6

V3

V27 V22

Anhui Tibet

V2

Hubei

Sichuan

Hunan

V19

V7

Zhejiang

Chongqing

V26

V10 V18

Jiangxi Fujian

Guizhou

V25

V9 V8

Yunnan Guangxi

Taiwan

Guangdong

V23

V17

V24

Net inflow Net outflow Hainan

V28

Fig. 11. Simplified distribution networks among neighboring provinces.

and gradually expands to the terminal point. Then, it records the path when it comes to a point called label. Dijkstra algorithm consists of two kinds of labels: T (tentative) label and P (permanent) label. All labels are T label at the beginning, and then one of the T labels changes into P label if the shortest path is found to this point in a cycle. According to Assumption 1, all participants in a deregulated electricity market are rational economic men. TD companies make efforts to maximize their profits or minimize their cost (line loss rate) in a spot market, as shown in Eq. (5). The subscripts i and j denote the electricity transmitted from province i to province j respectively. The symbol U represents the minimum total line loss rate when electricity is transmitted from province a to province b. The symbol rij denotes the line loss rate between province i and j. Iij is Bernoulli distribution variable. The shortest path problem is formulated in the following linear programming model.

Minmize U ¼

n X

rij Iij

(5)

i;j¼1

subject to 0  rij  1 i; j ¼ 1; 2; :::; n  1 rij is on the shortest path Iij ¼ 0 rij is not on the shortest path n X Iij ¼ Iab i; j ¼ 1; 2; :::; n

(6)

Step 2. Vs [start point] is labeled P, where PðVs Þ ¼ 0,TðVi Þ ¼ þ∞; i ¼ 1; :::; 28 and iss Step 3. If Vi has been labeled P, considering all neighbors of the current node Vi , such as Vj : ðVi ; Vj Þ3E and Vj is T label. And PðVj Þ is the minimal distance from Vs to Vi . Then, modify TðVj Þ: T(Vj) ¼ min[T(Vj), P(Vi) þ lij]

(8)

Step 4. Let PðVi Þ ¼ min½TðVi Þ, considering all neighbors of the current node. Step 5. If all the labels are labeled P, it is the end. Otherwise, step back to the third step. Thus, the line loss cost C loss can be calculated by inputting the line loss rate rij into the Dijkstra algorithm above, which is shown below.


 C loss ¼ P spot  P on $Q pp $U

(9)

It is worth noting that the line loss cost Ctloss is calculated under optimal conditions without considering the issue of congestion at busy time in a network, which will be discussed in the following part.

i;j¼1

The average line loss rate within a province is given by NEB. The line loss rate between two electricity load centers is calculated as the average line loss rate when electricity is transmitted between two provinces.

rij ¼

ri þ rj 2

(7)

where ri is line loss rate of province i; rj is line loss rate of province j, and i,j are neighboring provinces. The solving processes include these steps: Step 1. Line loss rate rij [including UHV lines] is assigned to each arc length.

3.2.2. Congestion cost approximation The line loss and congestion loss are regarded as opportunity costs in economics, which would be transmitted in electricity market. Besides, congestion problems occur under conditions of uncertainty. Thus the congestion cost is defined as follows.


 C cong ¼ P spot  P on $Q pp $ð1  UÞ$Pr:ðcongÞ

(10)

The congestion cost arising from dispatching power is calculated in a form of probability. In order to calculate congestion cost, congestion probability Pr:ðcongÞ is formulated by queuing theory. Blocking probability is an important issue in queuing system. The first M in M/M/C/C queuing system means that the arrival rate follows a Poisson distribution. The second M means that service time follows an exponential distribution. The loss queue is a

