Multi-Objective Joint Optimal Operation of Reservoir System and Analysis of Objectives Competition Mechanism: A Case Study in the Upper Reach of the Yangtze River

Abstract

The multi-objective optimal operation and the joint scheduling of giant-scale reservoir systems are of great significance for water resource management; the interactions and mechanisms between the objectives are the key points. Taking the reservoir system composed of 30 reservoirs in the upper reaches of the Yangtze River as the research object, this paper constructs a multi-objective optimal operation model integrating four objectives of power generation, ecology, water supply, and shipping under the constraints of flood control to analyze the inside interaction mechanisms among the objectives. The results are as follows. (1) Compared with single power generation optimization, multi-objective optimization improves the benefits of the system. The total power generation is reduced by only 4.09% at most, but the water supply, ecology, and shipping targets are increased by 98.52%, 35.09%, and 100% at most under different inflow conditions, respectively. (2) The competition between power generation and the other targets is the most obvious; the relationship between water supply and ecology depends on the magnitude of flow required by the control section for both targets, and the restriction effect of the shipping target is limited. (3) Joint operation has greatly increased the overall benefits. Compared with the separate operation of each basin, the benefits of power generation, water supply, ecology, and shipping increased by 5.50%, 45.99%, 98.49%, and 100.00% respectively in the equilibrium scheme. This study provides a widely used method to analyze the multi-objective relationship mechanism, and can be used to guide the actual scheduling rules.

Full text

water
Article
Multi-Objective Joint Optimal Operation of Reservoir
System and Analysis of Objectives Competition
Mechanism: A Case Study in the Upper Reach of the
Yangtze River
Mufeng Chen, Zengchuan Dong *, Wenhao Jia, Xiaokuan Ni and Hongyi Yao
College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China;
chenmf@hhu.edu.cn (M.C.); wenhao@hhu.edu.cn (W.J.); hynxk@hhu.edu.cn (X.N.); yaohy@hhu.edu.cn (H.Y.)
*Correspondence: zcdong@hhu.edu.cn
Received: 28 October 2019; Accepted: 29 November 2019; Published: 1 December 2019


Abstract:
The multi-objective optimal operation and the joint scheduling of giant-scale reservoir
systems are of great significance for water resource management; the interactions and mechanisms
between the objectives are the key points. Taking the reservoir system composed of 30 reservoirs in
the upper reaches of the Yangtze River as the research object, this paper constructs a multi-objective
optimal operation model integrating four objectives of power generation, ecology, water supply, and
shipping under the constraints of flood control to analyze the inside interaction mechanisms among
the objectives. The results are as follows. (1) Compared with single power generation optimization,
multi-objective optimization improves the benefits of the system. The total power generation is
reduced by only 4.09% at most, but the water supply, ecology, and shipping targets are increased by
98.52%, 35.09%, and 100% at most under different inflow conditions, respectively. (2) The competition
between power generation and the other targets is the most obvious; the relationship between water
supply and ecology depends on the magnitude of flow required by the control section for both targets,
and the restriction effect of the shipping target is limited. (3) Joint operation has greatly increased
the overall benefits. Compared with the separate operation of each basin, the benefits of power
generation, water supply, ecology, and shipping increased by 5.50%, 45.99%, 98.49%, and 100.00%
respectively in the equilibrium scheme. This study provides a widely used method to analyze the
multi-objective relationship mechanism, and can be used to guide the actual scheduling rules.
Keywords:
giant reservoir system; joint operation; multi-objective optimization; interaction
relationship mechanism
1. Introduction
With the rapid development of urbanization and the population explosion, the demand for water
resources is also increasing. It is predicted that compared with the global water consumption for
energy sectors in 2012, it will increase by 85% in 2030 [
1
]. This makes the problem of water resources
become one of the most important problems in the world today. Reservoirs, as a basic component
of complex water resources systems, form part of engineering measures to store and redistribute
natural water resources [
2
], which play a significant role in the allocation of river water resources.
The operation of the reservoirs not only guarantees the flood control safety of the river, but also plays
various roles in power generation, water supply, ecological environment maintenance, and navigation.
In power systems, hydropower stations are used for peak shaving and frequency modulation because
of their cleanliness and flexible switching dispatch [
3
]. However, because of bearing the influence of
multiple benefits, their power generation capacity is often greatly limited [
4
]. Due to the different
Water 2019,11, 2542; doi:10.3390/w11122542 www.mdpi.com/journal/water

Water 2019,11, 2542 2 of 23
requirements for the water head and flow of hydropower stations between power generation and other
benefit objectives, there exists mutual influence and interdependence among these benefit objectives [
5
].
Therefore, how to deal with the impact between these objectives and maximize the benefit of limited
water resources is the focus and difficult point of current research. Many scholars have focused on the
optimal operation of reservoirs and reservoir groups in specific areas.
Many algorithms can be used to solve reservoir optimal operation and water management
problems with the development of computing ability; such algorithms can be classified as classic or
evolutionary methods [
6
]. However, the classic methods always perform poorly in solving complex
problems, which makes the evolutionary methods develop rapidly [
7
]. Therefore, evolutionary
methods are frequently used in water management problems, such as particle swarm optimization
(PSO) [
8
–
10
], genetic algorithm (GA) [
11
–
13
], and so on [
14
–
16
]. With the increase in the pursuit of
multi-objective benefits by decision makers, the multi-objective optimization algorithms (MOEAs)
have received more attention and been improved a lot, such as gravity search algorithm (GSA) [
7
],
strength Pareto evolutionary algorithm (SPEA) [
17
], non-dominated sorting genetic algorithm-III
(NSGA-III) [
18
], and so on. With the development and improvement of these methods, researchers
have carried out plenty of research work on the multi-objective optimization of reservoirs. Cheng
et al. [
19
] studied the flood control and water supply shortages with an integrated approach using
an optimization model and Monte Carlo simulations in Da-Ha creek basin in Taiwan. Tilmant [
20
],
Wu, and Chen [
21
] made the reference of optimal dispatching for the balance between reservoir
power generation and water supply in an irrigation area within the basin. Si at al. [
22
] analyzed the
contradictory relationship between hydropower generation and water supply in the reservoir system
of the trunk river basin, and constructed a water–energy–food model. Meng et al. [
6
] proposed an
improved multi-objective cuckoo search algorithm and discussed the competition relationship between
power generation and water supply of the Xiaolangdi cascade hydropower stations on the Yellow River.
In addition, more and more water resources management, water allocation, and reservoir operation
problems have also been studied [23–26].
In China, the water resources problem is also one of the most important strategic problems
affecting the development of the country. The Yangtze River plays an irreplaceable role in promoting
the economic and social development of our country [
3
], and the upper reaches of the Yangtze River,
from the source to Yichang, Hubei Province, have huge potential hydropower development capacity
and utilization value due to its large terrain difference and high flowrate volume. In the year 2018, 21
completed controlled reservoirs in the upper reaches of the Yangtze River were included in the joint
flood control operation; about 11.1 billion m
3
of flood was retained and stored by upstream reservoirs,
and the total water supply was about 48.1 billion m
3
until November [
27
]. They had made tremendous
contributions to flood control and benefit development in the river basin. With the completion of
a series of controlled reservoirs in the upper reaches of the Yangtze River, the maximization of the
utilization value of water energy and water resources has become an important task of reservoir system
development, and the optimal operation of reservoirs in the upper reaches of the Yangtze River is
increasingly important [28].
At present, there has been some research on the optimal dispatching of reservoirs and the
relationship between various benefit objectives in the upper reaches of the Yangtze River. Liu et al. [
29
]
enhanced the flood control capacity and power generation benefits of the Three Gorges Reservoir in
flood season by optimizing the sequence and quantity of spillway operation. Zhou et al. [30] studied
the contradiction between flood control and water storage at the end of flood season of Jinsha River
and the Three Gorges Reservoir. Jia [
31
], Wang [
32
], and Lu et al. [
33
] studied the relationship between
power generation and ecology in Jinsha River cascade reservoirs and the Three Gorges cascade. In
terms of multi-objective coordination and optimization, Zhou et al. [
34
] studied the competition among
flood control, power generation, and shipping in the Three Gorges cascade and the comprehensive
operation plan in flood season. Most of the existing studies choose the Three Gorges–Gezhouba
cascade reservoirs or a single tributary cascade reservoir group in the upper reaches of the Yangtze

Water 2019,11, 2542 3 of 23
River as the research area. Although these results can provide theoretical support for the optimal
operation of reservoirs in a single basin, there is a lack of research on the joint optimal operation of the
giant reservoirs system in the upper reaches of the Yangtze River, which causes a limitation in spatial
breadth. These researches destroy the integrity and connectivity of the reservoir group system in the
upper reaches of the Yangtze River [
35
]. In addition, current research studies mostly focus on no more
than three objectives, which leads to deficiencies in integrity because the most basic benefits brought
by the construction of hydropower stations include the five benefits of flood control, power generation,
water supply, ecology, and shipping. The existing studies isolate the five benefits and lack of overall
grasp of the mutual restriction among them, leading to a discount on the applicability of these optimal
dispatching decisions.
Therefore, in view of the problems in recent studies, based on the Joint Regulation Scheme of
the reservoir group in the upper reaches of the Yangtze River in 2018, a giant reservoir group system
model including 30 controlled reservoirs that have been constructed, are under construction, or are
planned in the upper reaches basin was built. Taking this system as the object, this paper studied
the multi-objective joint optimal dispatching problem of a giant reservoir group system with four
economic benefits of power generation, ecology, water supply, and shipping on the premise of meeting
the flood control requirements. This model will be described in Sections 2and 3. After analyzing the
rationality of model calculation, this study explores the multi-objective optimal dispatching mode of
the reservoir group system in the upper reaches of the Yangtze River, compares the similarities and
differences of the multi-objective competition relations under different inflow conditions, and probes
into the causes of the interaction of the benefit objectives. The advantages of joint optimal dispatching
are also discussed. These analyses mentioned will be shown in Section 4. The results of this study
not only increase the comprehensive development benefit of the system on the premise of ensuring
the scheduling requirements, but also provides some technical reference and theoretical support for
the reservoir dispatching mode in the upper reaches of the Yangtze River to meet the different benefit
demands for decision makers. Some suggestions for further study will be shown in Section 5. The
research process of this study is shown in Figure 1.

