An optimization model for integrated water allocation in the parallel system of Segawe regulating weir and Wonorejo multipurpose dam, Tulungagung, East Java

The parallel system of Segawe Regulating Weir and Wonorejo Multipurpose Dam is one of waterworks in the Brantas river basin. Segawe Regulating Weir was built to divert its local inflow into Wonorejo Reservoir as well as to release certain amounts of water downstream needed for ecosystem maintenance and irrigation. On the other hand, Wonorejo Multipurpose Dam was built to serve for ecosystem maintenance, irrigation, domestic water supply and electricity generation. This research discusses an optimization model that integrates the purposes of the two river structures based on the release-demand ratio and by considering the priority constraints. The optimization model was used to derive the operating pattern under requirement for the initial condition of Wonorejo Reservoir in the first period must be the same as the final condition in the last period. The results show that the reliabilities of Segawe Regulating Weir and Wonorejo Multipurpose Dam for all the purposes can reach 100% in dry, normal and wet years, where the potential energies are 20.33, 22.45 and 24.16 GWh, respectively. However, the results come with some trade-offs in the release capability of each river structure due to the integration concept.


Introduction
Segawe Regulating Weir and Wonorejo Multipurpose Dam are two river structures located in Pagerwejo District, Tulungagung Regency, East Java Province, Indonesia, where the two structures stand in approximately parallel to each other in the Song river (7°59'46.90"S-111°49'11.63"E) and the Gondang river (8°1'11.87"S-111°48'18.91"E),respectively.The two river structures were built in 1994 to 2000 as one system and are now under the water resources management of Perusahaan Umum Jasa Tirta I (Jasa Tirta I Corporation) for irrigation, domestic water supply, flood control and electricity generation.In such parallel system, Segawe Regulating Weir releases some of the river flow downstream to irrigate three paddy fields, namely Blader, Kluwih and Gelang (PF Blader-Kluwih-Gelang), and discharges the remaining river flow through a connector tunnel to be stored in Wonorejo Reservoir.Meanwhile, Wonorejo Multipurpose Dam releases its storage to irrigate the Paingan paddy field (PF Paingan) and to supply domestic water to the City of Surabaya, which simultaneously generates the electricity with a maximum load of 6.5 MW to be fed into the electrical grid.
For irrigation and domestic water supply, the operation of Segawe Regulating Weir and Wonorejo Multipurpose Dam must comply with the operating pattern that consists of release rules in three conditions, namely dry, normal and wet years.The three release rules need to be derived from simulations of water allocation using a standard operating policy that applies the mass conservation IOP Publishing doi:10.1088/1755-1315/1343/1/012021 2 between inflow, storage and outflow [1][2][3].The simplest mechanism to allocate the water for each purpose is by focusing the potential release of the two river structures in any given period to satisfy all the demands.However, as this mechanism neglects the potential releases in subsquent periods, it tends to result in inefficient water allocation of Wonorejo Multipurpose Dam due to insufficient inflow and reservoir capacity.Optimization is therefore needed to accommodate the two river structures to satisfy the demands for irrigation and domestic water supply.This paper will discuss an optimization model that was developed to derive the operating pattern complying with all water allocation requirements in the parallel system of Segawe Regulating Weir and Wonorejo Multipurpose Dam.In addition, this paper will also discuss the method for hydropower analysis relevant to the operational guidelines of Wonorejo Multipurpose Dam [1].

