## 2 Control Strategies Description
### Model Description
#### 2.6.2 Load and DERs Data  
The considered LV grid consists of 78 nodes, and to each node three different loads are connected. All loads are considered to be household loads and they are generated by using the methodology proposed in [36]. Overall, 200 different single-phase domestic load profiles are generated and grouped in clusters of three, which are connected to each node to a different phase. They are grouped such that the relative deviation between the loads, at any time instance, is minimum. These clusters are connected to the different nodes. By clustering the loads, the difference in the average power at each node is very low, which will help to limit and keep the voltage unbalance below 2%. In this article, all loads are assumed to have PF = 0.9. All loads are 15 min-based, and the sum of the apparent power of all loads is depicted in Figure 4. The load profiles are generated for one year, which gives a total of 35,136 values. In this article, 5 three-phase DERs and 14 single-phase DERs are considered to be connected in the LV grid. The rated active power and phase connections are presented in Table 1. The maximum power  
Figure 4: Aggregated load profile of all different single-phase load profiles. Figure 3: Feeder topology used to assess the performance the examined control strategies. of the considered DERs is selected such that power quality problems like overvoltages occur at the most distant locations of the feeders when maximum solar irradiation is available. Note that, this power selection is done when all DERs are equipped with the classical non-drooped positive-sequence and single-phase control strategies. Therefore, further installation of new DERs is no longer possible. DERs with nominal power higher than 5 kW are interfaced via three-phase connection and can perform voltage control via active power drooping (unless otherwise specified). All DERs with rated power lower than 5 kW are equipped with variable PF as a function of the injected power. In this particular case, the total installed peak power is 214 kW, which related to the nominal power of the MV/LV transformer gives a penetration level of 85%. Solar irradiation profile based on real measurements is used as an input for all DERs. The normalized solar irradiation profile that is used to perform the power flows is depicted in Figure 5.  
A few test cases are examined in order to compare the different results. The cases are defined as follows. * In the first case _C0_, the grid only consists of loads. * In the second case _C1_, all DERs inject their maximum power, and this case will be used as a reference case to check how much power is been curtailed or drooped. * In the next case _C2_, the classical hard curtailment is implemented together with voltage control based on reactive power exchange is in all DERs. Single-phase control strategy of this type is described in [12], while the three-phase positive-sequence control strategy is described in Section 2.3. More information about the implementation of the hard curtailment will be given later on in this section. * The combination of active power drooping together with the positive-sequence control strategy forms case _C3_ where only active power is considered to be drooped and injected. This control strategy is described in Sections 2.1 and 2.3. * The drooped three-phase damping control strategy, which mitigates only the negative-sequence voltage components is assigned to case _C4_. The drooped part is described in Section 2.1. The analytical description of the damping control strategy is given in Section 2.5. * Cases _C5_, _C6_, and _C7_ represent the modified three-phase drooped damping control strategy with initial damping conductance values of \(g_{d}=3\) p.u. \(g_{d}=10\) p.u., and \(g_{d}=50\) p.u., respectively. In order to compare the difference in damping capabilities and power quality performance between test cases _C4_ and _C7_, the value of \(g_{d2}\) is chosen to be equal to 50 p.u., similarly to case _C7_.