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Hydrological Sciences Journal

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Derivation of water and power operating rules formulti-reservoirs

Yanlai Zhou, Shenglian Guo, Pan Liu, Chong-yu Xu & Xiaofeng Zhao

To cite this article: Yanlai Zhou, Shenglian Guo, Pan Liu, Chong-yu Xu & Xiaofeng Zhao (2016)Derivation of water and power operating rules for multi-reservoirs, Hydrological Sciences Journal,61:2, 359-370, DOI: 10.1080/02626667.2015.1035656

To link to this article: http://dx.doi.org/10.1080/02626667.2015.1035656

Accepted author version posted online: 01Apr 2015.Published online: 04 Dec 2015.

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Derivation of water and power operating rules for multi-reservoirsYanlai Zhoua,b, Shenglian Guoa, Pan Liua, Chong-yu Xua,c and Xiaofeng Zhaod

aState Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China; bChangjiang RiverScientific Research Institute, Wuhan, China; cDepartment of Geosciences, University of Oslo, Oslo, Norway; dHubei Provincial WaterResources and Hydropower Planning Survey and Design Institute, Wuhan, China

ABSTRACTWater operating rules have been universally used to operate single reservoirs because of theirpracticability, but the efficiency of operating rules for multi-reservoir systems is unsatisfactory inpractice. For better performance, the combination of water and power operating rules is pro-posed and developed in this paper. The framework of deriving operating rules for multi-reservoirsconsists of three modules. First, a deterministic optimal operation module is used to determinethe optimal reservoir storage strategies. Second, a fitting module is used to identify and estimatethe operating rules using a multiple linear regression analysis (MLR) and artificial neural networks(ANN) approach. Last, a testing module is used to test the fitting operating rules with observedinflows. The Three Gorges and Qing River cascade reservoirs in the Changjiang River basin, China,are selected for a case study. It is shown that the combination of water and power operating rulescan improve not only the assurance probability of output power, but also annual averagehydropower generation when compared with designed operating rules. It is indicated that thecharacteristics of flood and non-flood seasons, as well as sample input (water or power), shouldbe considered if the operating rules are developed for multi-reservoirs.

ARTICLE HISTORYReceived 3 January 2013Accepted 10 November2014

EDITORD. Koutsoyiannis

ASSOCIATE EDITORnot assigned

KEYWORDSmulti-reservoirs; operatingrule; progressive optimalityalgorithm; geneticalgorithm; aggregation–decomposition

1 Introduction

Reservoirs are among the most effective systems forintegrated water resources development and manage-ment. Currently, reservoirs have played an increasinglyimportant role in balancing the contradiction betweensocial development and water resources scarcity (Guoet al. 2004, Li et al. 2013, Urbaniak et al. 2013). Severalmodels and methods for reservoir operation have beenproposed and reviewed (e.g. Yakowitz 1982, Yeh 1985,Simonovic 1992, Wurbs 1993). However, it is difficultto apply a single best model or method to solve theoperation problem of a multi-reservoir system (Labadie2004).

Operating rules are often used to provide guidelinesfor reservoir releases to maintain the best interests of areservoir, being consistent with certain inflow andexisting storage levels (Tu et al. 2003, Chang et al.2005). Deriving operating rules involves optimization,fitting, refinement and simulation (Yeh 1985, Wurbs1993, Labadie 2004, Celeste and Billib 2009, Liu et al.2011a, 2011b). How to select an operating rule turnedout to be one of the challenges in their derivation (Saadet al. 1994); two forms of operating rules, i.e. wateroperating rules (Karamouz and Houck 1982,

Ostadrahimi et al. 2012) and power operating rules(Terry et al. 1986, Oliveira and Loucks 1997, Liuet al. 2011a), were used to coordinate the operationamong cascade reservoirs. Although the fitting methodcontributes to the derivation of types of operating rulefor a single reservoir, the goodness-of-fit criterion forderiving operating rules in water units does not alwaysobtain the best operating rule for cascade reservoirs.