Water Allocation Scheme
Segawe Regulating Weir and Wonorejo Multipurpose Dam along with other river structures are parts of watershed system of the Ngrowo river that feeds into the Brantas river as shown in Figure 1.The catchment area of Segawe Regulating Weir (87.6 km 2 ) is approximately twice greater than that of Wonorejo Multipurpose Dam (42.6 km 2 ), hence the connector tunnel discharge can be considered as the major inflow of Wonorejo Reservoir.However, especially for dry season, the first priority of Segawe Regulating Weir is to release the Song river flow for ecosystem maintenance (duty flow) and the PF Blader-Kluwih-Gelang irrigation (1,806 ha).The distribution of water released from Wonorejo Reservoir is managed by Tiudan Regulating Dam that has a maximum storage capacity of 0.792 MCM (million cubic meters).Before releasing its storage to the domestic supply canal, Tiudan Regulating Dam must first ensure that the water it will release downstream satisfies the demands for the Gondang river duty flow and is sufficient for the PF Paingan irrigation (551 ha).Wonorejo Reservoir capacity is divided into effective, conservation and inactive zones.The dam may release its storage for ecosystem maintenance, irrigation and domestic water supply when the reservoir is on the effective zone of which the low water level is 153 mMSL (meters above mean sea level).When the reservoir is on the conservation zone below 153 mMSL, the dam may release its storage to be prioritized for ecosystem maintenance and irrigation until the water level reaches the top of the inactive zone (141 mMSL).As shown in Figure 2, the power plant can efficiently generate electricity when the reservoir is on the effective zone and the penstock flow rate is in the range of 4.8 and 12.0 m 3 /s.In order to get a high efficiency, the power plant may generate electricity only at peak demand that can last for 10 hr/day, hence Wonorejo Multipurpose Dam may release its storage at the

Potential Release
It can first be noted that Segawe Regulating Weir may have a storage capacity; however, the storage capacity has always been neglected in the water allocation, since the connector tunnel inlet is actually an ogee-crested weir over which water would freely flow [1].Therefore, the potential release of Segawe Regulating Weir in this research was defined as the local inflow, I j S (m 3 /s), which was then divided into the downstream release and the connector tunnel discharge, I j T (MCM).The downstream release might include the Song river duty flow, R j SD , and the PF Blader-Kluwih-Gelang irrigation, R j IK .
In this case, the demand for the Song river duty flow, D j SD , was prioritized over R j IK , where if I j S ≥ D j SD , then R j SD = D j SD and R j IK ≤ I j S -R j SD , otherwise R j SD = I j S and R j IK = 0.
The potential release of Wonorejo Multipurpose Dam, V j (MCM), was determined using equation ( 1) and (2), where S j i , I j W , E j , S E min and d j are the initial storage, the local inflow, the reservoir evaporation, the minimum effective storage and the number of days in j-th period, respectively.
Similar to R j SD , the demand for the Gondang river duty flow, D j GD , was prioritized over the releases for the PF Paingan irrigation, R j IP , and domestic water supply, R j DS .In this case, if V j ≥ D j GD , then

Reservoir Final Condition
The basic of standard operating policy used in the simulation of Wonorejo Multipurpose Dam is the reservoir water balance as in equation ( 3) and (4).
Equation ( 3) states that the total change in the reservoir storage in one year must equal 0, while equation ( 4) states that total reservoir inflow in one year must equal the total outflow and evaporation.The two equations are the mass conservation form of the operating pattern requirement for the reservoir initial condition in the first period must be the same as the final condition in the last period [2,3].In this case, the final storage of Wonorejo Reservoir, S j f , and the reservoir spill, F j , in j-th period were determined according to the maximum effective storage, S max , as in equation ( 5) and ( 6).

Indicators
The reliability of each river structure was evaluated according to the k factors as in equation ( 8), where the reliability for the purpose p in one year, r p , was defined as the percentage of periods in which the k factors were greater than or equal to the minimum allowable k factor.The k factor itself is simply the release-demand ratio, k j p = R j p /D j p , that has been commonly used as a parameter in water resources management in Java [4].
In terms of priority, the purpose a was stated of being prioritized over or equally prioritized as the purpose b if the priority factor from equation ( 9), p j a:b , was greater than or equal to 1.
As if the purpose b should not be prioritized over the purpose a, p j a:b from the second alternative in equation ( 9) was essentially derived to prevent k j b from moving towards 1 unproportionately faster than k j a in the optimization.However, p j a:b from the equation itself would be undefined when k j a = 1, whereas the demand for the purpose a would be 100% satisfied.It was then simply decided that p j a:b = 1 if k j a = 1, since k j b would be insignificant when k j a = 1 as long as k j b ≤ 1.

