Water Resour Manage (2014) 28:715–729 DOI 10.1007/s11269-013-0510-1

Evaluation of Real-Time Operation Rules in Reservoir Systems Operation Y. Bolouri-Yazdeli & O. Bozorg Haddad & E. Fallah-Mehdipour & M. A. Mariño

Received: 8 February 2013 / Accepted: 29 December 2013 / Published online: 12 January 2014 # Springer Science+Business Media Dordrecht 2014

Abstract Reservoir operation rules are logical or mathematical equations that take into account system variables to calculate water release from a reservoir based on inflow and storage volume values. In fact, previous experiences of the system are used to balance reservoir system parameters in each operational period. Commonly, reservoir operation rules have been considered to be linear decision rules (LDRs) and constant coefficients developed by using various optimization procedures. This paper addresses the application of real-time operation rules on a reservoir system whose purpose is to supply total downstream demand. Those rules include standard operation policy (SOP), stochastic dynamic programming (SDP), LDR, and nonlinear decision rule (NLDR) with various orders of inflow and reservoir storage volume. Also, a multi-attribute decision method, elimination and choice expressing reality (ELECTRE)-I, with a combination of indices, objective functions, and reservoir performance criteria (reliability, resiliency, and vulnerability) are used to rank the aforementioned rules. The ranking method employs two combinations of indices: (1) performance criteria and (2) objective function and performance criteria by using the same weights for all criteria. Y. Bolouri-Yazdeli : O. Bozorg Haddad (*) : E. Fallah-Mehdipour Department of Irrigation & Reclamation Engineering, Faculty of Agricultural Engineering & Technology, College of Agriculture & Natural Resources, University of Tehran, Karaj, Tehran, Iran e-mail: [email protected] Y. Bolouri-Yazdeli e-mail: [email protected] E. Fallah-Mehdipour e-mail: [email protected] M. A. Mariño Department of Land, Air & Water Resources, University of California, 139 Veihmeyer Hall, Davis, CA 95616-8628, USA e-mail: [email protected] M. A. Mariño Department of Civil & Environmental Engineering, University of California, 139 Veihmeyer Hall, Davis, CA 95616-8628, USA M. A. Mariño Department of Biological & Agricultural Engineering, University of California, 139 Veihmeyer Hall, Davis, CA 95616-8628, USA

716

Y. Bolouri-Yazdeli et al.

Results show that the NLDR gives an appropriate rule for real-time operation. Moreover, NLDR validation is presented by testing predefined curves for dry, normal, and wet years. Keywords Real-time operation . Reservoir performance criteria . Operational rules

1 Introduction Population growth, improvement in living standards which causes an increase in consumption (Seifollahi-Aghmiuni et al. 2011, 2013), migration to urban regions, limitation of water resources (Soltanjalili et al. 2013), and conflicts among decision-making groups (FallahMehdipour et al. 2011a) are important reasons to design and operate optimally existing and future water systems (Ghajarnia et al. 2011; Karimi-Hosseini et al. 2011; RasoulzadehGharibdousti et al. 2011; Bozorg Haddad et al. 2008a, 2010; Bozorg Haddad and Mariño 2011) in general and reservoirs in particular (Bozorg Haddad et al. 2009a, 2011; FallahMehdipour et al. 2011b). Reservoirs are important structures that can store and release water based on decisions made by operators of the system (Farhangi et al. 2012). Those decisions directly affect the purpose of the operation, such as supplying downstream demands, generating hydropower energy, and controlling floods. Prior experience helps the operator to make an appropriate decision to calculate how much (amount) and when (time) to release water from a reservoir (Fallah-Mehdipour et al. 2013a). Extraction the optimal rule curves for reservoir operation (Fallah-Mehdipour et al. 2012), cultivation plans (Bozorg Haddad et al. 2009b), and conjunctive use of surface water and groundwater (Fallah-Mehdipour et al. 2013b) have been the focus of many recent investigations. Different types of decision rules have been widely used to extract operational rules such as LDRs, SOP, and hedging rules (HRs). Bower et al. (1966) analyzed operating procedures and their HR in the design of water-resource systems. Revelle et al. (1969) formulated a LDR easily solved as a linear programming (LP) problem to design and manage a reservoir. The LDR specified the release during any period of reservoir operation as the difference between the storage at the beginning of the period and a decision parameter for the period. They indicated that a reservoir management problem may be formulated either in a deterministic or a stochastic environment. Loucks (1970) commented on LDRs and chance constraints for reservoir design and operation. He proposed reservoir storage and inflow at the beginning of a period in a LDR and considered a constant value added to the release function in each period. Eisel (1972) developed a more general reservoir operation rule than previously available chance-constrained reservoir models. He illustrated possible convolution problems associated with chance-constrained models of water resource systems. Klemes (1977) used operation policy optimization for a reservoir fed with a random lognormal input. Optimal results showed a negligible sensitivity to the considered random distribution of input data. Karamouz and Houck (1982) developed reservoir operation rules by deterministic optimization. They proposed an algorithm that cycled through a deterministic dynamic program, a regression analysis, and a simulation model. The algorithm was tested in 48 cases (annual operation rules were determined for 12 cases and monthly operation rules were determined for 36 cases), demonstrating the usefulness of the algorithm in selecting reservoir operation rules. Hashimoto et al. (1982) illustrated the performance of a water supply reservoir with a variety of operation rules, especially a HR that considered reliability (likelihood of system failure), resiliency (system recovery time from failure), and vulnerability (severity of consequences of failure). Mariño and Mohammadi (1983) employed a combination of linear programming (LP) and

