Journal of Hydrology 524 (2015) 166–181
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Deriving joint optimal refill rules for cascade reservoirs with
multi-objective evaluation
Yanlai Zhou a,b,⇑, Shenglian Guo a, Chong-Yu Xu a,c, Pan Liu a, Hui Qin b
a
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Changjiang River Scientific Research Institute, Wuhan 430010, China
c
Department of Geosciences, University of Oslo, Norway
b
a r t i c l e
i n f o
Article history:
Received 28 November 2014
Received in revised form 19 February 2015
Accepted 20 February 2015
Available online 28 February 2015
This manuscript was handled by Geoff
Syme, Editor-in-Chief
Keywords:
Joint optimal refill rule
Multi-objective evaluation
Flood control risk
Utilization benefits analysis
Cascade reservoirs
s u m m a r y
Reservoirs are one of the most efficient infrastructures for integrated water resources development and
management; and play a more and more important role in flood control and conservation. Optimal refill
operation before the end of flood season is a valuable and effective approach to compromise the flood
control, hydropower generation and comprehensive utilization of water resources of river basins. An
integrated model consisting of a flood control risk analysis module, a utilization benefits analysis module
and a multi-objective evaluation module was proposed in this study to derive joint optimal refill rules for
cascade reservoirs. The Jinsha River and Three Gorges cascade reservoirs in the Changjiang River basin of
China are selected for a case study. Sixty-one years of observed daily runoff data from 1950 to 2010 have
been used to test the model. The results indicate that the proposed model can make an effective tradeoff
between flood control and utilization benefits. Joint optimal synchronous and asynchronous refill rules
can generate 3.25% and 2.78% more annual average hydropower, respectively and improve the fullness
storage rate without increasing flood control risk comparing with the original designed operating rules.
Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction
Climate change, rapid economic development and increase of
the human population are considered as the major triggers of
increasing water-related challenges all over the world. The necessity of efficient planning and management for water resources
becomes more and more urgent. Reservoirs play a vital role in
regulating water resources in different space and time through
optimal operation (Labadie, 2004; Guo et al., 2004; Jia et al.,
2014). Reservoir reoperation to balance human and ecological
water requirements may be a potential approach to alleviate the
effects of climatic and socio-economic changes.
Operating rules are often used to provide guidelines for reservoir releases to obtain the best interests of the whole reservoir system, consistent with certain inflow and existing storage levels (Tu
et al., 2003; Chang et al., 2005). They are often predefined at the
planning stage of the reservoir construction through simulation
techniques. The operating rule curve is one of the most simple
and frequently used ways for guiding and managing the reservoir
operation (Liu et al., 2011a). It is usually presented in the form of
⇑ Corresponding author at: Changjiang River Scientific Research Institute, Wuhan
430010, China. Tel./fax: +86 27 68773568.
E-mail address: zyl23bulls@whu.edu.cn (Y. Zhou).
http://dx.doi.org/10.1016/j.jhydrol.2015.02.034
0022-1694/Ó 2015 Elsevier B.V. All rights reserved.
graphs or tables to guide release of the reservoir systems according
to actual storage level, hydro-meteorological conditions and time
of year (Yeh, 1985; Ngo et al., 2007). Consequently, it is desirable
to do research on how to find effective operating rules aimed at
significantly increasing utilization benefits for flood control, energy
production, navigation, ecology as well as water supply.
Some reservoir operating rules are typically applicable to reservoir refill. Clark (1956) proposed the New York City rule (NYC),
which used probability of spills rather than direct amounts of physical spill in the minimization of expected shortages. Bower et al.
(1966) proposed a space rule, as a special case of the NYC rule,
which tried to minimize the total volume of spills. Jain et al.
(1998) carried out a reservoir operation study for the India’s
Sabarmati River System using historically observed flows, and
developed a judicious operation policy for conservation and flood
control using simulation techniques. Lund and Guzman (1999)
explored the LP-NYC rule, which had the advantage of being able
to incorporate other short-term reservoir operation constraints,
e.g. minimum or maximum flows downstream of each reservoir
or required diversions below a subset of reservoirs. Liu et al.
(2006) developed a dynamic programming neural-network simplex model using a simulation-based optimization method to
derive refill rules for the Three Gorges Reservoir (TGR). They show
that it performs better than original design rule curves. Liu et al.
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
(2011b) proposed a multi-objective refill operation model for single reservoir by combining flood control and conservation together. The simulation–optimization-test framework and hybrid multiobjective genetic algorithm were used to optimize the rule curves
of TGR. Li et al. (2013) developed a refill operation model coupling
a flood risk module with utilization benefits analysis module to
derive the optimal refill rule of TGR. Wang et al. (2014) proposed
a joint refill operation model for cascade reservoir solved by using
electromagnetism-like mechanism algorithm, however, they did
not evaluate those refill rules combining with flood risk and utilization benefits analysis.
Current studies of optimal refill operation paid more attention
to single reservoir rather than cascade reservoirs. The aim of this
study is to develop a joint optimal refill operation model for cascade reservoirs. Since there are hydraulic connections and storage
compensations between the upstream and downstream reservoirs
in cascade reservoirs, the optimal refill operation will become
more and more complex as the number of reservoirs increases. In
this study, a joint optimal refill operation model for cascade reservoirs is proposed and developed to solve the conflict between the
flood control and refill operation. The Jinsha River cascade reservoirs and the Three Gorges cascade reservoirs in the Changjiang
River basin of China are selected as a case study.
The paper is organized as follows: Section 2 briefly introduces
the study area, after which the current operation rules of the investigated cascade reservoirs are discussed. Section 3 describes the
method adopted in this study, which comprises three parts: introduction of a general framework for joint optimal refill operation
model by firstly setup a flood control risk analysis module
(Section 3.1), secondly setup a utilization benefits analysis module
(Section 3.2), and finally setup a multi-objective evaluation module
(Section 3.3). In Section 4 simulation results for the cascade reservoirs are presented and discussed. The conclusions are drawn in
Section 5.
2. Jinsha River and Three Gorges cascade reservoirs
The Changjiang River or Yangtze, known in China as the ‘‘long
river’’, is the longest river in Asia and the third-longest river in
the world. It flows for 6418 km from glaciers on Qinghai-Tibet
Plateau (where it is called the Jinsha River) eastward across southwest, central and eastern China before emptying into the East
China Sea at Shanghai. It is also one of the biggest rivers by discharge volume in the world. The Changjiang drains one-fifth of
the land area of China, and its river basin is home to one-third of
the nation’s population. The Jinsha River cascade reservoirs
167
(Xiluodu, Xiangjiaba) and Three Gorges cascade reservoirs (Three
Gorges, Gezhouba) as shown in Fig. 1 are selected as case study.
Since the Gezhouba reservoir is a run-of-the-river hydropower
plant with small regulation storage, joint optimal refill operation
model is only applied to simulate reoperation of the Xiluodu reservoir, Xiangjiaba reservoir and TGR.
The Jinsha River’s basin area is 0.47 million km2. At the end of
the Jinsha River, two-step cascade reservoirs have been constructed comprising from upstream to downstream Xiluodu and
Xiangjiaba reservoirs, the distances between them are 151 km.
The Xiluodu reservoir is the third largest water conservancy project ever undertaken in the world, with a normal pool level at
600 m above mean sea level and a total reservoir storage capacity
of 12.91 billion m3, of which 4.65 billion m3 is flood control storage
and 6.46 billion m3 is conservation regulating storage. The
Xiangjiaba reservoir is the third largest water conservancy project
ever undertaken in China, with a normal pool level at 380 m above
mean sea level and a total reservoir storage capacity of 5.20 billion
m3, of which 0.903 billion m3 is flood control storage and 0.903 billion m3 is conservation regulating storage.
The TGR is a vitally important and backbone project in the
development and harnessing of the Changjiang River in China.
