Hydrological Sciences Journal
ISSN: 0262-6667 (Print) 2150-3435 (Online) Journal homepage: http://www.tandfonline.com/loi/thsj20
Derivation of water and power operating rules for
multi-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 (2015):
Derivation of water and power operating rules for multi-reservoirs, Hydrological Sciences
Journal, 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: 01
Apr 2015.
Published online: 04 Dec 2015.
Submit your article to this journal
Article views: 36
View related articles
View Crossmark data
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=thsj20
Download by: [University of Oslo]
Date: 26 January 2016, At: 02:25
HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES, 2015
http://dx.doi.org/10.1080/02626667.2015.1035656
Derivation of water and power operating rules for multi-reservoirs
Yanlai Zhoua,b, Shenglian Guoa, Pan Liua, Chong-yu Xua,c and Xiaofeng Zhaod
Downloaded by [University of Oslo] at 02:25 26 January 2016
a
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China; bChangjiang River
Scientific Research Institute, Wuhan, China; cDepartment of Geosciences, University of Oslo, Oslo, Norway; dHubei Provincial Water
Resources and Hydropower Planning Survey and Design Institute, Wuhan, China
ABSTRACT
ARTICLE HISTORY
Water operating rules have been universally used to operate single reservoirs because of their
practicability, but the efficiency of operating rules for multi-reservoir systems is unsatisfactory in
practice. For better performance, the combination of water and power operating rules is proposed and developed in this paper. The framework of deriving operating rules for multi-reservoirs
consists of three modules. First, a deterministic optimal operation module is used to determine
the optimal reservoir storage strategies. Second, a fitting module is used to identify and estimate
the 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 observed
inflows. 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 rules
can improve not only the assurance probability of output power, but also annual average
hydropower generation when compared with designed operating rules. It is indicated that the
characteristics of flood and non-flood seasons, as well as sample input (water or power), should
be considered if the operating rules are developed for multi-reservoirs.
Received 3 January 2013
Accepted 10 November
2014
1 Introduction
Reservoirs are among the most effective systems for
integrated water resources development and management. Currently, reservoirs have played an increasingly
important role in balancing the contradiction between
social development and water resources scarcity (Guo
et al. 2004, Li et al. 2013, Urbaniak et al. 2013). Several
models and methods for reservoir operation have been
proposed and reviewed (e.g. Yakowitz 1982, Yeh 1985,
Simonovic 1992, Wurbs 1993). However, it is difficult
to apply a single best model or method to solve the
operation problem of a multi-reservoir system (Labadie
2004).
Operating rules are often used to provide guidelines
for reservoir releases to maintain the best interests of a
reservoir, being consistent with certain inflow and
existing storage levels (Tu et al. 2003, Chang et al.
2005). Deriving operating rules involves optimization,
fitting, refinement and simulation (Yeh 1985, Wurbs
1993, Labadie 2004, Celeste and Billib 2009, Liu et al.
2011a, 2011b). How to select an operating rule turned
out to be one of the challenges in their derivation (Saad
et al. 1994); two forms of operating rules, i.e. water
operating rules (Karamouz and Houck 1982,
CONTACT: Yanlai Zhou
© 2015 IAHS
zyl23bulls@whu.edu.cn
EDITOR
D. Koutsoyiannis
ASSOCIATE EDITOR
not assigned
KEYWORDS
multi-reservoirs; operating
rule; progressive optimality
algorithm; genetic
algorithm; aggregation
–decomposition
Ostadrahimi et al. 2012) and power operating rules
(Terry et al. 1986, Oliveira and Loucks 1997, Liu
et al. 2011a), were used to coordinate the operation
among cascade reservoirs. Although the fitting method
contributes to the derivation of types of operating rule
for a single reservoir, the goodness-of-fit criterion for
deriving operating rules in water units does not always
obtain the best operating rule for cascade reservoirs.
The dimensionality problem often arises in the
operation of cascade reservoirs in water units. At the
same time, the efficiency of optimization algorithms is
also reduced by redundancy parameters of operating
rules in water units. However, the aggregation–decomposition method, which is one of the most efficient
methods for converting cascade reservoirs into an
equivalent reservoir, has been used to derive operating
rules of cascade reservoirs. Hall and Dracup (1970)
originally proposed a method of surmounting the
dimensionality problem of dynamic programming
(DP) for cascade reservoirs by aggregating all reservoirs
into an equivalent reservoir, in which the optimal solutions for the aggregated reservoir were decomposed
into individual solutions for the single reservoirs.
Then Turgeon (1981) applied this concept to cascade
reservoirs using stochastic DP. Valdés et al. (1992)
Downloaded by [University of Oslo] at 02:25 26 January 2016
2
Y. ZHOU ET AL.
aggregated reservoirs in a hydropower system in power
units rather than water units. Oliveira and Loucks
(1997) showed that the aggregated reservoir approach
was useful for making decisions regarding total releases
for water supply of cascade reservoirs. Liu et al. (2011a)
studied the optimal operating rule curves of cascade
reservoirs based on the aggregation–decomposition
method. Similar approaches have been proposed and
developed to carry out optimization, fitting, refinement
and 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 and
Guzman 1999, Koutsoyiannis and Economou 2003,
Rani and Moreira 2010, Chen et al. 2013) has applied
those methods to derivation of operating rules for
cascade reservoirs.
