Optimal Operation of Cascade Hydropower Plants Shenglian Guo Xiang Li Pan Liu Fuqiang Guo State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University Wuhan, 430072, People’s Republic of China
[email protected] Abstract—A new model is presented based on combined guide curves for optimizing hydropower production and for better storage distribution among cascade reservoirs. The model is optimized with the particle swarm optimization algorithm and storage distribution among cascade reservoirs is achieved by the storage effectiveness index method. The model is applied to the Qingjiang cascade hydropower plants and optimized combined reservoir operation chart is obtained for ShuibuyaGeheyan reservoirs. Comparing with the current design, the proposed model is capable to produce an extra amount of 201GW.h electrical energy (a 2.77% increment) and save 1067 Mm3 of flood water resources (a 38.96% reduction) annually. Keywords-hydropower plants; cascade reservoir; power generation; optimal operation
I.
INTRODUCTION
Water is becoming a scarce resource as a result of the growing demand for its use in various purposes such as hydropower, irrigation, water supply, etc. Reservoirs are one of the major storages of surface water and optimally operating single or multi-reservoir network forms an integral part in water resources management [1]. During the past few decades, various optimization and simulation models have been developed in order to support the decision-making process of the reservoir operation and reviewed by many authors [2, 3, 4]. Despite the potential for the use of optimization in realtime reservoir operation, with some exceptions, optimization models still play a minor role in identifying possible reservoir releases. Most of the hydropower plants are still managed on fixed predefined operating rules. This is mainly due to institutional, rather than technological and mathematical limitations [5]. These predefined operating rules are usually presented in the form of graphs and tables [2, 3] and called reservoir operation charts. It represents all the regular functions of operating rules and provides guidance to system operators. Although various operation models based on optimization and simulation models are available, conventional simulation model is still widely used for deriving operation rules due to its concise and directviewing. However it is used in single reservoir operations, and cannot be used in combined operation of cascade reservoirs. Therefore poor storage distribution can be seen among cascade reservoirs. Hence, much of flood water resources are wasted during flooding seasons. Several attempts have been made to solve this problem in the recent past. The Storage Effectiveness Index (SEI) which has been introduced by U.S. Army Corps of Engineers [6] is one of the decision making rules in the cascade reservoirs operation for maximizing firm hydropower production. Reference [7] presented an analytical solution method to determine which reservoir would be drawn down first to optimize marginal energy demands from reservoirs in series. The HEC-ResSim model which was most recently
introduced by U.S. Army Corps of Engineers [8] is an interesting tool for hydropower plants simulations. A new combined reservoir operation model was proposed and applied to the Qingjiang cascade hydropower plants in this paper. The proposed model was compared with designed operation charts. II.
COMBINED RESERVOIR OPERATION MODEL
The proposed combined reservoir operation model consists of three components: (1) combined guide curves, (2) storage distribution, and (3) optimization. During the release process, it is required that combined reservoir operation model can synthesize reflecting hydrological characteristics of the river basin and unique features of reservoirs. It should also satisfy with the guide rules of reservoirs in different inflow scenarios and different water level conditions. A. Combined Reservoir Operation Chart The proposed combined reservoir operation chart for a hypothetical cascade with two reservoirs is shown in Fig.1. It is similar to conventional operation charts, and mainly consists of different guide curves and corresponding operational zones. Accordingly, upper and lower combined guide curves of each individual operation chart divide the whole storage space into three operational zones, named higher capacity zone Z1 , firm capacity zone Z 2 and lower capacity zone Z3. The combined guide curves have particular features relative to conventional operation charts. Those reflect the total generation capacity of the cascade hydropower plants in every time interval. But, it does not mention the individual reservoir generation capacity in any time interval. However, guide curves in the conventional operation chart correspond to individual reservoir generation capacity. The combined guide curves display the relationship between reservoir water level and the total generation capacity of the hydropower plants through each reservoir operation chart. When water levels are in higher capacity zone, firm capacity zone and lower capacity zone, corresponding total generation capacities of the cascade are N1 , N 2 and N3 , respectively ( N1 > N 2 > N3 ). Another unique feature of the combined guide curve is that it demonstrates the optimized power generation capacity and better storage distribution among cascade reservoirs. There are three steps in using the combined reservoir operation chart: (1) obtain the current water levels of each reservoir in the cascade, (2) compare each reservoir water level and decide the total generation capacity of the cascade (here, some empirical judging rules were introduced for determining the total generation capacity), and (3) determine each reservoir’s hydropower demand according to the total generation capacity using the “Storage Effectiveness Index” method and establish better storage distribution among cascade reservoirs.
