An Income Distributing Optimization Model for Cooperative Operation among Different Types of Power Sellers Considering Different Scenarios

Abstract

To alleviate the shortcomings of large-scale grid connections for clean energy, which require stable thermoelectric units to provide backup services, a stable cooperative alliance among different energy types of power sellers must be established. Consequently, a reasonable method to distribute income is required, due to different contributions of each entity in the alliance. Therefore, this paper constructs a comprehensive correction algorithm for income distribution using an improved Shapely value method. We analyze the operating mode of the power seller, and establish the net income calculation model under both independent and alliance operations. We then establish an alliance operation optimization model that considers the constraints of unit output, as well as the balance between supply and demand, with the goal of maximizing income. Finally, an industrial park in a province of northern China is taken as an example to verify the model’s practicability and effectiveness. The results show that the power sales alliance can effectively promote clean energy consumption. The maximum reduction in thermal power generation and CO₂ is 8510 MW and 684.515 tons, respectively. We apply the algorithm to income distribution and find that the thermal power seller’s income increased by ¥1,463,870, which enhances the stability of the alliance. Therefore, our income distributing optimization model guarantees the interests of each participant to the greatest extent, and serves as an important reference for income distribution.

1. Introduction

The distribution and the sales in China are being gradually liberalized under the continued implementation of the new electric power system reform and the policy of controlling the transmission, and opening the generation and sales sides. Thus, new types of power sellers have emerged, which effectively promotes the development of clean energy, including wind and photovoltaic [1]. However, significant uncertainty and intermittency occur during renewable energy generation in a large-scale grid connection, leading to the reduction of grid stability and power quality, requiring stable thermal power units to provide backup services. Simultaneously, different clean energy power sellers participate in power generation, crowding the available space for thermal power generation. This has led to the reduction of thermal power sellers’ enthusiasm to participate in power generation. Therefore, it is important to further study different scenarios of cooperative operation with respect to different types of power sellers, as well as income distribution for all participants involved. Such work is necessary to establish a stable multi-energy hybrid power system (MEHPS) and guarantee the participation of every power seller.

We first divide the MEHPS based on different types of power sellers, and construct scenarios of cooperative operation regarding multi-energy power sellers. Then we construct an income distribution model for the operation of the park power sales alliance (PPSA) based on an improved Shapley value method. Compared with the extant literature, our study contributes in the following ways:

(1)

The MEHPS is divided based on different types of power sellers. We determine the basic demands of establishing a PPSA, and construct the net income calculation models under both individual and alliance operation.

(2)

We set up different scenarios of cooperative operation for the alliance. We then analyze the degree of multi-energy complementarity, income of power sellers, and CO₂ emissions under different scenarios using the general algebraic modeling (GAMS) software, and finally determine the optimal scenario of alliance operation.

(3)

We introduce cost, risk, and contribution factors to improve the original Shapley value model, and then construct the income distribution model for the PPSA operation. This model comprehensively considers various actual factors that can provide important references for PPSA income distribution.

The remaining paper is organized as follows. In Section 2, we provide the literature review. In Section 3, we analyze the power sellers’ operation modes, introduce the whole power supply system in the park, and determine the basic conditions of establishing the PPSA. In Section 4, we construct two kinds of net income calculation models under both individual and alliance operation. In Section 5, we build a cooperative optimization operation model of the PPSA to maximize income, and consider the constraint of balancing supply and demand as well as unit output. In Section 6, we improve the original Shapley value method based on cost, risk, and contribution factors, and then propose an income distribution model for the PPSA operation. In Section 7, we select an industrial park in northern China to prove the validity and application of our income distribution model. In Section 8, we emphasize the contributions and conclusions of this study.

2. Literature Review

Currently, most research on the MEHPS is technical, and mainly focused on capacity allocation and optimal operation, while only a few studies consider the cooperative operation of different types of power sellers.

Regarding capacity allocation, Wu et al. [2] constructed an optimal distribution model of the power supply system for industrial parks based on the minimization of total cost. Using an improved differential evolution algorithm, Yang et al. [3] determined the optimal input capacity by developing a multifunction complementary system. Further, Li et al. [4] constructed an economic optimization model considering the reliability of the power supply and the complementary system of wind and photovoltaic energies. This method solved problems in optimal capacity allocation of different power supplies in the system. Cheng et al. [5] proposed a constant volume allocation method of mixing wind and photovoltaic systems by introducing an innovative probabilistic power flow algorithm. Fahd et al. [6] proposed an optimal solution of photovoltaic/wind/diesel/battery to maximize the proportion of renewable energy and minimize greenhouse gas emissions, while Hong et al. [7] determined the optimal capacity allocation between wind, photovoltaic, and diesel generation in independent power systems using a genetic algorithm.

Regarding optimal operation, Zhang et al. [8] constructed a planning model of collaborative optimization, and proposed optimization strategies for system operation based on the functions and characteristics of the MEHPS. Liu et al. [9] proposed a microgrid optimal operation strategy considering island performance constraints using the optimization algorithm, while Ju et al. [10] proposed a solution for MEHPS’s optimal operation from economic and environmental aspects. Yang et al. [11] studied the optimal operation of the MEHPS to minimize economic cost and power supply variance. Ming et al. [12] proposed a multi-objective optimization method for a renewable energy system under the islanding and the grid connected modes. Bai et al. [13] constructed a bi-level optimization model of the MEHPS to yield the lowest annual total cost and the highest primary energy economic ratio.

Nevertheless, the aforementioned studies neglect to analyze the economic and social characteristics of the operating processes.

