## 6 Case Studies
### Effects of Different Conversion Levels of Electrical Power to Gas/Heat  
Wind and solar power are typical intermittent renewable energy sources with high uncertainty. Under some special conditions, e.g., when high wind and/or solar power output and low electricity loads occur simultaneously, the surplus wind and/or solar power has to be curtailed to maintain the security of the electricity network. Clearly, this curtailment is undesirable and many efforts have been made to reduce or avoid it. As mentioned above, the utilization of both P2G and P2H provides a promising prospect for accommodating renewable energy. In this subsection, we study the effects posed by the utilization of P2G and P2H on the operation of the EGH-IES and wind/solar power accommodation. Note that P2G/P2H are expected to convert wind and solar power to gas/heat in this paper, where they act as variable (or uncertain) electricity loads to the electricity network and variable (or uncertain) sources to the gas /heating networks and thus pose variable effects on the operation of the EGH-IES. In order to study these variable effects, the PEF analysis proposed is conducted in this subsection with a focus on the effects of different conversion levels of electrical power to gas/heat (i.e., different \(\lambda_{\text{P2G}}\) and \(\lambda_{\text{P2H}}\)) on the operation of the EGH-IES. Accordingly, the following two cases are designed. Case 1: \(\lambda_{\text{P2G}}\) is set be 0, 0.2 and 0.4, while \(\lambda_{\text{P2H}}\) is kept at 0 (i.e., P2H is off). Case 2: \(\lambda_{\text{P2H}}\) is set be 0, 0.2 and 0.4, while \(\lambda_{\text{P2G}}\) is kept at 0 (i.e., P2G is off). Note that correlation coefficients among electricity/gas/heat load, wind speed and photovoltaic power are kept the same as those in the last subsection. \(\bullet\)**Case 1**  
Figure 6 depicts the CDFs of voltage magnitude of bus 32, which is the bus connected to wind farms and P2G, and Figure 7 shows the SDs of voltage magnitudes of buses 29-32. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Indices** & \(\mu_{\text{loss}}\) & \(\sigma_{\text{loss}}\) & \(\mu_{\text{F}}\) & \(\sigma_{\text{F}}\) & \(\mu_{\text{T}}\) & \(\sigma_{\text{T}}\) \\ \hline MCS-LN & 0.3383 & 0.1027 & 30.0006 & 1.1139 & 98.8400 & 0.0450 \\ MCS-SN & 0.3377 & 0.0984 & 29.9975 & 1.1220 & 98.8400 & 0.0453 \\ Relative error & 0.17\% & 4.37\% & 0.01\% & 0.72\% & 0 & 0.66\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of PEF for EGH-IES. As shown in Figure 6, the CDFs of voltage magnitude of node 32 vary dramatically as \(\lambda_{\rm{P2G}}\) changes. When P2G is off (\(\lambda_{\rm{P2G}}=0\)), the probability of the voltage magnitude at bus 32 exceeding its upper limit (set to be 1.05 pu) is up to 56.1%. However, this probability is dramatically reduced to 40% when \(\lambda_{\rm{P2G}}=0.2\) and 12.6% when \(\lambda_{\rm{P2G}}=0.4\). This indicates that the high wind and solar power output pose a high overvoltage threat to the electricity network, and the utilization of P2G can effectively alleviate this threat. From Figure 7, it can be seen that the SDs of voltage magnitude of bus 32 (connected to wind farms), bus 31 (connected to solar plants) and bus 30 (close to bus 31) are much greater than that of bus 29. This indicates that buses 30-32 are affected greatly by the volatility of wind/solar power. It's worth mentioning that as \(\lambda_{\rm{P2G}}\) increases, there is a dramatic decrease in the SDs of voltage magnitude, especially at buses 30-32, which suggests that the utilization of P2G can also reduce the voltage fluctuation posed by the variable wind/solar power. In addition to the voltages shown in Figures 6 and 7, the output variables of the gas network are also investigated. The CDFs of gas flow within pipeline 7 (connected to gas nodes 3 and 8) and the SDs of gas flow within all pipelines are depicted in Figures 8 and 9, respectively.