*4.1. Results for the IEEE 33-Bus System*

The first step of the study was the choice of the maximum CB stock used for optimization. For this purpose, the load profile of the network for 24 h, given in Figure 13, was analyzed. Since the purpose was to test the performance of each algorithm, the CB stock was set at 70 × 7.5 kVar units, which would ensure a maximum of 525 kVar of VAR compensation, about half of the minimal value of the reactive load, occurring at night hours. In this way, the number of possible CB allocation variants is maximized, while reducing the investment cost.

**Figure 13.** The active and reactive load profiles of the IEEE 33-bus test system—hourly values.

The GA, PSO, BOA, WOA, and SWA were run using this CB stock, the initial parameters from Table 3, and the same initial population. The solution identified by each algorithm, compared with the reference case (no reactive power compensation), and their corresponding fitness functions (percent losses) are presented in Table 7. The first line of Table 7 also presents the maximum number of CBs that can be allocated in each bus, computed according to the minimal reactive power load, so that constraint Cr2 would be always fulfilled. The same results are displayed graphically in Figure 14. In Figure 15, the parallel evolution of the fitness function of each algorithm over the first 350 generations is presented, on a typical run, emphasizing the fact that the SWA and BOA obtain the solutions corresponding to the lowest loss values, followed by the PSO, GA, and BAT.


### *Energies* **2019** , *12*, 4239

*Energies* **2019**, *12*, 4239

**Figure 14.** The number of CBs allocated in the buses of the IEEE 33-bus system by each algorithm.

**Figure 15.** The fitness of the optimal solution found by the metaheuristic algorithms after 360 iterations, for the IEEE 33-bus system.

The results from Table 7 and Figure 14 show that the best fitness function values are obtained when maximum compensation is applied at buses 18 (feeder end), 29–32 (feeder end), and 12–14, while for other buses with compensation potential, such as 21–25, where the reactive load is high, no capacitor banks are allocated. All the algorithms use the entire CB stock available, with differences in the buses chosen for compensation and number of CBs allocated to each bus.

The results regarding the active power losses, for each hour and algorithm, compared with the reference case are plotted in Figure 16 and presented in Table 8. Table 9 gives the loss reduction in percent, against the reference case, for which the total values are represented in Figure 17. The loss reduction ranges between 6.55% and 16.78%, depending on the algorithm and network load. The improvement is higher in off-peak hours, and the best results are obtained with SWA (8.17% to 16.78%), with a global value of 10.51% over 24 h. PSO, WOA, and SWA are the closest to the optimal solution.

**Figure 16.** Hourly active power losses in the IEEE 33-bus system, for each algorithm.


**Table 8.** Hourly and total active power losses in the IEEE 33-bus system, in kW, for each algorithm.


**Table 9.** Hourly and total power loss reduction in the IEEE 33-bus system, in %, for each algorithm.

**Figure 17.** The total active power loss reduction in the IEEE 33-bus system, in kW, for each algorithm.

Compared with the reference case, the best compensation solution found by the SWA leads to a loss reduction of 726.73 kW for the analyzed day, which, if it is extrapolated for a year, amounts to 265.26 MW loss saving. The difference between SWA and the second best result, given by WOA, is of 6.25 kW per day or 2.28 MW for an entire year. As Figure 16 shows, SWA achieves these savings mainly during two hours, at 19.00 and 24.00.

Reactive power compensation with capacitor banks is mainly used in EDN for voltage profile improvement, where specific networks configurations and load patterns lead to high voltage drops along the feeders. In the case of the IEEE 33-bus system, the nominal voltage setting for the slack bus and the load profiles from Appendix A lead, in the reference case without compensation, to the voltage profile described by Figure 18.

**Figure 18.** The bus voltages in the IEEE 33-bus system without compensation, for each hour from the analyzed day.

The values show voltage drops that exceed the lower limit of –10% prescribed by the Romanian standards, in several buses located near the end of the main two supply paths, ending in buses 18 and 33. For bus 18, the voltage has the minimum value of 0.858 pu, at hours 19.00 and 20.00, while for bus 33, the minimum voltage is 0.882 pu, at hour 10.00.

The improvement of the voltages obtained hourly with each algorithm is depicted in Figure 19 for bus 18 and in Figure 20 for bus 33. The percent improvements over the reference values (no compensation) are given in Tables 10 and 11, respectively. Again, the SWA gives the best results, with the maximum voltage improvement. The minimum reference voltage value of 0.858 pu in bus 18 (hour 10.00) is raised by 1.65%, to 0.872 pu. However, the voltages remain below the 0.9 pu minimum allowed limit, for 10 h from the 24-h analysis interval. Better voltage regulation can be possible using a larger CB stock or raising the voltage in the reference bus, by changing the HV/MV transformer tap position from the substation at bus 1.

**Figure 19.** Voltage improvement after compensation for bus 18, the IEEE 33-bus system.

**Figure 20.** Voltage improvement after compensation for bus 33, the IEEE 33-bus system.

**Table 10.** Hourly reference voltage values for bus 18 and percent improvements after compensation, the IEEE 33-bus test system.



**Table 11.** Hourly reference voltage values for bus 33 and percent improvements after compensation, the IEEE 33-bus test system.

The voltage improvements are smaller for bus 33, with a maximum of 1.28% with the SWA, but with three algorithms (SWA, PSO and WOA), the voltage levels are raised after compensation above the maximum –10% deviation allowed by the regulations during 7 h (8.00, 9.00, 12.00, 13.00, 18.00, 19.00, and 20.00), only two hours remaining below this threshold (10.00 and 11.00), as it can be seen in Figure 20.
