## 5 Case Study
### IEWS Test A
Compared with Model 1, the LOELP, EENS, LOWLP, EWNS, PWL, EWL, and \(C_{\text{ENS}}\) of Model 3 increase. This is due to the fact that the multi-state operation model of the pipeline is considered in Model 3. When the water supply pipe is in the leakage state, the power consumption of the pumps will increase to meet the water demand of the users, and the overall power consumption of the WS increases, as well as the operational pressure of the power system, thus leading to a decrease in the reliability of the power system. At the same time, compared with the fault state, pipeline leakage is not easy to detect, and maintenance \begin{table}
\begin{tabular}{c c c c c} \hline
**Reliability Indices** & **Model 1** & **Model 2** & **Model3** & **Model 4** \\ \hline LOELP & 0.0036 & 0.0100 & 0.0055 & 0.01311 \\ EENS (MWh/year) & 833.32 & 2626.08 & 2455.03 & 3005.88 \\ LOWLP & 0.0047 & 0.0041 & 0.0049 & 0.0031 \\ EWNS (m\({}^{3}\)/year) & 44,833.17 & 20,737.16 & 46,540.79 & 14,338.015 \\ PWL & 0.00024 & 0.00028 & 0.001178 & 0.00130 \\ EWL (m\({}^{3}\)/year) & 505.59 & 677.25 & 1279.377 & 1379.589 \\ \(C_{\text{ENS}}\) (USD/year) & \(1.11\times 10^{5}\) & \(2.11\times 10^{5}\) & \(2.30\times 10^{5}\) & \(2.33\times 10^{5}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Reliability evaluation indices of case A.  
Figure 10: Pipeline leakage in different inefficient operating states of RO desalination plant. costs are relatively high, resulting in the inability to repair the pipeline on time, resulting in more serious leakage and thus reducing the level of reliability of the water system. Compared with Model 1, the reliability level of the power system in Model 4 is significantly reduced, the reliability of the water system is improved, and the probability and expected value of pipeline leakage are increased. It can be seen that the two-state model of water supply pipes and the RO desalination plant overestimate the reliability of the power system in the IEWS. At the same time, ignoring pipeline leakage, the operation of the WS cannot be accurately simulated. Compared with Model 2, the LOELP, EENS, PWL, and EWL of Model 4 increase. This is because the multi-state operation model of the pipeline is considered in Model 4. In order to meet user needs when there is a pipeline leakage, the water pump must be in a high-power operation state, increasing the operating pressure of the power system and reducing its reliability. This shows that only considering the multi-state of the RO desalination plant and ignoring the existence of pipeline leakage will still overestimate the reliability of the power system. Compared with Model 3, the LEOLP, EENS, PWL, and EWL of Model 4 all increase. This is because the RO desalination plant's multi-state operation features are considered in Model 4. This shows that when the RO desalination plant operates inefficiently, the energy consumption of producing the same quality of water increases, putting operating pressure on the power system. In addition, due to the continuous water supply, pipeline leakage will also increase. This shows that only considering the two-state of the water supply pipeline and ignoring the inefficient operation of the RO desalination plant will overestimate the reliability of the power system. Therefore, it is necessary to consider the multi-state model of the RO desalination plant and the water supply pipeline at the same time. In summary, the multi-state reliability model of the water supply pipes and RO desalination plant proposed in this paper can fully consider the existence of leakage in the water supply pipes and the electric load shedding caused by the inefficient operation of the seawater desalination plant. Thus, they can avoid overestimating the reliability level of the power system during the joint operation of the IEWS.