X. Peng, X. Tao / Energy 145 (2018) 152e170

queuing system consisting of C servers and C customers (See Fig. 12). There is no waiting room for potential arrivals. A customer will be lost or denied by the system if all servers are busy at the time of arrival (See Fig. 12) [54,59]. A number of literature about estimating blocking probability in overflow loss networks and systems have been proposed. Overflow loss network is an important class of loss network, known as a circuit-switched network [60]. Roughly speaking, a loss network is defined as an overflow loss network if calls blocked at one server group are permitted to overflow to another server group in some cases [61,62]. The M/M/C/C queuing system is adopted to estimate the blocking probability in transregional grids. Define M/M/C/C as a loss queue with a Poisson process, whose arrival rate is lðtÞ. And each customer (dispatching assignment) spends an exponential amount of time with mean 1=m in the system (see Fig. 13). The service (electricity transmission) requested by any arrival (dispatching assignment) is performed by a server (transmission network). Since the queue has C customers (dispatching assignments) and C servers (transmission networks) in a network, there is no waiting room for potential arrivals, thus resulting in a congestion problem in electricity market. Define n as the number of the customers in a system. In the stationary case, the arrival rate is constant l. The probability of n customers in a system is defined as Pn :

Pn ¼

8 < lim Pn ðtÞ t/∞

: Pn* ðtÞ

1þ

Define service intensity c as l=m, then Sn ¼

Pn ¼ Sn P0 ¼ ðcn =n!ÞP0 , P0 ¼ 1

1þ

C X

.

(15) !

,

ci i! z1

i¼1

.

ci i!

(16)

i¼1

, n

C X

n

Pn ¼ ðc =n!ÞP0 ¼ ðc =n!Þ 1

C X

. c i!

!

i

(17)

i¼1

When the system is filled with C customers, there is no waiting room for more customers. The potential arrivals will be rejected by the servers (transmission networks). Blocking probability in M/M/C/C queuing system is formulated as follows.

!! , C  . .  X i Pr:ðcongÞ ¼ PC ¼ c C! 1 c i! 

C

(18)

i¼1

Thus, congestion cost is calculated as follows.


 C cong ¼ P spot  P on $Q pp $ð1  UÞ$Pr:ðcongÞ

(19)

(11)

n ¼ 1; 2; :::C

C X

3.2.3. Bottom-up modeling In this section, a bottom-up modeling is adopted to simulate the cooperative game in a deregulated electricity market [63]. Moreover, power plant model, retailer model and TD company model are introduced into this model. A cooperative game of electricity retailers is an effective way to balance national energy allocation and promote competition in a spot market.

(12)

Idle probability when there is no customer in the system is shown below.

P0 ¼ 1

(14)

cn =n!,

t/∞

ln1 ln2 :::l0 ; mn mn1 :::m1

,

Pn ¼ Sn P0

if lim exists

others; where lim dPn* ðtÞ=dt ¼ 0

where Pn is the solution of statistical equilibrium state when there are n customers in the system. In order to calculate the congestion probability Pr:ðcongÞ, it needs to firstly figure out Pn . The cumulative service rate is formulated as follows.

Sn ¼

163

! Si

(13)

3.2.3.1. Power plant model. The power plants sell power to TD companies, while power generation corporations should bid at marginal production costs to maximize their profits in a perfectly competitive market. Profit of power plant is formulated as follows.

X X

i¼1

The probability of n customers in the system is formulated as follows.

q2j t2T

 pp Pton  CqPP ;t $Qt

(20)

C servers C customers waiting queue

S1

New arrivals ...

1

2

...

c

S2

...

Denied by system

SC

Fig. 12. M/M/C/C queuing system.

164

X. Peng, X. Tao / Energy 145 (2018) 152e170

Fig. 13. M/M/C/C state-transition diagram.

