Multi-Objective Reservoir Operation with Sediment ...

Water Resour Manage DOI 10.1007/s11269-014-0806-9

Multi-Objective Reservoir Operation with Sediment Flushing; Case Study of Sefidrud Reservoir Reza Hajiabadi & Mahdi Zarghami

Received: 8 February 2014 / Accepted: 30 September 2014 # Springer Science+Business Media Dordrecht 2014

Abstract In this study, the non-dominated sorting genetic algorithm (NSGA-II) is used for the multi-objective optimization of the Sefidrud reservoir in Northern Iran. The main objectives include water supply, hydropower generation and sediment flushing. In addition to some physical constraints such as the reservoir storage and the outlet flow, maximum flushing outflow and non-flushing in irrigation seasons, the environmental constraints as fish migration and spawning are taken into an account. After obtaining the Pareto optimal solutions by means of the weighted objective functions and non-symmetric Nash bargaining, various scenarios are defined. Then these scenarios are analyzed by introducing a new sustainability index. Furthermore, the different percentages of downstream water demand are considered in order to achieve a better evaluation of the scenarios. The results of study indicate that the optimal solutions are more sustainable than those of the current operation of Sefidrud reservoir, which increase the sediment flushing by 37 million tons compared to the current operation, with the same hydroelectric energy and downstream water supply. The proposed methodology could be used successfully in other reservoir operations including the sediment flushing. Keywords Multi-objective optimization . Sefidrud reservoir . Pareto optimal points . Sustainability index

1 Introduction Effective water resources management is a multi-disciplinary issue and traditional single objective approaches are not more able to solve the water shortages. Concerned with multiobjective issues, the objectives are often in conflict with each other, so improvement in one objective may cause others to suffer or get worsen. In addition, in contrast to the singleobjective problems that benefit from only one optimal solution, a set of optimal solutions entitled Pareto optimal points could be obtained in the multi-objective approach. R. Hajiabadi : M. Zarghami (*) Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran e-mail: [email protected] Present Address: M. Zarghami Department of Civil and Environmental Engineering, Tufts University, Medford, USA e-mail: [email protected]

