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 b Changjiang River Scientific Research Institute, Wuhan 430010, China c Department of Geosciences, University of Oslo, Norway article info 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 summary 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 neces- sity 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 reser- voir releases to obtain the best interests of the whole reservoir sys- tem, 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 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 reser- voir refill. Clark (1956) proposed the New York City rule (NYC), which used probability of spills rather than direct amounts of phy- sical 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 sim- plex 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. http://dx.doi.org/10.1016/j.jhydrol.2015.02.034 0022-1694/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author at: Changjiang River Scientific Research Institute, Wuhan 430010, China. Tel./fax: +86 27 68773568. E-mail address: [email protected](Y. Zhou). Journal of Hydrology 524 (2015) 166–181 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol
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, Chinab Changjiang River Scientific Research Institute, Wuhan 430010, Chinac Department of Geosciences, University of Oslo, Norway
a r t i c l e i n f o
Article history:Received 28 November 2014Received in revised form 19 February 2015Accepted 20 February 2015Available online 28 February 2015This manuscript was handled by GeoffSyme, Editor-in-Chief
Keywords:Joint optimal refill ruleMulti-objective evaluationFlood control riskUtilization benefits analysisCascade reservoirs
s u m m a r y
Reservoirs are one of the most efficient infrastructures for integrated water resources development andmanagement; and play a more and more important role in flood control and conservation. Optimal refilloperation before the end of flood season is a valuable and effective approach to compromise the floodcontrol, hydropower generation and comprehensive utilization of water resources of river basins. Anintegrated model consisting of a flood control risk analysis module, a utilization benefits analysis moduleand a multi-objective evaluation module was proposed in this study to derive joint optimal refill rules forcascade reservoirs. The Jinsha River and Three Gorges cascade reservoirs in the Changjiang River basin ofChina are selected for a case study. Sixty-one years of observed daily runoff data from 1950 to 2010 havebeen used to test the model. The results indicate that the proposed model can make an effective tradeoffbetween flood control and utilization benefits. Joint optimal synchronous and asynchronous refill rulescan generate 3.25% and 2.78% more annual average hydropower, respectively and improve the fullnessstorage rate without increasing flood control risk comparing with the original designed operating rules.
� 2015 Elsevier B.V. All rights reserved.
1. Introduction
Climate change, rapid economic development and increase ofthe human population are considered as the major triggers ofincreasing water-related challenges all over the world. The neces-sity of efficient planning and management for water resourcesbecomes more and more urgent. Reservoirs play a vital role inregulating water resources in different space and time throughoptimal operation (Labadie, 2004; Guo et al., 2004; Jia et al.,2014). Reservoir reoperation to balance human and ecologicalwater requirements may be a potential approach to alleviate theeffects of climatic and socio-economic changes.
Operating rules are often used to provide guidelines for reser-voir releases to obtain the best interests of the whole reservoir sys-tem, consistent with certain inflow and existing storage levels (Tuet al., 2003; Chang et al., 2005). They are often predefined at theplanning stage of the reservoir construction through simulationtechniques. The operating rule curve is one of the most simpleand frequently used ways for guiding and managing the reservoiroperation (Liu et al., 2011a). It is usually presented in the form of
graphs or tables to guide release of the reservoir systems accordingto actual storage level, hydro-meteorological conditions and timeof year (Yeh, 1985; Ngo et al., 2007). Consequently, it is desirableto do research on how to find effective operating rules aimed atsignificantly increasing utilization benefits for flood control, energyproduction, navigation, ecology as well as water supply.
Some reservoir operating rules are typically applicable to reser-voir refill. Clark (1956) proposed the New York City rule (NYC),which used probability of spills rather than direct amounts of phy-sical 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’sSabarmati River System using historically observed flows, anddeveloped a judicious operation policy for conservation and floodcontrol using simulation techniques. Lund and Guzman (1999)explored the LP-NYC rule, which had the advantage of being ableto incorporate other short-term reservoir operation constraints,e.g. minimum or maximum flows downstream of each reservoiror required diversions below a subset of reservoirs. Liu et al.(2006) developed a dynamic programming neural-network sim-plex model using a simulation-based optimization method toderive refill rules for the Three Gorges Reservoir (TGR). They showthat it performs better than original design rule curves. Liu et al.
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181 167
(2011b) proposed a multi-objective refill operation model for sin-gle reservoir by combining flood control and conservation togeth-er. The simulation–optimization-test framework and hybrid multi-objective genetic algorithm were used to optimize the rule curvesof TGR. Li et al. (2013) developed a refill operation model couplinga flood risk module with utilization benefits analysis module toderive the optimal refill rule of TGR. Wang et al. (2014) proposeda joint refill operation model for cascade reservoir solved by usingelectromagnetism-like mechanism algorithm, however, they didnot evaluate those refill rules combining with flood risk and uti-lization benefits analysis.