Water 2019,11, 2542 4 of 23
Water 2019, 11, x FOR PEER REVIEW 4 of 24
Figure 1. Flow chart of the research process of this study.
2. Study Area
The upper reaches of the Yangtze River, which controls about 1 million km
2
of river basins, are
well developed with abundant hydroelectric energy. The average annual runoff is over 450 billion
m
3
, accounting for half of the total water resources in the whole Yangtze River basin. The built,
under construction, and proposed controlled reservoirs in the upper reaches of the Yangtze River
have gradually formed the joint operation pattern of the giant reservoir system in this area.
However, reservoirs undertake many tasks at the same time, which require different water levels
and discharge. Conflicts occur between these targets. The task of power generation requires high
water level or large discharge. However, this may destroy the water supply demand if the inflow is
stored in the reservoir to maintain the water level; or, the ecological requirement may be damaged if
the discharge is much larger than the ecological suitable flow, as well as for shipping. Therefore, this
paper is aimed at analyzing the relationship mechanism between these benefit targets and studying
the joint operation of a giant reservoir system.
In this study, the observed data of hydrological station flow at the dam site of all the built,
under construction, and proposed reservoirs were taken as basic data, and the monthly average
water level was taken as the decision variable. Therefore, the hydropower stations with small
regulation capacity, such as daily and weekly regulation hydropower stations, will be transformed
into runoff hydropower stations. The fine scheduling process of these reservoirs is not considered,
but their power generation is included in the total generation of the system to add these hydropower
Figure 1. Flow chart of the research process of this study.
2. Study Area
The upper reaches of the Yangtze River, which controls about 1 million km
2
of river basins, are
well developed with abundant hydroelectric energy. The average annual runoffis over 450 billion
m
3
, accounting for half of the total water resources in the whole Yangtze River basin. The built,
under construction, and proposed controlled reservoirs in the upper reaches of the Yangtze River
have gradually formed the joint operation pattern of the giant reservoir system in this area. However,
reservoirs undertake many tasks at the same time, which require different water levels and discharge.
Conflicts occur between these targets. The task of power generation requires high water level or large
discharge. However, this may destroy the water supply demand if the inflow is stored in the reservoir
to maintain the water level; or, the ecological requirement may be damaged if the discharge is much
larger than the ecological suitable flow, as well as for shipping. Therefore, this paper is aimed at
analyzing the relationship mechanism between these benefit targets and studying the joint operation
of a giant reservoir system.
In this study, the observed data of hydrological station flow at the dam site of all the built, under
construction, and proposed reservoirs were taken as basic data, and the monthly average water level
was taken as the decision variable. Therefore, the hydropower stations with small regulation capacity,
such as daily and weekly regulation hydropower stations, will be transformed into runoffhydropower
stations. The fine scheduling process of these reservoirs is not considered, but their power generation is
included in the total generation of the system to add these hydropower stations with smaller regulation
capacity to the model calculation. The influence of the total generation of the reservoir group system
on other profit-making objectives can be considered.

Water 2019,11, 2542 5 of 23
The water units, storage and extraction work, control nodes, and channels in the reservoir group
system were converted into points and lines based on analyzing the utilization and management of
water resources in this system. According to the topological relationship, the system composed of
these 20 reservoirs was generalized. The overview diagram is shown in Figure 2. The characteristics of
the 20 reservoirs are listed in Table 1.
1
(a)
(b)
Figure 2.
20 controlled reservoir group systems in the upper reaches of the Yangtze River.
(a) Geographical location of case study area; (b) Generalization diagram of the reservoir system.

Water 2019,11, 2542 6 of 23
Table 1. List of characteristic parameter values of the reservoirs.
Area Reservoir Construction
Status
Normal Storage
Water Level/m
Flood Limited
Water Level/m
Installed
Capacity/MW
Annual Average
Generating
Capacity/×108kW·h
Yalong River
Lianghekou under
construction 2865 2845 3000 110.62
Jinping Class I completed 1880 1859 3600 166.2
Ertan completed 1200 1190/1192 3300 170
Jingsha
River
Wudongde under
construction 975 952 8700 387
Baihetan under
construction 825 785 14,000 602
Xiluodu completed 600 560 13,860 571
Xiangjiaba completed 380 370 6400 307
Dadu River
Xiaerxia planning 3120 3105 540 22.21
Shuangjiangkou
under
construction 2500 2485 2000 83.41
Pubugou completed 850 836.6/841 3600 147.9
Minjiang
River Zipingpu completed 877 850 760 34.17
Jialing River
Bikou completed 704 697/695 300 14.63
Baozhusi completed 588 583 700 12
Tingzikou completed 458 447 1100 31.75–29.51
Wujiang
River
Hongjiadu completed 1140 1138 600 27.73
Dongfeng completed 970 968 695 24.2
Wujiangdu completed 760 755 1250 40.56
Goupitan completed 630 626.24/628.12 3000 96.82
Pengshui completed 293 287 1750 63.51
Main Stream Three Gorges completed 175 145 22,500 882
3. Model and Solution
3.1. Objective Function
In this study, the optimal operation objectives of reservoir groups in the upper reaches of the
Yangtze River include the following five objectives: power generation, water supply, ecology, shipping,
and flood control. The daily or lower step size of flood control fine operation is generally selected as the
dispatching scale; however, it is inconsistent with the research step selected in this study. Meanwhile,
if the flood control fine operation is considered, the dimensions of the model decision variables will be
too large, and the calculation difficulty will be increased. Therefore, the flood control task of reservoirs
is treated as the constraint condition to ensure that each reservoir is maintained at its flood limited
water level during the flood season.
The objective functions for each target are expressed as follows.
(1).
Power generation objective: maximum total power generation of reservoir system
max f1=maxE=
M
X
m=1
T
X
t=1
Nt
m×∆t(1)
Nt
m=km×qt
m×ht
m(2)
where
f1
is the power generation objective function,
E
is the total power generation of the reservoir
system, kW
·
h;
Nt
m
is the output of the m-th hydropower station in the t-th period, kW; Mis the total
number of reservoirs; Tis the calculation period length, year;
km
is the hydropower generation
efficiency of the m-th reservoir;
qt
m
is the power generation flow of the m-th hydropower station in
the t-th period, m
3
/s;
ht
m
is the average hydropower head of the m-th reservoir in the t-th period,
m; and ∆tis the unit calculation time step size, months.

Water 2019,11, 2542 7 of 23
(2).
Water supply objective: minimum water shortage
min f2=
K
X
k=1
T
X
t=1
(qt−Qkt)(qt<Qkt)(3)
where
f2
is the water supply objective function,
K
is the number of socioeconomic water demand
areas;
qt
is the reservoir water supply capacity in the t-th period, m
3
/s;
Qkt
is the flow rate of the
t-th period corresponding to the total water demand of the k-th area, m
3
/s. All the water demand
data of each water supply control station are extracted from the regional yearbook and water
resources bulletin, and are referred to the minimum control flow index of the basic water supply
control section in the Yangtze River basin.
(3).
Ecological objective: minimum suitable ecological flow deviation
min f3=
L
X
l=1
T
X
t=1


Rit −Eapp
it 

(4)
where
f3
is the ecological objective function,
L
is the total number of ecological control sections in
river reach;
Eapp
it
is the suitable ecological flow of section
l
in period t, m
3
/s; and
Rit
is the real flow
of section lin period t, m3/s.
The suitable ecological flow of each ecological control section was calculated by the monthly
frequency method [36], and the results are shown in Table 2.
(4).
Shipping objective: minimum suitable navigable flow deviation
min f4=
S
X
s=1
T
X
t=1
Qst (5)
Qst =








qt−SUapp qt>SUapp
0SLapp <qt<SUapp
SLapp −qtqt<SLapp
(6)
where
f4
is the shipping objective function;
S
is the total number of the channels;
Qst
is the
absolute value of the interval difference between the discharge and shipping suitable flow in each
calculation period, m
3
/s; and
SUapp
and
SLapp
are the upper and lower bounds for the range of
shipping suitable flow, which are defined by each channel dispatching procedure, m3/s.
Table 2. List of each ecological control section’s suitable ecological flow (m3/s).
Control Sections Month
1 2 3 4 5 6 7 8 9 10 11 12
Xiaodeshi 476 423 421 503 808 1899 3400 3082 3367 1972 1023 646
Pingshan 1655 1400 1331 1469 2151 4532 9284 9283 9939 6117 3416 2167
Fuluzhen 410 356 368 509 1016 2176 2726 2178 2223 1685 910 573
Pengshan 133 114 135 226 427 672 915 747 645 454 258 177
Wusheng 186 162 196 295 475 520 1290 927 1076 637 366 240
Wulong 1135 1002 722 459 341 359 419 807 1675 2617 2643 1536
Yichang
25,250 17,613
9450 5810 4308 3867 4217 6261
11,227 17,683 29,246 26,200
Each channel’s shipping suitable flow is shown in Table 3.

