## 3 Comparison of Different Control Strategies in a Test Feeder  
To validate the conclusions drawn from the theoretical calculations, simulations are performed in a test network using PSS SINCAL. Figure 10 depicts the equivalent circuit of a LV feeder with \(n=20\), where 20 households are connected. An overhead line with \(R^{\prime}=0.3264\)\(\Omega/\)km and \(X^{\prime}=0.3557\)\(\Omega/\)km is simulated, whereby each feeder segment is 0.1 km long. To investigate the effects of different control strategies on the feeder behavior, it is assumed that the prosumers do not have their own consumption (\(P_{load}=Q_{load}=0\)). The largest possible PV penetration is simulated by installing a 5.0-kWp PV facility on each house roof. The \(Q(U)\) control is applied on each PV inverter, or only the \(L(U)\) control is applied at the end of the feeder. Figure 11 shows a schematic presentation of the power flows when \(Q(U)\) is applied. Figure 11a presents the active and reactive power flows supplied by the PV inverters as red and blue colored, respectively. Each PV facility injects its peak active power \(P_{inv}=5\) kW into the grid. The active power flow at the feeder beginning is defined by the number of PV facilities, their production \(P_{inv}\), and feeder loss, \(\Delta P_{d}\). The latter modifies the active power flows at the feeder beginning. Each inverter consumes reactive power; \(Q_{inv}\) conforms with its \(Q(U)\) characteristic, as shown in Figure 11b. They are over-dimensioned by a factor of 1:0.9 to enable reactive power support with \(\cos(\varphi)=0.9\) also during peak active power production. The main goal of using \(Q(U)\) local control is the elimination of violations of upper voltage limit. Normally, the dead band of the characteristic and the slope gradient are defined to cause minimal losses and reactive flow by avoiding oscillations [21]. Since in our case the simulated feeder is about two kilometers long, the dead band of the characteristic is set as narrow to eliminate all of the voltage violations [25]. The reactive power flow at the beginning of the feeder--i.e., \(Q^{ex}\)--is defined by the number of PV facilities, their individual \(Q(i)\) production, and the feeder loss \(\Delta Q_{d}\). Figure 10: Equivalent circuit of an LV feeder where the distributed \(Q(U)\) or concentrated \(L(U)\) local control strategies can be applied. Figure 9: The impact of the distributed and concentrated var-sink cases on voltage profile. Figure 12 depicts a schematic presentation of the active and reactive power when the concentrated \(L(U)\) local control strategy is exercised. \(L(U)\) is modeled as a variable inductance that is connected when the \(U_{set-point}\) is exceeded. Both active and reactive feeder loss, \(\Delta P_{c}\) and \(\Delta Q_{c}\), respectively, increase the power flows at the beginning of the feeder. The reactive power consumption of the sink (coil) is set at the feeder end, and the feeder loss \(\Delta Q_{c}\) defines the reactive power flow at the feeder beginning. In the following, the influence of active and reactive power on the voltage profile is analyzed in detail. Figure 13 presents the voltage profiles for different control strategies. When no control is applied, \(P_{inv}\) provokes the violation of the upper voltage limit. The voltage violation begins at node 15 (0.6 km from the feeder head bus) and reaches 8.85% at the feeder-end-bus (node 1, \(U(1)\) = 271.06 V). The use of the \(Q(U)\) or \(L(U)\) control strategy eliminates all of the voltage violations and stabilizes the voltage at the feeder-end-bus at 1.08 p.u. In both cases, the voltage profile shows a concave behavior, but the concavity caused by the \(Q(U)\) control is weaker than the one caused by the \(L(U)\) control strategy. As well as the theoretical results, \(Q(U)\) achieves lower voltage profile values than the \(L(U)\) control. This is because the control strategy \(Q(U)\) causes higher reactive power consumption than \(L(U)\). This behavior is discussed in detail below.