Abstract

Reservoir operation charts have been widely researched and applied to reservoir operation. However, these achievements are generally used for a single reservoir and have rarely been applied to cascade reservoirs. Considering the requirements of flood control and water supply, this paper studied the extraction and application of energy storage operation chart (ESOC) for cascade reservoirs. Steps in the methodology mainly include: (1) model building of cascade reservoirs operation optimization (CROO), (2) extracting ESOC based on discriminant coefficient method (DCM) and CROO model, (3) simulation operation of ESOC based on DCM, (4) choosing the optimal ESOC and verifying its efficiency through the results. Cascade reservoirs in the Yangtze River of China were selected for a case study. Compared with the conventional operation method, the simulation results show that the ESOC presents better performance in terms of power generation, guaranteed output and assurance rate. In detail, the annual power generation of ESOC can be increased by 0.9%, the total guaranteed output can be increased by 3.4% and the assurance rate can be increased by 9.6%, which indicates that the proposed ESOC method can greatly improve the hydropower energy efficiency and reliability of cascade reservoirs’ power supply.

INTRODUCTION

As one of the most stable renewable energy, hydropower can be commercially developed and utilized on a large scale (Lu et al. 2015). After the reservoir is built, how to exert its function as much as possible, and to improve the efficiency of hydropower generation on the premise of guaranteeing the water supply and flood control requirements (Jiang et al. 2015) is the focus of many scholars and managers in the world, which is also the problem that needs to be solved by the reservoir operation optimization (Valipour 2013).

Nowadays, many methods are used to guide the optimal reservoir operation. One kind is the traditional optimization algorithms, such as the linear programming (Li et al. 2013), dynamic programming (DP) (Shokri et al. 2013), progressive optimality algorithm (Lu et al. 2013), and fuzzy theory (Chang et al. 2005), etc. Another kind is the intelligent optimization algorithms, such as genetic algorithm (Momtahen & Dariane 2007), particle swarm optimization (Zhang et al. 2014), and neural network algorithm (Valipour 2015), etc. However, in the actual reservoir operation, especially in the long or mid-term operation, the established operating rules through the historical data are dependent on the natural uncertainties of inflow in the future.

To obtain the optimal operating rules for reservoirs, large numbers of studies and practices have been developed in recent years (Ma et al. 2013), which vary significantly in their extraction methods and applications. For example, in 2007, Chaleeraktrakoon and Kangrang proposed a DP approach for finding the optimal rule curves of single and multi-reservoir systems, compared with the traditional method, results of the case study demonstrated that the proposed approach is generally fast and robust (Chaleeraktrakoon & Kangrang 2007). In 2013, Zhou and Guo developed an integrated adaptive optimization model (IAOM) for derivation of multipurpose reservoir operating rule curves (Zhou & Guo 2013); the innovation of this work is that the obtained optimal multipurpose reservoir operating rule curves by IAOM can reflect the hydrologic characteristics of future climate change. In 2014, using a constrained genetic algorithm and a penalty strategy, Trieu et al. proposed a methodology for establishing the optimal operation rule curves based on a multi-use reservoir system (Trieu et al. 2014). The proposed model was formulated by including various water demands configured into the objective function, and it was demonstrated as an effective and powerful tool for optimal strategy searching for multi-use reservoir operations. In 2015, Afshar et al. developed a set of piecewise linear operating rule curves for water supply and hydropower reservoirs by employing an imperialist competitive algorithm (Afshar et al. 2015). In 2016, Najl et al. provided a simulation optimization model for deriving an operating policy for multi-reservoir systems, and two adjustable monthly rule curves were introduced to each reservoir in the system and a self-adaptive genetic algorithm was developed to maximize the system's hydropower production (Najl et al. 2016). To a certain extent, the above research results effectively improved the hydropower generation efficiency of the applied reservoir system, and obtained a considerable economic benefit, and it also effectively promotes the development of reservoir operation around the word.