Sponsored by National Natural Science Foundation of China (50609017)
978-1-4244-2487-0/09/$25.00 ©2009 IEEE
L'a
Z2
La
Z3
Upper combined guide curve
Water level
Water level
Z1
Lower combined guide curve
Z1
L'b
Z2 Z3
Lb
Time
Time Reservoir a Reservoir b Figure 1. Combined reservoir operation chart for a hypothetical cascade
B. Judging Rules • Rule 1: “If the water levels of every reservoir are in the same operational zone, the cascade total generation capacity would be the same as individual generation capacities in the corresponding operation zone”. As an example, at the current time t , water levels of reservoirs a and b in Fig. 1 are La′ and Lb′ respectively. The corresponding generation capacities are N1 in both cases. Since both water levels are in the same operation zone Z1 , N1 is considered as the total generation capacity of the cascade. •
Rule 2: If water levels of each reservoir are in different operational zones, the judging rule becomes complex than the above. The principle in such a case is, water levels of each reservoir should be in the same operational zone or as close as possible after releases are made at the current timestep. This is achieved by releasing water for power generation from the reservoir which has highest total generation capacity at the current time while other reservoirs reduce or stop their releases. As an example, if water levels of two reservoirs in Fig.1 are La and Lb which are in different operational zones, corresponding total generation capacities are N 2 and N 3 , respectively ( N 2 > N 3 ). In this case, reservoir a undertakes the main role in power generation by increasing its generation rate while reservoir b reduces its generation rate to push water levels into the same operational zone. Main steps of this rule can be summarized as follows.
First assume N 2 as the cascade total generation capacity and undertake power generation to push each reservoir’s water level into the same operation zone or as close as possible at the end of the current time-step. Second, when water level of each reservoir comes into the same operational zone, releases are made according to storage effectiveness index for better storage distribution among cascade reservoirs. During the first step it should avoid increasing the reservoir b ' s generation rate more than the total generation capacity of the cascade, N 2 . If the actual generation rate, N t is smaller than N 3 during the computing time interval, then decide N 3 as the total generation capacity of the cascade. If water levels are still in different operation zones after the estimation and also actual generation rate, N t is less than N 2 and larger than N 3 ( N 2 > N t > N 3 ) then the total generation capacity of the cascade is considered as N t . It is neither N 2 nor N 3 .