Current studies of optimal refill operation paid more attentionto single reservoir rather than cascade reservoirs. The aim of thisstudy is to develop a joint optimal refill operation model for cas-cade reservoirs. Since there are hydraulic connections and storagecompensations between the upstream and downstream reservoirsin cascade reservoirs, the optimal refill operation will becomemore and more complex as the number of reservoirs increases. Inthis study, a joint optimal refill operation model for cascade reser-voirs is proposed and developed to solve the conflict between theflood control and refill operation. The Jinsha River cascade reser-voirs and the Three Gorges cascade reservoirs in the ChangjiangRiver basin of China are selected as a case study.
The paper is organized as follows: Section 2 briefly introducesthe study area, after which the current operation rules of the inves-tigated cascade reservoirs are discussed. Section 3 describes themethod adopted in this study, which comprises three parts: intro-duction of a general framework for joint optimal refill operationmodel 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 reser-voirs are presented and discussed. The conclusions are drawn inSection 5.
2. Jinsha River and Three Gorges cascade reservoirs
The Changjiang River or Yangtze, known in China as the ‘‘longriver’’, is the longest river in Asia and the third-longest river inthe world. It flows for 6418 km from glaciers on Qinghai-TibetPlateau (where it is called the Jinsha River) eastward across south-west, central and eastern China before emptying into the EastChina Sea at Shanghai. It is also one of the biggest rivers by dis-charge volume in the world. The Changjiang drains one-fifth ofthe land area of China, and its river basin is home to one-third ofthe nation’s population. The Jinsha River cascade reservoirs
Fig. 1. Sketches of the Jinsha River
(Xiluodu, Xiangjiaba) and Three Gorges cascade reservoirs (ThreeGorges, Gezhouba) as shown in Fig. 1 are selected as case study.Since the Gezhouba reservoir is a run-of-the-river hydropowerplant with small regulation storage, joint optimal refill operationmodel is only applied to simulate reoperation of the Xiluodu reser-voir, Xiangjiaba reservoir and TGR.
The Jinsha River’s basin area is 0.47 million km2. At the end ofthe Jinsha River, two-step cascade reservoirs have been construct-ed comprising from upstream to downstream Xiluodu andXiangjiaba reservoirs, the distances between them are 151 km.The Xiluodu reservoir is the third largest water conservancy pro-ject ever undertaken in the world, with a normal pool level at600 m above mean sea level and a total reservoir storage capacityof 12.91 billion m3, of which 4.65 billion m3 is flood control storageand 6.46 billion m3 is conservation regulating storage. TheXiangjiaba reservoir is the third largest water conservancy projectever undertaken in China, with a normal pool level at 380 m abovemean sea level and a total reservoir storage capacity of 5.20 billionm3, of which 0.903 billion m3 is flood control storage and 0.903 bil-lion m3 is conservation regulating storage.
The TGR is a vitally important and backbone project in thedevelopment and harnessing of the Changjiang River in China.The upstream of Changjiang River is intercepted by the TGR, witha length of the main course about 4.5 � 103 km and a drainage areaof 1.00 million km2. The TGR is the largest water conservancy pro-ject ever undertaken in the world, with a normal pool level at175 m above mean sea level and a total reservoir storage capacityof 39.3 billion m3, of which 22.15 billion m3 is flood control storageand 16.5 billion m3 is conservation regulating storage, accountingfor approximately 3.7% of the dam site mean annual runoff of451 billion m3. The Gezhouba reservoir is located at the lowerend of the TGR in the suburbs of Yichang City, 38 km downstreamof the TGR. The dam is 2606 m long and 53.8 m high, with a totalstorage capacity of 1.58 billion m3 and a maximum flood discharg-ing 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. Thecharacteristic parameter values of the totally four cascade reser-voirs are given in Table 1. The original operation water levels dur-ing the annual cycle in Xiluodu reservoir, Xiangjiaba reservoir andTGR are shown in Fig. 2 (HCCEC, 2013), Fig. 3 (HCZEC, 2013) andFig. 4 (CWRC, 1997), respectively. Only the designed operating rulecurves of the TGR are described briefly, because those of others aresimilar. According to the Chinese Flood Control Act, reservoir waterlevels generally are not allowed to exceed the flood limited waterlevel (FLWL) during flood season in order to offer adequate storage
basin and TGR basin in China.
Table 1List of characteristic parameter values of these four reservoirs.
