Journal of Hydrology 519 (2014) 248–257
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Joint operation and dynamic control of flood limiting water levels
for mixed cascade reservoir systems
Yanlai Zhou a,b,⇑, Shenglian Guo a, Pan Liu a, Chongyu Xu a,c
a
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Water Resources Department, Changjiang River Scientific Research Institute, Changjiang Water Resources Commission, Wuhan 430010, China
c
Department of Geosciences, University of Oslo, Norway
b
a r t i c l e
i n f o
Article history:
Received 18 May 2014
Received in revised form 11 July 2014
Accepted 12 July 2014
Available online 22 July 2014
This manuscript was handled by Geoff
Syme, Editor-in-Chief
Keywords:
Joint operation
Flood limiting water level
Dynamic control
Flood prevention
Hydropower generation
s u m m a r y
Reservoirs are one of the most efficient infrastructures for integrated water resources development and
management; and play a more and more important role in flood control and conservation. Dynamic control of the reservoir flood limiting water level (FLWL) is a valuable and effective approach to compromise
the flood control, hydropower generation and comprehensive utilization of water resources of river
basins during the flood season. The dynamic control models of FLWL for a single reservoir and cascade
reservoirs have been extended for a mixed reservoir system in this paper. The proposed model consists
of a dynamic control operation module for a single reservoir, a dynamic control operation module for cascade reservoirs, and a joint operation module for mixed cascade reservoir systems. The Three Gorges and
Qingjiang cascade reservoirs in the Yangtze River basin of China are selected for a case study. Three-hour
inflow data series for representative hydrological years are used to test the model. The results indicate
that the proposed model can make an effective tradeoff between flood control and hydropower generation. Joint operation and dynamic control of FLWL can generate 26.4 108 kW h (3.47%) more hydropower for the mixed cascade reservoir systems and increase the water resource utilization rate by
3.72% for the Three Gorges reservoir and 2.42% for the Qingjiang cascade reservoirs without reducing
originally designed flood prevention standards.
Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction
With the rapid economic development, the role of reservoirs
has become more and more important to meet society’s energy
and water requirements. Reservoirs are among the most efficient
tools for integrated water resource development and management.
By altering the spatial and temporal distribution of runoff, reservoirs serve many purposes, such as flood control, hydropower generation, navigation, recreation and ecology (Yeh, 1985; Labadie,
2004; Guo et al., 2004; Ahmed and Sarma, 2005; Eum et al.,
2012; Ostadrahimi et al., 2012; Zhou and Guo, 2013; Lu et al.,
2013). On the other hand, operation of large reservoirs has also
impact on the downstream ecological and water system (e.g.,
Yang et al., 2012; Li et al., 2013; Urbaniak et al., 2013). In order
to address the conflicts between flood control and conservation
in China, a great number of research works and practices of the
⇑ Corresponding author at: State Key Laboratory of Water Resources and
Hydropower Engineering Science, Wuhan University, Wuhan 430072, China.
Tel./fax: +86 27 68773568.
E-mail address: zyl23bulls@whu.edu.cn (Y. Zhou).
http://dx.doi.org/10.1016/j.jhydrol.2014.07.029
0022-1694/Ó 2014 Elsevier B.V. All rights reserved.
flood limiting water level (FLWL) has been carried out in recent
years. The FLWL is an important parameter to trade-off conflicts
between flood control and conservation (Cheng et al., 2008; Liu
et al., 2008; Yun and Singh, 2008; Eum and Simonovic, 2010;
Chen et al., 2013). The FLWL is determined by propagating the
annual design storm or annual design flood through reservoir regulation; and has fixed values during the flood season. According to
the Chinese Flood Control Act, the pool level of reservoir should be
kept below the FLWL during the flood season to provide enough
storage for flood prevention in China. After the inflow hydrograph
reaches its peak and begins to recede, the reservoir water level
must be drawn down to the FLWL as soon as possible to make storage available for the next flood event. The currently designed
approach is called static control of the FLWL (SC-FLWL). The advantage of SC-FLWL is its simplicity, but it neglects annual and seasonal variation of inflows and wastes water resources, which
often results in the reservoir being unable to refill to the normal
water level by the end of the year.
With advancements in meteorological and hydrological
forecasting capabilities, it is desirable to improve the operational
efficiency of existing reservoir to maximize comprehensive
Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
benefits (Li et al., 2010). For seasonally flooded river basins, the
flood season can be divided into several sub-seasons. Seasonally
variable flood storage allocation is advocated by the US Army Corp
of Engineers (USACE 1998). Seasonal FLWLs can be adapted to
obtain more economic benefits without reducing flood prevention
standards. Liu et al. (2008) developed a simulation-based optimal
seasonal FLWL model to simultaneously maximize benefits under
the condition that the seasonal FLWL risk is less than that of an
annually designed one. Yun and Singh (2008) suggested two
approaches to increase water storage of a reservoir, while maintaining its security for flood control. One is a multiple duration limited water level, which employs a multiple duration design storm,
rather than the traditional annual FLWL. The other is dynamic control of the FLWL (DC-FLWL), whereby the water level can fluctuate
within dynamic control bounds.
