## 4 Case Studies
### Optimization Results of the Proposed Model  
The optimized dispatch results of ESSs for the 33- and 69-bus distribution networks are shown in Figures 5 and 6, respectively. The ESSs charge energy from the network during the valley and flat periods when the electricity prices are low (e.g., \(t=1\)-6 and \(t=13\)-17), and release the stored power to support the network during peak periods (e.g., \(t=10\)-12 and \(t=18\)-22), which indicates that ESSs are able to reduce the operation cost by shifting some load to valley periods. In addition, the SOC of the ESSs is always between 20% and 90% so as to extend the battery life and the final state of ESSs are equal to the initial state in a day.  
Figure 4: Topology of 69-bus distribution network.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Hours** & **Electricity Price (V/kWh)** \\ \hline Peak period & 09:00–12:00, 17:00–22:00 & 1.15 \\ Flat period & 06:00–09:00, 12:00–17:00 & 0.68 \\ Valley period & 00:00–06:00, 22:00–24:00 & 0.33 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Time-of-use electricity price.  
Figure 3: Day-ahead power prediction of the load, wind turbine (WT) and photovoltaics (PVs).  
Comparison of MT output with and without ESS for 33-bus distribution network is shown in Figure 7. As can be seen from the figure, during the peak period and flat period, the electricity price of the main grid is higher than the generation cost of MT. So, it is reasonable that MT generates maximum output to decrease the purchase cost from the main grid. It is worth noting that in valley periods when the cost of MT power generation is a little higher than the electricity price of the main grid, the MT still has a certain output. The reason is analyzed as follows. Due to the large R/X ratio of distribution systems, the active power scheduling affects the power losses as well. MT can help the network run more economically through reducing the network power losses, though the cost of MT power generation is slightly higher. In addition, the comparison between with ESS and without ESS indicates that the MT can cooperate with ESS to further reduce the operation cost of ADN, resulting in more MT output in valley times.  
Figure 5: The optimized dispatch results of ESSs for 33-bus distribution network.  
Figure 6: The optimized dispatch results of ESSs for 69-bus distribution network.  
Figure 8 shows the optimized hourly dispatch results of OLTC for the two distribution networks. It can be clearly seen that the constraints of OLTC action times are satisfied.  
The results of different reactive power-regulating devices for 33-bus distribution network are shown in Figure 9. It is easy to see that the reactive power outputs of all the devices are within respective output limits, and the constraints of action time of CBs are satisfied. Note that the reactive power outputs of PV2 and WT are opposite to their active power due to the limit of the inverter capacity, while the reactive power output of PV1 still has a certain regulation range, which will enhance its ability to deal with system uncertainties.  
The detailed results before and after the coordinated optimization are indicated in Table 4. It can be calculated that for the 33-bus distribution network, the power losses, the total operation cost and the voltage deviation are decreased by 57.10%, 7.27%, and 75.34%, respectively. For the 69-bus distribution network, the power losses, the total operation cost, and the voltage deviation are decreased by 46.98%, 6.87%, and 47.32%, respectively. The curves of bus voltage amplitude of 33- and 69-bus distribution  
Figure 8: The optimized dispatch results of on-load tap changer (OLTC).  
Figure 7: Output of micro turbine (MT).  
It can be concluded that both the economy and security of the distribution networks are enhanced through coordinated optimization.