C. Storage Distribution Storage Effectiveness Index (SEI) which has been developed by U.S. Army Corps of Engineers [6] is used to achieve better storage distribution among cascade reservoirs. SEI is one of the decision making rules in the hydropower plants operation for maximizing firm hydropower production. For each reservoir in the cascade, a “SEI” is calculated for each time-step, using forecast inflow and power demands for the current time-step and remaining time-steps. In the release process, it is accomplished according to the magnitude sequence of SEI values of each reservoir. The reservoir with lowest SEI value is drawn down first during the release season and, vice versa during the refill season or period. Here, the refill season is defined as the season when system inflows exceed the needs to meet hydropower production demands. Assuming all flow can be utilized through turbines for power generation, SEI can be computed as following, N
Eq = Ex − ∑ 9.8ηi I i H i Δt
˄1 ˅
i =1
where Eq is the energy shortage for current time interval; Ex is the energy requirement for the current time interval; i is the reservoir index; N is the total number of reservoirs in the cascade; ηi is the turbine efficiency of reservoir i ; I i is the inflow to reservoir i during the current time interval; H i is the hydropower head as a function of reservoir storage of reservoir i ; and Δt is the computing time interval. ΔSi = Eq /(9.8ηi H i )
˄2 ˅
where ΔSi is the drawdown storage of reservoir i for power generation. Ei = 9.8ηi (Woi + Wqi ) H i ( Si − ΔSi )
˄3 ˅
where Ei is the drawdown period power loss due to drawdown of reservoir i by ΔSi ; Woi is the cumulative outflow capacity of upstream reservoir i during the remainder of the drawdown season; Wqi is the cumulative inflow capacity of upstream reservoir i during the remainder of the drawdown season; Si is the current reservoir storage of reservoir i . SEI i = Ei / Eq
˄4 ˅
where SEI i is the storage effectiveness index of reservoir i . The SEI method is used with the proposed combined operation chart as following: •
If the water levels of every reservoir are in the same operational zone, the SEI method is directly used to achieve better storage distribution among cascade reservoirs. The sequence of release is the same with SEI of each reservoir from small to large during the drawdown period, and vice versa during the reservoir refill period.
•
If the water level of each reservoir is in different operational zones, the reservoir with highest total generation capacity supplies water for power production first. Other reservoirs reduce or stop their releases for bringing the water level of each
reservoir into the same operational zone. When the water levels of each reservoir come into the same operational zone, the SEI method is used to determine storage distribution and the procedure is same the above. D. Objective Function and Constraints If all hydropower plants meet the required water supply and initial power supply, the objective is to generate maximum power from the whole system, i.e., T
max
N
f = ∑∑ 9.8Ci ,tηi H i ,t Qi ,t Δt
t = 1, 2, ⋅⋅⋅, T
Figure 2. The Qingjiang cascade hydropower plants
t =1 i =1
i = 1, 2, ⋅⋅⋅, N (5) where t is the computation time interval index; T is the total number of computation time intervals; Qi ,t is the flow rate use for power generation of reservoir i during the time interval t ; Ci ,t is the price for the electricity of reservoir i
Reference [12] has used PSO algorithm to solve the short term generation scheduling of a hydro-system in a deregulated environment. Since its better characteristics as an optimization tool, and also ascertain its ability in using reservoir operation, PSO algorithm is used for guide curve optimization in this study.
during the time interval t ; H i ,t is the hydropower head of reservoir i during the time interval t ; and other notations have same meaning with above.
Vi ,t +1 = Vi ,t + ( I i ,t − qi ,t )Δt
Subject to,
(6)
I i +1,t = qi ,t + IBi ,t
(7)
qi ,min ≤ qi ,t ≤ qi ,max
(8)
N
N
i =1
i =1
III.
N f ≤ ∑ N i ,t ≤ ∑ NTi
(9)
where Vi ,t is the storage of reservoir i at the beginning of the time interval t ; I i ,t , qi ,t are the inflow and outflow of reservoir i during the time interval t , respectively; IBi ,t is the inflow between reservoir i and i + 1 during the time interval t ; qi min is the minimum discharge capacity of reservoir i for down stream ecological requirements; qi max is the maximum discharge capacity of reservoir i and it is limited by the down stream flood prevention limitations; N f is the firm capacity of the cascade hydropower plants;
NTi is the maximum generation capacity of reservoir i ; and N i ,t is the generation capacity of reservoir i during the time interval t . E. Optimization Particle Swarm Optimization (PSO) is a population based stochastic optimization technique proposed by [9]. PSO shares many characteristics with other evolutionary computation techniques such as Genetic Algorithms (GA) and a PSO system combines local search methods with global search methods, attempting to balance exploration and exploitation [10]. Reference [11] demonstrated that PSO can get better results in a faster, cheaper way compared with other optimization methods such as GA and simulated annealing for some problems. TABLE I.
