The middle route of the south–north water transfer project (SNWTP) was built to relieve the pressure of increasing water demand in northern China. Serving as one of the major storage systems, optimal operation rules should be proposed promptly for Danjiangkou Reservoir, completed by a heightening project. In this paper, in order to seek out the optimal operation rules for Danjiangkou Reservoir, a multi-objective optimal operation model is developed, considering the inflow uncertainty, multi-year regulation cycle and water supply for the SNWTP. Three evaluation indexes (hydropower generation, water impoundment condition and shortage index) are adopted to assess the impacts of three influence factors (starting regulation level (SRL), inflow condition and flood control level) on Danjiangkou Reservoir operations. Finally, some critical operation strategies for Danjiangkou Reservoir are proposed. The results show that the optimal SRL for Danjiangkou Reservoir is 158 m and the recommended range of the water level at the end of the first year varies between 162–166 m (very wet), 164–166 m (wet), and 162–164 m (normal) on the basis of setting 158 m as the SRL.

INTRODUCTION

The pressure on water supply has become a major issue in the north of China over the past few years due to rapid increase in water demand and a long-term decline in groundwater resources. The south–north water transfer project (SNWTP) was built to ease the pressure, mainly involving water infrastructure for transport and distribution of water over long distances across China. As the water source for the middle route of the SNWTP, Danjiangkou Reservoir was heightened and more attention should be paid to water allocation for multi-users rather than single power generation. After dam heightening, reservoir regulation changed from annual regulation to multi-year regulation and the reservoir should have more storage to make better use of inter-annual and annual inflow to cope with the increasing water demand brought by the SNWTP. How to utilize the inflow efficiently and allocate storage to multi-users reasonably are critical to Danjiangkou Reservoir.

Previous studies mainly focused on annual regulation of the reservoir (Zhou & Guo 2013; Wang et al. 2014a, 2014b; Zhao et al. 2014), and were not suitable for multi-year regulation characteristics. Zhou & Guo (2013) proposed some operating rule curves involving the ecological requirement to cope with climate change. Zhao et al. (2014) proposed an improved multiple-objective dynamic programming (DP) algorithm for the optimization of reservoir operation without considering the new characteristics and inflow uncertainty. However, historical reservoir inflow data show that the impacts of inflow uncertainty and inter-annual inflow should not be neglected. Therefore, it is necessary to propose an optimal operation scheme for the reservoir for inflow uncertainty and multi-year regulation.

Factors influencing long-term reservoir operation have been addressed in the past, including reservoir size (Ma et al. 2013; Mu et al. 2015), inflow conditions (You & Cai 2008; Campos et al. 2014), starting regulation levels (SRLs) (Zhang et al. 2015), flood control level (Zhou et al. 2014; Ouyang et al. 2015), water level at the end of year (WLE) and so on. Hejazi et al. (2008) discussed the influence of hydrologic information on reservoir operation under different climate conditions, reservoir sizes, reservoirs' main usages, inflow uncertainty, etc. Wang et al. (2014a, 2014b) investigated the influences of reservoir water level variations of the operation rule curves on different objectives, especially on ecological objectives. Zhang et al. (2015) took inflow conditions and SRLs into consideration and adopted decision trees to determine the WLE for a multi-year regulation reservoir. Li et al. (2010) developed a dynamic control operation model which considered inflow uncertainty and derived a dynamic control bound of reservoir flood control level by using forecasting pre-release and Monte Carlo simulation.

Various methods have been proposed to analyze the impact of inflow uncertainty on reservoir operation such as: stochastic DP or modified stochastic DP (Tilmant & Kelman 2007; El-Shafie & El-Manadely 2011; Shokri et al. 2013; Anvari et al. 2014; Xie & Huang 2014), fuzzy theory (Li et al. 2008; Akbari et al. 2011; Kumar et al. 2013), interval programming (Maqsood et al. 2005; Nikoo et al. 2014), and bootstrapping methods (Lerat et al. 2011). In addition, Monte Carlo simulation is one of the most common methods in simulating reservoir inflows and reservoir operation based on specified probability distributions (Andrew et al. 2008; Nohara & Hori 2014).