R. Hajiabadi, M. Zarghami

In recent years, Evolutionary Algorithms (EAs) have been used effectively to solve nonlinear multi-objective optimization problems. Deb (2001) and Coello et al. (2007) have provided a complete review on EAs. EAs have been used in different applications such as water distribution systems (Liong et al. 2004; di Pierro et al. 2009; Montalvo et al. 2010; Wu et al. 2013), rainfall-runoff modeling (Liu 2009), finding hydrologic model parameters (Vrugt et al. 2003) , urban water management (Zarghami and Hajykazemian 2013) , reservoirs management (Chen 2003; Chang et al. 2005; Chen et al. 2007; Chang et al. 2010), aquifer management (Kourakos and Mantoglou 2013) and pumping systems (Afshar and Rajabpour 2008). One of the most significant multi-objective issues is the reservoir operation. Increasing in population and then water demand on one hand, and on the other hand, the effects of climate change, sedimentation and also the importance of environmental objectives have made multipurpose reservoirs operation as one of the most essential issues. However, water resource sustainability has formed a challenge to managers for the development of better methods, and in turn the fulfillment of future demands and expectations (Solis et al. 2011). In this study to satisfy these objectives, it is necessary to quantify system performance, so a new index is defined to quantify such systems in different situations. Different solutions are applied to multi-objective reservoirs operation. Celeste and Billib (2009) tested the performance of seven stochastic models based on implicit and explicit stochastic optimization. Hejazi and Cai (2011) applied stochastic dynamic programming (SDP) to Shelbyville reservoir in USA and they demonstrated that how data mining techniques could perform in reservoir operation. Shokri et al. (2013a) used a SDP model to determine the optimal management, meeting water demand and sediment flushing simultaneously in the Sefidrud reservoir; however, their work does not incorporate the hydropower generation by reservoir. Safavi et al. (2013) used fuzzy logic to develop operation rules through a combined of both surface and ground water resources in the Zayandehrood reservoir, Iran. An appropriate solution approach for the multi-objective operation of reservoirs is EAs which have been recently used by many researchers. Tang et al. (2007) applied the Master– slave and Multiple-Population versions of the NSGA-II to solve three various problems including hydrologic model calibration, long-term groundwater monitoring and an extremely difficult test derived from the computer science literature. Chang and Chang (2009) used the non dominated sorting genetic algorithm to the multi-objective optimization of a multireservoir system (Feitsui and Shihmen) in northern Taiwan. They applied the shortage indices to both of the reservoirs and developed a daily operational simulation model. The results show that the NSGA-II causes an improvement in the reservoir system operation. Malekmohammadi et al. (2011) applied NSGA-II to cascade reservoir systems and used ELECTRE-TRI method for ranking optimal solutions. They considered flood control and water supply as a short term and long term objectives, respectively. Wang et al. (2011) divided a complicated system into several small sub-systems and applied a multi-tier interactive genetic algorithm to optimize Shihmen reservoir operation, Taiwan. Some researchers investigated the combination of EAs and intelligent models (Malekmohammadi et al. 2009; Hakimi-asiabar et al. 2010; Hakimiasiabar et al. 2009; Shokri et al. 2013b) to improve efficiency and to reduce the number of simulations and time required in EAs. Khan et al. (2012) developed an optimal operation model for Tarbela dam in Pakistan based on GA called ROSSE with the aim of minimizing the irrigation deficit. Chang et al. (2013) and Fallah-Mehdipour et al. (2011) used particle swarm optimization-genetic algorithm and multi-objective particle swarm optimization respectively to multi reservoir system optimization. In this study, NSGA-II is applied to the multi-objective optimization of the Sefidrud reservoir in order to satisfy water supply, hydropower generation and sediments flushing

Multi-Objective Reservoir Operation with Sediment Flushing

simultaneously. After obtaining the Pareto optimal set by using the weighted objective functions and decision-making techniques the non-dominated solutions are obtained, and by introducing a new sustainability index, the solutions are analyzed. Also, in order to achieve a better evaluation of the scenarios, different percentages of downstream water demand are considered, and environmental constraints along with physical constraints are considered for optimization model. This new approach makes significant improvement in this reservoir operation and the methodology is suggested for other cases. In the rest of paper, the case study is introduced in section 2, and in section 3 the methodology will be described. The outcomes of manipulation the methodology on the case study will be presented in section 4 and section 5 concludes the paper.

2 Case Study The Sefidrud reservoir with a buttress dam is located following the confluence of the Qizilowzan and Shahrood rivers in the Gilan province, North of Iran (Fig. 1). The reservoir’s main purposes include water supply for irrigation and produce hydroelectric power. After building the Sefidrud dam, farmlands increased from about 90 thousand hectares by more than 240 thousand hectares. Tarik dam which is located 35 km downstream of Sefidrud reservoir allocates it’s releases for irrigation and river level regulation. It should be noted that the main product of these farms is rice which need a lot of water so Sefidrud reservoir plays an effective role in economy of the region.

