A method for evaluating the gas supply reliability of a natural gas pipeline network based on a pipeline network degradation model

Abstract

The present invention provides a method for evaluating the gas supply reliability of a natural gas pipeline network based on a pipeline network degradation model, belonging to the technical field of evaluating the gas supply reliability of a natural gas pipeline network; the technical problem to be solved is: to provide a method for evaluating the gas supply reliability of a natural gas pipeline network based on a pipeline network degradation model; the technical solution adopted to solve this technical problem is: considering the specific influence of the degradation of compressor stations and the random degradation of pipelines on the natural gas pipeline network system, and according to the different influence laws of the gas supply volume of the natural gas pipeline network system by the degradation of the two, respectively model the degradation process of compressor stations and the random degradation process of pipelines; analyze and calculate the probabilities of various operating states of the pipeline network, and based on the maximum gas supply volume of the pipeline network affected by the degradation of the pipeline and the compressor station, evaluate the supply-demand relationship of the pipeline network in various states, so as to evaluate the gas supply reliability of the pipeline network; the present invention is applied to the evaluation of the gas supply reliability of a natural gas pipeline network.

Description

Technical Field

[0001] The present invention provides a method for evaluating the gas supply reliability of a natural gas pipeline network based on a pipeline network degradation model, belonging to the technical field of evaluating the gas supply reliability of a natural gas pipeline network. Background Art

[0002] As a low-carbon clean energy source between traditional fossil energy and renewable energy, natural gas can reduce carbon dioxide emissions by 45%-55% compared with coal under the same calorific value. Currently, it is an energy source that is vigorously promoted in the transformation and development of the energy system. With the increasing demand for natural gas, the scale of the pipeline network is gradually expanding, the structure is becoming increasingly complex, and the problem of short supply of natural gas is gradually emerging, posing challenges to economic development and social stability. The reason is that as key transmission equipment of the natural gas pipeline network, the performance of distribution stations and pipelines tends to deteriorate with the continuous operation of the pipeline network, which in turn leads to a decline in the overall performance of the pipeline network, unable to meet the growing demand for natural gas, and resulting in gas supply shortages.

[0003] At present, the intelligent detection equipment equipped in the pipeline network can accurately detect the degradation state of the pipeline network equipment and plays an important role in the operation and maintenance of the pipeline network. Therefore, starting from the pipeline network degradation state data, based on the influence characteristics of the pipeline network equipment on the gas supply capacity of the pipeline network, constructing a pipeline network performance evaluation model that simultaneously affects the degradation of stations and pipelines, and formulating a scientific maintenance strategy according to the pipeline network performance evaluation results is an effective way to solve the problem of gas supply shortage in the pipeline network. For natural gas pipeline networks, the pipeline network reliability can be divided into structural reliability and gas supply reliability. Among them, structural reliability focuses on evaluating the probability that the pipeline network equipment maintains its complete function, while gas supply reliability focuses on evaluating the ability of the pipeline network gas supply volume to meet user needs. From the perspective of the pipeline network structure, the laying of pipeline network equipment has a certain redundancy, and the degradation or even failure of a certain equipment does not necessarily affect the overall gas supply volume of the pipeline network. The primary task of the pipeline network is to continuously supply natural gas that meets user needs. Therefore, based on the emphasis on meeting the task of end-user gas consumption in the pipeline network, gas supply reliability is more suitable for evaluating the reliability of the pipeline network.