The upstream of Changjiang River is intercepted by the TGR, with
a length of the main course about 4.5 103 km and a drainage area
of 1.00 million km2. The TGR is the largest water conservancy project ever undertaken in the world, with a normal pool level at
175 m above mean sea level and a total reservoir storage capacity
of 39.3 billion m3, of which 22.15 billion m3 is flood control storage
and 16.5 billion m3 is conservation regulating storage, accounting
for approximately 3.7% of the dam site mean annual runoff of
451 billion m3. The Gezhouba reservoir is located at the lower
end of the TGR in the suburbs of Yichang City, 38 km downstream
of the TGR. The dam is 2606 m long and 53.8 m high, with a total
storage capacity of 1.58 billion m3 and a maximum flood discharging capability of 110,000 m3/s.
The main functions of the cascade reservoirs are flood control,
power generation, water supply as well as navigation, etc. The
characteristic parameter values of the totally four cascade reservoirs are given in Table 1. The original operation water levels during the annual cycle in Xiluodu reservoir, Xiangjiaba reservoir and
TGR are shown in Fig. 2 (HCCEC, 2013), Fig. 3 (HCZEC, 2013) and
Fig. 4 (CWRC, 1997), respectively. Only the designed operating rule
curves of the TGR are described briefly, because those of others are
similar. According to the Chinese Flood Control Act, reservoir water
levels generally are not allowed to exceed the flood limited water
level (FLWL) during flood season in order to offer adequate storage
Fig. 1. Sketches of the Jinsha River basin and TGR basin in China.
168
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Table 1
List of characteristic parameter values of these four reservoirs.
Reservoir
Unit
8
Total storage
Flood control storage
Crest elevation
Normal pool level
Flood limited water level
Install capability
Annual average hydropower generation
Regulation ability
3
10 m
108 m3
m
m
m
MW
Billion kW h
–
Xiluodu
Xiangjiaba
TGR
Gezhouba
115.7
46.5
610
600
560
13,860
57.24
Seasonal
51.63
9.03
384
380
370
7750
30.75
Seasonal
393
221.5
185
175
145.0
22,400
84.7
Seasonal
15.8
–
70
66
–
2715
15.7
Daily
610
Region A
Reservoir water level (m)
600
Region
B
590
Region C
Region
B
Region A
580
570
Region D
560
550
Region
C
540
Month
July
Upper boundary
Curve (m)
Lower boundary
Curve (m)
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
560.0 560.0 580.0 600.0 600.0 600.0 600.0 592.0 580.0 565.0 540.0 560.0
540.0 560.0 580.0 600.0 600.0 585.0 580.0 572.0 560.0 545.0 540.0 540.0
Fig. 2. The original operating rule curves of Xiluodu reservoir.
382
Region A
Reservoir water level (m)
380
Region
B
378
376
374
Region
B
Region C
Region C
Region D
Region A
372
370
368
Month
Upper boundary
Curve (m)
Lower boundary
Curve (m)
July
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
370.0 370.0 375.0 380.0 380.0 380.0 380.0 380.0 380.0 378.0 376.0 370.0
370.0 370.0 370.0 373.0 378.0 380.0 378.0 376.0 374.0 372.0 370.0 370.0
Fig. 3. The original operating rule curves of Xiangjiaba reservoir.
for flood prevention (Li et al., 2010; Zhou and Guo, 2014). The
water level of TGR will be kept at between 145 m and 175 m
depending on flood control needs (region A). Although it is hard
to capture when typical floods occur in TGR, the reservoir can offer
enough flood storage capacity for a 1000-year design flood. During
the refill period, the storage level will be raised from the FLWL on
October 1 to the normal pool level by the end of October. If the
storage level is below the normal pool level by the end of
October, water level rising will continue into November. From
November to the end of April in the following year, the water level
of the reservoir will generally be operated at region B or C and it
will be lowered gradually through operation of the hydropower
plant, which depends on the inflow. In some wet years, water
should be spilled to ensure the reservoir water level not to exceed
175 m when it is on the top of upper boundary curve. However, in
normal or dry years, the inflow is not enough to satisfy the need of
generating the firm output which is very important to the stability
of the power system, and then the water level of the reservoir will
be lowered gradually to offer adequate release discharge for generating the firm output (region C), otherwise the generators are
turned to maximum output if the water level is in region B. In some
abnormal dry year, firm output can’t be satisfied and output will be
169
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Fig. 4. The original operating rule curves of TGR.
Table 2
The start and end time for three refill operation schemes.
Refill time
Schemes
Cascade reservoirs
Xiluodu
Xiangjiaba
TGR
Starting time
SOP
Synchronous refill
Asynchronous refill
September 10
August 20–September 10
August 20–September 5
September 10
August 20–September 10
August 25–September 10
October 1
August 20–September 10
September 1–September 10
Ending time
SOP
Synchronous refill
Asynchronous refill
September 30
September 30
September 30
September 30
September 30
September 30
October 31
October 31
October 31
decreased, and the storage level will be dropped below the lower
boundary curve (region D). The designed operating rules can be
regarded as a standard operating policy (SOP) (Liu et al., 2006;
Liu et al., 2011a,b; Li et al., 2013; Zhou et al., 2014). The SOP means
that the reservoir water level should be increased from annual
FLWL to normal pool level linearly.
Based on the SOP, the proposed refill rule proved by the
Ministry of Water Resources (MWR, 2009), Changjiang Water
Resources Commission (CWRC, 2010) as well as administrators
can be regarded as reoperation refill rule for individual reservoir.
The following boundary conditions and constraints should be considered: (1) the starting time of refill operation cannot be further
advanced to the end of main-flood season; (2) the starting water
level is equal to annual FLWL; (3) the phased water level is less
than or equal to seasonal FLWL. The seasonal FLWL and its flood
risk are determined by flood control risk analysis based on flood
seasonality (Chen et al., 2010; Liu et al., 2011b; Li et al., 2013;
Zhou and Guo, 2014). The start and end times for three refill operation schemes (including SOP, synchronous refill time, asynchronous refill time) are shown in Table 2. Time step for the start
time of refill operation is equal to 5 or 6 days. Besides, the end of
main-flood season for Changjiang River basin is not earlier than
August 20 (Liu et al., 2011b; Li et al., 2013; Zhou and Guo, 2014).
3. Development of methodology
The general framework of joint optimal refill operation model
for cascade reservoirs is shown in Fig. 5. The proposed model consists of three modules: (1) a flood control risk analysis module
based on flood seasonality for determining seasonal FLWL and
evaluate its flood risk, (2) a utilization benefits analysis module
based on the proposed refill rules for evaluating utilization benefits
for three refill operation schemes of the cascade reservoirs, (3) a
multi-objective evaluation module based on projection pursuit
method and optimization algorithm for deriving joint optimal refill
rules with multi-objective evaluation.
3.1. Flood control risk analysis module
3.1.1. Flood control operating rules
The prerequisite of refill earlier for Jinsha River cascade reservoirs and Three Gorges cascade reservoirs is that it shall not
increase the flood control risk in the middle and lower reaches of
the Changjiang River basin compared with SOP. The current flood
control operating rules of Jinsha River cascade reservoirs (HCCEC,
2013; HCZEC, 2013) and Three Gorges cascade reservoirs (CWRC,
1997; MWR, 2009; Zhou et al., 2014; Wang et al., 2014) are shown
in Table 3.
3.1.2. Flood control risk analysis
Risk is a complex and difficult concept, and there is still no consensus on how the risk should be expressed and interpreted (Aven
and Pörn, 1998; Emma et al., 2006). For cascade reservoirs, more
and more researchers noticed that realistic economic or utility analysis must take account of both the frequency and the severity of
failure (Botzen et al., 2009; Lind et al., 2009).
To determine seasonal FLWL, the iterative calculation methods
are used to regulate seasonal design inflow hydrographs (Xiao
et al., 2009; Li et al., 2010, 2011b; Liu et al., 2011b; Zhou and
Guo, 2014). The intersection of these seasonal FLWLs, named the
highest safety water level Z0, is the highest storage level that can
regulate seasonal design inflow hydrograph safely, and the capacity below Z0 is used to regulate large flows during the refill period.
Reservoir refill operation can be carried out according to the refill
rule curve when no floods occur. In this way, flood control is combined with reservoir refill operation as shown in Fig. 6.