Water 2019,11, 2542 8 of 23
Table 3. List of channel’s shipping suitable flow (m3/s).
Location
Jinsha River Jialing River Wujiang River Main Stream
Downstream of
Xiangjiaba
Downstream of
Tingzikou
Downstream of
Pengshui
Downstream of
the Three Gorges
Suitable flow
range/m3/s1200–12,000 120–8000 280–5000 5000–56,700
3.2. Constraint Condition
(1).
Water balance constraint
Vm,t−Vm,t−1=(Im,t−Qm.t)×∆t(7)
Im,t=Qm−1,t+Inm−1,t−Em,t(8)
where
Vm,t
and
Vm,t−1
are the storage capacity of the m-th reservoir at the end and the beginning
of the t-th period, m
3
. The water level value of the reservoir can be deduced by
V
according to the
water level–storage capacity curve; and
Im,t
and
Qm,t
are the average inflow and outflow of the
m-th reservoir in the t-th period, m
3
/s. The outflow refers to the total amount of water discharge
from the reservoir through all the gates and spillways to the downstream channel, regardless
of the fine dispatching process during the flood season;
Inm,t
is the interval inflow between the
m-th reservoir and the (m+1)-th reservoir in the t-th period, m
3
/s;
Em,t
is the lost flow of the m-th
reservoir in the t-th period, which is mainly caused by the evaporation and infiltration in the
process of water transfer between two reservoirs. m
3
/s; and
∆t
is the unit calculation time step
size, months.
(2).
Reservoir discharge limits
Qmin
m,t≤Qm,t≤Qmax
m,t(9)
where
Qmin
m,t
and
Qmax
m,t
are the minimum and maximum outflow of the m-th reservoir during the
t-th period, m3/s.
(3).
Reservoir water-level limits
Each reservoir should meet the water level limit in every period of operation.
Zmin
m,t≤Zm,t≤Zmax
m,t(10)
where
Zmin
m,t
is the minimum water level of the m-th reservoir during the t-th period, which is equal to
the flood limited water level, m;
Zmax
m,t
is the maximum water level of the m-th reservoir during the
t-th period, which is equal to the flood control water level during the flood season and equal to the
normal storage water level during the non-flood season, m. According to the documents of the General
Command of Flood Control and Drought Relief of the Yangtze River, the period of the flood season is
shown in Table 4.

Water 2019,11, 2542 9 of 23
Table 4.
Period of flood season of each reservoir; the reservoir water level should be kept at the flood
control water level during this period.
Area Reservoir Time
Yalong River
Lianghekou
JUN–JUL
Jinping Class I
Ertan
Jingsha River
Wudongde
JUL–SEP
Baihetan
Xiluodu
Xiangjiaba
Dadu River
Xiaerxia
JUN–SEP
Shuangjiangkou
Pubugou
Minjiang River Zipingpu JUN–SEP
Jialing River
Bikou MAY–SEP
Baozhusi JUN–SEP
Tingzikou JUN–AUG
Wujiang River
Hongjiadu
JUN–AUG
Dongfeng
Wujiangdu
Goupitan
Pengshui MAY–AUG
Main Stream Three Gorges JUN–SEP
(4).
Power generation limits
The actual output of the reservoir shall meet the output limit in every period of operation.
Nmin
m,t≤Nm,t≤Nmax
m,t(11)
where
Nmin
m,t
and
Nmax
m,t
are the minimum and maximum power limit of the m-th reservoir during the
t-th period, 104kW.
3.3. Model Solving
In this study, the NSGA-III algorithm is adopted, which is improved in detail based on the
framework of the original NSGA-II algorithm using reference points to select better individuals.
The method of the normal boundary intersection point proposed by Das and Dennis is used to
determine reference points [
37
]. This improvement makes the optimal solution more uniformly
distributed on the non-dominant layer when solving the high-dimensional target problem, and
effectively prevents the algorithm from falling into local optimum [
18
]. This method is widely used in
multi-objective optimization problems [
38
,
39
]. In addition, in order to evaluate the optimization effect
of the multi-objective optimization model for each benefit target, the PSO was used to optimize the
maximum power generated in the reservoir system.
Figure 3shows the flow chart of NSGA-III and PSO.

Water 2019,11, 2542 10 of 23
Water 2019, 11, x FOR PEER REVIEW 10 of 24
3.3. Model Solving
In this study, the NSGA-III algorithm is adopted, which is improved in detail based on the
framework of the original NSGA-II algorithm using reference points to select better individuals. The
method of the normal boundary intersection point proposed by Das and Dennis is used to determine
reference points [37]. This improvement makes the optimal solution more uniformly distributed on
the non-dominant layer when solving the high-dimensional target problem, and effectively prevents
the algorithm from falling into local optimum [18]. This method is widely used in multi-objective
optimization problems [38,39]. In addition, in order to evaluate the optimization effect of the
multi-objective optimization model for each benefit target, the PSO was used to optimize the
maximum power generated in the reservoir system.
Figure 3 shows the flow chart of NSGA-III and PSO.
(a)
(b)
Figure 3. Flow chart of non-dominated sorting genetic algorithm-III (NSGA-III) and particle swarm
optimization (PSO).
(a) NSGA-III; (b) PSO.
In this study, the platEMO2.0 platform written by Ye Tian [40] and other scholars is used as the
carrier to solve the multi-objective optimization calculation. The annual runoff in the upper reaches
of the Yangtze River is calculated by frequency and the year, with a corresponding frequency of
25%, 50%, and 75% being selected as a typical year for wet (1964), normal (1988), and dry (1959). The
average monthly water level values in three typical years were taken as the decision variables, the
number of decision variables was 240, the population size was 120, and the number of iterations was
10,000. In order to make the optimal operation results more in line with the requirements in the
actual operation, the starting and ending regulation water levels were both set as the normal storage
water level. However, the total amount of water is small after the flood season in the dry year, so it is
hard to return to the normal storage water level at the end of the calculation period. Meanwhile, this
study paid more attention to benefit optimization of the reservoir group system. Therefore, the
water level was not strictly limited to the normal storage level in the last calculation period in the
dry year.
The conception of hyper volume (HV) was used to prove the convergence of the model under
the given time of iterations in this study. HV is the only unary measure used to measure the size of
the dominant region of a non-dominant solution set [41] and to prove that one set of non-dominant
solutions is not inferior to another. In this kind of discrete multi-objective optimization problem, the
Figure 3.
Flow chart of non-dominated sorting genetic algorithm-III (NSGA-III) and particle swarm
optimization (PSO). (a) NSGA-III; (b) PSO.
In this study, the platEMO2.0 platform written by Ye Tian [
40
] and other scholars is used as the
carrier to solve the multi-objective optimization calculation. The annual runoffin the upper reaches of
the Yangtze River is calculated by frequency and the year, with a corresponding frequency of 25%,
50%, and 75% being selected as a typical year for wet (1964), normal (1988), and dry (1959). The
average monthly water level values in three typical years were taken as the decision variables, the
number of decision variables was 240, the population size was 120, and the number of iterations was
10,000. In order to make the optimal operation results more in line with the requirements in the actual
operation, the starting and ending regulation water levels were both set as the normal storage water
level. However, the total amount of water is small after the flood season in the dry year, so it is hard to
return to the normal storage water level at the end of the calculation period. Meanwhile, this study
paid more attention to benefit optimization of the reservoir group system. Therefore, the water level
was not strictly limited to the normal storage level in the last calculation period in the dry year.
The conception of hyper volume (HV) was used to prove the convergence of the model under
the given time of iterations in this study. HV is the only unary measure used to measure the size of
the dominant region of a non-dominant solution set [
41
] and to prove that one set of non-dominant
solutions is not inferior to another. In this kind of discrete multi-objective optimization problem, the
HV value will gradually maximize and stabilize with the increase of iteration time if and only if the
solution set is the Pareto optimal solution [42].
In this study, the most disadvantageous points (the minimum power generation value and the
maximum damage rate of ecology, water supply, and shipping) were set as the reference point to
calculate the HV values of different evolution times. The trend curve is shown in Figure 4. It shows
that when the evolution time reaches 6000 generations, the HV value began to be stable. This proves
the convergence of the algorithm under the designed times of iterations, and the final set of solution
can be considered as the Pareto optimal solution.

