3.1. 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,
represents the probability of the component’s failure [
30]. A random number
is generated in the interval [0, 1]; when
,
Sk = 0, which means the component is in the operational state. Otherwise, when
,
Sk = 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,
l1 and
l2, where
represents lines that occur in more than one minimal cut set and
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
where
is the set of all lines in the minimal cut set
r,
is the spare capacity of cut set
r,
is the maximum allowable transmission capacity of line
l,
is the ongoing transmission task of line
l,
is the calculated transmission loss contribution of line
l in cut set
r at the
i-th simulation after proportional allocation, and
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. After determining the gas loss of the line, the cut set with the larger spare capacity
is reallocated to the line gas loss [
34], and the gas loss of the remaining lines
is calculated proportionally for each line in turn, which can be respectively expressed as
where
is the finalized gas loss of line
l1 in the
i-th simulation after proportional allocation,
R is the number of minimal cut sets,
is the finalized gas loss of line
l2 in simulation
i after proportional allocation,
represents the gas loss of line
l2 in the
i-th simulation due to component failure before proportional allocation,
is the set of all lines that occur only in cut set
r, and
is the set of all lines in cut set
r that also appear in other cut sets.
Multiple Monte Carlo simulations are then performed to obtain the actual volume of natural gas delivered by the pipeline system [
35], which can be used as input to the power system, equal to
.
3.2. 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
occurs can be respectively expressed as
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
where
is the power generated by the gas unit at node
i during the gas supply fluctuation event
,
is the calorific value of natural gas, and
is the power-generation efficiency of the gas unit.
Thus, the reserve capacity of the power system can be expressed as
where
is the maximum power generation of coal-fired units at node
i in the power system,
is the power generation of gas-fired units at node
i during the gas supply fluctuation event
,
is the power load at node
i in the initial state, and
is the number of nodes in the power system.
According to the above equation, if
, 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
occurs, the output power of a coal-fired unit at node
i is equal to
, and the power load
can be respectively expressed as
where
denotes the power generated by the coal-fired unit at the initial state of node
i.
Otherwise, when
, 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]. Therefore, after the gas supply fluctuation event
occurs, the output power of the coal-fired unit at node
i, which is expressed as
, and the power load
can be respectively expressed as
To evaluate the impact of the natural gas supply on the power system, the following reliability-assessment indicators of the power system are selected, including Expected Demand Not Supplied (
EDNS), Severity Index (
SI), and Service Availability (
SA) [
40,
41].
Expected Demand Not Supplied
EDNS: Indicating the amount of power load lost from the system in MW in the event of a gas supply fluctuation event
, which can be expressed as
where
indicates the amount of electrical load lost at node
i when the gas supply fluctuation event
occurs;
Ns is the number of loads. The larger the
EDNS, the larger the electrical load removed due to the fault and the lower the system reliability.
Severity Index
SI: Based on the
EDNS obtained from (14), calculating the ratio of the electric load removed from the system at the load point due to a gas supply fluctuation event
(e.g., due to policy regulation or economic fluctuations) to the total electrical load that would have occurred if no gas supply loss event had occurred, which can be expressed as
where
is the total system electrical load and
T is the time from the gas supply loss event to repair.
SI represents the system severity, and the larger this indicator is, the greater the severity of the system failure and the lower the system reliability.
Average Service Availability Index
ASAI: Indicating the ratio of the normal electrical load of the system in this scenario to the total electrical load when no gas loss event occurs [
42], which can be expressed as
where
ASAI is the power supply availability of the system. The larger the value, the higher the power supply margin of the system and the higher the system reliability.
Average Energy Not Supplied
AENS: Indicating the average amount of power shortage at each node when a load-shedding event occurs, which can be expressed as
where
AENS is the average amount of load loss per node in a power system. The more severe the power system failure, the lower the system reliability.