There are many kinds of operating rules in the actual reservoir operation (Chiamsathit et al. 2014), while the reservoir operation chart is the frequently used at present, which is the graphical representation of operating rules, and it consists of several operation curves and zones (Ai & Gao 2011). Through the above review, it can be seen that the research of reservoir operating rule or operation chart has made a great progress, especially in the field of single reservoir operation (Jiang et al. 2014). However, previous studies are mostly based on the optimization algorithms, models and the data processing technologies. Although it is simple and easy to get the joint operation chart of cascade reservoirs by optimization algorithms, these methods are usually insufficient in terms of physical significance. Especially for intelligent optimization algorithms, there is a big randomness in their optimization, so the reliability of optimization results is not high enough (Jiang et al. 2016). Nowadays, along with the formation of cascade reservoirs systems around the world, the joint operation of cascade reservoirs is becoming very necessary, while it has an output allocation problem. In the actual operation, it is found that discriminant coefficient method (DCM) is a relatively matured output allocation method in guiding the joint operation of cascade reservoirs compared with the other methods. However, through a sufficient literature survey, it is found that the achievements about the joint operation chart research based on DCM are rarely around the world (Liu et al. 2011).

Thus, in order to obtain the best way of energy storage operation, so that to improve the water resources utilization efficiency and get the maximum energy using the limited hydropower resources, this paper takes the cascade reservoirs of the upstream reaches of the Yangtze River as an instance, to research the extraction and application of energy storage operation chart (ESOC) considering the requirements of flood control and water supply. Meanwhile, in order to make more reasonable total output distribution for the cascade hydropower stations and avoid the randomness of intelligent optimization algorithms in extracting ESOC, the DCM is coupled in the extraction and application of ESOC in this paper, which can effectively improve and guarantee the output stability and reliability of the obtained ESOC.

FORMULATION OF CROO PROBLEM

The major objective of cascade reservoirs operation is maximizing the water resource benefits which are mainly related to hydroelectric energy. Generally, the objective function of the optimization model can be described as follows:  
formula
(1)
where E is the total power generation over the entire planning horizon; T is the number of stages; Nti is the output of the ith hydropower station in the tth stage; n is the number of reservoirs; Hti is the average water level of the ith hydropower station in the tth stage; Δt is the duration of a stage; qti is the outflow through the turbines of the ith reservoir in the tth stage; ki is the efficiency coefficient of the ith hydropower station; Nit,exp is the expected output, which is the maximum output of the unit under a working water head, and it is usually measured by experiments.

Subject to the following equality and inequality constraints.

  • (1)
    Water volume balance:  
    formula
    (2)
    where Wti is the redundant water outflow through flood outflow gate of the ith reservoir in the tth stage; Iti is the inflow of the ith reservoir in the tth stage; Evti is the evaporation capacity of the ith reservoir in the tth stage; Vit is the storage volume of the ith reservoir in the tth stage.
  • (2)
    Reservoir volume limits:  
    formula
    (3)
    where Vit,min is the lower limit of Vit, which is corresponding to dead level; Vit,max is the upper limit of Vit, which is corresponding to flood control level in flood season and normal level in dry season.
  • (3)
    Comprehensive utilization of water resources required at downstream reservoir limits:  
    formula
    (4)
    where Qit is the total outflow of the ith reservoir in the tth stage, including qti and Wti; Qit,min is the lower limit of Qit, which is determined by the ecological flow of downstream; Qit,max is the upper limit of Qit, which is determined by the downstream river channel capacity.
  • (4)
    Output limits:  
    formula
    (5)
    where Nit,min is usually determined by the allowed minimum output; Nit,max is usually determined by the installed capacity or expected output.

  • (5)
    The assurance rate limit of power generation:  
    formula
    (6)
    where Nb is the guaranteed output of the cascade system; φ() is the statistical function, represents the times that the actual total output of the cascade system is greater than Nb; P is the statistical assurance rate of cascade system in each simulation operation, it means the degree of reliability of the output Nb being satisfied in a long operation period; Pmin is the lower limit of the assurance rate.
  • (6)
    The guaranteed output limit of power generation:  
    formula
    (7)
    where Nb,min is the lower limit of guaranteed output of cascade system.

ESOC MODEL AND ITS SOLVING

Extraction of ESOC based on DCM

In the single reservoir operation, we usually use the reservoir operation chart to guide the actual operation, which takes the water level as the operation indicator that can fully reflect the current energy state of the reservoir. However, in the joint operation of cascade reservoirs, the same amount of water has different energy in different reservoirs because of the geographical position, so we take a comprehensive indicator which is the total energy storage of cascade system to represent its overall energy state, and use the corresponding ESOC to guide the actual operation. The following section will introduce the extraction process of ESOC based on DCM and the cascade reservoirs joint optimization model described in the previous section.