Water 2019,11, 2542 11 of 23
Water 2019, 11, x FOR PEER REVIEW 11 of 24
HV value will gradually maximize and stabilize with the increase of iteration time if and only if the
solution set is the Pareto optimal solution [42].
In this study, the most disadvantageous points (the minimum power generation value and the
maximum damage rate of ecology, water supply, and shipping) were set as the reference point to
calculate the HV values of different evolution times. The trend curve is shown in Figure 4. It shows
that when the evolution time reaches 6000 generations, the HV value began to be stable. This proves
the convergence of the algorithm under the designed times of iterations, and the final set of solution
can be considered as the Pareto optimal solution.
Figure 4. Hyper volume (HV) value trend curves of the model under different evolution numbers.
4. Results and Discussion
4.1. Advantage Analysis of Multi-Objective Optimization
In order to verify the rationality of the calculation results, this study uses PSO to calculate the
total power generation of the reservoir system in the upper reaches of the Yangtze River and
compares the value of each benefit objective in the single-objective and multi-objective optimization.
The comparison results are shown in Table 5 below.
Table 5. Comparison of single-objective and multi-objective optimization results for total power
generation of reservoir system.
Objective Wet Year (1964) Normal Year (1988) Dry Year (1959)
Single Multiple Single Multiple Single Multiple
Power generation
/×10
11
kW·h 5.69 5.56
(−2.82%)
1
5.09 4.84
(−4.09%) 4.63 4.61
(−0.43%)
Water shortage
/m
3
/s 8652 128
(+98.52%)
2
5415 570
(+89.47%) 9689 584
(+93.97%)
Suitable ecological flow
deviation
/×10
5
m
3
/s
1.14 0.74
(+35.09%) 0.81 0.59
(+27.16%) 0.90 0.77
(+14.44%)
Suitable navigable flow
deviation
/m
3
/s
2150 0
(+100.00%) 106 0
(+100.00%) 114 88
(+22.81%)
1
The percentage represents the ratio of the multi-objective optimization benefit change value to that
of the single objective optimization.
2
The positive percentage indicates that the target benefit is
increased, while the negative percentage indicates that the benefit is reduced.
The actual annual average electricity generation is about 4.68 × 10
11
kW·h. The amount is less
than that after optimizing in the wet year and the normal year and just 1.52% more than that in the
Figure 4. Hyper volume (HV) value trend curves of the model under different evolution numbers.
4. Results and Discussion
4.1. Advantage Analysis of Multi-Objective Optimization
In order to verify the rationality of the calculation results, this study uses PSO to calculate the
total power generation of the reservoir system in the upper reaches of the Yangtze River and compares
the value of each benefit objective in the single-objective and multi-objective optimization.
The comparison results are shown in Table 5below.
Table 5.
Comparison of single-objective and multi-objective optimization results for total power
generation of reservoir system.
Objective Wet Year (1964) Normal Year (1988) Dry Year (1959)
Single Multiple Single Multiple Single Multiple
Power generation/×1011
kW·h5.69 5.56
(−2.82%) 15.09 4.84
(−4.09%) 4.63 4.61
(−0.43%)
Water shortage/m3/s8652 128
(+98.52%) 25415 570
(+89.47%) 9689 584
(+93.97%)
Suitable ecological flow
deviation/×105m3/s1.14 0.74
(+35.09%) 0.81 0.59
(+27.16%) 0.90 0.77
(+14.44%)
Suitable navigable flow
deviation/m3/s2150 0
(+100.00%) 106 0
(+100.00%) 114 88
(+22.81%)
1
The percentage represents the ratio of the multi-objective optimization benefit change value to that of the single
objective optimization.
2
The positive percentage indicates that the target benefit is increased, while the negative
percentage indicates that the benefit is reduced.
The actual annual average electricity generation is about 4.68
×
10
11
kW
·
h. The amount is less
than that after optimizing in the wet year and the normal year and just 1.52% more than that in the dry
year, indicating that the model did increase the benefit of the system. It can be seen from the table that
the total system power generation of single-objective optimization is larger than that of multi-objective
optimization. This is because the other three benefit objectives have an impact on the total amount of
system power generation in multi-objective optimization. The requirements for reservoir discharge
and water head are different, such that the ecological benefit target requires the discharge flow to be
maintained near the appropriate discharge, but this flow obviously cannot meet the flow requirements
to produce as much power as possible. A specific analysis of the impact between objectives is described
in detail below.
However, in the multi-objective optimization, the other benefit objectives except for power
generation are improved, and the optimization effect is obvious, which shows that our model did
optimize the scheduling methods. Besides, although part of the power generation lost, the increase in

Water 2019,11, 2542 12 of 23
other benefits is more in line with the requirements of modern dispatching planning in the pursuit of
comprehensive development.
4.2. Objective Benefit and Multi-Objective Relation Analysis
Through the calculation of the model, the multi-objective non-inferior solution sets of the reservoir
system in the upper reaches of the Yangtze River under the conditions of wet, normal, and dry water
are obtained, respectively (Figure 5). The non-inferior fronts are drawn in the three-dimensional
coordinate system in which the three coordinate systems correspond to the objective values of power
generation, ecology, and water supply, respectively, and the changes of the shipping target values are
represented by color.
Water 2019, 11, x FOR PEER REVIEW 12 of 24
dry year, indicating that the model did increase the benefit of the system. It can be seen from the
table that the total system power generation of single-objective optimization is larger than that of
multi-objective optimization. This is because the other three benefit objectives have an impact on the
total amount of system power generation in multi-objective optimization. The requirements for
reservoir discharge and water head are different, such that the ecological benefit target requires the
discharge flow to be maintained near the appropriate discharge, but this flow obviously cannot meet
the flow requirements to produce as much power as possible. A specific analysis of the impact
between objectives is described in detail below.
However, in the multi-objective optimization, the other benefit objectives except for power
generation are improved, and the optimization effect is obvious, which shows that our model did
optimize the scheduling methods. Besides, although part of the power generation lost, the increase
in other benefits is more in line with the requirements of modern dispatching planning in the pursuit
of comprehensive development.
4.2. Objective Benefit and Multi-Objective Relation Analysis
Through the calculation of the model, the multi-objective non-inferior solution sets of the
reservoir system in the upper reaches of the Yangtze River under the conditions of wet, normal, and
dry water are obtained, respectively (Figure 5). The non-inferior fronts are drawn in the
three-dimensional coordinate system in which the three coordinate systems correspond to the
objective values of power generation, ecology, and water supply, respectively, and the changes of
the shipping target values are represented by color.
(a)
(b)
(c)
Figure 5.
Non-inferior frontiers in wet, normal, and dry years considering flood control, power
generation, ecology, water supply, and shipping in the upper Yangtze River using NSGA-III. (
a
) Wet
year (1964); (b) normal year (1988); (c) dry year (1959).
There are obvious differences among the value and distribution of the objective function due to
the difference of incoming water quantity (Table 6).

Water 2019,11, 2542 13 of 23
Table 6. Range of the four objectives values in wet, normal, and dry years.
Year
Objective
Power Generation/×
1011 kW·h
Water
Shortage/m3/s
Suitable Ecological Flow
Deviation/×104m3/s
Suitable Navigable
Flow Deviation/m3/s
wet year (1964) 5.50–5.57 39–2379 7.1–7.9 0–1131
normal year (1988) 4.81–4.85 304–3495 5.7–6.4 0–888
dry year (1959) 4.58–4.63 387–4860 7.4–8.2 0–1080
It can be seen from the table that the power generation shows an obvious decreasing trend with
the decrease of incoming water quantity. Adequate water inflow will contribute to the great efficiency
of power generation by allowing a greater discharge flow when maintaining the same water level.
The water shortage increased rapidly along with the water volume decreasing, while the ecological
condition can be better met in the normal year as the inflow is closer to the requirements of the suitable
ecological flow, and both cannot be fully satisfied due to the constraints of flood control and other
objectives. For shipping objective, it was better met in the normal year, as the discharge may be better
held between the upper and lower limits of shipping requirements, and it can be fully satisfied due the
limit not being too tight as the expression of a flow range.
Each target has different responses in terms of the value and fluctuation range with the change of
incoming water quantity. At the same time, the satisfaction or benefit of a goal is not only related to
the goal itself, but also affected by other goals that need to be met.
In a dry year with less incoming water, the satisfaction degree of each goal is more seriously
restricted by the water quantity, thus weakening the interactions among the goals themselves. According
to Figure 6, the non-inferior solutions in the wet year and the normal year can be evenly distributed in
space, and the performance in the wet year is better. Thus, the Pareto front of the wet year is projected
onto 12 plane Cartesian coordinate systems, in which each has two targets as the coordinate axis.
Water 2019, 11, x FOR PEER REVIEW 14 of 24
Figure 6. Matrix scatter diagram in a wet year to show the relationships among the four objectives of
power generation, water supply, ecology, and shipping.
It can be seen from Figure 6 that the ecological objective and power generation in the wet year
show an obvious competitive relationship; with the increase of the total power generation, the
satisfaction degree of suitable ecological flow decreases continuously. This is because in order to
meet the requirements of ecological water demand, the reservoir needs to increase the discharge in
the non-flood season to achieve the ecological suitable flow, which leads to the reservoir not being
able to operate at a high water level during the dry season and causing the decrease of power
generation; and in the flood season, the reservoir shall control the discharge flow to satisfy the
ecological appropriate flow restriction, which hinders the power station from making maximum use
of the large incoming water during the flood season. Therefore, the ecological benefits and power
generation benefits of hydropower stations are contradictory and restricted. When the water supply
shortage is below 1100 m3/s in Figure 6, the reservoir system can play its coordinating and
dispatching role to ensure that the flow requirements of shipping are met to a greater extent, and at
this time, the damage degree of shipping and water supply are both small. When the satisfaction
degree of the shipping target decreases, the water supply shortage of the reservoir system has the
same changing trend; that is to say, there is a certain synergy between them. The main reason is that
the minimum water volume requirement of each water supply control station is less than the lower
limit of the suitable flow of the river channel (except in the Three Gorges the former (6000 m3/s) is
slightly higher than the latter (5000 m3/s)). When the water supply cannot be satisfied, it means that
the water supply in the river is insufficient; in this case, the minimum flow requirement of shipping
is more likely to be damaged.
The matrix scatter diagram (Figure 6) also shows that in addition to the above groups of
relationships, the pairwise relations between the other groups are scattered on the scatter point
diagram. The main reason is that the relationship between these objectives is weak, and the
competition for water demand is more complex when the four-dimensional benefit objectives and
flood control requirements work together. This will be analyzed in detail in the following parts.
Figure 6.
Matrix scatter diagram in a wet year to show the relationships among the four objectives of
power generation, water supply, ecology, and shipping.

