Economic research on application of electric heating system based on game theory

0 Introduction

The vast majority of traditional heating boilers use a fossil fuel such as coal,oil,or natural gas as the main energy source.However,a large number of pollutants such as carbon dioxide are emitted during the combustion process,which not only increase the demand for environmental governance but are also constitute some of the main factors for global climate change.Countries around the world have turned their attention to new energy sources for power generation,such as solar,wind,ocean,and biomass power generation.In addition,they are trying to replace fossil fuel combustion heating with electrical heating.During the heating season,using electrical energy for heating is an important way to increase the electrical load and reduce the burning of fossil raw materials.

Driven by the goal of “2060 carbon neutrality”,China will continue to vigorously develop new energy sources and increase the installed capacity of wind power and photovoltaic [1,2],and the large-scale grid connection of new energy sources is facing a serious problem of consumption,while the promotion of “electrified” is conducive to increasing the electric load,improving the consumption of new energy and reducing carbon emissions,which has become a priority for the future.The “electric heating” project has the goal of replacing traditional thermal heating systems with electrical heating systems [3],and the promotion of electric heating has been proven to significantly reduce CO2 emissions and improve atmospheric quality [4].Current research on “electric heating” is mainly divided into the development of methods to improve the efficiency of electric heating systems [5-7],analyses of the demand characteristics of heat users to realize the optimal dispatch of heating [8-10],and the joint optimal dispatch with electric energy [11-13].However,feasible plans and business models to promote electric heating are rare because of the particularity of power production,transmission,and supply,and the low price of coal in China.The use of coal-fired boilers to provide central heating in residential buildings still has quite a significant price advantage over electric heating.Current solutions to price issues include the use of new energy sources for power supply,heating during underestimated periods,and policy subsidies,but there is a need to overcome high electricity prices,insufficient subsidies,and insufficient access to new energy sources It is difficult to promote a “coal-toelectricity” transformation [14,15].Moreover,there are few discussing economic analysis models for electric heating.A game relationship between the government and the power grid company based on game theory for the electric heating promotion project was established in reference[16],but this model lacked practicality because it did not consider the willingness of users.When the heating price of the electric heating project is greater than the price of coal heating,users are not willing to use electric heating,which makes it impossible to implement the electric heating project.The game relationship between the government,power grid company,and heating users in western China has been analyzed based on game theory for the electric heating promotion project,and a game model to maximize the benefits for the government,power grid company,and users was established,with the constraints of new energy consumption,the grid renovation area,and user satisfaction as variables.In addition,an electric heating promotion scheme under four application scenarios has been proposed in reference [17].However,new energy consumption was used as a variable,which is not applicable in areas where new energy is not abundant; and user satisfaction is a vague concept,which cannot accurately quantify the motivation of the users.An increasing number of general economic analysis models for electric heating are expected.

Game theory is mainly used to study the interactions between formulaic incentive structures and is a mathematical theory and method for studying phenomena with a struggle or competitive nature [18].In one study,a tripartite evolutionary game model involving the central government,local governments,and coal enterprises was constructed and used to examine the dilemma of overcapacity governance and alternative policies [19].A three-party evolutionary game model that considered the strategies of the service platform,government,and consumers was built,and a governance mechanism was proposed to prevent the service platform from using big data discriminatory pricing (BDDP)[20].Another study proposed an energy-trading model based on the Nash bargaining game to study the cooperative benefits between an IESand several EVCSs [21].A new differential game was also proposed for solar heating systems with several consumers (players)to describe the temperature change of the solar storage and the change in the players’ payoffs over time,considering the heat recharge and heat loss of the storage as well [22].However,the analytical method for solving the Nash equilibrium point is slow and is usually combined with intelligent algorithms to solve the problem,such as particle swarm algorithms and genetic algorithms [23-25].

In conclusion,the existing literature mainly focuses on combined heat and power,electric heating coordination and dispatch,and electric heating technology realization [26-30],or proposes policy recommendations for the promotion of electric heating [31,32].However,little research has been done to enable more investors to share the high onetime investment and construction cost of electric heating,find a variety of operating modes,and propose plans to promote the commercialization and scale of electric heating.Optimization models that can quantify the impact of different variables on stakeholders are even rarer.A plan that is beneficial to all stakeholders should be proposed for large-scale electric heating promotion.The current study investigated a new method for optimizing the revenue of the stakeholders in the electric heating promotion project.The electric heating promotion power,heating electricity price,and government subsidy unit price were used as variables to make the model more applicable.The model for the pursuit of the maximum benefits to the stakeholders was transformed into a multi-objective optimization model,and an arithmetic example was used to analyze the influence of the electricity price on electric heating promotion.