The Shapley value method is often adopted to study income distribution [14,15,16], and it is mainly divided into two types: the original method and the improved method. For example, Bremer et al. [17] proposed a solution for the future smart grid alliance surplus allocation strategy using the original Shapley value method. Xie et al. [18] proposed a solution for income distribution in different power plants using the original method too, as did Tan Z [19], to solve income distribution under a large-scale wind and thermal power-combined delivery system. Similarly, Lu et al. [20] proposed a solution of income distribution using this method.

However, there are practical limitations in the original Shapley value method. For example, it considers monotonous factors, neglects the individual participant’s effort, and assumes that all participants take the same risks. These limitations have a negative effect on income distribution, which motivated scholars to improve the model for more efficient and practical application. Thus, we find that Xu et al. [21] improved the Shapley value method based on risk factors, ecological investment, and technological level to distribute the income of China’s Green Supply Chain. Cao et al. [22] improved it to distribute the income of a cross-regional hydropower project based on the principles of fairness and efficiency, as well as return and risk, while Xu et al. [23] used it based on the modified interval to solve income distribution in hydropower “Public-Private-Partnership”(PPP) projects. Moreover, Hu et al. [24] introduced cost and risk factors to construct the income distribution model for supply chains in eco-industrial parks. Li et al. [25] allocated the cost of ecological construction and protection in upstream areas using the improved Shapley value method. They thereby enhanced the enthusiasm of the upstream area for ecological protection. Zhang et al. [26] solved income distribution in the new energy vehicle supply chain, and Zhang et al. [27] corrected the Shapley value by introducing the “ecological compensation factor” to solve income distribution in mineral resources development.

Yet again, the aforementioned studies tend to lack application in the electric power industry. With the implementation of the new electric power policy and emerging power sellers, it is important to study the income distribution of different power sellers to enhance the stability of distributing and selling electricity.

Above all, many scholars have extensively studied the MEHPS and income distribution using both Shapley value methods. These studies offer numerous insights that form the theoretical foundation of our research. However, as noted earlier, the extant literature is largely focused on the technical aspects of the MEHPS and the application of either Shapley value methods is mainly in the context of non-power industries. Therefore, we divide the MEHPS based on different types of power sellers to study its internal economic characteristics. Then, we apply the improved Shapley distribution strategy to the income distribution process of the PPSA to enhance its stability and participants’ enthusiasm.

3. Operating Mode of Power Sellers

On 15 March 2015, the Central Committee of the Communist Party of China and the State Council issued a programmatic document on the reform of the power system titled “Several Opinions on Further Deepening the Reform of the Power System”, which clearly stated an orderly opening of the electricity business to social capital [28]. In recent years, with the in-depth implementation of relevant policies, new types of power sellers have emerged.

Currently, the power sellers include thermal power sellers (TPSs), which use conventional energy to generate electricity; and wind power sellers (WPSs) and photovoltaic power sellers (PVPSs), which generate electricity using clean energy. A TPS has the advantage of stable output, but fossil energy is scarce and the least environmental-friendly. WPSs and PVPSs have the advantages of using renewable resources, and being clean and offering environmental protection, but there is greater uncertainty and risk when it comes to their output. Therefore, if TPSs combine with clean energy power sellers to establish an MEHPS, it could alleviate the energy crisis, and promote clean energy consumption and environmental improvement [29,30].

In this study, we consider the context of an industrial park. First, there is a Park Power Trading Center and three power sellers comprising a TPS, WPS, and PVPS, each with its own power supply in the park. The Park Power Trading Center is mainly responsible for determining the park’s power demand; it releases information about the quantity of electricity and the price; and it coordinates the three power sellers to ensure they are jointly responsible for the electrical load demand of the park’s industrial users. The types of PPSA, without taking any alliance constraints into consideration, include the following: the WT, (the WPS and TPS are jointly responsible for the internal power supply of the park, while the PVPS directly runs the external sales business), the WP (the WPS and PVPS are jointly responsible for the internal power supply of the park, while the TPS directly runs the external sales business), the PT (the TPS and PVPS are jointly responsible for the internal power supply of the park, while the WPS runs the external sales business directly), and the WPT (the three types of sellers together provide the internal electricity supply first, and the rest is supplied for the external). Figure 1 represents the power supply system of the industrial park.

To maximize the guarantee of clean energy consumption, the stability of electricity used by the end-users, and the security of the grid operation, some basic hypotheses are proposed for the operating modes of the three power sellers.

Hypothesis 1. 

Hypothesis on the basic output of the three power sellers.

Wind and photovoltaic power generation are based on the principle of maximum likelihood, that is, maximizing power generation under natural conditions based on installation determination. Under the premise of meeting the constraints of generating units, thermal power generation is carried out according to the maximum load requirements of users in each period of the park.

Hypothesis 2. 

Hypothesis on the operating mode of TPS.

To ensure clean energy consumption and alleviate environmental issues, with the appearance of the PVPS and the WPS, the TPS must cooperate with clean energy power sellers, and internal and external power sales cannot be separately performed.

Hypothesis 3. 

Hypothesis on the operation of clean energy power sellers.

To ensure the stability of electricity use by end-users in the park, they must cooperate with the TPS; otherwise, it can only conduct external power sales.

Hypothesis 4. 

Hypothesis on the willingness to establish the PPSA.

All power sellers are willing to join the park alliance.

Hypothesis 5. 

Hypothesis on the gross generation by the alliance.

Under the control of the Park Power Trading Center, the gross generation of an alliance shall not exceed 120% of the energy demand of the end-users in the park.

Hypothesis 6. 

Hypotheses on the alliance’s power sales business.

