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Research ArticleEvolutionary Game Analysis of Cooperation betweenMicrogrid and Conventional Grid

Chengrong Pan1,2 and Yong Long1

1School of Economics and Business Administration, Chongqing University, Chongqing 400030, China2School of International Business, Sichuan International Studies University, Chongqing 400031, China

Correspondence should be addressed to Yong Long; [email protected]

Received 1 June 2015; Accepted 9 August 2015

Academic Editor: Vladimir Turetsky

Copyright © 2015 C. Pan and Y. Long. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper employs the evolutionary game theory to analyze the cooperation between microgrid and conventional grid, with thediscussion focusing on the factors that influence the game players’ selection of strategies, and additionally makes a numericalsimulation analysis. The results of analysis based on the evolutionary game model suggest that the two parties’ undertaking ofcooperative strategies and uncooperative strategies during the game is the stable point of their evolution and that the probabilityof their unanimous choice of cooperative strategies positively correlates with the direct benefits and indirect benefits of theircooperation as well as the government subsidies but negatively correlates with the cooperation costs and spending on cooperationrisks. Based on the findings, the paper puts forward a series of policy suggestions aiming to deepen the cooperation betweenmicrogrid and conventional grid.

1. Introduction

Since the mid-20th century, in the wake of the great demandof electricity by large-scale industrial production and thestimulation of cheap fossil energy, centralized and unitarypower supply systems which feature “high-capacity genera-tor, large power system, and high voltage” have been con-structed in major economies and even internationally [1, 2].As power networks expand day by day, the drawbacks of theconventional grid, such as high cost and difficult operation,become more prominent and can no longer meet users’increasing need for safety, reliability, and diversity [3–6]. Atthe same time, energy shortage and environmental deteri-oration resulting from the rapid development of the powerindustry turn out to be issues that urgently need to beaddressed [7, 8]. Therefore, developing low-carbon economycharacterized by low energy consumption, low emission, andlow pollution, reducing carbon emission in the electricalindustry, and improving the structure of power source haveattracted particular attention all around the world [9–11].Against this backdrop, researchers in 21st century proposedthe concept of aMicrogrid [12], which is defined to be a group

of interconnected loads and distributed energy resourceswithin clearly defined electrical boundaries which acts asa single controllable system providing heat and power fora local region. Most importantly, a microgrid can realizethe reliable supply of energy in various forms, especiallydistributed energy and clean energy [13]. Microgrid, ifcollaborating with conventional grid in power supply, canreasonably allocate electric power within a broader scope andincrease the utilization rate of distributed energy and cleanenergy with the help of the sound power transmission anddistribution (PTD) system of large power networks [14]. Onthe other hand, if conventional grid connects to microgrid,it can give more impetus to the construction of Smart Gridand the technological innovation in this field, meanwhilehelping to solve the power supply problems in remote areasand autonomous regions [13]. In addition, the cooperationbetween microgrid and conventional grid can enlarge theproportion of distributed energy and clean energy in energyformation, which is conductive to the optimization of energystructure, energy conservation, and emission reduction in thepower sector, as well as the enhancement of social welfare[15].

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 103206, 10 pageshttp://dx.doi.org/10.1155/2015/103206

2 Mathematical Problems in Engineering

At present, the research and construction ofmicrogrid areput in an accentuated position in more and more countries.Taking the practical issues of the domestic power systemsinto consideration, these countries are actively involved inthe construction of microgrid pilot projects along with theestablishment of microgrid technical standards and manage-ment norms. In the United States, since the first microgridproject,Madriver, undertaken by North American Corpora-tion was accomplished, a sequence of microgrid demonstra-tion projects have been built up at University of Wisconsin-Madison, Sandia National Laboratories, Lawrence BerkeleyNational Laboratory, and other places. The development ofmicrogrids in the United States is committed to increasingthe reliability of power supply to critical loads, providingcustomized levels of high quality of electric energy, cuttingdown costs, and making power generation and transmissiontruly smart [16]. Microgrid in Europe is represented byBornholm Microgrid in Denmark, Microgrid at NationalTechnical University of Athens, and Bronsbergen Microgridin Netherlands. The main purposes of these pilot projectsare to test the ability of microgrid to switch between islandmode and grid-connected mode, communication protocolverification, and demand-side management [17]. Typicalmicrogrids in Japan include demonstration projects in Kyotoand Sendai as well as the one undertaken by Tokyo Gas.Theyare aimed at testing power quality control, load following,optimal operation, and load prediction of microgrid [18].More microgrid pilot projects are currently underway inCanada, Australia, and some other countries.

