# Research on Energy Storage Optimization Operation Schedule in an Island System
## 4 Results
### Case 1  
For case 1, the total cost of power generation was 2245 kNTD (new Taiwan dollars), the total startup cost was 14 kNTD, and the total economic cost was 2259 kNTD with a total number of two startups. The result of the power flow for optimization for the day with minimum load is shown in Figure 4. Note that the sumP (violet) is the net load that also considers the charging and discharging of the PSS. In addition, the SOC (brown) is expressed in percentage using the right \(y\)-axis.  
In Figure 5, the power output of each generator for the day with the least load is shown. Figure 5 shows that the system was mainly supplied by the two Phase III units (Plant1_9 and Plant1_10), and a Phase II unit (Plant 1_6). In addition, two other Phase II units only operated at certain hours. Plant 1_7 operated from 3:00 p.m. to 11:00 p.m., while Plant 1_5 operated from 5:00 p.m. to 1:00 a.m. the following day.  
Figure 3: Load and PV profile with the net load for (**a**) case 1: day with minimum load, and (**b**) case 2: day with maximum load.  
Figure 4: Case 1 power flow results.  
Figure 5: Case 1 hourly power generation of each fuel generator.  
Figure 6 shows the hourly up- and down-spinning reserve for the day with minimum load. Notice that the up and down reserve changed whenever a generator turned off (1:00 a.m. and 11:00 p.m.) or turned on (4:00 p.m. and 6:00 p.m.). The green and the dark blue line shows the up and down reserve, respectively, this time considering the PSS as an additional ancillary service.  
The up-spinning reserve was at the minimum up reserve at the 1 st, 15 th, 17 th, and 23 rd hours because of the transition of the system when a diesel generator turned off or on. With this transition, the PSS operated to maintain the up-spinning reserve limit. At the 1 st and 2 nd hour, the PSS-available power was added to the operating reserve allowing the shutdown of one unit. During the 15 th and 17 th hours, because of the increase in load, an additional unit was turned on with the PSS providing small power outputs (compare from Figure 4) for support and maintaining the up reserve limit. This was also seen at the 23 rd hour when a unit shut down. This means that the system used the PSS to keep the operating reserve at its limit.  
The down-spinning reserve, on the other hand, was at the minimum from the 4 th to the 8 th, 10 th, and 12 th hours. This may be due to the scheduled discharge of PSS in the early hours, causing the SOC to be lower than 50% (see Figure 4 of SOC). During this period, the use of the PSS was very limited until around the 10 th hour. In addition, in the 4 th to 11 th hours, the gray line overlaps the dark blue line because the down-spinning reserve was maintained at the boundary through small PSS charging and discharging because of low SOC (compare with Figure 4 PSS_power and SOC).  
Figure 7 shows the hourly power generation cost for case 1. It can be seen that even though the net load increased from 16 MW (5 th hour) to 30 MW (18 th hour), the average power generation cost decreased for these hours. It is reasonable to speculate that because the only generators operating were of heavy diesel types, the cost (Phase III generators) would not change and would be more economical when the load increases. Furthermore, the low load would cause the generator to operate at low efficiency, as was also discussed in Section 3.1, giving a higher power generation cost. The full-load condition of generators increased the efficiency, allowing the average cost of power generation to slightly change. The results show that the economic effect of using the PSS to doing peak-shaving in this condition was not that significant.  
Figure 6: The up- and down-spinning reserve for the day with minimum load (case 1).