Taking Danjiangkou Reservoir as an example, this paper aims to put forward new operation rules by considering inflow uncertainty and multi-year regulation to satisfy the water demand of the SNWTP. An autoregressive model (AR), Monte Carlo method and DP with variable time step are adopted to derive optimal schemes under different inflow conditions. Different influence factors (SRL, inflow condition and flood control level) and indexes (hydropower generation, water impoundment condition and SI) are utilized to summarize the operation rules on the basis of the optimal schemes.

STUDY AREA

Danjiangkou Reservoir is located on the Han River in Central China and has a storage capacity of 29.05 billion m3 after dam heightening as shown in Figure 1. Its salient features are presented in Table 1. Due to the dam heightening project, the height of dam changed from 162 m to 176.6 m, while the normal storage water level and dead storage level changed from 157 m to 170 m and 139 m to 150 m, respectively. So, the reservoir regulation changed from annual regulation to multi-year regulation. In addition, compared with the water demand of all users and the history inflow data of Danjiangkou Reservoir, the percentage of fulfilling the storage capacity at least once within the operation period of 3 years is 96.15%, which illustrates the reason for choosing 3 years as the operation horizon later. The 3-year design annual runoffs of Danjiangkou Reservoir are shown in Table 2, which are derived by statistical analysis based on history runoff data (1956–2009).
Figure 1

Location map of the Danjiangkou Reservoir.

Figure 1

Location map of the Danjiangkou Reservoir.

Table 1

The salient features of the Danjiangkou Reservoir after the dam heightening

  Danjiangkou Reservoir
 
Reservoir properties Before After 
Annual average inflow/m3/s 1,200  
Annual average runoff/billion m3 37.9  
Standard pool level/m 157.0 170 
Design flood level/m 160 172.2 
Dead water level/m 139 150 
Flood control level 149/152.5 160/163.5 
Storage capacity/billion m3 20.95 33.91 
Active storage/billion m3 10.22 16.36 
Regulation cycle Annual regulation Multi-year regulation 
  Danjiangkou Reservoir
 
Reservoir properties Before After 
Annual average inflow/m3/s 1,200  
Annual average runoff/billion m3 37.9  
Standard pool level/m 157.0 170 
Design flood level/m 160 172.2 
Dead water level/m 139 150 
Flood control level 149/152.5 160/163.5 
Storage capacity/billion m3 20.95 33.91 
Active storage/billion m3 10.22 16.36 
Regulation cycle Annual regulation Multi-year regulation 
Table 2

The 3-year design annual runoff of Danjiangkou Reservoir

  Very wet Wet Normal Dry Very dry 
3-year (billion m3q > 46.28 36.92 < q ≤ 46.28 31.62 < q ≤ 36.92 26.96 < q ≤ 31.62 q ≤ 26.96 
  Very wet Wet Normal Dry Very dry 
3-year (billion m3q > 46.28 36.92 < q ≤ 46.28 31.62 < q ≤ 36.92 26.96 < q ≤ 31.62 q ≤ 26.96 

After dam heightening, reservoir storage and inflows have been allocated successively to meet the demand of downstream ecological water (DEW), downstream domestic water (DDW), Qingquangou irrigation water (QIW), water consumption of the SNWTP and water consumption for power generation. DDW and DEW are also used for power generation. Water supply for the SNWTP consumes 26.36% of the annual average runoff, which plays an important role in Danjiangkou Reservoir water allocation.

METHOD

Due to the multi-year regulation, multi-users and inflow uncertainty, an AR model, Monte Carlo method and DP are applied to derive optimal operation schemes. Figure 2 shows the flowchart of the technique solution of this paper. First, five sets of 500 synthetic 3-year runoff sequences are generated by the AR model and Monte Carlo sampling method. Each of the 500 synthetic sequences represent one kind of inflow conditions, which are divided by the 3-year design annual runoff in Table 2. Secondly, taking the synthetic streamflow time series as the input variables, a multi-objective optimal operation model for Danjiangkou Reservoir is established and computed by using DP with variable time step. Finally, the impacts of three factors are analyzed by three evaluation indexes and the optimal operating rules are summarized on the basis of the optimized release schemes.
Figure 2

Technique solution of this paper.

