# Sustainable Operation of Active Distribution Networks
## 4 Case Study
These energy consumption profiles were obtained by the building electrical agent that belongs to the category of MAS local agents. Figure 11: Building clusters’ HVAC power consumption in each distribution network node. Figure 10: Total buildings’ HVAC and electrical power consumption. (**a**) Optimal operation. (**b**) Typical operation. Figure 14a,b depicts the total active power and the stored energy of the aggregated batteries of the PEVs together with their respective upper and lower limits. These trajectories were obtained by the application of the proposed ADN optimal operation scheduling technique and the business-as-usual ADN operation scenario. Positive power means that the equivalent aggregate battery injects power to the main grid. Figure 14: (**a**) Total active power. (**b**) Total stored energy of the PEVs aggregate battery. Figure 12: Indoor temperatures of the buildings hosted in the distribution network. (**a**) Optimization. (**b**) Typical case. Figure 13: Electrical power consumption of two indicative buildings of the network. The energy stored in the equivalent aggregate battery of the PEVs as well as the respective upper and the lower limits shown in Figure 14b vary with time because of the continuously changing number of PEVs and the electricity price variations. In the optimal operation scenario, it was observed that the proposed algorithm stores energy in time periods of low electricity price (e.g., at 15:00), as the goal of the applied optimization strategy is to minimize the daily operation cost of the ADN. In the business-as-usual scenario, \"dump charging\" was applied to the PEVs. As shown in Figure 14a, the total power of the equivalent aggregate battery took exclusively negative values, which means that given the used generator convention, the PEVs only absorb the necessary amount of energy from the main grid in order to charge their batteries and reach the desired energy target at their disconnection time. In both of the examined scenarios, the obtained results verified that all PEVs reached their stored energy target, while all of their technical and operational constraints were satisfied. Figures 15a and 16a depict the active power of two indicative clusters of PEVs located at nodes 21 and 31 of the examined ADN, while Figures 15b and 16b depict their stored energy, respectively. Moreover, their corresponding limits are given in the same figures. It was noticed that both the active power that clusters of PEVs share with the network and their battery energy were kept between their permitted ranges. These quantities were obtained by the implementation of the optimal dispatch of the total active power of the network's equivalent aggregate PEV battery, according to the proposed flexibilities of the PEV clusters to change their power. The total power consumptions of the buildings and PEVs together with the ADN load, the active power the distribution network exchanges with the main electric grid, and RES generation are shown in stacked form in Figure 17.  
Figure 18a indicates that the reactive power set-points of each PEV cluster resulted from the OPF problem solution in order to keep the voltages of the distribution network busses between their permissible bounds and to meet the power flow constraints. Specifically, the reactive power set-points resulted from the OPF exploitation are forwarded back to the PEVs' cluster agents to be optimally dispatched to each PEV they supervise. The maximum and minimum voltage bounds were set to 1.1 and 0.9 (p.u. ), respectively, while the nominal voltage was considered as 1 p.u. As shown in Figure 18b, all node voltages did not violate their bounds. The reactive powers of the PEV clusters and the voltages of the nodes of the examined ADN are indicated with different colors in Figures 18a and 18b, respectively. Figure 17: Buildings and PEVs’ total power demand, ADN load, RES generation, and main grid power. Figure 8:0 (a) Reactive power of PEVs clusters. (b) Distribution network node voltages.