Reservoir Unit Xiluodu Xiangjiaba TGR Gezhouba
Total storage 108 m3 115.7 51.63 393 15.8Flood control storage 108 m3 46.5 9.03 221.5 –Crest elevation m 610 384 185 70Normal pool level m 600 380 175 66Flood limited water level m 560 370 145.0 –Install capability MW 13,860 7750 22,400 2715Annual average hydropower generation Billion kW h 57.24 30.75 84.7 15.7Regulation ability – Seasonal Seasonal Seasonal Daily
Fig. 3. The original operating rule curves of Xiangjiaba reservoir.
168 Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
for flood prevention (Li et al., 2010; Zhou and Guo, 2014). Thewater level of TGR will be kept at between 145 m and 175 mdepending on flood control needs (region A). Although it is hardto capture when typical floods occur in TGR, the reservoir can offerenough flood storage capacity for a 1000-year design flood. Duringthe refill period, the storage level will be raised from the FLWL onOctober 1 to the normal pool level by the end of October. If thestorage level is below the normal pool level by the end ofOctober, water level rising will continue into November. FromNovember to the end of April in the following year, the water levelof the reservoir will generally be operated at region B or C and it
will be lowered gradually through operation of the hydropowerplant, which depends on the inflow. In some wet years, watershould be spilled to ensure the reservoir water level not to exceed175 m when it is on the top of upper boundary curve. However, innormal or dry years, the inflow is not enough to satisfy the need ofgenerating the firm output which is very important to the stabilityof the power system, and then the water level of the reservoir willbe lowered gradually to offer adequate release discharge for gener-ating the firm output (region C), otherwise the generators areturned to maximum output if the water level is in region B. In someabnormal dry year, firm output can’t be satisfied and output will be
Fig. 4. The original operating rule curves of TGR.
Table 2The start and end time for three refill operation schemes.
Refill time Schemes Cascade reservoirs
Xiluodu Xiangjiaba TGR
Starting time SOP September 10 September 10 October 1Synchronous refill August 20–September 10 August 20–September 10 August 20–September 10Asynchronous refill August 20–September 5 August 25–September 10 September 1–September 10
Ending time SOP September 30 September 30 October 31Synchronous refill September 30 September 30 October 31Asynchronous refill September 30 September 30 October 31
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181 169
decreased, and the storage level will be dropped below the lowerboundary curve (region D). The designed operating rules can beregarded 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 meansthat the reservoir water level should be increased from annualFLWL to normal pool level linearly.
Based on the SOP, the proposed refill rule proved by theMinistry of Water Resources (MWR, 2009), Changjiang WaterResources Commission (CWRC, 2010) as well as administratorscan be regarded as reoperation refill rule for individual reservoir.The following boundary conditions and constraints should be con-sidered: (1) the starting time of refill operation cannot be furtheradvanced to the end of main-flood season; (2) the starting waterlevel is equal to annual FLWL; (3) the phased water level is lessthan or equal to seasonal FLWL. The seasonal FLWL and its floodrisk are determined by flood control risk analysis based on floodseasonality (Chen et al., 2010; Liu et al., 2011b; Li et al., 2013;Zhou and Guo, 2014). The start and end times for three refill opera-tion schemes (including SOP, synchronous refill time, asyn-chronous refill time) are shown in Table 2. Time step for the starttime of refill operation is equal to 5 or 6 days. Besides, the end ofmain-flood season for Changjiang River basin is not earlier thanAugust 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 modelfor cascade reservoirs is shown in Fig. 5. The proposed model con-sists of three modules: (1) a flood control risk analysis modulebased on flood seasonality for determining seasonal FLWL andevaluate its flood risk, (2) a utilization benefits analysis modulebased on the proposed refill rules for evaluating utilization benefitsfor three refill operation schemes of the cascade reservoirs, (3) a
multi-objective evaluation module based on projection pursuitmethod and optimization algorithm for deriving joint optimal refillrules with multi-objective evaluation.
3.1. Flood control risk analysis module
3.1.1. Flood control operating rulesThe prerequisite of refill earlier for Jinsha River cascade reser-
voirs and Three Gorges cascade reservoirs is that it shall notincrease the flood control risk in the middle and lower reaches ofthe Changjiang River basin compared with SOP. The current floodcontrol 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 shownin Table 3.
3.1.2. Flood control risk analysisRisk is a complex and difficult concept, and there is still no con-
sensus on how the risk should be expressed and interpreted (Avenand Pörn, 1998; Emma et al., 2006). For cascade reservoirs, moreand more researchers noticed that realistic economic or utility ana-lysis must take account of both the frequency and the severity offailure (Botzen et al., 2009; Lind et al., 2009).