3.2.3.2. Retailer model. The electricity retailers determine the procured amount of power from the spot market and the adjusted amount from the real-time market. Considering that congestion and line loss costs cannot be ignored in a real-time market, selling price or buying price are different. Retailers' decision-making is correlated with the amount of procured power

Qtspot

in a spot

market, the amount of adjusted power qRT t in a real-time market and selling price SPt . It's worth noting that the selling price is further classified into residential, industrial and commercial electricity prices in China. Retailer's objective function is to maximize the expected profit with the spot price Ptspot and real-time price pRT t . The real-time price is based on real-time market, depending on scenario q occurring with probability Pr:ðqÞ. The power imbalance between supply and demand must be eliminated in a real-time market. Therefore, the buying and selling real-time prices pRTþ q;t , are set. Furthermore, we assume that real-time buying price pRT q;t and selling price are proportional to spot prices (See Eqs. (21) and (22)). Retailers' real-time buying price is usually higher than spot price in electricity market due to the unexpected extra power supply from transmission and distribution system. Consequently, real-time selling price is usually lower than spot price. It can be seen that retailers have a strong incentive to reduce the unnecessary imbalance in electricity market. Network tariff is regarded as a part of retailer's cost.

X X q2j t2T



(24)

where Cqgf is a payment for government funds, and it has been

included in the SPti as a surcharge. CqTD is the network tariff which includes line loss cost Cqloss , congestion cost Cqcong , allowable profit P a and electricity price tax d in a spot market. Thus, profit of electricity retailer is formulated as follows.

XX X spot spot gf RT RTþ TD SPti Qti þpRT pRTþ q;t qq;t Pq;t Qt q;t qq;t Cq;t Cq

!

q2j t2T i2M

(25) 3.2.3.3. TD company model. In order to transmit power from power plants to local electricity load center, PP-owned retailers and independent retailers without transmission networks have to pay network tariff to local TD companies. The calculation of network cong

tariff CqTD is based on line loss cost Cqloss , congestion cost Cq;t , ;t ;t a allowable profit P and electricity price taxd. Line loss and congestion cost is defined as opportunity cost. Network tariff is formulated as follows.

CqTD ;t

PqRTþ ¼ Pqspot ð1 þ aÞ ;t ;t

gf RTþ TD Pqspot Qtspot þ pRTþ q;t qq;t þ Cq;t þ Cq ;t

¼



Cqloss ;t

(21)

þ

cong Cq;t

0 1  DPqspot ;t þ P @1 þ spot Að1 þ dÞ Pq;t a

(26)

Revenue of TD companies is formulated as follows. where a is a proportional parameter.

X X q2j t2T

spot

PqRT ;t ¼ Pq;t ð1  bÞ

(22)

X X X q2j t2T i2M

q2j t2T

(23)

q2j t2T

RT on PP pRT q;t qq;t þ Pt Qt



(28)

i X Xh spot spot RTþ TD RT RT on PP Pq;t Qt þpRTþ q;t qq;t þCq;t pq;t qq;t Pt Qt

(29)

q2j t2T

Cost of electricity retailer is formulated as follows.

X X

(27)

Profit of TD companies is formulated as follows.

! RT SPti Qti þ pRT q;t qq;t



Cost of TD companies is formulated as follows.

X X

where b is a proportional parameter. Revenue of electricity retailer is formulated as follows.

RTþ TD Pqspot Qtspot þ pRTþ q;t qq;t þ Cq;t ;t

The formula can be rewritten as follows.

0 1 3   DP spot 4P spot Q spot þ pRTþ qRTþ þ C loss þ C cong þ P a @1 þ q;t Að1 þ dÞ  pRT qRT  P on Q PP 5 t t t q;t q;t q;t spot q;t q;t q;t q;t P 2

q;t

(30)

X. Peng, X. Tao / Energy 145 (2018) 152e170

where; QtPP ¼ Qtspot þ qRT q;t

(31)

3.3. Cooperative game Cooperative game theory is concerned with coalitions that coordinate their actions and pool their winnings. It is a booming research area with rapid developments in the last few years [64]. The basic concept of this theory was proposed by John von Neumann and Oskar Morgenstern in 1944 [65]. The classical cooperative game is transferable utility game (TU-game). A cooperative game with transferable utility has been applied in many fields. In a TU-game, agents are either fully involved or not involved at all in cooperation with others [66]. The cooperative game model is established in this paper to describe the relationship between participants in a deregulated electricity market, including power plants, power transmission and distribution companies and electricity retailers. 3.3.1. Cooperative game theory Cooperative game is used to divide the extra earnings (or cost savings) among members of formed coalitions. Various solution concepts for cooperative TU-games have been proposed by scholars [67]. Let N be a non-empty finite set of players, and N ¼ f1; :::; ng. And each subset S3N is called a coalition. The set of all subsets of N is 2N . For each S22N , eS denotes the characteristic vector of S [68].