In China, with the introduction of the standards andincentive measures concerned with microgrid constructionand grid connection, there emerges an improving environ-ment for microgrid construction, which redounds to theflourishing of microgrid demonstration projects nationwide.According to the 12th Five-Year Plan for Renewable EnergyDevelopment released by National Energy Administration,30 new-energy microgrid demonstration projects shouldbe completed by 2015. So far, some projects have beenfinished and grid connections have been put into practice, forexample, the first phase of Zhangjiakou National Wind-SolarHybrid Power Storage and Transmission DemonstrationProject, Old Barag BannerMicrogridDemonstration Project,Shiquan RiverWater-Solar Hybrid PowerMicrogrid Demon-stration Project, and Luxi Island Microgrid DemonstrationProject. On September 10, 2013, Ministry of Finance issuedthe Notice on Adjusting the Standards for the Collection ofSurcharges on Renewable Energy Power Prices, and on March12, 2014, National Energy Administration released the Noticeon Making Sufficient Efforts in Wind Power Grid Connectionand Consumption. Later in December, Test Specificationfor Microgrids’ Access to Distribution Network and SystemDebugging and Acceptance Specification for Microgrids’ Accessto Distribution Network were both approved. These moveshave greatly improved the status quo of microgrid in Chinaand facilitated the construction, operation, and managementof new-energy microgrid all around the country. It is safe tosay that the institutional and field constructions of microgridare becoming increasingly mature.

Restricted by natural monopolies of conventional gridsboth home and abroad, research on grids cooperation haslong been left out by the academic circle. In recent years,however, with the development of distributed energy andmicrogrid construction, studies on grids cooperation fromtechnical perspective have yielded fruitful results. For thepurpose of achieving a seamless transfer fromgrid-connectedto island mode, paper [19] proposes a cooperative frequencycontrol method which consists of microgrid central controland microgrid local control and can increase the frequencystability of islanded microgrid during both primary andsecondary frequency control. Paper [20] comes up with aformation mechanism for the optimal microgrid coalition inthe smart power distribution system, that is, HR coalitionwhich boasts remarkable computational efficiency and isapplicable to a wide range of microgrids. This mechanism ispropitious for real-time processing and can bring down thepower loss of a 500-microgrid-connected network by 26%–80%. In the meantime, in order to relieve time variation andintermittency imposed on conventional grid by renewableenergy power generation, paper [21] finds out that gridscan achieve the most benefits from cooperation if there arelimited storage devices, but when there are adequate high-capacity storage devices, the benefits gained from cooper-ation are not desirable. Besides, on the basis of renewableenergy power generation, paper [22] studies the real-timeenergy management under the cooperation between twomicrogrids, discusses the relationship between grid distanceand power generation cost, and puts forward the allocationalgorithm for optimal off-grid energy management. On topof that, it attempts to simulate this algorithm with the datafrom Tucson Electric Power. What is more, since there arevarying coordination control strategies for the operation ofmicrogrids under grid-connected and island mode, paper[23] presents the strategy for the coordination and control ofdifferent parts of microgrid and evaluates the managementperformance of this strategy throughmicrogrid experimentalprojects.The results reveal that this strategy can guarantee thestability of microgrid operated under islandmode by keepingthe voltage of the public connection point within a reasonablerange.

The evolutionary game theory, based on limited ratio-nality, dynamically analyzes the behavior strategy of humanbeings by using the method of studying the evolution andstability of the biological population. In an evolutionarygame, different individual will get the appropriate degreeof “fitness” through different behavior strategy. When thefitness of a strategy is higher than the average fitness of thepopulation, this strategy will be developed in the population,until the fitness of the strategy is not longer than the averagefitness of the population. The 1970s is the critical period forthe formation and development of evolutionary game theory.Smith and Price [24] introduced the concept of evolutionarytheory into the game theory and put forward the concept ofevolutionary game theory and evolutionary stability strategy(ESS) in their paper “The Logic of Animal Conflicts” in 1973,which marks the birth of evolutionary game theory. In 1978,Taylor and Jonker [25] initiated the basic dynamic conceptreplicator dynamics so that evolutionary game theory has

Mathematical Problems in Engineering 3

a clear research goal.Thus, the study on the theory and appli-cation of evolutionary game theory is developing rapidly.