To determine seasonal FLWL, the iterative calculation methodsare used to regulate seasonal design inflow hydrographs (Xiaoet al., 2009; Li et al., 2010, 2011b; Liu et al., 2011b; Zhou andGuo, 2014). The intersection of these seasonal FLWLs, named thehighest safety water level Z0, is the highest storage level that canregulate seasonal design inflow hydrograph safely, and the capa-city below Z0 is used to regulate large flows during the refill period.Reservoir refill operation can be carried out according to the refillrule curve when no floods occur. In this way, flood control is com-bined 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 areused to evaluate the risks of different refill rules (Li et al., 2013;Zhou and Guo, 2014). Rf represents the frequency of flood controlrisk events occurrence; Rs represents the occupancy degree of
The number of refill rules N=N+1
N< Nmax
Multi-objective evaluation module
Deriving the joint optimal refill rules
No
Yes
Fig. 5. The general framework of joint optimal refill operation model for cascadereservoirs.
Table 3The current flood control operating rules of cascade reservoirs.
Reservoir Reservoir inflow Water levelQin (m3/s) in dam Z (m)
Qin > 76,200 Z 6 166.9Qin 6 82,200 –82,200 < Qin 6 97,400 Z 6 166.9
Z > 166.997,400 < Qin 6 111,500 Z 6 175.0Qin > 111,500 Z > 175.0
storage capacity used for regulating the seasonal design inflow,which can reflect the extent of losses in the downstream area indi-rectly. The losses in the downstream area suffered from flood dis-aster mainly depend on the flood volume that cannot be retainedin the reservoir. The bigger the value of Rs is, the worse the floodlosses at the downstream region are. They can be expressed as
Rf ¼ PðZf max > Z0Þ ¼ nf =n ð1Þ
where n is the total number of the simulated calculation; Zfmax isthe highest water level; nf is the time of Zfmax being higher than Z0.
Rs ¼ðVf max�V0ÞðVnor�V0Þ
Vf max P V0
0 Vf max < V0
(ð2Þ
V ¼ f ðZÞ ð3Þ
where V0 and Vnor are the storage capacities corresponding to thehighest safety water level and the Normal pool level, respectively;Vfmax is the storage capacity corresponding to Zfmax; (Vnor � V0) isthe part of storage capacity used for regulating the seasonal designinflow 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 beendeveloped as shown in Fig. 7. The procedure is described asfollows:
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 thehighest water level Zmax can be ascertained by flood regulatingcalculation according to the flood control operating rules duringthe 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 iterativecalculation. Otherwise, Zb,g is taken as the seasonal FLWL Z0,g. Ifall the seasonal design inflow hydrographs have been calculat-ed, the intersection of these seasonal FLWLs is taken as thehighest safety water level. Otherwise, g = g + 1.Step 3: Historical daily inflow series are used to simulate therefill operation which is guided by the selected refill rule. Thehighest water level is denoted by Zf,i in the ith year. Then, theRf and Rs corresponding to a certain return period can be calcu-lated by Eqs. (1) and (2), respectively.
Water level in Reservoir outflowShashi station Z0 (m) Qout (m3/s)
Fig. 6. Sketch of the highest safety water level and seasonal FLWL.
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181 171
3.2. Utilization benefits analysis module
A utilization benefits analysis module has been developed toobtain the evaluation indexes (Li et al., 2013), as shown in Fig. 8.This module can analyze utilization benefits of the refill operationwhich is guided by the proposed refill rules. The historical dailyinflow series are employed as the input data to simulate the refilloperation. The procedures are described as follows:
Start
Historical inflow series
Flood routing
Zf,1,Zf,2, ,Zf,i, ,Zf,nVfmax=max{f(Zf,i)}
i > imax
Z0=G(Z0,g)V0=f(Z0)
Output Rf and R
No
Yes
i =i +
1
Yes
Fig. 7. The flowchart of floo
Step 1: Input initial data series including the selected refill ruleof and historical daily inflow series, etc.Step 2: Determining the preliminary reservoir storage level ateach calculation interval according to the refill curve of theselected rule, and calculating the corresponding water dis-charge Qout by the water balance equation. If Qout exceeds thesafety discharge in the downstream Qsafe, then let Qout = Qsafe.Step 3: Calculating the output of the hydropower plant Ns by
Ns ¼min½AQoutH; f NðHÞ� ð4Þ
where A is the coefficient of hydropower generation; H is the aver-age water head; min[�] is the function getting the minimum valueand fN(�) is the function expressing the relationship between themaximum output Nmax and H.