Most previous studies for operating rules paid more
attention to a single reservoir or cascade reservoirs rather
than multi-reservoirs (including parallel reservoirs and
cascade reservoirs). Since there are hydraulic connections
and storage compensations between the upstream and
downstream reservoirs in multi-reservoirs, derivation of
operating rules will become more and more complex as
the number of reservoirs is increased. Our study aims to
attempt to extend the operating rules from single reservoir to multi-reservoirs. We find that the forms of the
rules, i.e. the variables and function forms, allow us to
deduce the best decision, and our framework allows the
analysis of the optimal release schedule obtained from the
deterministic optimal operation module using a multiple
linear regression analysis (MLR) and artificial neural network (ANN) approach. The operating rules were further
tested with observed inflows. A multi-reservoir system,
consisting of the Three Gorges cascade and Qing River
cascade reservoirs in the Changjiang (Yangtze) river
basin of China, is selected as a case study.
The paper is organized as follows: Section 2 gives a
general description of the modelling framework and
then details the components of the model, i.e. a deterministic optimal operation module, a fitting operating
rules module, and a testing operating rules module. In
Section 3 the case study is introduced briefly and the
simulation results for the multi-reservoir system are
discussed. Section 4 contains the conclusions.
operation: explicit stochastic optimization (ESO) and
implicit stochastic optimization (ISO). In ESO, the
inflow process is directly described using its probability
distributions, and then traditional optimization methods can be applied to solve the problem. One typical
example of the ESO approach is stochastic dynamic
programming (SDP; Karamouz and Houck 1987).
Although the ESO approach may seem germane (Yeh
1985), its application in practice presents considerable
difficulties. For large systems it entails a great deal of
calculation that severely restricts its application. For
deterministic modelling, five reservoirs is considered
large-scale, but for ESO modelling, three reservoirs is
large-scale (Labadie 2004). Therefore, for stochastic
optimization with more than five reservoirs, it is not
realistic to use the ESO approach.
The ISO approach uses a deterministic optimization
method to operate the reservoir system with a series of
historical or Monte-Carlo generated inflows, and then
examines the optimal operating results to develop
operating rules. Such rules can serve as guides to the
reservoir operators in actual operation.
In ISO, the stochastic optimization is decomposed into
two stages: deterministic operation and operating rule
derivation. This greatly reduces model dimensionality
and calculation complexity, thus making the ISO
approach much more applicable than the ESO approach,
especially for the actual operation of large-scale reservoirs.
Therefore, in this study, the framework of deriving
operating rules for multi-reservoirs under the ISO
approach is proposed. The framework consists of the
following three modules:
(1) A deterministic optimal operation module is used to
determine the optimal reservoir storage strategies, in
which the Monte Carlo method is used to simulate
the values of boundary conditions and coarse DP is
used to determine the initial feasible solutions of the
progressive optimality algorithm (POA) used to
derive the optimal solutions.
(2) A fitting module is used to identify and estimate
the forms and variables of the preliminary operating rules using the MLR and ANN approach.
(3) A testing module is used to test the fitting operating rules with observed inflows.
The details of each step are as follows.
2 Methodology
The optimal operation of a multi-reservoir system is
challenging, especially taking into consideration the
inflow uncertainty. The stochastic nature of inflow
can be incorporated into the optimization model either
explicitly or implicitly, which generates two approaches
for reservoir and hydropower stochastic optimal
2.1 Deterministic optimal operation module for
sample generation
The deterministic optimal operation module is used to
determine the optimal reservoir storage strategies for
multi-reservoirs to generate as much hydropower as
possible.
HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES
2.1.1 Objective function
If the multi-reservoirs can meet the water supply and
initial power generation requirements, then the objective
function that generates maximum hydropower is
selected, i.e.:
max HG ¼
Nt X
Nm
X
TOPt;i Δt
(1)
3
2.1.2.4 Comprehensive utilization of water required at
reservoirs’ downstream limits.
Dmin t;j Dt;j Dmax t;j
(6)
where Dmin t,j and Dmax t,j are the minimum and maximum water discharge, respectively, for all downstream
uses in period t (m3/s).
t¼1 i¼1
Downloaded by [University of Oslo] at 02:25 26 January 2016
where HG is the sum of the hydropower generation of
the cascade reservoirs (kWh); Nt (t = 1, 2, . . .) is the
number of time period; Nm (i = 1, 2, . . .) is the number
of cascade reservoirs in the multi-reservoir; TOPt,i is
the total output power of the ith cascade reservoirs in
period t (kW); and Δt is the interval of time.
2.1.2.5 Power generation limits.
OPmin t;j OPt;j OPmax t;j
where OPmin t,j and OPmax t,j are the minimum and
maximum output power limitations of the reservoir,
respectively, in period t (kW).