Figure 2

Technique solution of this paper.

Table 3 shows the comparison of statistical results of historical and synthetic series based on a long sequence test. The result illustrates that the AR model could better fit the streamflow of Danjiangkou Reservoir.

Table 3

Statistical results of historical and synthetic series based on a long sequence test

Series Mean (m3Cs Cv SD r1 
Synthetic series 299.831 0.328 0.313 93.702 −0.426 
History series 299.784 0.327 0.313 93.866 −0.428 
Series Mean (m3Cs Cv SD r1 
Synthetic series 299.831 0.328 0.313 93.702 −0.426 
History series 299.784 0.327 0.313 93.866 −0.428 

NUMERICAL MODEL

Objective function and constraints

The objective function is the summation of water supply benefit and power generation benefit, which is calculated as follows: 
formula
1
where qijws = water supply discharge for water use jJ (j = 1,2,3 individually represents water users of DDW, QIW and the SNWTP) in time period iI, qijws∈ real number > 0, m3/s; qirr = generating flow in time period iI, qirr∈ real number >0, m3/s; η = the coefficient of power generation, which is a function of water head; Δt = calculation step, s; H = water head, m; g = acceleration due to gravity, m/s2; ρ = the density of water, kg/m3; C1 and C2 = water price and electricity price, respectively.
The constraints include the water balance constraint (Equation (2)), minimum and maximum release constraint (Equation (3)), and storage capacity constraint (Equation (4)), respectively, as follows: 
formula
2
 
formula
3
 
formula
4

In Equations (2)–(4), Vi = storage capacity at the end of time period iI, m3; qiin = average reservoir inflow during time period iI, m3/s; Dimin = ecological water requirement downstream during time period iI, m3/s; Qimax = maximum allowed release during time period iI, m3/s; Dijws = practical water demand during time period iI for use jJ, m3/s; Zmax = normal water level, m; Zfc = flood control level, m; zunfs = reservoir storage level during non-flood season, m; zufs = reservoir storage level during flood season, m.

Optimization algorithm

For the sake of simplicity, DP with variable time step is applied to reduce the calculation dimension. The whole operation horizon lasts 3 years and is divided into 24 stages. Because of the relatively steady inflow during the non-flood season, a seasonal time step is adopted in the non-flood season to reduce the total calculation stages. Taking the time node of the flood control level into consideration, the calculation steps of the numerical model are shown in Figure 3. The number of the state variable (reservoir storage level) discretization is 400 and the algorithm is implemented with Matlab 2010 on a desktop with Intel(R) Core(TM) i5-2400 CPU, 4.00GB of RAM.
Figure 3

Schematic of the variable time step.

Figure 3

Schematic of the variable time step.

RESULT AND DISCUSSION

Impact of SRL

Different SRLs for a carryover storage reservoir correspond to different reservoir statistical indicators. The impact of an SRL could be obtained from the analysis of changes in these statistical values. To get rid of the influence of water quantity, the final water levels (FWLs) are defined as the same level as the SRLs (FWL = SRL). Figure 4 illustrates the effect of SRL on hydropower generation and SI under different inflow situations. The shortage index (SI) (Hsu & Cheng 2002; Tu et al. 2008) involving the shortage of DDW, QIW and the SNWTP is calculated as follows: 
formula
5
in which I = reservoir operation horizon; Di1,2,3ws and TSi1,2,3 = water demand and water shortage of DDW, QIW and the SNWTP in period i, m3/s, respectively.
Figure 4

The impact of different SRLs on hydropower generation and SI under different inflow situations.

Figure 4

The impact of different SRLs on hydropower generation and SI under different inflow situations.

For hydropower generation, the cumulative generation rises with SRL, which is an obvious consequence of the increasing average water head caused by the rise of the SRL. Power generation of different SRLs are nearly the same in normal, wet and very wet years, which imply that the SRL has little effect on hydropower generation when the inflow is relatively abundant.