If Ns is less than the firm output Np, then let Ns = Np. A temporarywater discharge Qtemp is calculated by Qtemp = Np/A�H; If|Qout � Qtemp| is greater than a satisfying accuracy (e = 0.1), thenQout ¼ ðQ out þ Q tempÞ=2 and steps 2–3 are repeated. Otherwise, letQout = Qtemp. If Ns is greater than Ny, the release discharge forhydropower plants Qo is calculated by Qo = Ny/(A�H) and the spilledwater Qw is the difference between Qout and Qo.
Step 4: Calculating the reservoir water level. If the reservoirwater level is greater than the normal pool level, let Qout = Qin
(reservoir inflow), in order to ensure that the reservoir waterlevel is not increase.
Seasonal design inflow hydrographs
Zb,g=Zb,g+ΔZ
Calculating Zmax by flood routing
Zmax >Znor
Z0,g=Zb,g
g > gmax
s
g =g
+1
No
No
Yes
d control risk module.
Input initial data series
Calculate requirements of discharges by the proposed refill rules
Adapt discharges to satisfying requirements of flood control
Zup Zdown Zlost
N<Np N<Ny
Qtemp2=Np/(A·H)
H=Zup-Zdown-ZlostNs=A·Qout·H
Ns=Ny
|Qout-Qtemp2|>e
Qout=(Qout+Qtemp2)/2
Qe=Ny/(A·H)
Qs=Qout-Qe
Satisfy constraints
Output Utilization benefit indices
No NoYes
No
Yes
No
Yes
Yes
Fig. 8. The flowchart of utilization benefits analysis module.
172 Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
Step 5: Validation constraints. Before going on to the next step,make sure all of constraints are satisfied. Otherwise, steps 2–4are repeated.Step 6: Calculating the utilization benefit indices on the basis ofthe reservoir inflow, water discharge, spilled water, storagecapacity and power output.
3.3. Multi-objective evaluation module
3.3.1. Multi-objective evaluation indicesReservoir management and operation are one of the most com-
plex problems in water resources management due to the multi-objective nature of reservoir operation. Since the function ofJinsha River and Three Gorges cascade reservoirs is multi-purpose,
it is very difficult to find a single index that is universally acceptedfor evaluating the comprehensive utilization benefits. Therefore,five evaluation indices which are flood control risk (Rf), flood lossrate (Rs), hydropower generation, fullness storage rate and guaran-tee rate of navigation are selected to calculate the comprehensiveutilization benefits, including flood control as well as utilizationbenefits. They are described as follows:
(4) Maximum fullness storage rate at the end of refill period(FR)
max FR ¼maxXM
k¼1
akFRf ;k
!ð8Þ
FRf ;k ¼Vk
high;i � Vkmin
Vkmax � Vk
min
� 100% ð9Þ
where
Rf,k flood control risk of kth reservoirRs,k flood loss rate of kth reservoirHGk hydropower generation of kth reservoir, kW hFRf,k fullness storage rate of kth reservoir
Vkmin the minimum storage capacity of kth reservoir, m3
Vkmax the maximum storage capacity of kth reservoir, m3
Vkhigh;i the highest storage of kth reservoir in the ith year, m3
ak the weight for fullness storage rate of kth reservoirM the number of reservoirs
3.3.2. ConstraintsThe following constraints should be satisfied in the flood
regulating and refill operation of Jinsha River and Three Gorgescascade reservoirs:
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.
Ngen ≥ 2
Max. generation ?
Accelerating cycle: gain the new interval of the variables
Obtain the joint optimal refill rules
Save the smartchromosome
No
Yes
No
Yes
Fig. 9. Flowchart of the AGA.
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181 173
(4) Navigation. It is noted that guarantee rates of navigation ofcascade reservoirs are improved to 99% by setting minimumnavigation flow (Peng et al., 2014; Wang et al., 2014).
Table 5The highest safety water levels of TGR corresponding to 1000-year seasonal designinflow (without considering refill operation of Xiluodu reservoir and Xiangjiabareservoir).
174 Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
DQk the maximum water discharge fluctuation of kth reservoir,m3/s
Zkdmin the minimum water level at downstream of kth dam site,
m
Zkdmax the maximum water level at downstream of kth dam site,
m
Zkdði;jÞ the water level at downstream of kth dam site on the jth
day in the ith year, mf(�) the function expressing the relationship between reservoirwater discharge and water level
3.3.3. Projection pursuit methodProjection 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 stan-dardization, linear projection, selecting projection index and pro-jection pursuit optimization. To learn about the steps ofprojection pursuit method, readers are referred to Wang et al.(2006). As Friedman and Turkey (1974) pointed out, projectionpursuit method strongly depends on the ability of the optimizationalgorithm to find substantive optima of the projection indexamong a forest of dummy optima caused by sampling fluctuations.Therefore, an efficient algorithm is one of the key issues of the pro-jection pursuit method.