 i  1 eS ¼ 0

i2S i2N\S

165

3.3.2. Shapley function Shapley value is one of the most well-known solutions to cooperative game. Shapley (1953) proposed the value Shi to a player i in an n-person game vðSÞ; S4N, where N is the set of players, S is one of the 2n sub-coalitions of N [70]. vðSÞ is the characteristic function which assigns a value to every coalition S. In order to clarify the Shapley function, the marginal contribution vector should be explained first [71]. The marginal contribution vector is defined as follows.

msi ðvÞ ¼ vðP s ðiÞ∪figÞ  vðP s ðiÞÞ

ci2N

(38)

where s is the number of players in sub-coalition S, and n is the number of all players in coalition N. The benefit allocation provides a benefit distribution of the total benefit vðNÞ among participants. The Shapley value ShðvÞ of a game v is the average of the marginal vectors of the game.

ShðvÞ ¼

1 X ms ðvÞ n! s2pðNÞ

(39)

Permutation s is an element of pðNÞ. The ith coordinate Shi ðvÞ is the expected payoff of player i according to this random procedure. The Shi ðvÞ can be rewritten as follows using the definition of marginal contribution vectors.

Shi ðvÞ ¼

1 X ðvðP s ðiÞ∪figÞ  vðP s ðiÞÞÞ n! s2pðNÞ

ci2N

(40)

There are s!ðn  s  1Þ! orderings for which one has P s ðiÞ ¼ S. Thus, the Shapley value Shi ðvÞ can be rewritten as follows.

(32) Shi ðvÞ ¼

X s!ðn  1  sÞ! ðvðS∪iÞ  vðSÞÞ n! S:i;s

ci2N

(41)

Definition 1. A cooperative game in characteristic function form is an ordered pair 〈N; v〉 consisting of the player set N and the characteristic function v. And v is a mapping.

4. Empirical results

v : 2N /R

(33)

4.1. Participants in a cooperative game

vð4Þ ¼ 0

(34)

Appropriate participants should be selected in a deregulated electricity market. Taking China as an example, three participants (except customers) are included in this paper, including power plants, transmission and distribution companies and electricity retailers. N people are involved in the cooperative game. Set N ¼ 3, representing the three participants in the cooperative game. Three players are defined as follows in a deregulated electricity market:

where vðSÞ represents the maximal profit or cost saving, and the member of S could be obtained by their cooperation. Once the characteristic function vðSÞ is determined, the cooperative game can provide a rational scheme for distributing the total benefit among the sub-coalitions. The set GN of characteristic functions of coalitional games with the player set N forms with the usual operations of addition and scalar multiplication of functions a (2jNj  1)-dimensional linear space. A basis of this space is defined as the unanimity games uT [69].

 uT ðSÞ ¼ cT ¼

X

1 0

T3S others

ð  1ÞjTjjSj vðSÞ

(35)

(36)

A: Power plants [including thermal power plant, renewable energy power plant, etc.]; B: Transmission and distribution companies; and. C: Electricity retailers.

4.2. Profit allocation under different coalitions

S:S3T

v¼

X T22N \f0g

cT uT

(37)

The profit allocation is calculated in different alliances. Table 4 summarizes the possible coalition modes in a deregulated electricity market. For a coalition, the characteristic function value represents excess profit obtained by all participants in this coalition. It is