Evaluation of Real-Time Operation Rules

717

dynamic programming (DP) to solve reservoir operation problems efficiently, by considering water supply and hydropower generation simultaneously. They presented an efficient algorithm for the monthly operation of a system of two parallel multipurpose reservoirs. Mohammadi and Mariño (1984a) proposed an efficient algorithm for the real-time monthly operation of a multipurpose reservoir. They combined LP (used for month-by-month optimization) and DP (used for annual optimization). They considered water and energy maximization, water and energy maximization with flood control considerations, and water and energy maximization for peak demand months. Thus, models provided the reservoir operator with different choices for annual optimization. LP, NLP, and DP techniques have been used successfully in reservoir operation problems. For example, Chu and Yeh (1979) and Mohammadi and Mariño (1984b) used NLP and LP-DP respectively to develop real-time hourly and daily operation rules for multipurpose, multiple reservoir systems while Devamane et al. (2006) and Arunkumar and Jothiprakash (2012) used NLP in real-time hourly operation in a multipurpose, multiple reservoir and optimal reservoir operation for hydropower generation, respectively. SDP has the same components as a DP; the only modification is to the state transition equation. When events in the future (for example inflow in reservoir operation) are uncertain, the state does not evolve deterministically; instead, states and actions lead to a distribution over possible states in the future. Several investigators (e.g., Stedinger et al. 1984; Huang et al. 1991; Vasiliadis and Karamouz 1994; and Shokri et al. 2012) have successfully employed SDP in reservoir operation studies. Perera and Conder (1998) introduced limitation rules, rule curves, and released water as a function of storage volume and inflow in the design and operation of a water supply system. They used and verified several methods based on SDP in terms of computational efficiency and accuracy by using a hypothetical example of three interconnected urban water supply reservoirs. Results showed that these methods allow SDP to be more applicable for developing optimal operation rules for multiple urban water supply reservoirs. Neelakantan and Pundrikanthan (1999) used a simulation-optimization model for planning the operation of a drinking water reservoir by using a HR, which is a more appropriate rule for reservoir operation under deficit conditions. They increased the speed of calculations in a neural network model for the simulation of the reservoir operation instead of a conventional simulation model. Labadie (2004) reviewed simulation and optimization methods used in reservoir operation, including implicit stochastic optimization (ISO), explicit stochastic optimization (ESO), real-time control, and heuristic programming. In recent years, heuristic algorithms have been widely used in reservoir operation in general and real-time operation of single and multi-reservoir system in particular. Oliveira and Loucks (1997) focused on genetic algorithms (GAs) to develop multi-reservoir operation rules by using real-valued vectors containing information needed to define both system release and individual reservoir storage volume targets as functions of total storage in each of multiple within-year periods. They applied the proposed algorithm in example reservoir systems used for water supply and hydropower. Sharif and Wardlaw (2000) employed GA to develop reservoir operation rules to manage a reservoir system in Indonesia by considering the existing development situation in the basin and two future water resource development scenarios. GAobtained final objective function values were very near to optimal results calculated by discrete differential dynamic programming (DDDP). Chang and Chang (2001) combined GA and the adaptive network-based fuzzy inference system (ANFIS) to improve real-time reservoir operation. GA was used to search the optimal reservoir operation histogram based on a given inflow series, which can be recognized as the base of input–output training patterns in the next step. The ANFIS was then built to create the fuzzy inference system, to construct the suitable structure and parameters, and to estimate the optimal water release according to the reservoir

