*4.2. Results for the 215-Bus Distribution Network*

In this case, the CB stock used for compensation was chosen using the 24-h load profile of the network from Figure 21. In comparison with the IEEE 33-bus system, the minimum off-peak reactive load is reduced, while the number of buses available for compensation increases significantly, allowing a higher number of possible solutions. Thus, the CB stock was set at 90 units of 7.5 kVar each, providing a maximum of 675 kVar of reactive power. As the solutions from Figure 22 and Table 12 show, all the algorithms use the entire stock, with different bus allocation. The SWA provides the best solution (6.19% active power losses), followed by the PSO (6.21%). In Table 12, since the VAR compensation is performed at the LV side of the substation transformers, the bus numbers are given for both the MV buses denoted in Figure 12, and for their corresponding LV transformer busbars. In Figure 22, only the LV bus numbers are used, for better readability. Figure 23 presents the evolution of the fitness function of each metaheuristic algorithm over the first 360 generations, on a typical run.

**Figure 21.** The active and reactive load profiles of the 215-bus network—hourly values.

**Figure 22.** The number of CBs allocated in the buses of the 215-bus network by each algorithm: (**a**)—buses 136-175, (**b**)—buses 176-215.

For this network, as Figure 22 shows, the best two solutions (SWA, PSO) are mainly differentiated by the CB allocation at buses 151, LV side (28, MV side); 153 (31); 155 (34); 156 (35); and 157 (36), located at the beginning of the network, and having significant reactive power loads. This behavior is triggered by the use of the 90 CB stock, which is close to the maximum possible number of CBs that can be allocated for compensation, 107, and because of the sufficient stock, most of the buses can use the maximum possible CB allocation.

The comparison between the hourly active power losses computed by the Newton–Raphson algorithm for the reference case (no compensation) and the losses determined for each best compensation solution found by the metaheuristic algorithms is presented in Table 13 and Figure 24. Furthermore, Table 14 gives the percent reduction in losses obtained using the compensation solutions, while Figure 25 allows for an overview of the total losses obtained in each case, based on the values computed in Table 13.



**Figure 23.** The fitness of the optimal solution found by the metaheuristic algorithms after 360 iterations, for the 215-bus network.


**Table 13.** Hourly and total active power losses in the 215-bus network, in kW, for each algorithm.

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

**Figure 24.** Hourly active power losses in the IEEE 33-bus system, for each algorithm.


**Table 14.** Hourly and total power loss reduction in the 215-bus network, in %, for each algorithm.

**Figure 25.** The total active power loss reduction in the 215-bus network, in kW, for each algorithm.

The best CB allocation solution, obtained with the SWA, achieves a loss reduction of 833.91 kW or 10.36% for the entire network, in 24 h, which amounts to 304.38 MW in an entire year. The next best solution, found with the PSO algorithm, achieves only 816.58 kW (10.15%). The difference between the two solutions is of 17.33 kW in the analyzed day, or 6.32 MW in a year. The improvement over the IEEE 33-bus system regarding the loss reduction can be attributed to the presence of the MV/LV transformers.

The bus voltage levels for all 24 h and buses from the 215-bus network are presented in Figure 26. The length of the main feeder and the bus loadings lead to low voltage levels at the last buses on the main supply path, with values below the 0.9 pu limit at the LV side. At the MV side, the voltages are inside the allowed range, varying from 1.060 pu in the slack bus to 0.940 pu.

**Figure 26.** The bus voltages in the 215-bus network without compensation, for each hour from the analyzed day.

Figures 27 and 28 depict the effect of VAR compensation on the voltages at bus 135 (MV) and 215 (LV). By allocating the available CB stock according to the solutions found by the five metaheuristic algorithms, the bus voltages increase with maximum 1.36%, as shown in Table 15 for bus 215 (LV). This increase is not sufficient for raising the lowest voltage values above the desired limit of 0.9 pu. Since the CB stock is near the maximum allowed reactive load compensation which fulfills constraint Cr2 specified by the optimization model, an alternative solution is to change the MV/LV transformer tap settings in the affected buses.

**Figure 27.** Voltage improvement after compensation for bus 135, medium voltage, the 215-bus network.

**Figure 28.** Voltage improvement after compensation for bus 215, low voltage, the 215-bus network.


**Table 15.** Hourly reference voltage values for bus 215 and percent improvements after compensation, the 215-bus network.