Objective Function
The optimization model in this research was basically developed by combining the demands for irrigation of the PF Blader-Kluwih-Gelang and the PF Paingan into D j IKP as in equation (10).The objective function was then defined to maximize the total release from Segawe Regulating Weir and Wonorejo Multipurpose Dam for irrigation and domestic water supply as in equation ( 11), where the combined release for irrigation, R j IKP , was separated into R j IK and R j IP according to the respective demands as in equation ( 12).
It can already be noted that the main consequence from the application of this optimization model was R j IK and R j IP would be dependent on each other as in equation ( 13).

Constraints
The optimization constraints were defined on the basis of minimum values and can be categorized into the water allocation constraints and the Wonorejo Reservoir constraints.The water allocation constraints were defined as in equation ( 14) to (17).Equation ( 14) is the constraint for the downstream release from Segawe Regulating Weir, R j SD + R j IK , should not be greater than the local inflow.This is mainly due to a negative number of I j S -R j SD -R j IK would decrease the local inflow of Wonorejo Multipurpose Dam for the potential release as in equation ( 1) and (2).Equation (15) states that the releases for irrigation of the PF Blader-Kluwih-Gelang and the PF Paingan (IK and IP) as well as for domestic water supply (DS) should not be greater than the respective demands, while equation ( 16) states that the k factor of each purpose should not be less than the minimum allowable k factor.Equation ( 17) is the constraint for domestic water supply should not be prioritized over the PF Paingan irrigation as in equation ( 9).The reservoir constraints were specifically added in order to derive the rule curves in dry, normal and wet years that are suitable for Wonorejo Multipurpose Dam.These constraints were defined as in equation ( 18) to (21).and wet rule curves, respectively.The constraint in equation ( 18) was needed to satisfy the water balance of Wonorejo Reservoir as in equation ( 3) and (4).Equation ( 19) is the constraint for the dry rule curve should not be lower than the effective low water level shown in Figure 2. Equation ( 20) is the constraint for the normal rule curve should not be lower than the dry rule curve, and likewise equation ( 21).The absence of the constraints in equation ( 20) and ( 21) would likely result in intersecting rule curves that are practically unusual.

Load Time and Flow Rate
The turbine flow rate, Q j (m 3 /s), and the hydropower load time, t j (hr/day), were determined according to the total release of Wonorejo Multipurpose Dam as in equation ( 22) and ( 23), where Q max , t peak and Q min are the maximum allowable flow rate, the peak demand time and the minimum allowable flow rate, respectively.It can be noted that t j was derived from equation ( 23) as an integer.

Potential Power
The hydropower, P j (MW), was determined using the equation of gravitational potential energy as in equation ( 24), where ρ, g, H j net and η j are water density, gravitational acceleration, the net head and the efficiency in j-th period, respectively.H j net was determined by considering the major and minor head losses as in equation ( 25), where H j gross , f j , l, D h , k minor and v j are the gross head, the Darcy friction factor, the length of penstock, the inner diameter of penstock, the coefficient of minor head loss and the average flow velocity, respectively [5,6].
Since the water level of Wonorejo Reservoir may change over time, H j gross was defined as the average gross head from the initial and final conditions in j-th period.Meanwhile, f j depends on the Reynolds number, Re j = v j D h /ν, where ν is water kinematic viscosity.A penstock flow tends to have Re j ≥ 4,000 (turbulent flow), hence f j can be implicitly determined using the Colebrook-White equation in accordance with the penstock relative roughness, ε/D h , and Re j [5,6].In this research, f j was determined using the Vatankhah approximation as in equation ( 26) and (27) [7].

