# Compliance of Distribution System Reactive Flows with Transmission System Requirements
## 3 Case Study
### Results, Full Day  
Figure 10 depicts the average active power exchange with the transmission network for each hour of the day. The first seven hours belong to the third region (\(r=3\)) of Figure 1, i.e., reactive power export limit is \(Q_{D1}\). Hour 8 belongs to the second region (\(r=2\)), while the rest of the day belongs to the first region (\(r=1\)), see also Figure 11. The pattern indicates that the distribution network is importing power from the transmission system  
Figure 8: Evolution of the average reactive power exchange \(\hat{Q}_{1,r}\), and the corresponding import/export TSO requirement limits until time step \(\tau\) during the 8 th hour of the chosen day using the proposed method (Q:1—proposed), the QV droop (Q:1 QV droop) and the zero case (Q:1—zero case). Figure 9: Reactive power support from the DERs for each time step \(\tau\) during the 8 th hour of the chosen day and the corresponding voltage at one of the nodes with DER. until the 7 th hour, but it is apparent that load is low. As morning progresses, power from PVs is ramping up, and for the 8 th hour, the average power exchange is such that the average reactive power exchange limit is set in \(r=2\), where it is a linear function of the active power. Then, PV generation is ramping up more but wind power is temporarily reduced, see hours 9-11. However, the exchange is such that \(r=3\) limits are applied on reactive power exchange and stay as such for the rest of the day. From hour 12, wind power ramps up again and is added to the PV generation which fluctuates along with the natural irradiation levels of a summer day leading to a day with significant export of reactive power, especially around noon. Figure 11 illustrates how the average active power exchange of Figure 10 impacts the limits on reactive power along with the average reactive power under the zero case, i.e., no reactive power support from DERs. It is apparent that without support, the low load conditions lead to reactive power flowing from the distribution network to the transmission network, exceeding respective limits of each hour. Night hours are the worst in terms of violation, as due to the limits being in the 3 rd region (\(r=3\)), the reactive power export limit is stricter that the rest of the day. Figure 11: Reactive power exchange with the transmission system for the entire day when no reactive power support from DER is utilised (zero case). Figure 10: Active power exchange with the transmission system for the day under test in the case study. Figure 12 shows the reactive power exchange under the benchmark case of the QV droop curve. We see that violation of the exchange limit happens in considerably fewer hours than the zero case. However, one can observe that in the first seven hours no improvement occurs. This is due to low generation from both the WT and the PV, which in turns leads to minimal voltage raise and consequently no contribution by the QV droop. Additionally, the import limit is reached during hours of abundant WT and PV generation later in the day due to the significant voltage rise this large generation creates. Figure 13 illustrates the reactive power exchange when the proposed method is used. One can observe that the limits are respected for all hours. Compared to the benchmark, the method succeeds in addressing the limit violations during night hours. This is because it does not react to temporary and local information, such as the voltage at the DER nodes, in order to provide reactive power support. Instead, the control algorithm, having an overview of the entire system and the horizon, actively instructs the DERs to provide any available support in order to solve a remote (spatially and temporally) problem, such as the violation of the average reactive power export limits at the end of the hour. Moreover, it employs the minimum volume of reactive support, marginally keeping the system within limits.