To avoid two types of situations, which are ‘‘the FLWL is too low
due to enhance flood prevention capacity’’ and ‘‘the FLWL is too
high due to increase conservation benefits’’, a reasonable bound
of DC-FLWL must be estimated, which is a key element for implementing reservoir FLWL dynamic control operation. Li et al. (2010)
presented a dynamic control operation model of the FLWL. The
model was applied to the Three Gorges reservoir, and results show
that the dynamic control of the reservoir FLWL could effectively
increase hydropower generation and the floodwater utilization
rate without increasing flood control risks. For a single reservoir,
the higher the water level is, the more hydropower will be generated. The technique of DC-FLWL for a single reservoir is very different from that of DC-FLWL for cascade reservoirs. Chen et al. (2013)
proposed a simulation-based optimization model of DC-FLWL that
made an effective tradeoff between the flood control and hydropower generation for the Qingjiang River cascade reservoirs.
Since there are hydraulic connections and storage compensations between the upstream and downstream reservoirs in cascade
reservoirs or between inter-basin reservoirs in mixed reservoir systems, the DC-FLWL will become more and more complex as the
number of reservoirs is increased. In this study, joint operation
and use of a dynamic control model of DC-FLWL for mixed cascade
reservoir systems are proposed and developed to maximize hydropower generation without reducing flood prevention standards.
The Three Gorges reservoir (TGR) and the Qingjiang cascade reservoirs in the Yangtze River basin of China are selected as a case
study.
The paper is organized as follows: Section 2 introduces the
study area briefly, after which the current operation rules of the
investigated cascade reservoir systems are discussed. Section 3
249
addresses the method adopted in this study, which comprises
three parts: introduction of a general framework for joint operation and use of a dynamic control model for mixed cascade reservoir systems by firstly, setup of dynamic control operation module
for TGR (Section 3.1), and secondly, setup of a dynamic control
operation module for the Qingjiang River cascade reservoirs (Section 3.2), as well as setup of a joint operation module for mixed
cascade reservoir systems (Section 3.3). In Section 4 simulation
results for the mixed cascade reservoir systems are presented
and discussed. The conclusions are drawn in Section 5.
2. Three Gorges and Qingjiang cascade reservoirs
The Three Gorges cascade reservoirs (Three Gorges, Gezhouba)
and Qingjiang cascade reservoirs (Shuibuya, Geheyan, Gaobazhou)
as shown in Fig. 1 are selected as case study, which is a typical
mixed cascade reservoir systems. Since the Gezhouba and
Gaobazhou reservoirs are run-of-the-river hydropower plants with
small regulation storages, joint operation and the dynamic control
model are only applied to simulate the operation of the TGR,
Shuibuya and Geheyan reservoirs.
The TGR is a vitally important and backbone project in the
development and harnessing of the Yangtze River in China. The
upstream of Yangtze River is intercepted by the TGR, with a length
of the main course about 4.5 103 km and a drainage area of
1 million km2. The TGR is the largest water conservancy project
ever undertaken in the world, with a normal pool level at 175 m
above mean sea level and a total reservoir storage capacity of
39.3 billion m3, of which 22.15 billion m3 is flood control storage
and 16.5 billion m3 is a conservation regulating storage, accounting
for approximately 3.7% of the dam site mean annual runoff of
451 billion m3.
The Gezhouba reservoir is located at the lower end of the TGR in
the suburbs of Yichang City, 38 km downstream of the TGR. The
dam is 2606 m long and 53.8 m high, with a total storage capacity
of 1.58 billion m3 and a maximum flood discharging capability of
110,000 m3/s.
The Qingjiang is one of the main tributaries of Yangtze River,
and its basin area is 17,600 km2. The mean annual rainfall, runoff
depth and annual average discharge 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
Qingjiang, a three-step cascade of reservoirs has been constructed
comprising from upstream to downstream Shuibuya, Geheyan and
Fig. 1. The location of the Three Gorges and Qingjiang cascade reservoirs.
250
Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
Gaobazhou, the distances between these reservoirs are 92 km,
50 km, and 142 km, respectively. The main functions of the cascade
reservoirs are power generation and flood control. The characteristic parameter values of the totally five reservoirs are given in
Table 1.
The designed operating rules can be regarded as a standard operating policy (SOP). Only the designed operating rule curves of the
TGR and the 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 a FLWL of 145 m. 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 maximum electrical power. The reservoir water level will be lowered during the period, 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 is shown in Fig. 3, in which the whole storage
space is divided into five operational zones. If the water level rises
to the FLWL or into the flood prevention zone during 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.
3. Joint operation and dynamic control model
The general framework of joint operation and use of a dynamic
control model for mixed cascade reservoir systems is shown in
Fig. 4. The proposed model consists of three modules: (1) a
dynamic control operation module based on the capacity-constrained pre-release method for a single reservoir, (2) a dynamic
control operation module based on the large-scale system decomposition and coordination method for cascade reservoirs, (3) a simulation operation module for mixed cascade reservoir systems. The
first and second modules are applied to dynamically control of
FLWL for TGR and Qinjiang cascade reservoirs, respectively. The
third module is used to find and update the optimal storage allocation strategy in order to maximize the benefits of the mixed cascade reservoir systems based on designed operating rules.
Table 1
List of characteristic parameter values of these five reservoirs.
