## 3 Simulation Results
### Description of the OpenDSS Model
The total amount of injected energy by all DERs is presented in Figure 11. Case _C1_ injects all available power and no control is applied whatsoever. The total injected power by this case is 248 MWh, which will be used as a reference for the other cases. The reactive power voltage support and hard active power curtailment allow Case C2 to inject a total of 218.3 MWh/a. By using different colors, a segregation of the injected energy per DER is presented. In Case C2, some of the single-phase connected DERs are curtailed and also DER\({}_{24}\) and DER\({}_{52}\). When the three-phase positive-sequence control strategy is used, DER\({}_{24}\) droops slightly more energy compared to case C2, while DER\({}_{52}\) injects almost twice the energy compared with the same case. In addition, none of the single-phase DERs is subjected to hard curtailment. Overall, in case _C3_ total of 219.5 MWh/a are injected which is 1.2 MWh/a more compared to case C2. The negative-sequence voltage component mitigation is assigned to case C4. The annual injected energy by this case is 220 MWh, which is slightly more compared to the previous cases. This control strategy considered an initial value of the \(g_{d2}=50\) p.u. Although such a high value of the damping conductance is used, the injected energy is lower compared to the modified damping control strategy with initial value of \(g_{d}=3\) p.u. (case _C5_). In this case, total of 224.7 MWh/a are injected, which is 2.7 MWh/a more compared to case _C4_. Cases _C6_ and _C7_ represent the modified damping control strategy with initial values of the damping conductance 10 and 50 p.u., respectively. The difference between these cases in terms of annual energy exchange is very small--231.1 MWh and 231.3 MWh, respectively. Despite the fact that cases _C4_ and _C7_ use the same value of the damping conductance, impacting the zero-sequence component results in less energy drooping. A common trend in all active power drooping control strategies is that with increasing the damping conductance, the injected energy by DER\({}_{24}\) and DER\({}_{52}\) gradually increases. Almost no energy  
Figure 8: Concatenated voltage results of the entire LV grid when cases _C5_ to _C7_ are examined. is drooped by \(\text{DER}_{59}\) and \(\text{DER}_{70}\) because the penetration level of renewables in their feeders is very low and no power quality issues are observed. Figure 10: Concatenated VUFs results of the entire LV grid when cases \(C5\) to \(C7\) are examined. Figure 9: Concatenated VUFsresults of the entire LV grid when cases \(C1\) to \(C4\) are examined. The aggregated energy losses in all feeders are presented in Figure 12. Case _C0_ considers only loads and it leads to losses of 8.26 MWh/a. When DER inject all available power (_C1_) the losses are doubled and reach 16.52 MWh/a. In case C2, some active power is curtailed which reduces the losses to 12.4 MWh/a. The drooped positive-sequence control strategy does not inject any reactive power which leads to lower losses (10.57 MWh/a) compared to C2. In case _C4_, the negative-sequence component mitigation leads to slightly more losses (10.7 MWh/a) compared to _C3_. Since both cases do not impact the zero-sequence component, the only reason for the loss increase is the higher energy injection of 1.2 MWh/a compared to case _C3_. The modified three-phase damping control strategy with \(g_{d}\) values of 3 p.u., 10 p.u. and 50 p.u. is represented by cases _C5_, 6 and _C7_, respectively. These cases lead to losses of 9.83 MWh/a, 9.64 MWh/a and 9.59 MWh/a, respectively. This is a grid performance improvement between 2.57 MWh/a and 2.81 MWh/a compared to case C3. From the presented case studies it can be seen that even the drooped positive-sequence control strategy has a better performance compared to the hard active power curtailment with reactive  
Figure 11: Total annual injected power by DERs when different control strategies are applied.