2.1.2.6 Boundary conditions limit.
2.1.2 Constraints
The following constraints were imposed:
W1;j ¼ Wini j
WNp þ1;j ¼ Wfin j
2.1.2.1 Firm output power constraints of the cascade
reservoirs.
TOPt;i ¼ OPCt;i vp FOPi OPCt;i
(2)
OPCt;i ¼
Nc
X
OPt;j
(3)
j¼1
where OPCt,i is the output power of the ith cascade
reservoirs in period t (kW); FOPi is the ith cascade
reservoirs’ firm output power (kW); v is a variable (= 1
if OPCt,i ≥ FOPi; = 0 otherwise); p is a positive number
for penalty; OPt,j is the output power of the jth reservoir in period t (kW); and Nc is the number of reservoirs 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 period
t (m3); It,j is the inflow of the jth reservoir in period
t (m3/s); Dt,j is the water discharge of the jth reservoir in period t (m3/s); and ESt,j is the sum of
evaporation and seepage of the jth reservoir in period t (m3/s).
2.1.2.3 Reservoir water level limits.
Wmin t;j Wt;j Wmax t;j
(7)
(5)
where Wt,j is the reservoir water level; and Wmin t,j and
Wmax t,j the minimum and maximum water level,
respectively, of the jth reservoir in period t (m).
(8)
It is worth mentioning that the principle that the final
water level WNp+1,j is the same as the initial water level
W1,j (or as close as possible) in reservoir operation is
only appropriate for reservoirs with annual regulation
ability, but not always suitable for reservoirs with
multi-year, seasonal and daily regulation ability.
Therefore, to reflect the uncertainty of the boundary
conditions limit, the Monte Carlo method is used to
simulate 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 Wmin Np þ1;j þ Wmax Np þ1;j Wmin Np þ1;j Rand
(9)
where Wini j and Wfin j are the reservoir water level of
the jth reservoir in the initial and final time steps,
respectively (m); and Rand is the random number of
uniform distribution in the range [0,1].
2.1.3 Optimality algorithm
Comparison of modified DP algorithms, such as dynamic
programming successive approximations (DPSA), discrete
differential 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 a
better 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 algorithm
are input as the initial solution of the POA, after which a
subsequent optimization routine is executed. For detailed
description of the coupling between the coarse DP
4
Y. ZHOU ET AL.
algorithm and POA, readers are referred to Liu et al. (2006)
and Chen et al. (2013).
Downloaded by [University of Oslo] at 02:25 26 January 2016
2.1.4 Transformation to potential energy
An aggregated reservoir can preserve and describe some
features of the multi-reservoir system without considering
their interactions (Liu et al. 2011a, Chen et al. 2013). The
reservoirs in a hydropower system are aggregated in energy
units rather than in water units and an optimal operation
policy for the equivalent aggregated reservoir is determined
based on a deterministic optimal operation module. The
aggregation was carried out to convert the water stored in
each reservoir into energy units, based on an approach
originally suggested by Arvanitidis and Rosing (1970),
and applied by Turgeon (1981) and Valdés et al. (1992).
The total initial potential energy (TIPEt) stored in cascade reservoirs i to Nc at the end of period t is as follows:
TIPEt ¼
Nc X
Nc
X
ci St;j S0;j
(10)
j¼1 i¼j
The inflow of potential energy (IPEt) to reservoirs i to
Nc in period t is:
IPEt ¼
Nc X
Nc
X
ci It;j
(11)
step, TPEt, and outflow of potential energy, OPEt,
for an aggregated reservoir.
(b) Independent variables should be as comprehensive
as possible, so the model can fully reflect the status
of the reservoir and power station, such as inflow,
It,j, and reservoir storage at the beginning of the
time step, St,j, for a single reservoir, as well as total
initial potential energy, TIPEt, and inflow of potential energy, IPEt, for an aggregated reservoir.
(c) Variables should be independent of each other.
Independence means, for instance, the reservoir
storage status can be described in three ways: reservoir water level, reservoir storage status and storage
energy. However, not all of them need to be
adopted in the independent variables set, because
they 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 for
water operating rules in a single reservoir, and inflow
of potential energy, IPEt, and total initial potential
energy, TIPEt, are chosen as independent variables for
power operating rules in an aggregated reservoir. Liu
et al. (2011a) explained the meaning and calculation of
independent variables in detail.
j¼1 i¼j
and the outflow of potential energy (OPEt) from reservoirs i to Nc in period t is:
OPEt ¼
Nc
X
cj Dt;j
(12)
j¼1
where S0,j is the inactive storage of the jth reservoir
(m3); ci is the conversion factor of the ith reservoir; and
cj the conversion factor of the jth reservoir.
