## 6 Case Studies
### Effects of Different Conversion Levels of Electrical Power to Gas/Heat
As shown in Figure 8, as \(\lambda_{\text{P2G}}\) increases, the gas flow within pipeline 7 tends to decrease, and thus the possibility of gas overloading also decreases. On the other hand, as \(\lambda_{\text{P2G}}\) increases, SDs of gas flow within pipeline 7 obviously increases (see Figure 9), and so does that of pipeline 10 (connected to gas nodes 6 and 8) and pipeline 11 (connected to nodes 7 and 8). These observations indicate that the utilization of P2G is helpful to reduce the overloading risk of the gas network, but may introduce harmful fluctuations resulted from uncertain wind/solar power to the gas flow especially within the pipeline directly connected to node 7 (to which the P2G is connected) and its nearby pipelines. As mentioned above, there are three special gas users connected with nodes 7-9, and thus three electricity-driven compressors are installed to meet their pressure requirements. Figure 10 presents the mean values of the gas pressures of nodes 7-9 and Figure 11 gives further the mean values of voltages of the buses connected to the compressors. Figure 11: Mean values of voltage magnitudes of buses 6, 7 and 8. Figure 10: Mean values of pressures of nodes 9, 10 and 11. Figure 9: SDs of gas flow within all pipelines in the gas network. As shown in Figure 10, the mean values of gas pressure of nodes 7-9 rise with the increase of \(\lambda_{\rm P2G}\), which indicates that the utilization of P2G is also helpful in improving the gas pressure of the end users. Additionally, it can be seen from Figure 11 that with the increase of \(\lambda_{\rm P2G}\), the voltages of buses 6-8 also increase. This is because the electrical power consumed by compressors decreases owing to the increased gas pressures (see (4) and (5)) and, accordingly, the voltages of the buses connected to the compressors improves. \(\bullet\) **Case 2**  
Figure 12 depicts the CDFs of the voltage magnitude of bus 31 (connected to P2H) and Figure 13 gives the mean values of all voltage magnitudes in the electricity network. It can be seen that the utilization of P2H decreases the voltage level of bus 31 (see Figure 13), and thus the probability of bus 31 exceeding its upper voltage limit (see Figure 12), which is similar to the effect of P2G on the voltage of bus 32 in Case 1. Figures 14 and 15 present the mean values and SDs, respectively, of mass flow rates within pipes in the heating network. It can be observed from Figure 14 that as \(\lambda_{\rm P2H}\) increases, the mass flow rates within some heavily loaded pipes (such as pipes 1-3) decrease remarkably, which indicates that P2H may contribute to reducing the potential overloading risks of the heating network. On the other hand, as \(\lambda_{\rm P2H}\) increases, the SDs of mass flow rates within the main pipes (i.e., pipes 1-5) notably increases, because uncertainties in wind/solar power are introduced into the heating network via P2H. Note that the effects of P2H on overloading alleviation and SD increase are also similar to the effects of P2G on the gas network shown in Figures 8 and 9 in Case 1. Figure 12: CDFs of voltage magnitude of bus 31. Figure 13: Mean values of voltage magnitudes. However, different from Case 1, where P2G is the only uncertain gas source to the gas network, both P2H and CHP are uncertain heat sources for the heating network in Case 2, because the EGH-IES considered is working in the \"electricity/gas following heat\" mode. As mentioned above, in this mode, the CHP unit maintains the overall heat power balance of the heating network. Therefore, the uncertain output of the P2H due to uncertain wind/solar power will lead to uncertainty in the heat power generated by the CHP unit and finally impose uncertain impacts on both the electricity and gas networks. These uncertain impacts can be found in Figure 13, above, and Figure 16, shown below, which present the mean values of the gas pressures of all nodes in the gas network.