Fig. 1 Sefidrud basin and its location in the map of Iran

R. Hajiabadi, M. Zarghami

The Sefidrud dam is 106 m tall, 425 m long at the crest and its catchment area is 56,200 Km2. The reservoir’s storage and power capacity is 1,760 Million Cubic Meters (MCM) and 87.5 MW (MW), respectively. Total discharge capacity of Sefidrud dam is 6,140 m3/s that its evacuation facilities include two auxiliary spillways (2,000 m3/s), two morning glory spillways (3,000 m3/s), five bottom outlets (980 m3/s), and five power intakes (160 m3/s) (Shokri et al. 2013a). Average annual inflow water volume is 4,500 million cubic meters per year (MCM/Y). Due to poor vegetation cover and high soil erosion annually a huge amount of sediment load enter the reservoir. Average annual inflow sediment load is 43 million tons per year (Mton/Y) which 35 Mton comes from Qizilowzan river, 6 Mton comes from Shahrood river and 2 Mton comes from other sources. In the normal operation period (1963–1982), the reservoir’s capacity reduced to 1040 MCM and it shows a storage capacity loss of 2.3 % per year due to the sedimentation. Therefore to increase the reservoir’s capacity sediment flushing was performed and capacity loss slowed down (Fig. 2). By sediment flushing, a part of the lost capacity was returned but reservoir is unable to restore all the lost capacity because of the consolidation of the sediments in many years (Shokri et al. 2013a). Iran Department of Environment has considered Sefidrud river (downstream of Sefidrud dam) as one of the most polluted rivers in Iran. One of the pollution sources is the presence of sediments. Sediment flushing in Sefidrud dam causes several problems in downstream such as loss of many fishes. Environmental problems on one hand and need to evacuate sediment on the other hand have made Sefidrud operation more and more complicated and also essential. Due to the high potential of growth in the Sefidrud basin, there are various concerns over defining the new water rights, already resulted in conflict among the stakeholders. There are eight provinces benefiting from this basin and each of them has resrevoirs, water transfers, and irrigation networks in operation, construction, or in the designing stage. The capacity of basin is only a small portion of the total size of these water resources projects (Zarghami et al. 2008). Consequently, studying the Sefidrud reservoir operation as the main downstream dam in the basin is needed and has high value for research.

Fig. 2 Sefidrud reservoir capacity reduction (Shokri et al. 2013a)

Multi-Objective Reservoir Operation with Sediment Flushing

The present study mainly attempts to perform a multi-objective Sefidrud reservoir optimization by using NSGA-II and sustainable management. The objective functions include water supply, hydropower generation and sediments flushing. In the next section detailed of the modeling is presented.

3 Methodology The optimization problems generally consist of three main components, including required input data, objective functions and constraints of the problem. To model the Sefidrud reservoir problem, along with the reservoir and the power plant’s characteristics, 10-day time series inflow and downstream water demand is used within a year (early spring to late winter based on the traditional year in Iran, April 2008March 2009). The main reason to select the period to test the methodology is Sefidrud reservoir operation policies. In Sefidrud reservoir, flushing is not performed in dry years. Dry year occurs when the annual inflow water volume to the reservoir is less than the downstream water demand. In this paper, the annual inflow to the reservoir in the year selected for investigation is 872.72 MCM, while the downstream water demand volume is 1286.87 MCM. Therefore, dry year occurs and flushing is not performed. The present study discusses on the possibility of the flushing in dry years and shows the best management on drought. Figure 3 shows that the maximum inflow to the reservoir occurs in early spring and Fig. 4 demonstrates that a significant part of the downstream water demand is related to the first half of the year (spring and summer). 3.1 Optimization Problem 3.1.1 Objective Functions In multi-purpose reservoir operation, various objective functions are developed such as the minimization of the deviation from the desired output during operation. In the present study, the Eq. 1 (to be minimized) is used as an objective function for meeting the water demands. As the water demands at the 10-day periods are not important equally in the current study, the demands higher than 20 MCM have more importance.