First, we assume that the PPSA must prioritize the internal load demand of the park, that is, it has to sell power to the end-users in the park, and then the outsider. The internal power sales are settled by the peak-valley time-of-use (TOU) price, and the external power sales are settled by the on-grid electricity price. Non-alliance sellers can only conduct the external power sales. Second, clean energy power sellers must prioritize selling power when the PPSA engages in the power sales business, and the shortfall is supplemented by the TPS.

Based on the basic Hypothesis 4, the specific boundary conditions for the PPSA are as follows:

(1)

When the gross generation of the alliance participants at any time is greater than the basic load demand at the corresponding time of the end-users in the park, the second step may be determined, or the alliance is not established.

(2)

If the total income obtained by the alliance is higher than the gains obtained by the alliance members running the internal sales of the park independently, the alliance is established; otherwise, it is not.

Figure 2 represents the conditions for establishing the PPSA.

4. Net Income Calculation Model for Power Sellers

The participants of the PPSA discussed in this study include the TPS, WPS, and PVPS. In this section, we measure the net income of the power sellers under independent and alliance operation, respectively. Various factors such as the decision to participate in an alliance, electricity quantity, and electricity price and cost, all affect the sellers’ net income.

4.1. Net Income Calculation under Independent Operation

Based on Hypothesis 2 and 3, to ensure clean energy consumption and alleviate environmental problems, the TPS must cooperate with the clean energy power sellers, and cannot independently carry out the internal and external power sales. Further, to ensure the stability of the electricity used in the park, the WPS and the PVPS can only conduct the external power sales when they operate independently.

Therefore, when it comes to the calculation of the net income under independent operation, only the external power sales of the WPS and the PVPS are included. The specific model is as follows:

(1)

Net income of the WPS:

$$f_{out}^w=R_{out}^w-C_{nc}^w$$

(1)

where

$$R_{out}^w=[p{c}_{out}^w\cdot {\displaystyle \sum _{t=1}^t{Q}_{out}^w(t)}]$$

(2)

$$C_{nc}^w=C^w-R_b^w$$

(3)

$$R_b^w=p{c}_b^w\cdot {\displaystyle \sum _{t=1}^t(}{P}^w(t))$$

(4)

$$C^w=p{c}^w\cdot {\displaystyle \sum _{t=1}^t(}{P}^w(t))$$

(5)

(2)

Net income of the PVPS:

$$f_{out}^p=R_{out}^p-C_{nc}^p$$

(6)

where

$$R_{out}^p=[p{c}_{out}^p\cdot {\displaystyle \sum _{t=1}^t{Q}_{out}^p(t)}]$$

(7)

$$C_{nc}^p=C^p-R_b^p$$

(8)

$$R_b^p=p{c}_b^p\cdot {\displaystyle \sum _{t=1}^t(}{P}^p(t))$$

(9)

$$C^p=p{c}^p\cdot {\displaystyle \sum _{t=1}^t(}{P}^p(t))$$

(10)

4.2. Net Income Calculation under Alliance Operation

The PPSA that does not consider any alliance constraints includes four alliance scenarios: WT, PT, WP, and WPT. However, based on Hypothesis 3, the WPS and the PVPS must cooperate with other conventional power sellers. Evidently, WP does not accord with the alliance constraints. Therefore, we focus on the other three alliance scenarios.

Based on Hypothesis 6, wherein non-alliance participants can only conduct external power sales, the income of non-alliance participants only includes external sales. The net income calculation model refers to Equations (1)–(10). Alliance participants prioritize the internal power sales to meet the needs of the park’s users, and then they can conduct the external power sales. Therefore, the income includes the internal sales of the park, and then the external, and so on. The net income of the alliance depends on the relationship between electricity sales, electricity price, and cost. The specific net income calculation model is as follows:

(1)

Net income of the TPS under alliance operation:

$$f_c^{all}=R_{in}^c+R_{out}^c-C^c$$

(11)

$$R_{in}^c={\displaystyle \sum _{t=1}^t(p{c}^{in}(t)\cdot Q_{in}^c(t)})$$

(12)

$$R_{out}^c=[p{c}_{out}^c\cdot {\displaystyle \sum _{t=1}^t{Q}_{out}^c(t)}]$$

(13)

$$C^c={\zeta }_c{\displaystyle \sum _{t=1}^t{\displaystyle \sum _{i=1}^i[u_{i,t}\cdot (a_i^c+b_i^c{P}_i^c(t)+c_i^c{P}_i^c{(t)}^2)+}}{u}_{i,t}(1-u_{i,t-1})\cdot C_{U,i}]$$

(14)

Particularly, the CO₂ emission from the TPS is calculated as:

$$Q_{C{O}_2}=\kappa ·[a_i^c+b_i^c{P}_i^c(t)+c_i^c{P}_i^c{(t)}^2]$$

(15)

(2)

Net income of the WPS under alliance operation:

$$f_w^{all}=R_{in}^w+R_{out}^w+R_b^w-C_w$$

(16)

$$R_{in}^w={\displaystyle \sum _{t=1}^t(p{c}^{in}(t)\cdot Q_{in}^w(t)})$$

(17)

(3)

Net income of the PVPS under alliance operation:

$$f_p^{all}=R_{in}^p+R_{out}^p+R_b^p-C_p$$

(18)

$$R_{in}^p={\displaystyle \sum _{t=1}^t(p{c}^{in}(t)\cdot Q_{in}^p(t)})$$

(19)

Thus, based on the above, the total net income calculation model for the power seller alliance is:

$$f(\mathrm{WT})=f_c^{all}+f_w^{all}$$

(20)

$$f(\mathrm{PT})=f_c^{all}+f_p^{all}$$

(21)

$$f(\mathrm{WPT})=f_c^{all}+f_p^{all}+f_w^{all}$$

(22)

5. Cooperative Operating Optimization Model for the PPSA

Based on a variety of alliance scenarios, we now build a cooperative operating optimization model for the PPSA to maximize net income by considering power balance, unit output, and other constraints. Here, we use the GAMS software for the overall optimization.