Unit
TGR
Gezhouba
Shuibuya
Geheyan
Gaobazhou
Total storage
Flood control storage
Crest elevation
Normal water level
Flood limited water level
Install capability
Annual generation
Regulation ability
108 m3
108 m3
m
m
m
MW
billion kW h
–
393
221.5
185
175
145.0
22,400
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
Reservoir storage level (m)
Reservoir
Month
175
III
II
II
165
I
IV
155
II
145
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Upper boundary curve
145
145
145
145
175
175
175
175
175
175
175
155
Lower boundary curve
145
145
145
145
145
156.3
169.6
166.6
160.9
155
155
145
Fig. 2. Designed operating rule curves of the Three Gorges reservoir (I is flood control zone, II is install output power zone, III is firm output power zone and IV is lower output
power zone).
Fig. 3. Designed operating rule curves of the Shuibuya reservoir (I is flood control zone, II is install output power zone, III is increasing output power zone and IV is firm
output power zone, and V is lower output power zone).
Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
251
Begin: initializaton
Forecasting information
Dynamic control module for Qingjiang River
cascade reservoirs
Dynamic control module for TGR
Joint operation module for mixed multi- reservoirs
No
Convergent constraint
Flood control rules
Yes
Progressive optimal
algorithm
Dynamic control scheme of FLWL
Fig. 4. The framework of joint operation of DC-FLWL model for mixed cascade reservoir systems.
3.1. Dynamic control operation module for TGR
Dynamic control operation module based on the capacityconstrained pre-release method (Li et al., 2010) is applied to
dynamically control of the FLWL for TGR. Flood control operations
for a flood hydrograph can be divided into three stages as shown in
Fig. 5 (Li et al., 2010), namely pre-release operation at rising flood
stage, normal flood control operation at large flood stage, which is
conducted by current operation rules, and refill operation at recession flood stage. Since the reservoir water level must be decreased
to the current FLWL in effective lead-time before large inflow
occurs, the upper bound of dynamic control is tightly related to
the reservoir’s release capacity (Li et al., 2010).
3.1.1. Pre-release operation
The reservoir pre-release operation is shown in Fig. 5, where Qs
is the safety discharge in the downstream flood protection section,
Tf is effective lead-time of inflow forecasting, and ti (i = 1–4) is the
time. The pre-release operation is used to determine the upper
bound of dynamic control at the planning and designing stage in
order to provide adequate flood storage at the real-time operation.
The pre-release operation uses the effective lead-time of inflow
forecasting and the maximum safety discharge of downstream to
estimate the upper bound of dynamic control, while the current
FLWL is often used as the lower bound, i.e.,
V0 ¼ Vu þ
Z
t c þT f
Q in ðtÞdt Q max T c
ð1Þ
tc
Inflow
Inflow hydrograph
Os
Pre-release
Normal flood
Control operation
Tc
t1
Refill
Time
Tc
t2
t3
t4
Fig. 5. Sketch of reservoir pre-release and refill operation.
where Z0 is the current FLWL, Zu is the upper bound of DC-FLWL, V0
is the reservoir storage corresponding to Z0, Vu is the reservoir
storage corresponding to Zu, tc is the current time. Tf is effective
lead-time of inflow forecasting in TGR, Qin (t) is the forecasted
inflow and Qmax is the maximum safety discharge of downstream.
3.1.2. Refill operation
Refill operation is adopted to meet conservation demands during the flood recession period, but the reservoir water level of
refill cannot surpass the upper dynamic control bound. As shown
in Fig. 5, if the forecasting inflow at time t4 is less than Qs, then
there are two alternatives. If the reservoir water level at time t3
is lower than the upper boundary, then the refill operation is performed with minimum discharge not being less than the release
of generating firm capacity. If the reservoir water level at time
t3 lies over the upper boundary, and the discharge exceeds or
equals inflow then the reservoir water level maintains the upper
bound Zu.
3.2. Dynamic control operation module for Qingjiang River cascade
reservoirs
Chen et al. (2013) proposed a dynamic control operation module of FLWL for the Qingjiang cascade reservoirs. To solve highdimensional optimization problem, the cascade reservoirs were
considered as an ‘‘aggregated reservoir’’ combined with large-scale
system decomposition and coordination. The configuration of the
cascade reservoirs is illustrated in Fig. 6 (Chen et al., 2013), where
A and B represent the upstream and downstream reservoirs, QA and
QB are the inflows of reservoir A and B, respectively, F1 and F2 represent the flood control objectives downstream of reservoir A and
B, and Qmax,A and Qmax,B are the maximum safety discharge of reservoir A and B, respectively.
The main procedures of the dynamic control operation module
for cascade reservoirs are given as follows:
3.2.1. Aggregation method
The aggregation method is used to estimate the maximum
available flood prevention storage of ‘‘aggregated reservoir’’ for
the cascade reservoirs (Chen et al., 2013). The aggregation method
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Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
Reservoir B :
Qqj
Z
t c þT f
Q out;B ðtÞdt Z
tc
t c þT f
Q B ðtÞdt
tc
¼ fB ðZ 0B ðtÞÞ fB ðZ B ðtÞÞ
QA
ð6Þ
The hydraulic connection between upstream reservoir A and
downstream reservoir B can be described by the Muskingum
method (e.g. Al-Humoud and Esen, 2006), i.e.,
Qmax, A
Q B ðtÞ ¼ C 0 Q out;A ðtÞ þ C 1 Q out;A ðt 1Þ þ C 2 Q B ðt 1Þ þ Q qj ðtÞ
QB
in which the outflows of reservoir A and reservoir B should satisfy
flood control constraints, i.e.