Fig. 3 Inflows to Sefidrud reservoir in the study period (April 2008-March 2009)

R. Hajiabadi, M. Zarghami

Fig. 4 Downstream water demand in the study period (April 2008-March 2009)

Equations 2 and 3 are for the flushing and hydropower objective functions (both to be maximized), respectively. 8 ! n X > > 2 > ðDi −Ri Þ > for Di ≥20 & Ri ≤Di ⇒ f ¼ 2  > > < i¼1 ! n f ðSupplyÞ ¼ X ð1Þ 2 > > ðDi −Ri Þ for Di < 20 & Ri ≤Di ⇒ f ¼ > > > > i¼1 : if Ri > Di ⇒ f ¼ 0

f ðFlushingÞ ¼

n X

Qsi

ð2Þ

i¼1

f ðHydropowerÞ ¼

n X

Pi

ð3Þ

i¼1

In Eq. 1, Ri (MCM) is the release of the reservoir, Di (MCM) is water demand both at the ith interval, and n is the number of intervals in the study period. In Eq. 2, Qsi (Mton) is flushing sediment load at the ith interval and, in Eq. 3, Pi (Mkwh) is hydropower generation at the ith interval, which both of them will be described in detail in the following sections. 3.1.2 Sediment Flushing To calculate the transporting capacity of flushing flows, an empirical method reported in IRTCES based on the observations on flushing at the reservoirs in China is used (Atkinson 1996). The method is based on Eq. 4:

Qsi ¼ ψ

Qfi 1:6 S i 1:2 W i 0:6

ð4Þ

where Qsi (ton/s) is sediment transporting possible discharge, Qfi (m3/s) is flushing discharge both at the ith interval, Si is bed slope, Wi (m) is channel width and Ψ is a

Multi-Objective Reservoir Operation with Sediment Flushing

constant set from the sediment type, as indicated in Table 1. Si and Wi are calculated by following equations: Si ¼

ELmax −ELfi L

ð5Þ

where ELmax (m) is the elevation of the maximum water level above river bed at the dam, ELfi (m) is the water level during the flushing and L (m) is reservoir length.  ð6Þ W i ¼ min W resi ; W fi

W fi ¼ 12:8  Qfi0:5

ð7Þ


 W resi ¼ W bot þ 2  SS res Elfi −El min

ð8Þ

where Wbot , SSres are representative bottom width and side slope for the reservoir respectively and ELmin is minimum bed elevation. 3.1.3 Hydropower Generation Energy which is produced by hydroelectric plants is obtained by using the Eq. 9 (Revelle 1999). Pi ¼ 2:73  10−3 ðqi  hi  eÞ

ð9Þ

where, Pi (Kw/s) is generated hydroelectric energy, qi (m3/s) is discharge through the turbine, hi (m) is water level above turbine, all in the initial of the ith interval, and e is turbine efficiency that based on previous observations the value of 0.82 is used. 3.1.4 Constraints Sediment flushing has created many environmental problems in the downstream of Sefidrud dam. So in the present study, in addition to physical constraints, the environmental constraints are considered.

4 Physical Constraints I. Continuity equation and the extremes on reservoir capacity and outflow as follows: S iþ1 ¼ S i þ I i −Ri

ð10Þ

Table 1 Ψ values based on sediment type Sediment type

Ψ

Loess sediment

1,600

Other sediments with median size finer than 0.1 mm

650

Sediment with median size larger than 0.1 mm

300

Flushing with a low discharge

180

R. Hajiabadi, M. Zarghami

50 ≤S i ≤1180

ð11Þ

1:5≤ Ri ≤ 180

ð12Þ

where Si+1 (MCM) is reservoir storage at the initial of i + 1th interval, Si (MCM) is reservoir storage at the initial of ith interval, Ii (MCM) is reservoir input water and Ri (MCM) is the reservoir output including the releases for irrigation, hydropower and flushing in ith interval. II. Hydropower constraints 15≤qi ≤160

ð13Þ

hmin ≤hi

ð14Þ

where qi (m3/s) is the discharge through the turbines and hi (m) is water level above the turbines related to the water storage, Si and hmin is minimum water level on which hydroelectric energy can be generated. In this research hmin is considered to be 42 m above bottom outlets and hydroelectric energy is not generated during sediment flushing.