APPLICATION
A. Qingjiang Cascade Hydropower plants The Qingjiang basin is situated at southwest Hubei province with basin area of 17600 km2. Abundant rainfall is found in the basin and mean annual rainfall is approximately 1460mm. Mean annual runoff depth is 876mm and mean annual runoff is 423m3/s. A three-step cascade hydropower plants is found from upstream to downstream namely, Shuibuya, Geheyan and Gaobazhou. Main objectives of this cascade hydropower plants are power generation and flood control. A diagram of Qingjiang cascade hydropower plants is shown in Fig. 2, and the basic physical parameters are listed in Table 1. Ten-day interval inflow records from 1951 to 2005 were used in this study. With this inflow records, Qingjiang combined reservoir operation chart is optimized by using the PSO model. B. Analysis of Guide Curves Qingjiang cascade optimized combined reservoir operation chart is obtained by the proposed combined reservoir operation model and shown in Fig.3. In the Fig. 3, ķ is the installed capacity zone,ĸ is the higher capacity zone,Ĺ is the firm capacity zone, andĺ is the lower capacity zone. According to the runoff records, the mean runoff discharge of Qingjinag basin is high during May to September and low during October to April. With the fluctuating inflow capacity, the corresponding guide curves also fluctuate, and it can be seen from Fig. 3. Before the flood season, higher capacity zones enlarge and increase the electricity generation capacity to avoid spilling. After ceasing the flood season, the area of the higher capacity zones decreases and reduce water usage for electricity generation to avoid water level falling excessively. Higher capacity and firm capacity zones of Shuibuya reservoir are large and the lower capacity zone is small, while it is opposite in Geheyan reservoir.
BASIC PHYSICAL PARAMETERS OF THE QINGJIANG CASCADE HYDROPOWER PLANTS
Reservoir
Normal Pool Level ˄m˅
Flood Prevention water level ˄m˅
Dead water Level ˄m˅
Total storage ˄Mm3˅
Shuibuya Geheyan Gaobazhou
400 200 80
391.8 193.6 78.5
350 160 78
4,345 3,120 356
Dead storage Installed capacity Firm Capacity Regulation ability ˄Mm3˅ ˄MW˅ ˄MW˅ 1,941 1,642 305
1,600 1,200 270
310.0 241.5 77.3
Multiyear Annual Daily
400 390 380 370 360 350
Upper combined guide curve
ķ ĸ
Ĺ ĺ
5
6
7
Lower combined guide curve
200
ĸ
Water level
Water level (m)
Flood preventing water level
ķ ĸ
195 190
Ĺ
Ĺ
185
Ĺ
ĺ
180 8
9 10 11 12 Month
1
2
3
5
4
(a) Shuibuya reservoir
6
7
8
9
10 11 12 Month
1
2
3
4
(b) Geheyan reservoir
Figure 3. Combined reservoir operation guide curves for Qingjiang cascade hydropower plants TABLE II. Parameter Annual electricity generation (GW.h) Annual spillage (Mm3)
SIMULATION RESULTS OF COMBINED RESERVOIR GUIDE CURVES AND INDIVIDUAL GUIDE CURVES Comparing parameter
SIMULATION RESULTS AND DISCUSSION
Using ten-day interval inflow records of Qingjiang cascade reservoirs from 1951-2005, a simulation was carried out with the proposed combined reservoir operation model. A parallel simulation was also done with the current design for the same data set for comparison purposes. The simulation results are summarized in Table 2. Accordingly, Shuibuya and Geheyan hydropower plants can generate additional 26 and 146 GW.h annually when using combined reservoir operation model, respectively. The whole cascade power generation increment is 201 GW.h and it is a 2.77% improvement over the current design. Besides, combined reservoir operation model is capable to store 160 Mm3 and 340 Mm3 flood water resources annually in Shuibuya and Geheyan reservoirs, respectively. The total reduction of spill release is 1067 Mm3 per year and it is a 38.96% reduction to the current design. V.