The dimensionality problem often arises in theoperation of cascade reservoirs in water units. At thesame time, the efficiency of optimization algorithms isalso reduced by redundancy parameters of operatingrules in water units. However, the aggregation–decom-position method, which is one of the most efficientmethods for converting cascade reservoirs into anequivalent reservoir, has been used to derive operatingrules of cascade reservoirs. Hall and Dracup (1970)originally proposed a method of surmounting thedimensionality problem of dynamic programming(DP) for cascade reservoirs by aggregating all reservoirsinto an equivalent reservoir, in which the optimal solu-tions for the aggregated reservoir were decomposedinto individual solutions for the single reservoirs.Then Turgeon (1981) applied this concept to cascadereservoirs using stochastic DP. Valdés et al. (1992)

CONTACT: Yanlai Zhou zyl23bulls@whu.edu.cn

HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES, 2016VOL. 61, NO. 2, 359–370http://dx.doi.org/10.1080/02626667.2015.1035656

© 2015 IAHS

aggregated reservoirs in a hydropower system in powerunits rather than water units. Oliveira and Loucks(1997) showed that the aggregated reservoir approachwas useful for making decisions regarding total releasesfor water supply of cascade reservoirs. Liu et al. (2011a)studied the optimal operating rule curves of cascadereservoirs based on the aggregation–decompositionmethod. Similar approaches have been proposed anddeveloped to carry out optimization, fitting, refinementand simulation of operating rules and a vast literature(Turgeon 1981, Terry et al. 1986, Valdés et al. 1992,Saad et al. 1994, Archibald et al. 1997, Lund andGuzman 1999, Koutsoyiannis and Economou 2003,Rani and Moreira 2010, Chen et al. 2013) has appliedthose methods to derivation of operating rules forcascade reservoirs.

Most previous studies for operating rules paid moreattention to a single reservoir or cascade reservoirs ratherthan multi-reservoirs (including parallel reservoirs andcascade reservoirs). Since there are hydraulic connectionsand storage compensations between the upstream anddownstream reservoirs in multi-reservoirs, derivation ofoperating rules will become more and more complex asthe number of reservoirs is increased. Our study aims toattempt to extend the operating rules from single reser-voir to multi-reservoirs. We find that the forms of therules, i.e. the variables and function forms, allow us todeduce the best decision, and our framework allows theanalysis of the optimal release schedule obtained from thedeterministic optimal operation module using a multiplelinear regression analysis (MLR) and artificial neural net-work (ANN) approach. The operating rules were furthertested with observed inflows. A multi-reservoir system,consisting of the Three Gorges cascade and Qing Rivercascade reservoirs in the Changjiang (Yangtze) riverbasin of China, is selected as a case study.

The paper is organized as follows: Section 2 gives ageneral description of the modelling framework andthen details the components of the model, i.e. a deter-ministic optimal operation module, a fitting operatingrules module, and a testing operating rules module. InSection 3 the case study is introduced briefly and thesimulation results for the multi-reservoir system arediscussed. Section 4 contains the conclusions.

2 Methodology

The optimal operation of a multi-reservoir system ischallenging, especially taking into consideration theinflow uncertainty. The stochastic nature of inflowcan be incorporated into the optimization model eitherexplicitly or implicitly, which generates two approachesfor reservoir and hydropower stochastic optimal

operation: explicit stochastic optimization (ESO) andimplicit stochastic optimization (ISO). In ESO, theinflow process is directly described using its probabilitydistributions, and then traditional optimization meth-ods can be applied to solve the problem. One typicalexample of the ESO approach is stochastic dynamicprogramming (SDP; Karamouz and Houck 1987).Although the ESO approach may seem germane (Yeh1985), its application in practice presents considerabledifficulties. For large systems it entails a great deal ofcalculation that severely restricts its application. Fordeterministic modelling, five reservoirs is consideredlarge-scale, but for ESO modelling, three reservoirs islarge-scale (Labadie 2004). Therefore, for stochasticoptimization with more than five reservoirs, it is notrealistic to use the ESO approach.

The ISO approach uses a deterministic optimizationmethod to operate the reservoir system with a series ofhistorical or Monte-Carlo generated inflows, and thenexamines the optimal operating results to developoperating rules. Such rules can serve as guides to thereservoir operators in actual operation.

In ISO, the stochastic optimization is decomposed intotwo stages: deterministic operation and operating rulederivation. This greatly reduces model dimensionalityand calculation complexity, thus making the ISOapproach much more applicable than the ESO approach,especially for the actual operation of large-scale reservoirs.