718

Y. Bolouri-Yazdeli et al.

depth and inflow situation. Simulation results demonstrated that that developed model has considerable performance with regard to the prediction of total water deficit and generalized shortage index (GSI). Chang et al. (2005a) investigated efficiency and effectiveness of two GAs, i.e., binary and real coded, to develop multipurpose reservoir operation rule curves on the Shih-Men reservoir in Taiwan. Those curves were assumed to be linear functions where the coordinates of inflection points are the unknowns. Results showed that the GAs provided an adequate, effective and robust way for searching the decision rule curves. Chang et al. (2005b) used GA and fuzzy rule base (FRB) to extract knowledge based on historical inflow data with a design objective function and on the operation rule curves, respectively. Results demonstrated the efficiency of GA to search the optimal patterns and the FRB can extract the knowledge from the operation rule curves. Bozorg Haddad et al. (2008b) and Afshar et al. (2011) employed the honey-bee mating optimization (HBMO) algorithm to extract single- and multi-reservoir system operation LDRs. Results indicated that the HBMO algorithm was capable to determine the best solution in the aforementioned reservoir systems. The LDRs developed by Bozorg Haddad et al. (2008b) were used by Fallah-Mehdipour et al. (2013c) to extract optimal reservoir releases as well as cultivated areas in an irrigation system using GA, particle swarm optimization (PSO), and shuffled frog leaping algorithm (SFLA). While GA, PSO, and SFLA were successful in computing optimal solutions, the SFLA produced the best objective function value. In most of the aforementioned investigations, a LDR which was a function of inflow, storage volume, and released water from the reservoir was considered as an operation rule. This mathematical formulation of decision rule has been limited in some simple forms which may not be efficient in real-time reservoir operation. Moreover, different types of NLDRs may have more capabilities to produce a better performance of a reservoir system. To extract an operational rule, two main methods are employed in reservoir operation: (1) simulation and (2) optimization. SOP is one of the simulation methods which is widely used in reservoir operation. It is the simplest and most often-used reservoir rule in which releases are made, if possible, to satisfy only the demand required in each period, and does not preserve water for future requirements. If sufficient water is not available to meet demand, the reservoir is emptied. If there is excess water, the reservoir will fill and then spill the excess water (Rittima 2009). SDP, which is an optimization method, attempts to solve a DP recursion relation adapted to stochastic problems. In SDP, simplified decision rules need not be assumed, and only probability distributions are used to develop optimal rules without any knowledge of future inflow events (Labadie 2004). SDP are similar in style but take advantage of the fact that probability distributions governing the data are known or can be estimated. This method discretizes the decision space to limited alternatives and chooses the best alternative. Thus, to achieve a more precise rule, the number of discretizations should be increased. LDRs and NLDRs search the decision space in a continuous manner. The structures of these rules are a predefined linear or nonlinear equation which is embedded in the operational model. In this paper, various orders of NLDRs, which have a more flexible structure with a nonlinear mathematical function, are extracted and compared to other operational rules, including SOP as a simulation method, SDP as a discrete optimization method, LDR as a continuous optimization method and by ELECTRE-I as a multi-criteria decision making tool. Reliability, resilience, and vulnerability are used as system performance criteria. Results show the efficiency of the NLDRs compared to those of SOP, SDP, and LDR which use a predefined relation between releases and reservoir state variables.

Evaluation of Real-Time Operation Rules

719

1.1 Reservoir Operation Model In this paper, the purpose of reservoir operation is considered to be meeting downstream demand. Thus, the objective function is expressed as the minimization of the total squared deviation of the released water: Min:

Z¼

2 T  X Rt −Dt DMax: t¼1

ð1Þ

in which Rt = release from the reservoir at period t; Z = objective function; T = number of operating periods; Dt = downstream demand of reservoir at period t; and DMax. = maximum downstream demand in the time-series. The reservoir system model calculates reservoir behavior under various conditions with different purposes by using a mass balance or continuity equation: S tþ1 ¼ S t þ Qt −Rt −SPt −Lt

ð2Þ

in which St = storage volume of the reservoir at the beginning of the tth period; Qt = inflow to the reservoir during period t; St+1 = reservoir storage volume at the end of tth period; SPt = volume of spilled water from reservoir at period t; and Lt = volume of lost water from the reservoir at period t. In this paper, lost water is considered to be a nonlinear function of evaporation:   ð3Þ Lt ¼ F 1 Evt ; At where F1 = lost water function; Evt = evaporation depth at period t; and At = average water surface corresponding to storage volume at period t. The average surface is a linear function of storage volume: At ¼ ðAt þ Atþ1 Þ=2

ð4Þ

At ¼ F 2 ðS t Þ

ð5Þ

in which At and At+1 = water surface at the start and end of period t; and F2 = linear function for transferring storage volume to water surface. The model’s formulation is constrained by the following relations: RMin: ≤Rt ≤RMax:

ð6Þ

S Min: ≤S t ≤S Max:

ð7Þ

in which RMin., RMax. = minimum and maximum capacity for release from reservoir; and SMin., SMax. = minimum and maximum storage of reservoir, respectively. Moreover, spilled water from the reservoir is calculated by the following equation:  SPt ¼

S t þ Qt −Rt −S max 0

; ;

S t þ Qt −Rt > S max S t þ Qt −Rt < S max

ð8Þ

In general, reservoir operation can be grouped as: (1) long-term and (2) real-time operation. In long-term operation, a specific inflow time series is used in the operation process and it is assumed that time series will be observed in the future. In contrast, in real-time operation, a reservoir is operated by using current system parameters that include inflow, downstream demand, and storage volume at the beginning of each period. Although real-time operation is

720

Y. Bolouri-Yazdeli et al.

less precise than long-term operation, it is advantageous because a system operation can be changed upon making a decision at any time. To determine a decision rule, a general mathematical equation can be included in the model equations: Rt ¼ a1 þ b1  S 1t þ … þ bn  S tn þ c1  Q1t þ … þ cn  Q nt

