Application of LP in optimizing Qeysereq singlepurpose

Transcription

1 Application of LP in optimizing Qeysereq singlepurpose reservoir volume M.T.Sattari (1), A.H.Nazemi (2), D.Farsadizadeh (3) (1) Tabriz University, Faculty of agriculture, Department of Irrigation, Tabriz, Iran. Abstract Limitation of water resources and higher cost of hydraulic structures intensify the need for an optimum volume and operation for Iranian reservoir systems. Due to the complexity of water resources systems and some constraints, application of mathematical models and optimization techniques for computing the optimum reservoir volume seems to be necessary. For optimum computation of Qeysereq reservoir volume, an optimizing mathematical model was applied. This model was only used for within-year regulation. Qeysereq reservoir is an off-river system and applied for irrigation of 325 ha farmlands with a channel from the Cheki-Chay River. The objective function is to minimize reservoir volume Ka during a specific demand and reservoir inflow in request months. This volume is the active storage capacity; therefore for computing the total reservoir capacity the dead storage capacity must be added to Ka. The result of the model shows that the Ka is m 3. Key words Mathematical models; Optimization techniques; Reservoir management and Singlepurpose reservoir system 1 Introduction As water resources have been limited in Iran, building hydraulic structures costs more, so it is of high necessity to have optimum volume and operation for reservoir system. Due to the complexity of water resources systems and the presence of many constraints and limitations, application of mathematical models and optimization techniques for computing the optimum reservoir volume are necessary. In Iran water resources and water needs are not always compatible and the regulation is carried out by storage reservoirs. Although water resources are called renewable, the average usable amount is constant. To consider the optimality of capacity of reservoirs and effective use of them is so important that have not seriously noticed in Iran yet. The reservoir planning and

2 operation studies, which have made progresses in recent decades, are based on Rippl's graphical method. The weakness of this method, which can only consider a constant need, was overcome by Thoma's Sequent Peak algorithm. How to design the capacity of water reservoir systems and operate them is a multi-stage decision problem. Dorfman first used the Linear Programming (LP) for the solution of those problems. After Yeh's (1985) state of the art study, Dynamic Programming (DP) and Linear Programming (LP) methods have commonly been used in the solution of that problem. Rogres (1969) and Mclaughlin (1967) proposed LP formulation to obtain optimal capacities of reservoirs. Revelle et al.(1969) proposed a linear decision rule(ldr) to make release decisions for a single reservoir system. Louks (1968) proposed a stochastic linear programming model to determine a strategy for release, giving the current state of the system and previous inflow. Lund (1996) applied the application of deterministic optimization to the Missouri River reservoir system in order to deduce optimal operation rules. Philip D.Crawley (1993), applying a monthly planning and operational model, developed a model for the Adelaide head works system in South Australia, Australia. This model used linear goal programming to aid in the identification of optimum operating policies for the system. Abbas Afshar (1991) developed a mixed integer linear optimization model for irrigation. The model was chance-constrained optimization models which considered the interaction between design and operation parameters (reservoir capacity, delivery system capacity, etc.). Needhom (2000) applied LP to flood control on the Iowa and Des Moines River reservoirs. Teixeira (2002) developed a forward dynamic programming (FDP) model to solve the problem of reservoir operation and irrigation scheduling. The typical scenario in application of the model was composed of a system of two reservoirs in parallel supplying water to as many as three irrigation districts. 2 Research location Qeysereq dam is located in Azerbaijan, a state in Iran. The dam height is 1680 m above the sea level. This basin lies between east latitude 45 16' and north latitude 38 4'. The nearest climatologic station in which 27-year statistical data have been recorded is Mirkuh. It has semi-dry and cold whether. Maximum temperature is 36 C in August and minimum temperature is 25 C in January. Annual average temperature in all statistical period is 8.4 C and the average of monthly evaporation from free surface is shown in table 1. Table 1-Rate of evaporation from free surface (mm) EV Average annual precipitation is 315mm; its maximum that achieved in 1968 was 539mm and its minimum that achieved in 1998 was 179.5mm. The maximum of monthly average precipitation in the region is 63.2mm that is 20% of all annual precipitation in May, and the minimum of monthly average of precipitation is 6.4mm that is 2% of all annual precipitation in August. Therefore the spring season with 48% of precipitation is considered as the wettest season in the year. Average precipitation on reservoir area is shown monthly in table 2. 2