5 Environmental Constraints I. Flushing allowance The flushing is unauthorized in two time periods including irrigation season and fishes’ migration and spawning season. Figure 5 shows the allowed intervals. II. Flushing discharge In addition to the unauthorized times, the maximum flushing flow should not exceed a limit.  . ð15Þ Qfi ≤100 m3 s

Fig. 5 Allowed periods for sediment flushing

Multi-Objective Reservoir Operation with Sediment Flushing

5.1 Non Dominated Sorting Genetic Algorithm (NSGA-II) Srinivas and Deb (1994) proposed a type of multi-objective GA called the Non-dominated Sorting Genetic Algorithm (NSGA). Then Deb et al. (2002) improved NSGA algorithm, called NSGA-II. In Fig. 6, its general procedure is presented. Pt is the parent population and Qt is the offspring population at generation t. F1, F2 and F3 are solutions classes. So F1 is the best solutions set among the parents and offspring and F2 is the second best solutions set, and so on (Coello et al. 2007). The NSGA-II algorithm consists of two important sorting procedures: non-dominated sorting and crowding distance sorting, which are the main differences between NSGA-II and other EAs. The non-dominated sorting is a fast and simple approach to speed up sorting process and to compare population individuals. The mathematical definition of the dominance is based on Eq. 16. X ¼ fx1 ; x2 ; …; xn g Y ¼ fy1 ; y2 ; …; yn g X Dom Y ⇔∀i : xi ≤yi and∃j : x j < y j

ð16Þ

where X and Y are two individuals of population and xi and yi are objective functions that should be minimized and n is number of objectives. The crowding distance represents the density of individuals in the same class and it keeps the population diverse and consistently spread-out Pareto-optimal front. Between two individuals in the same class (front) one with a greater crowding distance is better (Chang and Chang 2009). The crowding distance values of each individual are calculated by Eq. 17. m f kþ1 − f k−1 X j j ð17Þ Dðk Þ ¼ min f max j −f j j¼1 where D(k) is crowding distance of kth individual, fjk+1 is jth objective function value of k + 1th individual , fjk-1 is jth objective function value of k-1th individual, fjmax is maximum or ideal value of jth objective function, fjmin is the minimum or the worst values for the jth objective function and m is the number of objectives. The real values used for the ideal and worst parameters are shown in Table 2. Figure 7 shows that NSGA-II flowchart which is coded in MATLAB.

Fig. 6 The main loop of NSGA-II procedure (Deb et al. 2002)

R. Hajiabadi, M. Zarghami Table 2 Ideal and worst values for the objectives Objective

Worst value

Ideal value

Water deficit (MCM/year)

384.82

207.93

Sediment flushing (Mton/year) Hydropower generation (Mkwh/year)

0.00

125.96

121.07

146.45

5.2 Non-Symmetric Nash Solution In contrast to single objective optimizations, there is not usually single solution in multiobjective optimizations that satisfies all objectives. Instead, there is a set of solutions which are all optimal, known as the Pareto optimal set. Choosing the best solution in Pareto set depends on the weight or importance of the objective functions, and in order to select the best solution, conflict resolution techniques can be used. In this paper the non-symmetric Nash solution is used to find the best solution among the Pareto optimal points set. The non-symmetric Nash solution is introduced by Harsanyi and Selten (1972). It is a unique optimal solution of the Eq. 18 (Raquel et al. 2007). m

