**4. Results**

The OCBA problem was solved using the metaheuristics presented in Section 2, with the aim of comparing the performance of the newer algorithm designs, BOA, WOA, and SWA against the two well established methods, GA and PSO. For comparison purposes, all the algorithms had a common representation for the members of the population, illustrated in Figure 9, and the same fitness function, active power and energy loss minimization, computed with Equation (19) and subjected to the constraints given by Equations (20) to (23), Section 3. The initial parameters used for the algorithms are presented in Table 3.

Since for all algorithms there was no improvement for the optimal solution beyond generation 350, the graphical representations of the results will be limited to the first 360 generations.

Two test networks were used to validate the comparison: the smaller sized IEEE 33-bus MV radial voltage distribution system (Figure 11) and a larger 215-bus MV EDN from a residential area of a major city from Romania (Figure 12).

Synthetic data regarding the physical characteristics for the IEEE 33-bus system is given in Table 4. The system does not include MV/LV transformer data; thus, the active power losses computed by the algorithms do not include transformer losses. The extended data regarding branch characteristics (connecting buses, type line or transformer, electrical parameters resistance and reactance, maximum branch current) is provided in Appendix A, Table A1. For the active and reactive bus loads, the study uses a custom representation consisting of daily 24-h profiles, described below.

For this particular test system, the literature provides only a set of instantaneous active and reactive bus loads. In this paper, these values were used as reference, in conjunction with a set of typical load profiles (TLP) provided in the Supplementary Materials attached to the paper, to create 24-h profiles. The TLPs considered several types of loads, residential, industrial, and their distribution in the network is summarized in Table 5.


**Table 3.** The initial parameters used for the metaheuristic algorithms.

**Figure 11.** The IEEE 33-bus test system.

**Figure 12.** The residential 215-bus EDN.



(1) Only the total resistance and reactance is known for each branch



The second test system used in the case study is a much larger EDN, consisting of 135 MV buses to which 80 loads are connected through MV/LV transformers. For simplicity, the transformers are omitted in Figure 12, together with the corresponding 80 bus numbers for the transformer LV busbars (from 136 to 215). A summary of the transformer rated power, together with the feeder and bus general information, is given in Table 6. The electrical parameters of the branches are given in Appendix A, Table A2. For this network, the bus loads were also modelled as 24-h daily profiles, being measured by the smart metering infrastructure installed by the local distribution utility for a typical working day.


**Table 6.** The physical characteristics of the 215-bus EDN.

Because a 24-h voltage profile was not available for the 215-bus network, the voltage reference for the slack bus was recommended by the distribution utility at the value of 1.06 pu. For the IEEE 33-bus system, the setpoint was 1 pu (nominal voltage). The slack bus for both networks is bus 1, and all the other buses are modeled as PQ (consumer) buses.