ð9Þ

in which {a1,b1,…,bn,c1,…,cn}= coefficient values that are calculated by the operation rule. 1.2 Performance Criteria Hashimoto et al. (1982) reported three performance criteria (reliability, resiliency and vulnerability), to investigate system performance. These measures describe how likely a system is to fail (reliability), how quickly it recovers from failure (resiliency), and how severe the consequences of failure may be (vulnerability). Generally, the aforementioned criteria are calculated by: α ¼ 1−

f T

ð10Þ

γ ¼ 1−

1 f fs

ð11Þ

fs X

λ¼

Maxðshk Þ

k¼1

fs

ð12Þ

where α= reliability; f= number of failure periods; γ= resiliency; fs = number of continued failure periods; λ= vulnerability; and shk = volume of deficit at kth period of failure series. High values of reliability and resiliency and a low value of vulnerability indicate a high system efficiency and performance. If the reservoir operation purpose is supplying downstream demand, α, γ, and λ will be respectively calculated by Eqs. (13), (14), and (15): T

N ðDt > Rt Þ

α ¼ 1− t¼1

T

ð13Þ

T−1

γ¼

N ðDtþ1 ≤Rtþ1 jDt > Rt Þ

t¼1

T

ð14Þ

N ðDt > Rt Þ

t¼1

! Dt −Rt λ ¼ Max: Dt > R t t¼1 Dt T

ð15Þ

Evaluation of Real-Time Operation Rules

in which

721

T

N ð D t > Rt Þ ¼

number of time periods in which demand is not supplied; number of reservoir success to supply a desired demand (an specific t¼1 percentage of demands)  after a failure state (deficit of downstream demand supply); and T  t maximum relative deficiencies in the failure series. Max: DtD−R jD > R t t t T

t¼1

N ðDtþ1 ≤Rtþ1 jDt > Rt Þ ¼

t¼1

1.3 Ranking Operational Rules ELECTRE is a multi-criteria decision-making tool, first proposed by Roy (1968). It is based on choosing, ranking, and sorting processes to show the best decision alternative. ELECTRE was successfully employed by Duckstein et al. (1994), Raju et al. (2000), Zahraie et al. (2008) in ranking groundwater management alternatives, sustainable water resources planning, and sustainable water supply and demand management, respectively. In this paper, ELECTRE is used to rank operational rules by considering objective function values and performance criteria. At the first step, vector priority criteria and an alternative matrix, consisting of m rows (alternatives) and n columns (criteria), are created. At the second step, a vector priority is multiplied to the alternative matrix and denoted by w. At the third step, a concordance matrix is computed by considering the following relation for each index: 1 wþ þ w¼ 2 cij ¼ þ w þ w¼ þ w−

i ¼ 1; …; m

j ¼ 1; …; n

ð16Þ

where cij = preferable level of ith alternative compared to the jth alternative; w+ and w= = total weights for ith alternative that is better than and equal to the jth alternative, respectively; and w− = total weights for jth alternative that is better than the ith alternative. The discordance matrix elements are calculated by Eq. (17): Max: I ji d ij ¼ K


ð17Þ

Reservoir data sets

Simulation model

SOP

Optimization model

SDP

Finding objective function and performance criteria Perform alternative matrix and rank operational rule Fig. 1 Flowchart of methodology

LDR

NLDR

722

Y. Bolouri-Yazdeli et al.

in which dij = discordance matrix index; Iji = maximum difference between ith and jth alternatives, in which jth alternative is preferable to ith alternative; and K*= maximum difference between ith and jth alternatives without considering any preference. At the fourth step, two thresholds for concordance and discordance are considered and alternatives are sorted by considering the maximum of concordance and minimum of discordance for each element. In particular, to rank reservoir operation rules, an objective function (Z) and reservoir performance criteria including reliability, resiliency, and vulnerability are vector priority criteria and different operational rules are alternatives. Thus, an m×4 matrix in which m= number of different operational rules is formulated as follows:

Fig. 2 Location of case study in the Karoon Basin

Evaluation of Real-Time Operation Rules

Table 1 Annual inflow and monthly demand of Karoon IV

Alternatives SOP NLP LDR ⋮ NLDR

723

Period

Average inflow (106 m3)

Demand (106 m3)

4 years

43 years

1

660.2

986.7

2

651.3

830.6

562.2

3

389.7

515.8

6,545.4

4

274.1

337.5

698.8

5 6

198.4 146.2

231.5 169.2

666.0 574.2

7

125.2

143.1

403.6

8

146.5

188.3

249.9

9

157.4

290.6

176.0

10

162.3

254.7

148.6

11

279.7

360.8

169.7

12

535.1

673.2

292.9

Resiliency Vulnerability x1;3 x1;4 x2;3 x2;4 x3;3 x3;4 x⋮;3 x⋮;4 xm;3 xm;4

3

2 Z x1;1 6 x2;1 6 6 x3;1 6 4 x⋮;1 xm;1

Reliability x1;2 x2;2 x3;2 x⋮;2 xm;2

437.2

7 7 7 7 5

ð18Þ

If there are four criteria, vector priority will be a 1×4 matrix in which 1st, 2nd, 3rd, and 4th indexes relate to Z, reliability, resiliency, and vulnerability, respectively.