Therefore, in this study, the framework of derivingoperating rules for multi-reservoirs under the ISOapproach is proposed. The framework consists of thefollowing three modules:(1) A deterministic optimal operation module is used to

determine the optimal reservoir storage strategies, inwhich the Monte Carlo method is used to simulatethe values of boundary conditions and coarse DP isused to determine the initial feasible solutions of theprogressive optimality algorithm (POA) used toderive the optimal solutions.

(2) A fitting module is used to identify and estimatethe forms and variables of the preliminary operat-ing rules using the MLR and ANN approach.

(3) A testing module is used to test the fitting operat-ing rules with observed inflows.

The details of each step are as follows.

2.1 Deterministic optimal operation module forsample generation

The deterministic optimal operation module is used todetermine the optimal reservoir storage strategies formulti-reservoirs to generate as much hydropower aspossible.

360 Y. ZHOU ET AL.

2.1.1 Objective functionIf the multi-reservoirs can meet the water supply andinitial power generation requirements, then the objectivefunction that generates maximum hydropower isselected, i.e.:

maxHG ¼XNt

t¼1

XNm

i¼1

TOPt;i � Δt (1)

where HG is the sum of the hydropower generation ofthe cascade reservoirs (kWh); Nt (t = 1, 2, . . .) is thenumber of time period; Nm (i = 1, 2, . . .) is the numberof cascade reservoirs in the multi-reservoir; TOPt,i isthe total output power of the ith cascade reservoirs inperiod t (kW); and Δt is the interval of time.

2.1.2 ConstraintsThe following constraints were imposed:

2.1.2.1 Firm output power constraints of the cascadereservoirs.

TOPt;i ¼ OPCt;i � vp FOPi �OPCt;i� �

(2)

OPCt;i ¼XNc

j¼1

OPt;j (3)

where OPCt,i is the output power of the ith cascadereservoirs in period t (kW); FOPi is the ith cascadereservoirs’ firm output power (kW); v is a variable (= 1if OPCt,i ≥ FOPi; = 0 otherwise); p is a positive numberfor penalty; OPt,j is the output power of the jth reser-voir in period t (kW); and Nc is the number of reser-voirs in cascade reservoirs.

2.1.2.2 Water balance equation.

Stþ1;j ¼ St;j þ It;j � Dt;j � ESt;j� �

Δt (4)

where St,j is the storage of the jth reservoir in periodt (m3); It,j is the inflow of the jth reservoir in periodt (m3/s); Dt,j is the water discharge of the jth reser-voir in period t (m3/s); and ESt,j is the sum ofevaporation and seepage of the jth reservoir in per-iod t (m3/s).

2.1.2.3 Reservoir water level limits.

Wmin t;j � Wt;j � Wmax t;j (5)

where Wt,j is the reservoir water level; and Wmin t,j andWmax t,j the minimum and maximum water level,respectively, of the jth reservoir in period t (m).

2.1.2.4 Comprehensive utilization of water required atreservoirs’ downstream limits.

Dmin t;j � Dt;j � Dmax t;j (6)

where Dmin t,j and Dmax t,j are the minimum and max-imum water discharge, respectively, for all downstreamuses in period t (m3/s).

2.1.2.5 Power generation limits.

OPmin t;j � OPt;j � OPmax t;j (7)

where OPmin t,j and OPmax t,j are the minimum andmaximum output power limitations of the reservoir,respectively, in period t (kW).

2.1.2.6 Boundary conditions limit.

W1;j ¼ Wini j

WNpþ1;j ¼ Wfin j(8)

It is worth mentioning that the principle that the finalwater level WNp+1,j is the same as the initial water levelW1,j (or as close as possible) in reservoir operation isonly appropriate for reservoirs with annual regulationability, but not always suitable for reservoirs withmulti-year, seasonal and daily regulation ability.Therefore, to reflect the uncertainty of the boundaryconditions limit, the Monte Carlo method is used tosimulate the values of Wini j and Wfin j, as follows:

Wini j ¼ Wmin 1;j þ Wmax 1;j �Wmin 1;j� � � Rand

Wfin j ¼ WminNpþ1;j þ WmaxNpþ1;j �WminNpþ1;j

� �� Rand

(9)

where Wini j and Wfin j are the reservoir water level ofthe jth reservoir in the initial and final time steps,respectively (m); and Rand is the random number ofuniform distribution in the range [0,1].