Maximize

∏ j¼1



f j −f min j

u j

subject to

max f min j ≤f j≤ f j

ð18Þ

where uj is the weight or importance of the jth objective, and other variables are already described for Eq. (17). 5.3 Sustainability Index The concept of sustainability in water resources has been widely discussed among many researchers and considerable attempts are made to provide a suitable definition for it. Loucks (1997) believes that water resources systems are sustainable when designed and managed to improve the society objectives at the present and future, while caring the environmental, ecological and hydrological properties. Several indexes have been developed to measure the sustainability of water resources systems (e.g. Loucks 1997; Zongxue et al. 1998; Xu et al. 2002; Chavez and Alipaz 2007; Solis et al. 2011). The present study introduces a modified version of the sustainability index, SI, (Solis et al. 2011) consistent with the optimization period scale (10 day). The SI index tries to evaluate the sustainability in water allocation for agricultural users just located in the downstream of Sefidrud dam, however in next studies it may be extended to consider the whole of the basin including the upper provinces having water rights, flushing and also hydropower generation. In that case the SI will be the sum of single SIs. In this research since it just evaluates the Sefidrud reservoir operation with already defined inputs to the reservoir, then we proceed with single SI. Eq. 19 expresses the formula.
  ð19Þ SI ¼ ð1−VulnerabilityÞ  1−Deficit10 day  ð1−DeficitAnnual Þ According to Eq. 19, the sustainability index has three parameters: Vulnerability which represents the average failure. It is a dimensionless value calculated by Eq. 20. It should be noticed that if the vulnerability values are higher than the average water demand value then they should be divided by the maximum water demand values, instead of dividing by the

Multi-Objective Reservoir Operation with Sediment Flushing

Start

Set the parameters

Create initial population (Pt)

Crossover and mutation to create offspring population (Qt)

Evaluate fitness function and constraints of population (Pt+Qt)

Non-dominated sorting and classification

Sorting by crowding distance for last remaining class

Selecting the best parents

Is stop criterion reached? Yes Finish Fig. 7 NSGA-II flowchart

No

R. Hajiabadi, M. Zarghami

average water demand. Deficit10day represents the worst-case 10 day deficit that has become dimensionless through dividing by the maximum value of 10 day water demand (Eq. 21). DeficitAnnual also represents the annual deficit and it has become dimensionless through dividing by annual water demand (Eq. 22).’ Vulnerability½xŠ ¼

½sum of positive values of ðDi −Ri ފ=½N Š average water demand 10 day

ð20Þ

where Di and Ri are the demand and release of reservoir respectively. N is the number of unsatisfied (failed) periods. Deficit10 day ¼

max deficit 10 day max water demand 10 day

ð21Þ

deficitAnnual water demand Annual

ð22Þ

DeficitAnnual ¼

6 Results and Discussion 6.1 Pareto Optimal Set and Scenarios The present paper aims to investigate the multi-objective operation of the Sefidrud reservoir. Three objective functions are considered including meeting water demand, sediment flushing and hydroelectric generation. The Pareto optimal set obtained by using NSGA-II is shown in Fig. 8. The objective function values are normalized between zero and unit, so that the worst value of the objective function is equal to zero and the best value of the objective function is equal to one. In finding the Pareto frontier the objective functions are

1 Hydropower Objective

Hydropower Objective

1 0.8 0.6 0.4 0.2 0 1 0.8 0.6 0.4 Flushing Objective

0.2 0

0.2

0

0.6

0.4

0.8

0.8 0.6 0.4 0.2 0 1

1

0.8 0.6 0.4

Demand Objective

0.2

Demand Objective

0

1

Hydropower Objective

1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 Flushing Objective

0.8

Fig. 8 Different views of the Pareto optimal points

1

1

0.8

0.6

0.4

0.2

Demand Objective

0

0.8

0.6

0.4

0.2

Flushing Objective

0

Multi-Objective Reservoir Operation with Sediment Flushing Table 3 Weights of objectives in different scenarios Objective

Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario 1 2 3 4 5 6 7 8

Water demand satisfaction

1

0.7

0.7

0.5

0.33

0.5

0

0

Sediment flushing

0

0.3

0

0

0.33

0.5

1

0

Hydropower generation

0

0

0.3

0.5

0.33

0

0

1

normalized between zero and unit. For each objective in the Pareto curve the best point equals to unit and the worst point equals to zero. For the water supply objective the ideal value was minimum value, but after normalization in the Pareto curve it equals to one and the worst point (maximum value of water supply objective) equals to zero. Reversely for flushing and hydropower objectives the ideal point was maximum value so after normalization in the Pareto curve it equals to one and the worst point (minimum values of flushing and hydropower objectives) equals to zero. To select the best solution among the Pareto optimal points, the importance (weight) of each objective must be specified. The weight of an objective can be determined based on dam operation policies. In this study, eight scenarios for weight values are defined (Table 3). In order to select the solution corresponding to each scenario, the non-symmetric Nash solution is used. Figure 9 shows the Pareto points that correspond to each scenario