For water supply, the SI rises at the 162 and 160 m SRLs, while the values of SIs are similar at the SRLs of 158, 156 and 154 m. For high SRL, the storage for water supply in the third years and the storage regulation capacity diminish with the increase of SRL. As a result, the SI rises with the SRL and the water shortage mainly happens in the third year, according to the rule of FWL = SRL. For low SRL, the initial storage for water supply is not enough for the water demand of all users in very dry years, which results in serious water shortage in both DDW and SNWTP in the first year. Although the SIs of 156 and 154 m are nearly the same as that of 158 m, the water demand of DDW could not be fulfilled when the first year is very dry, the rates of which are respectively 5.8% and 9.4%. The lower SRL in the very dry years will also result in higher risk of continuous damage to reservoir operation.

The water impoundment condition (Figure 5) obviously reduces with inflows. All the water impoundment conditions are nearly the same under different SRLs, which is mainly caused by the limitation of the flood control level of 160 m during summer. Additionally, the water abandoning conditions (WAC) of the SRLs of 162 and 160 m are relatively higher than those of others in abundant inflow conditions in the first year, because of the diminishing regulation capacity caused by the increasing SRL. The WAC is calculated as follows: 
formula
6
 
formula
7
where M = 500, the simulation series length; qmirr is the total water discharge including the generating flow of the mth simulation data in time period i, m3/s. From Figure 5, it could be inferred that the water impoundment condition mainly relates to inflow and flood control level, while the SRL has less impact on it. To improve the water impoundment condition, reservoir managers could attempt to use the dynamic flood control level or early reservoir refill method after more detailed studies.
Figure 5

The impact of different SRLs on the water impoundment condition (3-year) and the WAC in the first year under different inflow situations.

Figure 5

The impact of different SRLs on the water impoundment condition (3-year) and the WAC in the first year under different inflow situations.

In summary, a high SRL will cut down the regulation and storage capacity and adversely affect multi-year scheduling according to the scheduling rules of FWL = SRL. Low SRL will cause the risk of water shortage in first year, poor performance in power generation and a water impoundment condition and this effect will continue even in the following two years. Therefore, due to good performance in all aspects, 158 m is recommended as the optimal SRL for Danjiangkou Reservoir. However, when the future inflow condition is predictably abundant, the recommended SRL could be slightly smaller than 158 m, or vice versa.

Impact of the inflow condition

The impact of the inflow condition on hydropower generation, water impoundment condition, water supply and the WLE is discussed on the basis of SRL = 158 m.

Hydropower generation

From Figure 6(a), the cumulative hydropower generation increases with the inflow condition and the reservoir could generate at least 7 billion kWh under a very dry inflow situation. In addition, the standard deviation (SD) in very dry years is only 0.65, and obviously less than in others, which implies the effect of inflow uncertainty diminishes with the reduction of the inflow situation. The reason can be explained as follows. In the very dry years, inflow can only satisfy the DEW and DDW and is not sufficient for the SNWTP water. In this situation, cumulative generation mainly depends on the stable DEW and DDW, which results in the lower deviation of power generation. Furthermore, sequences which consume less water than average but generate more electricity are picked out and named S1. In Figure 6(b), the inflow variation range of S1 is obviously smaller than in the whole sequences, which indicates that a steady inflow process is beneficial for increasing hydropower generation.
Figure 6

(a) Maximum, average and minimum cumulative hydropower generation and SDs under different inflow situations and (b) the comparison result of annual inflow distributions between S1 and whole series.

Figure 6

(a) Maximum, average and minimum cumulative hydropower generation and SDs under different inflow situations and (b) the comparison result of annual inflow distributions between S1 and whole series.

Water impoundment condition

From Table 4, data indicate that the reservoir could reach the normal water level at the end of the flood season at least once in 3 years under relatively abundant inflow conditions, while in dry or very dry years the ratio reduces to 80.6% and 29.8%, respectively. Besides, the reservoir could hardly be filled simultaneously at each end of the flood season under dry or very dry inflow conditions during the operation horizon, while in very wet and wet years the ratio could reach 60.8% and 22.6%. In summary, the statistical result verifies that the water impoundment condition is improved with the increase in reservoir inflow.