[0004] In recent years, the research on the reliability assessment of pipeline gas supply can generally be summarized into three steps: the establishment of a pipeline network degradation model, the solution of the gas supply volume of the pipeline network, and the assessment of the reliability of the pipeline network gas supply. From the perspective of the pipeline network degradation model, pipelines and compressor stations are mostly regarded as the key equipment affecting the reliability of the pipeline network gas supply. The degradation states of these two types of equipment are divided into discrete multi-states, and it is assumed that there is a corresponding relationship between the pipeline capacity and the degradation state. For example, Su et al. and Fan et al. believe that pipelines and compressor stations may be in three states: normal, degraded, and failed, and use the Markov process to describe their stochastic degradation process; Yu et al. also make a similar division of the degradation states of these two types of equipment, but choose the Monte Carlo method to simulate the pipeline network state transition process; Chen et al. and Yang et al. assume that pipelines and each compressor have two states: normal and failed, then the degradation state of the compressor station composed of compressors in parallel can be divided into discrete multi-states, and the degradation processes of pipelines and compressor stations are modeled as Markov processes. In addition, in engineering practice, the compressor station can be regarded as a cold standby system of k out of n, and the capacity of the surrounding pipelines affected by the degradation of the compressors in the station can be divided into multiple discrete stages. Therefore, it is reasonable to divide the station degradation state into discrete multi-states. However, corrosion is one of the main reasons for pipeline failure, and pipeline corrosion degradation has the characteristic of continuous monotonic increase. As the corrosion depth of the pipeline gradually increases, the maximum allowable operating pressure of the pipeline gradually decreases, thus causing the gas transmission capacity of the pipeline to gradually decline. Therefore, the gas supply volume of the pipeline network shows a continuous decreasing trend under the influence of pipeline corrosion degradation. Modeling the degradation processes of compressor stations and pipelines as discrete and continuous stochastic processes respectively, and on this basis constructing a stochastic capacity model corresponding to the degradation states of these two types of equipment can more accurately describe the gradual change process of the gas supply volume of the pipeline network under the simultaneous degradation of these two types of equipment.

[0005] From the perspective of the solution methods of the gas supply volume of the pipeline network, scholars either use simulation methods to simulate the gas supply volume of the pipeline network under different working conditions, or use analytical methods to solve the actual gas supply volume corresponding to various degradation states of the pipeline network. For example, Su et al. realized the thermal-hydraulic model of the pipeline network through the simulation software TGNET to simulate the gas supply volume under different degradation states of the pipeline network. Yu et al. used the commercial software SPS to analyze the variation law of the actual gas supply volume after the pipeline network degrades to different states. Yu et al. established a hydraulic model considering the importance of users, hydraulic and pressure constraints, and the coupling effect of equipment failure on the gas supply volume of the pipeline network, and used the mixed integer linear programming method to solve it. Chen et al. introduced the maximum flow algorithm to solve the actual gas supply volume of the pipeline network under the simultaneous degradation of pipelines and compressor stations. Yang et al. considered the priority order of user gas supply and completed the gas supply distribution of the pipeline network with the help of the maximum flow algorithm. In fact, using the simulation method to solve the actual gas supply volume of the pipeline network can, although more accurately simulate the gas supply situation of the pipeline network, considering the uncertainty of the pipeline network operation state, the huge computational burden will make the efficiency of the gas supply reliability assessment model low.

[0006] From the perspective of the evaluation methods of the reliability of pipeline network gas supply, most scholars have established evaluation indexes for gas supply reliability from different perspectives. For example, Su et al. proposed gas supply reliability indexes for pipeline networks from both the pipeline network and users. Yu et al. proposed two reliability indexes, namely gas supply satisfaction and gas supply guarantee ability, to quantify the gas supply capacity. Yu et al. established an evaluation index for the reliability of pipeline network gas supply based on demand-side analysis from the perspectives of quantity and time. Yang et al. proposed an evaluation index for the reliability of pipeline network gas supply from the perspectives of the degree of natural gas shortage and the economic loss of shortage. Fan et al. established an evaluation index for gas supply reliability considering the probability and consequences of supply shortage events from both the pipeline network and users.

[0007] However, based on the evaluation indexes, the evaluation of the reliability of pipeline network gas supply cannot be separated from the large-scale sampling analysis of the operation status of the pipeline network, and the calculation cost is relatively high. Therefore, Chen et al. calculated the probabilities of the pipeline network under various operation scenarios based on the Markov process and reliability theory, and selected the scenarios with higher occurrence probabilities for the evaluation of gas supply reliability. However, only focusing on high-probability scenarios may ignore the impact of extreme events with low probabilities but high consequences on the safety of pipeline network gas supply, and underestimate the potential risks of natural gas pipeline networks. Therefore, at this stage, it is necessary to comprehensively consider the probabilities of various degradation states of the pipeline network and the supply-demand relationship of the pipeline network under the corresponding states, and re-evaluate the reliability of pipeline network gas supply comprehensively. Summary of the Invention

[0008] In order to overcome the deficiencies in the prior art, the technical problem to be solved by the present invention is to provide a method for evaluating the reliability of natural gas pipeline network gas supply based on a pipeline network degradation model.