170
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Two indexes of flood control risk Rf and flood loss rate Rs are
used to evaluate the risks of different refill rules (Li et al., 2013;
Zhou and Guo, 2014). Rf represents the frequency of flood control
risk events occurrence; Rs represents the occupancy degree of
storage capacity used for regulating the seasonal design inflow,
which can reflect the extent of losses in the downstream area indirectly. The losses in the downstream area suffered from flood disaster mainly depend on the flood volume that cannot be retained
in the reservoir. The bigger the value of Rs is, the worse the flood
losses at the downstream region are. They can be expressed as
Rf ¼ PðZ f max > Z 0 Þ ¼ nf =n
ð1Þ
where n is the total number of the simulated calculation; Zfmax is
the highest water level; nf is the time of Zfmax being higher than Z0.
( ðV
Rs ¼
The number of refill rules N=N+1
f max V 0 Þ
ðV nor V 0 Þ
0
V f max P V 0
ð2Þ
V f max < V 0
V ¼ f ðZÞ
ð3Þ
where V0 and Vnor are the storage capacities corresponding to the
highest safety water level and the Normal pool level, respectively;
Vfmax is the storage capacity corresponding to Zfmax; (Vnor V0) is
the part of storage capacity used for regulating the seasonal design
inflow for a certain return period; (Vfmax V0) is the part of
(Vnor V0) to be occupied.
To calculate the Rf and Rs, a flood control risk module has been
developed as shown in Fig. 7. The procedure is described as
follows:
Yes
N< Nmax
No
Multi-objective evaluation module
Deriving the joint optimal refill rules
Fig. 5. The general framework of joint optimal refill operation model for cascade
reservoirs.
Step 1: Input initial data series including the selected refill rule,
seasonal design inflow hydrographs for a given return period,
and historical daily inflow series, etc.
Step 2: Assuming an initial water level Zb,g based on which the
highest water level Zmax can be ascertained by flood regulating
calculation according to the flood control operating rules during
the refill period. If Zmax is less than the normal pool level Znor,
Zb,g is increased by a given step size (DZ = 0.1) with the iterative
calculation. Otherwise, Zb,g is taken as the seasonal FLWL Z0,g. If
all the seasonal design inflow hydrographs have been calculated, the intersection of these seasonal FLWLs is taken as the
highest safety water level. Otherwise, g = g + 1.
Step 3: Historical daily inflow series are used to simulate the
refill operation which is guided by the selected refill rule. The
highest water level is denoted by Zf,i in the ith year. Then, the
Rf and Rs corresponding to a certain return period can be calculated by Eqs. (1) and (2), respectively.
Table 3
The current flood control operating rules of cascade reservoirs.
Reservoir
Reservoir inflow
Qin (m3/s)
Water level
in dam Z (m)
Water level in
Shashi station Z0 (m)
Reservoir outflow
Qout (m3/s)
Xiluodu
Qin 6 7000
7000 < Qin 6 10,000
10,000 < Qin 6 20,000
20,000 < Qin 6 30,000
Qin > 30,000
–
–
–
–
–
–
–
–
–
–
Qout = Qin
Qout = 7000
Qout = 8000
Qout = 15,000
Qout = 20,000
Xiangjiaba
Qin 6 7000
7000 < Qin 6 10,000
10,000 < Qin 6 20,000
20,000 < Qin 6 30,000
Qin > 30,000
–
–
–
–
–
–
–
–
–
–
Qout = Qin
Qout = 7000
Qout = 8000
Qout = 15,000
Qout = 20,000
TGR
Qin 6 76,200
Z 6 145.0
145.0 < Z < 166.9
Z 6 166.9
–
Z 6 166.9
Z > 166.9
Z 6 175.0
Z > 175.0
Z0 6 43.0
Z0 6 43.0
–
Z0 6 44.5
–
–
–
–
Qout 6 39,900
Qout = 39,900
Discharge by releasing capacity
Qout 6 53,900
Qout 6 53,900
Qout 6 76,000
Qout 6 Qin
Discharge by releasing capacity
Qin > 76,200
Qin 6 82,200
82,200 < Qin 6 97,400
97,400 < Qin 6 111,500
Qin > 111,500
171
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Step 1: Input initial data series including the selected refill rule
of and historical daily inflow series, etc.
Step 2: Determining the preliminary reservoir storage level at
each calculation interval according to the refill curve of the
selected rule, and calculating the corresponding water discharge Qout by the water balance equation. If Qout exceeds the
safety discharge in the downstream Qsafe, then let Qout = Qsafe.
Step 3: Calculating the output of the hydropower plant Ns by
Ns ¼ min½AQ out H; f N ðHÞ
Fig. 6. Sketch of the highest safety water level and seasonal FLWL.
3.2. Utilization benefits analysis module
A utilization benefits analysis module has been developed to
obtain the evaluation indexes (Li et al., 2013), as shown in Fig. 8.
This module can analyze utilization benefits of the refill operation
which is guided by the proposed refill rules. The historical daily
inflow series are employed as the input data to simulate the refill
operation. The procedures are described as follows:
ð4Þ
where A is the coefficient of hydropower generation; H is the average water head; min[] is the function getting the minimum value
and fN() is the function expressing the relationship between the
maximum output Nmax and H.
If Ns is less than the firm output Np, then let Ns = Np. A temporary
water discharge Qtemp is calculated by Qtemp = Np/AH; If
|Qout Qtemp| is greater than a satisfying accuracy (e = 0.1), then
Q out ¼ ðQ out þ Q temp Þ=2 and steps 2–3 are repeated. Otherwise, let
Qout = Qtemp. If Ns is greater than Ny, the release discharge for
hydropower plants Qo is calculated by Qo = Ny/(AH) and the spilled
water Qw is the difference between Qout and Qo.
Step 4: Calculating the reservoir water level. If the reservoir
water level is greater than the normal pool level, let Qout = Qin
(reservoir inflow), in order to ensure that the reservoir water
level is not increase.
No
Historical inflow series
Seasonal design inflow
hydrographs
Flood routing
Zb,g=Zb,g+ΔZ
i > imax
Calculating Z max by flood
routing
g =g +1
i = i +1
Start
Yes
Zf,1,Zf,2, ,Zf,i, ,Zf,n
Vfmax=max{f(Zf,i)}
Z max >Z nor
No
Yes
Z0,g=Zb,g
Z0=G(Z0,g)
V0=f(Z0)
Yes
g > gmax
Output Rf and Rs
Fig. 7. The flowchart of flood control risk module.
No
172
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Input initial data series
Calculate requirements of discharges by the proposed refill rules
it is very difficult to find a single index that is universally accepted
for evaluating the comprehensive utilization benefits. Therefore,
five evaluation indices which are flood control risk (Rf), flood loss
rate (Rs), hydropower generation, fullness storage rate and guarantee rate of navigation are selected to calculate the comprehensive
utilization benefits, including flood control as well as utilization
benefits. They are described as follows:
(1) Minimum flood control risk (R1)
Adapt discharges to satisfying requirements of flood control
min R1 ¼ min½maxðRf ;1 ; Rf ;2 ; ; Rf ;k ; ; Rf ;M Þ
Zup
Zdown
ð5Þ
(2) Minimum flood loss rate (R2)
Zlost
min R2 ¼ min½maxðRs;1 ; Rs;2 ; ; Rs;k ; ; Rs;M Þ
ð6Þ
(3) Maximum hydropower
generation (HG)
!
H=Zup-Zdown-Zlost
Ns=A·Qout·H
max HG ¼ max
M
X
HGk
ð7Þ
i¼1
N<N p
N<Ny
No
No
Yes
(4) Maximum fullness storage rate at the end of refill period
(FR)
!
max FR ¼ max
Yes
M
X
ak FRf ;k
ð8Þ
100%
ð9Þ
k¼1
Q temp2=N p /(A·H)
Ns=Ny
FRf ;k ¼
V khigh;i V kmin
V kmax V kmin
where
|Qout-Qtemp2|>e
Q e=N y /(A·H)
No
Yes
Qout=(Qout+Qtemp2)/2
Qs=Qout-Qe
Rf,k flood control risk of kth reservoir
Rs,k flood loss rate of kth reservoir
HGk hydropower generation of kth reservoir, kW h
FRf,k fullness storage rate of kth reservoir
V kmin the minimum storage capacity of kth reservoir, m3
V kmax the maximum storage capacity of kth reservoir, m3
V khigh;i the highest storage of kth reservoir in the ith year, m3
ak the weight for fullness storage rate of kth reservoir
M the number of reservoirs
Satisfy constraints
No
Yes
Output Utilization benefit indices
Fig. 8. The flowchart of utilization benefits analysis module.