2.2.1 Water operating rules
Because of the simplicity of the water operating rules, the
general forms of linear (Karamouz and Houck 1982,
Ostadrahimi et al. 2012) and nonlinear operating rules
(Neelakantan and Pundarikanthan 2000, Chandramouli
and Raman 2001, Liu et al. 2006) have been often used in
reservoir operation. Based on the results of the deterministic optimal operation module, the following linear and
nonlinear water operating rules for each time period can
be 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)
2.2 Fitting operating rules module
Dependent and independent variables constitute the
basic framework of operating rules. Proper selection
of these variables has great importance for model accuracy. There are several principles for the formulation
and 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 output
power, OPt,j, reservoir storage at the end of the
time 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
where αi (i = 0, 1 and 2) is the parameter of linear
water operating rules; εi (i = 0 or 1) is the random
variable of water operating rules; and f(⋅) is the nonlinear function of water operating rules.
2.2.2 Power operating rules
Based on the results of the aggregated reservoir for
cascade reservoirs, the linear (Liu et al. 2011a) and
nonlinear power operating rules (Turgeon 1981) for
HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES
each time period, which are used to describe the quantitative relationship between the total output power of
the aggregated reservoir, TOPt, and the optimal aggregated energy, can be established:
TOPt ¼ β0 þ β1 TIPEt þ β2 IPEt þ ε3
TOPt ¼ f ðTIPEt ; IPEt Þ þ ε4
(15)
(16)
Downloaded by [University of Oslo] at 02:25 26 January 2016
where βi (i = 0, 1 and 2) is the parameter of linear
power operating rules; and εi (i = 3 or 4) is the random
variable of power operating rules.
2.2.3 Fitting methods
Multiple linear regression (Karamouz and Houck 1982,
Liu et al. 2011a, Ostadrahimi et al. 2012) and artificial
neural networks (Saad et al. 1994, Chandramouli and
Raman 2001, Liu et al. 2006) are employed to develop
the operating rules for multi-reservoirs. For a detailed
description of MLR and ANN used in this paper, readers are referred to Liu et al. (2006).
2.3 Testing operating rules module
It is necessary to test whether the operating rules are
able to deduce the best decision, because the operating
rules are the approximate quantitative relationships
among reservoir variables. The operation period is
divided into calibration and validation periods.
2.3.1 Testing water operating rules
Once the water operating rules have been determined,
their performance can be evaluated and assessed by
simulation with observed inflows in the calibration
and verification periods.
2.3.2 Testing power operating rules
The decomposition method is aimed at decomposing the
total output power of an aggregated reservoir and maximizing the total initial potential energy at the end of
period t for a multi-reservoir system. The objective function that generates maximum total potential energy,
TPEt+1, for the end period is selected, maxTPEt+1 subject
to output power of the multi-reservoir system limit conNc
P
straint TOPst ¼
OPt;j , where TOPts is the simulation
j¼1
output power of the jth reservoir in period t (kW). Other
limit constraints are the same as equations (2)–(9).
Although POA is applied to sample generation for
the operating rules, the genetic algorithm (GA) is
selected as the optimal algorithm for testing the operating rules. Compared with POA, the combination of
MLR, ANN and GA is easily applied to derive
5
operating rules effectively (Chang and Chang 2001,
Naresh and Sharma 2001). A general flowchart of the
genetic algorithm is shown in many studies in the
literature (e.g. Oliveira and Loucks 1997, Hınçal et al.
2011, Liu et al. 2011a). The GA is used to solve the
whole model, including maxTPEt+1 and equations
(2)–(9).
2.3.3 Evaluation criteria
Different disciplines have different performance
indices. For example, the oldest and most widely
used performance criteria for water resources systems are reliability, resiliency and vulnerability
(Hashimoto et al. 1982, Moy et al. 1986). Criteria
such as the Nash-Sutcliffe efficiency, root mean
square error and relative error are used to evaluate
the prediction abilities of hydrological models
(Bennett et al. 2013). For particular reservoirs or a
system of hydropower stations, the assurance probability of output power and mean hydropower
energy, for example, are used to compare the performance of different operation schemes and models
(Liu et al. 2006). Therefore, three evaluation criteria
were selected to compare the performance of the
different schemes for the multi-reservoir system: (a)
the assurance probability of output power, P; the
mean hydropower energy, MHE; and the NashSutcliffe efficiency index, R2. The three indices are
defined as follows:
n
P ¼ 100%
(17)
Nt
MHE ¼
Nt X
Nc
1 X
TOPt;i Δt
Ny t¼1 i¼1
(18)
The Nash-Sutcliffe efficiency index is used to assess the
performance of these two fitting methods, and is
given by:
2
3
Ny 2
P
s
OPi OOPi 7
6
6
7
(19)
R2 ¼ 61 Ni¼1
7 100%
4
5
Py
2
ðOOPi MOOPÞ
i¼1
where MHE is the mean hydropower energy in simulation years (kWh); n is the number of occurrences of
TOPi,t ≥ FOPi; OOPi is the optimal output power in
year i for a single or aggregated reservoir (MW); OPis is
the simulated output power in year i for a single
reservoir or aggregated reservoir (MW); MOOP is the
mean of optimal output power in year i for a single or
aggregated reservoir (MW); and Ny the number of
years.