Data Used
In the same manner as the actual operation, the simulation of Segawe Regulating Weir and Wonorejo Multipurpose Dam was carried out on 10-day steps.The local inflow of each river structure in dry, normal and wet years were defined by exceedance probabilities (dependable inflows) of 65%, 50% and 35%, respectively [3].The inflow-duration curves in 36 periods for the weir and the dam were plotted from the data in 2006 to 2020 and 2002 to 2021, respectively.The exceedance probability of each inflow element was determined using the Weibull equation [8].
The zones division and the reservoir characteristic curves shown in Figure 2 were used in the simulation of Wonorejo Multipurpose Dam.The evaporation rates of Wonorejo Reservoir along with the demands for irrigation and domestic water supply in three cropping seasons (CS) are shown in

Results and Discussion
The programming in this research was done in Microsoft Excel and the optimization was performed with the help of Solver Add-in.As shown in Figure 4, the first step in performing the optimization was to determine initial values for the decision variables in equation ( 11).The initial values were then checked and fitted into the initial condition needed for Solver to run successfully, which can in general be related to the constraints in equation ( 14) to (21).It needs to be noted that when the method used is GRG Nonlinear or Evolutionary, Solver cannot guarantee that the solution it provides for the objective function will be the best one [9].Hence, even if the constraints had all been satisfied, the water allocation provided by Solver from an optimization was not simply regarded as the optimum solution without further consideration.
Originally, the main parameters considered in decision-making of optimum water allocations were the rule curves of Wonorejo Reservoir in dry season that can occur within May to November, j ∈ D. In this case, if the minimum difference between the water level of the rule curve in question (dry, normal or wet year) and the minimum allowable water level defined as in equation ( 19), (20) or (21) was greater than 0, min j∈D ൫Z j -Z j min ൯ > 0, the operating pattern was not regarded optimum and the optimization would continue until min j∈D ൫Z j -Z j min ൯ = 0.This was unless the demands for all the purposes were 100% satisfied, k j p = 1, as shown in Figure 4.The idea behind the decision-making of optimum water allocation was that if the operating pattern could be obtained with min j∈D ൫Z j -Z j min ൯ = 0 for the three rule curves, it can conceptually be the reference in the actual operation for the dam to soundly release its storage in dry season.Moreover, if the operating pattern was obtained with min j∈D ൫Z j -Z j min ൯ > 0, there must be some potential release left by considering that the lower the rule curve had to be, the greater the storage the dam had to release.However, as shown in Figure 5, min j∈D ൫Z j -Z j min ൯ = 0 could not be achieved for the wet rule curve due to the dependencies defined as in equation ( 13) and (17).Equation (17) states that the priority factor between the PF Paingan irrigation and domestic water supply should not be less than 1, p j IP:DS ≥ 1.As in equation ( 9), the constraint in equation ( 17 defined to prevent domestic water supply from being prioritized over the PF Paingan irrigation based on the given k factor (release-demand ratio) of each purpose, k j DS and k j IP , as well as on the minimum allowable k factors, by which the release for domestic water supply would be dependent on the release for the PF Paingan irrigation.Meanwhile, as in equation ( 13), the release for the PF Paingan irrigation was dependent on the release for the PF Blader-Kluwih-Gelang irrigation, where k j IP = k j IK .Such integration concept ensured that the water allocation in the parallel system of Segawe Regulating Weir and Wonorejo Multipurpose Dam would comply with the priority order, where the minimum allowable k factors for irrigation and domestic water supply adopted in this research were 0.70 and 0.85, respectively.For instance, if k j IK and k j IP were equal 0.70, then k j DS should not be greater than 0.85 in order to satisfy the priority constraint.Furthermore, if p j IP:DS = 1, then the increase in k j DS must be accompanied by the proportional increase in k j IK and k j IP .However, the integration concept based on the release-demand ratio could also result in inadequate release from Wonorejo Multipurpose Dam.
As shown in Figure 6 to 8, when the release for the PF Blader-Kluwih-Gelang irrigation could reach a certain k factor as the downstream release from Segawe Regulating Weir should not exceed the local inflow, the release for the PF Paingan irrigation would reach the same k factor and limit the release for domestic water supply to a certain k j DS .Particularly for the wet year in which p j IP:DS for all periods had reached the minimum value of 1, Wonorejo Multipurpose Dam must release its storage in the 1 st period of August to the 2 nd period of September less than it theoretically could, since the downstream release from Segawe Regulating Weir was equal to the local inflow.By comparison, the optimization model also guided Segawe Regulating Weir to decrease the release for the PF Blader-Kluwih-Gelang irrigation in the dry year and to supply the remaining local inflow to be stored in Wonorejo Reservoir.The dam reliability for domestic water supply could therefore reach 100% as in equation ( 8) and the priority order was not violated just as k j IK = k j IP and p j IP:DS ≥ 1.Although its potential energy was not considered in the objective function, the power plant of Wonorejo Multipurpose Dam assumes responsibility to feed one of the electrical grids in East Java at peak demand.As shown in Table 1, the optimization model could result in the potential energies of 20.00, 22.15 and 23.81 GWh in dry, normal and wet years, respectively, where the hydropower and the load time for each period are shown in Figure 8.

