Multi-Agent Cooperation Mechanism of Hydropower Plants in

Central China Based on Raiffa Solution

Man Jiang

, Shunming Bai

, Kun Xiao

and Debin Fang

State Grid Huazhong Branch, Wuhan 430077, Hubei, China

School of Economics and Management, Wuhan University, Wuhan 430072, Hubei, China

Keywords:

Carbon Emission Reduction, Clean Energy, Cooperative Game, Hydropower Cooperative Alliance, Raiffa

Solution Algorithm.

Abstract:

“Carbon peak” and “carbon neutrality” have been national development strategies in China. The power

industry is crucial for achieving the carbon reduction targets. However, the dysfunctional competition of

hydropower plants in Central China leads to massively inefficient utilization of clean hydropower, which also

has an adverse impact on the consumption of wind power and photovoltaic energy. To solve this problem, this

paper proposes the regional hydropower alliance mechanism based on the cooperative game model. By using

the Raiffa solution algorithm, the models are performed based on the technical and economic parameters of

typical provinces and river basins in Central China. The results demonstrate that the benefit from the

hydropower cooperation alliances across river basins and the same river basins in Central China can be

feasibly distributed. What’s more, the research has vital guiding significance on building an efficient regional

power market order in Central China and promoting carbon emission reduction in power generation.

1 INTRODUCTION

Climate change caused by greenhouse gas emissions

has been a key issue concerning the destiny of

mankind and sustainable development. In 2020,

Chinese President Xi Jinping clearly stated that

carbon peak and carbon neutrality in China would

have been respectively reached by 2030 and 2060

(Wu, 2021). However, the problem of carbon

emissions in China is very serious. According to

statistics from the U.S. Energy Administration, as the

world’s largest carbon emitter, China emits more than

10 billion tons of greenhouse gases each year, of

which nearly 40% comes from its power generation

industry. Therefore, reducing carbon emission in

power generation is a key way to speed up the

realization of the “dual carbon” strategy in China.

Nowadays, in China, the problems of carbon

emissions in power generation mainly come from its

reliance upon fossil fuels, and coal power still

occupies the main position of the power generation

structure (Xiao, 2020). Therefore, it is an important

measure to promote carbon emission reduction in

China’s power generation by replacing thermal power

with clean hydropower, wind power, photovoltaic

and other forms. In this context, hydropower and

clean energy power generation in Central China have

developed rapidly, and the proportion of installed

capacity has increased significantly. Figure 1 shows

the development trend of the power generation

installation structure in Central China.

Figure 1: Development trends of power generation

installation types in Central China.

Although hydropower, wind power, and

photovoltaic power generation in Central China have

developed rapidly, the problem that clean energy

power generation in Central China is not fully utilized

has also been prominent. For example, in 2020, the

underutilized hydropower, wind power, and

photovoltaic power generation in Central China were

469 million kWh, 292 million kWh, and 2.55 million

Jiang, M., Bai, S., Xiao, K. and Fang, D.

Multi-Agent Cooperation Mechanism of Hydropower Plants in Central China Based on Raiffa Solution.

DOI: 10.5220/0011736100003607

In Proceedings of the 1st International Conference on Public Management, Digital Economy and Internet Technology (ICPDI 2022), pages 325-330

ISBN: 978-989-758-620-0

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

325

kWh, respectively. The power generation space

corresponding to these underutilized clean energy

resources is actually filled by coal-fired thermal

power, which is detrimental to the realization of

carbon emission reduction in power generation and

China’s “dual carbon” strategic goal.

It is found through field survey that although there

are many rivers in Central China, and hydropower has

been fully developed, the interest conflicts between

power generation and water use still occur along

upstream and downstream for many hydropower

plants in the same river basin. Meanwhile, the

contradiction that hydropower plants across river

basins seize market share also appears. What is

worse, water conflicts lead to malicious release or

closure of power plants in the same river basin,

resulting in deficient utilization of water energy and

hindering the maximization of power generation

efficiency. At the same time, in the cross-basin

competition, the rush to generate hydropower in each

river basin directly squeezes the grid-connected space

of wind power and photovoltaic power generation.

What is more, the hydropower game due to

competition not only damages the full utilization of

water energy in the river basin, but also harms the

consumption of wind power and photovoltaic power

generation. This game model is not conducive to

establishing an orderly and efficient power market

and dispatching order in Central China at the micro-

level, and also hinders the achievement of carbon

emission reduction in power generation and the

realization of the “dual carbon” goal at the macro

level. Therefore, it is imminent to change the

situation of bad hydropower competition in Central

China. Based on the cooperative game model, this

study builds a hydropower distribution mechanism in

Central China to explore the role of this mechanism

on promoting carbon emission reduction of power

generation in Central China.