6
Y. ZHOU ET AL.
3 Case study
Downloaded by [University of Oslo] at 02:25 26 January 2016
3.1 Three Gorges cascade and Qing River cascade
reservoirs
A multi-reservoir system consisting of the Three
Gorges cascade reservoirs (Three Gorges, Gezhouba)
and the Qing River cascade reservoirs (Shuibuya,
Geheyan, Gaobazhou) in the Changjiang River basin
of China, as shown in Fig. 1, is selected as a case study.
The Three Gorges Reservoir (TGR) is a vitally
important and backbone project in the development
and harnessing of the Changjiang River in China. The
upstream of the Changjiang, with main course length
of about 4.5 × 103 km and a drainage area of
1.0 × 106 km2, is intercepted by the TGR. The TGR is
the largest water conservancy project ever undertaken
in the world, with a normal pool level at 175 m and a
total reservoir storage capacity of 39.3 × 109 m3, of
which 22.15 × 109 m3 is flood control storage and
16.5 × 109 m3 is a conservation regulating storage
volume, accounting for approximately 3.7% of the
dam site mean annual runoff of 451 × 109 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 × 109 m3 and a maximum flood discharging capability of 110 000 m3/s.
The Qing River is one of the main tributaries of the
Changjiang River and its basin area is 17 600 km2. The
mean annual rainfall, runoff depth and annual runoff
are approximately 1460 mm, 876 mm and 423 m3/s,
respectively. The total length of the mainstream is
423 km, with a hydraulic drop of 1430 m. Along the
Qing River, a three-step cascade of reservoirs
(Shuibuya, Geheyan and Gaobazhou) has been constructed from upstream to downstream. The main
functions of these cascade reservoirs are power generation and flood control. The characteristic parameter
values of these five reservoirs are given in Table 1.
3.2 Results and discussion
The multi-reservoirs are composed of the Three Gorges
cascade reservoirs and Qing River cascade reservoirs.
The Gezhouba and Gaobazhou reservoirs are runoff
hydropower plants with small regulation storages;
therefore, water operating rules are applied to simulate
the operation of the TGR, and water and power operating rules are applied to simulate the operation of the
Shuibuya and Geheyan reservoirs. Aside from the
water and power operating rules, two other schemes,
conventional operation and optimal operation rules,
are also implemented to simulate the operation of the
multi-reservoirs for comparative purposes. The operation 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
Total storage
Flood control storage
Crest elevation
Normal water level
Flood limited water level
Install capability
Annual generation
Regulation ability
Unit
TGR
Gezhouba
Shuibuya
Geheyan
Gaobazhou
108 m3
108 m3
m
m
m
MW
109 kWh
—
393
221.5
185
175
145.0
22400
84.7
Seasonal
15.8
—
70
66
—
2715
15.7
Daily
42
5.0
409
400
391.8
1840
3.41
Multi-years
34
5.0
206
200
192.2
1212
3.04
Annual
5.4
—
83
80
—
270
0.93
Daily
Table 2. Comparison of operation results with observed inflow
from 1951 to 2011.
Reservoir
Three Georges
cascade
Qing River
cascade
Mixed multireservoirs
Scheme
SOP
DOO
NWOR
SOP
DOO
NPOR
SOP
DOO
NWORNPOR
Calibration
Validation
R2
(%)
P
(%)
MHE
(109
kWh)
95
98
97
95
98
97
95
98
97
96.06 —
100.98 —
98.77 97.91
8.30 —
9.31 —
9.30 97.45
104.36 —
110.29 —
108.07 97.39
R2
(%)
P
(%)
MHE
(109
kWh)
95
98
96
94
98
96
94
98
96
96.01 —
100.56 —
98.30 97.34
8.28 —
9.27 —
9.17 97.21
104.29 —
109.83 —
107.47 97.24
7
storage space is divided into five operational zones. If
the water level rises to FLWL or into the flood prevention zone during the flood season, the reservoir is
operated according to designed flood control rules.
Otherwise, the hydropower plant is operated between
the upper and lower basic guide curves. The designed
operating rules do not acknowledge the potential for
coordinated operation between the multi-reservoirs.
Due to the potential profits when compared with the
deterministic optimal operation (DOO in Table 2), it is
feasible to jointly operate the multi-reservoirs to
improve the hydropower benefits and generation assurance rate. The DOO is based upon the observed inflow
series and can be seen as an ideal operation in theory.
Two fitting methods are used to derive the water
and power operating rules based on the results of the
deterministic optimal operation. One is multiple linear
regression analysis, i.e. the linear water and power
operating rules are derived from MLR analysis of the
optimal release schedule in the calibration period. The
other is the ANN method, in which the nonlinear
water and power operating rules are derived by analysing the optimal release schedule in the calibration
period.
Figure 4 shows that the fitting accuracy of operating
rules in the flood season is better than that of operating
rules in the non-flood season in both the TGR and the
Qing River cascade reservoirs (QRCR). The fitting
accuracy of nonlinear operating rules (R2 = 95.95% in
TGR and R2 = 96.13% in QRCR) is better than that of
linear operating rules (R2 = 89.89% in TGR and
R2 = 88.52% in QRCR) in the non-flood season; however, the fitting accuracy of nonlinear operating rules
(R2 = 99.86% in TGR and R2 = 98.77% in QRCR)
1951 to 2011) is divided into a calibration period
(1951–1991) and a validation period (1992–2011), and
the time interval is 10 days.