Water 2019,11, 2542 14 of 23
It can be seen from Figure 6that the ecological objective and power generation in the wet
year show an obvious competitive relationship; with the increase of the total power generation,
the satisfaction degree of suitable ecological flow decreases continuously. This is because in order to
meet the requirements of ecological water demand, the reservoir needs to increase the discharge in the
non-flood season to achieve the ecological suitable flow, which leads to the reservoir not being able to
operate at a high water level during the dry season and causing the decrease of power generation; and
in the flood season, the reservoir shall control the discharge flow to satisfy the ecological appropriate
flow restriction, which hinders the power station from making maximum use of the large incoming
water during the flood season. Therefore, the ecological benefits and power generation benefits of
hydropower stations are contradictory and restricted. When the water supply shortage is below
1100 m
3
/s in Figure 6, the reservoir system can play its coordinating and dispatching role to ensure that
the flow requirements of shipping are met to a greater extent, and at this time, the damage degree
of shipping and water supply are both small. When the satisfaction degree of the shipping target
decreases, the water supply shortage of the reservoir system has the same changing trend; that is to
say, there is a certain synergy between them. The main reason is that the minimum water volume
requirement of each water supply control station is less than the lower limit of the suitable flow of
the river channel (except in the Three Gorges the former (6000 m
3
/s) is slightly higher than the latter
(5000 m
3
/s)). When the water supply cannot be satisfied, it means that the water supply in the river is
insufficient; in this case, the minimum flow requirement of shipping is more likely to be damaged.
The matrix scatter diagram (Figure 6) also shows that in addition to the above groups of
relationships, the pairwise relations between the other groups are scattered on the scatter point diagram.
The main reason is that the relationship between these objectives is weak, and the competition for water
demand is more complex when the four-dimensional benefit objectives and flood control requirements
work together. This will be analyzed in detail in the following parts.
4.3. Mechanism of Interaction among Multi-Objectives
In order to study the mechanism of the interaction between the objectives in the multi-objective
optimization problem, this study selected an equilibrium scheme on the Pareto front as a contrast,
and discussed the variation of the other benefit target values when selecting the operation scheme in
favor of one objective. This helps analyze how the benefit objectives interact with each other when
meeting the requirements of flood control, so as to provide guidance for the operation of a reservoir
group system in actual production.
There is no direct dominant relationship between the schemes in the Pareto non-inferior solution
set, and each scheme corresponds to multiple attributes. Considering that the objectives interact with
each other in this study, it is difficult to clearly define the conversion relationship between the objectives
in a quantitative way, nor can we absolutely judge which benefit goal needs to be satisfied first. So,
the fuzzy evaluation method is used to calculate the membership degree of each non-inferior solution
with the indices of power generation, water shortage, suitable ecological flow deviation, and suitable
navigable flow deviation so as to select the equilibrium solution among 120 non-inferior solutions.
The position of the selected solutions on the Pareto frontier is shown in Figure 7.

Water 2019,11, 2542 15 of 23
Water 2019, 11, x FOR PEER REVIEW 15 of 24
4.3. Mechanism of Interaction among Multi-Objectives
In order to study the mechanism of the interaction between the objectives in the multi-objective
optimization problem, this study selected an equilibrium scheme on the Pareto front as a contrast,
and discussed the variation of the other benefit target values when selecting the operation scheme in
favor of one objective. This helps analyze how the benefit objectives interact with each other when
meeting the requirements of flood control, so as to provide guidance for the operation of a reservoir
group system in actual production.
There is no direct dominant relationship between the schemes in the Pareto non-inferior
solution set, and each scheme corresponds to multiple attributes. Considering that the objectives
interact with each other in this study, it is difficult to clearly define the conversion relationship
between the objectives in a quantitative way, nor can we absolutely judge which benefit goal needs
to be satisfied first. So, the fuzzy evaluation method is used to calculate the membership degree of
each non-inferior solution with the indices of power generation, water shortage, suitable ecological
flow deviation, and suitable navigable flow deviation so as to select the equilibrium solution among
120 non-inferior solutions. The position of the selected solutions on the Pareto frontier is shown in
Figure 7.
Figure 7. The equilibrium and other preferred solutions on the Pareto frontier.
Table 7 shows the changes of the four objectives under each preference scheme compared with
the values of the objectives of the equilibrium solution, in which the power generation, water
supply, and ecology are expressed in percentages, while the shipping is expressed as a specific value
(the shipping conditions can be fully satisfied ( 4
f
= 0) in the equilibrium solution, so it cannot be
calculated in the form of a percentage). The positive number indicates that the target benefit is
improved, while the negative number indicates that the benefit is reduced, and the degree of
damage is increased.
Table 7. Changes of the four objectives under a preference scheme compared with the equilibrium
solution.
Objective
Power
Generation/
× 1011 kW·h
Water
Shortage/
m3/s
Suitable Ecological
Flow Deviation/
× 104m3/s
Suitable Navigable
Flow Deviation/
m3/s
Figure 7. The equilibrium and other preferred solutions on the Pareto frontier.
Table 7shows the changes of the four objectives under each preference scheme compared with
the values of the objectives of the equilibrium solution, in which the power generation, water supply,
and ecology are expressed in percentages, while the shipping is expressed as a specific value (the
shipping conditions can be fully satisfied (
f4
=0) in the equilibrium solution, so it cannot be calculated
in the form of a percentage). The positive number indicates that the target benefit is improved, while
the negative number indicates that the benefit is reduced, and the degree of damage is increased.
Table 7.
Changes of the four objectives under a preference scheme compared with the equilibrium solution.
Objective Power Generation/×
1011 kW·h
Water
Shortage/m3/s
Suitable Ecological Flow
Deviation/×104m3/s
Suitable Navigable Flow
Deviation/m3/s
Optimal power
generation 0.32% −167.10% −6.76% 0
Optimal water
supply −0.16% 69.19% 0.34% 0
Optimal ecology −0.99% −1413.62% 3.60% −736.86
Optimal shipping −0.95% −572.87% 3.50% 0
For the power generation objective, the shipping targets are less affected by it; as we can see,
the suitable navigable flow deviation remains 0 in the partial power generation scheme. However, both
the water supply and the ecological condition will be sacrificed due to generating more power, among
which the damage degree of the water supply may be better than that of the ecology (167.1% for water
shortage and 6.67% for ecological deviation in the first scheme). On the one hand, the basic number of
the water supply shortage in the equilibrium solution is small. This leads to the fact that although
the benefit of water supply changes little in other schemes, the value is large when it is presented in
percentage. On the other hand, in the dry season, in order to make the power generation in the system
as large as possible, the discharge will be appropriately reduced to maintain the reservoir at high water
head operation. At this time, if there is the case that
Qkt
>
Eapp
it
, and the reservoir discharge is more
closer to the
Eapp
it
, then the damage degree of the water supply will greatly increase compared with that
of the ecology. In a word, the power generation target will restrict the satisfaction of the ecological and
water supply objectives.
For the water supply objective, the reservoir cannot keep the high head operation for a long time
in order to ensure the water supply during the dry season, and this may affect power generation.
However, for the shipping objective, when
SUapp
>
Qkt
>
SLapp
, both targets can be satisfied if
qt<SUapp
;

