## 3 Simulation Results
### Description of the OpenDSS Model  
The grid is simulated in a time series manner by using OpenDSS that is interfaced with Matlab. The single line diagram of the grid is depicted in Figure 3 and as can be seen there are 78 nodes. The location of the DER, rated power, and phase connection are shown as well. The majority of DER is single-phase connected with rated power between 2 and 5 kWp. Since the physical area of the grid is small, it is assumed that all DERs have the same solar irradiation. The solar irradiation profiles, presented in Figure 5 are provided by [37] and used by all DERs. The examined period is one year with a 15 min basis between the samples. As mentioned above, the power of all DERs is chosen such that overvoltages occur at the end of the longest feeders. The simulations are performed with time series and the corresponding values of the vectors of the solar irradiation and the load profiles are simulated. Case \(C2\) represents the massively used positive-sequence control strategy with a variable PF as function of the active power and hard curtailment. Suppose that at some point nodes 54 to 52 experience overvoltages, then \(\text{DER}_{52}\) and \(\text{DER}_{54}\) will be turned off immediately for that time step and the simulation will move to the next step. This, however, will result in a large power curtailment, which actually may not happen in practice because of the discretisation of 15 min. In practice, \(\text{DER}_{54}\) will turn off before \(\text{DER}_{52}\), because it is further connected from the MV/LV transformer. This might be sufficient to prevent the overvoltages and it may not be necessary to turn off \(\text{DER}_{52}\) at all. In order to overcome this disadvantage of the time series simulations and prevent false overvoltage tripping, an internal loop is introduced. This internal loop is accessed only if an overvoltage problem occurs. In this loop, the set power is increased gradually to the maximum set point, which will trip the DERs one by one in case of overvoltages and not all at once. Thus a more realistic behavior of the model is achieved and the curtailed power will not be overestimated. Cases \(C3\) to \(C8\) use active power drooping as a function of the grid voltages, which requires a different approach to perform the power flow because OpenDSS does not have controllable DER strategies in its library. In [38], a four-step approach for implementing active power drooping in OpenDSS is proposed. In the first step, the normalized solar irradiation profile is multiplied with the rated power of the DERs as well as the load profiles. Then an asymmetrical power flow is performed in OpenDSS. In this step, the DERs do not droop any power, which will result in overvoltages. In the second step, the drooped power is calculated as a function of the grid voltages. As there is always  
Figure 5: Solar irradiance profile used in the simulation model [37]. some voltage unbalance present in the LV grid, the maximum among the phase voltages is chosen to calculate the injected power. In the third step, another power flow is ran with the new values of the drooped power. In the last step, a convergence check is performed based on predefined tolerance. The absolute error between the current values of the phase voltages and the previous values is made. If the result is lower that 0.023V the simulation continues with the next time series. If this is not the case, the simulation repeats step 2. More information about the droop implementation can be found in [12] and the developed simulation model in [38]. In the last reference, the proposed combination of OpenDSS and Matlab is also compared with a Matlab and Simulink model. The results show very good agreement between the two models. The total length of the solar and load vectors is 35,136 points while the node numbers are 78. This results in a matrix of 78 rows and 35,136 columns. In order to avoid unnecessary data and figures, a box plot will be used to represent some of the obtained simulation results.