The designed operating rules can be regarded as a
standard operating policy (SOP in Table 2). Only the
designed operating rule curves of the TGR and
Shuibuya Reservoir are described briefly; the designed
operating rule curves of the TGR are shown in Fig. 2.
From the end of May to the beginning of June, the
reservoir water level will be lowered to 145 m (flood
limited water level, FLWL). In October, the reservoir
water level will be raised gradually to the normal pool
level of 175 m. From November to the end of April in
the following year, the reservoir water level should be
kept at as high as possible to generate more electrical
power. The reservoir water level will be lowered
further, but should not fall below 155 m before the
end of April to satisfy navigation conditions. The
designed operating rule curves of the Shuibuya
Reservoir are shown in Fig. 3, in which the whole
175
II
170
Reservoir water level (m)
Downloaded by [University of Oslo] at 02:25 26 January 2016
HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES
II
III
165
I
160
155
IV
150
145
II
140
Month
Upper boundary
Curve (m)
Lower boundary
Curve (m)
Jun
July
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
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
Figure 2. Designed operating rule curves of the Three Gorges Reservoir (I: flood control zone; II: install output power zone; III: firm
output power zone; and IV: lower output power zone).
8
Y. ZHOU ET AL.
Reservoir water level (m)
400
II
390
II
I
III
III
380
IV
370
V
360
350
340
Month
Jun
Upper boundary
Curve (m)
Lower boundary
Curve (m)
July
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
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
Non-flood season in TGR
100.00
100.00
99.80
95.00
99.60
90.00
R2(%)
R2(%)
Flood season in TGR
99.40
85.00
99.20
80.00
99.00
May
June
July
August
September
75.00
November
October
LWOR
NWOR
Mean of LWOR
Mean of NWOR
97.00
95.00
94.00
90.00
R2(%)
100.00
91.00
85.00
88.00
80.00
June
July
LPOR
Mean of LPOR
August
September
October
NPOR
Mean of NPOR
January
February
March
April
NWOR
Mean of NWOR
Non-flood season in Qing River cascade reservoirs
100.00
85.00
May
December
LWOR
Mean of LWOR
Flood season in Qing River cascade reservoirs
R2(%)
Downloaded by [University of Oslo] at 02:25 26 January 2016
Figure 3. Designed operating rule curves of the Shuibuya Reservoir (I: flood control zone; II: install output power zone; III: increasing
output power zone; IV: firm output power zone; and V: lower output power zone).
75.00
November
December
January
LPOR
Mean of LPOR
February
March
April
NPOR
Mean of NPOR
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.
approximates to that of linear operating rules
(R2 = 99.58% in TGR and R2 = 92.36% in QRCR) in
the flood season. The NWOR scheme can perform
better than the LWOR scheme for the TGR, and
NPOR 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 characteristic of operating rules is noticeable in the flood
season; however, the nonlinear characteristic of
operating rules is noticeable in the non-flood season.
(b) The ANN method shows not only the linear characteristics but also the nonlinear characteristics, while
the MLR analysis only represents linear characteristics.
As a further visual analysis, surfaces for nonlinear
operating rules are shown in Figs 5 and 6, which show
that the linear characteristics of operating rules are more
remarkable than the nonlinear characteristics for the
TGR in October, and the nonlinear characteristics of
operating rules are more remarkable than the linear
characteristics in January. However, the linear characteristics of operating rules are more remarkable than the
nonlinear characteristics for the aggregated reservoir in
October, and the nonlinear characteristics of operating
rules are more remarkable than the linear characteristics
in 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
9
Downloaded by [University of Oslo] at 02:25 26 January 2016
HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES
Figure 5. Comparison of surfaces for operating rules in the TGR.
nonlinear power operating rules for the QRCR) is
given in Table 2. Table 2 shows that P and MHE are
improved in the NWOR-NPOR scheme when compared to the standard operating policy (SOP) scheme.
For the calibration period, the NWOR-NPOR scheme
can generate 3.71 × 109 kWh more power (an increase
of 3.55%) than the SOP scheme; P increased from 95%
to 97% and R2 = 97.39% for the multi-reservoir. For the
validation period, the NWOR-NPOR scheme can generate 3.18 × 109 kWh more power (an increase of
3.05%) compared with the SOP scheme; P increased
from 94% to 96% and R2 = 97.24% for the multireservoir. It is shown that the combination of water
and power operating rules can improve not only the
Y. ZHOU ET AL.
Downloaded by [University of Oslo] at 02:25 26 January 2016
10
Figure 6. Comparison of surfaces for operating rules in the QRCR.
assurance probability of output power but also the
mean hydropower generation, when compared with
the 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. The
Three Georges cascade reservoirs and Qing River cascade reservoirs were selected as a case study. The main
conclusions are summarized as follows:
(1) The characteristics of flood and non-flood seasons,
and sample input (water or power) should be considered if operating rules are being derived for
multi-reservoirs.