[0009] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for evaluating the reliability of natural gas pipeline network gas supply based on a pipeline network degradation model, including the following evaluation steps:

[0010] Step 1: Considering the specific influence of the compressor station and pipeline random degradation factors on the natural gas pipeline network system, and according to the different influence laws of the degradation of the two on the gas supply volume of the natural gas pipeline network system, respectively establish models for the random degradation processes of the compressor station and the pipeline.

[0011] Step 2: Analyze and calculate the probabilities of various operation states of the pipeline network, and based on the maximum gas supply volume of the pipeline network affected by the degradation of the pipeline and the compressor station, evaluate the supply-demand relationship of the pipeline network in various states, so as to evaluate the reliability of pipeline network gas supply, specifically including:

[0012] Step 2.1: Conduct reliability evaluation for the compressor station;

[0013] Step 2.2: Conduct reliability evaluation for the pipeline considering capacity;

[0014] Step 2.3: Conduct reliability evaluation for the reliability of pipeline network gas supply;

[0015] Step 2.4: Evaluate the gas supply reliability of the pipeline network considering the degradation of compressor stations and pipelines.

[0016] The specific method for modeling the degradation process of compressor stations in Step 1 is as follows:

[0017] Step 1.1: Describe and express the pipeline network system. The simplified topological structure of the natural gas pipeline network is represented by the following formula:

[0018] G≡(V, S);

[0019] where V = {1, 2,..., N} is the set of all N nodes in the pipeline network, and each node represents a compressor station. S = {(i, j)|i, j ∈ V} is the set of all m edges in the pipeline network, and each edge represents a section of natural gas pipeline;

[0020] Step 1.2: Define that each compressor station is composed of n identical compressors in parallel, among which there are n - a operating compressors and a cold standby compressors. Each compressor has two states: normal and faulty. Specifically, the state of the entire station is defined by the number of faulty compressors in the compressor station:

[0021] Use the stochastic process {X i (t), t ≥ 0} to represent the degradation process of compressor station i;

[0022] where X i (t) represents the state of compressor station i at time t, satisfying X i (t) ∈ {0, 1, 2,..., n};

[0023] When the number of faulty compressors ranges from 0 to a, it is regarded as the normal operating state of the compressor station, denoted as:

[0024] W = {0, 1,..., a};

[0025] When the number of faulty compressors is greater than the number of standby compressors, that is, when the number of faulty compressors ranges from a + 1 to n, it is regarded as the faulty state of the compressor station, denoted as:

[0026] F = {a + 1, a + 2,..., n};

[0027] Assume that the failure time and repair time of each compressor follow an exponential distribution, and the failure rate and repair rate are represented by λ and μ respectively.

[0028] Describe the state evolution of the compressor station using a Markov process. The transition rate of the compressor station is represented by matrix A as:

[0029]

[0030] Then the matrix form of the Markov process is expressed as:

[0031]

[0032] Among them, P(t) = (P j (t)) represents the state probability vector of the compressor station at time t, and P j (t) = P{X i (t) = j}.

[0033] The specific method for modeling the random degradation process of the pipeline in the first step is as follows:

[0034] Step 1.3: Model the pipeline degradation process:

[0035] Define the maximum corrosion depth of pipeline (i, j) at time t as: D i,j (t);

[0036] It is assumed that the change in the corrosion depth conforms to the Gamma process, and the expression of its probability density function is:

[0037]

[0038] Among them,

[0039] Step 1.4: Model the random capacity:

[0040] Adopt the finite element model and use the arc-length method in ANSYS software to obtain the maximum pressure value that the pipeline can withstand under different corrosion states. The expression is:

[0041]

[0042] Among them, P i,j cor (t) represents the maximum pressure that the corroded pipeline (i, j) can withstand at time t, P0 is the maximum bearing pressure of the intact pipeline, wt is the wall thickness of the pipeline, a1 and a2 are undetermined constants, c2 = a1P0 - a2P0 is also a constant;

[0043] Define that when the compressor station at node i is working normally, the maximum allowable pressure at the inlet of pipeline (i, j) is the maximum pressure it can withstand in the current corrosion state, denoted as P i,j cor (t);