166

X. Peng, X. Tao / Energy 145 (2018) 152e170 Table 4 Coalition modes. Independent

A B C AB AC BC ABC

Two collective alliances

Three collective alliances

calculated as the sum of surplus profit of this coalition. The characteristic function value vðSÞ in different coalitions is illustrated below. vðNÞi ¼ vðfA; B; CgÞi , vðNÞi is the characteristic function value of sub-coalitions of N in province i.vðfA; BgÞi is the characteristic function value of sub-coalitions of A and B in province i.vðfA; CgÞi is the characteristic function value of sub-coalitions of A and C in province i. vðfB; CgÞi is the characteristic function value of subcoalitions of B and C in province i. vðfAgÞi is the characteristic function value of A in province i.vðfBgÞi is the characteristic function value of B in province i. vðfCgÞi is the characteristic function value of C in province i. As this paper is focused on the cooperative game of electricity retailers in a spot market, only sub-coalitions with participant C are considered (See Table 4). 4.3. Profit allocation among different provinces Three independent participants and four strategic alliances may

appear in a restructured electricity market (See Table 4). In reality, electricity spot market has not been built in China. A total of eight provinces, including Guangdong, Inner Mongolia West, Zhejiang, Shanxi, Shandong, Fujian, Sichuan and Gansu are chosen as the pilot provinces this year. Hence, electricity price and electricity consumption data in 2014 are adopted to simulate the cooperative game of electricity retailers in a spot market. The characteristic function values of {C} among different provinces are shown below. Coalitions may increase the alliances' benefits, especially retailers. Fig. 14 displays the characteristic function value of independent participant C in an electricity market. It can be found that Hebei, Jiangsu, Fujian and Hubei provinces have a high characteristic function value in 2014. However, most provinces have little benefits or even negative characteristic function value in 2014, such as Shanxi, Shaanxi, Henan, Hunan, Sichuan, Chongqing, Guangdong, and Guangxi provinces. The negative characteristic function value is due to high on-grid price, transmission price and low selling price in these provinces. It seems that retailers have a lower market force compared with TD companies and power plants in a deregulated electricity market. Thus, the cooperative game solution may be a possible method to balance the benefits allocation among different participants in electricity market. According to cooperative game theory, retailers may form different sub-coalitions through ownership relationship. As shown in Fig. 2, four sub-coalitions of electricity retailers, including TNowned retailers, DN-owned retailers, PP-owned retailers and independent retailers are formed with converging interests and goals in an electricity market. The “Power plant-Electricity retailer” sub-

V {C}

Characteristic function value of V({C})(108CNY)

150 100 50 0 -50 -100 -150 Provinces

Fig. 14. Characteristic function value of {C} among different provinces.

Characteristic function value of V({A,C})(108CNY)

V {A,C} 2500 2000 1500 1000 500 0

Provinces

Fig. 15. Characteristic function value of sub-coalition {A, C}.

X. Peng, X. Tao / Energy 145 (2018) 152e170

coalition is denoted as {A, C}, and the characteristic function value of {A, C} in different provinces, as shown in Fig. 15. The “TD companies-Electricity retailer” sub-coalition is denoted as {B, C}, and the characteristic function value of {B, C} in different provinces is shown in Fig. 16. Compared with sub-coalition {A, C}, sub-coalition {B, C} has a lower average characteristic function

value, as shown in Figs. 15 and 16. Moreover, the sub-coalitions {A, C} and {B, C} have a higher benefit allocation than independent {C} in a cooperative game. The “Power plant-TD companies-Electricity retailer” subcoalition is denoted as {A, B, C}, and the characteristic function value of {A, B, C} is shown in Fig. 17. In theory, this sub-coalition has

Characteristic function value of V({B,C})(108CNY)

V {B,C} 1400 1200 1000 800 600 400 200 0

Provinces

Fig. 16. Characteristic function value of sub-coalition {B, C}.

Characteristic function value of V({A,B,C})(108CNY)

V {A,B,C} 2500 2000 1500 1000 500 0

Provinces

Fig. 17. Characteristic function value of coalition {A, B, C}.

ShC 400

Shapley value of C (108CNY)

167

300 200 100 0 -100 -200 Provinces Fig. 18. Shapley value of {C}.