2.1.3 Optimality algorithmComparison of modified DP algorithms, such as dynamicprogramming successive approximations (DPSA), discretedifferential dynamic programming (DDDP) and POA(Yeh 1985, Labadie 2004, Guo et al. 2011, Liu et al.2011a, Chen et al. 2013), reveals that the POA produces abetter optimal solution but depends on the initial solution(Turgeon 1980, 1981, Liu et al. 2011a, Chen et al. 2013).Thus the results obtained from the coarse DP algorithmare input as the initial solution of the POA, after which asubsequent optimization routine is executed. For detaileddescription of the coupling between the coarse DP

HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES 361

algorithm and POA, readers are referred to Liu et al. (2006)and Chen et al. (2013).

2.1.4 Transformation to potential energyAn aggregated reservoir can preserve and describe somefeatures of the multi-reservoir system without consideringtheir interactions (Liu et al. 2011a, Chen et al. 2013). Thereservoirs in a hydropower system are aggregated in energyunits rather than in water units and an optimal operationpolicy for the equivalent aggregated reservoir is determinedbased on a deterministic optimal operation module. Theaggregation was carried out to convert the water stored ineach reservoir into energy units, based on an approachoriginally suggested by Arvanitidis and Rosing (1970),and applied by Turgeon (1981) and Valdés et al. (1992).

The total initial potential energy (TIPEt) stored in cas-cade reservoirs i to Nc at the end of period t is as follows:

TIPEt ¼XNc

j¼1

XNc

i¼j

ci � St;j � S0;j� �

(10)

The inflow of potential energy (IPEt) to reservoirs i toNc in period t is:

IPEt ¼XNc

j¼1

XNc

i¼j

ci � It;j (11)

and the outflow of potential energy (OPEt) from reser-voirs i to Nc in period t is:

OPEt ¼XNc

j¼1

cj � Dt;j (12)

where S0,j is the inactive storage of the jth reservoir(m3); ci is the conversion factor of the ith reservoir; andcj the conversion factor of the jth reservoir.

2.2 Fitting operating rules module

Dependent and independent variables constitute thebasic framework of operating rules. Proper selectionof these variables has great importance for model accu-racy. There are several principles for the formulationand selection of dependent and independent variables(Ji et al. 2010a, 2010b):(a) The dependent variable should be intuitive and

easy to operate in actual operation, such as outputpower, OPt,j, reservoir storage at the end of thetime step, St+1,j, and the reservoir discharge, Dt,j,for a single reservoir, as well as total output power,TOPt, total potential energy at the end of the time

step, TPEt, and outflow of potential energy, OPEt,for an aggregated reservoir.

(b) Independent variables should be as comprehensiveas possible, so the model can fully reflect the statusof the reservoir and power station, such as inflow,It,j, and reservoir storage at the beginning of thetime step, St,j, for a single reservoir, as well as totalinitial potential energy, TIPEt, and inflow of poten-tial energy, IPEt, for an aggregated reservoir.

(c) Variables should be independent of each other.Independence means, for instance, the reservoirstorage status can be described in three ways: reser-voir water level, reservoir storage status and storageenergy. However, not all of them need to beadopted in the independent variables set, becausethey are in a one-to-one relationship.Considering the principles above, in this paper we

take reservoir output power (N) as a decision variable.Reservoir storage at the beginning of the time step, St,j,and inflow, It,j, are chosen as independent variables forwater operating rules in a single reservoir, and inflowof potential energy, IPEt, and total initial potentialenergy, TIPEt, are chosen as independent variables forpower operating rules in an aggregated reservoir. Liuet al. (2011a) explained the meaning and calculation ofindependent variables in detail.

2.2.1 Water operating rulesBecause of the simplicity of the water operating rules, thegeneral forms of linear (Karamouz and Houck 1982,Ostadrahimi et al. 2012) and nonlinear operating rules(Neelakantan and Pundarikanthan 2000, Chandramouliand Raman 2001, Liu et al. 2006) have been often used inreservoir operation. Based on the results of the determi-nistic optimal operation module, the following linear andnonlinear water operating rules for each time period canbe established:

OPt;j ¼ α0 þ α1 � It;j þ α2 � St;j þ ε1 (13)

OPt;j ¼ f It;j; St;j� �þ ε2 (14)

where αi (i = 0, 1 and 2) is the parameter of linearwater operating rules; εi (i = 0 or 1) is the randomvariable of water operating rules; and f(⋅) is the non-linear function of water operating rules.

