Competence-Oriented Decision Model for Optimizing the Operation of a Cascading Hydroelectric Power Reservoir

The operation of the four Perak cascading reservoirs namely, Temenggor, Bersia, Kenering and Chenderoh analyzed using the newly developed genetic algorithm model. The reservoirs are located in the state of Perak of Peninsular Malaysia that used for hydroelectric power generation and flood mitigation. The hydroelectric potential of the cascading scheme is 578 MW. However, the actual annual average generation was 228 MW, which is about 39% of the potential. The research aimed to improve the annual average hydroelectric power generation. The result of the fitness value used to select the optimal option from the test of eight model runs options. After repeated runs of the optimal option, the best model parameters are found. Therefore, optimality achieved at population size of 150, crossover probability of 0.75 and generation number of 60. The operation of GA model produced an additional of 12.17 MW per day. The additional power is found with the same total annual volume of release and similar natural inflow pattern. The additional hydroelectric power can worth over 22 million Ringgit Malaysia per year. In addition, it plays a significant role on the growing energy needs of the country.


INTRODUCTION
The real-world reservoir operation is very complex (Mousavi et al., 2004;Liu et al., 2011) and the application of operation rule in the case of cascade reservoirs that recapture the inflow is the most complex (Lund, 2000). Normally, the planning and the management of water in a reservoir systems ends with the optimization of the reservoir operation (Schumann, 1995). Therefore, different models and algorithms were developed to determine the reservoirs operation rules (Homayoun-Far et al., 2010) and the operation methods were presented as a form of a rule-curve. A rule-curve is a guideline for the long-term reservoir operation (Hormwichian et al., 2009). Hedging rule (Shiau, 2009;Tu et al., 2008), dynamic programming neural-network simplex model to developed the refill operation (Liu et al., 2006), an integrated rough set approach (Barbagallo et al., 2006) were some of the techniques that developed to operate the reservoir.
Genetic Algorithm (GA) is among the modern optimization technique applied in water resource planning and management. Cheng et al. (2008) mentioned that GA model has been widely applicable in water resource system optimization. The model also used to optimize a reservoir operation. For example, Mathur and Nikam (2009) used GA to optimize reservoir operation and the result showed that the model could perform efficiently if it applies in the real world   Reservoir  -----------------------------------------------------------------------------------Res-1  Res-2  Res-3  Res-4  Installed power capacity  MW  348  72  120  38  Storage capacity at maximum operating level  10 6 m 3  6050  70  345  operation of a reservoir. The research of Azamathulla et al. (2008) compared GA and linear programming in the operation of irrigation reservoir and it found that the performance of GA model was superior to the linear programming. In addition, Asfaw and Saiedi (2011) compared GA and excel optimization solver on the operation of a hydroelectric power reservoir, it showed that the result found from the GA model advanced in two ways: greater electricity generation and convenience in operation.
This research conducted on the operation of four cascading reservoirs that found along the Perak River of Peninsular Malaysia. As shown in Fig. 1, the river comprises Temenggor (Res-1), Bersia (Res-2), Kenering (Res-3) and Chenderoh (Res-4) reservoirs that found in cascade from upstream to downstream, respectively. In addition, Table 1 presented the details of the reservoirs. The largest storage capacity reservoir, Res-1 locates at most upstream side and then follows the smallest storage capacity, Res-2. The reservoirs are used for hydroelectric power generation and flood mitigation. The research aimed to maximize the annual hydroelectric power generation of the cascading scheme using the genetic algorithm. Therefore, analysis was made taking the hydroelectric power generation as the fundamental purpose and the flood mitigation as one of the constraint of the operation.

DETERMINATION OF INFLOW RATE
Depending on the relative position of the reservoir in the cascading system, inflow rate has two features. For the most upstream reservoir, the rate of inflow relies on the catchment characteristics and the hydrometeorological situations. However, in the case of the downstream reservoirs the major inflow takes place from the release of the preceding reservoir. The aggregate of the release from preceding reservoir and the direct (natural) inflow constitutes the total inflow to the reservoir. Direct (natural) inflow occurs from the catchment area that found between the reservoirs of interest to its immediate preceding ones.
Twenty years (1991-2010) data used to determine the rate of inflow to the most upstream reservoir. Figure  2 showed the average weekly long-term Historical Average (HA) inflow to the most upstream reservoir, Res-1. Furthermore, water balance equation used to equate the total inflow to the downstream reservoirs. The difference between total inflow and the release from preceding reservoir equal to direct (natural) inflow to the reservoir. The relationship expressed as: where, I it is the total inflow rate, Q it is the direct (natural) inflow rate to the reservoir i during the week t; whereas, R (i-1)t is the rate of release from the preceding reservoir during the week t. In all cases, the release from preceding reservoir joins to the next down reservoir within few hours. The maximum lag time occurs between Res-3 and Res-4, that is 7 h.