5.1. Objective Function

This model is constructed to maximize the net income of the alliance:

$$F=\max (f(\mathrm{WT}),f(\mathrm{PT}),f(\mathrm{WPT}))$$

(23)

5.2. Constraints

(1)

Supply and demand balance:

$$P^p(t)(1-{\partial }_p)+P^w(t)(1-{\partial }_w)+[{\displaystyle \sum _{i=1}^i{P}_i{}^c(t)](1-{\partial }_c)}=Q^{in}(t)+Q^{out}(t)$$

(24)

(2)

Constraints of the thermoelectric units’ output:

$$\underset{\_}{P^c}(t)\le P^c(t)\le \overline{P_c}(t)$$

(25)

$$\Delta P_i^{c-}\le P_i^c(t)-P_i^c(t-1)\le \Delta P_i^{c+}$$

(26)

(3)

The start and stop constraints of the thermoelectric units:

$$(T_{ion}^{t-1}-T_{ion}^M)(u_i^{t-1}-u_i^t)\ge 0$$

(27)

$$(T_{ioff}^{t-1}-T_{ioff}^M)(u_i^t-u_i^{t-1})\ge 0$$

(28)

In the above, Equation (25) is the output constraint of the thermoelectric units, Equation (26) is the ramping constraint of the thermoelectric units, and Equations (27) and (28) are the start and stop constraints of thermoelectric units.

(4)

Total power generation constraints of different types of PPSAs:

(a)

Total power generation constraint of WT:

$${\displaystyle \sum _{t=1}^t{P}^w(t)+}{\displaystyle \sum _{t=1}^t{P}^c(t)\le }[{\displaystyle \sum _{t=1}^t{Q}^{in}(t)}]\cdot (1+20\%)$$

(29)

(b)

Total power generation constraint of PT:

$${\displaystyle \sum _{t=1}^t{P}^p(t)+}{\displaystyle \sum _{t=1}^t{P}^c(t)\le }[{\displaystyle \sum _{t=1}^t{Q}^{in}(t)}]\cdot (1+20\%)$$

(30)

(c)

Total power generation constraint of WPT:

$${\displaystyle \sum _{t=1}^t{P}^w(t)+}{\displaystyle \sum _{t=1}^t{P}^p(t)+}{\displaystyle \sum _{t=1}^t[{\displaystyle \sum _{i=1}^i{P}_i{}^c(t)}]\le }[{\displaystyle \sum _{t=1}^t{Q}^{in}(t)}]\cdot (1+20\%)$$

(31)

(5)

The output constraint of a wind turbine unit:

$$0\le P^w(t)\le \overline{P^w}(t)$$

(32)

(6)

The output constraint of a photovoltaic power unit:

$$0\le P^p(t)\le \overline{P^p}(t)$$

(33)

6. Income Distribution Method for PPSA

6.1. Role Positioning of Alliance Participants

There are two types of roles in the PPSA. The TPS must cooperate with the clean energy generator first, and provide backup services for clean energy power sellers. This leads to frequent starting and stopping of the units, which in turn raises the costs and lowers the profits. Participating in the alliance will harm its interests, and so the TPS is the favored party. Clean energy power sellers benefit from their cooperation with the TPS. To a certain extent, it squeezes some of the TPS’s sales, which expands its utilization and increases its profit significantly. Therefore, to ensure the stability of the alliance, clean energy power sellers make a concession. Figure 3 illustrates the rationale behind the role positioning in the alliance and the specific division of roles.

6.2. Cooperative Income Distribution Model for the PPSA

From the perspective of the individual participant of the hybrid power supply system in the park, the premise of participating is that alliance cooperation can generate higher income than noncooperation would; otherwise, the individual will give up the opportunity to cooperate. Therefore, we can use cooperative game theory to study the income distribution issues of the MEHPS.

The Shapley value method is commonly used to solve the issues of cooperative games. It reflects the number of contributions that the participants make for the alliance, and how important the participants in it are [31,32]. In the PPSA, clean energy power sellers provide clean energy, while the TPS focuses on the peak-load regulation services for the WPS and the PVPS. In this case, the cooperation will bring more benefits. Therefore, the income distribution of the PPSA is consistent with the hypotheses of the Shapley value method. Hence, it can be used to distribute income to the PPSA participants.

However, the factor that the Shapley value method considers is monotonous. The participants are expected to have no individual characteristics, and the method does not fully consider the internal differences of stakeholders in the actual project. Therefore, to better apply this to the income distribution of specific projects, we improve the method by combining the theoretical model with the actual conditions.

First, we build the Shapley value model. Second, the cost, risk, and contribution factors are respectively introduced to improve it. Finally, we construct a comprehensive correction algorithm based on the Shapley value method by combining the above three factors.

6.2.1. Shapley Value Method

The Shapley value means that the income shared by the participants is equal to its expected value for the marginal contribution of the alliance [33]. In this study, the Shapley value method accords with the symmetry axiom, that is, the distribution value of cooperative income does not change with the change of participants’ marks or orders in cooperation.

The specific Shapley model is:

$$V_i={\displaystyle \sum _{S\subseteq Ni}\frac{\left|S\right|!(\left|N\right|-\left|S\right|-1)!}{\left|N\right|!}}(v(S\cup i)-v(S))\forall i\in N$$

(34)

The criterion condition is:

$$V_i\ge X_i$$

(35)

This means that the income from participating in the cooperation is greater than individual actions.

$${\displaystyle \sum _{i\subset I}{V}_i}=V$$

(36)

This means that the income of the participants involved in the cooperation is the total income of the alliance.

$$V(\varnothing )=0$$

(37)

This means that there is no income for the seller who does not participate in the alliance.