Research on the application of evolutionary game theory,in retrospect, mainly involves such areas as supply chainmanagement, corporate governance, and financial invest-ment. Paper [26] analyzes the game relationship betweengovernment and core enterprises in the green supply chainand discovers that the costs and benefits that core enterprisesget from the implementation of green supply chain as well asthe government subsidies and punishment will exert a directimpact on the result of the game. In the long run, govern-ment should enact and enforce more strict environmentalregulations and increase relevant allowances and penalties soas to achieve a win-win result, while core enterprises shouldactively be devoted to environmentalmanagement practice togain experience and set examples for enterprises in the upperand lower reaches. In developing green supplier-buyer rela-tionship in themanufacturing industry, we find that, throughestablishing dynamic game models and observing the trendof cooperation between the stakeholders of green purchasing,trading behaviors can serve as policy and payoff functions ofsuppliers andproducers. According to the analog experiment,manufacturing industry can obtain sustainable development,and the recycle ability of suppliers directly determines howgreen a supply chain is [27]. Some researchers have appliedevolution mechanism to centipede game analysis, findingthat evolution mechanism is conductive to delaying the riskof decision-making during the centipede game and evenfacilitates the full cooperation between the game players.Thisis particularly true to games that last for a fixed period oftime, since human cooperative behaviors are characterizedby “irrationality” [28]. As to the research on enterprisecredit behaviors, when two companies form an allianceand carry out reasonable admission and exit mechanismsunder the condition of sustainable development, credit riskscan be effectively managed and controlled [29]. Paper [30]discusses how to take advantage of innovative financial toolsto help enterprises raise fund with environmental protectiontechnologies.The study concludes that as long as the expectedrevenue is greater than the average revenue, a financialmarket can be built up between economic agents and publicadministrations.The establishment of such a financialmarketwill not only add to public benefits but also stimulate allenterprises to adopt environment-friendly technologies.

From the literature review above, it can be seen that thecooperation between microgrid and conventional grid hasrarely been studied before and there is little research on theevolutionary game analysis of strategy selection regardingcooperation betweenmicrogrid and conventional grid. How-ever, as grids connection demonstration projects are in fullswing, the issue on the cooperation between microgrid andconventional grid is arousing more academic concern. Basedon the evolutionary game theory, this paper studies the choicebehavior concerning the cooperation betweenmicrogrid andconventional grid, analyzes the factors that influence theircooperative game, and provides data for microgrid researchand industrial decision-making for reference.

The rest of the paper is arranged as follows: Section 2introduces the fundamental assumptions of modeling;

Section 3 establishes the evolutionary game model and ana-lyzes the evolutionary stable strategies of the two parties;Section 4 analyzes the factors influencing the cooperativegame between microgrid and conventional grid; Section 5makes a numerical simulation analysis of the evolutionarygame strategies proposed in this paper; Section 6 is researchconclusions.

2. Fundamental Assumptions

Modeling and analysis will be conducted on the premise ofthe following assumptions.

(1) There are two subjects, namely, microgrid and con-ventional grid, for the game, denoted as 𝑀 and 𝐶,respectively. The sets for the strategies of a micro-grid and a conventional grid are both {cooperation,noncooperation}, and one side can choose its opti-mum strategy in response to the strategy of the otherside. Suppose the probability of a conventional grid’schoice of cooperation with a microgrid is 𝑥 and theprobability of its choice of noncooperation is 1 −𝑥, while the probability of a microgrid’s choice ofcooperation with a conventional grid is 𝑦 and theprobability of its choice of noncooperation is 1 − 𝑦(0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 1).

(2) Suppose that a microgrid and a conventional gridchoose to cooperate on the basis of resources sharingand complementation; both parties can benefit morefrom cooperation strategy. When a microgrid anda conventional grid both resort to noncooperationstrategy, their respective income from operation is𝐴1, 𝐴2; when they both adopt cooperation strategy,

their respective income from the cooperative opera-tion is 𝑈

1, 𝑈2.

(3) When both microgrid and conventional grid adoptcooperation strategy, they collaborate with each otherto ensure power supply. Under the umbrella of con-ventional grid’s sound power transmission and dis-tribution system, the phenomena of abandoned windpower and abandoned solar power in microgrid canbe relieved. More importantly, more electric energycan be generated with the use of renewable energy,which enables microgrid to yield more direct income.Meanwhile, the flexibility and decentralization ofmicrogrid make it possible for conventional gridto supply economical electric power in islands andremote areas, saving the high costs for grid construc-tion and operation. Suppose the direct income of amicrogrid and a traditional grid gained from theircooperation is𝐷

1and𝐷

2.

(4) Apart fromdirect income, indirect income can also begenerated from the cooperation between microgridand conventional grid.Their cooperation cannot onlyincrease the proportion of renewable energy andclean energy in power generation but also improve thesocial energy structure and ecological environment.


Table 1: Payoff matrix in the gaming between microgrid and conventional grid.

Conventional grid 𝐶Cooperation 𝑥 Noncooperation 1 − 𝑥

Microgrid𝑀Cooperation 𝑦 𝑈

1= 𝐴1+ 𝐷1+ 𝐼1+ 𝐺1− 𝐶1− 𝐹1, 𝑈2= 𝐴2+ 𝐷2+ 𝐼2+ 𝐺2− 𝐶2− 𝐹2

𝐴1− 𝐶1, 𝐴2

Noncooperation 1 − 𝑦 𝐴1, 𝐴2− 𝐶2

𝐴1, 𝐴2

Besides, the cooperation betweenmicrogrid and con-ventional grid is not confined to power supply butcan be extended to technological innovation for gridconnection and exploration of different cooperationmodes, providing technical support andmanagementexperience for grid-connection projects. Therefore,we presume the indirect income of a microgrid anda conventional grid gained from their cooperation is𝐼1and 𝐼2.