3 Table 2-Rate of precipitation on reservoir area (mm) PP The Chaky-Chay River The Chaky-Chay River is a sub-river of the Aji-Chay River and streams from Mount Yaghli. This river, near the Alan village, flows from Alan diversion dam in East-North into the Aji-Chay River in West-South. The area of basin in the Alan dam point is km 2. According to 46-year statistical data, the rate of inflow was calculated with some probability as shown in Table 3. Table 3-Discharge of river inflow (m 3 /s) 75% % The water of the river after stored behind the Alan Dam has been divided into two parts. One part has a fixed amount of water which flows into the concrete channel as an input of Qeysereq reservoir (table 4). Table 4-Volume of inflow to the reservoir (1000m 3 ) QF Qeysereq reservoir is an off-river. Some of water, which is totally m 3, from subbasins in wet seasons added to the reservoir as an inflow (Table 5). Table 5-Volume of inflow from sub basin to the reservoir (1000m 3 ) IN Meanwhile, some of water as a result of leakage loss could not be controlled. After empirical assessment the amount of this water was computed (Table 6). Table 6-Volume of outflow as a loss from the reservoir (1000m 3 ) O In this plan, totally irrigated area is 325 ha. Many kinds of products are to be cultivated in this land. Whole water demand was calculated using Cropwat4 software (Table 7). Table 7-Volume of Demand (1000m 3 ) D

4 3 Model developing Linear programming models have been applied extensively to optimal resource allocation problems. As the name implies, LP models have two basic characteristics, that is, both the objective function and constraints are linear functions of decision variables. In this research GAMS 1 Software applied for running of model. Due to the reservoir storage-area relationship is nonlinear; an alternatively linear programming model is possible using a linearization of the storage-area relationship as shown in Eq.1. A = A0 + η ST (1) A = ST R 2 = 0.98 Where A is reservoir area and ST is the storage volume. A 0 and η are parameters of linear equation. The essential feature of an optimization model for reservoir capacity determination is the mass balance equation, STt + 1 = STt + QFt + PPt Rt EVt + IN t SPt t = 1,2,...,12 (2) Where ST t is the reservoir storage at the beginning of time period t, QF t is the reservoir inflow in period t, PP t is the precipitation amount on the reservoir surface in period t, R t is the reservoir release in period t, EV t is the evaporation and SP t is the seepage loss during period t. IN t is the a mount of water that flowes from sub basin to the reservoir. A model to determine the minimum active storage capacity (K a ) for a specified release as a demand formulated as O.F Minimize Ka (3) Reservoir capacity cannot be exceeded during any time period, thus: ST K + K ) (4) t ( a d ST = (Reservoir is within-year) 1 ST 13 Where k d is dead storage (100000m 3 ). In case that evaporation and precipitation volumes are a function of surface area of the reservoir which, in turn, depends on the reservoir storage, one could incorporate the storage-area relationship in the optimization model. The storage-area relationship can be derived from conducting a topographical survey that determines the storage volume and surface area for a given elevation. For almost all reservoir sites, the relationship between storage volume and surface area is nonlinear. Therefore, the model represented by Eq. (2) is a nonlinear optimization model. The nonlinear storage-area relation can be approximated by a linear function (Eq. 1) to facilitate implementation of linear programming. Thus EV and PP can be simplified using the linear approximation: 1 - General Algebraic Modeling System 4