168

X. Peng, X. Tao / Energy 145 (2018) 152e170

Electricity price(CNY/1000kW.h)

Coal-fired power

Gas-fired power

Hydropower

FITs for wind power

Nuclear power

FITs for solar power

FITs for biomass power

1550 1350 1150 950 750 550 350 150

Provinces

Fig. 19. On-grid price in different provinces in 2015. Note: a The data is collected from National Energy Board.

the maximum benefit allocation in a cooperative game. However, it is worth noting that this sub-coalition is different from the original vertical integration mode in the 1980s. Participants join the electricity market on their own to maximize their profits. {A, B, C} subcoalition is just one possible alliance in a cooperative game. The Shapley value averages the marginal contribution. Thus, the Shapley value of {C} sub-coalition can be obtained after inputting the characteristic function value of each coalition into the formula below. The Shapley value ShC ðvÞ is calculated as follows:

0!2! 1!1! ½vðfCgÞ  vð4Þ þ ½vðfA; CgÞ  vðfAgÞ 3! 3! 1!1! 2!0! ½vðfB; CgÞ  vðfBgÞ þ ½vðfA; B; CgÞ  vðfA; BgÞ þ 3! 3!

ShC ðvÞ ¼

(42)

In Shapley function, the Shapley value is deemed as the average of the marginal contributions, and the benefit is distributed fairly by an outside arbitrator. It can be found that Shapley value of {C} is better than the characteristic function value V{(C)} (see Fig. 18). As shown in Fig. 14, most benefits are close to zero or even negative in many provinces, which improves electricity retailer's competitiveness in a deregulation electricity market. 5. Conclusion China's electricity load shows the characteristics of reverse regional distribution. The gap between power supply and demand kept enlarging in the 1990s. In order to relieve these problems, twice electricity market reforms were implemented in China after 2002. This paper proposes an inter-regional power transaction model to formulate the benefit allocation of participants among different provinces in a spot market. Furthermore, a cooperative game under different coalitions is introduced in this paper to improve electricity retailers' competitiveness. As one of the wellknown solutions to a cooperative game, Shapley value is used to distribute profits among multiple participants in an electricity market. (1) During the last decades, twice electricity market reforms were implemented by the Chinese government. Two conventional electricity market modes, including vertical integration mode and single buyer mode have been applied in China's electricity market. However, the pricing mechanism

and operating mechanism of China's power sector are still under government control. In the new round of electricity market reform, retail competition mode is introduced into this market. The original state-owned enterprise (SOE) is no longer the monopoly in a retail market. (2) China's energy resources and electricity load are reverse distribution. The power supply is concentrated in western regions, while power demand is concentrated in eastern regions. This imbalanced distribution leads to serious problems in China's electricity market. Trans-regional power transmission is an effective measure to guarantee power demand in eastern regions. Inter-regional power transaction model in a spot market is proposed in this paper. (3) As the major revenue of TD companies in a deregulated electricity market, network tariff includes line loss cost, congestion cost, allowable profit and electricity price tax in a spot market. In reality, it can hardly calculate the line loss cost and congestion cost in trans-regional power transmitting process. Hence, Dijkstra algorithm is adopted to estimate the possible minimum line loss rate, which is also known as the shortest path problem. As opportunity cost, congestion cost would be considered in electricity market. Thus, it is formulated by probability formula. In addition, M/ M/C/C queuing theory is introduced in this paper to simulate the occurring probability. (4) There are obvious on-grid price differences among different provinces, as shown in Fig. 19. Electricity retailers can benefit from the regional price difference through electricity transactions. According to Assumption 1, if network tariff charged by TD companies is lower than local supply cost, retailers will procure more power to improve their profits through electricity transaction in a spot market. Retailers can make a profit until network tariff is equal to marginal price. The feed-in tariff (FIT) is a subsidization policy designed to increase investment in renewable energy. In the context of a feed-in tariff, renewable energy, including wind power, solar power and biomass power, is charged at a cost-based higher price. This mechanism helps finance renewable energy investments. (5) The cooperative game method is implemented to simulate electricity retailers' behaviors in a spot market. Various

X. Peng, X. Tao / Energy 145 (2018) 152e170

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