1 Evolutional Game Model and Analysis

Game theory is a common optimization method that is widely used for analyses in economics,sociology,and psychology.This theory studies the interaction among the participants involved in a game (i.e.,players).The participants are faced with a series of actions and gain certain benefits or losses based on their choices.Based on different rules and hypotheses,game theory can not only provide the best solution (i.e.,the overall benefits to all the subjects reach their maximum values)but also the greatest number of possible solutions (i.e.,the interest of each subject is satisfied but the overall benefits are not the optimum values)[13].

Traditional game theory asks each participant in the game to be purely rational.They should fully understand their opponent’s decisions and probabilities,the rules of the game,and the payoff structure,as well as have the ability to deduce the best strategy.However,in real life,the participants often have bounded rationality.Therefore,the best response strategy is often achieved through trial and error methods and experiments rather than complex calculations [14].The participant makes choices based on the experience of their predecessors.They also learn and duplicate the choices of others.This situation is more common and realistic in a real-life optimization problem.Therefore,it is used in the analysis of electrification projects.

1.1 Participants in electric heating

In the initial stage of the marketization of electric heating,the main participants are the government,electric heating users,and power grid company.Their objectives are listed as follows.

The government hopes to promote electric heating as much as possible to reduce coal combustion and achieve emission reduction targets.

The heat users unconditionally accept electric heating when the electric heating price does not exceed the traditional heating price; if it does exceed that price,they will not accept it,unless there is a mandatory energy-saving policy.

The power grid company is the most important participant in electric heating and is responsible for the transformation and expansion of power supply facilities.Its behavioral incentives come from the ability to increase sales of electricity and obtain government funding.

In this way,it is clear that the three participants are closely related,and the target benefits of these multiple parties are affected by the strategies of the other parties.This is a typical game problem.The game relationship between government,grid and users is shown as Fig.1.Based on the above analysis,it is clear that the government,power grid,and users all have individual rationality and there is no agreement between them.It is assumed that in each round of decision-making,all the participants have complete information about the others.Therefore,a noncooperative dynamic game model can be established [33]:

Fig.1 The game relationship between government,grid and users

where L is the participant vector,Ω is the strategy vector,and I is the income/payment function vector.The game participants,L,in this project are the government,power grid company,and users.

1.2 Revenue model

The profit/payment of the utility function on both sides of the game is the goal pursued by each participant and is a function of strategies.The structure of the income/payment function has a significant influence on the solution of the game model.

The government will reward the power grid with funds based on an increase in clean power consumption due to the promotion of electric heating.In other words,the promotion of electric heating reduces the consumption of traditional energy and pollutant emissions.Its revenue function is as follows:

where IZ is the government’s revenue; e1 is the emission reduction benefit for 1 kWh of electric heating; Ce is the government subsidy for the electric heating consumption of 1 kWh; and Pi is the electric heating promotion power.

The income function of the power grid company is as follows:

where IG is the power grid company’s revenue; and Cs and Cc are the electricity sales cost and investment cost per kilowatt hour of electricity,respectively.

The user’s payment function or revenue function is as follows:

where IU is the user’s revenue; and pb and pa are the price of traditional heating and the cost of electric heating,respectively,where pb is equal to Cs.

1.3 Boundary conditions

The government,as the initiator of the use of electric heating,hopes to promote electric heating as planned,and the constraints of the added power consumption for electric heating are defined as follows:

where PG,min and PG,max are the minimum and maximum electric heating promotion power,respectively.

Constrained by factors such as the investment cost of electric heating retrofits,government promotion can only be achieved by providing appropriate subsidies to the power grid.It is assumed that the power grid fully promotes electric heating when the government subsidy reaches a certain level.In contrast,if the government subsidy does not reach this value,the enthusiasm of the power grid to expand the modification of the power distribution network decreases.This will decrease the incentive for users to install electric heating equipment and slow down the implementation of the electric heating policy,which is detrimental to the government’s response to electric heating:

where Ce,min and Ce,max are the minimum and maximum government subsidies for the electric heating consumption of 1 kWh,respectively.

To promote the development of electric heating,the power grid company needs to investigate potential electric heating users and then determine the upper limit of the added power.Therefore,the boundary of the power grid company promotion and transformation power is as follows:

where Ps is the added power; and Pmin and Pmax are the minimum and maximum values for the added power of the power grid company.

When promoting electric heating,the PM2.5 value in winter will drop,which could significantly reduce the number of smog days.Therefore,it is assumed that users will unconditionally accept electric heating if its price is the same as that of conventional heating.The price of electric heating is defined by pmax (¥/kWh),which is the highest electric heating price that can be accepted by users under the given comprehensive environmental protection and pollution emissions considerations:

where pmin and pmax are the lowest and highest electric heating prices,respectively.

