# Optimal Coordination of PV Active Power Curtailment and EVs Charging among Aggregators
## 5 Results and Discussion  
This section presents and analyses the results obtained by employing the proposed coordination strategy among two aggregators considering two different penetration levels of PVs and EVs. Figure 1 shows the statistical daily power generation for a 5 kW single-phase PV system with a 10 min resolution interval as a result of the model in Section 2.1. Based on these outcomes, the PV power output of each end user within the \(k\)th aggregator is randomly generated based on the mean and standard deviation value at each time step from the above figure. Then, the resulting PV power profiles are aggregated using Equation (1). For the aggregation of EVs, Figure 2 compares the upper power boundaries, the maximum charging power \((P_{ch}^{max})\), the overloading conditions \((OL_{k})\) and the optimal charging power \((P_{k}^{EV})\) from both aggregators as a result of the proposed optimisation problem. Figure 2a-c show that the power needs from both aggregators are met thanks to the delay in the charging process and the dynamic adjustment of \(\Delta_{k}^{P}\). However, in Figure 2c, it can be seen that the second aggregator surpasses the remaining capacity of its feeder in order to fulfill its charging requirements. Although it seems to occur for an extended period (16:00 to 22:00), in reality, the overloading condition only occurs discontinuously from 20:00 to 22:00 because this situation is analysed from the point of view of the net power on the feeder. For each aggregator, Figures 3 and 4 depict how the energy supplied to their EVs evolves between their aggregated energy boundaries as a result of the optimal charging profile for both penetration levels. This means that a total of 324 kWh and 446 kWh were delivered by combining the network  
Figure 1: Box plot of a 5 kW PV inverter: output power derived from yearly meteorological data using the model in Section 2.1. Figure 2: Optimal charging profile for a moderate and critical penetration level: (**a,b**) aggregator 1 and (**c,d**) aggregator 2. In terms of energy, this means to export 415 kWh and 460 kWh to the network and self-consuming 536 kWh and 648 kWh, respectively. Nonetheless, for complete PV penetration, an average export limit of 99% and 94% for aggregator 1 and 2 were found, respectively. This means an aggregated curtailment of 36 kWh and 250 kWh for aggregator 1 and 2, respectively. The results show that, as expected, the larger the aggregation of PV, the more reverse power flow and, hence, the lower the average value of \(\zeta\). As the power demand increases by the EVs charging power at midday, the PV power curtailment is lower thanks to the self-consumption capability. The total net power through the distribution transformer and the main cables of the feeders for both PL is presented in Figure 6. For a moderate PL, it is evident that the network's assets are sufficiently sized for accommodating both the additional demand and local generation, assuming that their nominal capacity does not increase. In Figure 6b,c, it can be seen that for a critical PL, both aggregators limit the reverse power flow to the rated capacity of their feeders (\(P_{Line_{\xi}}^{rated}=141.5\) kW) due to the operating constraint in (13). However, during the evening peak demand period, aggregator 2 experiences different overloading events which intermittently vary from \(P_{Line_{2}}^{rated}\) to 161 kW for approximately 1.6 h. This occurs due to the objective function being penalised because of the large number of EVs charging simultaneously at that time. Despite these operational conditions, the loading level on the main transformer is maintained below its rated capacity, as shown in Figure 6a. Notice that the results from this scenario would give to the DSO the input data for planning the reinforcement of their assets.