Water 2019,11, 2542 16 of 23
when
Qkt
<
SLapp
, even
qt
>
Qkt
, navigation limits may be satisfied or destroyed. n this case, the amount
of water in the system needs to be adjusted in order to meet both of the targets at the same time. That
is why the navigation flow deviation can be maintained at zero in the partial water supply scheme.
When we take the ecological objectives into account, the relationship between them may be
related to the relationship among the different water demands for each objective and the discharge of
reservoirs. They may show a competitive or a synergistic relationship under different requirements
and discharge conditions.
(i) When
Qkt
<
Eapp
it
, if
Eapp
it
>
qt
>
Qkt
, the damage to both is small; if
qt
<
Qkt
, the damage degree
increases to both; if
qt
>>
Eapp
it
, the damage to the ecology increases, but is not caused by the requirement
of water supply. So, the two assume a cooperative relationship in this case.
(ii) When
Qkt
>
Eapp
it
, if
qt
>
Qkt
, the requirement of water supply can be satisfied, but the damage
to ecology will increase; if
Eapp
it
<
qt
<
Qkt
, the opposite is true. In this case, there is a competitive
relationship between them. However, when
qt
<
Eapp
it
, the damage degree increases to both, which
means that they have a cooperative relationship.
It can be found that if the discharge is controlled within a certain range, a co-win between the
two targets will be achieved. According to the analysis above, when
Qkt
>
Eapp
it
in a certain calculation
period, the range of discharge flow needs to be controlled more strictly, as the effect of different flow
processes on the degree of satisfaction of the two objectives is large in such cases. In the reservoir
system of the upper reaches of the Yangtze River, this case occurred at the downstream section of
Pubugou and the Three Gorges during the second to fourth period (from December to February).
The discharge hydrograph line of the two reservoirs is shown in Figure 8. In the partial water supply
scheme, the dispatching mode will give priority to the water supply, and then the reservoirs make
the discharge as close as possible to the ecologically suitable flow on the premise of ensuring a small
degree of water supply damage. Therefore, when the water supply requirement is prior, the water
supply benefit and ecological benefit both increased compared with the equilibrium scheme. While the
ecological objective is prior, the reservoir discharge will be closer to the suitable ecological flow. If the
ecological suitable flow is much less than the water supply demand during that calculation period,
there will be a large difference between the water supply and water demand, and the satisfaction of
water supply will decrease greatly.
Water 2019, 11, x FOR PEER REVIEW 17 of 24
February). The discharge hydrograph line of the two reservoirs is shown in Figure 8. In the partial
water supply scheme, the dispatching mode will give priority to the water supply, and then the
reservoirs make the discharge as close as possible to the ecologically suitable flow on the premise of
ensuring a small degree of water supply damage. Therefore, when the water supply requirement is
prior, the water supply benefit and ecological benefit both increased compared with the equilibrium
scheme. While the ecological objective is prior, the reservoir discharge will be closer to the suitable
ecological flow. If the ecological suitable flow is much less than the water supply demand during
that calculation period, there will be a large difference between the water supply and water demand,
and the satisfaction of water supply will decrease greatly.
(a) (b)
Figure 8. The discharge hydrograph line of Pubugou and the Three Gorges in a partial water supply
scheme and partial ecology scheme compared with the ecological and water supply requirements.
(a) Pubugou; (b) the Three Gorges.
For the ecological scheme, it affects power generation obviously; as the amount of power
decreases the most among all the four schemes, the competitive relationship between ecology and
power generation is strong. The satisfaction of the shipping target will be destroyed when
app
it
E
<
app
SL
. Thus, the strict control conditions of the ecological objectives on discharge are the main factor
that restricts the development of the reservoir in meeting the multi-benefit goal.
For shipping objective, the wide range of shipping constraints means that the reservoirs have
no need to increase discharge or maintain high water level operation, which results in the reduction
of power generation. As to the water supply objective, when
kt
Q
>
app
SL
, the
t
q
may not meet the
water supply demand when meeting shipping requirements, so the water supply benefits decrease
in the fourth scheme; for the ecological objective, if
app
SU
>
app
it
E
>
app
SL
, then the ecological
demand is easier to be satisfied, if
app
it
E
<
app
SL
, the reservoir can also make the discharge as close
to the ecological suitable discharge as possible on the basis of meeting the shipping requirement,
thus increasing the ecological benefits. In the case of abundant water over the whole year, the impact
of shipping on other objectives is relatively small, and it plays a limited role in restricting
comprehensive optimization. The impact of shipping on other objectives is relatively small, and it
plays a limited role in restricting comprehensive optimization.
Table 8. Interaction relationship between the four benefit objectives.
Objective Power Generation Water Supply Ecology Shipping
Power generation \ moderate
1
high
1
low
1
Water supply moderate \ no conflict
/low
2
low
Ecology high no conflict
/low
2
\ low
Figure 8.
The discharge hydrograph line of Pubugou and the Three Gorges in a partial water supply
scheme and partial ecology scheme compared with the ecological and water supply requirements.
(a) Pubugou; (b) the Three Gorges.
For the ecological scheme, it affects power generation obviously; as the amount of power decreases
the most among all the four schemes, the competitive relationship between ecology and power
generation is strong. The satisfaction of the shipping target will be destroyed when
Eapp
it
<
SLapp
. Thus,
the strict control conditions of the ecological objectives on discharge are the main factor that restricts
the development of the reservoir in meeting the multi-benefit goal.
For shipping objective, the wide range of shipping constraints means that the reservoirs have
no need to increase discharge or maintain high water level operation, which results in the reduction

Water 2019,11, 2542 17 of 23
of power generation. As to the water supply objective, when
Qkt
>
SLapp
, the
qt
may not meet the
water supply demand when meeting shipping requirements, so the water supply benefits decrease in
the fourth scheme; for the ecological objective, if
SUapp
>
Eapp
it
>
SLapp
, then the ecological demand is
easier to be satisfied, if
Eapp
it
<
SLapp
, the reservoir can also make the discharge as close to the ecological
suitable discharge as possible on the basis of meeting the shipping requirement, thus increasing the
ecological benefits. In the case of abundant water over the whole year, the impact of shipping on other
objectives is relatively small, and it plays a limited role in restricting comprehensive optimization.
The impact of shipping on other objectives is relatively small, and it plays a limited role in restricting
comprehensive optimization.
Table 8shows the interaction effect and the strength of the relationship among the four objectives.
In multi-objective optimization, there are competitive relationships between power generation and
other objectives, and there is no win–win situation. When considering other objectives, the reservoir
will always sacrifice the amount of power generation. The relationship between water supply and
ecology is affected by some reservoirs with complex discharge requirements for these two objectives.
The main restriction of water supply objective and ecological objective is from power generation.
Meanwhile, the relationship between shipping and other objectives is not obvious. Under the premise
of satisfying shipping conditions, other targets are not obviously restricted, and can be brought into
full play through the water distribution function in the system.
Table 8. Interaction relationship between the four benefit objectives.
Objective Power Generation Water Supply Ecology Shipping
Power generation \moderate 1high 1low 1
Water supply moderate \no conflict /low 2low
Ecology high no conflict /low 2\low
Shipping low low low \
1
‘-’ indicates a competitive relationship. ‘low’, ‘moderate’, and ‘high’ indicate the strength of the competitive
relationship. 2This indicates that there may be different relationships in different situations.
In the actual operation of the reservoir, the main purpose of reservoir operation during the water
supply period is to ensure the satisfaction of the water supply demand in the basin. At this time, the
power generation function of the reservoir needs to make concessions. In other periods, with the
increasing demand for ecological environment today, the reservoir group cannot blindly increase
power generation, but must sacrifice part of the electrical function to meet the flow limitations in
ecological sections. At the same time, it is necessary to weigh the requirements of water supply
objectives and ecological objectives for reservoirs and the importance of these two objectives to the
region in order to reasonably control the discharge of reservoirs to reduce the total benefit loss when
there is a contradictory relationship between ecology and water supply objectives.
In addition, this study also considered the limitation of flood control to reservoir operation.
The main task of reservoirs in the flood season is to ensure the safety of the dam and downstream basin.
During this period, the importance of the flood control function is greater than all the other objectives,
and the reservoirs must follow the principle of flood control. In the flood season, the demand of power
generation and water supply can always be met, but the ecological and shipping conditions are easy to
be destroyed. Therefore, on the basis of ensuring the safety of flood control in flood season operation,
it is necessary to focus more on meeting the ecological and shipping requirements in order to increase
the total benefit of the reservoir system.
4.4. Analysis on the Advantages of Joint Optimization of Reservoir Group System
In view of the disadvantages of dividing the upper reaches of the Yangtze River into several
sub-basins in existing studies, a giant reservoir group system considering the joint operation of 30
reservoirs in this area is constructed in order to study the advantages of joint operation of giant -scale

Water 2019,11, 2542 18 of 23
systems and the interaction between reservoirs. Table 9shows the values of the four benefit targets
under the condition of joint operation and separate operation.
Table 9. Comparison of benefit targets of the system under different operation schemes.
Schemes
Objective Power Generation/×
1011 kW·h
Water Shortage/×
105m3/s
Suitable Ecological
Flow Deviation/m3/s
Suitable Navigable
Flow Deviation/m3/s
Optimal
power
generation
Separate 5.31 1.50 12,080 1912
Joint 5.57
(4.90%) 1
0.79
(47.33) 2
343
(97.16%)
0
(100.00%)
Optimal
ecology
Separate 5.21 1.33 10,307 5082
Joint 5.50
(5.57%)
0.71
(46.62%)
1942
(81.16%)
737
(85.50%)
Optimal
water
supply
Separate 5.21 1.36 7987 4627
Joint 5.55
(6.53%)
0.74
(45.59%)
39
(99.51%)
0
(100.00%)
Optimal
shipping
Separate 5.28 1.42 8469 137
Joint 5.50
(4.17%)
0.71
(50.00%)
863
(89.81%)
0
(100.00%)
Equilibrium
solution
Separate 5.27 1.37 8461 170
Joint 5.56
(5.50%)
0.74
(45.99%)
128
(98.49%)
0
(100.00%)
1
The percentage represents the ratio of the joint operation benefit change value to that of the separate operation.
2
The positive percentage indicates that the target benefit is increased.
It can be seen from the table that no matter which benefit the system favors, the value of each
benefit target of joint operation is better than that of separate operation. This shows that in joint
dispatching, through the redistribution of water volume in time and space, the requirements of the
whole system for various benefit objectives can be better met, the reservoir capacity of all reservoirs
in the system can be fully utilized, and the discarded water in flood season can be reduced, so as to
compensate for the insufficiency of water volume of other reservoirs in the system and alleviate the
excessive discharge of some reservoirs in some periods. As a result, the overall benefit of the reservoir
system has been improved. Especially for reservoirs with a large regulating capacity on the main
stream, branch reservoirs can store or discharge branch inflow rationally to make up for the shortage
of downstream water or control the water volume to avoid excessive discharge. So, the flow and head
of the reservoir with strong regulation ability and great benefit responsibility can be maintained in a
range that can not only increase power generation but also better meet the needs of ecology, water
supply, and shipping.
Take the Three Gorges as the example, as the most important controlled reservoir in the middle
and upper reaches of the Yangtze River, the response of the Three Gorges’ benefit objectives is the
most representative and valuable. This study compared its performances of each benefit objective
under two schemes in the wet year. Scheme 1 was the single reservoir operation of the Three Gorges
Reservoir, and the inflow was the natural runoffprocess from the upper reaches of the Three Gorges in
1964. Scheme 2 was the joint operation of the reservoir system in the upper reaches of the Yangtze
River, and the inflow had been regulated by the controlled reservoirs on the main and tributaries of the
Yangtze River in the upstream of the Three Gorges. This research analyzes and compares the values of
the four benefit targets under different scheduling schemes, and the results are shown in Table 10.