Scenario 4 Scenario 8 Scenario 5

Scenario 3

Scenario 7

Scenario 6

Fig. 9 Corresponding optimal points for each scenario

Scenario 2

Scenario 1

R. Hajiabadi, M. Zarghami

Fig. 10 Reservoir’s release in optimization period

and Figs. 10 and 11 indicate the reservoir’s release and storage during the optimization period, respectively. 6.2 Flushing and Hydropower of Scenarios While there is no significant difference between hydroelectric generations by the scenarios, the notable differences could be seen in sediment flushing (Fig. 12). The scenarios 7 and 8 have the maximum and minimum output sediments respectively, while the situation is reversed in the hydropower generation. Therefore, scenario 7 and 8 have the minimum (121 Mkwh) and maximum (146.4 Mkwh), hydropower generation respectively; so the difference between maximum and minimum hydropower generation in new model is only 21 %. Also there are some minor differences between hydropower generation in scenario 1 (129 Mkwh), scenario 2 (128.3 Mkwh) and real operation (128.1 Mkwh). The sediment flushing in the scenarios 1, 3,

Fig. 11 Reservoir’s storage in optimization period

Multi-Objective Reservoir Operation with Sediment Flushing

Fig. 12 Sediment flushing and hydropower generation of Scenarios

4, 8 and real operation is insignificant (in scenario 8, the output sediment is zero). Also scenario 2 increases the output sediment load by more than 37 million ton with the same observed hydroelectric generation. 6.3 Sustainability of Scenarios In order to perform an appropriate analysis of the scenarios, sustainability index of Eq. 19 is calculated for different percentages of downstream water demand but they don’t represent decreasing of downstream water demand. In fact, the lower percentages of the downstream demand show the treatment of the scenarios in the failed 10-day periods; in addition, they indicate that to what extent the percentage of the downstream water demand is satisfied. By using the defined SI values for these percentages, the supply rate of downstream water demand in the failed 10 day periods can be found. It is also possible that a scenario has high value of SI

Fig. 13 Annual deficit of scenarios in different percentages of downstream demand

R. Hajiabadi, M. Zarghami

Fig. 14 Maximum 10 day deficit of scenarios in different percentages of downstream demand

in the 100 % of downstream demand but it doesn’t show the scenario’s situation in the 10 day periods which failed. Figure 13 shows the scenarios’ annual deficit. Figure 13 indicates that the real operation is better when only 100 % downstream demand is considered. While the annual deficit values in other percentages of downstream demand reveal that the real operation in failed 10-day periods has a bad treatment. Scenario 1 in 100 % downstream demand has an annual deficit similar to the real operation, and in the other percentages it has a better performance than the real operation. Although the annual deficit in scenario 1 in the 70 % downstream demand is 5.86 MCM, it is 58.83 MCM in real operation. These values show that in failed 10-day periods, scenario 1 can satisfy more percentage of downstream demand (more than 70 %). However, there are failed 10-day periods which real operation cannot even meet 70 % of them because the annual deficit is equal to 58.83 MCM. So, considering different percentages of downstream demand, scenario 1 has a better treatment and minimum deficits. Meanwhile scenario 7 and 8 (in which water supply objective weight is zero) are worse ones. The same condition observed in maximum 10-day deficit, except that in the 100 % downstream demand the real operation is not better than other scenarios (Fig. 14).