2 COOPERATION GAME

MODEL CONSTRUCTION OF

HYDROPOWER PLANTS IN

THE BASIN OF CENTRAL

CHINA

For each hydropower plant in the same watershed, the

expectation of cooperation rather than malicious

competition is that cooperation can make the

individual obtain more benefits than the competition

(Ambec, 2008). However, the basis of cooperation

lies in the reasonable distribution of cooperation

income, otherwise, the collapse of the cooperative

alliance will damage the income of the alliance, and

the relationship that individual returns to competitive

will also hurt the income of the individual.

2.1 Construction of Game Model for

Hydropower Cooperation in the

Same Basin of Central China

It is assumed that there are

hydropower plants on

each river.

refers to the collection of river basins

in Central China, and

is a natural number, which

represents the serial number of the river (

iI⊂

). For

watershed

={1,2, , n }



represents the set

of game players of all hydropower plants in

watershed

, and

iii

SNS∀⊆ ≠∅

is called a

cooperative alliance, whose characteristic function is

vR→

, and

() 0

is the set of real

numbers. Moreover,

()

indicates the

maximum benefit that each participant in the

cooperative alliance

obtains under the condition

forming the alliance, and then

{

}

iii

TNv= ，

denotes the game alliance on

For a single watershed

and the cooperative

game

{

}

iii

TNv= ，

of hydropower plants on the

watershed, if there is a real array

()

ij iIjS

∈∈

then:

()

ij i i

iIjS

∈∈



(1)

()

ij iIjS

∈∈

can be called the feasible payment

vector of

, and the economic meaning of

()

ij iIjS

∈∈

denotes the share of each individual

allocated from the total income

()

. When

SN=

, namely when all individuals participate in

the cooperative alliance, if

()

ij iIjS

∈∈

, then:

({ }),( ),( [1, ])

()

ij i i

viIjn

xvN

≥∈∈















(2)

()

ij iIjS

∈∈

will be called a feasible profit

distribution solution of the cooperative game. For

alliance game

, if the set of all individual

allocations of hydropower plants in basin

ICPDI 2022 - International Conference on Public Management, Digital Economy and Internet Technology

326

Hunan Province is recorded as

()

, then:

() { | ,() ( )}

ii ij i ij i i i i

Ev x R x vxn vN=∈ ≥ =

(3)

Equation (3) is the rational condition for

individual

in each hydropower plant. What is

more, for the game subject

, if the income gained

by joining the single-watershed cooperative game

alliance is less than the income gained when

leaves the cooperative alliance and acts alone,

will withdraw from the alliance. Therefore, the

collective rationality condition of all hydropower

plants in a single basin is based on the super-

additivity of Equation (3), which can be derived as

follows:

()

ij i i

≥



(4)

At the same time, considering that the total

allocated amount of all hydropower plants in a single

basin

cannot exceed the total income of the basin,

we have:

()

ij i i

≤



(5)

According to Equations (4) and (5), it can be

known that if the Equation (3) can be satisfied,

namely when the individual rationality and collective

rationality conditions of a single-basin hydropower

cooperative game are met at the same time, it means

that all hydropower plants in basin

will

completely distribute all the benefits. The remaining

question below is what the allocation of each

hydropower plant is to achieve

()

ij i i



Assuming that the profit of all individuals in the

Central China basin

is recorded as

, the profit

of the remaining

n −

parties when no individual

participates is recorded as

(\ ) , [1, ]

ij i

vj biIj n=∈∈，

, while

,1 , 2 ,

[, ,, ]

iii in

bbb b= 

. In addition, the distribution of

all cooperation among the parties is marked as

,1 ,2 ,

[, ,, ]

iii in

xx x=  .

2.2 Construction of Game Model for

Inter-basin Hydropower

Cooperation in Central China

As is shown in Section 2.1, I is used to denote the

collection of river basins in Central China. It is

assumed that these rivers cooperate in a unified cross-

basin optimal dispatch. At this time, the individual

participating in the cooperation is basin

. Suppose

its cooperative alliance is denoted as

, and the

distribution of cooperative income by each individual

is denoted as vector

[, , , ]

yyy y= 

(

is the

number of rivers in set I).