Water 2019,11, 2542 19 of 23
Table 10. Comparison of benefit targets of the Three Gorges under different operation schemes.
Schemes
Objective Power Generation/×
1011 kW·h
Water Shortage/×
105m3/s
Suitable Ecological
Flow Deviation/m3/s
Suitable Navigable
Flow Deviation/m3/s
Optimal power
generation
Single 1.13 10,152 1.12 1691
Joint 1.15
(1.77%) 1
79
(99.22%) 2
0.43
(61.61%)
0
(100.00%)
Optimal
ecology
Single 1.07 8045 0.99 5000
Joint 1.14
(6.54%)
639
(92.06%)
0.38
(61.62%)
0
(100.00%)
Optimal water
supply
Single 1.10 8000 1.06 5000
Joint 1.14
(3.64%)
0
(100.00%)
0.43
(59.43%)
0
(100.00%)
Optimal
shipping
Single 1.12 8628 1.08 137
Joint 1.14
(1.79%)
204
(97.64%)
0.38
(64.81%)
0
(100.00%)
Equilibrium
solution
Single 1.10 8168 1.02 589
Joint 1.14
(3.64%)
0
(100.00%)
0.39
(61.76%)
0
(100.00%)
1
The percentage represents the ratio of the joint operation benefit change value of the Three Gorges to that of the
separate operation.2The positive percentage indicates that the target benefit is increased.
Table 8shows that the value of each benefit objective in the joint scheduling of the Three Gorges
Reservoir is better than or equal to the corresponding value of the single reservoir operation. This result
proves that the compensation and regulation between hydropower stations in the system has been
brought into full play in the joint integrated operation of reservoir groups. The upstream hydropower
station compensates the downstream of the whole system by sacrificing a part of its own benefits.
By adjusting the space–temporal distribution of incoming water, it can ensure that the downstream
power station, especially the control reservoir with a great regulation capacity, which has an important
position in power generation and water supply, can operate at a reasonable water level interval,
give full play to the regulation and storage function of the reservoir, and reasonably distribute the
uneven water inflow process that is not conducive to the benefit throughout the year. As a result,
the downstream reservoir can freely adjust the discharge flow process of the reservoir according to
the water demand of the other benefit targets, so as to increase its own benefit as well as that to the
overall system.
This paper shows the water-level change process of 20 reservoirs in the upper reaches of the
Yangtze River when biased toward different benefit objectives in the wet year, together with the
equilibrium solution (Figure 9). It can be seen from the diagram that the variation range and amplitude
of the water level of each tributary leading the reservoirs in equilibrium solution are large due to the
small influence of other reservoir operation modes, but the water-level change of the reservoir in the
downstream position is much more stable. In addition, the water-level change of each reservoir in
the equilibrium solution is basically kept between the upper and lower outer lines of the range of
water-level variation when partial to the single-target solution. The results above, on the one hand,
show that the equilibrium solution does play a role in coordinating the benefit objectives and reflects
the influence of each objective on reservoir operation in the case of multi-objective comprehensive
optimization. On the other hand, it also shows the characteristics of the interaction between the
reservoirs in the reservoir system.

Water 2019,11, 2542 20 of 23
Water 2019, 11, x FOR PEER REVIEW 21 of 24
each reservoir in the equilibrium solution is basically kept between the upper and lower outer lines
of the range of water-level variation when partial to the single-target solution. The results above, on
the one hand, show that the equilibrium solution does play a role in coordinating the benefit
objectives and reflects the influence of each objective on reservoir operation in the case of
multi-objective comprehensive optimization. On the other hand, it also shows the characteristics of
the interaction between the reservoirs in the reservoir system.
Figure 9. The water-level process line of each reservoir under different partial schemes.
5. Conclusions
Taking the reservoir system composed of 30 controlled reservoirs in the upper reaches of the
Yangtze River as the research object under the condition of ensuring the restriction of flood control,
this paper discusses the competitive relationship among the four benefit objectives of power
generation, ecology, water supply, and shipping under the constraint of flood control and draws the
following conclusions:
Figure 9. The water-level process line of each reservoir under different partial schemes.
5. Conclusions
Taking the reservoir system composed of 30 controlled reservoirs in the upper reaches of the
Yangtze River as the research object under the condition of ensuring the restriction of flood control, this
paper discusses the competitive relationship among the four benefit objectives of power generation,
ecology, water supply, and shipping under the constraint of flood control and draws the following
conclusions:
(1).
Power generation is the main factor that restricts the other benefit functions of the reservoir,
and is restricted by them. During reservoir operation, it is more likely to sacrifice part of
power generation to improve the satisfaction of other benefits, among which the competitive
relationship with ecological objectives is the most obvious; there may be a competitive or
synergistic relationship between water supply and ecology under different water supply and
ecological demands; the shipping objective plays a limited role in restricting the realization of
other objectives, and the degree of influence from other objectives is also small compared with
the intensity of competition among other objectives.

Water 2019,11, 2542 21 of 23
(2). The benefit value of joint operation is greater than that of the separate operation, which is reflected
in the four objectives of power generation, ecology, water supply, and shipping. This is mainly
because in the joint operation, the water volume in the system has more room for distribution
in time and space. In addition, the operation of the downstream reservoirs will be affected by
the upstream reservoirs schedule because of the hydraulic connection that exists between the
upstream and downstream reservoirs. Reservoirs with larger water volume can supplement the
shortage of other reservoirs and reduce the wastewater in the system. Furthermore, reservoirs
with a strong regulation ability and large utilizable capacity, such as the Three Gorges Reservoir,
perform better in joint dispatching. This reflects the compensation and regulation function of
hydropower station systems in the integrated operation of reservoir groups.
This study shows the possibility of increasing the comprehensive benefits of the giant reservoir
system in the upstream of the Yangtze River, which matches the development requirements of our
country. This modeling method and analysis idea can also be applied to other river basins and
reservoir systems in order to promote local development and fully excavate the utilization value of
water resources.
However, there is still a need for improvement in this study. Some more refined quantitative
analysis methods can be used to analyze the relationship between the four benefit objectives. In addition,
the flood control may be regarded as one of the research objectives, and the refined dispatching mode
with smaller step size in the flood season can be studied to optimize the benefit of the reservoir system
throughout the year. Furthermore, the hydraulic model and hydrological model can be combined to
deepen the thinking of the multi-objective optimization problem.
Author Contributions:
Conceptualization, M.C.; Formal analysis, M.C.; Funding acquisition, Z.D.; Methodology,
M.C.; Project administration, Z.D. and W.J.; Software, M.C., X.N. and W.J.; Supervision, Z.D., W.J.; Validation,
X.N.; Visualization, M.C. and H.Y.; Writing—original draft, M.C.; Writing—review & editing, M.C. and W.J.
Funding:
This research was funded by the National Key Research and Development Project of China, grant
number 2016YFC0402209.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Duan, C.; Chen, B. Energy–Water nexus of international energy trade of China. Appl. Energy
2017
,194,
725–734. [CrossRef]
2.
Giuliani, M.; Anghileri, D.; Castelletti, A.; Vu, P.N.; Soncini-Sessa, R. Large storage operations under climate
change: Expanding uncertainties and evolving tradeoffs. Environ. Res. Lett. 2016,11, 35009. [CrossRef]
3.
Chang, X.; Liu, X.; Zhou, W. Hydropower in China at present and its further development. Energy
2010
,35,
4400–4406. [CrossRef]
4.
Wang, X.; Chang, J.; Meng, X.; Wang, Y. Short-term hydro-thermal-wind-photovoltaic complementary
operation of interconnected power systems. Appl. Energy 2018,229, 945–962. [CrossRef]
5.
Uen, T.; Chang, F.; Zhou, Y.; Tsai, W. Exploring synergistic benefits of Water-Food-Energy Nexus through
multi-objective reservoir optimization schemes. Sci. Total Environ. 2018,633, 341–351. [CrossRef]
6.
Meng, X.; Chang, J.; Wang, X.; Wang, Y. Multi-objective hydropower station operation using an improved
cuckoo search algorithm. Energy 2019,168, 425–439. [CrossRef]
7.
Bozorg-Haddad, O.; Janbaz, M.; Lo
á
iciga, H.A. Application of the gravity search algorithm to multi-reservoir
operation optimization. Adv. Water Resour. 2016,98, 173–185. [CrossRef]
8.
Nagesh Kumar, D.; Janga Reddy, M. Multipurpose Reservoir Operation Using Particle Swarm Optimization.
J. Water Res. Plan. Manag. 2007,133, 192–201. [CrossRef]
9.
Afshar, M.H. Large scale reservoir operation by Constrained Particle Swarm Optimization algorithms. J.
Hydro Environ. Res. 2012,6, 75–87. [CrossRef]
10.
Lu, B.; Li, K.; Zhang, H.; Wang, W.; Gu, H. Study on the optimal hydropower generation of Zhelin reservoir.
J. Hydro Environ. Res. 2013,7, 270–278. [CrossRef]