DCM

After the cascade system's total output determined, there is an allocation problem in the joint operation of cascade reservoirs by ESOC. Only if the total output is allocated to each power station reasonably, the cascade system can get a high energy efficiency (Zhu et al. 2014). DCM's basic principle is to determine the optimal order of water storage and water supply for cascade reservoirs, so that to maximize the power generation and minimize the energy loss as far as possible. The computational formula of discriminant coefficient for each reservoir in DCM can be simply described as follows, and the detailed derivation can be found in the literature by Jiang et al. (2016).

In the water supply operation, due to the water supply of the ith hydropower station, the extra energy loss to unit electricity generation is  
formula
(8)
where Kit,loss is the extra energy loss to unit electricity generation of the ith hydropower station; ΔEW-supply is the extra hydropower loss of the ith reservoir in generating hydroelectric power by the amount of inflow water Wti in the ith stage; ΔEV-supply is the extra energy decrement of the upstream reservoirs’ available storage water ∑Vavai to current reservoir; ΔEsupply is the energy provided by the supplied water of the ith reservoir; Wti is the amount of inflow water of the ith reservoir in the ith stage; ∑Vavai is the upstream reservoirs’ available storage water of current reservoir; Fti is the average water surface area of the ith reservoir in the tth stage; ∑Hti is the sum of average water head of the ith reservoir and downstream reservoirs in the tth stage.
In the water storage operation, due to the water storage of the ith hydropower station, the extra energy obtainment to unit of stored energy of the ith hydropower station is  
formula
(9)
where Kit,obtain is the extra energy obtainment to unit of stored energy of the ith hydropower station; ΔEW-store is the extra energy obtainment of the ith reservoir in generating hydroelectric power by the amount of inflow water Wti in the tth stage; ΔEV-store is the extra energy obtainment of the upstream reservoirs’ available storage water ∑Vavai to current reservoir; ΔEstore is the energy stored by the ith reservoir.

In general, the value of Kit,loss or Kit,obtain of each reservoir is different in a cascade system. When the water need to be stored, the best reservoir for storing water is the one that can maximize the extra energy increment caused by storing unit energy, so the reservoir with the maximum Kit,obtain value should store water first. Similarly, when the water needs to be supplied, the best reservoir for supplying water is the one that can minimize the energy loss caused by generating unit electrical energy, so the reservoir with the minimum Kit,loss value should supply water first.

Extraction process of ESOC

In the actual reservoir operation, there are three output situations which are increased output, guaranteed output and reduced output, respectively. So there are three kinds of operation zones and curves in ESOC, correspondingly. The upper boundary and lower boundary of the guaranteed output zone are corresponding to the upper basic operation curve and lower basic operation curve, respectively. The increased output curves are the boundaries of increased output zones, and the reduced output curves are the boundaries of reduced output zones. The ESOC can be obtained by a reverse calculation using the hydrological process of typical years. The specific steps of choosing typical years have been recorded in the literature by Shao et al. (2010) and Yu et al. (2011). The specific reverse extracting processes for the three main operation curves are shown in Figure 1.

Figure 1

Flowchart of extracting the operation curves.

Figure 1

Flowchart of extracting the operation curves.

Simulation operation of ESOC based on DCM

Suppose TOchart represents the total output read from ESOC according to the current energy state of cascade system, and TOrunoff represents the total output calculated by the runoff of current stage, as shown in Figure 2, where the runoff here means the average input rate of water for the reservoir in a stage, including the runoff generated by the precipitation in the upper reaches of the reservoir and the direct precipitation on the water surface of the reservoir. Then, the specific operation steps by ESOC and DCM are as follows.

Figure 2

Simulation process using ESOC in the cascade reservoirs operation.

Figure 2

Simulation process using ESOC in the cascade reservoirs operation.