COMPUTATION OF STATE TRANSFORMATION EQUATION
where, S t = The storage volume Q t = The natural inflow F = The areal rainfall over the reservoir E = Open water evaporation A t = The average water surface area R t = The turbine release during the week t

OPTIMIZATION USING THE GENETIC ALGORITHM MODEL
The head of water and the rate of turbine release are the two major influential variables for the generation of a hydroelectric power. The weekly hydroelectric power generation from a reservoir is computed using: Although the annual hydroelectric power generation from the entire cascading system determined using the relationship of: In Eq. (3) and (4), P it is the hydroelectric power generation, R it is the rate of the turbine release and h it(net) is the effective head of water for reservoir i during the week t; η i is the overall efficiency for reservoir i, γ is unit weight of water, β i and λ i are the stage-storage relationship constants; whereas, a i and b i are the efficiency-stage relationship constants of the reservoir i.
An efficient optimization algorithm is depends on its searching ability for global optimum solution and its accuracy (Kuo et al., 2004). GA is an efficient tool for large-scale nonlinear optimization problems (Gallagher and Sambridge, 1994) and powerful in searching optimal strategy for multi-use reservoir operation (Chang et al., 2010). This research used the GA optimization technique to optimize the hydroelectric power generation of the Perak cascading scheme. The fitness function was to minimize the difference between the total potential (P pot ) and sum of actual generation capacities of the entire cascading schemes and it is expressed as: The constraints are related to the state transformation equation of the reservoir, the threshold value for flood release, the maximum and the minimum headrace level and the rate of release, the relationship between the cumulative turbine releases and inflow volume. Hence, the constraints are expressed as: where, R it = The rate of turbine release h ij = The headrace level F it = The areal rainfall E it = The rate of open water evaporation of the reservoir i for the week of t, k 1i and k 2i are the constants that depend on the stagestorage relationship and k 3i is the unit conversion factor. Analysis started from the most upstream reservoir that is from Res-1.
The developed GA model had 208 equality and 104 inequality constraint equations. Only eight GA run options analyzed since the other provided infeasible Initially, all runs options were tested using generation number of 50 and crossover probability of 0.8. As shown in Fig. 3, the fitness value was the major criteria of determine the optimal values of population size, crossover probability and generation number. The best GA run option has found after the repeated runs. The optimal value decided when the fitness value has no more improvement after the repeated runs. The stopping criterion of the iterations was the generation number.
Population Size (PS) is a critical parameter in GA, if it is too small the solution is poor or if it is too large it spends unnecessary computational resources (Lobo and Goldberg, 2004). Hence, the research used PS of 20 as the initial value. Consequently, the impact of PS was studied by randomly increase the value up to 1000. Likewise, the generation number examined between 20 and 200. Similarly, the test of the crossover probability analyzed between 0.60 and 0.95 with consideration of the fitness value.

RESULTS AND DISCUSSION
Optimal parameters of GA: among the eight GA run options, comparatively the result found from option 2 was optimal. The optimal run option used fitness scaling of rank, selection of uniform, crossover option of scattered and mutation option of constraint dependent. Based on the variation of the fitness function as shown in Fig. 4, the impact of the PS categorized into three groups: up to PS of 150, between PS of 150 and 300 and over PS of 300. The improvement of fitness value up to the PS of 150 was large, while between the PS of 150 and 300 an apparent change observed for only three options (Options 2, 6 and 8). Over PS of 300, the change of the fitness value was insignificant. Hence, the choice of optimal PS relied on between 150 and 300. Likewise, for the operation of reservoir using GA McMahon and Farmer (2009) obtained the optimal PS value in the range 64 to 300. However, this study adopted PS of 150 as an optimal value with consideration of the computational runtime.
As shown in Fig. 5a, the actual hydroelectric power generation continuously improving up to the generation number of 60, while after the PS of 100 the value was decreasing. The minimum fitness value attained at the generation number of 60. Therefore, optimal generation number was 60. Similarly, the test result of CRP as shown in Fig. 5b indicated that the optimal value achieved at 0.75.
The model achievement: the model decision on the energy-storage, the weekly rate of turbine release pattern and the hydroelectric power generation presented comparatively to the long-term Historical Average (HA) values. As shown in Fig. 6a, the weekly energy-storage at Res-1 using the GA provides higher than the HA. Hence, decision of GA maintained a higher head of water in each week of the year. In the other three downstream reservoirs, the maximum variation of headrace level was found 1.35, 1.15 and 1.07 m, respectively in the case of GA operation, while 0.23, 0.96 and 0.52 m of the HA at Res-2, Res-3 and Res-4, respectively. It showed that the annual variation of the energy-storage using the operation of HA had smaller variation than the GA. Figure 7 and Table 2 showed the weekly release pattern and its statistical analysis, respectively. The maximum release made by the operation of HA was greater than the corresponding GA, while the standard deviation of the weekly releases made by the GA was less than the HA. Only the release data of Res-3 positively skewed. It indicated that over 50 percent of the total operational period, the rate of the release was above the annual average. Furthermore, the GA release data at Res-2 had positively skewed and negative kurtosis. However, both values were close to zero (it means the data follow the normal distribution). As shown in, the HA power generation was 228.07 MW (39.46% of the potential); while, the operation of GA improved in to 240.24 MW (41.56% of the Fig. 7: Release decisions of the HA and the GA operations potential). Additional of 12.17 MW per day power found with the same annual volume of releases and inflow patterns. The economic benefit of the additional power evaluated with the consideration of the current energy price of Malaysia. The Tenaga Nasional Berhad (TNB), the major electricity utility of the country, classified the electricity tariff rate based on the type of customers and quantities of power utilized per the billing month. Accordingly, analysis was made taking the domestic customers that utilizes less than 200 kWh per the billing month. On this condition, the tariff rate per kWh is 0.218 Ringgit Malaysia. It is the least tariff rate of the utility. Taking transmission efficiency of 95%, the total benefit of the additional power became more than 22 million Ringgit Malaysia.

CONCLUSION
The sensitivity of the three most important GA parameters namely, PS, CRP and generation number were analyzed. The test results showed Table 3, optimality reached at PS of 150, CRP of 0.75 and generation number of 60. Similarly, Jothiprakash and Shanthi (2006) used GA for the optimization of a reservoir operation and optimality attained at PS of 150 and CRP of 0.76.
The comparison of the GA and HA showed that the weekly turbine release decision using the GA model had been smaller range and standard deviation than the HA. In addition, the entire period of the GA model operation at Res-1 provided higher headrace level than