3.3.4. Accelerating genetic algorithmAccelerating Genetic Algorithm (AGA, Yang et al., 2005; Wang
et al., 2006; Chen and Yang, 2007; Fang et al., 2009) is used to opti-mize the projection pursuit problem, as shown in Fig. 9. The stepsof AGA are composed of encoding, initialization of parent popula-tion, fitness evaluation, reproduction, crossover, mutation, evolu-tion and iteration as well as accelerating cycle. In order to knowabout the steps of AGA, readers are referred to Fang et al. (2009).
Generally, the operations of reproduction, crossover and muta-tion of genetic algorithm (GA) are executed in series. However, the-se operations are performed in parallel for AGA, which will furtherprotect the genetic information of each individual. Thus, AGA mayhave much more opportunities to reach the global optimal solutionto GA. The interval accelerating mechanism in Step 8 acceleratesthe convergence of the optimization process.
4. Results and discussion
4.1. Flood control risk analysis
4.1.1. The proposed refill rulesSixty-one years of observed daily runoff data from 1950 to 2010
have been used to analysis the proposed refill rules for cascadereservoirs. The daily runoff data of Xiluodu reservoir andXiangjiaba reservoir is derived from reference hydrology stationPingshan and the daily runoff data of TGR is derived from referencehydrology station Yichang by revivification. Besides, the frequencyand magnitude of interval inflow between Xiangjiaba reservoir andTGR is the same as that of Pingshan station and equal to the differ-ence between Yichang station and Pingshan station. The highestsafety water levels for refill rules of Xiluodu reservoir, Xiangjiabareservoir and TGR based on joint operation of cascade reservoirscorresponding to different seasonal design inflows (only taking1000-year seasonal design inflow as an example) are summarizedin Table 4. The highest safety water levels for the proposed refillrules (without considering refill operation of Xiluodu reservoirand Xiangjiaba reservoir) of TGR based on single reservoir opera-tion corresponding to 1000-year seasonal design inflow are sum-marized in Table 5 (Li et al., 2013). Generally speaking, thehighest safety water level is inversely related to the start time of
refill operation and the return period of seasonal design inflow,as shown in Tables 4 and 5. In other words, reservoir inflowdecreases gradually with the delay of the start time of refill opera-tion or with the increase of the return period of seasonal designinflow, which makes the highest safety water level increasegradually.
Taking the start time Aug.20 of refill operation and 1000-yearseasonal design inflow of 1952 typical year as an example, the
Table 6The proposed synchronous refill rules of cascade reservoirs.
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181 175
seasonal FLWLs corresponding to different seasonal stages are564.4 m, 566.5 m, 570.3 m, 574.6 m, and 578.8 m for Xiluodureservoir, 371.8 m, 372.6 m, 372.9 m, 374.3 m, and 374.6 m forXiangjiaba 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 seasonalFLWLs corresponding to different seasonal stages for TGR (withoutconsidering refill operation of Xiluodu reservoir and Xiangjiabareservoir) 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 increaseabout 0.3–1.1 m considering refill operation of Xiluodu reservoirand Xiangjiaba reservoir in 1952 typical year. The intersection ofthese seasonal FLWLs for cascade reservoirs is selected as highestsafety water levels based on 1952 typical year, because these sea-sonal 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 thestart time and time step of refill operation, the highest safety water
levels are shown in Tables 6 and 7, respectively. The hydrographsof SOP, synchronous and synchronous refill rules for cascade reser-voirs are shown in Figs. 10 and 11, respectively.
4.1.2. Risk analysisSixty-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 decreasegradually with the delay of the start time of refill operation or withthe decrease of the return period of seasonal design inflow. For thestart time of refill rules after Sep.5, the values of flood control riskand 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 forTGR in Table 8 are less than those for TGR in Table 9. The main rea-son is that flood control pressure for TGR at the lower reach is
Fig. 10. The hydrographs of synchronous refill rules for cascade reservoirs.
176 Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
reduced by flood control operation of Xiluodu reservoir andXiangjiaba reservoir at the upper reach. At the same time, thevalues of flood control risk and flood loss rate of the proposedsynchronous refill rules for cascade reservoirs in Table 8 aregreater than those of the proposed asynchronous refill rules forcascade reservoirs in Table 10. As a result of asynchronousstart time of refill operation, flood control pressure of asyn-chronous refill rules is markedly decreased by reserving floodcontrol storage among cascade reservoirs comparing withsynchronous refill rules.