Step 1: At the beginning of the current stage, the total energy storage of cascade reservoirs can be calculated by formula (10) according to Viavai,t and Hit, where et is the total energy storage of cascade reservoirs in the tth stage; eit is the energy storage of the ith reservoirs in the tth stage; ρ is the density of water; g is the acceleration of gravity; Viavai,t is the available amount of water of the ith reservoir in the tth stage.  
formula
(10)

Step 2: Read a TOchart from ESOC according to et, and calculate TOrunoff by the runoff of current stage.

Step 3: If TOrunoff > TOchart, the cascade system should store water. We arrange the reservoirs to store water according to the calculated Kit,obtain at the beginning of current stage, until the total output calculated by the flow of natural inflow minus the stored flow is equal to TOchart.

Step 4: If TOrunoff < TOchart, the cascade system should supply water. We arrange the reservoirs to supply water for power generation according to the calculated Kit,loss at the beginning of the current stage, until the total output calculated by natural inflow and supplied flow is equal to TOchart.

Step 5: If TOrunoff = TOchart, there should be no water storage or supply. The cascade system generates the electricity by the natural inflow only.

The simulation process using ESOC to guide the cascade reservoirs operation can be described by Figure 2.

The optimal ESOC confirmation

The design guaranteed output and assurance rate for a reservoir are determined at the design or construction phase, which are relatively fixed values. However, when the cascade reservoirs system formed with multiple reservoirs and implements the joint operation, the total guaranteed output and assurance rate of cascade system will have some changes because of the mutual compensation effect among reservoirs. Therefore, when we determine the optimal ESOC, the effect of the changes of guaranteed output and assurance rate must be taken into consideration. Usually, in order to choose the optimal ESOC reasonably, we need to get the variations of power generation and assurance rate with the changes of guaranteed output, by which we can get the optimal ESOC.

To achieve the above purpose, we discrete the total guaranteed output in a certain range (for example, the design guaranteed output fluctuation within 20%), and for each discretized guaranteed output, we extracted the corresponding ESOC according to the method in ‘Extraction of ESOC based on DCM’, and then use the method in ‘Simulation operation of ESOC based on DCM’ to implement the simulation by the historical runoff data and the obtained ESOC, and get the corresponding statistical assurance rate and power generation. Taking the same calculation for all the discretized guaranteed output, we can finally get the variations of power generation and assurance rate with the changes of guaranteed output.

According to the obtained relation curve of guaranteed output, power generation and assurance rate, we can determine the optimal ESOC corresponding to the maximum power generation under the actual requirements of guaranteed output and assurance rate.

CASE STUDY

Basic data

The Yangtze and Jinsha River basin is the largest river basin in China. There are two hydropower stations in the upstream of the Yangtze River main stream, which are Three Gorges and Ge Zhouba (Chen et al. 2014), and Three Gorges reservoir has a seasonal regulation performance. There are four planned hydropower stations with a good regulation performance in the downstream reaches of Jinsha River, which is Wu Dongde, Bai Hetan, Xi Luodu and Xiang Jiaba, but only Xi Luodu and Xiang Jiaba hydropower stations have been put into operation at present (Xie et al. 2015). Considering the reservoir regulation performance and the availability of data, this paper takes the Xi Luodu, Xiang Jiaba and Three Gorges reservoirs as a cascade system instance to study the ESOC. The basic parameters of this three hydropower stations are shown in Table 1, and the plane sketch map of the studied cascade hydropower stations is shown in Figure 3.

Table 1

Parameters of the Xi Luodu, Xiang Jiaba and Three Gorges reservoirs

ItemsUnitXi LuoduXiang JiabaThree Gorges
Normal level 600 380 175 
Dead level 540 370 145 
Regulation performance None Annual Season Season 
Design guaranteed output MW 3,350 2,009 4,990 
Coefficient of output None 8.5 8.5 8.5 
Flood control level 560 370 155 
Flood season Month 5–9 5–9 5–9 
ItemsUnitXi LuoduXiang JiabaThree Gorges
Normal level 600 380 175 
Dead level 540 370 145 
Regulation performance None Annual Season Season 
Design guaranteed output MW 3,350 2,009 4,990 
Coefficient of output None 8.5 8.5 8.5 
Flood control level 560 370 155 
Flood season Month 5–9 5–9 5–9 
Figure 3

Plane sketch map of the studied cascade hydropower stations.