Qmax, B
Fig. 6. Sketch of cascade reservoirs.
is used to adjust the FLWL from the water level Z at the planning
and design stage to water level Z 0 by pre-release operation. If the
forecasted shows that there will be a large flood event, then the
reservoirs can pre-release to provide enough flood storage space.
The pre-release operation uses the effective lead-time of inflow
forecasting and the safe discharge for downstream flood protection
to estimate the upper bound of DC-FLWL. The maximum allowed
FLWL, Z 0 ðtÞ, is
0
f ðZ ðtÞÞ ¼ f ðZðtÞÞ þ
Z
tc
tc þT f
Q agg
out ðtÞdt
Z
tc þT f
tc
Q agg
in ðtÞdt
ð2Þ
Q out;A ðtÞ 6 Q max;A
ð8Þ
Q out;B ðtÞ 6 Q max;B
ð9Þ
The relationship of reservoir DC-FLWL pre-storage between the
upstream reservoir A and downstream reservoir B can be solved
from downstream reservoir B to upstream reservoir A. A reverse
successive estimation is used to solve this problem.
The probable inflow of reservoir B can be derived from the outflow constraint in the downstream control point F2 and the state
storage of reservoir B. That is, from Eqs. 6–9; we have:
Z
max V yx ðtÞ ¼ f ðZ ðtÞÞ f ðZðtÞÞ
3.2.2. Decomposition method
The decomposition method is used to find the flood prevention storage relationship between upstream and downstream
reservoirs and allocate the maximum available flood prevention
storage into individual reservoir units (Chen et al., 2013). Based
on the principle of decomposition techniques and a subsequent
iterative determination of individual reservoir operation
policies, the storage decomposition method is used to allocate
the available flood prevention storage into each individual
reservoir.
The maximum available flood prevention storage is determined
by the current reservoir storage, flood control objectives and forecast information. The relationship of DC-FLWL for cascade reservoirs is established without affecting flood prevention standards,
and the bound of DC-FLWL is satisfied with the reservoir flood control constraints.
As there is a hydraulic connection between the upstream and
downstream reservoirs, the maximum available flood space of a
reservoir is affected by the current storage capacity of the other
reservoirs. Therefore, there is a mutual restraint relationship
between the upstream and downstream reservoirs. The module
can estimate the maximum allowable FLWL of reservoirs in period
t, according to their spatial relationship and flood control constraints, i.e.
max Z 0A ðtÞ max Z 0B ðtÞ
ð4Þ
where the relationship between reservoir A and B is given by
Reservoir A :
Z
t c þT f
Q out;A ðtÞdt Z
tc
¼ fA ðZ 0A ðtÞÞ fA ðZ A ðtÞÞ
t c þT f
Q A ðtÞdt
tc
ð5Þ
Q out;B ðtÞdt Z
tc þT f
tc
Z
t c þT f
Q max;B dt 6
tc
¼ Q max;B T f ð3Þ
agg
where Q agg
in ðtÞ is the inflow of ‘‘aggregated reservoir’’, Q out ðtÞ is the
outflow of ‘‘aggregated reservoir’’, tc is the current time f ðÞ is the
relationship between reservoir water level and storage.
t c þT f
tc
The maximum available flood prevention storage V yx ðtÞ of
‘‘aggregated reservoir’’ at the current time t is then
0
ð7Þ
Z
Z
Q B ðtÞdt ¼ fB ðZ 0B Þ fB ðZ B Þ
t c þT f
Q B ðtÞdt
tc
t c þT f
Q B ðtÞdt
ð10Þ
tc
Since intermediate variables Q out;A ðt 1Þ, Q B ðt 1Þ and Q qj ðtÞ in
period t are known, the relationship between Q B ðtÞ and Q out;A ðtÞ can
be expressed by
Q B ðtÞ ¼ C 0 Q out;A ðtÞ þ KðtÞ
ð11Þ
where KðtÞ ¼ C 1 Q out;A ðt 1Þ þ C 2 Q B ðt 1Þ þ Q qj ðtÞ. Eq. (10) can be
rewritten as
fB ðZ 0B Þ fB ðZ B Þ 6 Q max;B T y Z
t c þT f
ðC 0 Q out;A ðtÞ þ KðtÞÞdt
ð12Þ
tc
The maximum allowed FLWL of reservoir A can be estimated
based on inflow forecasting, allowed outflow and current storage,
i.e.,
Z
tc
t c þT f
Q out;A ðtÞdt ¼
Z
t c þT f
tc
Q A ðtÞdt þ fA ðZ 0A ðtÞÞ fA ðZ A ðtÞÞ
ð13Þ
From Eqs. (12) and (13), we have
Z tc þT f
fB ðZ 0B Þ 6 fB ðZ B Þ þ Q max;B T y C 0
Q A ðtÞdt þ fA ðZ 0A Þ fA ðZ A Þ KðtÞT y
tc
ð14Þ
Eq. (14) is the relationship of reservoir DC-FLWL pre-storage
between upstream reservoir A and downstream reservoir B.