5 STt + STt + 1 EVt = et A0 + η (5) 2 STt + STt + 1 PPt = pt A0 + η (6) 2 Where p t and e t are the deterministic depths of precipitation and evaporation per unit area during period t, respectively. In this model QF t, IN t, SP t and R t (as a demand) are known parameters. The model was solved and the value of the objective function was computed. 4 Results The result of the model shows that the Ka is m 3. Meanwhile, the volumes of decision variables delivered (Table 8). Table 8- Results of model ST (1000*m 3 ) PP (1000*m 3 ) EV (1000*m 3 ) Reservoir operation curve for all month in a year was drawn. ST (1000*m 3 ) Reservoir oeration curve ST (1000*m3) Series O N D J F M A M J J A S Month 5

6 The above curve shows that in June, due to less demand, ST has the highest amount. 5 References 1. Louks, D. P. & Stedinger, J. R., and Halth, D. A. (1981). Water resource systems planning and analysis. Prentice-Hall Inc., Englewood cliffs, N. J. 2. Larry W. Mays & Yeou-Koung Tung. (1992) Hydrosystems engineering and management. McGraw-Hill, Inc. 3. Thomas, H. A. and Burden, R. P. (1963). Operation research in water quality Management. Harvard University, Cambridge, MA. 4. Ashnab Consulting Engineers, Hydrological report of Qeysereq reservoir. (2001). 5. Abbas Afshar, Miguel A. Marino, Ahmad Abrishamchi. (1991). Reservoir planning for Irrigation district. Water resources planning and management. 117(1). (PP.74-85). 6. Benedito P.F. Braga, William W-C. Yeh, Leonard Becker. (1991). Stochastic Optimization of multiple-reservoir system operation. Water resources planning and management. 117(4). (PP ). 7. C. Russ Philibrick, Jr and peter K. Kitandis. (1999). Limitations of deterministic Optimization applied to reservoir operation. Water resources planning and Management. 125(3). (PP ). 8. Eastman, J., (1973). Linear decision rule in reservoir management and design. 3. Direct Capacity determination and intrapersonal constraints. Water resources research. 9(1). (PP.29-42). 9. Hsu, N. and Kuo, J. (1995). Proposed daily stream flow-forecasting model for reservoir Operation. Water resources planning and management. 121(2). (PP ). 10. Jay R. Lund, Ines Ferreira. (1996). Operation rule optimization for Missouri river Reservoir system. Water resources planning and management. 124(1): Jain, S. K. (1999). Application of ANN for reservoir in flow predication and operation. Water resources planning and management. 125(5) (PP ). 6

7 12. Louks D. P. (1970). Some comments on linear decision rule and chance constraints. Water resources research. 11(6) (PP ). 13. Lound, J. R., and Guzman, J. (1999). Derived operating rules for reservoirs in series or in Parallel. Water resources planning and management. 125(3). (PP ). 14. Numan R. Mizyed, Jim C. Lofits, Darrell G. Fontane. (1992). Operation of large Multireservoir systems using optimal-control theory. Water resources planning And management. 118(4) (PP ). 15. Philip D. Crawley, Grame C. Dandy. (1993). Optimal operation of multiplereservoir System. Water resources planning and management. 119(1). (PP.1-17). 16. Revelle, C., (1969). The linear decision rule in reservoir management and design, 1, Development of the stochastic model. Water resources research. 5(4) (PP ). 17. Jason T.Needham & David W. Watkins. (2000) linear programming for flood control on the Iowa and Des Moines rivers. Water resources planning and management. 126(3) (PP ). 18. Adunias dos Santos Teixeira (2002). Coupled reservoir operation-irrigation Scheduling by dynamic programming. Irrigation and drainage engineering, 128(2). (PP.63-73). 6 Presentation of Author Mohammad Taghi Sattari is an instructor at Department of Irrigation, Tabriz University, Tabriz, Iran. His main fields of interest are Water resources management and Reservoir operation. 7