(5) Given the high cost of electricity production withrenewable energy and clean energy, Chinese gov-ernment will give price allowances to electricitygenerated by renewable energy and clean energy toencourage the sale and purchase of this kind ofelectric power. At the same time, following the centralgovernment’s opinions on the reformation of electricpower system, Chinese power grid enterprises willchange their previous profit model of price differencebetween purchase and sale into a cost-plus-benefitmodel in charging wheeling cost. And in order tomotivate conventional grids to renovate their facilitiesfor grid access and control and to transmit anddistribute more electricity generated by renewableenergy and clean energy, a certain amount of com-pensation of value should be offered to conventionalgrid. Suppose the subsidies for a microgrid and aconventional grid are 𝐺

1and 𝐺

2, respectively.

(6) When a microgrid and a conventional grid choose tocooperate, their cooperation costs are closely relatedto their respective input of production factors. Beforethe cooperation is reached, cost on partner selectionand negotiation will arise. After the cooperation isnailed down, if one side pulls back from it, the otherside who is cooperative is likely to trap in a difficultsituation where all the possible opportunities andbenefits are gone, because the assets it has investedcan hardly be used for other purposes due to thehigh level of asset specificity (Williamson, 1975) [31]of the resources input into the power industry. Con-sequently, compared with the uncooperative side, thecooperative side needs to jack up its spending but can-not gain the cooperation benefit it deserves. Supposethe cost of a microgrid during the cooperation is 𝐶

1

and that of a conventional grid is 𝐶2.

(7) Microgrid and conventional grid will meet risksparticular to their cooperation, such as uncertainincidents, opportunism, and free rider problems, and

thus they have to pay the costs arising from supervi-sion, coordination, and control to copewith such kindof risks. Suppose the risk costs of a microgrid and aconventional grid are 𝐹

1and 𝐹

2.

3. Evolutionary Game Analysis of Cooperationbetween Microgrid and Conventional Grid

3.1. Modeling. Power grid enterprises, as commercial organi-zations, have natural economic aspirations. Their willingnessto choose cooperation strategy depends on whether thisstrategy can maximize their own benefits. Meanwhile, asproviders of electricity, a necessity of social life, they alsohave noneconomic appeals including social benefits, environ-mental benefits, and political benefits, driven by the publicvoice and corporate social responsibilities. It follows that theirchoice of cooperation is a result of the evolutionary game.From the evolutionary game theory’s perspective, the payoffmatrix in the gaming can be expressed as shown in Table 1.

The necessary condition for a microgrid and a conven-tional grid to simultaneously choose cooperation strategyis that the sum of their direct benefits, indirect benefits,and government subsidies is greater than the sum of theircooperation costs and risk expenses; that is, the followingconditions should be satisfied:

𝐴1+ 𝐷1+ 𝐼1+ 𝐺1> 𝐶1+ 𝐹1,

𝐴2+ 𝐷2+ 𝐼2+ 𝐺2> 𝐶2+ 𝐹2.

(1)

The benefits for a microgrid in choosing cooperationstrategy are

𝑀𝑐= 𝐴1+ 𝑥 (𝐷

1+ 𝐼1+ 𝐺1− 𝐹1) − 𝐶1. (2)

The benefits for a microgrid in choosing noncooperationstrategy are

𝑀𝑛= 𝑥𝐴1+ (1 − 𝑥)𝐴

1. (3)

The average benefits for a microgrid in choosing mixedstrategies can be derived as

𝑀∗= 𝑦𝑀

𝑐+ (1 − 𝑦)𝑀

𝑛

= 𝐴1+ 𝑦 [𝑥 (𝐷

1+ 𝐼1+ 𝐺1− 𝐹1) − 𝐶1] .

(4)

Similarly, the average benefits for a conventional grid inchoosing mixed strategies can be derived as

𝐶∗= 𝑥𝐶𝑐+ (1 − 𝑥) 𝐶

𝑛

= 𝐴2+ 𝑥 [𝑦 (𝐷

2+ 𝐼2+ 𝐺2− 𝐹2) − 𝐶2] .

(5)


Table 2: Stability of local equilibrium point.

Equilibrium point det(J) trJ Local stability𝑦 = 0, 𝑥 = 0 + − ESS𝑦 = 0, 𝑥 = 1 + + Unstable point𝑦 = 1, 𝑥 = 0 + + Unstable point𝑦 = 1, 𝑥 = 1 + − ESS

𝑦 =𝐶2

𝐷2+ 𝐼2+ 𝐺2− 𝐹2

𝑥 =𝐶1

𝐷1+ 𝐼1+ 𝐺1− 𝐹1

− 0 Saddle point

Note: this table is valid when𝐶2 < 𝐷2 +𝐼2 +𝐺2 −𝐹2,𝐶1 < 𝐷1 +𝐼1 +𝐺1 −𝐹1.