Improved Optimization Model
Particularly for the wet year, it can be observed in Figure 5 and 7 that the reservoir water balance as in equation ( 3) and (4) theoretically allows the spill of Wonorejo Reservoir in the 2 nd period of January to be released in the 1 st period of August to the 2 nd period of September.Hence, the inadequate release from the dam due to limited inflow of Segawe Regulating Weir in the 1 st period of August to the 2 nd period of September (Figure 6 and 8) may be regarded unnecessary.The optimization model can therefore be improved by rederiving the releases for the PF Blader-Kluwih-Gelang irrigation, R j IK , and the PF Paingan irrigation, R j IP , from equation (12) into equation ( 28) and (29), respectively.
When equation ( 12) is replaced by equation ( 28) and (29), Wonorejo Multipurpose Dam can still be integrated with Segawe Regulating Weir; however, it will not have to depend on the weir in a period where the release for the PF Blader-Kluwih-Gelang irrigation is equal to the potential release, I j S -R j SD .It can also be noted that equation ( 28) is equivalent to the constraint in equation ( 14), hence the constraint will be no longer needed when equation ( 28) is applied.The model improvement can be justified in order to maximize the releases for the PF Paingan irrigation and domestic water supply in

Figure 1 .
Figure 1.(a) Catchtments delineation of Segawe Regulating Weir and Wonorejo Multipurpose Dam; (b) Water allocation scheme in the parallel system of Segawe Regulating Weir and Wonorejo Multipurpose Dam.

Figure 3 .
The evaporation rates are the average values from the data in 2003 to 2006 and 2008 to 2015, while the demands for irrigaton and domestic water supply are the average values from the data in 2006 to 2021.All the data were obtained from Jasa Tirta I Corporation.

Figure 3 .
Figure 3. Evaporation rates of Wonorejo Reservoir along with demands for irrigation in the Blader-Kluwih-Gelang and Paingan paddy fields and for domestic water supply.

Figure 4 .
Figure 4. Optimization procedure for water allocation in the parallel system of Segawe Regulating Weir and Wonorejo Multipurpose Dam.

Figure 5 .
Figure 5. Optimized rule curves of Wonorejo Reservoir in dry, normal and wet years.
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I F Dec. Jan.Feb.Mar.Apr.May Jun.Jul.Aug. Sep.Oct.

Figure 6 .
Figure 6.Optimized water allocations in Segawe Regulating Weir in dry, normal and wet years.

Figure 7 .
Figure 7. Optimized water allocations in Wonorejo Multipurpose Dam in dry, normal and wet years.

Figure 8 .
Figure 8. Indicators of the optimized water allocations in the parallel system of Segawe Regulating Weir and Wonorejo Multipurpose Dam in dry, normal and wet years.

Table 1 .
Indicators recapitulation of the optimized water allocation in the parallel system of Segawe Regulating Weir and Wonorejo Multipurpose Dam in dry, normal and wet years.
a Minimum allowable k factor: 0.70 for irrigation; 0.85 for domestic water supply.