Table 4

The water impoundment condition in different inflow situations

Inflow condition P3 P2 P1 P0 
Very wet 60.8% 99.8% 100% 
Wet 22.6% 89.4% 100% 
Normal 3.4% 59.2% 99.4% 
Dry 14.8% 80.6% 19.4% 
Very dry 29.8% 70.2% 
Inflow condition P3 P2 P1 P0 
Very wet 60.8% 99.8% 100% 
Wet 22.6% 89.4% 100% 
Normal 3.4% 59.2% 99.4% 
Dry 14.8% 80.6% 19.4% 
Very dry 29.8% 70.2% 

P3 = the probability of reservoir filled simultaneously at each end of flood season; P2 = the probability of reservoir filled at least twice in 3 years; P1 = the probability of reservoir filled at least once in 3 years; P0 = the probability of reservoir never filled in 3 years.

Water supply

Figure 4 shows that water shortage mainly occurred under relatively dry inflow conditions, especially for very dry years. Therefore, more attention is paid to the performance of reservoir water supply for the SNWTP in very dry years in this part. Figure 7 illustrates the SI distribution of the 500 synthetic 3-year series under very dry inflow conditions. The sequences of SI < 12 mean that the overall water shortage is less than 5 billion m3 and its percentage is 34.4% when the reservoir encounters very dry years. The sequences of 12 < SI < 42 mean that the overall water shortage is between 5 and 10 billion m3 and its rate is 56.8%. The sequences of SI > 42 mean that the overall water shortage is larger than 10 billion m3 and its rate is 8.8%. The above implies that the risk of failing to supply water for the SNTWP and its corresponding shortage level are relatively higher in very dry years.
Figure 7

The SI distribution of synthetic series.

Figure 7

The SI distribution of synthetic series.

The above analysis could summarize suggestions that would be useful to the operation for Danjiangkou Reservoir. On the one hand, when the inflow condition is relatively abundant (very wet, wet and normal), inflow is generally enough for the water supply and reservoir managers could pursue maximum power generation on the basis of meeting the demands of all water users. On the other hand, when the inflow condition is relatively dry (dry and very dry), the risk of water shortage for the SNWTP will be high without using the reservoir capacity. Therefore, reservoir managers should make full use of the regulation capacity to store water in relatively wet periods for the water supply in dry periods or use the reservoir capacity to meet the water demand if necessary.

Impact of flood control level

To make full use of the middle and small flood waters, reservoir managers could attempt to raise the flood control level temporarily without increasing flood control risk based on forecasting pre-release. The so-called forecasting pre-release here can be explained as follows. During the flood season, reservoir managers could temporarily improve the flood control level from 160 m to 160.5 m (during summer) and from 163.5 m to 164 m (during autumn) for Danjiangkou Reservoir, respectively. Once a flood is forecast, the release should exceed the inflow with a certain discharge to bring the water level back to 160 or 163.5 m in one day.

As shown in Figure 8, hydropower generation and SI decrease with the increase in flood control level. Attributed to the increase in beneficial capacity, the SI declines by 0.11 with every 0.1 m increase in the flood control level, which is equivalent to 0.83 million m3 of water increase for the SNWTP per month. For hydropower generation, every 0.1 m increase in the flood control level will result in a 2.15 million kWh decrease in cumulative hydropower generation, because more water in the flood season is stored for water supply in the non-flood season. Moreover, water impoundment conditions are nearly the same when the enhanced degree of flood control levels is 0.5 m. Since water supply for the SNWTP is much more important than power generation for Danjiangkou Reservoir, it is advisable to raise the flood control level temporarily without increasing flood control risk to reduce water shortage in the SNWTP.
Figure 8

The impact of flood control levels on the SNWTP SI and hydropower generation.

Figure 8

The impact of flood control levels on the SNWTP SI and hydropower generation.