Figure 3

Plane sketch map of the studied cascade hydropower stations.

Considering the flood control requirements of reservoir in flood season, and the water supply requirements of downstream in dry season, the water level and outflow constraints of each reservoir in each stage are shown in Table 2, where Max Z and Min Z respectively represent the allowed maximum and minimum water level in power generation operation, and Max Q and Min Q respectively represent the allowed maximum and minimum outflow.

Table 2

Constraints of water level and outflow in the practical power generation operation

Xi Loudu Reservoir
Xiang Jiaba Reservoir
Three Gorges Reservoir
Name ItemMax Z
(m)
Min Z
(m)
Max Q
(m3/s)
Min Q
(m3/s)
Max Z
(m)
Min Z
(m)
Max Q
(m3/s)
Min Q
(m3/s)
Max Z
(m)
Min Z
(m)
Max Q
(m3/s)
Min Q
(m3/s)
Jan. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Feb. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Mar. 600 560 43,700 1,500 380 370 49,800 1,500 175 145 98,800 4,500 
Apr. 600 560 43,700 1,500 380 370 49,800 1,500 175 145 98,800 4,500 
May 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Jun. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Jul. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Aug. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Sep. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Oct. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Nov. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Dec. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Xi Loudu Reservoir
Xiang Jiaba Reservoir
Three Gorges Reservoir
Name ItemMax Z
(m)
Min Z
(m)
Max Q
(m3/s)
Min Q
(m3/s)
Max Z
(m)
Min Z
(m)
Max Q
(m3/s)
Min Q
(m3/s)
Max Z
(m)
Min Z
(m)
Max Q
(m3/s)
Min Q
(m3/s)
Jan. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Feb. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Mar. 600 560 43,700 1,500 380 370 49,800 1,500 175 145 98,800 4,500 
Apr. 600 560 43,700 1,500 380 370 49,800 1,500 175 145 98,800 4,500 
May 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Jun. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Jul. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Aug. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Sep. 560 560 43,700 1,500 370 370 49,800 1,500 145 145 98,800 4,500 
Oct. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Nov. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 
Dec. 600 560 43,700 1,500 380 370 49,800 1,500 175 155 98,800 4,500 

The long series observed runoff data of this cascade system is available from 1959 to 2000, a total of 42 years. Five hydrological years which are 1959, 1970, 1976, 1977 and 1997 are selected as the typical years. The observed runoff data of these typical years is shown in Table 3.

Table 3

Runoff data of typical years for each hydropower stations (unit: m3/s)

