## 3 Power System Reliability Assessment Considering Natural Gas Supply Fluctuations  
Assessment of Gas Supply Capacity of Natural Gas Pipeline System Based on the Monte Carlo Simulation Method  
The natural gas supply chain is a complex system, where a single- or multiple-component failure can potentially cause gas loss events in the supply chain. Exhaustive simulation of all failures through brute force is computationally intensive. Monte Carlo simulation, on the other hand, can solve the problem of dimension explosion caused by brute force and can describe the characteristics of random events and physical processes. Therefore, Monte Carlo simulation is adopted to simulate and calculate natural gas supply failures [29]. The system component states are simulated using the non-sequential Monte Carlo simulation method, which determines each component's state in the system based on the sampling of the component probability distribution and combines each component state as the natural gas supply chain system state. For component \(k\), \(p_{k}\) represents the probability of the component's failure [30]. A random number \(\xi_{k}\) is generated in the interval \([0,1]\); when \(\xi_{k}\geq p_{k}\), \(S_{k}=0\), which means the component is in the operational state. Otherwise, when \(0<\xi_{k}\leq p_{k}\), \(S_{k}=1\), which means the component is in the failed state. The gas-transmission capacity in the case of system failure is calculated based on the result of the minimal cut set division. Each pipeline in the natural gas system has an upper limit of transmission capacity and a certain transmission margin, i.e., reserve capacity. The reliability of the complex pipeline network system is modeled based on the minimal cut set theory, where each minimal cut set consists of gas-transmission lines in parallel. If a gas-transmission line fails, the gas loss of that line can be compensated for by increasing the gas-transmission capacity of other lines in the same cut set, and vice versa. Next, the amount of gas lost for the minimal cut set \(r\) is calculated. Each line has a maximum allowable gas-transmission volume and an ongoing gas-transmission task, and the difference between the two is the reserve capacity of the line [31]. The reserve capacity of the minimal cut set is equal to the sum of the reserve capacities of all the gas-transmission lines that make up the minimal cut set. The line \(l\) is divided into two categories, \(l_{1}\) and \(l_{2}\), where \(l_{1}\) represents lines that occur in more than one minimal cut set and \(l_{2}\) represents lines that occur in only one cut set \(r\). If the spare capacity in the minimal cut set \(r\) is less than the lost gas volume of all lines in that cut set, the gas volume of that line cannot be fully compensated. Therefore, the gas loss of line \(l\) in cut set \(r\) needs to be proportionally allocated according to its share of the lost gas volume of all lines that failed. The gas loss of the line \(l\) in cut set \(r\) can be calculated and expressed as  
\[L_{r,l,i}^{aft}=(\sum_{l\in T_{r}}L_{l,i}^{bef}-B_{r})\cdot\frac{L_{l,i}^{bef }}{\sum\limits_{l\in T_{r}}L_{l,i}^{bef}} \tag{2}\]  
\[B_{r}=\sum_{l\in T_{r}}C_{l}-\sum_{l\in T_{r}}S_{l} \tag{3}\]  
where \(T_{r}\) is the set of all lines in the minimal cut set \(r\), \(B_{r}\) is the spare capacity of cut set \(r\), \(C_{l}\) is the maximum allowable transmission capacity of line \(l\), \(S_{l}\) is the ongoing transmission task of line \(l\), \(L_{r,l,i}^{aft}\) is the calculated transmission loss contribution of line \(l\) in cut set \(r\) at the \(i\)-th simulation after proportional allocation, and \(L_{l,i}^{bef}\) is the transmission loss due to component failure of line \(l\) before proportional allocation at the \(i\)-th simulation. All minimal cut sets are traversed, and according to the short-board effect, the minimal cut set with the smallest spare capacity determines the amount of gas loss of the line [32,33]. The gas loss of line \(l\) is equal to its maximum gas loss contribution value within all cut sets.