Based on these, if a microgrid and a conventional gridboth choose cooperation strategy, the replicator dynamicsdifferential equation (variant with time) is

𝑑𝑦

𝑑𝑡= 𝑦 (𝑀

𝑐−𝑀∗)

= 𝑦 (1 − 𝑦) [𝑥 (𝐷1+ 𝐼1+ 𝐺1− 𝐹1) − 𝐶1] ,

𝑑𝑥

𝑑𝑡= 𝑥 (𝐶

𝑐− 𝐶∗)

= 𝑥 (1 − 𝑥) [𝑦 (𝐷2+ 𝐼2+ 𝐺2− 𝐹2) − 𝐶2] .

(6)

A(0, 1) B(1, 1)

O(0, 0)

C(1, 0)

E(y∗, x

∗)

Figure 1: Schematic diagram of dynamic evolution (𝐶2< 𝐷2+ 𝐼2+

𝐺2− 𝐹2, 𝐶1< 𝐷1+ 𝐼1+ 𝐺1− 𝐹1).

From (6), the evolution strategy matrix concerning thecooperation between a microgrid and a conventional gridcan be conducted. The stability of the equilibrium pointof the evolution system can be obtained by analyzing thelocal stability of the Jacobian matrix of this system. Supposethe Jacobian matrix of (6) is 𝐽, which can be expressedas

𝐽 = [

(1 − 2𝑦) [𝑥 (𝐷1+ 𝐼1+ 𝐺1− 𝐹1) − 𝐶1] 𝑦 (1 − 𝑦) (𝐷

1+ 𝐼1+ 𝐺1− 𝐹1)

𝑥 (1 − 𝑥) (𝐷2+ 𝐼2+ 𝐺2− 𝐹2) (1 − 2𝑥) [𝑦 (𝐷

2+ 𝐼2+ 𝐺2− 𝐹2) − 𝐶2]

] . (7)

Thereof det(𝐽) is

det (𝐽) = (1 − 2𝑦) [𝑥 (𝐷1+ 𝐼1+ 𝐺1− 𝐹1) − 𝐶1]

⋅ (1 − 2𝑥) [𝑦 (𝐷2+ 𝐼2+ 𝐺2− 𝐹2) − 𝐶2]

− 𝑦 (1 − 𝑦) (𝐷1+ 𝐼1+ 𝐺1− 𝐹1) 𝑥 (1 − 𝑥)

⋅ (𝐷2+ 𝐼2+ 𝐺2− 𝐹2)

(8)

and tr𝐽 is

tr𝐽 = (1 − 2𝑦) [𝑥 (𝐷1+ 𝐼1+ 𝐺1− 𝐹1) − 𝐶1]

+ (1 − 2𝑥) [𝑦 (𝐷2+ 𝐼2+ 𝐺2− 𝐹2) − 𝐶2] .

(9)

From formula (8) and formula (9), the values and denotationsof determinant and trace of 𝐽 can be obtained.

3.2. Analysis of the Evolutionary Stable Strategies of the GamePlayers. According to the stability condition of Jacobianmatrix, when 𝑑𝑦/𝑑𝑡 = 0, 𝑑𝑥/𝑑𝑡 = 0, there are five local equi-librium points that can be found on the plane 𝑆 = [(𝑦, 𝑥) |0 ≤ 𝑦, 𝑥 ≤ 1]. They are 𝑂(0, 0), 𝐴(0, 1), 𝐶(1, 0), 𝐵(1, 1), and𝐸(𝑦∗, 𝑥∗)(𝐶2/(𝐷2+ 𝐼2+ 𝐺2− 𝐹2), 𝐶1/(𝐷1+ 𝐼1+ 𝐺1− 𝐹1)).

Put them, respectively, into formula (8) and formula (9), andthe list of local stability is obtained (see Table 2).

In Table 2, there are five equilibrium points of which 𝑂and 𝐵 are in evolutionary steady state, 𝐴 and 𝐶 are unstablepoints, and𝐸 is a saddle point.Theprocess of the evolutionarygame is shown as Figure 1.