The basis of cross-basin hydropower cooperation

is that the benefits obtained by basin i when

participating in the cooperation are at least not lower

than the benefits when it leaves the cooperative

alliance, and the excess profits obtained from the

cooperation need to be distributed to each individual

participating in the cooperation with a reasonable

manner. Besides, hydropower cross-basin

cooperative game distribution is the most important

concept of cooperative game. To obtain an executable

distribution, the distribution formed is classified,

forming the core concept, which can be defined as

follows:

(,) ()

eTS y vTS y

∈

=−



(6)

In Equation (6),

(,)eTS y

reflects the

satisfaction of the Hunan Inter-basin Hydropower

Cooperation Alliance (denoted as

) with the

allocation plan

. When

(,)eTS y

is larger, it

means that the cross-basin hydropower cooperation

alliance is more dissatisfied with the distribution plan

. At this time, the total income of all participating

entities in the cooperative alliance (that is, the

collection of hydropower in each basin) is far less

than the cooperative added value

()vTS

generated

by it, and the stability of the distribution plan is poor.

When A is smaller, it means that the inter-basin

hydropower cooperation alliance is more satisfied

with the allocation plan

, showing that the

allocation plan is more effective.

Obtaining the solution of Equation (6) is

equivalent to finding the allocation plan that

minimizes the maximum overrun in the cooperative

alliance, that is, nucleolus

. What is more,

compared with the core that may be an empty set, the

nucleolus always exists and contains only one

element. First, the core of the cooperative game can

be found:

yyd

≥













(7)

In Equation (7),

represents the total income

Multi-Agent Cooperation Mechanism of Hydropower Plants in Central China Based on Raiffa Solution

327

obtained by hydropower in different river basins after

forming a cooperative alliance. The core of this set of

inequalities can be solved as follows:

() {( , ): }

ii i i i

Cv cyy yd y cyd=− ≤≤−

(8)

2.3 Solution Algorithm of Hydropower

Cooperation Game Model

The prerequisite for multiple game players to form a

cooperative alliance is still individual rationality. If

the cooperative alliance damages the interests of the

individual without compensation, the subject will

have the urge to withdraw from the alliance, and then

obtain greater benefits through its own actions or

strategies. Therefore, a “fair and reasonable”

distribution plan is very important in a cooperative

alliance, and the distribution plan is reasonable only

when it reaches the rational goals of the participating

subjects. Moreover, many scholars in the field of

game theory have explored the issue of “fairness of

distribution”, and representative solution concepts

include Nash-Harsanyi negotiation solution, Raiffa

value, etc. It can be deduced mathematically that the

negotiation solution is equivalent to the Raiffa value

(Lozano, 2020), and the method of obtaining the

solution of the cooperative game based on the

Shapley value is only suitable for the case where the

number of individuals in the set is not more than 3

(Eissa, 2021). In this study, there are more individuals

in the same and cross-basin cooperative game

alliances (

3n >

and

n >

). Therefore, the Raiffa

value is used to solve the solution of the cooperative

game distribution mode of hydropower in Central

China. The Raiffa value algorithm is carried out in the

following steps:

（1）For basin

, according to the profits of the

cooperation of

and

n −

sides, the lower limit

of the distribution of all sides, namely

,,,

ij ij ij

=+ −



, is used as the basis of

distribution.

（2）When an individual

of basin

joins

the cooperation of

1n −

side

without

, the

increase in profit, namely the marginal benefit of

is calculate:

iij

Bb=− .

（3）Assign

,ij

according to two steps.

Firstly, the individual

in the basin

and the

n −

side hydropower plant without

are

equally divided, and then the

n −

side

hydropower plant is divided equally, namely:

,,,

,,,,[1,],

22(1)

ij ik

ikij ik i

xx iIjk nkj

==+ ∈∈≠

−

(9)

（4） Taking j as

1, 2, , n

, repeat step (3), and

then sum and average, to get the final distribution as:

[],,[1,]

22(1)

ijij i

ii i

xxjkn

nn n

≠

−

=⋅+ + ∈

−



(10)

Substituting the vector

and

, Equation (10)

can be expressed as:

,,,

[],,[1,]

2( 1)

ij ij ij i

ii i

bbiIj n

nnn

−

=+ − ∈∈

−



(11)

Equation (11) is the Raiffa equilibrium solution of

the cooperative game.

3 GAME DISTRIBUTION

SOLUTION OF INTER-BASIN

HYDROPOWER

COOPERATION IN HUNAN

PROVINCE OF CENTRAL

CHINA

In this paper, taking the typical provinces of Central

China and the typical river basins of Lishui in Hunan

as examples, the quarterly power generation and unit

power generation price of each hydropower plant in

the river basins of Hunan Province in 2020 are

substituted into the hydropower cooperation game

model and its solution algorithm in Central China, to

obtain the revenue distribution plan of the

hydropower cooperation game. In addition, since the

value corresponding to this solution can be regarded

as value or electricity, the RaiIffa solution is

normalized and converted into a proportional value

that is the proportion of cooperative game revenue

distribution based on the Raiffa solution to avoid unit

inconsistency, which is more convenient for practical

implementation.