Vector priority ¼



Z w1;1

Reliability Resiliency w1;2 w1;3

Vulnerability  w1;4

ð19Þ

This vector priority is multiplied to rows of an alternative matrix and a new weighted matrix is computed. Then, concordance and discordance matrices are respectively computed by using Eqs. (16) and (17). Finally, different alternatives will be sorted by the maximum of concordance and minimum of discordance. It is noted that if performance criteria are used as the criteria, then the first column of the alternative matrix and vector priority will be eliminated. Figure 1 displays a flowchart of the applied methodology. Table 2 SDP characteristics and obtained objective function

Number of months for Number of storage Number of inflow Z transition matrix classification classification 48

20

5

4.064

48 516

20 20

20 5

4.284 6.084

516

20

20

4.022

724

Y. Bolouri-Yazdeli et al.

Table 3 Obtained objective function and performance criteria for SOP, SDP, and various rules

Method

Z

Reliability

Resiliency

Vulnerability

SOP

6.324

0.417

0.179

0.745

SDP S1-Rule

4.022 2.775

0.229 0.271

0.163 0.143

0.639 0.615

S2-Rule

2.600

0.188

0.154

0.567

S3-Rule

2.517

0.208

0.158

0.394

Q1-Rule

2.650

0.146

0.122

0.478

Q1S1-Rule

2.426

0.188

0.128

0.488

Q1S2-Rule

2.453

0.125

0.143

0.399

Q1S3-Rule

2.613

0.188

0.179

0.527

Q2-Rule Q2S1-Rule

2.451 2.389

0.167 0.188

0.125 0.128

0.507 0.506

Q2S2-Rule

2.384

0.188

0.128

0.436

Q2S3-Rule

2.405

0.229

0.216

0.362

Q3-Rule

2.428

0.167

0.125

0.487

Q3S1-Rule

2.692

0.208

0.158

0.529

Q3S2-Rule

2.382

0.208

0.105

0.536

Q3S3-Rule

2.398

0.229

0.135

0.570

1.4 Case Study Various operational rules are employed in the operation of the Karoon IV reservoir in Iran, located on the Karoon River, with an annual average inflow of 5,400×106 m3. Figure 2 shows the location of the Karoon IV reservoir in the Karoon Basin. The minimum and maximum allowable storage volumes are 1441.29 and 2,190×106 m3, respectively. To compare the performance of several rules, 48 periods are selected to supply downstream demand. Table 1 shows annual average inflow and monthly demand at Karoon IV. To increase calculation accuracy, Eq. (6) is used in the nonlinear form with three orders for Karoon IV. Moreover, to compute optimal rule curves, language for interactive general optimization (LINGO) is used (LINDO Systems Inc 2010).

2 Results and Discussion To determine the best system state, the reservoir operation optimization model is run by using LINGO without considering any rule curve. The obtained objective function value for the

Table 4 Ranking operational rules based on performance criteria Method

SOP

Q2S3

S3

S1

Q1S3

Q3S1

Rank

1

2

3

4

5

6

Method

Q2S2

Q3S3

Q1S1

S2

Q2S1

SDP

Rank

7

8

9

10

11

11

Method

Q3S2

Q3

Q1S2

Q2

Q1

Rank

12

13

14

14

15

Evaluation of Real-Time Operation Rules

725

Table 5 Ranking operational rules based on the objective function and performance criteria Method

Q2S3

S3

S1

Q1S3

Q3S1

Q2S2

Rank

1

2

3

4

5

6

Method

Q3S3

Q1S1

S2

Q2S1

Q3S2

Q3

Rank

7

8

8

9

10

11

Method Rank

Q2 12

Q1S2 13

Q1 13

SOP 13

SDP 14

considered time-series (48 periods) is 2.328. Moreover, this value is 63.19 % lower (better) than the value obtained by SOP (6.324) as a simulation method. SDP is used to illustrate rule curves. The transition probability matrix of the SDP method was calculated by 48 and 516 periods in time-series. Then, two values of storage volume and inflow classifications were used with each transition matrix in the optimization process. Table 2 presents SDP characteristics and obtained objective functions. As it is shown, the best (minimum) value of Z by the transition probability matrix with 516 periods in time-series is just 1.03 % less than the value obtained by the transition probability matrix with 48 periods in time-series. LDRs and NLDRs considered all combinations of inflow and storage volume parameters in the rule pattern with a maximum order of three for the aforementioned parameters, which were extracted by LINGO. Table 3 shows obtained objective function values and performance criteria for SOP, SDP, and various rules. To follow results more easily, each rule was named by order of inflow and storage volume. For example, Q1S2-Rule means a NLDR with a maximum order of 1 and 2 for the inflow and storage volume, respectively. As presented in Table 3, the best (minimum) and worst (maximum) values of Z are found by the Q3S2-Rule SOP. Moreover, the obtained objective function values by different rules with more flexibility are less than the values obtained by SOP and SDP. Values of the objective function with increasing parameter orders are closer to the NLP result. Accordingly, Q3S2-, 900 SOP