As seen in Figure 1, when the benefits that a microgridand a conventional grid gain from cooperation are greaterthan the benefits gained fromnoncooperation, in their evolu-tionary game, they either simultaneously adopt cooperationstrategy or adopt noncooperation strategy. When the initialstate falls in the bottom-left area of the system formed byAOCE, the system converges to 𝑂(0, 0). That means bothmicrogrid and conventional grid adopt noncooperation strat-egy. When the initial state falls in the upper right area ofthe system formed by AECB, the system converges to 𝐵(1, 1).That means both the microgrid and the conventional gridadopt cooperation strategy. When one party adopts coop-eration strategy and the other party adopts noncooperationstrategy, the system is in an unstable point. At this point,one party gets the maximum benefits and the other suffersfrom the maximum loss, so the cooperation fails to reachPareto Optimality. In the long run, if one party is found to



Equilibrium point det(J) trJ Local stability𝑦 = 0, 𝑥 = 0 + − ESS𝑦 = 0, 𝑥 = 1 + + Unstable point𝑦 = 1, 𝑥 = 0 − Uncertain Saddle point𝑦 = 1, 𝑥 = 1 − Uncertain Saddle pointNote: this table is valid when𝐶2 > 𝐷2 +𝐼2 +𝐺2 −𝐹2,𝐶1 < 𝐷1 +𝐼1 +𝐺1 −𝐹1.

commit “free-riding,” “fleecing,” and some other optimisticbehaviors, the other party will also choose noncooperationstrategy in order to minimize its loss. As a result, both partieswill abandon cooperation strategy and 𝑂(0, 0) indicates astable confrontation state. If both parties choose to cooperate,amicrogrid can fully exploit its flexibility and ability to utilizeclean energy and distributed energy, and a conventional gridcan take advantage of its sound power transmission anddistribution network, ultrahigh voltage grid, and financialstrength to provide fund and experience for the constructionand technological innovation of microgrid. Only in this waycan their cooperation reach Pareto Optimality and theirbenefits be maximized, as the point of convergence 𝐵(1, 1)shows.

However, when there are changes in the direct benefits,indirect benefits, government subsidies, cooperation cost,and risk expense, the total income of the bilateral cooperationmight be less than the sum of cooperation cost and risk cost.Detailed analysis is as follows:

(1) When 𝐶2> 𝐷2+ 𝐼2+ 𝐺2− 𝐹2, 𝐶1< 𝐷1+ 𝐼1+ 𝐺1−

𝐹1(i.e., the income of a conventional grid is less than

its cooperation cost and risk expense when it adoptscooperation strategy, while the income of a microgridis greater than the cooperation cost and risk expensewhen it adopts cooperation strategy), there are fourequilibrium points in the system which converges to𝑂(0, 0), as seen from Table 3 and Figure 2. It suggeststhat noncooperation strategy that both parties adoptis actually an evolutionary stable strategy.

(2) When 𝐶2< 𝐷2+ 𝐼2+ 𝐺2− 𝐹2, 𝐶1> 𝐷1+ 𝐼1+

𝐺1− 𝑧𝐹1(i.e., the income of a large grid is greater

than its cooperation cost and risk expense whenit adopts cooperation strategy, while the income ofa microgrid is less than the cooperation cost andrisk expense when it adopts cooperation strategy),there are four equilibrium points in the system (seeTable 4), and it can be inferred from Figure 3 thatnoncooperation strategy that both parties adopt isactually an evolutionary stable strategy, as the systemconverges to 𝑂(0, 0).

(3) When 𝐶2> 𝐷2+ 𝐼2+ 𝐺2− 𝐹2, 𝐶1> 𝐷1+ 𝐼1+

𝐺1− 𝐹1(i.e., the income of a large grid is less than

its cooperation cost and risk expense when it adoptscooperation strategy, and this is the same for a micro-grid), there are four equilibrium points in the system(see Table 5), and it can be inferred from Figure 4

A(0,1) B(1,1)

O(0,0) C(1,0)


𝐺2− 𝐹2, 𝐶1> 𝐷1+ 𝐼1+ 𝐺1− 𝐹1).


Equilibrium point det(J) trJ Local stability𝑦 = 0, 𝑥 = 0 + − ESS𝑦 = 0, 𝑥 = 1 − Uncertain Saddle point𝑦 = 1, 𝑥 = 0 + + Unstable point𝑦 = 1, 𝑥 = 1 − Uncertain Saddle pointNote: this table is valid when𝐶2 < 𝐷2 +𝐼2 +𝐺2 −𝐹2,𝐶1 > 𝐷1 +𝐼1 +𝐺1 −𝐹1.


Equilibrium point det(J) trJ Local stability𝑦 = 0, 𝑥 = 0 + − ESS𝑦 = 0, 𝑥 = 1 − Uncertain Saddle point𝑦 = 1, 𝑥 = 0 − Uncertain Saddle point𝑦 = 1, 𝑥 = 1 + + Unstable pointNote: this table is valid when𝐶2 > 𝐷2 +𝐼2 +𝐺2 −𝐹2,𝐶1 > 𝐷1 +𝐼1 +𝐺1 −𝐹1.

that the way that both parties are adopting non-cooperation strategy is an evolutionary stable strat-egy, as the system converges to 𝑂(0, 0).

