## 6 Case Studies
### Effects of Different Conversion Levels of Electrical Power to Gas/Heat
As shown in Figure 13, increasing \(\Lambda_{\rm P2H}\) leads to a voltage drop at bus 17 (connected to the CHP unit) and its nearby buses (i.e., buses 15 and 16). This is because with the output increase of the P2H, there is a decrease in the heat power output and correspondingly a decrease in the electrical power output of the CHP unit given that the overall heat loading level is unchanged, which finally results in a decrease in the voltages of bus 17 and its nearby buses. From Figure 16, it can be seen that nodal pressures will increase with the increase of \(\Lambda_{\rm P2H}\). This is because the amount of gas consumed by the CHP unit decreases due to its decreased heat and electrical power generation. This decreased gas consumption means a decrease in the overall gas loading level and therefore leads to an increase in nodal pressures. Note that this pressure increment also leads to a decrease in the electrical power consumed by the compressors (see (4) and (5)), and therefore increases in the voltages of buses connected to compressors and their nearby buses (see Figure 13 for voltages of buses 5\(\sim\)9). Taking bus 8 as an example, CDFs of its voltage magnitude are shown in Figure 17. It can be observed from Figure 17 that as \(\Lambda_{\rm P2H}\) increases, the probability of voltage magnitude exceeding the lower limit (set to be 0.94 pu) decreases dramatically. This indicates that the utilization of P2H is helpful in improving the voltages  
Figure 14: Mean values of mass flow rates within pipes in the heating network. Figure 15: SDs of mass flow rates within pipes in the heating network. As shown in Figure 18a, in Case 1, uncertainties in the wind/solar power are transmitted to the gas network via P2G. These external uncertainties and the internal uncertainties in the gas loads make the operation states of the gas network more uncertain. On the other hand, uncertainties in the operation of the gas network, including the uncertainties from the external wind/solar powers, are transmitted back to the electricity network via electricity-driven compressor. Therefore, both electricity and gas networks suffer greater uncertainty because of the coupling between them by P2G and the electricity-driven compressor. Note that in Case 1, the heating network is unaffected by the uncertainties in the wind/solar power because of the following facts: (a) the P2H is off in Case 1; (b) the EGH-IES is working in a \"electricity/gas following heat\" operation mode, where no uncertainty will transmit from the electricity network to the heating network. As shown in Figure 18b, interactions among different subnetworks in Case 2 are more complicated than those in Case 1 because all three subnetworks are involved in Case 2. Uncertainties in wind/solar power are transmitted to the heating network via P2H. These uncertainties are further transmitted to the gas network and back to the electricity network through the CHP unit because of the role of the CHP unit in the \"electricity/gas following heat\" operation mode. Additionally, uncertainties in the gas network are also transmitted to the electricity network via the compressor, which is similar to Case 1. However, different from Case 1, uncertainties in wind/solar power in Case 2 are transmitted among all three subnetworks, including the heating network, and the operation uncertainty of all the three subnetworks, and thus the whole EGH-IES, is aggravated and complicated. It is clear from the comparison above that the uncertain transmission among the subnetworks depends on the uncertainty sources, coupling equipment and their operation, and the operation mode of EGH-IES. However, given that there is coupling between any two subnetworks, the operation uncertainty of some (or all) subnetworks will be inevitably aggravated and complicated. This calls for probabilistic energy flow analysis to provide an accurate assessment of the operation of EGH-IES, thus motivating the studies in this paper.