[0044] Connect the outlet of pipeline (i, j) to the compressor station, and the minimum allowable pressure at its outlet is the minimum inlet pressure P C of compressor station j, where P Cis a constant determined by the performance of the compressor station;

[0045] Define the capacity c of pipeline (i, j) at time t i,j (t) is calculated by the formula:

[0046]

[0047] where F is a constant, P i,j cor (t) is the maximum pressure that pipeline (i, j) can withstand, but its value cannot be greater than the design pressure of the pipeline, P C is the minimum inlet pressure of the compressor station, D is the inner diameter of the pipeline, λ is the friction coefficient, Δ is the relative density of the gas, J is the gas compression factor, T0 is the average temperature of the pipeline, L i,j is the length of pipeline (i, j);

[0048] According to the maximum pressure value and capacity calculation situation, the pipeline capacity c i,j (t) and the maximum corrosion depth d i,j (t) have the following functional relationship:

[0049]

[0050] where, c4 = P C 2 are all constants;

[0051] Combined with the probability density function of the maximum corrosion depth d i,j (t), the expression of the probability density function of the pipeline capacity c i,j (t) is:

[0052]

[0053] where, is a constant.

[0054] The specific method for reliability assessment of the compressor station in step 2.1 is as follows:

[0055] Define that if the state probability vector of the initial state of the compressor station satisfies then the reliability of compressor station i is the probability that the compressor station has been in normal operation until time t, that is, it satisfies:

[0056]

[0057] P in the formula j (t), j ∈ W satisfies the following differential equations:

[0058]

[0059] Among them, P W (t)=(P0(t), P1(t), …, P a (t)) represents the probability vector of the compressor station being in the working state at time t, is a block matrix of matrix A, and matrix B is in the block form in matrix A, indicating that the state of the compressor station is in the normal working state before and after the conversion. The specific form of matrix B is expressed as:

[0060]

[0061] Perform Laplace transform on both ends of the above differential equations and solve to obtain:

[0062]

[0063] Among them, I is the identity matrix;

[0064] Substitute the above formula into the calculation formula of the reliability of compressor station i, and calculate to obtain:

[0065]

[0066] Among them, e W is an (a + 1)-dimensional column vector with all components being 1;

[0067] For in the above formula, perform inverse Laplace transform, and the system reliability of compressor station i at time t can be obtained, denoted as:

[0068] The specific method for reliability assessment of the pipeline considering capacity in step 2.2 is as follows:

[0069] Define that at t = 0, the pipeline (i, j) is put into operation in a brand-new state, and the corrosion depth is denoted as d i,j (t)=0, and the pipeline reliability at this time is denoted as

[0070] When the pipeline runs to time t, the corrosion depth of the pipeline is d i,j (t), and the maximum capacity of the pipeline at this time is c i,j (t), that is, when the transportation task of the pipeline (i, j) is less than or equal to the capacity c i,j (t), the pipeline can maintain reliable operation. Then, comprehensively considering all situations of the corrosion depth d i,j (t), the calculation formula for the reliability of the pipeline (i, j) at time t is:

[0071]

[0072] Among them, L is the corrosion failure threshold of the pipeline.

[0073] The specific method for evaluating the gas supply reliability of the pipe network in step 2.3 is as follows:

[0074] Calculate the maximum flow rate of the pipe network. The input is the capacity matrix of each pipe segment, denoted as C = (c i，j (t)) n×n ;

[0075] Among them, the element c i,j (t) is the capacity of the pipeline (i, j) affected by the degradation of the pipeline and the compressor station;

[0076] If there is no pipeline connection between nodes i and j, it is denoted as: c i,j (t) = 0;

[0077] Calculate the maximum flow rate G(t) of the pipe network at time t. It is specifically solved by the following mathematical optimization model:

[0078] Objective:

[0079]

[0080] Constraints:

[0081] 0 ≤ Q i,j (t) ≤ c i,j (t);

[0082]

[0083] Among them, Q i,j (t) is the actual flow rate of the pipeline (i, j), S is the super source point of the pipe network, and E is the super sink point of the pipe network;