Water 2019,11, 2542 22 of 23
11.
Islam, S.; Talukdar, B. Application of artificial immune system in optimization of reservoir operation. Int. J.
Water Resour. Manag. 2012,3, 241–254.
12.
Zhang, Z.; Zhang, S.; Wang, Y.; Jiang, Y.; Wang, H. Use of parallel deterministic dynamic programming and
hierarchical adaptive genetic algorithm for reservoir operation optimization. Comput. Ind. Eng.
2013
,65,
310–321. [CrossRef]
13.
Chang, J.; Meng, X.; Wang, Z.; Wang, X.; Huang, Q. Optimized cascade reservoir operation considering ice
flood control and power generation. J. Hydrol. 2014,519, 1042–1051. [CrossRef]
14.
Yaseen, Z.; Allawi, M.; Karami, H.; Ehteram, M.; Farzin, S.; Najah, A.; Koting, S.; Mohd, N.; Jaafar, W.;
Afan, H.; et al. A hybrid bats—Warm algorithm for optimizing dam and reservoir operation. Neural Comput.
Appl. 2019,31, 8807–8821. [CrossRef]
15.
Karami, H.A.E.M. Optimization of energy management and conversion in the water systems based on
evolutionary algorithms. Neural Comput. Appl. 2019,31, 5951–5964. [CrossRef]
16.
Ehteram, M.; Mousavi, S.; Karami, H.; Farzin, S.; Emami, M.; Binti Othman, F.; Amini, Z.; Kisi, O.; El-Shafie, A.
Fast convergence optimization model for single and multi-purposes reservoirs using hybrid algorithm. Adv.
Eng. Inform. 2017,32, 287–298. [CrossRef]
17.
Zitzler, E.; Thiele, L. An evolutionary algorithm for multiobjective optimization: The strength Pareto
approach. In Computer Engineering and Networks Laboratory (TIK); Swiss Federal Institute of Technology
Zürich (ETH): Zürich, Switzerland, 1998.
18.
Deb, K.; Jain, H. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based
Nondominated Sorting Approach, Part I: Solving Problems with Box Constraints. IEEE Trans. Evol. Comput.
2014,18, 577–601. [CrossRef]
19.
Cheng, W.; Huang, C.; Hsu, N.; Wei, C. Risk Analysis of Reservoir Operations Considering Short-Term Flood
Control and Long-Term Water Supply: A Case Study for the Da-Han Creek Basin in Taiwan. Water
2017
,9,
424. [CrossRef]
20.
Tilmant, A.; Goor, Q.; Pinte, D. Agricultural-to-hydropower water transfers: Sharing water and benefits in
hydropower-irrigation systems. Hydrol. Earth Syst. Sci. 2009,13, 1091–1101. [CrossRef]
21.
Wu, Y.; Chen, J. Estimating irrigation water demand using an improved method and optimizing reservoir
operation for water supply and hydropower generation: A case study of the Xinfengjiang reservoir in
southern China. Agric. Water Manag. 2013,116, 110–121. [CrossRef]
22.
Si, Y.; Li, X.; Yin, D.; Li, T.; Cai, X.; Wei, J.; Wang, G. Revealing the water-energy-food nexus in the Upper
Yellow River Basin through multi-objective optimization for reservoir system. Sci. Total Environ.
2019
,682,
1–18. [CrossRef] [PubMed]
23.
Veintimilla-Reyes, J.; De Meyer, A.; Cattrysse, D.; Tacuri, E.; Vanegas, P.; Cisneros, F.; Van Orshoven, J. MILP
for Optimizing Water Allocation and Reservoir Location: A Case Study for the Mach
á
ngara River Basin,
Ecuador. Water 2019,11, 1011. [CrossRef]
24.
Wu, L.; Bai, T.; Huang, Q.; Wei, J.; Liu, X. Multi-Objective Optimal Operations Based on Improved NSGA-II
for Hanjiang to Wei River Water Diversion Project, China. Water 2019,11, 1159. [CrossRef]
25.
Alahdin, S.; Ghafouri, H.R.; Haghighi, A. Multi-reservoir System Operation in Drought Periods with
Balancing Multiple Groups of Objectives. KSCE J. Civ. Eng. 2019,23, 914–922. [CrossRef]
26.
Yang, G.; Guo, S.; Liu, P.; Li, L.; Xu, C. Multiobjective reservoir operating rules based on cascade reservoir
input variable selection method. Water Resour. Res. 2017,53, 3446–3463. [CrossRef]
27.
Chen, M.; Chen, G.; Chen, J.; Fang, Q. Practices and achievements of multi-reservoir-joint dispatching in the
upper reaches of the Yangtze River in 2018. China Flood Drought Manag. 2019,29, 6–9.
28.
Huang, L.; Li, X.; Fang, H.; Yin, D.; Si, Y.; Wei, J.; Liu, J.; Hu, X.; Zhang, L. Balancing social, economic and
ecological benefits of reservoir operation during the flood season: A case study of the Three Gorges Project,
China. J. Hydrol. 2019,572, 422–434. [CrossRef]
29.
Liu, X.; Lu, C.; Zhu, Y.; Singh, V.P.; Geng, Q.; Guo, X. Multi-objective reservoir operation during flood season
considering spillway optimization. J. Hydrol. 2017,552, 554–563. [CrossRef]
30.
Zhou, Y.; Guo, S.; Xu, C.Y.; Pan, L.; Hui, Q. Deriving joint optimal refill rules for cascade reservoirs with
multi-objective evaluation. J. Hydrol. 2015,524, 166–181. [CrossRef]
31.
Jia, W.; Dong, Z.; Duan, C.; Ni, X.; Zhu, Z. Ecological reservoir operation based on DFM and improved
PA-DDS algorithm: A case study in Jinsha river, China. Hum. Ecol. Risk Assess. Int. J.
2019
, 1–19. [CrossRef]

Water 2019,11, 2542 23 of 23
32.
Wang, X.M.; Zhou, J.Z.; Ou Yang, S.; Zhang, Y.C. TGC eco-friendly generation multi-objective optimal
dispatch model and its solution algorithm. J. Hydraul. Eng. 2013,44, 154–163.
33.
Lu, Y.L.; Zhou, J.Z.; Wang, H.; Zhang, Y.C. Multi-objective optimization model for ecological operation in
Three Gorges cascade hydropower stations and its algorithms. Adv. Water Sci. 2011,22, 780–788.
34.
Zhou, J.; Li, C.; Chen, F.; Zhang, Y. Integrated utilization of the Three Gorges Cascade for navigation and
power generation in flood season. J. Hydraul. Eng. 2017,48, 31–40.
35.
Zhou, J.; Zhang, Y.; Zhang, R.; Ouyang, S.; Wang, X.; Liao, X. Integrated optimization of hydroelectric energy
in the upper and middle Yangtze River. Renew. Sustain. Energy Rev. 2015,45, 481–512. [CrossRef]
36. Jin, N.I.; Cui, S.; Tian, L.I.; Jin, L. On water demand of river ecosystem. J. Hydraul. Eng. 2002,9, 14–26.
37.
Das, I.; Dennis, J.E. Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in
Nonlinear Multicriteria Optimization Problems. SIAM J. Optim. 1998,8, 631–657. [CrossRef]
38.
Ni, X.; Dong, Z.; Xie, W.; Jia, W.; Duan, C.; Yao, H. Research on the Multi-Objective Cooperative Competition
Mechanism of Jinsha River Downstream Cascade Reservoirs during the Flood Season Based on Optimized
NSGA-III. Water 2019,11, 849. [CrossRef]
39.
Chen, C.; Yuan, Y.; Yuan, X. An Improved NSGA-III Algorithm for Reservoir Flood Control Operation. Water
Resour. Manag. 2017,31, 4469–4483. [CrossRef]
40.
Tian, Y.; Cheng, R.; Zhang, X.; Jin, Y. PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective
Optimization [Educational Forum]. IEEE Comput. Intell. Mag. 2017,12, 73–87. [CrossRef]
41.
Zitzler,E.; Thiele, L.; Laumanns, M.; Fonseca, C.M.; Da Fonseca, V.G.Performance assessment of multiobjective
optimizers: An analysis and review. IEEE Trans. Evol. Comput. 2003,7, 117–132. [CrossRef]
42.
Fleischer, M. The Measure of Pareto Optima Applications to Multi-Objective Metaheuristics; Evolutionary
Multi-Criterion Optimization: Berlin/Heidelberg, Germany, 2003; pp. 519–533.
©
2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).