If the initial adjusted water level of upstream reservoir A is
fixed, the maximum allowed FLWL of downstream reservoir B
can also be estimated by the effective lead-time inflow forecasting,
current storage and flood control constraints, where Z 0A ðtÞ is the
allowable FLWL of reservoir A in period t, Z 0B ðtÞ is the allowed FLWL
of reservoir B in period t, Z A ðtÞ is the FLWL of reservoir A in period t,
Z B ðtÞ is the FLWL of reservoir B in period t, tc is the current time, Tf
is the effective lead-time of inflow forecasting in Qingjiang River,
Q A ðtÞ is the inflow of reservoir A in period t, Q B ðtÞ is the inflow of
reservoir B in period t, Q qj ðtÞ is the mediate basin inflow between
reservoir A and reservoir B, C0 is the coefficient of the Muskingum
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Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
equation, C1 is the coefficient of the Muskingum equation and C2 is
the coefficient of the Muskingum equation.
Because the relationship of reservoir DC-FLWL pre-storage
between the upstream reservoir A and downstream reservoir B is
so explicit in Eq. (14), refill operation is also adopted to meet conservation demands during the flood recession period for cascade
reservoirs. Furthermore, the reservoir water level of refill cannot
surpass the upper dynamic control bound of upstream reservoir
A or downstream reservoir B at the same time.
3.3.2. Constraints
(1) Water balance equation
V i ðt þ 1Þ ¼ V i ðtÞ þ ðIi ðtÞ Q i ðtÞ Li ðtÞÞDt
(2) Reservoir water level limits
ZLi ðtÞ 6 Z i ðtÞ 6 ZU i ðtÞ
ð18Þ
(3) Comprehensive utilization of water required at downstream
reservoir limits
QLi ðtÞ 6 Q i ðtÞ 6 QU i ðtÞ
3.3. Joint operation module for mixed cascade reservoir systems
3.3.1. Objective function
Since the long-term inflow prediction is uncertain, the reservoir
is operated by the decision-maker according to real-time forecasting results. The optimal strategies for mixed cascade reservoir systems are determined by the current reservoir storage, flood control
objectives and forecasting information. Moreover, storage compensation operation for a mixed cascade reservoir system is a rolling
cyclic process of ‘‘forecast-decision-implementation’’. Since the
effective lead times of inflow forecasting of the TGR and Qingjiang
cascade reservoirs are 24 h (Li et al., 2010) and 6 h (Chen et al.,
2013; Yan et al., 2013), respectively, the operation period is taken
24 h in this study. If the mixed cascade reservoir systems can meet
the water supply and initial power generation requirements, then
the objective function that generates maximum hydropower is
selected, i.e.,
Max E ¼
tc
t c þL1
!
Z
n1
X
Ni ðtÞ dt þ
i¼1
tc
tc þ4L2
n2
X
!
Ni ðtÞ dt
ð15Þ
i¼1
Ni ðtÞ ¼ K i Q i ðtÞHi ðtÞ
ð19Þ
(4) Power generation limits
The joint operation module is used to find and update the optimal storage allocation strategy in order to maximize the benefits of
mixed cascade reservoir systems based on the pre-release operation, the refill operation, and the designed operating rules during
maximum effective lead time of inflow forecast.
Z
ð17Þ
ð16Þ
There are hydraulic connections and storage compensations
between the upstream and downstream reservoirs in cascade reservoirs or between inter-basin reservoirs in mixed reservoir
systems.
NLi ðtÞ 6 Ni ðtÞ 6 NU i ðtÞ
ð20Þ
where E is the sum of the hydropower generation of the cascade
reservoirs, Dt is the interval of time, tc is the current time, L1 is
the effective lead time of inflow forecast for TGR, L2 is the effective
lead time of inflow forecast for Qingjiang cascade reservoirs, N i ðtÞ is
output power of the ith reservoir in period t, Ki is the comprehensive output coefficient for the ith reservoir, Hi ðtÞ is the hydraulic
head for the ith reservoir in period t, n1 is the number of reservoirs
in the Three Gorges cascade, n2 is the number of reservoirs in the
Qingjiang cascade, V i ðtÞ is the storage of the ith reservoir in period
t, Ii ðtÞ is the reservoir inflow of the ith reservoir in period t, Q i ðtÞ is
the water discharge of the ith reservoir in period t, Li ðtÞ is the sum of
evaporation and seepage of the ith reservoir in period t, QLi ðtÞ is the
minimum water discharge for all downstream uses in period t,
QU i ðtÞ is the maximum water discharge for all downstream uses
in period t, Z i ðtÞ is the reservoir water level of the ith reservoir in
period t, ZLi ðtÞ is the minimum water level of the ith reservoir in
period t, ZU i ðtÞ is the maximum water level of the ith reservoir in
period t, NLi ðtÞ is the minimum power limits of reservoir in period
t, NU i ðtÞ is the maximum power limits of reservoir in period t.