For No. 1 of synchronous and asynchronous refill rules in Tables8 and 10, the values of flood control risk and flood loss rate corre-sponding 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 floodcontrol risk and flood loss rate for synchronous and asynchronousrefill rules are increased because of raising the seasonal FLWLs inthe refill operation.
Above all, the flood control pressure is gradually increased forSOP, asynchronous refill rules and synchronous refill rules.However, joint optimal refill rules are required to make a balancebetween flood risk and utilization benefits. As a result, it is neces-sary to analyze the utilization benefits of the proposed refill rulesfor cascade reservoirs.
4.2. Utilization benefits analysis
Meanwhile, 61 years of observed runoff data from 1950 to 2010have been used to analyze the utilization benefits of the proposedrefill rules for cascade reservoirs. Two evaluation indexes ofhydropower 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 listedin Tables 11–13, respectively. It is shown that the proposed syn-chronous and asynchronous refill rules can improve the hydropow-er generation and fullness storage rate comparing with SOP forcascade reservoirs. Furthermore, the values of hydropower gen-eration and fullness storage rate for TGR in Table 11 are greaterthan those for TGR in Table 12. The main reason is that water headof hydropower generation for TGR at the lower reach is raised byflood control operation of Xiluodu reservoir and Xiangjiaba reser-voir at the upper reach. At the same time, the values of hydropowergeneration and fullness storage rate of the proposed synchronousrefill rules for cascade reservoirs in Table 11 are also greater thanthose of the proposed asynchronous refill rules for cascade reser-voirs in Table 13. As a result of synchronous start time of refilloperation, hydropower generation and fullness storage rate ofasynchronous refill rules is markedly improved by raising waterhead of hydropower generation for cascade reservoirs at the lowerreach comparing with asynchronous refill rules.
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181 177
Table 9The risk analysis results of the proposed synchronous refill rules for TGR (without considering refill operation of Xiluodu reservoir and Xiangjiaba reservoir).
Table 11The annual average utilization benefits analysis results of the proposed synchronousrefill rules for cascade reservoirs.
Number Start timeof refilloperation
Values Xiluodu reservoir
Hydropowergeneration(billion kW h)
Fullnessstoragerate (%)
1 Aug.20 Value 27.65 97.98Difference (rate) 0.54(1.97%) 1.21(1.25%)
2 Aug.25 Value 27.57 97.94Difference (rate) 0.45(1.67%) 1.18(1.22%)
3 Sep.1 Value 27.40 97.66Difference (rate) 0.28(1.03%) 0.89(0.92%)
4 Sep.5 Value 27.26 97.3Difference (rate) 0.15(0.54%) 0.53(0.55%)
5 and6 (SOP)
Sep.10 Value 27.12 96.77
Xiangjiaba reservoir
Hydropowergeneration(billion kW h)
Fullnessstoragerate (%)
1 Aug.20 Value 14.07 93.47Difference (rate) 0.31(2.25%) 10.43(12.56%)
2 Aug.25 Value 14.03 92.80Difference (rate) 0.27(1.97%) 9.76(11.75%)
3 Sep.1 Value 13.93 90.35Difference (rate) 0.18(1.27%) 7.30(8.79%)
4 Sep.5 Value 13.86 87.49Difference (rate) 0.10(0.74%) 4.45(5.35%)
5 and6 (SOP)
Sep.10 Value 13.76 83.04
TGR
Hydropowergeneration(billion kW�h)
Fullnessstoragerate (%)
1 Aug.20 Value 35.72 98.90Difference (rate) 3.29(10.13%) 1.39(1.42%)
2 Aug.25 Value 35.42 98.80Difference (rate) 2.99(9.22%) 1.29(1.32%)
3 Sep.1 Value 34.88 98.51Difference (rate) 2.45(7.56%) 1.00(1.03%)
4 Sep.5 Value 34.56 98.17Difference (rate) 2.13(6.56%) 0.67(0.68%)
5 Sep.10 Value 34.00 97.88Difference (rate) 1.57(4.84%) 0.37(0.38%)
6 (SOP) Oct.1 Value 32.43 97.51
178 Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181
For No. 3 of synchronous and asynchronous refill rules in Tables11 and 13, the values of hydropower generation and fullness stor-age 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 billionkW h and 89.24% for Xiangjiaba reservoir as well as 34.88 billionkW h, 98.51%, 34.06 billion kW h and 98.02% for TGR. Comparedwith SOP, the values of hydropower generation and fullness stor-age rate for synchronous and asynchronous refill rules are sig-nificantly improved because of raising the water head ofhydropower generation in the refill operation. In a word, thehydropower generation and fullness storage rate is also graduallyincreased for SOP, asynchronous refill rules and synchronous refillrules.