Geheyan
Gaobazhou
3,525 3,551 26 0.71 355 195 160 45.06
2,903 3,049 146 5.04 815 475 340 41.75
835 864 29 3.52 1,568 1,001 567 36.14
Original design Combined operation model Increment of generation Increasing rate (%) Original design Combined operation model Reduced spillage Reducing rate (%)
Because, when optimizing combined operation model of two reservoirs, higher priority is given to the Shuibuya reservoir for electricity generation while Geheyan reservoir is maintained a higher water level. The lower combined guide curve of Shuibuya reservoir has its highest value during the flood season. During the dry season, it is very close to the dead water level. The lower combined guide curve of Geheyan reservoir reaches to its maximum twice during the flood season. In overall, Geheyan reservoir’s combined guide curves are entirely different from Shuibuya reservoir’s guide curves. This is due to recapturing Shuibuya reservoir’s release by Geheyan reservoir and raises its water level during May to October. IV.
Individual reservoir Shuibuya
CONCLUSIONS
A novel combined reservoir operation model is proposed based on combined guide curves for optimizing hydropower production and for better storage distribution among cascade reservoirs. The model is applied to Qingjiang cascade hydropower plants and optimized combined reservoir operation chart is obtained for Shuibuya-Geheyan reservoirs. By satisfying Qingjiang cascade’s guaranteed output rate and flood prevention standards, the model is able
Total 7,263 7,464 201 2.77 2,738 1,671 1,067 38.96
to produce 7464GW.h hydropower and reduce is 1067Mm3. spill release annually. Therefore it can be concluded that the proposed combined reservoir operation model can enhance power production and improve the flood water resources utilization of cascade hydropower plants. REFERENCES [1]
S. Guo, H. Zhang, H. Chen, D. Peng, P. Liu and B. Pang, “A reservoir flood forecasting and control system in China,” Hydrol. Sci. J., vol. 49, 2004, pp. 959-972. [2] W.W.-G. Yeh, “Reservoir management and operations models: A state-of-the-art review.” Water Resour. Res., vol. 21, 1985, pp. 17971818. [3] R. A. Wurbs, “Reservoir-system simulation and optimization models,” J. Water Resour. Plan. Manage., vol. 119, 1993, pp. 455472. [4] J. W. Labadie, “Optimal operation of multireservoir systems: Stateof-the-art review,” J. Water Resour. Plan. Manage., vol. 130, 2004, pp. 93-111. [5] R. Oliveira and D. P. Loucks, “Operating rules for multireservoir systems,” Water Resour.Res., vol. 33, 1997, pp. 839-852. [6] J. R. Lund and J. Guzman, “Some derived operating rules for reservoirs in series or in parallel,” J. Water Resour. Plan. Manage., vol. 125, 1999, pp. 143-153. [7] J. R. Lund, “Derived power production and energy drawdown rules for reservoirs,” J. Water Resour. Plan. Manage., vol. 126, 2000, pp. 108-111. [8] J. D. Klipsch, “HEC-ResSim: Reservoir System Simulation,” User’s manual, US Army Corps of Engineers, Hydrologic Engineering Centre, Davis, CA, 2003. [9] J. Kennedy and R. Eberhart, “Particle swarm optimization,” Proc., IEEE Int’l. Conf. on Neural Networks (Perth Australia), IEEE, service center, Piscataway, NJ, 1995, pp. 1942-1948. [10] M. A. Abido, “Optimal design of power–system stabilizers using particle swarm optimization,” IEEE Trans. on Energy Conversion, vol. 17, 2002, pp. 406-412. [11] X. Hu, R. Eberhart and Y. Shi, “Engineering optimization with particle swarm,” Proc., IEEE Swarm Intelligence Symposium, Indianapolis, USA, 2003, pp. 53-57. [12] J. Chuanwen and E. Bompard, “A self-adaptive chaotic particle swarm algorithm for short term hydroelectric system scheduling in deregulated environment,” Energy Conversion and Manage., vol. 46, 2005, pp. 2689-2696.