3.3.3. Optimization algorithm
Since the optimal allocation based on the operation module for
mixed cascade reservoir systems is a multidimensional and multistage optimization problem, modified dynamic programming (DP)
algorithms such as discrete differential dynamic programming
(DDDP), dynamic programming successive approximations (DPSA),
and progressive optimality algorithm (POA) have often been used
to identify near-optimal solutions (Turgeon, 1981; Yeh, 1985;
Labadie, 2004; Kumar and Baliarsingh, 2009; Rani and Moreira,
2010; Guo et al., 2011; Liu et al., 2011a, 2011b, 2011c; Chen
Table 2
Results comparison between SC-FLWL and DC-FLWL models for a mixed cascade reservoir systems.
Reservoir
Wet year
Normal year
Dry year
HG
(108 kW h)
SW
(108 m3)
HG
(108 kW h)
SW
(108 m3)
HG
(108 kW h)
SW
(108 m3)
TGR
SC-FLWL
DC-FLWL
Difference
Rate
243.64
251.12
7.48
3.07%
496.21
479.76
16.45
3.32%
228.78
237.70
8.92
3.90%
195.08
179.44
15.64
8.02%
198.97
206.47
7.50
3.77%
86.52
77.17
9.35
10.81%
Shuibuya
SC-FLWL
DC-FLWL
Difference
Rate
20.70
20.90
0.20
0.97%
25.64
24.84
0.80
3.12%
19.01
19.14
0.13
0.68%
6.03
5.28
0.75
12.44%
11.28
11.35
0.07
0.62%
0.71
0.00
0.71
100.00%
Geheyan
SC-FLWL
DC-FLWL
Difference
Rate
14.26
15.21
0.95
6.66%
17.96
15.18
2.78
15.48%
14.60
15.26
0.66
4.52%
10.44
7.87
2.57
24.62%
10.40
10.89
0.49
4.71%
1.71
0.00
1.71
100.00%
Mixed cascade reservoirs system
SC-FLWL
DC-FLWL
Difference
Rate
278.60
287.23
8.63
3.10%
539.81
519.78
20.03
3.71%
262.39
272.10
9.71
3.70%
211.55
192.59
18.96
8.96%
220.65
228.71
8.06
3.65%
88.94
77.17
11.77
13.23%
Notes: SC-FLWL is static control of flood limiting water level, DC-FLWL is dynamic control of flood limiting water level, HG is hydropower generation, and SW is spilled water.
254
Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
et al., 2013). A comparison of these algorithms has revealed that
the POA produces a more optimal solution but depends on the initial solution. Thus the results obtained from the coarse DP algorithm are used as initial solution of the POA. The POA divides a
multi-stage problem into several two-stage problems. It is run iteratively to solve the optimization of a two-stage problem, while the
other stage variables remain fixed. After solving the problem at the
stage below, the next two-stage problem is considered, with the
optimal result of the previous stage problem used as the next initial condition. The algorithm continues its iteration until the difference between the current value of every state variable and the
value at the last iteration is less than a specified precision limit.
When the condition is reached, the resulting values represent the
optimal path as they satisfy the principle of progressive optimality
(Guo et al., 2011; Chen et al., 2013). Therefore, the POA is chosen to
solve this multidimensional and multi-stage optimization
problem.
1953 to 2012. For simulation operation, 3-h runoff data series during 2:00 on June 1 to 23:00 on July 31 is used in this study.
For a comparative study, joint operation based on both SC-FLWL
and DC-FLWL for mixed cascade reservoir systems is performed.
The results of hydropower generation (HG) and spilled water
(SW) during the operation period estimated by these operation
models are summarized in Table 2. It is shown that the joint operation of DC-FLWL can generate 26.4 108 kW h (or an increase of
3.47%) more hydropower than that of SC-FLWL. Compared with SCFLWL, DC-FLWL for mixed cascade reservoir systems can increase
hydropower
production
by
8.63 108 kW h
(3.1%),
8
8
9.71 10 kW h (3.7%), and 8.06 10 kW h (3.65%) in the wet,
normal and dry years, respectively. At the same time, spilled water
have been greatly decreased by 20.03 108 m3 (3.71%),
18.96 108 m3 (8.96%), and 11.77 108 m3 (13.23%) in the wet,
normal and dry years, respectively.
Results of water resources utilization rates that denote the
water resources utilization efficiency (Chen et al., 2013) for a reservoir during the operation period are also calculated and listed
in Table 3. Water resource utilization rates using DC-FLWL for
the TGR increase by 2.24%, 3.34%, and 4.15% in the wet, normal
and dry year, respectively, compared to SC-FLWL. Besides, water
4. Results and discussion
Three typical hydrological years, i.e. a wet year (1982), a normal
year (1987), and a dry year (1992) are selected as case study from
Table 3
Comparison of water resource utilization rates between SC-FLWL and DC-FLWL models.