6.2.2. Shapley Value Correction Algorithm

Based on the literature reviewed, the Shapley value method has its own shortcomings: the factors it considers are too monotonous, the model is too simple, every stakeholder is regarded an equal status in the distribution of income, and there is a lack of consideration for stakeholders in terms of responsibilities, costs, and risks. To solve these problems, we introduce the cost, risk, and contribution factors to improve the Shapley value method. The model considers the operating costs, the magnitude of risk, and the contribution ratio of the actual power supply of the participants of the PPSA.

(1) Modified Algorithm with Cost Factor

In the PPSA, owing to the characteristics of the units and the different energies used, the electricity generation costs of the power sellers are different. Therefore, the cost factor is introduced to improve the Shapley value method. That is,

$$C=C^c+C_{nc}^p+C_{nc}^w$$

(38)

$$V_i^{\prime }=(\frac{C_i}{C}-\frac{1}{n})\cdot V+V_i,C_i=C^c/C_{nc}{}^p/C_{nc}{}^w$$

(39)

(2) Modified Algorithm with Risk Factor

The Shapley value method assumes that the risk of each side is $\overline{R}=1/n$. However, in actual situations, the risks of the alliance participants are different. Therefore, the risk factor is introduced to improve the Shapley value method.

Assuming that $R_i$ is the actual risk, then an improved model based on the difference between the actual risk and the average risk can be expressed as:

$$V_i^{″}=(R_i-\frac{1}{n})\cdot V+V_i\begin{array}{cc},& R_i=R_c/R_w/R_p\end{array}$$

(40)

To further determine the actual operating risk of each power seller, we construct an indicator system to evaluate the operating risks of the power sellers (we include three secondary indicators: physical, economic, and social).

Table 1. Risk indicators system.

Secondary Indicator	Third-Grade Indicator
Physical indicator	Construction risk
	Output risk
	Equipment failure risk
	Equipment maintenance risk
Economic indicator	Net present value rate
	Investment Yield
	Dynamic Investment Return Period
Social indicator	Ecological environment protection
	Political risk

represents the risk indicator evaluation system.

The different values of the risk indicator weights will have a significant impact on the evaluation results. Therefore, we use the fuzzy comprehensive evaluation method [34,35] combined with the actual characteristics of the park’s power sellers in order to assign weights to the secondary indicators, and then to the third-grade indicators, based on the secondary indicators. Finally, based on the actual operating conditions and data of the power sellers in the park, we determine the actual operating risks of the three power sellers according to the weight of each indicator.

(3) Modified Algorithm with Contribution Factor

Owing to the difference in installed capacity, the contribution rate of the power seller is indirectly generated when the user’s load demand is met. Therefore, the contribution factor is introduced to the improved Shapley value method. That is,

$$V_i^{‴}=(\frac{D_i}{D}-\frac{1}{n})\cdot V+V_i\begin{array}{cc},& D_i=D_c/D_w/D_p\end{array}$$

(41)

6.2.3. Comprehensive Correction Algorithm

The improved comprehensive correction algorithm for Shapley value, that is, the income distribution algorithm for the PPSA, is:

$$V_i^{*}=\lambda V_i^{\prime }+\theta V_i^{″}+\mu V_i^{‴}$$

(42)

$$\lambda +\theta +\mu =1$$

(43)

Therefore, we use the method combining the analytic hierarchy process (AHP) and entropy method (EM) according to the actual conditions in order to assign the weights [36,37]. The criterion conditions of the improved comprehensive correction algorithm for Shapley value are shown in Equations (35)–(37).

6.3. Indicators of Cooperative Intensity Change under Different Distribution Strategies

$$B_{i,c-w}=\frac{V_{i,N-a-r}-V_{i,O-a-r}}{V_{i,O-a-r}},V_{i,N-a-r}=V_i/V_i^{\prime }/V_i^{″}/V_i^{‴}/V_i^{*}$$

(44)

$$P_{i,c-w}=1+B_{i,c-w}$$

(45)

$$P_{c-w-n}={\displaystyle \sum _i^3{P}_{i,c-w}}$$

(46)

In the above equations, $P_{i,c-w}$ is the willingness of a seller to cooperate. A value greater than zero indicates that the seller’s willingness to cooperate is enhanced under this distribution strategy, while a value less than zero represents a reduction in willingness to cooperate. $P_{c-w-n}$ is the degree of alliance stability under the nth distribution strategy—the greater the value is, the more stable the alliance is.

6.4. Steps of the Income Distribution Algorithm for the PPSA

Based on the study of the Shapley value method and its modification by combining many factors, we can determine the income distribution for each participant of the PPSA using the following steps:

(1)

Based on Equation (34), combined with the actual data in the operation of the PPSA, the initial Shapley value is obtained.

(2)

According to the actual data of the net cost of daily generation of the power sellers in the alliance, and combined with Equations (38) and (39), the improved Shapley value based on the power generation cost is obtained.

(3)

First, the basic weights of physical, economic, and social indicators are calculated by fuzzy comprehensive evaluation method based on the indicator evaluation construction. Second, by determining the weights of secondary indicators, the weights of third-grade indicators, such as construction and output risks, are calculated using the fuzzy comprehensive evaluation method in the same way. Finally, combined with the actual conditions and basic weight value of the sellers in the park, the actual operating risk of each seller is obtained. Using Equation (40), the improved Shapley value based on operating risks is obtained.