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 ofhydropower generation and fullness storage rate (Eqs. (7) and(8)) are selected as multi-objectives indices. Values of the AGA’sparameters must be defined before the algorithm is used. These
parameters include the sample-size population and the probabil-ities of crossover and mutation. Although it is important to deter-mine the best parameter values, and several studies have tried todo so (Grefenstette, 1986; Schaffer et al., 1989), no universal ruleshave yet been found. In this circumstance, one relies on experienceand trial-and-error to find a good set of parameter values. The sug-gested sets of values that consistently lead to good results in thisstudy are shown in the following: population size = 400, maximumiteration = 100, probability of crossover = 0.80 and probability of
Table 12The annual average risk analysis results of the proposed synchronous refill rules for TGR (without considering refill operation of Xiluodu reservoir and Xiangjiaba reservoir).
Y. Zhou et al. / Journal of Hydrology 524 (2015) 166–181 179
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mutation = 0.20 (Wang et al., 2006; Chen and Yang, 2007; Fanget al., 2009). The multi-objectives evaluation results are listed inTable 14. It is shown that joint optimal refill rules are No. 4 withprojection value 1.4683 in synchronous refill schemes and No. 3with projection value 1.4635 in asynchronous refill schemes. Thehydropower generation of synchronous refill schemes is greaterthan that of asynchronous refill schemes, however, the fullnessstorage rate of synchronous refill schemes is less than that of asyn-chronous refill schemes. Besides, unit projection vector a are equalto 0.6226, 0.7768, 0.0814, and 0.0481 for flood control risk, floodloss rate, hydropower generation and fullness storage rate, respec-tively. It indicates that the importance of flood risk indexes is supe-rior to that of utilization benefits indexes in multi-objectiveevaluation. Most of all, joint optimal refill rules No. 4 in syn-chronous refill schemes as well as No. 3 in asynchronous refillschemes can improve utilization benefits with flood control risk0.00 and flood loss rate 0.00 without reducing originally designedflood prevention standards comparing with SOP.
Above all, the recommended joint optimal refill rules are No. 4in synchronous refill rules with start time of refill operation Sep.5for cascade reservoirs as well as No. 3 in asynchronous refill ruleswith start time of refill operation Sep.1, Sep.5 and Sep.10 forXiluodu reservoir, Xiangjiaba reservoir and TGR, respectively.
5. Conclusion and recommendations
A joint optimal refill operation model for cascade reservoirs isproposed and developed to solve the conflict between the floodcontrol and refill operation. The Jinsha River cascade reservoirsand Three Gorges cascade reservoirs in the Changjiang River basinof China are selected as a case study. The following conclusions aredrawn:
(1) The hydropower generation and fullness storage rate isgradually increased for designed operating rules,asynchronous refill rules and synchronous refill rules,however, the flood control pressure is also graduallyincreased. The recommended joint optimal refill rules aresynchronous refill rules with start time of refill operationSep.5 for cascade reservoirs as well as asynchronous refillrules with start time of refill operation Sep.1, Sep.5 andSep.10 for Xiluodu reservoir, Xiangjiaba reservoir and TGR,respectively.
(2) Joint optimal synchronous and asynchronous refill rules cangenerate 2.38 billion kW h (3.25%) and 2.04 billion kW h(2.78%) more annual average hydropower and increase full-ness storage rate by 0.81% and 0.87% respectively for the cas-cade reservoirs without reducing originally designed floodprevention standards comparing with the designed operat-ing rules.
This paper summarizes the results from a first attempt of jointoptimal refill operation model for reservoir systems combiningwith flood risk, utilization benefits analysis and multi-objectiveevaluation. There are several issues that will be addressed in futurestudies, this includes:
(1) Real-time operation: derivation of joint optimal refill rules isa topic and task in the planning and designing stage.However, how to implement the joint optimal refill rulesfor real-time operation is a future challenge.
(2) Hydrological forecasting uncertainty: because hydrologicalforecasting information is not incorporated into the inputinflow data, more studies are required so as to reduce thehydrological forecasting uncertainty.
Acknowledgements
This study is financially supported by the Open Foundation ofState Key Laboratory of Water Resources and HydropowerEngineering Science in Wuhan University (2014SWG02) andNational Natural Science Foundation of China (51079100,51190094 and 51209008). The authors would like to thank the edi-tor and anonymous reviewers for their review and valuable com-ments related to this manuscript.
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