3.3.2. Constraints
The following constraints should be satisfied in the flood
regulating and refill operation of Jinsha River and Three Gorges
cascade reservoirs:
(1) Water balance equation
h
i
V ki;jþ1 ¼ V ki;j þ Q kinði;jÞ Q koutði;jÞ Dt;
i ¼ 1; . . . ; ny ;
j ¼ 1; . . . ; mp
ð10Þ
Step 5: Validation constraints. Before going on to the next step,
make sure all of constraints are satisfied. Otherwise, steps 2–4
are repeated.
Step 6: Calculating the utilization benefit indices on the basis of
the reservoir inflow, water discharge, spilled water, storage
capacity and power output.
3.3. Multi-objective evaluation module
3.3.1. Multi-objective evaluation indices
Reservoir management and operation are one of the most complex problems in water resources management due to the multiobjective nature of reservoir operation. Since the function of
Jinsha River and Three Gorges cascade reservoirs is multi-purpose,
(2) Reservoir capacity
V kmin 6 V ki;j 6 V kmax ;
i ¼ 1; . . . ; ny ;
j ¼ 1; . . . ; mp
ð11Þ
(3) Power generation
Pkmin 6 Ak Q koði;jÞ Hki;j 6 Pkmax ;
i ¼ 1; . . . ; ny ;
j ¼ 1; . . . ; mp
ð12Þ
(4) Reservoir discharge
Q kmin 6 Q koutði;jÞ 6 Q ksafe ;
i ¼ 1; . . . ; ny ;
jQ koutði;jþ1Þ Q koutði;jÞ j 6 DQ k ;
j ¼ 1; . . . ; mp
i ¼ 1; . . . ; ny ;
j ¼ 1; . . . ; mp
ð13Þ
ð14Þ
173
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Start
Create initial population of chromosomes and initialize
the generation index Ngen =0
Calculate fitness, evaluate fitness, and rank the
chromosomes in descending order
Selection
Crossover
Mutation
Generate the first
offspring N
Generate the second
offspring N
Generate the third
offspring N
Evaluate and rank the obtained 3*N chromosomes, and
save the first N. Then, Ngen=Ngen+1.
Save the smart
chromosome
No
Ngen ≥ 2
Yes
Max. generation ?
Yes
No
Accelerating cycle: gain the new
interval of the variables
Obtain the joint
optimal refill rules
Fig. 9. Flowchart of the AGA.
(4) Navigation. It is noted that guarantee rates of navigation of
cascade reservoirs are improved to 99% by setting minimum
navigation flow (Peng et al., 2014; Wang et al., 2014).
Z kdmin
Z kdði;jÞ
6
Z kdði;jÞ
¼
f ðQ koutði;jÞ Þ;
6
Z kdmax ;
i ¼ 1; . . . ; ny ;
j ¼ 1; . . . ; mp
ð15Þ
Q koutði;jÞ the water discharge of kth reservoir on the jth day in the
ith year, and it equals sum of Q koði;jÞ and Q kwði;jÞ , m3/s
Q koði;jÞ the water discharge for hydropower generation of kth
reservoir on the jth day in the ith year, m3/s
Q kwði;jÞ the spilled water discharge of kth reservoir on the jth day
i ¼ 1; . . . ; ny ;
j ¼ 1; . . . ; mp
ð16Þ
where
in the ith year, m3/s
Pkmin the minimum power limits of kth hydropower plant, kW
Pkmax the maximum power limits of kth hydropower plant, kW
V ki;j the kth reservoir storage at the beginning of the jth day in
the ith year, m3
Q kmin the minimum water discharge for downstream of kth
reservoir, m3/s
Q kinði;jÞ the kth reservoir inflow on the jth day in the ith year,
Q ksafe the maximum water discharge for flood control safety
(shown in Table 3) in downstream of kth reservoir, m3/s
m3/s
174
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
DQk the maximum water discharge fluctuation of kth reservoir,
m3/s
Z kdmin the minimum water level at downstream of kth dam site,
m
Z kdmax the maximum water level at downstream of kth dam site,
m
Z kdði;jÞ the water level at downstream of kth dam site on the jth
day in the ith year, m
f() the function expressing the relationship between reservoir
water discharge and water level
3.3.3. Projection pursuit method
Projection pursuit method is one of effective multi-objective
evaluation means (Friedman and Turkey, 1974; Wang et al.,
2006). The steps of projection pursuit method include data standardization, linear projection, selecting projection index and projection pursuit optimization. To learn about the steps of
projection pursuit method, readers are referred to Wang et al.
(2006). As Friedman and Turkey (1974) pointed out, projection
pursuit method strongly depends on the ability of the optimization
algorithm to find substantive optima of the projection index
among a forest of dummy optima caused by sampling fluctuations.
Therefore, an efficient algorithm is one of the key issues of the projection pursuit method.
3.3.4. Accelerating genetic algorithm
Accelerating Genetic Algorithm (AGA, Yang et al., 2005; Wang
et al., 2006; Chen and Yang, 2007; Fang et al., 2009) is used to optimize the projection pursuit problem, as shown in Fig. 9. The steps
of AGA are composed of encoding, initialization of parent population, fitness evaluation, reproduction, crossover, mutation, evolution and iteration as well as accelerating cycle. In order to know
about the steps of AGA, readers are referred to Fang et al. (2009).
Generally, the operations of reproduction, crossover and mutation of genetic algorithm (GA) are executed in series. However, these operations are performed in parallel for AGA, which will further
protect the genetic information of each individual. Thus, AGA may
have much more opportunities to reach the global optimal solution
to GA. The interval accelerating mechanism in Step 8 accelerates
the convergence of the optimization process.
4. Results and discussion
4.1. Flood control risk analysis
refill operation and the return period of seasonal design inflow,
as shown in Tables 4 and 5. In other words, reservoir inflow
decreases gradually with the delay of the start time of refill operation or with the increase of the return period of seasonal design
inflow, which makes the highest safety water level increase
gradually.
Taking the start time Aug.20 of refill operation and 1000-year
seasonal design inflow of 1952 typical year as an example, the
Table 4
The highest safety water levels of cascade reservoirs corresponding to 1000-year
seasonal design inflow.
Start time of
refill operation
Typical
year
Aug.20
1952
1964
1952
1964
1952
1964
1952
1964
1952
1964
Aug.25
Sep.1
Sep.5
Sep.10
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
564.4
565.8
566.5
567.1
566.5
567.1
570.3
572.9
570.3
572.9
570.3
572.9
574.6
576.4
574.6
576.4
574.6
576.4
574.6
576.4
578.8
579.5
578.8
579.5
578.8
579.5
578.8
579.5
578.8
579.5
The highest safety water level of Xiangjiaba
reservoir (m)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
1952
1964
1952
1964
1952
1964
1952
1964
1952
1964
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
371.8
372.2
372.6
372.9
372.6
372.9
372.9
373.2
372.9
373.2
372.9
373.2
374.3
374.7
374.3
374.7
374.3
374.7
374.3
374.7
374.6
375.3
374.6
375.3
374.6
375.3
374.6
375.3
374.6
375.3
The highest safety water level of TGR (m)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
4.1.1. The proposed refill rules
Sixty-one years of observed daily runoff data from 1950 to 2010
have been used to analysis the proposed refill rules for cascade
reservoirs. The daily runoff data of Xiluodu reservoir and
Xiangjiaba reservoir is derived from reference hydrology station
Pingshan and the daily runoff data of TGR is derived from reference
hydrology station Yichang by revivification. Besides, the frequency
and magnitude of interval inflow between Xiangjiaba reservoir and
TGR is the same as that of Pingshan station and equal to the difference between Yichang station and Pingshan station. The highest
safety water levels for refill rules of Xiluodu reservoir, Xiangjiaba
reservoir and TGR based on joint operation of cascade reservoirs
corresponding to different seasonal design inflows (only taking
1000-year seasonal design inflow as an example) are summarized
in Table 4. The highest safety water levels for the proposed refill
rules (without considering refill operation of Xiluodu reservoir
and Xiangjiaba reservoir) of TGR based on single reservoir operation corresponding to 1000-year seasonal design inflow are summarized in Table 5 (Li et al., 2013). Generally speaking, the
highest safety water level is inversely related to the start time of
The highest safety water level of
Xiluodu reservoir (m)
1952
1964
1952
1964
1952
1964
1952
1964
1952
1964
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
155.7
162.3
162.5
163.9
162.5
163.9
166.9
167.5
166.9
167.5
166.9
167.5
167.8
168.5
167.8
168.5
167.8
168.5
167.8
168.5
169.6
171.2
169.6
171.2
169.6
171.2
169.6
171.2
169.6
171.2
Table 5
The highest safety water levels of TGR corresponding to 1000-year seasonal design
inflow (without considering refill operation of Xiluodu reservoir and Xiangjiaba
reservoir).