(4)

Based on the actual contributions of the participants to meet the energy demand of the end-users, and using Equation (41), the improved Shapley value based on cooperative contributions is obtained.

(5)

First, we combine the AHP with EM, finding the weights of generation costs, operating risks, and cooperative contributions. Second, combined with the values obtained in Equation (42), and steps 2–4, a comprehensively improved Shapley value is obtained.

Figure 4 illustrates a basic flow chart of the improved Shapley algorithm.

7. Example Analysis

7.1. Scenario Settings

To find the optimal situation, it is necessary to compare the energy complementarity, net costs of power sellers, net income, and CO₂ emissions under different circumstances of the PPSA. We thus divide the PPSA into different scenarios. Besides, to reflect the changes in the number of starts and stops of the thermoelectric units, reduction of CO₂ emissions, and fossil energy consumption at the utmost, the TPS is set as a reference scenario. The GAMS software will focus on the analysis of the reference scenario and scenarios 2–4.

Table 2. Scenario settings.

Scenario Classification	Scenario Classification	Alliance Participant(s)	Non-Alliance Participant(s)
Reference scenario	Scenario 1	TPS	WPS, PVPS
Alliance scenario	Scenario 2 (WT)	WPS, TPS	PVPS
	Scenario 3 (PT)	PVPS, TPS	WPS
	Scenario 4 (WPT)	WPS, TPS, PVPS	-

shows the power seller alliance scenario settings.

7.2. Basic Data

To verify the validity and applicability of the income distribution model for the PPSA, we selected an industrial park in a province of northern China as an example. The TPS, PVPS, and WPS in the park have their own power supply, with the following parameters: the TPS has five conventional thermal power generating units with a CO₂ emission factor of 0.2; the WPS has a total installed capacity of 1000 MW, and the equivalent utilization rate of each period is mentioned in by the authors of [19]. The generating units owned by the PVPS are PILKINGTON SFM 144Hx250wp. The area of each component is 2.16 m², the photoelectric conversion efficiency of each component is 13.44%, and the number of components of a photovoltaic array is 400. There are 720 PV arrays. Assume that the plant power consumption rate of each power seller is 0.2%.

Table 3. Parameters of the five thermoelectric units owned by the thermal power sellers (TPS).

Unit	${\mathit{a}}_{\mathit{i}}^{\mathit{c}}$	${\mathit{b}}_{\mathit{i}}^{\mathit{c}}$	${\mathit{c}}_{\mathit{i}}^{\mathit{c}}$/10−5	${\mathit{C}}_{\mathit{U},\mathit{i}}$(¥1000)	$△{\mathit{P}}_{\mathit{i}}^{\mathit{c}-}$(MW)
1	9.79	0.282	0.808	385	150
2	8.48	0.297	1.84	327	100
3	7.27	0.304	2.4	270	100
4	6.17	0.308	3.66	257	90
5	5.26	0.317	3.74	135	90
Unit	$△{\mathit{P}}_{\mathit{i}}^{\mathit{c}+}$(MW)	$△{\mathit{P}}_{\mathit{i}}^{\mathit{c}-}$(MW/h)	$△{\mathit{P}}_{\mathit{i}}^{\mathit{c}+}$(MW/h)	${\mathit{T}}_{\mathit{i}\mathit{o}\mathit{n}}^{\mathit{M}}$	${\mathit{T}}_{\mathit{i}\mathit{o}\mathit{f}\mathit{f}}^{\mathit{M}}$
1	600	−150	150	8	8
2	400	−100	100	7	7
3	350	−100	100	6	6
4	300	−90	90	5	5
5	300	−90	90	4	4

shows the operating parameters of the thermoelectric units.

According to the province’s average light intensity and wind turbine equivalent utilization rate, and combined with the basic model of wind and photovoltaic power generation [38,39], we obtain the basic output of the PVPS and the WPS. We collected the user loads in different periods of the park in around 90 days and solved their average as the basic power load demand of the park. Figure 5 shows the output of the PVPS and the WPS, as well as the load demands of the park users in a typical winter day, while

Table 4. Basic Data.

Category	Item	Price
Peak-valley TOU price	Valley hours	¥0.322/kW·h
	Peak hours	¥1.112/kW·h
	Flat hours	¥0.667/kW·h
On-grid price	On-Grid Price of Thermal power	¥0.32/kW·h
	On-Grid Price of Photovoltaic Power	¥0.65/kW·h
	On-Grid Price of Wind Power	¥0.45/kW·h
Generation cost	Wind power generation cost	¥0.35/kW·h
	Photovoltaic power generation cost	¥0.6/kW·h
Subsidized price	Subsidized price for wind power generation	¥0.18/kW·h
	Subsidized price for photovoltaic power generation	¥0.37/kW·h

presents the basic data.

7.3. Analysis of Results

7.3.1. Operating Results in the Reference Scenario

The TPS operates separately as the reference scenario. In this scenario, the TPS individually meets all the electrical loads of the end-users within the industrial park. Under the premise of satisfying its own power generation constraints, the thermoelectric units generate electricity according to the maximum load demand of each period of, and not exceeding 120% of the total demand of, the end-users. Figure 6 illustrates the start–stop state and the amount of power generation of the thermal power unit, while

Table 5. Data of the TPS in the reference scenario.

Power Seller	Total Generation (MW)	Net Cost (¥1000)	Net Income (¥1000)	Carbon Emission (t)
TPS	23,100	4759.73	12,135.61	1630.715

presents the data of the TPS in the reference scenario.

According to Figure 6, in the reference scenario, thermoelectric units are the only units of the park’s power supply that can meet the electric load demand of the end-users. Since the number of start and stop times of each unit is small, the energy supply is relatively stable. According to Table 5, the total power generation is 23,100 MW, the net income of both internal and external sales of the TPS is ¥12,135,610, and the carbon emissions are 1630.715 t.