2.2.2 Power operating rulesBased on the results of the aggregated reservoir forcascade reservoirs, the linear (Liu et al. 2011a) andnonlinear power operating rules (Turgeon 1981) for

362 Y. ZHOU ET AL.

each time period, which are used to describe the quan-titative relationship between the total output power ofthe aggregated reservoir, TOPt, and the optimal aggre-gated energy, can be established:

TOPt ¼ β0 þ β1 � TIPEt þ β2 � IPEt þ ε3 (15)

TOPt ¼ f TIPEt; IPEtð Þ þ ε4 (16)

where βi (i = 0, 1 and 2) is the parameter of linearpower operating rules; and εi (i = 3 or 4) is the randomvariable of power operating rules.

2.2.3 Fitting methodsMultiple linear regression (Karamouz and Houck 1982,Liu et al. 2011a, Ostadrahimi et al. 2012) and artificialneural networks (Saad et al. 1994, Chandramouli andRaman 2001, Liu et al. 2006) are employed to developthe operating rules for multi-reservoirs. For a detaileddescription of MLR and ANN used in this paper, read-ers are referred to Liu et al. (2006).

2.3 Testing operating rules module

It is necessary to test whether the operating rules areable to deduce the best decision, because the operatingrules are the approximate quantitative relationshipsamong reservoir variables. The operation period isdivided into calibration and validation periods.

2.3.1 Testing water operating rulesOnce the water operating rules have been determined,their performance can be evaluated and assessed bysimulation with observed inflows in the calibrationand verification periods.

2.3.2 Testing power operating rulesThe decomposition method is aimed at decomposing thetotal output power of an aggregated reservoir and max-imizing the total initial potential energy at the end ofperiod t for a multi-reservoir system. The objective func-tion that generates maximum total potential energy,TPEt+1, for the end period is selected, maxTPEt+1 subjectto output power of the multi-reservoir system limit con-

straint TOPst ¼

PNc

j¼1OPt;j, where TOPt

s is the simulation

output power of the jth reservoir in period t (kW). Otherlimit constraints are the same as equations (2)–(9).

Although POA is applied to sample generation forthe operating rules, the genetic algorithm (GA) isselected as the optimal algorithm for testing the oper-ating rules. Compared with POA, the combination ofMLR, ANN and GA is easily applied to derive

operating rules effectively (Chang and Chang 2001,Naresh and Sharma 2001). A general flowchart of thegenetic algorithm is shown in many studies in theliterature (e.g. Oliveira and Loucks 1997, Hınçal et al.2011, Liu et al. 2011a). The GA is used to solve thewhole model, including maxTPEt+1 and equations(2)–(9).

2.3.3 Evaluation criteriaDifferent disciplines have different performanceindices. For example, the oldest and most widelyused performance criteria for water resources sys-tems are reliability, resiliency and vulnerability(Hashimoto et al. 1982, Moy et al. 1986). Criteriasuch as the Nash-Sutcliffe efficiency, root meansquare error and relative error are used to evaluatethe prediction abilities of hydrological models(Bennett et al. 2013). For particular reservoirs or asystem of hydropower stations, the assurance prob-ability of output power and mean hydropowerenergy, for example, are used to compare the perfor-mance of different operation schemes and models(Liu et al. 2006). Therefore, three evaluation criteriawere selected to compare the performance of thedifferent schemes for the multi-reservoir system: (a)the assurance probability of output power, P; themean hydropower energy, MHE; and the Nash-Sutcliffe efficiency index, R2. The three indices aredefined as follows:

P ¼ nNt

� 100% (17)

MHE ¼ 1Ny

XNt

t¼1

XNc

i¼1

TOPt;i � Δt (18)

The Nash-Sutcliffe efficiency index is used to assess theperformance of these two fitting methods, and isgiven by:

R2 ¼ 1�PNy

i¼1OPs

i �OOPi� �2

PNy

i¼1OOPi �MOOPð Þ2

26664

37775� 100% (19)

where MHE is the mean hydropower energy in simula-tion years (kWh); n is the number of occurrences ofTOPi,t ≥ FOPi; OOPi is the optimal output power inyear i for a single or aggregated reservoir (MW); OPi

s isthe simulated output power in year i for a singlereservoir or aggregated reservoir (MW); MOOP is themean of optimal output power in year i for a single oraggregated reservoir (MW); and Ny the number ofyears.

HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES 363

3 Case study

3.1 Three Gorges cascade and Qing River cascadereservoirs

A multi-reservoir system consisting of the ThreeGorges cascade reservoirs (Three Gorges, Gezhouba)and the Qing River cascade reservoirs (Shuibuya,Geheyan, Gaobazhou) in the Changjiang River basinof China, as shown in Fig. 1, is selected as a case study.

The Three Gorges Reservoir (TGR) is a vitallyimportant and backbone project in the developmentand harnessing of the Changjiang River in China. Theupstream of the Changjiang, with main course lengthof about 4.5 × 103 km and a drainage area of1.0 × 106 km2, is intercepted by the TGR. The TGR isthe largest water conservancy project ever undertakenin the world, with a normal pool level at 175 m and atotal reservoir storage capacity of 39.3 × 109 m3, ofwhich 22.15 × 109 m3 is flood control storage and16.5 × 109 m3 is a conservation regulating storagevolume, accounting for approximately 3.7% of thedam site mean annual runoff of 451 × 109 m3.

The Gezhouba Reservoir is located at the lower endof the TGR in the suburbs of Yichang City, 38 kmdownstream of the TGR. The dam is 2606 m longand 53.8 m high, with a total storage capacity of1.58 × 109 m3 and a maximum flood discharging cap-ability of 110 000 m3/s.

The Qing River is one of the main tributaries of theChangjiang River and its basin area is 17 600 km2. Themean annual rainfall, runoff depth and annual runoffare approximately 1460 mm, 876 mm and 423 m3/s,respectively. The total length of the mainstream is423 km, with a hydraulic drop of 1430 m. Along theQing River, a three-step cascade of reservoirs(Shuibuya, Geheyan and Gaobazhou) has been con-structed from upstream to downstream. The mainfunctions of these cascade reservoirs are power genera-tion and flood control. The characteristic parametervalues of these five reservoirs are given in Table 1.

3.2 Results and discussion

The multi-reservoirs are composed of the Three Gorgescascade reservoirs and Qing River cascade reservoirs.The Gezhouba and Gaobazhou reservoirs are runoffhydropower plants with small regulation storages;therefore, water operating rules are applied to simulatethe operation of the TGR, and water and power oper-ating rules are applied to simulate the operation of theShuibuya and Geheyan reservoirs. Aside from thewater and power operating rules, two other schemes,conventional operation and optimal operation rules,are also implemented to simulate the operation of themulti-reservoirs for comparative purposes. The opera-tion period with 60 years of observed inflow (from

Figure 1. Location of the Three Gorges cascade and Qing River cascade reservoirs.

Table 1. List of characteristic parameter values of the multi-reservoir system.Reservoir Unit TGR Gezhouba Shuibuya Geheyan Gaobazhou

Total storage 108 m3 393 15.8 42 34 5.4Flood control storage 108 m3 221.5 — 5.0 5.0 —Crest elevation m 185 70 409 206 83Normal water level m 175 66 400 200 80Flood limited water level m 145.0 — 391.8 192.2 —Install capability MW 22400 2715 1840 1212 270Annual generation 109 kWh 84.7 15.7 3.41 3.04 0.93Regulation ability — Seasonal Daily Multi-years Annual Daily

364 Y. ZHOU ET AL.

1951 to 2011) is divided into a calibration period(1951–1991) and a validation period (1992–2011), andthe time interval is 10 days.

