## 3 Simulation Results
### Description of the OpenDSS Model
First, each voltage matrix is concatenated from 78 \(\times\) 35,136 to 1 \(\times\) 2,740,608. The same is done also for negative-sequence unbalance factor (VUF\({}_{2}\)) and zero-sequence unbalance factor (VUF\({}_{0}\)). The obtained simulation results of case _C0_ are depicted in Figure 6. All phase voltages are depicted in Figure 6a and as it can be seen, the mean phase voltages are within the standard limits set by [30]. Furthermore, even the outliers (the red plus signs) do not reach the bottom limit of the standard voltage band. In Figure 6b, the negative- and zero-sequence voltage unbalance factors are presented. The simulation results show that the mean value of VUF\({}_{2}\) is lower than 0.2% while the outliers do not exceed 2%. The outliers of VUF\({}_{0}\) reach 2.8%; however, there is no limit for this parameter in the currently acting standard. Based on the obtained simulation results, it can be concluded that the loads are properly distributed across the feeders because there are no power quality problems in the LV grid. In Figure 7a, the phase voltages are depicted when no control is applied to all DERs whatsoever. Because of the high penetration level of DERs, severe overvoltages can be observed in all phases, which reach almost 1.17 p.u. The obtained simulation results of case _C2_ are presented in Figure 7b. The mean values and the maximum deviations of the phase voltages are more or less the same as the previous case; however, the maximum values, reached by the outliers, are limited to 1.105 p.u. The drooped three-phase positive-sequence control strategy performs active power drooping as function of the grid voltages and it is able to provide lower and safer rms voltage levels in all phases. Figure 7c shows that the maximum voltage deviations are slightly lower compared to case _C2_ but the outliers barely reach 1.08 p.u. in phase \(b\) while in the other two phases the maximum values are lower than 1.07 p.u. Figure 6: Concatenated results of the entire low-voltage (LV) grid when case _C0_ is examined. The obtained results of case 4 are presented in Figure 7d. In this case, only negative-sequence component mitigation is applied and as it can be seen, the maximum deviation of \(|\underline{v}_{b}|\) is slightly wider compared to case C3 and also the maximum outliers are slightly lower in phase \(b\). In Figure 8a-c, the drooped three-phase damping control strategy is examined with \(g_{d}\) values of 3, 10, and 50 p.u. The simulation results show that the mean values of the phase voltages are rather the same for all three cases but the outliers are better equalized when a higher damping conductance value of 50 p.u. is used. The negative- and zero-sequence voltage unbalance factors of cases C1 to C4 are depicted in Figure 9a-d, respectively. Although case C1 does not consider any control of all DERs and overvoltages are present in all phases, VUF2 is smaller than 2%, which means the power of the loads and DERs is more or less distributed equally among the three phases. As cases C1 to C3 do not impact the sequence components, the range of the maximum deviations are VUF2 = 0.6% and VUF0 = 0.7%. The outliers of VUF2 for these cases also do not exceed 2% and the outliers of VUF0 are all lower than 3%. Case C4 impacts only the negative sequences, and as it can be seen in Figure 9d, the mean value of VUF2 is decreased down to 0.12%, while in the previous cases these values were around 0.2%. The maximum deviations of the quartiles are also decreased down to 0.35%, while the outliers hardly exceed 1.6%. The obtained simulation results of VUF0 are the same as the previous cases. In Figure 10 the obtained simulation results for cases C5 to C7 are depicted. By increasing the damping conductance from 3 p.u. to 50 p.u. in cases C5 to C7, it can be seen that the mean values of both unbalance factors decrease as well as their maximum deviation ranges. The outliers are also decreased and barely exceed 1.8% in all cases. Figure 7: Concatenated voltage results of the entire LV grid when cases C1 to C4 are examined.