# Compliance of Distribution System Reactive Flows with Transmission System Requirements
## 3 Case Study
### Results, Single Hour  
Before illustrating the overall performance of the proposed method for the entire day, we discuss details of the method by zooming in to a single hour. We choose the 8 th hour because it is located in the 2 nd (\(r=2\)) region of Figure 1. Figure 8 displays the evolution of the reactive power exchange limits during that hour. We see that we drift from the 3 rd region (\(r=3\)) (see in Figure 1 where the export limit is constant at \(Q_{d1}\)) to the 2 nd by the 8 th time step (see again Figure 1). When in the 2 nd region the export limit is a linear function of \(\overline{P}_{1,r}\), thus it is not constant regardless of \(\overline{P}_{1,r}\) (see how the straight line before time step 8--3 rd region--becomes a curve after that step--2 nd region). Note that the overall hour is defined by how the limits ended up at the last time step because at the end the average is that of the entire hour.  
The same figure shows the average reactive power exchange up until time step \(\tau\) for the zero, benchmark and the proposed case. Note that this is the current average, \(\hat{Q}_{1,\tau}\), and not the projected overall average \(\overline{Q}_{1,\tau}\) of the proposed model. We see that the proposed method anticipates the change in reactive power limits and achieves its control goal by the end of the control session. Note that it is not a problem that the limit appears to be violated for most of the control session, as the TSO requirements, and thus the method, only cares about the limit and the average reactive power exchange at the end of the hour.  
The QV droop also adapts to the change to some extent. It has no horizon so there is no reactive power exchange projection, \(\overline{Q}_{1,\tau}\), over the entire control session in the case of QV droop. There is only the current average in each time step, similar to \(\hat{Q}_{1,\tau}\). Although, the QV droop has only local scope, it reacts to overvoltage that occurs at node \(11\) due to large generation by the WT located there. However, the large WT generation is the reason the reactive power exchange limits drift. Therefore, the QV droop is partly effective in mitigating the issue. Finally, with no reactive power support from DERs (zero case) the TSO export limit is severely violated.  
Figure 7: Droop curve tested during studies for the Sundom pilot site, presented in [26].  
The two methods, the QV droop (benchmark) and the proposed, both decide on reactive power consumption (positive by convention here)/production (negative) that the DERs provide as support for the distribution network. Figure 9 illustrates the reactive power support (consumption in this case) by the WT under the two cases: QV droop and the proposed. We see that QV droop decides for zero support until the voltage at node 11 (where the WT is located) exceeds the droop activation limit of 1.0325 p.u. By contrast, the proposed method decides on a constant consumption of reactive power for the entire control session. Note that, as discussed in Section 2, this decision comes from the fact that we added a small penalty to the utilisation of reactive power by the method at each time step. This is done in order to force it to choose the solution with the least utilisation of reactive power among infinite equivalent solutions.