Because the government’s implementation of“electrification” is not compulsory,users’ environmental awareness may not be sufficient to encourage them to pay higher electric heating costs for economic reasons.A lower electric heating price is better for the customer.

As shown in equation (9),(2)-(8)can be converted into a multi-objective optimization model,with the maximum stakeholder benefit functions as the objectives and the boundary conditions as constraints:

where x represents the decision variables such as Ce,Pi,and Cs.

1.4 Strategies

First,it is assumed that all the participants in this game are bounded rational.The pure strategies of all the participants should take responsibility for their decisions and pay the corresponding economic costs.The pure strategies of the government are to promote or not promote the clean heating system.The pure strategies of the power grid company are to fully invest or not invest in the clean heating system.The pure strategies of the users are to accept or reject the electrical heating system.

The players’ payoffs when using these pure strategies are listed in Table 1.

Table 1 Pure strategies

Strategy 1 Strategy 2 Strategy 3 Strategy 4 power grid company fully invests(r1E, r1G, r1U)(r2E, r2G, r2U)(r3E, r3G, r3U)(r4E, r4G, r4U)power grid company completely does not invest(r5E, r5G, r5U)(r6E, r6G, r6U)(r7E, r7G, r7U)(r8E, r8G, r8U)

Strategy 1: The government fully promotes electric heating and the users reject it;

Strategy 2: The government fully promotes electric heating and the users reject it;

Strategy 3: The government does not promote electric heating,but the users choose it;

Strategy 4: The government does not promote electric heating,but the users choose it.

However,because they are bounded rational,they can adjust the proportions of their strategies.The government can promote the clean heating system in X% of the total plan while (100-X)% remains the same.The power grid company can change Y% of the potential users,with the rest developed in the future.The customers can actively decide whether to adopt the electrical heating system based on the electricity price: if pb ＜= pa,Z% = 100%,else Z% = 0.

1.5 Solutions

A multi-objective genetic algorithm is an effective tool for solving multi-objective optimization models [34,35].Therefore,a multi-objective genetic algorithm was used to solve the optimization model shown in (9).The flow chart of the solution algorithm is shown in Fig.2.

Fig.2 Flow chart of solution

2 Results

This study selected a region in China with abundant new energy resources and a large demand for electric heating to prepare a case to verify the effectiveness of the model and method proposed.The specific parameters of this region are listed in Table 2 The data in Table 2 such as the electricity prices,are empirical values from actual projects in China.The other variables such as PG,min are explained in (1)-(8).

Table 2 Parameters used in this study

Parameters Value PG,min 1×108 kWh PG,max 5×108 kWh Pmin 0 kWh Pmax 5×108 kWh e1 0.5 ¥/kWh Cemax 0.4 ¥/kWh pmax 0.36 ¥/kWh Cc 0.24 ¥/kWh pmax 0.25 ¥/kWh

Fig.3 shows the set of multi-objective optimization solutions.The three axes in Fig.3 represent the benefits to A government (Revenue 1),the B power grid company(Revenue 2),and C heat users (Revenue 3).It can be seen that there are multiple optimization solutions in the game model,but there is no solution where all three participants are profitable.The users are always in a state of loss,and the power grid company has the largest profit.Table 3 lists the solutions with the largest sum for the three participants,the largest A government interest,the largest the B power grid company interest,and the smallest C heat user loss when Cs is pmax.

Fig.3 Multi-objective optimization solution set

Table 3 Results with different solutions

Case Revenue 1 Revenue 2 Revenue 3 Case 1 ¥5 × 107 ¥2.6 × 108 ¥-5.5 × 107 Case 2 ¥5 × 107 ¥2.6 × 108 ¥-5.5 × 107 Case 3 ¥5 × 107 ¥2.6 × 108 ¥-5.5 × 107 Case 4 ¥1 × 107 ¥5.2 × 107 ¥-1.1 × 107

Table 4 lists the electric heating promotion power values corresponding to the above four optimization solutions.The electric heating promotion power values for the first three scenarios were equal to the upper limit,and when the customer benefit was the maximum,the electric heating promotion power was equal to the lower limit.This meant that when the electricity price was ¥0.36,the users were the least motivated,while the government and grid were the opposite.

