## 5 Case Study
### IEWS Test A  
1. Optimization results of the IEWS considering the equipment failures of the WS. In this section, three cases are set up to illustrate the impact of equipment failures in the WS on the operation of the IEWS. Case1: Water supply pipes, RO desalination plants, tanks, and valves operate normally. Case2: RO desalination plants, tanks, and valves operate normally; the water supply pipe I21 has a 10 mm hole leakage which fails from 1:00 a.m. to 11:00 a.m. and is repaired at 11:00 a.m.  
Figure 7: Flow chart of the IEWS reliability evaluation algorithm. Case3: The water supply pipes, tanks, and valves operate normally; the RO desalination plant's component 3 constituents are inefficient. Figure 8 represents the three cases of energy consumption for the pumps and desalination plants. From the figure, it can be seen that the power consumption of the water pumps and desalination plant in Case2 are higher than in Case1 from 1:00 a.m. to 11:00 a.m., which means when there is a leakage in the pipeline. The power consumption of the water pumps increases significantly to satisfy the users' demand for water as much as possible. The power consumption of the pumps in Case3 is the same as that in Case1. However, the power consumption of the desalination plant in Case3 is significantly higher than that in Case1 and Case2, because the desalination plant is in an inefficient operating condition and consumes more power to produce the same quality of fresh water. Figure 9 shows the electrical load shedding at every hour in different inefficient operation states of the RO desalination plant based on Case2 and assuming the failure of the generator set G1. During normal operation of the RO desalination plant, the total electrical load shedding is 194.16 MW, assuming the thermal generator G1 fails. From Figure 9, the electrical load shedding in different inefficient operating states of the RO desalination plant can all be seen to be higher than the shedding during normal operation. Figure 10 represents the pipe leakage at each moment in different states of the RO desalination plant. Since the pipeline leakage was repaired from 11:00 a.m. to 24:00 p.m., the figure shows the pipeline leakage from 1:00 a.m. to 10:00 a.m. The figure shows that when the desalination plant is operating inefficiently, the total pipeline leakage increases in all cases. Figure 8: Energy consumption of water pumps and RO desalination plants. Figure 9: The electrical load shedding in different inefficient operating states of the RO desalination plant. (2) System reliability analysis  
For the IEWS test A, the following four models are used to illustrate the advantages of the multi-state model equipment in the WS proposed in this paper. Model 1: The two-state model of water supply pipes and the RO desalination plant is adopted. Model 2: The two-state model of water supply pipes and the multi-state model of the RO desalination plant are adopted. Model 3: The multi-state model of water supply pipes and the two-state model of the RO desalination plant are adopted. Model 4: The proposed multi-state model of water supply pipes and the RO desalination plant has been adopted. The reliability evaluation indices of the IEWS for the four models are shown in Table 1.  
Compared with Model 1, the LOELP, EENS, EWL, PWL, and \(C_{\text{ENS}}\) of Model 2 increase, and the LOWLP and EWNS of Model 2 decrease. This is because the RO desalination plant's multi-state operating features are considered in Model 2. More electric energy will be consumed when the RO desalination plant is in an inefficient operation state, increasing the operation pressure of the power system and decreasing its reliability. For the WS, when the desalination plant operates inefficiently, it can still supply fresh water to the users of the WS to reduce water load shedding, so the reliability of the WS will still be improved, although the probability and expected value of the leakage will increase.