## 5 Example Analysis
### Results and Analysis of Siting and Sizing
#### 5.2.2 Scheme I: Power-Limited Mode of Gas Turbine  
The output power of the original gas turbine was reduced proportionally and, simultaneously, renewable energy such as wind and solar were incorporated. Considering that the economic and stability indicators were equally important, \(\xi_{1}(x)\) and \(\xi_{2}(x)\) were each assumed to be 1. When the gas-turbine output decreased by 50%, the optimization curve of the overall WT/PV was as shown in Figure 7. With the increase in the number of iterations, the overall balance decreased, and the optimal scheme which was acceptable to each optimization goal was reached. Considering the different capacities at each node, the WT/PV planning results obtained, based on varying output curves for WT/PV systems, are shown in Figure 8.  
The total WT capacity was 70 MW and the total PV capacity was 24 MW. Based on the optimized WT/PV capacity and the predicted output curves, power-flow calculations were performed during each time period. The power-flow distribution result is illustrated in Figure 9, where the \(x\)-axis represents the node number, the y-axis represents the per-unit voltage of the node, and the \(z\)-axis is the time measured in hours. Figure 8: Wind-turbine and photovoltaic capacity. Figure 7: Iterative curve. Figure 9: Power-flow distribution after WT/PV planning. According to the capacity after WT/PV planning and the load distribution of the distribution network, the second stage of cluster partition was carried out. Based on node 1 and node 10, the electrical distances between nodes 2-9 and 1 and between nodes 11-15 and 10 were calculated. The results are presented in Figure 10, where the \(x\)-axis indicates the node number and the \(y\)-axis indicates the electrical distance between each node and the reference node. Based on the electrical distance between nodes, we grouped together nodes whose electrical distance did not exceed 0.4 and partitioned them into sub-clusters. Nodes 1, 2, 6-8, nodes 3-5, node 9, and nodes 10-15 were partitioned into four sub-clusters, as shown in Figure 11.  
According to the cluster-partition results, as well as the internal voltage and loss sensitivity of each sub-cluster, it was decided to connect the ES to nodes 2, 5, and 14. Subsequently, through the optimization algorithm in the third stage, the ES capacities at node 2, 5, and 14 were calculated as 12, 13, and 8 MWh, respectively. Based on the configured energy-storage capacity, we conducted power-flow calculations for each hour to obtain the distribution of power flow, as shown in Figure 12.  
Figure 11: Cluster-partition results. Figure 10: Electrical distance between nodes: (**a**) nodes 2–9; (**b**) nodes 10–15. According to the operation state, the power penetration of the system was calculated as 62.80%. Since the load hardly changed, the power penetration and the capacity penetration were always the same. The energy penetration was 39.42% and the stability indicator was 0.057. The maximum values of the node voltage before and after the ES connection were 1.05 and 1.039, respectively, and the minimum values were 0.948 and 0.952, respectively. The fluctuation was significantly reduced. The single-objective optimization process of loss and voltage fluctuation in the total objective is shown in Figure 13. The losses before and after the ES connection were 49.1 MWh and 41 MWh, respectively, and the total voltage fluctuation of all the nodes' indicators before and after the ES connection were 9.23 and 8.04, respectively. Each objective was optimized through iteration. Using the same methodology, we first performed the siting and sizing of the WT/PV for different scenarios. The WT/PV planning results obtained when the gas-turbine output power decreased by 30% and 70% are shown in Figure 8.0  
When the output power of the gas turbine decreased by 30%, the total capacity of WT planned was 62 MW and the total capacity of PV was 21 MW. When the output power of the gas turbine decreased by 70%, the total capacity of WT planned was 105 MW and the total capacity of PV was 43 MW.