FLWL
Wet year (%)
Normal year (%)
Three Gorges Reservoir
SC-FLWL
DC-FLWL
Increase
62.58
64.82
2.24
84.62
87.96
3.34
92.58
96.73
4.15
75.19
78.91
3.72
Qingjiang cascade reservoirs
SC-FLWL
DC-FLWL
Increase
57.48
59.97
2.49
78.67
82.23
3.56
96.46
100.00
3.54
72.60
75.02
2.42
TGR
Discharge/m3 /s
120000
Inflow
100000
Outflow
60000
40000
20000
0
1/6
5/6
9/6
156
153
150
147
144
141
138
135
11/7 15/7 19/7 23/7 27/7 31/7
DC-FLWL
80000
13/6 17/6 21/6 25/6 29/6
3/7
7/7
Dry year (%)
SC-FLWL
Water level/m
Reservoir
d/m
Shuibuya reservoir
Discharge (m 3 /s)
Inflow
10000
Outlfow
DC-FLWL
SC-FLWL
395
8000
390
6000
4000
385
2000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
3/7
7/7
Water level (m)
400
12000
380
11/7 15/7 19/7 23/7 27/7 31/7
(d/m)
Geheyan reservoir
200
Inflow
Outlfow
DC-FLWL
SC-FLWL
20000
195
15000
190
10000
185
5000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
3/7
7/7
180
11/7 15/7 19/7 23/7 27/7 31/7
(d/m)
Fig. 7. Joint operation of DC-FLWL for mixed cascade reservoir systems in wet year.
Water level (m)
Discharge (m 3/s)
25000
Average (%)
255
TGR
Discharge/m3 /s
120000
Inflow
100000
Outflow
80000
60000
40000
20000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
156
153
150
147
144
141
138
135
11/7 15/7 19/7 23/7 27/7 31/7
DC-FLWL
3/7
7/7
SC-FLWL
Water level/m
Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
Shuibuya reservoir
10000
400
Inflow
Outflow
DC-FLWL
SC-FLWL
8000
395
6000
390
4000
385
2000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
3/7
7/7
Water level (m)
Discharge (m 3 /s)
d/m
380
11/7 15/7 19/7 23/7 27/7 31/7
(d/m)
Geheyan reservoir
Inflow
8000
Outflow
200
DC-FLWL
SC-FLWL
195
6000
190
4000
185
2000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
3/7
7/7
Water level (m)
Discharge (m 3 /s)
10000
180
11/7 15/7 19/7 23/7 27/7 31/7
(d/m)
TGR
120000
Inflow
100000
Outlfow
80000
60000
40000
20000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
156
153
150
147
144
141
138
135
11/7 15/7 19/7 23/7 27/7 31/7
DC-FLWL
3/7
7/7
SC-FLWL
Water level/m
Discharge/m3 /s
Fig. 8. Joint operation of DC-FLWL for mixed cascade reservoir systems in normal year.
Shuibuya reservoir
10000
Inflow
Outflow
400
DC-FLWL
SC-FLWL
8000
395
6000
390
4000
385
2000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
3/7
7/7
Water level (m)
Discharge (m 3 /s)
d/m
380
11/7 15/7 19/7 23/7 27/7 31/7
(d/m)
Geheyan reservoir
Inflow
Outflow
200
DC-FLWL
SC-FLWL
8000
195
6000
190
4000
185
2000
0
1/6
5/6
9/6
13/6 17/6 21/6 25/6 29/6
3/7
7/7
180
11/7 15/7 19/7 23/7 27/7 31/7
(d/m)
Fig. 9. Joint operation of DC-FLWL for mixed cascade reservoir systems in dry year.
Water level (m)
Discharge (m 3 /s)
10000
256
Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
resource utilization rates using DC-FLWL for the Qingjiang River
cascade reservoirs increase by 2.49%, 3.56%, and 3.54% in the wet,
normal and dry year, respectively, compared to SC-FLWL. On average, water resource utilization rates increase by 3.72% for the TGR
and 2.42% for the Qingjiang cascade reservoirs.
The jointly operated water levels using DC-FLWL for mixed cascade reservoir systems in the wet, normal and dry years are shown
in Figs. 7–9, respectively.
In the wet year, the inflow of the mixed cascade reservoir systems is small before July 10, where the DC-FLWL begins to prestorage water for the TGR, and the allowed pre-storage capacity
is allocated to the downstream Geheyan reservoir for the Qingjiang
cascade reservoirs, as shown in Fig. 7. The reason is that this storage allocation strategy can generate more hydropower for the
mixed cascade reservoir systems without reducing originally
designed flood prevention standards. When inflow begins to
increase after July 10, the reservoirs are operated based on the
SC-FLWL flood control rules, and water is discharged from the spillway to lower the water level to the FLWL for the upstream TGR and
Shuibuya reservoirs. The reservoir can pre-release water by using
forecasting information, thereby creating more flood space before
next large flood. When the reservoir receives the flood water and
the inflow exceeds the hydropower turbine capacity, the water
level is raised to avoid spill. The reservoir is operated based on
the forecasting inflow and the current reservoir capacity.
In the normal year, only small and medium floods occur. As
shown in Fig. 8, with the regulation of upstream TGR and Shuibuya
reservoirs, the water level of the Geheyan reservoir is relatively
stable and can be operated nearly at the upper bound by DC-FLWL
during the flood season, while the water level of the Shuibuya
12
Difference
SC-FLWL
300
DC-FLWL
250
200
150
100
50
Difference (10 8kWh)
or Rate (%)
Hydropower
generation (10 8 kWh)
350
10
Rate
8
6
4
2
0
0
Wet year
Normal year
Wet year
Dry year
600
Normal year
-25
Difference
DC-FLWL
400
300
200
100
Difference (10 8 m3)
or Rate (%)
Spilled water (10 8 m3 )
SC-FLWL
500
Dry year
Rate
-20
-15
-10
-5
0
0
Wet year
Normal year
Wet year
Dry year
Normal year
Dry year
Fig. 10. Performance indices of mixed cascade reservoir systems in two models.