Start time of
refill operation
Typical
year
The highest safety water level of TGR (m)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Aug.20
1952
1964
154.6
161.9
161.6
163.3
166.6
167.1
167.1
168.0
168.8
169.4
Aug.25
1952
1964
161.6
163.3
166.6
167.1
167.1
168.0
168.8
169.4
Sep.1
1952
1964
166.6
167.1
167.1
168.0
168.8
169.4
Sep.5
1952
1964
167.1
168.0
168.8
169.4
Sep.10
1952
1964
168.8
169.4
175
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Table 6
The proposed synchronous refill rules of cascade reservoirs.
Number
Start time of
refill operation
Synchronous refill rules of Xiluodu reservoir (m)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
1
2
3
4
5 and 6 (SOP)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
560.0
563.0
560.0
567.0
564.0
560.0
569.0
568.0
564.0
560.0
571.0
571.0
568.0
564.0
560.0
573.0
573.0
572.0
571.0
570.0
593.0
593.0
592.0
592.0
590.0
Synchronous refill rules of Xiangjiaba reservoir (m)
1
2
3
4
5 and 6 (SOP)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
370.0
372.0
370.0
372.5
372.0
370.0
373.0
373.0
372.0
370.0
374.0
374.0
373.0
372.0
370.0
375.0
375.0
374.0
374.0
373.0
378.0
378.0
377.5
377.5
377.5
Synchronous refill rules of TGR (m)
1
2
3
4
5
6 (SOP)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.30
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Sep.30
145.0
147.0
145.0
150.0
148.0
145.0
152.0
150.0
148.0
145.0
154.0
152.5
150.5
148.0
145.0
156.0
155.0
153.0
151.0
148.0
145.0
160.0
160.0
158.0
157.0
154.0
145.0
162.0
162.0
160.0
160.0
158.0
145.0
Table 7
The proposed asynchronous refill rules of cascade reservoirs.
Number
Start time of
refill operation
Asynchronous refill rules of Xiluodu reservoir (m)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
1
2
3
4
5 (SOP)
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
560.0
563.0
560.0
567.0
564.0
560.0
569.0
568.0
564.0
560.0
571.0
571.0
568.0
564.0
560.0
573.0
573.0
572.0
571.0
570.0
593.0
593.0
592.0
592.0
590.0
Asynchronous refill rules of Xiangjiaba reservoir (m)
Aug.20
1
2
3
4 and 5 (SOP)
Aug.25
Sep.1
Sep.5
Sep.10
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
370.0
372.0
370.0
373.0
372.0
370.0
374.0
373.0
372.0
370.0
375.0
374.0
374.0
373.0
378.0
377.5
377.5
377.5
Asynchronous refill rules of TGR (m)
Aug.20
1
2
3 and 4
5 (SOP)
Aug.25
Sep.1
Sep.5
Sep.10
Sep.30
seasonal FLWLs corresponding to different seasonal stages are
564.4 m, 566.5 m, 570.3 m, 574.6 m, and 578.8 m for Xiluodu
reservoir, 371.8 m, 372.6 m, 372.9 m, 374.3 m, and 374.6 m for
Xiangjiaba reservoir as well as 155.7 m, 162.5 m, 166.9 m,
167.8 m, and 169.6 m for TGR, respectively. Besides, the seasonal
FLWLs corresponding to different seasonal stages for TGR (without
considering refill operation of Xiluodu reservoir and Xiangjiaba
reservoir) are 154.6 m, 161.6 m, 166.6 m, 167.1 m, and 168.8 m,
respectively. It is shown that the seasonal FLWLs for TGR increase
about 0.3–1.1 m considering refill operation of Xiluodu reservoir
and Xiangjiaba reservoir in 1952 typical year. The intersection of
these seasonal FLWLs for cascade reservoirs is selected as highest
safety water levels based on 1952 typical year, because these seasonal FLWLs are safer comparing with those of 1962 typical year.
For the three proposed refill operation schemes (including SOP,
synchronous refill time, asynchronous refill time) considering the
start time and time step of refill operation, the highest safety water
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Sep.30
145.0
148.0
145.0
150.5
148.0
145.0
153.0
151.0
148.0
145.0
158.0
157.0
154.0
145.0
160.0
160.0
158.0
145.0
levels are shown in Tables 6 and 7, respectively. The hydrographs
of SOP, synchronous and synchronous refill rules for cascade reservoirs are shown in Figs. 10 and 11, respectively.
4.1.2. Risk analysis
Sixty-one years of observed daily runoff data from 1950 to 2010
have been used to derive the flood control risk and flood loss rate
(Eqs. (5) and (6)) of the proposed refill rules for cascade reservoirs.
The risk analysis results are listed in Tables 8–10, respectively.
Generally speaking, the flood risk and flood risk loss rate decrease
gradually with the delay of the start time of refill operation or with
the decrease of the return period of seasonal design inflow. For the
start time of refill rules after Sep.5, the values of flood control risk
and flood loss rate are equal to zero and are not listed in Tables 8–
10. Besides, the values of flood control risk and flood loss rate for
TGR in Table 8 are less than those for TGR in Table 9. The main reason is that flood control pressure for TGR at the lower reach is
176
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Refill water level (m)
600
595
Start time of refill operation
590
Aug.20
585
Aug.25
580
575
Sep.1
Sep.5
Sep.10
570
565
Xiluodu reservoir
560
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Refill water level (m)
380
Start time of refill operation
378
376
374
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
372
Xiangjiaba reservoir
370
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Refill water level (m)
175
170
Start time of refill operation
Aug.20
165
160
Aug.25
Sep.1
Sep.5
155
150
Sep.10
Sep.30
TGR
145
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Sep.30
Fig. 10. The hydrographs of synchronous refill rules for cascade reservoirs.
reduced by flood control operation of Xiluodu reservoir and
Xiangjiaba reservoir at the upper reach. At the same time, the
values of flood control risk and flood loss rate of the proposed
synchronous refill rules for cascade reservoirs in Table 8 are
greater than those of the proposed asynchronous refill rules for
cascade reservoirs in Table 10. As a result of asynchronous
start time of refill operation, flood control pressure of asynchronous refill rules is markedly decreased by reserving flood
control storage among cascade reservoirs comparing with
synchronous refill rules.
For No. 1 of synchronous and asynchronous refill rules in Tables
8 and 10, the values of flood control risk and flood loss rate corresponding to 1000-year seasonal design flood hydrograph are 4.92%,
41.10%, 3.28% and 31.56% for Xiluodu reservoir, 3.28%, 38.75%,
1.64% and 18.60% for Xiangjiaba reservoir, and 3.28%, 46.84%,
0.00% and 0.00% for TGR. Compared with SOP, the values of flood
control risk and flood loss rate for synchronous and asynchronous
refill rules are increased because of raising the seasonal FLWLs in
the refill operation.
Above all, the flood control pressure is gradually increased for
SOP, asynchronous refill rules and synchronous refill rules.
However, joint optimal refill rules are required to make a balance
between flood risk and utilization benefits. As a result, it is necessary to analyze the utilization benefits of the proposed refill rules
for cascade reservoirs.
