Table 4-7. Discretized load duration of IEEE 34 bus test feeder 

15 candidate locations are selected. Each capacitor size was represented by a 3 bit gray code. For fixed and switched capacitor allocation problem, 50 kvar of compensation was assigned to be the lowest possible fixed capacitor size to be place at any location. 75 kvar was removed since it is neither a multiple of 50 nor all of the higher size of capacitors are multiple of 75. 

For 3 bit representation of capacitor sizes, 15 candidate locations and 4 discrete load levels, there will be 180 bit long of chromosomes. This is one manifestation that this case has a higher degree of complexity than test case 1. 

Parameters
To obtain better quality solution, we assign a population size of 360 (2L) individuals. Experimental results showed that exponential normalization of the fitness value performs better than linear normalization. By probabilistic point of view, for large population size, individuals with higher fitness value has approximately equal chances of being selected for mating since the linearly normalized fitness of one individual is only 1 point higher to the next individual` s fitness. A mutation probability of 1/360 or 0.00278 was also assigned.

Results
The program was again run for five trials, then we take the best among the five as the solution for this test case. The graph of the savings and summary of the five trials are shown in table 4-8. The running time of the program for each trial with 100 generations is around two and a half hours.

Table 4-8. Summary of the results of load flow after compensation for test case 2

Taking the best solution among the five trials and comparing it to the solution in test case 1, we observed that the maximum savings of the two cases are almost the same. The minimum bus voltage at peak load and maximum bus voltage at light load of IEEE 34 after compensation are 0.942 p.u. and 1.0 p.u., respectively

Test case 3
The third test case is the implementation of the proposed method on 13.2 kV, 166 bus rural electric distribution system, the Tarlac Electric Cooperative II or TARELCO II. Feeder 1 summary, system data and characteristics of the TARELCO II are given in [6,7]. The system losses of TARELCO II are very low and there is no need for capacitor compensation. Sarmiento [6] applied a 50% load growth for the sake of demonstrating his proposed method of optimal capacitor placement. Using the three-phase load flow, the initial condition of the system before compensation is given in table 5-13. The Ke, Kp, and Kc for this case are 1.6032 Pesos/kWh, 1,155.84 Pesos/kW/year and 75 Pesos/kVar/year, respectively. 

Table 4-9. System losses and minimum voltage of TARELCO II feeder-1 before compensation

GA parameters and representation in test case 2 was also used for this case. The program was run five times for 100 generations which takes around 14 hours for every run. The summary of the results is given in table 4-10.

Table 4-10. Summary of the results of load flow after compensation for test case 3.

Table 4-11. Optimal capacitor allocation for test case 3. 

The trial that outputs the highest savings (trial 1) out of the 5 trials was taken as the solution. The optimal allocation of balanced three-phase capacitor banks is given in table 4-11. The minimum bus voltage at peak load and maximum bus voltage at light load of TARELCO II after compensation are 0.944 p.u. and 1.0 p.u., respectively