5.00%
SC-FLWL
Increase
DC-FLWL
80.00%
4.00%
Increase
Water resources utilization
rate
100.00%
60.00%
40.00%
20.00%
3.00%
2.00%
1.00%
0.00%
0.00%
Wet year
Normal year
Dry year
Average
Wet year
Dry year
Average
4.00%
SC-FLWL
Increase
DC-FLWL
80.00%
3.00%
Increase
Water resouces utilization
rate
100.00%
Normal year
Three Gorges reservoir
Three Gorges reservoir
60.00%
40.00%
2.00%
1.00%
20.00%
0.00%
0.00%
Wet year
Normal year
Dry year
Average
Qingjiang cascade reservoirs
Wet year
Normal year
Dry year
Average
Qingjiang cascade reservoirs
Fig. 11. Water resources utilization rate of Three Gorges reservoir and Qingjiang cascade reservoirs in two models.
Y. Zhou et al. / Journal of Hydrology 519 (2014) 248–257
reservoir remains at the lower bound. Because the total amount of
water stored in this system is limited, the aim of allocation of
limited amount of storage between these reservoirs is to maximize
hydropower production. This hydropower maximizing water
storage allocation depends on reservoir capacity, inflow, energy
production efficiency and total amount of water to be stored. Since
the storage capacity of Geheyan reservoir is less than that of
Shuibuya reservoir, the water head of Geheyan reservoir increases
more per unit volume of additional storage than that of the
Shuibuya reservoir. As the downstream reservoir receives more
direct and indirect inflow, the water level of Geheyan reservoir is
kept at a high level to take advantage of power generation. Besides,
the water level of the TGR is operated only under the upper bound
by DC-FLWL for comparative dispatching of the Qingjiang cascade
reservoirs that receive the medium floods before July 1.
As shown in Table 2, the runoff discharges are relatively small
during dry year, and the effect of joint operation of DC-FLWL for
the TGR is more remarkable than that for the Qingjiang cascade
reservoirs. Table 3 shows that the flood water resource utilization
rate is increased to 100% with DC-FLWL, compared to 96.46% with
SC-FLWL in the Qingjiang cascade reservoirs. Fig. 9 explains that
the water level of the Geheyan reservoir is kept high during the
flood season, whereas the water level of the Shuibuya reservoir is
kept lower, especially in the end of flood season. This is because
the reservoirs usually are operated with low water head to guarantee minimum power outputs. Besides, the water level of the TGR
can be operated nearly at the upper bound by DC-FLWL for comparative dispatching by the Qingjiang cascade reservoirs after July
10 in the dry year.
SC-FLWL and DC-FLWL are applied to generate reservoir operation policies. The statistical results from the two models are compared as shown in Figs. 10 and 11. HG and SW of mixed cascade
reservoir systems for each of the two models are presented in
Fig. 10. It can be seen that DC-FLWL has the maximum HG and
the least SW in three typical hydrological years. In addition, from
the data shown in Fig. 11, the difference in water resources utilization rate between SC-FLWL and DC-FLWL is increasing from wet
year to dry year in the TGR and the Qingjiang cascade reservoirs.
DC-FLWL can fully use flood water resources based on the forecasted inflow and the current state reservoir capacity in a dry year.
The results of this highlight the superiority of using DC-FLWL in
the simulation model. The optimization model leads to a better
policy, when the inflow forecast for the current period is perfect.
It can be concluded that the DC-FLWL model performs better than
the SC-FLWL model in deriving the optimal operating policy for the
mixed cascade reservoir systems.
5. Conclusions
Simulation-based optimization models of DC-FLWL for single
reservoir and cascade reservoirs have been extended to mixed cascade reservoir systems in this study. A joint operation and dynamic
control model is developed and solved by using the progressive
optimality algorithm. The Three Gorges reservoir and Qingjiang
River cascade reservoirs are selected as a case study with conclusions summarized as follows:
(1) Compared with current design operations based on
SC-FLWL, joint operation based on DC-FLWL can generate
26.4 108 kW h (3.47%) more hydropower for a mixed cascade reservoir systems and increase water resource utilization rate 3.72% for the TGR and 2.42% for the Qingjiang
cascade reservoirs on average during June 1–July 31.
(2) Since there are hydraulic connections and storage compensations between upstream and downstream reservoirs or
257
between inter-basin reservoirs, the allowable pre-storage
capacity allocated to downstream reservoir is an optimal reservoir storage strategy during the flood season, which can generate more hydropower from mixed cascade reservoir systems
without reducing original flood prevention standards.
Acknowledgements
This study is financially supported by the National Natural Science Foundation of China (51079100, 51190094). The authors
would like to thank the editor and anonymous reviewers for their
review and valuable comments related to this manuscript.
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