HYDROLOGICAL SCIENCES JOURNAL – JOURNAL DES SCIENCES HYDROLOGIQUES
(2) The combination of water and power operating
rules can improve not only the assurance probability of output power but also the mean hydropower
generation compared to the designed operating
rules. The mixed water and power operating rules
are effective and efficient for operation of multireservoirs because of their better performance
compared to the designed operating rules.
Acknowledgements
Downloaded by [University of Oslo] at 02:25 26 January 2016
The authors are grateful to Dr David Emmanuel Rheinheimer
for improvements to an early version of this paper. The
authors would also like to thank the editor and anonymous
reviewers for their reviews and valuable comments related to
the manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
This study is financially supported by the National Natural
Science Foundation of China (51079100, 51190094 and
51509008), Natural Science Foundation of Hubei Province
(2015CFB217) and Open Foundation of State Key Laboratory
of Water Resources and Hydropower Engineering Science in
Wuhan University (2014SWG02).
References
Archibald, TW., McKinnon, KIM., and Thomas, LC., 1997.
An aggregate stochastic dynamic programming model of
multi-reservoir systems. Water Resources Research, 33 (2),
333–340. doi:10.1029/96WR02859
Arvanitidis, NV. and Rosing, J., 1970. Composite representation of a multi-reservoir hydroelectric power system.
IEEE Transaction on Power Apparatus and System, 89
(2), 319–326.
Bennett, ND., et al., 2013. Characterising performance of
environmental models. Environmental Modelling and
Software, 40, 1–20. doi:10.1016/j.envsoft.2012.09.011
Celeste, AB. and Billib, M., 2009. Evaluation of stochastic
reservoir operation optimization models. Advances in
Water Resources, 32 (9), 1429–1443. doi:10.1016/j.
advwatres.2009.06.008
Chandramouli, V. and Raman, H., 2001. Multi-reservoir
modeling with dynamic programming and neural networks. Journal of Water Resources Planning and
Management, 127 (2), 89–98. doi:10.1061/(ASCE)07339496(2001)127:2(89)
Chang, F-J., Chen, L., and Chang, L-C., 2005. Optimizing the
reservoir operating rule curves by genetic algorithms.
Hydrological Processes, 19 (11), 2277–2289. doi:10.1002/
(ISSN)1099-1085
11
Chang, L. and Chang, F., 2001. Intelligent control for
modelling
of
real-time
reservoir
operation.
Hydrological Processes, 15 (9), 1621–1634. doi:10.1002/
(ISSN)1099-1085
Chen, J., et al., 2013. Joint operation and dynamic control of
flood limiting water levels for cascade reservoirs. Water
Resources Management, 27 (3), 749–763. doi:10.1007/
s11269-012-0213-z
Guo, SL., et al., 2004. A reservoir flood forecasting and
control system for China. Hydrological Sciences Journal,
49 (6), 959–972. doi:10.1623/hysj.49.6.959.55728
Guo, SL., et al., 2011. Joint operation of the multi-reservoir
system of the Three Gorges and the Qingjiang Cascade
Reservoirs. Energies, 4 (7), 1036–1050. doi:10.3390/
en4071036
Hall, WA. and Dracup, JA., 1970. Water resources systems
engineering. New York: McGraw-Hill.
Hashimoto, T., Stedinger, JR., and Loucks, DP., 1982.
Reliability, resiliency, and vulnerability criteria for water
resource system performance evaluation. Water Resources
Research, 18 (1), 14–20. doi:10.1029/WR018i001p00014
Hınçal, O., Altan-Sakarya, B., and Ger, AM., 2011.
Optimization of multi-reservoir systems by genetic algorithm. Water Resources Management, 25 (5), 1465–1487.
doi:10.1007/s11269-010-9755-0
Ji, CM., et al., 2010a. Model establishment and evaluation of
operation function for cascade reservoirs. Automation of
Electric Power Systems, 34 (3), 33–37. (in Chinese).
Ji, CM., Zhou, T., and Huang, HT., 2010b. Establishment
and evaluation of operation function model for cascade
hydropower station. Water Science and Engineering, 3 (4),
443–453.
Karamouz, M. and Houck, MH., 1982. Annual and monthly
reservoir operating rules generated by deterministic optimization. Water Resources Research, 18 (5), 1337–1344.
doi:10.1029/WR018i005p01337
Karamouz, M. and Houck, MH., 1987. Comparison of stochastic and deterministic dynamic programming for reservoir-operating rule generation. Journal of the American
Water Resources Association, 23 (1), 1–9. doi:10.1111/
jawr.1987.23.issue-1
Koutsoyiannis, D. and Economou, A., 2003. Evaluation of
the parameterization-simulation-optimization approach
for the control of reservoir systems. Water Resources
Research, 39 (6), 1170–1186. doi:10.1029/2003WR002148
Labadie, JW., 2004. Optimal operation of multi-reservoir
systems: State-of-the-art review. Journal of Water
Resources Planning and Management, 130 (2), 93–111.
doi:10.1061/(ASCE)0733-9496(2004)130:2(93)
Li, QF., et al., 2013. Impact of the Three Gorges Reservoir
operation on downstream ecological water requirements.