The designed operating rules can be regarded as astandard operating policy (SOP in Table 2). Only thedesigned operating rule curves of the TGR andShuibuya Reservoir are described briefly; the designedoperating rule curves of the TGR are shown in Fig. 2.From the end of May to the beginning of June, thereservoir water level will be lowered to 145 m (floodlimited water level, FLWL). In October, the reservoirwater level will be raised gradually to the normal poollevel of 175 m. From November to the end of April inthe following year, the reservoir water level should bekept at as high as possible to generate more electricalpower. The reservoir water level will be loweredfurther, but should not fall below 155 m before theend of April to satisfy navigation conditions. Thedesigned operating rule curves of the ShuibuyaReservoir are shown in Fig. 3, in which the whole

storage space is divided into five operational zones. Ifthe water level rises to FLWL or into the flood preven-tion zone during the flood season, the reservoir isoperated according to designed flood control rules.Otherwise, the hydropower plant is operated betweenthe upper and lower basic guide curves. The designedoperating rules do not acknowledge the potential forcoordinated operation between the multi-reservoirs.Due to the potential profits when compared with thedeterministic optimal operation (DOO in Table 2), it isfeasible to jointly operate the multi-reservoirs toimprove the hydropower benefits and generation assur-ance rate. The DOO is based upon the observed inflowseries and can be seen as an ideal operation in theory.

Two fitting methods are used to derive the waterand power operating rules based on the results of thedeterministic optimal operation. One is multiple linearregression analysis, i.e. the linear water and poweroperating rules are derived from MLR analysis of theoptimal release schedule in the calibration period. Theother is the ANN method, in which the nonlinearwater and power operating rules are derived by analys-ing the optimal release schedule in the calibrationperiod.

Figure 4 shows that the fitting accuracy of operatingrules in the flood season is better than that of operatingrules in the non-flood season in both the TGR and theQing River cascade reservoirs (QRCR). The fittingaccuracy of nonlinear operating rules (R2 = 95.95% inTGR and R2 = 96.13% in QRCR) is better than that oflinear operating rules (R2 = 89.89% in TGR andR2 = 88.52% in QRCR) in the non-flood season; how-ever, the fitting accuracy of nonlinear operating rules(R2 = 99.86% in TGR and R2 = 98.77% in QRCR)

Table 2. Comparison of operation results with observed inflowfrom 1951 to 2011.Reservoir Scheme Calibration Validation

P(%)

MHE(109

kWh)

R2

(%)P(%)

MHE(109

kWh)

R2

(%)

Three Georgescascade

SOP 95 96.06 — 95 96.01 —DOO 98 100.98 — 98 100.56 —NWOR 97 98.77 97.91 96 98.30 97.34

Qing Rivercascade

SOP 95 8.30 — 94 8.28 —DOO 98 9.31 — 98 9.27 —NPOR 97 9.30 97.45 96 9.17 97.21

Mixed multi-reservoirs

SOP 95 104.36 — 94 104.29 —DOO 98 110.29 — 98 109.83 —NWOR-NPOR

97 108.07 97.39 96 107.47 97.24

Res

ervo

irw

ater

leve

l(m

)

140

145

150

155

160

165

170

175

July Aug Sep Oct Nov Dec Jan Feb Mar Apr MayJun

145.0 145.0 145.0 175.0 175.0 175.0 175.0 175.0 175.0 175.0 175.0 175.0

145.0 145.0 145.0 145.0 156.3 169.6 166.6 160.9 155.0 155.0 155.0 155.0

Month

Upper boundaryCurve (m)

Lower boundaryCurve (m)

I

II

IIIIIII

IV

Figure 2. Designed operating rule curves of the Three Gorges Reservoir (I: flood control zone; II: install output power zone; III: firmoutput power zone; and IV: lower output power zone).

HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES 365

approximates to that of linear operating rules(R2 = 99.58% in TGR and R2 = 92.36% in QRCR) inthe flood season. The NWOR scheme can performbetter than the LWOR scheme for the TGR, andNPOR can perform better than LPOR for the QRCR.The explanations are as follows:(a) Influenced by the hydrological differences between

flood season and non-flood season, the linear char-acteristic of operating rules is noticeable in the floodseason; however, the nonlinear characteristic ofoperating rules is noticeable in the non-flood season.

(b) The ANN method shows not only the linear charac-teristics but also the nonlinear characteristics, whiletheMLR analysis only represents linear characteristics.

As a further visual analysis, surfaces for nonlinearoperating rules are shown in Figs 5 and 6, which showthat the linear characteristics of operating rules are moreremarkable than the nonlinear characteristics for theTGR in October, and the nonlinear characteristics ofoperating rules are more remarkable than the linearcharacteristics in January. However, the linear character-istics of operating rules are more remarkable than thenonlinear characteristics for the aggregated reservoir inOctober, and the nonlinear characteristics of operatingrules are more remarkable than the linear characteristicsin January and in the interim period in May.