ReservoirYearJun.Jul.Aug.Sep.Oct.Nov.Dec.Jan.Feb.Mar.Apr.May
Xi Loudu 1,959 5,116 6,139 9,200 5,434 4,776 3,129 1,817 1,478 1,313 1,351 1,524 2,041 
1,970 3,445 8,365 6,135 5,702 4,678 2,798 1,781 1,832 1,550 1,512 2,329 2,563 
1,976 2,863 7,776 7,245 10,435 5,036 2,720 1,835 1,671 1,412 1,288 1,336 1,310 
1,977 4,325 7,584 8,853 6,983 4,471 2,491 1,745 1,567 1,308 1,253 1,398 2,378 
1,997 6,042 5,988 5,775 6,718 4,420 2,283 1,651 1,647 1,388 1,476 1,855 2,363 
Xiang Jiaba 1,959 5,187 6,268 9,375 5,534 4,872 3,192 1,846 1,489 1,324 1,368 1,541 2,068 
1,970 3,473 8,507 6,213 5,761 4,762 2,862 1,815 1,876 1,595 1,533 2,354 2,583 
1,976 2,915 7,909 7,335 10,629 5,140 2,780 1,882 1,727 1,448 1,310 1,352 1,324 
1,977 4,392 7,682 8,943 7,085 4,553 2,539 1,781 1,607 1,338 1,279 1,425 2,427 
1,997 6,128 6,047 5,877 6,764 4,507 2,332 1,684 1,659 1,401 1,504 1,881 2,400 
Three Gorges 1,959 17,353 22,595 27,806 13,643 11,966 8,940 5,612 3,987 3,813 5,273 6,649 11,316 
1,970 20,890 29,538 19,286 14,467 16,047 8,227 4,519 4,735 4,279 6,089 10,750 16,706 
1,976 9,635 26,924 19,848 25,250 16,785 10,807 5,079 4,287 3,599 3,467 5,612 7,615 
1,977 17,683 24,180 16,911 17,313 13,539 8,969 4,504 3,915 3,430 4,215 6,832 13,729 
1,997 17,510 20,452 12,095 18,227 17,621 9,117 7,432 4,627 3,531 4,324 8,067 9,032 
ReservoirYearJun.Jul.Aug.Sep.Oct.Nov.Dec.Jan.Feb.Mar.Apr.May
Xi Loudu 1,959 5,116 6,139 9,200 5,434 4,776 3,129 1,817 1,478 1,313 1,351 1,524 2,041 
1,970 3,445 8,365 6,135 5,702 4,678 2,798 1,781 1,832 1,550 1,512 2,329 2,563 
1,976 2,863 7,776 7,245 10,435 5,036 2,720 1,835 1,671 1,412 1,288 1,336 1,310 
1,977 4,325 7,584 8,853 6,983 4,471 2,491 1,745 1,567 1,308 1,253 1,398 2,378 
1,997 6,042 5,988 5,775 6,718 4,420 2,283 1,651 1,647 1,388 1,476 1,855 2,363 
Xiang Jiaba 1,959 5,187 6,268 9,375 5,534 4,872 3,192 1,846 1,489 1,324 1,368 1,541 2,068 
1,970 3,473 8,507 6,213 5,761 4,762 2,862 1,815 1,876 1,595 1,533 2,354 2,583 
1,976 2,915 7,909 7,335 10,629 5,140 2,780 1,882 1,727 1,448 1,310 1,352 1,324 
1,977 4,392 7,682 8,943 7,085 4,553 2,539 1,781 1,607 1,338 1,279 1,425 2,427 
1,997 6,128 6,047 5,877 6,764 4,507 2,332 1,684 1,659 1,401 1,504 1,881 2,400 
Three Gorges 1,959 17,353 22,595 27,806 13,643 11,966 8,940 5,612 3,987 3,813 5,273 6,649 11,316 
1,970 20,890 29,538 19,286 14,467 16,047 8,227 4,519 4,735 4,279 6,089 10,750 16,706 
1,976 9,635 26,924 19,848 25,250 16,785 10,807 5,079 4,287 3,599 3,467 5,612 7,615 
1,977 17,683 24,180 16,911 17,313 13,539 8,969 4,504 3,915 3,430 4,215 6,832 13,729 
1,997 17,510 20,452 12,095 18,227 17,621 9,117 7,432 4,627 3,531 4,324 8,067 9,032 

Results and analysis

According to the ESOC model and its solving method described earlier, we set different discretized guaranteed output in the range of the sum of original design guaranteed output (i.e. 10,394 MW, form Table 1) plus and minus 20%, with 1% discrete interval, then, according to each discretized guaranteed output, we extracted the ESOC and implemented the simulation under the constraints of flood control and water supply; finally, the relation curve of guaranteed output, assurance rate and power generation can be obtained, as shown in Figure 4.

Figure 4

The relationship curve among guaranteed output, assurance rate and power generation.

Figure 4

The relationship curve among guaranteed output, assurance rate and power generation.

From Figure 4, it can be seen that the assurance rate of ESOC are gradually reduced with the increase of guaranteed output. There is a reciprocal relationship between the guaranteed output and assurance rate in reservoir operation. According to Figure 4, we can find that the maximum power generation of the cascade system is 1725.76 × 108 kWh, the corresponding guaranteed output and assurance rate is 10,750 MW and 99.07%, respectively. The corresponding optimal ESOC is shown in Figure 5.

Figure 5

The optimal energy storage operation chart.

Figure 5

The optimal energy storage operation chart.

In order to contrastingly analyze the ESOC method with the conventional method, simulation through the conventional single reservoir operation chart (as shown in Figure 6) has been done in this paper, and the annual average power generation, guaranteed output and assurance rate of the two methods are shown in Table 4.