4.2. Utilization benefits analysis
Meanwhile, 61 years of observed runoff data from 1950 to 2010
have been used to analyze the utilization benefits of the proposed
refill rules for cascade reservoirs. Two evaluation indexes of
hydropower generation and fullness storage rate (Eqs. (7) and
(8)) are chosen as evaluation objectives of utilization benefits.
The annual average utilization benefits analysis results are listed
in Tables 11–13, respectively. It is shown that the proposed synchronous and asynchronous refill rules can improve the hydropower generation and fullness storage rate comparing with SOP for
cascade reservoirs. Furthermore, the values of hydropower generation and fullness storage rate for TGR in Table 11 are greater
than those for TGR in Table 12. The main reason is that water head
of hydropower generation for TGR at the lower reach is raised by
flood control operation of Xiluodu reservoir and Xiangjiaba reservoir at the upper reach. At the same time, the values of hydropower
generation and fullness storage rate of the proposed synchronous
refill rules for cascade reservoirs in Table 11 are also greater than
those of the proposed asynchronous refill rules for cascade reservoirs in Table 13. As a result of synchronous start time of refill
operation, hydropower generation and fullness storage rate of
asynchronous refill rules is markedly improved by raising water
head of hydropower generation for cascade reservoirs at the lower
reach comparing with asynchronous refill rules.
177
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Refill water level (m)
600
595
Start time of refill operation
590
Aug.20
585
Aug.25
580
575
Sep.1
Sep.5
Sep.10
570
565
Xiluodu reservoir
560
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Refill water level (m)
380
Start time of refill operation
378
376
Aug.25
Sep.1
Sep.5
374
Sep.10
372
Xiangjiaba reservoir
370
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Refill water level (m)
175
170
Start time of refill operation
Sep.1
165
160
Sep.5
Sep.10
Sep.30
155
150
TGR
145
Aug.20
Aug.25
Sep.1
Sep.5
Sep.10
Sep.15
Sep.25
Sep.30
Fig. 11. The hydrographs of asynchronous refill rules for cascade reservoirs.
Table 8
The risk analysis results of the proposed synchronous refill rules for cascade reservoirs.
Number
Start time of
refill operation
Refill rules for Xiluodu reservoir
1
Aug.20
2
Aug.25
3
Sep.1
Aug.20
SOP
Aug.25
SOP
Sep.1
SOP
Refill rules for Xiangjiaba reservoir
1
Aug.20
2
Aug.25
3
Sep.1
Aug.20
SOP
Aug.25
SOP
Sep.1
SOP
Refill rules for TGR
1
Aug.20
2
Aug.25
3
Sep.1
Aug.20
SOP
Aug.25
SOP
Sep.1
SOP
Risk (%)
Risk loss rate (%)
P = 0.2%
P = 0.1%
P = 0.2%
P = 0.1%
3.28
3.28
3.28
3.28
0.00
0.00
4.92
4.92
3.28
3.28
1.64
0.82
29.41
24.10
22.19
18.03
0.00
0.00
41.10
35.97
33.22
27.31
5.26
2.63
P = 0.2%
P = 0.1%
P = 0.2%
P = 0.1%
1.64
1.64
1.64
1.64
0.00
0.00
3.28
3.28
1.64
1.64
0.00
0.00
31.66
24.00
20.56
16.74
0.00
0.00
38.75
34.09
33.91
29.15
0.00
0.00
P = 0.2%
P = 0.1%
P = 0.2%
P = 0.1%
1.64
1.64
1.64
1.64
0.00
0.00
3.28
3.28
1.64
1.64
0.00
0.00
36.89
31.12
28.17
20.87
0.00
0.00
46.84
41.32
40.63
33.16
0.00
0.00
Risk (%)
Risk loss rate (%)
Risk (%)
Risk loss rate (%)
178
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Table 9
The risk analysis results of the proposed synchronous refill rules for TGR (without considering refill operation of Xiluodu reservoir and Xiangjiaba reservoir).
Number
Start time of
refill operation
Refill rules for TGR
P = 0.2%
P = 0.1%
P = 0.2%
P = 0.1%
1
Aug.20
Aug.20
SOP
3.28
3.28
4.92
4.92
37.59
31.92
47.64
42.02
2
Aug.25
Aug.25
SOP
3.28
3.28
3.28
3.28
28.67
21.77
40.73
33.66
3
Sep.1
Sep.1
SOP
0.00
0.00
1.64
0.82
0.00
0.00
2.69
1.34
Table 10
The risk analysis results of the proposed asynchronous refill rules for cascade
reservoirs.
Start time
of refill
operation
Refill rules
for Xiluodu
reservoir
Risk (%)
P = 0.2%
P = 0.1%
P = 0.2%
P = 0.1%
1
Aug.20
2
Aug.25
3
Sep.1
Aug.20
SOP
Aug.25
SOP
Sep.1
SOP
3.28
3.28
1.64
1.64
0.00
0.00
3.28
3.28
3.28
3.28
0.00
0.00
28.53
19.52
10.21
6.49
0.00
0.00
31.56
27.54
23.32
20.86
0.00
0.00
Refill rules
for Xiangjiaba
reservoir
Risk (%)
Number
1
Aug.25
2
Sep.1
3
Sep.5
1
Sep.1
2
Sep.5
3
Sep.10
Risk loss
rate (%)
Risk loss rate (%)
P = 0.2%
P = 0.1%
P = 0.2%
P = 0.1%
1.64
1.64
0.00
0.00
0.00
0.00
1.64
1.64
0.00
0.00
0.00
0.00
29.76
19.20
0.00
0.00
0.00
0.00
18.60
14.66
0.00
0.00
0.00
0.00
Refill rules
for TGR
Risk (%)
Risk loss rate (%)
P = 0.2%
P = 0.1%
P = 0.2%
P = 0.1%
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
For No. 3 of synchronous and asynchronous refill rules in Tables
11 and 13, the values of hydropower generation and fullness storage rate are 27.4 billion kW h, 97.66%, 27.4 billion kW h and 97.66%
for Xiluodu reservoir, 13.93 billion kW h, 90.35%, 13.89 billion
kW h and 89.24% for Xiangjiaba reservoir as well as 34.88 billion
kW h, 98.51%, 34.06 billion kW h and 98.02% for TGR. Compared
with SOP, the values of hydropower generation and fullness storage rate for synchronous and asynchronous refill rules are significantly improved because of raising the water head of
hydropower generation in the refill operation. In a word, the
hydropower generation and fullness storage rate is also gradually
increased for SOP, asynchronous refill rules and synchronous refill
rules.
4.3. Multi-objective evaluation
Two flood risk indexes of flood control risk and flood loss rate
(Eqs. (5) and (6)) as well as two utilization benefits indexes of
hydropower generation and fullness storage rate (Eqs. (7) and
(8)) are selected as multi-objectives indices. Values of the AGA’s
parameters must be defined before the algorithm is used. These
Risk loss rate (%)
Table 11
The annual average utilization benefits analysis results of the proposed synchronous
refill rules for cascade reservoirs.