The TPS has the advantage of stability and safety when operating independently, but in this scenario, but considering energy structure, it is too monotonous and the benefits from the MEHPS cannot be demonstrated. Considering environmental protection, the power generation is large because of the continuous power generation of the thermoelectric units, so the CO₂ emissions are large too, and the pollution problems cannot be effectively solved.

7.3.2. Operating Results in Alliance Scenarios

The alliance scenarios in this section are scenario 2 (WT), scenario 3 (PT), and scenario 4 (WPT).

Figure 7, Figure 8 and Figure 9 show the start–stop statuses of the thermoelectric units and the power supply of the park in different alliance scenarios.

Table 6. Comparison of benefits in the alliance scenarios.

Scenario	Operating Mode	Seller Type	Total Generation (MW)	Net Income (¥1000)	Carbon Emissions (t)
Scenario 2	Alliance operation	TPS	15,370	8993.33	1032.299
		WPS	8610	3630.18	0
		Total	23,980	12,623.51	1032.299
	Individual operation	PVPS	727.077	299.26	0
Scenario 3	Alliance operation	TPS	22,880	11,934.25	1598.809
		PVPS	727.077	462.57	0
		Total	23,607.077	12,396.82	1598.809
	Individual operation	WPS	8610	2302.31	0
Scenario 4	Alliance operation	TPS	14,590	8850.99	946.2
		PVPS	727.077	462.57	0
		WPS	8610	3630.18	0
		Total	23,927.077	12,943.74	946.2

shows the income comparison among power sellers in different alliance scenarios.

Comparing Figure 7a, Figure 8a and Figure 9a with Table 5 and Figure 6, we find that the power generation in Scenarios 2, 3, and 4 is able to meet the needs of end-users at any time. The power sellers cannot run the internal power business upon independent operation, which means that the income of each individual seller would be zero. Therefore, the PPSA can be established in Scenarios 2, 3, and 4. Next, the start and stop times of the thermoelectric units increased, and the thermal power generation decreased by different degrees because of the participation of clean energy power sellers. Finally, according to Figure 7b, Figure 8b and Figure 9b, the number of different energy suppliers increased in the alliance scenarios, especially in Scenarios 2 and 4, because the effects of multi-energy hybrid power generation were remarkable.

According to Table 6, and considering thermal power generation, the total generation of the TPS in any alliance scenario is always less than that in the reference scenario. However, because of the different power generation of clean energy, the total power generation of the TPS varied in alliance scenarios—Scenario 4 was the best, reaching a minimum of 14,590 MW. Considering cost and net income, because of the reduction of total power generation by the TPS, the cost of the TPS reduced more than that in the reference scenario. Since the clean energy sellers participate in the internal power sales business, their net income increases with the same cost. Considering environmental protection, the alliance with the clean energy power sellers is useful for energy conservation and emissions reduction, especially the reduction of CO₂ emission. Here, Scenario 4 reached a minimum of 946.2 tons.

In summary, by comparing different alliance scenarios, and from an economic point of view, scenario 4 had the highest net income. From the environmental point of view, Scenario 4 had the least CO₂ emissions. Thus, Scenario 4 is optimal. The income of the alliance was higher than individual income, which satisfies the conditions of the convex game. Therefore, to ensure the stability of the alliance operation, we used the improved Shapley to distribute the income of the alliance optimal Scenario 4.

7.4. Results in the WPT Income Distribution

The original income distribution only considers the power sales of each seller. It neither considers the seller’s contributions to the goal of the alliance, nor does it reflect the process of mutual game playing. Therefore, we use the Shapley value method to improve the original income distribution results in this study. Based on Equation (34), we obtain the WPT alliance income distribution results.

Table 7. The distribution results based on the Shapley value method.

Power Seller Type	Original Distribution Result		Distribution Result Based on the Shapley Value Method
	Net Income (¥1000)	Proportion	Net Income (¥1000)	Proportion
WPS	3630.18	28.05%	2286.225	17.66%
TPS	8850.99	68.38%	8484.635	65.55%
PVPS	462.57	3.57%	2172.88	16.79%

presents the distribution results based on the Shapley value method.

Table 7 shows that, compared with the original distribution results, the proportions of net income of the TPS and the WPS decreased, while the proportion of the PVPS increased by 13.22%. This cannot reflect the collaborative value of the TPS in the MEHPS within the park, and over-expands the contribution value of the PVPS. Besides, the income distribution does not accord with the actual conditions of the park. Thus, we will improve the Shapley value method by introducing the generation cost, operating risk, and cooperating contribution.

The next process is based on Section 5.2. First, we use the actual operating data of the park combined with all indicators of operating risk assessment, as well as the fuzzy comprehensive evaluation method. We ascertain the actual operating risk proportions of the WPS, PVPS, and TPS. Second, combining the AHP and EM, we obtain the basic weights of power generation cost, operating risk, and cooperating contribution.

Table 8. Actual basic weight proportion.

Indicator	Weight Proportion	Seller Type	Original Proportion	Actual Proportion	Difference
Generation cost	0.217	WPS	1/3	0.309	−0.024
		TPS	1/3	0.601	0.267
		PVPS	1/3	0.090	−0.243
Operating risk	0.300	WPS	1/3	0.340	0.006
		TPS	1/3	0.122	−0.211
		PVPS	1/3	0.538	0.205
Cooperating contribution	0.483	WPS	1/3	0.389	0.055
		TPS	1/3	0.578	0.245
		PVPS	1/3	0.033	−0.300

presents the weights of power generation costs, operational risks, and cooperative contributions.