800

SDP

Q2S3-Rule

Demand

Release (106m3)

700 600 500 400 300 200 100 0 0

12

Fig. 3 Released water from Karoon IV reservoir

24 Month

36

48

726

Y. Bolouri-Yazdeli et al. 2400

SOP

Reservoir storage (106m3)

2300

SDP

Q2S3-Rule

Smin

Smax

2200 2100 2000 1900 1800 1700 1600 1500 1400 0

12

36

24

48

Month Fig. 4 Reservoir storage during operational horizon

Q2S2-, Q2S1-, and Q3S3-Rules achieve smaller Z values compared to values computed with LDRs. The reliability of SOP and S1-Rule which supply each period demand by storage volume is more than in other rules. The resiliency of the Q2S3-Rule has the best (maximum) value, which illustrates the quick recovery from failure periods. The vulnerabilities of LDRs and NLDRs are less than in SOP and SDP. The Q2S3-Rule reported the best (minimum) value of vulnerability. Based on these results, rule curves calculated optimal solutions with less value of vulnerability and more value of resiliency, meaning that these rules decrease deficit intensity and increase failure periods. Thus, LDRs and NLDRs in general and Q2S3-Rule in particular have more capability to compute an appropriate operation rule than other simulation and optimization methods. To determine an appropriate rank of real-time operational rules, ELECTRE-I was used based on (1) performance criteria and (2) objective function and performance criteria. At the first step, performance criteria with the same preference and weight (1/3) were used. Table 4 shows results of this ranking. Accordingly, SOP has the first rank because of its considerable reliability criterion and LDRs and NLDRs, which are higher-order functions of storage volume, have better ranks compared to SDP. The Q2S3-Rule, with a better value of resiliency and vulnerability compared to the SOP, has the second rank of operational rule. Table 6 Testing model results for dry, normal, and wet years

Rule curve

Z Dry year

Normal year

Wet year

NLP

0.677

0.209

0.135

SOP

1.575

0.892

0.712

SDP

1.116

0.733

0.553

Q3S3-Rule

0.761

0.248

0.169

Q3S2-Rule Q2S3-Rule

0.762 0.723

0.226 0.263

0.124 0.208

Q2S2-Rule

0.737

0.301

0.219

Evaluation of Real-Time Operation Rules

727

Based on Tables 3 and 4, because no considerable differences among performance criteria exist, some of the operational rules have the same rank. At the second step, objective function and performance criteria with the same weight (1/4) were used. Table 5 shows various ranks for operational rules by using aforementioned criteria. As it is mentioned, SOP has the maximum value of the objective function; thus, it is in the worst rank in this type of ranking. Several rule curves show no considerable changes and the Q2S3-Rule achieves the best (first) rank. Accordingly, in the LDRs and NLDRs, the lower the value of storage order, the higher (worse) the rank. Based on two aforementioned ranking processes, the Q2S3-Rule is the appropriate rule in reservoir operation. To illustrate reservoir states in different operational periods, Figs. 3 and 4 show released water and storage volume of Karoon IV for the SOP, SDP, and outstanding rule (Q2S3-Rule). Although SOP has the minimum number of deficit periods (Fig. 3), there is deficit intensity in some periods. Moreover, based on Fig. 4, SOP and SDP used more water from the reservoir to supply downstream demand, and storage volume in most periods is equal to the minimum allowable volume. To validate results of various rules in reservoir operation, some rules with better ranks including: Q3S3-, Q3S2-, Q2S3-, and Q2S2-Rules were tested and compared with results of the NLP without considering any rule, SOP, and SDP. Table 6 shows obtained objective function values for dry, normal, and wet periods. According to this table, the nominated rule gives less Z and more efficiency for all periods.

3 Concluding Remarks Reservoir operation rules are relations to regulate release water for meeting several operational purposes. In this paper, real-time operational rules, including SOP, SDP, LDRs, and NLDRs were extracted for the Karoon IV reservoir operation with the purpose of supplying downstream demand. These rules were computed for a 48-period horizon to achieve a global optimal solution by using the LINGO software. To select an appropriate operational rule, ELECTRE-I, as a multi-criteria decision-making tool which achieves appropriate results in water management, was used. Criteria employed in the decision process were (1) reservoir performance criteria and (2) objective function and reservoir performance criteria. Results showed that LDRs and NLDRs are capable to be used in reservoir operation with less vulnerability and high resiliency. In other words, those decision rules are flexible to embed in a mathematical model and adapt released water to the inflow and storage volume. The SOP, SDP, and optimal nominated rules were then tested for dry, normal, and wet periods involving 12 months. Results of the training and testing model illustrated that the Q2S3-Rule yielded the best real-time operational rule with the minimum value of the objective function. Although reservoir operation rules can be conducted by the operators to make appropriate decisions in various system conditions, there are some issues in real-world reservoir management that can affect the performance of existing rules. Different stakeholders (consumers) in downstream of reservoirs and the associated conflicts to allocate more water to each consumer, existing uncertainties on the reservoir system elements such as inflow which has unknown value in consequent periods, and satisfaction of downstream environmental needs can limit the applicability and feasibility of the existing reservoir operation rules. Thus, extraction of operating rules by considering more reservoir system details is recommended for future studies to adapt the existing rules with real-world system conditions.