The performance of the NWOR-NPOR scheme (i.e.nonlinear water operating rules for the TGR and

Res

ervo

irw

ater

leve

l(m

)

340

350

360

370

380

390

400

July Aug Sep Oct Nov Dec Jan Feb Mar Apr MayJun

397.0 391.8 391.8 397.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0

350.0 350.0 350.0 350.0 350.0 350.0 350.0 350.0 350.0 350.0 350.0 350.0

Month

Upper boundaryCurve (m)

Lower boundaryCurve (m)

IIII

II

IV

II

III

V

Figure 3. Designed operating rule curves of the Shuibuya Reservoir (I: flood control zone; II: install output power zone; III: increasingoutput power zone; IV: firm output power zone; and V: lower output power zone).

85.00

88.00

91.00

94.00

97.00

100.00

May June July August September October

R2 (

%)

Flood season in Qing River cascade reservoirs

LPOR NPOR

Mean of LPOR Mean of NPOR

75.00

80.00

85.00

90.00

95.00

100.00

November December January February March April

R2 (

%)

Non-flood season in Qing River cascade reservoirs

LPOR NPORMean of LPOR Mean of NPOR

99.00

99.20

99.40

99.60

99.80

100.00

May June July August September October

R2 (

%)

Flood season in TGR

LWOR NWOR

Mean of LWOR Mean of NWOR

75.00

80.00

85.00

90.00

95.00

100.00

November December January February March April

R2 (

%)

Non-flood season in TGR

LWOR NWOR

Mean of LWOR Mean of NWOR

Figure 4. Fitting accuracy of operating rules in the calibration period. LWOR and NWOR: linear and nonlinear water operating rules,respectively, for the TGR; LPOR and NPOR are the linear and nonlinear power operating rules for the Qing River cascade reservoirs,respectively.

366 Y. ZHOU ET AL.

nonlinear power operating rules for the QRCR) isgiven in Table 2. Table 2 shows that P and MHE areimproved in the NWOR-NPOR scheme when com-pared to the standard operating policy (SOP) scheme.For the calibration period, the NWOR-NPOR schemecan generate 3.71 × 109 kWh more power (an increaseof 3.55%) than the SOP scheme; P increased from 95%

to 97% and R2 = 97.39% for the multi-reservoir. For thevalidation period, the NWOR-NPOR scheme can gen-erate 3.18 × 109 kWh more power (an increase of3.05%) compared with the SOP scheme; P increasedfrom 94% to 96% and R2 = 97.24% for the multi-reservoir. It is shown that the combination of waterand power operating rules can improve not only the

Figure 5. Comparison of surfaces for operating rules in the TGR.

HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES 367

assurance probability of output power but also themean hydropower generation, when compared withthe designed operating rules.

4 Conclusions

The combination of water and power operating rules,which are modifications of the single water or power

operating rules, was proposed and developed. TheThree Georges cascade reservoirs and Qing River cas-cade reservoirs were selected as a case study. The mainconclusions are summarized as follows:(1) The characteristics of flood and non-flood seasons,

and sample input (water or power) should be con-sidered if operating rules are being derived formulti-reservoirs.

Figure 6. Comparison of surfaces for operating rules in the QRCR.

368 Y. ZHOU ET AL.

(2) The combination of water and power operatingrules can improve not only the assurance probabil-ity of output power but also the mean hydropowergeneration compared to the designed operatingrules. The mixed water and power operating rulesare effective and efficient for operation of multi-reservoirs because of their better performancecompared to the designed operating rules.

Acknowledgements

The authors are grateful to Dr David Emmanuel Rheinheimerfor improvements to an early version of this paper. Theauthors would also like to thank the editor and anonymousreviewers for their reviews and valuable comments related tothe manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This study is financially supported by the National NaturalScience Foundation of China (51079100, 51190094 and51509008), Natural Science Foundation of Hubei Province(2015CFB217) and Open Foundation of State Key Laboratoryof Water Resources and Hydropower Engineering Science inWuhan University (2014SWG02).

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