[0084] In the constraint formula, it respectively represents: the actual flow rate Q of the pipeline i,j (t) cannot exceed the pipeline capacity limit;

[0085] For the intermediate node i, all the flow rates flowing into node i are equal to all the flow rates flowing out of node i;

[0086] All the flow rates flowing out of the super source point S in the pipe network are equal to all the flow rates flowing into the super sink point E;

[0087] Define the specific gas supply reliability of the evaluated pipe network as: under each degradation state of the pipe network, the probability that the maximum gas supply of the pipe network is G(t) multiplied by the probability that the maximum gas supply G(t) is greater than or equal to the total demand Z(t). The specific calculation steps are as follows:

[0088] The calculation formula for the probability that the maximum gas supply of the pipe network is G(t) is:

[0089]

[0090] Among them, the function represents the reliability considering the series-parallel relationship of pipelines, is the reliability of the compressor station at node i at time t, and the function represents the structural reliability considering the series-parallel relationship of compressor stations;

[0091] Set the probability density function of the total network demand Z(t) as f Z (z(t)), then the expression for the probability that the maximum gas supply G(t) is greater than or equal to the total demand Z(t) is:

[0092]

[0093] In summary, the expression for the gas supply reliability of the pipeline network is:

[0094]

[0095] The specific method for evaluating the gas supply reliability of the pipeline network considering the degradation and renewal of compressor stations and pipelines in step 2.4 is as follows:

[0096] Set that the degradation difference shown by the pipeline in the actual environment only affects the scale parameter β of the Gamma process and has no effect on the shape parameter. Use the Bayesian update process to update the scale parameter β and consider the conjugate distribution family to simplify the analytical solution of the posterior distribution of the parameter:

[0097] Set the prior distribution of the scale parameter β as a Gamma distribution, denoted as Ga(u P , v P ). At the detection time t = lT, l = 1, 2,..., obtain the maximum corrosion depth data of the pipeline as Then, combined with the state data D (l-1) of the pipeline (i, j) at the previous detection time t = (l - 1)T, obtain the incremental data of the pipeline (i, j). The specific calculation steps are as follows:

[0098] Adopt the Bayesian update theorem. Based on the prior distribution f(β (l) ) of β (l) and the corresponding maximum likelihood function , the posterior distribution of β (l) can be obtained, and the expression is:

[0099]

[0100] Among them, when l = 1, f(β (l) ) is the prior distribution Ga(u P , v P), when \(l > 1\), \(f(β (l) ) is also the posterior distribution of \(β (l-1) . Based on the above formula, the posterior distribution of \(β (l) is as follows:

[0101]

[0102] Assume that the corrosion degradation of each pipeline is independent of each other. Combining with the expression of the posterior distribution of \(β (l) , the predicted reliability of pipeline \((i, j)\) at time \(t\) is obtained as :

[0103]

[0104] For the number of newly added compressor failures in the compressor station during the detection period , it follows a Poisson distribution with parameter \(\lambda\). The Poisson distribution and the Gamma distribution are conjugate distributions. Therefore, the prior distribution of \(\lambda\) is set as \(Ga(u C , v C );

[0105] At time \(k = 1, 2, \cdots\), the state data of the compressor station is obtained, denoted as

[0106] where represents the number of compressor failures at the \(k\)-th detection of the \(i\)-th compressor station;

[0107] Combining the state data \(X of the compressor station at the previous detection time (k-1) , the number of newly added failures of compressor station \(i\) is denoted as

[0108] Using Bayes' update theorem, based on the prior distribution \(f(\lambda (k) ) and the corresponding maximum likelihood function (k) , the posterior distribution of \(\lambda can be obtained, and the expression is: (k) :

[0109]

[0110] where, when \(k = 1\), \(f(\lambda (k) ) is the prior distribution of \(\lambda\) which is \(Ga(u C , v C ). When \(k > 1\), \(f(\lambda (k) ) is also the posterior distribution of \(\lambda (k-1) . Based on the above formula, the posterior distribution of \(\lambda (k) is as follows:

[0111]

[0112] Substitute the updated failure rate λ (k) into matrix B to obtain the updated transition rate block matrix, and the expression is:

[0113]

[0114] According to the updated transition rate block matrix B (k) and the state at the current moment further calculate the predicted reliability of compressor station i at time t The calculation formula is:

[0115]

[0116] where is the inverse Laplace transform, and P W (t) is the state probability vector of compressor station i at time t.