728

Y. Bolouri-Yazdeli et al.

References Afshar A, Shafii M, Bozorg Haddad O (2011) Optimizing multi-reservoir operation rules: an improved HBMO approach. J Hydroinformatics 13(1):121–139 Arunkumar R, Jothiprakash V (2012) Optimal reservoir operation for hydropower generation using non-linear programming model. Water Resour Manag 93(2):111–120 Bower BT, Hufschmidt MM, Reedy WW (1966) Operating procedures: Their role in the design of waterresource systems by simulation analyses. In: Maass A et al (eds) Design of water-resource systems. Harvard University Press, Cambridge, pp 443–458 Bozorg Haddad O, Adams BJ, Mariño MA (2008a) Optimum rehabilitation strategy of water distribution systems using the HBMO algorithm. J Water Supply: Res Technol - AQUA 57(5):327–350 Bozorg Haddad O, Afshar A, Mariño MA (2008b) Honey-bee mating optimization (HBMO) algorithm in deriving optimal operation rules for reservoirs. J Hydroinformatics 10(3):257–264 Bozorg Haddad O, Afshar A, Mariño MA (2009a) Optimization of non-convex water resource problems by honey-bee mating optimization (HBMO) algorithm. Eng Comput (Swansea, Wales) 26(3):267–280 Bozorg Haddad O, Moradi-Jalal M, Mirmomeni M, Kholghi MKH, Mariño MA (2009b) Optimal cultivation rules in multi-crop irrigation areas. Irrig Drain 58(1):38–49 Bozorg Haddad O, Mirmomeni M, Mariño MA (2010) Optimal design of stepped spillways using the HBMO algorithm. Civil Eng Environ Syst 27(1):81–94 Bozorg Haddad O, Mariño MA (2011) Optimum operation of wells in coastal aquifers. Proc Inst Civ Eng Water Manag 164(3):135–146 Bozorg Haddad O, Afshar A, Mariño MA (2011) Multireservoir optimisation in discrete and continuous domains. Proc Inst Civ Eng Water Manag 164(2):57–72 Chang L-C, Chang F-J (2001) Intelligent control for modeling of real-time reservoir operation. Hydrol Processes 15(9):1621–1634 Chang F-J, Chen L, Chang L-C (2005a) Optimizing the reservoir operating rule curves by genetic algorithms. Hydrol Processes 19(11):2277–2289 Chang Y-T, Chang L-C, Chang F-J (2005b) Intelligent control for modeling of real-time reservoir operation, part II: artificial neural network with operating rule curves. Hydrol Processes 19(7):1431–1444 Chu WS, Yeh WW-G (1979) A nonlinear programming algorithm for real-time hourly reservoir operation. J Am Water Resour Assoc 14(5):1048–1063 Devamane MG, Jothiprakash V, Mohan S (2006) Nonlinear programming model for multipurpose multireservoir operation. Hydrol J 29(3&4):33–46 Duckstein L, Treichel W, Magnouni S (1994) Ranking ground-water management alternatives by multicriterion analysis. J Water Resour Plann Manag (ASCE) 120(4):546–565 Eisel LM (1972) Chance-constrained reservoir model. Water Resour Res 8(2):339–347 Fallah-Mehdipour E, Bozorg Haddad O, Beygi S, Mariño MA (2011a) Effect of utility function curvature of Young’s bargaining method on the design of WDNs. Water Resour Manag 25(9):2197–2218 Fallah-Mehdipour E, Bozorg Haddad O, Mariño MA (2011b) MOPSO algorithm and its application in multipurpose multireservoir operations. J Hydroinformatics 13(4):794–811 Fallah-Mehdipour E, Bozorg Haddad O, Mariño MA (2012) Real-time operation of reservoir system by genetic programming. Water Resour Manag 26(14):4091–4103 Fallah-Mehdipour E, Bozorg Haddad O, Mariño MA (2013a) Developing reservoir operational decision rule by genetic programming. J Hydroinformatics 15(1):103–119 Fallah-Mehdipour E, Bozorg Haddad O, Mariño MA (2013b) Extraction of optimal operation rules in aquiferdam system: a genetic programming approach. J Irrig Drain Eng 139(10):872–879 Fallah-Mehdipour E, Bozorg Haddad O, Mariño MA (2013c) Extraction of multi-crop planning rules in a reservoir system: application of evolutionary algorithms. J Irrig Drain Eng (ASCE) 139(6):490–498 Farhangi M, Bozorg Haddad O, Mariño MA (2012) Evaluation of simulation and optimization models for WRP with performance indices. Proc Inst Civ Eng Water Manag 165(5):265–276 Ghajarnia N, Bozorg Haddad O, Mariño MA (2011) Performance of a novel hybrid algorithm in the design of water networks. Proc Inst Civ Eng Water Manag 164(4):173–191 Hashimoto T, Stedinger JR, Loucks DP (1982) Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation. Water Resour Res 18(1):14–20 Huang W, Harboe R, Bogardi J (1991) Testing stochastic dynamic programming models conditioned on observed or forecasted inflows. J Water Resour Plann Manag (ASCE) 117(1):28–36 Karamouz M, Houck MH (1982) Annual and monthly reservoir operating rules. Water Resour Res 18(5): 1337–1344 Karimi-Hosseini A, Bozorg Haddad O, Mariño MA (2011) Site selection of raingauges using entropy methodologies. Proc Inst Civ Eng Water Manag 164(7):321–333