Figure 2 shows the proportion of inter-basin

hydropower cooperation distribution in Hunan

Province in the Central China by quarter.

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328

Figure 2: Proportion of income distribution based on multi-year average of Hunan hydropower inter-basin cooperation game.

Table 1: Cooperative game distribution share of power plants in Lishui river basin.

Power plant name The first quarter The second quarter The third quarter The fourth quarter

Jiang Ya

21.45% 7.48% 24.88% 27.68%

Guan Menyan

7.91% 10.81% 5.68% 6.38%

Changtan Rive

12.76% 11.24% 5.68% 6.38%

Yu Ta n 11.86% 9.93% 15.77% 11.86%

Chalin Rive

11.41% 11.38% 5.68% 6.38%

Zao Cit

11.90% 12.26% 19.16% 17.74%

San Jiangkou 13.03% 8.63% 12.64% 12.05%

Yan Zhou 9.67% 28.26% 10.52% 11.53%

It can be seen from Figure 2 that the Yuanshui

River Basin has the highest proportion (about 38%),

and the Lishui River Basin is the lowest (less than

20%). The Xiangjiang River and Zishui River Basins

are approximately equal, which is consistent with the

order of hydropower generation value in each basin

from high to low, embodying the principle that

individuals distribute revenue according to the

contribution to the team. Moreover, individuals with

a high proportion of power generation value need to

reduce the proportion of revenue sharing and give

profits to individuals with a low proportion of power

generation value to maintain the cooperative alliance.

Based on the profit distribution solution of the

cross-basin hydropower cooperation game in Hunan

Province, the distribution accuracy of the cooperation

revenue can be determined on the hydropower

alliances of each basin, further gaining the

distribution mechanism in each of the basin

hydropower cooperation alliances. Meanwhile, the

proportion of each power plant’s share of revenue be

obtained too. The following obtains the solution of

the Lishui Hydropower Cooperation Alliance in a

typical river basin, which is listed in Table 1.

It can be seen from Table 1 that the Raiffa value

of the hydropower plant cooperative alliance in a

single basin has different magnitudes from monthly.

Although the difference is small, and the fluctuation

range is not more than 2% in most cases, the

cumulative difference or cross-quarter difference is

significantly larger. The main reason for the

difference is that the power plants are different in

sensitivity to water regimes and their adjustment

capabilities, and there is a certain asynchrony in

production during periods of high water, flat water,

and low water, which shows that the quarterly Raiffa

value distribution method is more reasonable than the

annual Raiffa value distribution.

In addition, the cooperative alliance of a single

basin hydropower plant is formed to redistribute

benefits, which reflects the contribution of each

power plant to the single basin cooperative alliance.

In other words, power plants that can produce higher

electricity value each month account for a larger

proportion of the benefit distribution. However, the

proportion of profit distribution is not the same as that

of the monthly power generation value of each power

plant. For power plants with high power generation

value, the proportion of profits is lower than that of

their power generation value. Conversely, power

plants that account for the proportion of power

generation value can obtain a higher proportion of

revenue in cooperation, which is consistent with the

principle of the Raiffa value algorithm considering

Multi-Agent Cooperation Mechanism of Hydropower Plants in Central China Based on Raiffa Solution

329

the “marginal contribution of the team” and

“protecting the weak”.

4 CONCLUSIONS

Based on the current practical problem that clean

energy is consumed inadequately due to malicious

competition among hydropower entities in Central

China, a hydropower cooperation game alliance in

Central China is established in this paper. Moreover,

with the help of the Raiffa solution algorithm, the

distribution plan of hydropower cooperative game

alliances in typical provinces and river basins in

Central China is calculated. It is proved that it is

feasible to establish a cooperative game alliance of

hydropower in Central China, and the distribution

plan is reasonable and incentively compatible. What

is more, the research methods and conclusions are of

practical guiding significance. In addition, the

hydropower cooperation alliance in Central China

will help regulate the power market and dispatch

order, thereby accelerating the consumption of clean

energy and promoting the realization of China’s

power generation carbon emission reduction and

“dual-carbon” strategic goals.

ACKNOWLEDGMENTS

This work was financially supported by the State Grid

Huazhong Branch.

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