Considering power generation cost, and based on the actual power generation cost data, we obtain the actual cost proportions of the three sellers (see Table 8). The original Shapley value method exaggerates the proportions of the actual generation cost of the clean energy power sellers.

Considering operating risk, the original Shapley value method ignores the characteristics of uncertainty and risks of clean energy generation, and exaggerates the risk of power generation by the TPS.

Considering cooperating contribution, the original Shapley value method exaggerates the contribution of the PVPS in meeting the demands of the park end-users.

Therefore, based on Table 8, we revise and re-determine the basic weights of all indicators, and then construct the improved Shapley value. Combined with Equations (38)–(43), we obtain the new income distribution results.

Table 9. Income distribution results based on the improved Shapley value method.

Seller Type	Improved Value Based on Generation Cost	Improved Value Based on Operating Risk	Improved Value Based on Cooperating Contribution	Comprehensive Improved Value
WPS	197.199	236.758	300.305	251.133
TPS	1194.589	574.864	1165.751	994.851
PVPS	−97.414	482.753	−171.682	48.39

presents the income distribution results based on the improved Shapley value method, while Figure 10 illustrates the proportion of income in different distribution strategies.

According to Table 9, the improvement of the Shapley value method based solely on the cost of power generation or cooperating contribution has led to excessive neglect of the role of the PVPS in reducing CO₂ emissions and enriching the seller’s type. This has caused serious losses to the PVPS. Considering the improvement of this method based on the operating risk, the net income of the PVPS was too high and the income of the TPS was significantly reduced, ignoring the important synergism of the thermoelectric units as backup units.

Therefore, it is necessary to improve the Shapley value using comprehensive considerations. We determine the final results according to the weight proportions.

Let us observe Figure 10. Considering the TPS and comparing the original results with the improved one, the proportion of the latter increased by 8.48% and the income increased by ¥1,097,520. Comparing the results based on the original Shapley value with the improved one, the proportion of the latter increased by 11.31% and the income increased by ¥1,463,875. This better reflects the auxiliary role of the TPS in the entire power supply system of the park and the collaborative value of the TPS; it enhances the enthusiasm of the TPS to participate in the alliance; and it promotes the stability of alliance operation. Considering the WPS and the PVPS, regardless of the distribution strategies used, the net income was higher when participating in the park’s electricity sales as opposed to independently.

7.5. Analysis of the Results of Changes in the Willingness to Cooperate under Different Distribution Strategies

Based on Equations (44) and (45), we obtain the results of the degree of changes in the willingness to cooperate under different distribution strategies.

Table 10. The willingness to cooperate under different distribution strategies.

Power Seller	Willingness to Cooperate
	Strategy Based on the Original Shapley Value	Strategy with Cost Factor	Strategy with Risk Factor	Strategy with Contribution Factor	Strategy with Comprehensive Improvement
WPS	0.63	0.543	0.652	0.827	0.692
TPS	0.959	1.35	0.649	1.317	1.124
PVPS	4.697	−2.106	10.436	−3.711	1.046
Stability degree of alliance	-	−0.213	-	−1.567	2.862

presents the willingness to cooperate under different distribution strategies.

Under the strategy based on the original Shapley value and that with the risk factor, both the income of the TPS and the degree of willingness to cooperate decreased (see Table 10), which does not accord with the role as favored party. Hence, these strategies are not feasible. Under the strategy with the cost factor, with the contribution factor, and with the comprehensive improvement, the ranking of the alliance stability is $P_{c-w-5}>P_{c-w-2}>P_{c-w-4}$. Thus, under the strategy with comprehensive improvement, the stability degree is the highest, and the willingness to cooperate of the WPS, TPS, and PVPS increased by −0.308, 0.046, and 0.124, respectively.

Above all, to ensure the stability of the PPSA and the enthusiasm of all participants, the improved Shapley value method should be used to distribute the income of the PPSA.

8. Conclusions

We divided the MEHPS based on different types of power sellers considering the new electric power system reform and emerging power seller types. On this basis, we studied multiple PPSA operation modes of the TPS, WPS, and PVPS. We also introduced the cost, risk, and contribution factors to revise the original Shapley value method, and then distributed the income of the optimal PPSA to ensure the stability of alliance operation. The results show that:

(1)

The PPSA can effectively manage resources and create more benefits in the whole cooperation process. From the economic aspect, the net profit of the PVPS and the WPS participating in the PPSA increased by ¥18,464,000 and ¥2,090,100, respectively, compared with gains from external sales. From the environmental aspect, the WPT reduced 8510 MW of power generation and 684.515 tons of CO₂ emissions by the TPS.

(2)

Using the improved Shapley value method with the cost, risk, and contribution factors, we constructed the income distribution model, which guarantees reasonable income to all participants in the alliance and promotes enthusiasm to participate. Under the strategy with comprehensive improvement, the TPS increased the income by ¥1,263,870, which embodies the important cooperative value of thermal power generation.

Above all, first, to improve the consumption of clean energy and alleviate environmental problems, the PPSA, including different types of energies, should be established actively, which can effectively integrate a variety of energy resources. Second, to maximize the stability of the PPSA operation, the comprehensively improved Shapley value method should be applied in the process of income distribution, which can solve the problem of uneven distribution of income among different role-oriented power sellers, ensure the rationality and fairness of each participant’s income, and improve the efficiency of the PPSA operation.

There are many factors that affect the income distribution of participants in an alliance. However, we only included the cost, risk, and contribution factors, which may not be sufficiently comprehensive. Further, each factor’s weight cannot be accurate. Therefore, future research must consider how to optimize and perfect the proportion of weight under limited information.