Distribution of the WLE

To take full advantage of a multi-year regulation reservoir with a large regulation capacity, the operation rules of the WLE are crucial. In Figure 9, water levels at the end of the first year mainly vary from 162 m to 168 m, 162 m to 168 m, and 160 m to 166 m in very wet, wet, and normal years, respectively, while water levels are more decentralized in dry or very dry inflow conditions. Table 5 summarizes the evaluation indexes of different water levels at the end of the first year under relatively abundant inflow situations. The sequences of water levels of 162–166 m, 164–166 m, and 162–164 m perform better in very wet, wet, and normal years in three indexes than the average of the whole series. Therefore, these individual ranges for the water levels at the end of the first year are suggested as the optimal ranges. Water levels at the end of the second year have similar overall features with the first year, but less obviously due to the different starting levels of the second year.
Figure 9

The distribution of water levels at the end of the first year in different inflow conditions.

Figure 9

The distribution of water levels at the end of the first year in different inflow conditions.

Table 5

The reservoir operation indexes of different water levels at the end of the first year in very wet, wet, and normal years

      WLE
 
  Whole series 160–162 m 162–164 m 164–166 m 166–168 m 
Very wet Cumulative hydropower generation (billion kWh) 18.71 18.73 18.74 18.74 18.55 
P3 60.8% 50% 72.3% 71.3% 20.78% 
SI 0.70 0.29 2.35 
Wet Cumulative hydropower generation (billion kWh) 14.47 14.01 14.34 14.60 14.80 
P3 22.6% 40.96% 26.49% 
SI 1.62 0.23 1.56 4.59 
Normal Cumulative hydropower generation (billion kWh) 12.00 11.75 12.00 12.22 12.27 
P3 3.4% 5.47% 4.72% 
SI 2.94 0.81 0.73 3.77 5.92 
      WLE
 
  Whole series 160–162 m 162–164 m 164–166 m 166–168 m 
Very wet Cumulative hydropower generation (billion kWh) 18.71 18.73 18.74 18.74 18.55 
P3 60.8% 50% 72.3% 71.3% 20.78% 
SI 0.70 0.29 2.35 
Wet Cumulative hydropower generation (billion kWh) 14.47 14.01 14.34 14.60 14.80 
P3 22.6% 40.96% 26.49% 
SI 1.62 0.23 1.56 4.59 
Normal Cumulative hydropower generation (billion kWh) 12.00 11.75 12.00 12.22 12.27 
P3 3.4% 5.47% 4.72% 
SI 2.94 0.81 0.73 3.77 5.92 

CONCLUSIONS

This paper sets up a multi-objective optimal operation model for Danjiangkou Reservoir to cope with the new task brought by the SNWTP. By assessing the impact of different influence factors on the operation of the reservoir, some optimal operation rules are obtained as follows:

  1. Comparing the performance of different SRLs in three reservoir operation indexes, the optimal SRL for Danjiangkou Reservoir is 158 m, which could guide realistic operation.

  2. Reservoir managers could pursue maximum power generation on the basis of meeting the demands of all water users in relatively abundant inflow conditions, while in dry inflow situations managers should make full use of the regulation capacity to store water in wet periods to cope with the shortage in dry periods or use the reservoir capacity to meet the water demand as necessary.

  3. To make full use of the middle and small flood resources, reservoir managers could apply a forecasting pre-release method. Results show that every 0.1 m increase in the flood control level will result in a 0.11 decrease of SI.

  4. For the WLE, the optimal ranges (162–166 m, 164–166 m, and 162–164 m) of water levels at the end of the first year (SRL = 158 m) during the very wet, wet and normal years are proposed based on the evaluation of indexes.

In addition, climate change, which is not considered in this paper, will bring more uncertainty to precipitation and inflow and should be paid more attention when there is enough research data. More detailed impacts of forecasting pre-release on releasing the water supply for the SNWTP also could be a future study. Moreover, aiming to reduce the risk of unacceptably large future water deficits at the cost of a series of allowed small deficits in dry years, optimal polices merging with hedging for Danjiangkou Reservoir could also be discussed in future research.

ACKNOWLEDGEMENTS

This study is supported by the Major National Science and Technology Project (2012ZX07205005), the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (51321065), the Tianjin Research Program of Application Foundation and Advanced Technology (13JCZDJC36200, 15JCYBTC21800), the National Natural Science Foundation of China (51109156), and the Programme of Introducing Talents of Discipline to Universities (B14012). The writers also acknowledge the assistance of anonymous reviewers.

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