4. Analysis of the Impact of ModelParameters on Cooperative Game

It can be concluded through the above analysis that the stablestrategies for evolutionary game between a microgrid anda conventional grid include (cooperation, cooperation) and(noncooperation, noncooperation). Pareto Optimality canbe achieved when the two parties choose the cooperationstrategy but a stable state can also be attained if the two partiesdo not choose the cooperation strategy, so factors influencingthe changes in the area of AOCE and AECB need to beanalyzed in order to determine towards which direction theevolutionary results will develop, thus obtaining the factorsinfluencing cooperation between the two parties. It can beobserved through model analysis that factors influencing


A(0, 1) B(1, 1)

O(0, 0)

C(1, 0)


𝐺2− 𝐹2, 𝐶1> 𝐷1+ 𝐼1+ 𝐺1− 𝐹1).

A(0, 1) B(1, 1)

O(0, 0)

C(1, 0)

Figure 4: Schematic diagram of dynamic evolution (𝐶2> 𝐷2+ 𝐼2+

𝐺2− 𝐹2, 𝐶1> 𝐷1+ 𝐼1+ 𝐺1− 𝐹1).

system convergence encompass cooperation cost, spendingon cooperation risk, direct earnings on cooperation, andindirect earnings on cooperation as well as government sub-sidies, and the impact of each factor on the state of coopera-tive game will be discussed in the following.

(1) Cooperation cost 𝐶𝑖: the greater the cooperation cost

is, the larger the area of AOCE in the system is, thegreater the system’s probability of evolving towards𝑂(0, 0) is, and the smaller the probability of adoptingcooperation strategy between microgrid and conven-tional grid is. Cooperation costs of microgrid andconventional grid are associated with their respectiveinputs, and therefore, for the sake of cost reduction, aplatform and mechanism for information communi-cation firstly should be established to eliminate infor-mation asymmetry and lower spending on communi-cation and selection and secondly close collaboration

andmanagementmode should be adopted to increasepenalty cost (restraining noncompliance behaviorsinstitutionally and legally) and decrease risk on theinvestment of specific asset.

(2) Spending on cooperation risk 𝐹𝑖: the increase of

cooperation risk will lead to considerable costs ofcoordination and control.The larger the area ofAOCEis, the greater the system’s probability of evolvingtowards 𝑂(0, 0) is and the smaller the probabilityof adopting cooperation strategy between microgridand conventional grid is. Cooperation risk primar-ily arises from the potential opportunistic behav-iors of cooperative members and conflicts of inter-est between the two parties. Opportunistic behav-iors are primarily manifested by partners’ breakingpromise, evading duties, and misappropriation ofpublic resources as well as information distortion,while conflicts of interest are mainly demonstratedas mergers or acquisitions by partners, thus givingrise to unfair distribution of interest. Therefore, itis necessary to enhance the transparency of bilateralcooperation by means of establishing a mechanismfor distribution of interests, a risk-sharing mecha-nism, and a penalty and oversight mechanism as well,thus reducing behaviors of information asymmetryoccurring in bilateral cooperation and lowering therisk of cooperation.

(3) Direct earnings on cooperation 𝐷𝑖: the greater the

direct earnings on bilateral cooperation are, the largerthe area of AECB in the system is, the greater thesystem’s probability of evolving towards𝐵(1, 1) is, andthe greater the probability of adopting cooperationstrategy between microgrid and conventional grid is.Microgrid and conventional grid can give full playto their comparative advantages in cooperation andboost the benefits of bilateral cooperation, therebybuilding trust through cooperation and helping toform a sound partnership. Based on this analysisand on comprehensive and repeated demonstration,great efforts will be made to construct microgrid andrenovate conventional grid in appropriate areas; inthe meantime, power supply capacity of microgridand conventional grid will be given an overall con-sideration. What is more, scientific and reasonablescheduling will be achieved through coordinationand arrangement, so more accommodation of windpower, photovoltaic power, and other renewable cleanenergy and power can be provided.

(4) Indirect earnings on cooperation 𝐼𝑖: the greater the

indirect earnings on bilateral cooperation are, thelarger the area of AECB in the system is, the greaterthe system’s probability of evolving towards 𝐵(1, 1) isand the greater the probability of adopting cooper-ation strategy between microgrid and conventionalgrid is. Further cooperation between microgrid andconventional grid can not only enhance technologicalinnovation such as the connection, control, protec-tion, and scheduling of microgrid and conventional


grid but also provide appropriate experiences and ref-erences for exploring the cooperation model of gridsand establishing industrial standards, thus promotingthe optimization of energy allocation of the powerindustry and improvement in ecological environmentand eventually increasing the well-being of the wholesociety. As a result, microgrid and conventional gridneed to raise awareness of cooperative effect and thegovernment will provide better policy guidance forthe cooperation and further encouragemicrogrid andconventional grid to cooperate in more areas.