Fig. 15 The vulnerability of the scenarios in supplying downstream demand

Multi-Objective Reservoir Operation with Sediment Flushing

Fig. 16 The sustainability index values of the scenarios in different percentages of the downstream demand

The vulnerability represents average 10 day deficit during the optimization period. The vulnerability of the real operation is better than other scenarios in supplying 100 % of the downstream demands (Fig. 15), may due to the number of the failed or unsatisfied periods. While the annual deficit in scenario1 and the real operation is similar in 100 % of downstream demand and also less than the other scenarios, the number of failed periods in the real operation is more than other scenarios such as scenario1. So according to the Eq. 20, the vulnerability of the real operation is less than that of other scenarios in the 100 % downstream demand. Nevertheless in other downstream demand percentages the vulnerability of the real operation decreases less than the vulnerability of other scenarios. After calculating the sustainability index, then it’s values for each scenario and different water demand percentages are shown in Fig. 16. The scenario 1 and the real operation in the year 2008–2009 have the same sustainability index in fulfilling 100 % of the downstream demand but when other percentages are considered, scenario 1 gets better results than those of the real operation. Scenario 7 and 8 have minimum sustainability index because the weight of water supply objective is zero in these scenarios. Among the scenarios, scenario 1 is based on the Sefidrud managers’ opinion and is similar to the real operation. Figure 16 shows that although scenario 1 and the real operation has the same sustainability index in 100 % of downstream demand, other percentages reveal that behavior of real operation in the failed 10-day periods is not proper. Scenario 2 has a better condition than the real operation at all percentages of the downstream demand except in the 100 %, while the water demand and flushing objectives weight in the scenario 2 is 0.7 and 0.3, respectively. Scenarios 7 and 8 are the worse scenarios in meeting downstream demand, because the weight of water supply objective is zero. Indeed supplying downstream water demand is the major objective in Sefidrud reservoir operation. Therfore the sustainability index is defined only for it and doesn’t consider flushing and hydropower generation.

7 Conclusions In the present study, NSGA-II was applied to the multi-objective operation of Sefidrud reservoir in Iran. The objectives included meeting water demands, hydroelectric generation and sediments flushing. Then by using the weighted objective functions and non-symmetric

R. Hajiabadi, M. Zarghami

Nash solution, various scenarios were defined in the study. Also the sustainability index was introduced to evaluate the scenarios at different downstream demand percentages. It was shown that the new model can lead to a better and more stable operation of the Sefidrud reservoir. Results of the applying various scenarios show that the weight of the hydropower generation objective is not of significance in new model and it would not be taken into account. In other words, the value of hydropower generation is not so sensitive for varying objective weights. Indeed the present model helps that with regardless the weight of hydropower objective function, required hydroelectric power is achieved. Scenario 2 indicates that in the years when the reservoir’s inflow is less than the downstream water demand (dry year), sediment flushing can be performed in the Sefidrud reservoir, unlike previous operation policies. Scenario 2 takes privilege of an adequate stability at the different percentages of the downstream demand, and its stability could be increased by taking other water resources into account such as wells, small dams and rainfall, because the downstream of Sefidrud reservoir is a high rainfall area. So scenario 2 is suitable for use, in order to fulfill the sediment evacuation policy in future dry years. However, if the sediment flushing is not needed, scenario 1 is offered for Sefidrud reservoir operation. A comparison of the scenario 1 and the real operation reveals that scenario 1 is more stable in supplying different percentage of the downstream water demand. Finally, the new model used in this study helps to increase in sediment evacuation and stable management in supplying downstream water demand especially in dry years while the environmental issues and hydropower generation are considered. This model can be useful in sediment-laden reservoirs in which sediment flushing causes environmental problems in their downstream. Acknowledgments The insightful comments of Dr. Nourani, the associate professor in the University of Tabriz and Mr. Asghari, as the head of Hydrology Section in the Sefidrud Dam are so appreciated.

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