## 3 Power System Reliability Assessment Considering Natural Gas Supply Fluctuations
### Power System Reliability Assessment Considering Gas Losses  
As a crucial part of the primary energy natural gas supply chain, the electric power system is located on the load side of the natural gas pipeline network supply chain [36]. This paper focuses on studying areas with a high gas-to-machine ratio, no external energy transmission, and high electricity load to evaluate the power system's reliability by considering the gas loss volume of the natural gas pipeline network as the input of the power system under various macro factors such as policy regulations and economic market fluctuations [37]. As the power-generation side of the power system comprises coal-fired units and gas-fired units, while the gas fluctuation event occurs the output of coal-fired units could be increased or part of the load could be cut to maintain the power balance and alter the power flow. Each gas-transmission line of the natural gas pipeline network corresponds to one gas unit on the power system side. The initial state of the gas-transmission line \(l\) at node \(i\) of the power system and the gas reduction at node \(i\) when the gas fluctuation event \(w_{\rm g}\) occurs can be respectively expressed as  
\[W_{i,\rm g}^{0}=S_{l} \tag{6}\]  
\[\Delta W_{i,\rm g}^{w_{\rm g}}=F_{l}^{aft} \tag{7}\]  
The above calculations can be used to determine the final power generated by each gas unit, and after linearizing the gas unit's generation model leads, it can be obtained as  
\[P_{i,\rm g}^{w_{\rm g}}=(W_{i,\rm g}^{0}-\Delta W_{i,\rm g}^{w_{\rm g}})\cdot h _{\rm g}\cdot\eta_{\rm g} \tag{8}\]  
where \(P_{i,\rm g}^{w_{\rm g}}\) is the power generated by the gas unit at node \(i\) during the gas supply fluctuation event \(w_{\rm g},h_{\rm g}\) is the caloric value of natural gas, and \(\eta_{\rm g}\) is the power-generation efficiency of the gas unit. Thus, the reserve capacity of the power system can be expressed as  
\[G_{\rm sp}=\sum\limits_{i=1}^{N_{\rm s}}(P_{i,\rm c}^{\rm max}+P_{i,\rm g}^{ w_{\rm g}}-D_{i,\rm L}^{0}) \tag{9}\]where \(P_{i,c}^{\max}\) is the maximum power generation of coal-fired units at node \(i\) in the power system, \(P_{i,\text{g}}^{\text{mg}}\) is the power generation of gas-fired units at node \(i\) during the gas supply fluctuation event \(w_{\text{g}}\), \(D_{i,L}^{0}\) is the power load at node \(i\) in the initial state, and \(N_{\text{s}}\) is the number of nodes in the power system. According to the above equation, if \(G_{\text{sp}}\geq 0\), it indicates that the power system has enough reserve capacity to achieve power balance by increasing the power output of each coal-fired unit proportionally [38]. Therefore, after the gas supply fluctuation event \(w_{\text{g}}\) occurs, the output power of a coal-fired unit at node \(i\) is equal to \(P_{i,c}^{w_{\text{g}}}\), and the power load \(D_{i,L}^{w_{\text{g}}}\) can be respectively expressed as  
\[P_{i,c}^{\text{mg}}=P_{i,c}^{0}+\sum\limits_{i=1}^{N_{\text{s}}}{(D_{i,L}^{0} -P_{i,c}^{0}-P_{i,g}^{\text{mg}})}.\frac{\cdot(P_{i,c}^{\max}-P_{i,c}^{0})}{ \sum\limits_{i=1}^{N_{\text{s}}}{(P_{i,c}^{\max}-P_{i,c}^{0})}} \tag{10}\]  
\[D_{i,L}^{w_{\text{g}}}=D_{i,L}^{0} \tag{11}\]  
where \(P_{i,c}^{0}\) denotes the power generated by the coal-fired unit at the initial state of node \(i\). Otherwise, when \(G_{\text{sp}}<0\), it means that the reserve capacity of the power system is insufficient at this time, and the power balance of the system cannot be achieved by increasing the output power of coal-fired units alone. The adjustment strategy at this point is to increase the output power of all coal-fired units to their maximum capacity and proportionally reduce part of the electric load [39].