## 3 Comparison of Different Control Strategies in a Test Feeder
Figure 11: Schematic presentation of the power flows when \(Q(U)\) is applied: (**a**) the active and reactive power flows supplied by the PV inverters; (**b**) \(Q(U)\) characteristic set by all of the inverters. Figure 12: Schematic presentation of the active and reactive power flows when \(L(U)\) is applied. Figure 14 depicts the particular impact of the injected active power, the absorbed reactive power caused by different control strategies, and the impact of their combination on the shape of the voltage profile. The \(P\)-impact curve shows that the distributed active power injection along the feeder continuously increases the voltage on it to reach the maximum value at its end. \(Q(U)\) and \(L(U)\) impact the shape of the voltage profile as in the theoretical case discussed above. The combined \(P\) and \(Q(U)\) increases the voltage by keeping it well below the upper limit, whereas the combined \(P\) and \(L(U)\) increases the voltage more by keeping it just below the upper limit. Figure 15 shows the amplitude of voltage drop, \(\mid\Delta U\mid\), in each feeder segment caused by \(P_{inv}\), distributed \(Q(U)\), and concentrated \(L(U)\) control strategies. The \(\mid\Delta U\mid\) caused by \(P_{inv}\) reaches the maximal value at the feeder beginning, fs20. The \(\mid\Delta U\mid\) caused by the distributed \(Q(U)\) shapes as in the theoretical case discussed above. In both cases, \(\mid\Delta U\mid\) steadily decreases to reach the minimum value at the feeder-end-bus, fs1. Whereas, the \(\mid\Delta U\mid\) caused by the concentrated \(L(U)\) shapes differently from the theoretical case shown in Figure 7. The \(\mid\Delta U\mid\) is not equal in all of the feeder segments. It is slightly increased at the beginning of the feeder, then begins to diminish up to the middle and further remains almost constant. The reason of the increase is the reactive loss, \(\Delta Q_{c}\) = 15.29 kvar (see Table 1), which is neglected in the theoretical case. \(\Delta Q_{c}\) is about 42% of \(Q_{c}^{ex}\). Figure 14: The particular impact of the injected active power, the absorbed reactive power caused by the different control strategies, and the impact of their combination on the shape of the voltage profile. Figure 15: The amplitude of voltage drop in every feeder segment caused by distributed active power, an injection of PV facilities, \(P_{inv}\), distributed \(Q(U)\), and concentrated \(L(U)\) control strategies. Table 1 shows the reactive power consumption, loss, and \(Q^{ex}\) for different control strategies. Meanwhile, Figure 16 presents a graphical overview of the consumed reactive power flows and \(Q^{ex}\) for the distributed \(Q(U)\) and concentrated \(L(U)\) control strategies. All of the inverters together consume more reactive power than the concentrated coil: 34.52 kvar and 22.77 kvar, respectively. Also, reactive power loss is higher for the distributed \(Q(U)\) local control strategy, 16.55 kvar, than for the concentrated \(L(U)\) local control strategy, 15.29 kvar. For the distributed control strategy, \(Q^{ex}\) is calculated by:  
\[Q^{ex}_{d}=\sum_{i=1}^{m}Q_{inv}(i)+\Delta Q_{d}, \tag{21}\]  
where \(Q^{ex}_{d}\)--reactive power exchange with distributed \(Q(U)\) control strategy; \(Q_{\text{inv}}(i)\)--reactive power consumption of the inverter \(I\); \(n\)--number of inverters; \(\Delta Q_{d}\)--feeder reactive power losses with the distributed \(Q(U)\) control strategy, and for the concentrated one by:  
\[Q^{ex}_{c}=Q_{c}+\Delta Q_{c}, \tag{22}\]  
where \(Q^{ex}_{c}\)--reactive power exchange with concentrated \(L(U)\) control strategy; \(Q_{c}\)--coil reactive power consumption; \(\Delta Q_{c}\)--feeder reactive power losses with the concentrated \(L(U)\) control strategy. Simulations have shown that to achieve the same voltage target at the end of the simulated test feeder, the \(Q^{ex}_{c}=38.06\) kvar caused by \(L(U)\) is about 26% smaller than the \(Q^{ex}_{d}=51.07\) kvar caused by \(Q(U)\).