Table 4

Results of ESOC method and conventional reservoir operation method

MethodPower generation (108 kWh)Guaranteed output (MW)Assurance rate (%)
ESOC 1725.76 10,750 99.07 
Conventional method 1710.02 10,394 90.41 
Increment 15.74 356 8.66 
MethodPower generation (108 kWh)Guaranteed output (MW)Assurance rate (%)
ESOC 1725.76 10,750 99.07 
Conventional method 1710.02 10,394 90.41 
Increment 15.74 356 8.66 
Figure 6

Conventional reservoir operation chart of each reservoir.

Figure 6

Conventional reservoir operation chart of each reservoir.

In Table 4, the guaranteed output of ESOC is the optimal guaranteed output that corresponds to Figure 5. While, for the conventional method, the total guaranteed output of cascade system is still the sum of the design guaranteed output of each hydropower station, which is unchanged because of without considering the joint operation. The assurance rates in Table 4 are the statistics of simulation operation with a long series of historical runoff data.

From Table 4, it can be seen that the ESOC method in this paper is superior to conventional method in terms of power generation, guaranteed output and assurance rate, especially in terms of assurance rate. The increment of these three indicators is 15.74 × 108 kWh (0.9% growth), 356 MW (3.4% growth) and 8.66 (9.6% growth), respectively. Therefore, compared with the conventional reservoir operation method which is currently used in the actual operation, it can be seen that the proposed ESOC method in this paper can effectively improve the energy efficiency and at the same time ensure a good stability and reliability of power supply for cascade system.

To further analyze the reasons of the difference of the two methods on the results, the average water level variations of each reservoir of the two methods are shown in Figure 7. It is important to note that the water level variations in Figure 7 are drawn by the beginning water level of each stage.

Figure 7

Average water level variations of the cascade reservoirs.

Figure 7

Average water level variations of the cascade reservoirs.

From Figure 7, it can be seen that, firstly, the water levels of the three reservoirs in the simulation operation are all within the feasible range, which means the water level constraints are both not destroyed in the two methods. Secondly, except the first reservoir of the cascade system, the reservoir water level falling is relatively slow in ESOC method compared with the conventional method. Especially for the Xiang Jiaba reservoir, its operating water level is lower and the fluctuation is bigger in conventional method than ESOC method; on the contrary, the operating water level basically maintains a high level in ESOC method, and only drops to a low water level in the last few stages because of the flood control requirements in flood season.

Therefore, the most operation stages of downstream reservoirs maintain a high water level in ESOC method, which can effectively raise the water head of downstream reservoirs, and increase the whole hydroelectricity benefit of the cascade system. This is the main reason why the three statistical indicators of ESOC method are superior to conventional method. In addition, comparing the water level variations of the three reservoirs in ESOC method, it can be found that the upstream reservoir releases the water earlier than the two downstream reservoirs in the dry period, to make full use of the high water head of downstream reservoirs to generate more electricity before it drops down. This phenomenon, which does not appear in the conventional method, is of great significance to guide the actual cascade reservoirs operation, and it is consistent with the basic principle of reservoir storage and supply. So, results reflect that the ESOC method can be applied to the practical operation so as to increase the hydropower generation.

CONCLUSION

A reservoir operation chart is the guideline for long- and mid-term reservoir operation. An efficient extracting technique is required to find the reasonable reservoir operation chart that can improve the water resources utilization efficiency and get the maximum energy using the limited hydropower resources. In this paper, based on DCM, we provided an efficient and practical joint operation method for cascade reservoirs, which is ESOC method. Through taking the cascade reservoirs in Yangtze River of China as an instance, it was found that, compared with the conventional operation method, 0.9% growth on power generation, 3.4% growth on guaranteed output and 9.6% growth on assurance rate can be obtained by ESOC, respectively. On the whole, it can be concluded that the provided ESOC method in this paper gets a good application effect in the cascade reservoirs of Yangtze River, which has a certain popularization value.

ACKNOWLEDGEMENTS

This study was financially supported by National Key R&D Program of China (2017YFC0405900), the CRSRI Open Research Program (Program SN: CKWV2016371/KY), the Natural Science Foundation of China (91647114) and the Fundamental Research Funds for the Central Universities (HUST: 2017KFYXJJ 198 and HUST: 2016YXZD047). The authors are grateful to the anonymous reviewers for their comments and valuable suggestions.

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