Evaluation of Real-Time Operation Rules

729

Klemes V (1977) Value of information in reservoir optimization. Water Resour Res 13(5):850–857 Labadie JW (2004) Optimal operation of multireservoir systems: state-of-the-art review. J Water Resour Plann Manag (ASCE) 13(2):93–111 LINDO Systems Inc. (2010) LINDO API 6.0 user manual, http://www.lindo.com/ Loucks DP (1970) Some comments on linear decision rules and chance constraints. Water Resour Res 6(2):668–671 Mariño MA, Mohammadi B (1983) Reservoir operation by linear and dynamic programming. J Water Resour Plann Manag 109(4):303–319 Mohammadi B, Mariño MA (1984a) Reservoir operation: choice of objective functions. J Water Resour Plann Manag 110(1):15–29 Mohammadi B, Mariño MA (1984b) Multipurpose reservoir operation, 2, Daily operation of a multiple reservoir system. J Hydrol 69:15–28 Neelakantan TR, Pundrikanthan NV (1999) Hedging rule optimization for water supply reservoir system. Water Resour Manag 13(6):409–426 Oliveira R, Loucks DP (1997) Operating rules for multireservoir systems. Water Resour Res 33(4):839–852 Perera JC, Conder GP (1998) Computational Improvement for stochastic dynamic programming models of urban water supply reservoirs. J Am Water Resour Assoc 34(2):267–278 Raju KS, Duckstein LD, Arondel C (2000) Multicriterion analysis for sustainable water resources planning: a case study in Spain. Water Resour Manag 14(6):435–456 Rasoulzadeh-Gharibdousti S, Bozorg Haddad O, Mariño MA (2011) Optimal design and operation of pumping stations using NLP-GA. Proc Inst Civ Eng Water Manag 164(4):163–171 Revelle C, Joeres E, Kirby W (1969) The linear decision rule in reservoir management and design. 1. Development of the stochastic model. Water Resour Res 5(4):767–777 Rittima A (2009) Hedging policy for reservoir system operation: a case study of Mun Bon and Lam Chae reservoirs. Kasetsart J (Natural Science) 43(4):833–842 Roy B (1968) Classement et choix en présence de points de vue multiples (la méthode ELECTRE). La Revue d’Informatique et de Recherche Opérationelle (RIRO) 8:57–75 Seifollahi-Aghmiuni S, Bozorg Haddad O, Omid MH, Mariño MA (2011) Long-term efficiency of water networks with demand uncertainty. Proc Inst Civ Eng Water Manag 164(3):147–159 Seifollahi-Aghmiuni S, Bozorg Haddad O, Mariño MA (2013) Water distribution network risk analysis under simultaneous consumption and roughness uncertainties. Water Resour Manag 27(7):2595–2610 Sharif M, Wardlaw R (2000) Multi-reservoir system optimization using genetic algorithms: case study. J Comput Civ Eng (ASCE) 14(4):225–263 Shokri A, Bozorg Haddad O, Mariño MA (2012) Reservoir operation for simultaneously meeting water demand and sediment flushing: a stochastic dynamic programming approach with two uncertainties. J Water Resour Plann Manag (ASCE) 139(3):277–289 Soltanjalili M, Bozorg Haddad O, Mariño MA (2013) Operating water distribution networks during water shortage conditions using hedging and intermittent water supply concepts. J Water Resour Plann Manag 139(6):644–659 Stedinger J, Sule B, Loucks D (1984) Stochastic dynamic programming models for reservoir operation optimization. Water Resour Res 20(11):1499–1505 Vasiliadis H, Karamouz M (1994) Demand-driven operation of reservoirs using uncertainty-based optimal operating policies. J Water Resour Plann Manag (ASCE) 120(1):101–114 Zahraie B, Fooladgar MM, Shanehsazzadeh A, Roozbahani A. (2008) “Framework of a decision support system for basin-scale sustainable water supply and demand management.” World Environmental and Water Resources Congress, Honolulu, Hawaii, United States, May 12–16. pp. 1–13