## 5 The Realization of ATC-Based Distributed Coordinated Optimization
### Simulation Results and Discussion
It illustrates that the proposed method includes coordinating RMGs and distribution system operation strategy to have peak shaving and smoothing for distribution load curve at the same time, which can benefit distribution system operators through existing grid capacity upgrade/expansion deferrals. Table 2 illustrates the daily operating costs and the active power losses for the distribution network under the un-optimized case and the proposed optimal coordinated operation mode. It can be derived from the above results that the operating cost and power loss has been reduced by 41.72% and 17.98% respectively during a day based on the proposed ATC-based distributed optimal coordinated operation method. It shows that the proposed method provides an effective solution for distribution system operators to improve economic operation and energy efficiency of DN. Figure 12 depicts the evolution of the proposed ATC-based method. According to the pre-determined convergence thresholds the method converges within 19 iterations. When it converged, the total computation \begin{table}
\begin{tabular}{c c c} \hline \hline
**Comparison Item** & **Un-Optimized Case** &
\begin{tabular}{c} **Optimal Coordinated** \\ **Operation Mode** \\ \end{tabular} \\ \hline Operation cost (\$) & 37,597 & 21,911 \\ Power loss (kW) & 5812 & 4767 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Daily Operating Costs and Active Power Losses for the Distribution Network. Figure 11: Optimized daily scheduling results for a typical household prosumer within RMG Power scheduling results of distributed generations in the distribution network (**a**) Power purchased from the upstream grid, which is indicated as HV; (**b**) Power output of the DG installed in bus 22; (**c**) Power output of the DG installed in bus 27; (**d**) Power output of the DG installed in bus 23.  
time consumed by the proposed method is 91.8s. As shown in Figure 12a, the maximal difference between virtual generation and virtual load \(G_{qp}\) is smaller than 0.01, while the relative difference in optimal feasible solutions \(R_{el}\) is smaller than 0.001, as shown in Figure 12b. It should be noted that the proposed hierarchical optimization uses a deterministic load modeling approach, but the iterative process in analytical target cascading algorithm based distributed optimization will convergence regardless of stochasticity [28] in load, although the global optimum, and thus number of iterations and the point of convergence, will be affected. The solutions to the proposed distributed method and the centralized method are compared in Table 3, the distributed result is close to the centralized result and relative error is 0.0146. It shows that the proposed ATC-based distributed coordinated method provides a feasible and effective solution to coordinate energy management and optimal operation between the RMGs and ADN. It should be mentioned that our design in this paper focuses on providing an interrelation between ADN and RMGs and aims at coordinating optimal hourly energy consumption scheduling and operation management between the two entities. Although simplified EV and shiftable load models and constant household profiles are adopted for simplicity in this work, the flexibility and generality of the proposed hierarchical optimization framework makes it suitable for further considering load modeling with better accuracy and rationality.