(5) Government subsidies 𝐺𝑖: microgrid and conven-

tional grid offer renewable energy, clean energy andelectricity, and so forth to the society. The greaterthe government subsidies the two parties gain fromthis practice are, the larger the area of AECB inthe system is, the greater the system’s probabilityof evolving towards 𝐵(1, 1) is, and the greater theprobability of adopting cooperation strategy betweenmicrogrid and conventional grid is. In view of thecharacteristics of microgrid construction and con-ventional grid renovation including high investmentand cost but low earnings in the early stage, higherearnings in mid-late stage, and unclear price for-mation mechanism, the government will, throughoffering subsidies to electricity price of renewableenergy and clean energy, encourage microgrid andconventional grid to explore and utilize throughcooperation distributed energy, clean energy, energyof transmission and distribution, clean energy andpower, and other projects, thus further improvingelectricity services of the whole society.

5. Numerical Analysis

Numerical simulation is carried out through Matlab pro-gramming to make an in-depth analysis of the evolutionof cooperation between microgrid and conventional grid.The parameters of the payoff matrix for the game betweenmicrogrid and conventional grid are as follows: 𝐶

1= 200,

𝐶2= 400, 𝐷

1= 300, 𝐷

2= 500, 𝐼

1= 300, 𝐼

2= 200, 𝐺

1=

300, 𝐺2= 200, 𝐹

1= 400, and 𝐹

2= 200. The evolution

of the system towards point 𝐵(1, 1) is described when theproportion (𝑦∗, 𝑥∗) of initial strategy of microgrid andconventional grid varies in the plane of [0, 1] ∗ [0, 1]. When(0.2, 0.6), (0.5, 0.5), and (0.6, 0.2) are taken as the initialvalues and the time period is [0, 100], it can be seen fromFigure 5 that the greater the possibility of choosing initialcooperation strategy by microgrid and conventional grid is,the faster the evolution towards the point 𝐵(1, 1) is and thatcooperation willingness of conventional grid plays a vitalrole in facilitating the cooperation between microgrid andconventional grid. In order to verify the impact of changesin a certain parameter on the model convergence when otherparameters remain unchanged, let 𝐶

1= 100, 𝐶

2= 200, 𝐷

1=

400, 𝐷2= 600, 𝐺

1= 500, and 𝐺

2= 400 when (0.5, 0.5)

is taken as the initial value of (𝑦∗, 𝑥∗) and [0, 100] asthe time period. As shown in Figure 6, compared with

0 0.8

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.60.40.2 1

1

y

x

(y, x) = (0.5, 0.5)

(y, x) = (0.2, 0.6)

(y, x) = (0.6, 0.2)

Figure 5: Schematic diagram of dynamic evolution of cooperationunder different initial values of (𝑦∗, 𝑥∗).

00

0.80.60.40.2 1y

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1

x

The initial valueD1 = 400, D2 = 600

G1 = 500, G2 = 400

C1 = 100, C2 = 200

Figure 6: Schematic diagram of dynamic evolution of cooperationunder different 𝐶

𝑖,𝐷𝑖, and 𝐺

𝑖values.

the initial values of 𝐶𝑖, 𝐷𝑖, and 𝐺

𝑖, lowering cooperation

cost and increasing direct earnings and government subsidieswill accelerate the evolution of the system towards point𝐵(1, 1) and increase the probability of cooperation betweenmicrogrid and conventional grid, which lends credence to theearly hypothesis.

6. Conclusions and Suggestions

This paper employs the evolution game theory to model theselection of cooperation strategies between microgrid andconventional grid. It is concluded that the probability oftheir unanimous choice of cooperative strategies positively


correlates with the direct benefits and indirect benefits oftheir cooperation as well as the government subsidies butnegatively correlates with the cooperation costs and spendingon cooperation risks. Based on the research results, the paperproposes the following suggestions:

(1) Government should not only formulate managementnorms for the planning, design, construction, opera-tion, and maintenance of microgrid but also improvethe technical standards and regulations for gridsconnection, in an effort to create a better policyenvironment for the cooperation between microgridand large grid.

(2) More backups should be given to the constructionof microgrid and the reformation of large grid inorder to ignite their willingness for cooperation andespecially encourage the participation of large grid. Aseries of measures such as electricity price subsidies,preferential tax, and allowances for research anddevelopment can be taken to motivate large grid totransport renewable energy and clean energy anddeepen the cooperation on technological innovationand the exploration of different cooperation modes.

(3) Communication, coordination, and risk preventionmechanisms for the cooperation between microgridand large grid should be established to eliminateinformation asymmetry, increase mutual trust, lowerthe risk of opportunism, and reduce cooperationcosts.

Conflict of Interests

The authors declare no conflict of interests.

Acknowledgments

This work was supported in part by the National ScienceFoundation of China (Grant no. 71172081) and the NationalSocial Science Foundation of China (Grant no. 14AZD130).

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