Number
Aug.25
SOP
Sep.1
SOP
Sep.5
SOP
Sep.1
SOP
Sep.5
SOP
Sep.10
SOP
Risk (%)
1
Start time
of refill
operation
Values
Aug.20
Value
Difference
Value
Difference
Value
Difference
Value
Difference
Value
2
Aug.25
3
Sep.1
4
Sep.5
5 and
6 (SOP)
Sep.10
Xiluodu reservoir
(rate)
(rate)
(rate)
(rate)
Hydropower
generation
(billion kW h)
Fullness
storage
rate (%)
27.65
0.54(1.97%)
27.57
0.45(1.67%)
27.40
0.28(1.03%)
27.26
0.15(0.54%)
27.12
97.98
1.21(1.25%)
97.94
1.18(1.22%)
97.66
0.89(0.92%)
97.3
0.53(0.55%)
96.77
Xiangjiaba reservoir
1
Aug.20
2
Aug.25
3
Sep.1
4
Sep.5
5 and
6 (SOP)
Sep.10
Value
Difference
Value
Difference
Value
Difference
Value
Difference
Value
(rate)
(rate)
(rate)
(rate)
Hydropower
generation
(billion kW h)
Fullness
storage
rate (%)
14.07
0.31(2.25%)
14.03
0.27(1.97%)
13.93
0.18(1.27%)
13.86
0.10(0.74%)
13.76
93.47
10.43(12.56%)
92.80
9.76(11.75%)
90.35
7.30(8.79%)
87.49
4.45(5.35%)
83.04
TGR
1
Aug.20
2
Aug.25
3
Sep.1
4
Sep.5
5
Sep.10
6 (SOP)
Oct.1
Value
Difference
Value
Difference
Value
Difference
Value
Difference
Value
Difference
Value
(rate)
(rate)
(rate)
(rate)
(rate)
Hydropower
generation
(billion kWh)
Fullness
storage
rate (%)
35.72
3.29(10.13%)
35.42
2.99(9.22%)
34.88
2.45(7.56%)
34.56
2.13(6.56%)
34.00
1.57(4.84%)
32.43
98.90
1.39(1.42%)
98.80
1.29(1.32%)
98.51
1.00(1.03%)
98.17
0.67(0.68%)
97.88
0.37(0.38%)
97.51
parameters include the sample-size population and the probabilities of crossover and mutation. Although it is important to determine the best parameter values, and several studies have tried to
do so (Grefenstette, 1986; Schaffer et al., 1989), no universal rules
have yet been found. In this circumstance, one relies on experience
and trial-and-error to find a good set of parameter values. The suggested sets of values that consistently lead to good results in this
study are shown in the following: population size = 400, maximum
iteration = 100, probability of crossover = 0.80 and probability of
179
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Table 12
The annual average risk analysis results of the proposed synchronous refill rules for TGR (without considering refill operation of Xiluodu reservoir and Xiangjiaba reservoir).
Number
Start time of refill operation
Values
TGR
1
Aug.20
2
Aug.25
3
Sep.1
4
Sep.5
5
Sep.10
6 (SOP)
Oct.1
Value
Difference
(rate)
Value
Difference
(rate)
Value
Difference
(rate)
Value
Difference
(rate)
Value
Difference
(rate)
Value
Hydropower generation (billion kWh)
Fullness storage rate (%)
35.39
3.36(10.49%)
98.59
3.20(3.35%)
35.12
3.09(9.65%)
98.52
3.12(3.27%)
34.58
2.55(7.97%)
98.29
2.90(3.04%)
34.26
2.23(6.97%)
98.00
2.61(2.73%)
33.70
1.68(5.23%)
97.70
2.30(2.41%)
32.03
95.39
Table 13
The annual average utilization benefits analysis results of the proposed asynchronous refill rules for cascade reservoirs.
Number
Start time of refill operation
Values
Xiluodu reservoir
1
Aug.20
2
Aug.25
3
Sep.1
4
Sep.5
5 (SOP)
Sep.10
Value
Difference
Value
Difference
Value
Difference
Value
Difference
Value
(rate)
(rate)
(rate)
(rate)
Hydropower generation (billion kW h)
Fullness storage rate (%)
27.65
0.54(1.97%)
27.57
0.45(1.67%)
27.40
0.28(1.03%)
27.26
0.15(0.54%)
27.12
97.98
1.21(1.25%)
97.94
1.18(1.22%)
97.66
0.89(0.92%)
97.30
0.53(0.55%)
96.77
Xiangjiaba reservoir
1
Aug.25
2
Sep.1
3
Sep.5
4
Sep.10
5 (SOP)
Sep.10
Value
Difference
Value
Difference
Value
Difference
Value
Difference
Value
(rate)
(rate)
(rate)
(rate)
Hydropower generation (billion kWh)
Fullness storage rate (%)
14.04
0.29(2.07%)
13.97
0.21(1.52%)
13.89
0.14(0.99%)
13.80
0.05(0.35%)
13.76
93.31
10.27(12.36%)
91.62
8.58(10.33%)
89.24
6.20(7.46%)
85.17
2.13(2.56%)
83.04
TGR
1
Sep.1
2
Sep.5
3
Sep.10
4
Sep.10
5 (SOP)
Oct.1
Value
Difference
Value
Difference
Value
Difference
Value
Difference
Value
(rate)
(rate)
(rate)
(rate)
Hydropower generation (billion kWh)
Fullness storage rate (%)
34.92
2.49(7.68%)
34.60
2.17(6.70%)
34.06
1.63(5.01%)
34.03
1.60(4.92%)
32.43
98.58
1.07(1.10%)
98.30
0.79(0.81%)
98.02
0.51(0.52%)
97.94
0.43(0.44%)
97.51
Table 14
The multi-objectives evaluation results of the proposed refill rules for cascade reservoirs.
Schemes
Number
Risk (%)
Risk loss rate (%)
Hydropower generation (billion kW h)
Fullness storage rate (%)
Projection value
Rank
Synchronous refill
1
2
3
4
5
4.92
3.28
1.64
0.00
0.00
46.84
40.63
5.26
0.00
0.00
77.43
77.01
76.21
75.68
74.87
98.43
98.33
97.95
97.51
96.99
0.1296
0.4290
1.1965
1.4683
1.4377
10
9
6
1
4
Asynchronous refill
1
2
3
4
3.28
3.28
0.00
0.00
31.56
23.32
0.00
0.00
76.61
76.13
75.34
75.09
98.21
97.94
97.57
97.26
0.5681
0.6877
1.4635
1.4497
8
7
2
3
SOP
1
0.00
0.00
73.30
96.73
1.3994
5
180
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
mutation = 0.20 (Wang et al., 2006; Chen and Yang, 2007; Fang
et al., 2009). The multi-objectives evaluation results are listed in
Table 14. It is shown that joint optimal refill rules are No. 4 with
projection value 1.4683 in synchronous refill schemes and No. 3
with projection value 1.4635 in asynchronous refill schemes. The
hydropower generation of synchronous refill schemes is greater
than that of asynchronous refill schemes, however, the fullness
storage rate of synchronous refill schemes is less than that of asynchronous refill schemes. Besides, unit projection vector a are equal
to 0.6226, 0.7768, 0.0814, and 0.0481 for flood control risk, flood
loss rate, hydropower generation and fullness storage rate, respectively. It indicates that the importance of flood risk indexes is superior to that of utilization benefits indexes in multi-objective
evaluation. Most of all, joint optimal refill rules No. 4 in synchronous refill schemes as well as No. 3 in asynchronous refill
schemes can improve utilization benefits with flood control risk
0.00 and flood loss rate 0.00 without reducing originally designed
flood prevention standards comparing with SOP.
Above all, the recommended joint optimal refill rules are No. 4
in synchronous refill rules with start time of refill operation Sep.5
for cascade reservoirs as well as No. 3 in asynchronous refill rules
with start time of refill operation Sep.1, Sep.5 and Sep.10 for
Xiluodu reservoir, Xiangjiaba reservoir and TGR, respectively.
5. Conclusion and recommendations
A joint optimal refill operation model for cascade reservoirs is
proposed and developed to solve the conflict between the flood
control and refill operation. The Jinsha River cascade reservoirs
and Three Gorges cascade reservoirs in the Changjiang River basin
of China are selected as a case study. The following conclusions are
drawn:
(1) The hydropower generation and fullness storage rate is
gradually increased for designed operating rules,
asynchronous refill rules and synchronous refill rules,
however, the flood control pressure is also gradually
increased. The recommended joint optimal refill rules are
synchronous refill rules with start time of refill operation
Sep.5 for cascade reservoirs as well as asynchronous refill
rules with start time of refill operation Sep.1, Sep.5 and
Sep.10 for Xiluodu reservoir, Xiangjiaba reservoir and TGR,
respectively.
(2) Joint optimal synchronous and asynchronous refill rules can
generate 2.38 billion kW h (3.25%) and 2.04 billion kW h
(2.78%) more annual average hydropower and increase fullness storage rate by 0.81% and 0.87% respectively for the cascade reservoirs without reducing originally designed flood
prevention standards comparing with the designed operating rules.
This paper summarizes the results from a first attempt of joint
optimal refill operation model for reservoir systems combining
with flood risk, utilization benefits analysis and multi-objective
evaluation. There are several issues that will be addressed in future
studies, this includes:
(1) Real-time operation: derivation of joint optimal refill rules is
a topic and task in the planning and designing stage.