Hydrology Research, 43 (1–2), 48–53.
Liu, P., et al., 2006. Deriving reservoir refill operating rules by
using the proposed DPNS model. Water Resources
Management, 20 (3), 337–357. doi:10.1007/s11269-006-0322-7
Liu, P., et al., 2011a. Derivation of aggregation-based joint
operating rule curves for cascade hydropower reservoirs.
Water Resources Management, 25 (13), 3177–3200.
doi:10.1007/s11269-011-9851-9
Liu, P., Cai, XM., and Guo SL., 2011b. Deriving multiple
near-optimal solutions to deterministic reservoir opera-
Downloaded by [University of Oslo] at 02:25 26 January 2016
12
Y. ZHOU ET AL.
tion problems. Water Resources Research, 47 (8), 1–20.
doi:10.1029/2011WR010998
Lund, JR. and Guzman, J., 1999. Derived operating rules for
reservoirs in series or in parallel. Journal of Water
Resources Planning and Management, 125 (3), 143–153.
doi:10.1061/(ASCE)0733-9496(1999)125:3(143)
Moy, W-S., Cohon, JL., and ReVelle, CS., 1986. A programming model for analysis of the reliability, resilience, and
vulnerability of a water supply reservoir. Water Resources
Research, 22 (4), 489–498. doi:10.1029/WR022i004p00489
Naresh, R. and Sharma, J., 2001. Reservoir operation using a
fuzzy and neural system for hydro generation scheduling.
International Journal of Systems Science, 32 (4), 479–486.
doi:10.1080/00207720119896
Neelakantan, TR. and Pundarikanthan, NV., 2000. Neural
network-based simulation- optimization model for reservoir operation. Journal of Water Resources Planning and
Management, 126 (2), 57–64. doi:10.1061/(ASCE)07339496(2000)126:2(57)
Oliveira, R. and Loucks, DP., 1997. Operating rules for
multi-reservoir systems. Water Resources Research, 33
(4), 839–852. doi:10.1029/96WR03745
Ostadrahimi, L., Mariño, MA., and Afshar, A., 2012. Multireservoir operation rules: multi-swarm PSO-based optimization approach. Water Resources Management, 26 (2),
407–427. doi:10.1007/s11269-011-9924-9
Rani, D. and Moreira, MM., 2010. Simulation-optimization
modeling: a survey and potential application in reservoir
systems operation. Water Resources Management, 24 (6),
1107–1138. doi:10.1007/s11269-009-9488-0
Saad, M., et al., 1994. Learning disaggregation technique for
the operation of long-term hydroelectric power systems.
Water Resources Research, 30 (11), 3195–3202.
doi:10.1029/94WR01731
Simonovic, S., 1992. Reservoir systems analysis: closing gap
between theory and practice. Journal of Water Resources
Planning and Management, 118 (3), 262–280. doi:10.1061/
(ASCE)0733-9496(1992)118:3(262)
Terry, LA., et al., 1986. Coordinating the energy generation
of the Brazilian national hydrothermal electrical generating system. Interfaces, 16 (1), 16–38. doi:10.1287/
inte.16.1.16
Tu, M-Y., Hsu, N-S., and Yeh, WWG., 2003. Optimization
of reservoir management and operation with hedging
rules. Journal of Water Resources Planning and
Management, 129 (2), 86–97. doi:10.1061/(ASCE)07339496(2003)129:2(86)
Turgeon, A., 1980. Optimal operation of multi-reservoir
power systems with stochastic inflows. Water Resources
Research, 16 (2), 275–283. doi:10.1029/WR016i002p00275
Turgeon, A., 1981. A decomposition method for the long-term
scheduling of reservoirs in series. Water Resources Research,
17 (6), 1565–1570. doi:10.1029/WR017i006p01565
Urbaniak, M., Kiedrzyńska, E., and Zalewski, M., 2013. The
role of a lowland reservoir in the transport of micropollutants, nutrients and the suspended particulate matter
along the river continuum. Hydrology Research, 43 (4),
400–411.
Valdés, JB., et al., 1992. Aggregation-disaggregation approach
to multi-reservoir operation. Journal of Water Resources
Planning and Management, 118 (4), 423–444. doi:10.1061/
(ASCE)0733-9496(1992)118:4(423)
Wurbs, RA., 1993. Reservoir-system simulation and optimization models. Journal of Water Resources Planning and
Management, 119 (4), 455–472. doi:10.1061/(ASCE)07339496(1993)119:4(455)
Yakowitz, S., 1982. Dynamic programming applications in
water resources. Water Resources Research, 18 (4), 673–696.
doi:10.1029/WR018i004p00673
Yeh, W., 1985. Reservoir management and operations models: A state-of-the-art review. Water Resources Research, 21
(12), 1797–1818. doi:10.1029/WR021i012p01797