Table 4 Promotion of electric heating corresponding to above four optimization solutions

Case Pi Cs Case 1 5×108 kWh ¥0.36 Case 2 5×108 kWh ¥0.36 Case 3 5×108 kWh ¥0.36 Case 4 1×108 kWh ¥0.36

The results listed in Table 3 show that the results of options 1,2,and 3 are consistent.They are all based on the greatest possible promotion of electric heating.The reason is that the environmental benefits of electric heating are greater than the financial subsidies,while the price of electricity sold by the B power grid company is greater than the cost of investment and transformation.Therefore,A government and the B power grid company hope to promote electric heating as much as possible; however,the users are losing money regardless of the situation,because the price of electric heating is higher than that of coal heating,and the promotion of electric heating also depends on the users.Therefore,if the electricity price for electric heating is ¥0.36,it will be difficult to promote it.

Fig.4 shows the set of the multi-objective optimization solutions when Cs is a variable and its optimization interval is ¥-0.5 to ¥+0.36.

Fig.4 Multi-objective optimization solution set

It can be seen from Fig.4 that when the electricity price is a variable,the user has a profitable solution.Although the power grid company may suffer losses,the government’s income has not changed too much.Table 5 lists the solutions with the largest sum for the three interests,the largest government interest,the largest power grid company interest,and the largest user interest.There is an antagonistic relationship between the power grid and users because a higher electricity price increases the revenue of the power grid by increasing the heating costs of the users.

Table 5 Results with different solutions

Case Revenue1 Revenue2 Revenue3 Case 1 ¥5 × 107 ¥4.45 × 107 ¥1.61 × 108 Case 2 ¥5 × 107 ¥4.45 × 107 ¥1.61 × 108 Case 3 ¥5 × 107 ¥2.6 × 108 ¥-5.47 × 107 Case 4 ¥5 × 107 ¥-1.68 × 107 ¥3.72 × 108

Table 6 lists the promotion of electric heating and electricity prices for the four scenarios.In case 4,the electricity price is ¥-0.5 and the user will be the most profitable and motivated,but Pi is equal to the lower limit,which means the grid is too negative to promote electric heating.However,the best solution is found for all three stakeholders in case 1 and case 2.It can be seen that when the electricity price is ¥-0.07,A government,the B grid companies,and C heat users can all benefit.It seems impossible,but the power grid company still receives revenues in this case because of the considerable subsidies provided by the government.In this scenario,users are still very active in using electric heating,because nothing is more exciting than free.In other words,the government is paying too much.Of course,the government can reduce fiscal subsidies,and the results will be very different,but the decreases in the enthusiasm of the power grid and users may cause the electric heating plan to be shelved.

Table 6 Promotion of electric heating corresponding to above four optimization solutions

Case Pi Cs Case 1 5 × 108 kWh ¥-0.07 Case 2 5 × 108 kWh ¥-0.07 Case 3 5 × 108 kWh ¥0.36 Case 4 1 × 107 kWh ¥-0.5

3 Conclusion

Electric heating has been proven to be an effective way to consume new energy and reduce carbon emissions,but the lack of a good business model has led to its low application in area with low coal prices and high electricity prices.This study investigated a promotion plan for electrical heating systems based on game theory by balancing the benefits of the government,power grid company,and users.A new game theory optimization model for the “electric heating” project was proposed and simulated based on actual data.

The following conclusions were drawn based on an actual case.

(1)If the equivalent environmental benefit per kilowatt hour of electricity for electric heating is greater than the subsidy per kilowatt hour,the government will always benefit.This may also be why the government is promoting electric heating projects.

(2)The electricity price is the most important factor affecting the promotion of electric heating.If the price of electric heating is higher than that of coal heating,it is almost impossible to promote electric heating.

(3)The price of electricity also determines the revenue of the power grid.Therefore,there is a significant conflict between the power grid and users.

(4)A solution for all three participants was finally found based on an electricity price of ¥-0.07.This conclusion seems impossible to achieve,but the power grid company would still receive revenues in this case because of government subsidies.Future research could further discuss direct government subsidies for users.Those results should also be very interesting.

Primarily,this paper proposed a quantitative model that will assist in promoting electric heating by calculating the stakeholders’ incomes based on the data for the use of electric heating.Future research will examine electric heating business models for different regions,considering more participants,more value creation,and capital recovery methods.

In the context of carbon neutrality,all countries need to promote electrical energy substitution,the electric heating optimization model in this paper has good applicability and extensibility,and other regions can adjust the optimization model according to their own actual situation,such as changing the participants (which can be two or more parties),electricity price,and the upper and lower limits of the parameters.

Acknowledgements

This work was supported by Central Universities Basic Scientific Research Business Project of Ministry of Education (Talent Special Project,DUT20RC (5)021)and State Grid Science and Technology Project of China(SGXJCJ00YJJS1800384).

Declaration of Competing Interest

We declare that we have no conflict of interest.