However, how to implement the joint optimal refill rules
for real-time operation is a future challenge.
(2) Hydrological forecasting uncertainty: because hydrological
forecasting information is not incorporated into the input
inflow data, more studies are required so as to reduce the
hydrological forecasting uncertainty.
Acknowledgements
This study is financially supported by the Open Foundation of
State Key Laboratory of Water Resources and Hydropower
Engineering Science in Wuhan University (2014SWG02) and
National Natural Science Foundation of China (51079100,
51190094 and 51209008). The authors would like to thank the editor and anonymous reviewers for their review and valuable comments related to this manuscript.
References
Aven, T., Pörn, K., 1998. Expressing and interpreting the results of quantitative risk
analysis, review and discussion. Reliab. Eng. Syst. Safety 61, 3–10.
Botzen, W.J., Aerts, J.C., Bergh, J.C., 2009. Dependence of flood risk perceptions on
socioeconomic and objective risk factors. Water Resour. Res. 45, W10440.
http://dx.doi.org/10.1029/2009WR007743.
Bower, B.T., Hufschmidt, M.M., Reedy, W.W., 1966. Operating Procedures: their Role
in the Design of Water-Resource Systems by Simulation Analyses. Harvard
University Press, Cambridge.
Chang, F., Chen, L., Chang, L., 2005. Optimizing the reservoir operating rule curves
by genetic algorithms. Hydrol. Process. 19 (11), 2277–2289.
Chen, J., Yang, X., 2007. Optimal parameter estimation for Muskingum model based
on Gray-encoded accelerating genetic algorithm. Commun. Nonlinear Sci.
Numer. Simul. 12 (5), 849–858.
Chen, L., Guo, S., Yan, B., Liu, P., Fang, B., 2010. A new seasonal design flood method
based on bivariate joint distribution of flood magnitude and date of occurrence.
Hydrol. Sci. J. 55 (8), 1264–1280.
Clark, E.J., 1956. Impounding reservoirs. J. Am. Water Works Assoc. 48 (4), 349–354.
CWRC (Changjiang Water Resources Commission), 1997. Comprehensive Utilization
and Reservoir Operation of Three Gorges Project. Hubei Science and Technology
Press, Wuhan (in Chinese).
CWRC (Changjiang Water Resources Commission), 2010. Rule of Flood Control and
Experimental Refill for the Three Gorges Reservoir in 2010, Wuhan (in Chinese).
Emma, J.T., Michael, J.C., Sally, J.P., 2006. Confronting flood risk: implications for
insurance and risk transfer. J. Environ. Manage. 81 (4), 351–359.
Fang, F., Ni, B., Yu, H., 2009. Estimating the kinetic parameters of activated sludge
storage using weighted non-linear least-squares and accelerating genetic
algorithm. Water Res. 43 (10), 2595–2604.
Friedman, J.H., Turkey, J.W., 1974. A projection pursuit algorithm for exploratory
data analysis. IEEE Trans. Computer 23 (9), 89–94.
Grefenstette, J.J., 1986. Optimization of control parameters for genetic algorithms.
IEEE Trans. Syst., Man Cybern. 16 (1), 122–128.
Guo, S., Zhang, H., Chen, H., Peng, D., Liu, P., Pang, B., 2004. A reservoir flood
forecasting and control system in China. Hydrol. Sci. J. 49 (6), 959–972.
HCCEC (Hydro China Chengdu Engineering Corporation), 2013. Research Report:
Refill and Flood Control Plans for Xiluodu Reservoir in Jinsha River (in Chinese).
HCZEC (Hydro China Zhongnan Engineering Corporation), 2013. Research Report:
Refill and Flood Control Plans for Xiangjiaba reservoir in Jinsha River, (in
Chinese).
Jain, S.K., Goel, K.M., Agrawal, P.K., 1998. Reservoir operation studies of Sabarmati
system, India. J. Water Resources Plan. Manage. 124 (1), 31–39.
Jia, B., Zhong, P., Wan, X., Xu, B., Chen, J., 2014. Decomposition–coordination model
of reservoir group and flood storage basin for real-time flood control operation.
Hydrology Research, in press. doi: 10.2166/nh.2013.
Labadie, J.W., 2004. Optimal operation of multireservoir systems: state-of-the-art
review. J. Water Resources Plan. Manage. 130 (2), 93–111.
Li, X., Guo, S., Liu, P., Chen, G., 2010. Dynamic control of flood limited water level for
reservoir operation by considering inflow uncertainty. J. Hydrol. 391, 124–132.
Li, Y., Guo, S., Guo, J., Wang, Y., Li, T., Chen, J., 2013. Deriving the optimal refill rule
for multi-purpose reservoir considering flood control risk. J. Hydro-Environ. Res.
8 (3), 248–259.
Lind, N., Pandey, M., Nathwani, J., 2009. Assessing and affording the control of flood
risk. Struct. Saf. 31, 143–147.
Liu, P., Guo, S., Xiong, L., Li, W., Zhang, H., 2006. Deriving reservoir refill rules by
using the proposed DPNS model. Water Resour. Manage. 20 (3), 337–357.
Liu, P., Guo, S., Xu, X., Chen, J., 2011a. Derivation of aggregation-based joint
operating rule curves for cascade hydropower reservoirs. Water Resour.
Manage. 25 (13), 3177–3200.
Liu, X., Guo, S., Liu, P., Chen, L., Li, X., 2011b. Deriving optimal refill rules for multipurpose reservoir operation. Water Resour. Manage. 25 (2), 431–448.
Lund, J.R., Guzman, J., 1999. Derived operating rules for reservoirs in series or in
parallel. J. Water Resources Plan. Manage. 125 (3), 143–153.
MWR (Ministry of Water Resources), 2009. Rule of Optimal Operation for the Three
Gorges Reservoir, Beijing (in Chinese).
Ngo, L.L., Madsen, H., Rosbjerg, D., 2007. Simulation and optimization modeling
approach for operation of the Hoa Binh reservoir, Vietnam. J. Hydrol. 336, 269–
281.
Peng, Y., Ji, C., Gu, R., 2014. A multi-objective optimization model for coordinated
regulation of flow and sediment in cascade reservoirs. Water Resour. Manage 28
(12), 4019–4033.
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Schaffer, J.D., Caruana, R.A., Eshelman, L.J., Das, R., 1989. A study of control
parameters affecting online performance of genetic algorithms for function
optimization. In: Proceedings on Third International Conference on Genetic
Algorithms, 51–60.
Tu, M.Y., Hsu, N.S., Yeh, W.W.G., 2003. Optimization of reservoir management
and operation with hedging rules. J. Water Resources Plan. Manage. 129 (2), 86–
97.
Wang, S., Zhang, X., Yang, Z., Ding, J., 2006. Projection pursuit cluster model based
on genetic algorithm and its application in karstic water pollution evaluation.
Int. J. Environ. Pollut. 28 (34), 253–260.
Wang, X., Zhou, J., Ouyang, S., Li, C., 2014. Research on joint impoundment
dispatching model for cascade reservoir. Water Resour. Manage 28 (15), 5527–
5542.
181
Xiao, Y., Guo, S., Liu, P., Yan, B., Chen, L., 2009. Design flood hydrograph based on
multi-characteristic synthesis index method. J. Hydrol. Eng. 14 (12), 1359–
1364.
Yang, X., Yang, Z., Lu, G.H., Li, J., 2005. A gray-encoded, hybrid-accelerated, genetic
algorithm for global optimizations in dynamical systems. Commun. Nonlinear
Sci. Numer. Simul. 10 (4), 355–363.
Yeh, W., 1985. Reservoir management and operations models: a state-of-the-art
review. Water Resour. Res. 21 (12), 1797–1818.
Zhou, Y., Guo, S., 2014. Risk analysis for flood control operation of seasonal floodlimited water level incorporating inflow forecasting error. Hydrol. Sci. J., 1–14
Zhou, Y., Guo, S., Liu, P., Xu, C., 2014. Joint operation and dynamic control of flood
limiting water levels for mixed cascade reservoir systems. J. Hydrol. 519, 248–
257.