[0117] The beneficial effects of the present invention compared with the prior art are as follows: By proposing a method for evaluating the gas supply reliability of a natural gas pipeline network based on a pipeline network degradation model, the present invention can accurately evaluate and predict the gas supply reliability of the natural gas pipeline network, accurately evaluate the current gas transmission capacity of the pipeline network and predict the change trend of the future gas supply reliability of the pipeline network, greatly reduce the economic losses caused by gas supply shortage events, and provide an accurate maintenance basis for the operation and maintenance of the pipeline network, ensure that the pipeline network maintains a high gas supply reliability operation, ensure the continuous smooth supply of the natural gas pipeline network, and at the same time can reduce the operation and maintenance costs of the natural gas company and increase the enterprise benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] The present invention will be further described below with reference to the accompanying drawings:

[0119] Figure 1 is a schematic diagram of the state conversion of the compressor station of the present invention;

[0120] Figure 2 is a schematic diagram of the structure of the connection between the compressor station and the pipeline of the present invention;

[0121] Figure 3 is a schematic diagram of the random capacity of the pipeline of the present invention;

[0122] Figure 4 is a schematic diagram of the structure of the pipeline network with virtual source and sink points added in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0123] The present invention proposes a method for evaluating the gas supply reliability of a natural gas pipeline network based on a pipeline network degradation model to achieve the purpose of accurately evaluating the current gas transmission capacity of the pipeline network and predicting the change trend of the future gas supply reliability of the pipeline network. The specific steps are as follows:

[0124] Step 1: Model the degradation of the pipeline network:

[0125] For a natural gas pipeline network system that simultaneously considers the random degradation effects of stations and pipelines, according to the different influence laws of the degradation of the two on the gas supply volume of the pipeline network, the degradation of the two is modeled separately.

[0126] Step 1.1: Describe and express the pipeline network system:

[0127] Since the natural gas pipeline network has the characteristics of diverse equipment types and complex network structures, in order to simplify the pipeline network degradation model, the present invention considers key equipment with higher failure rates such as compressor stations and pipelines, analyzes the impact of their degradation on the gas supply volume of the pipeline network, and specifically uses the following formula to represent the simplified topological structure of the natural gas pipeline network:

[0128] G = (V, S);

[0129] Among them, V = {1, 2,..., N} is the set of all N nodes in the pipeline network, and each node represents a compressor station. S = {(i, j)|i, j ∈ V} is the set of all m edges in the pipeline network, and each edge represents a section of natural gas pipeline.

[0130] Step 1.2: Model the degradation process of the compressor station:

[0131] Each compressor station is composed of n identical compressors in parallel, among which there are n - a operating compressors and a cold standby compressors. Each compressor has two states: normal and faulty. Specifically, the state of the entire station is defined by the number of faulty compressors in the compressor station: use the stochastic process {X i (t), t ≥ 0} to represent the degradation process of compressor station i. Among them, X i (t) represents the state of compressor station i at time t, satisfying X i (t) ∈ {0, 1, 2,..., n};

[0132] When the number of faulty compressors is less than or equal to the number of standby compressors, the standby compressors are immediately activated, and it will not affect the gas transmission capacity of the entire compressor station. Therefore, states 0 to a can be regarded as the normal operating states of the compressor station, denoted as W = {0, 1,..., a};

[0133] When the number of faulty compressors is greater than the number of standby compressors, the inlet natural gas flow of the compressor station will increase, and the remaining working compressors are likely to automatically shut down due to the stagnant state, resulting in a decrease in the inlet pressure of the pipeline connected to the compressor station and a decrease in the transmission capacity of the surrounding pipeline network. Therefore, states a + 1 to n can be regarded as the faulty states of the compressor station, denoted as F = {a + 1, a + 2,..., n}.

[0134] Assume that the failure time and repair time of each compressor satisfy the exponential distribution, and denote the failure rate and repair rate by λ and μ respectively. The state evolution of the compressor station can be described by a Markov process, and its evolution process and state transition probabilities are as Figure 1 shown.

[0135] Furthermore, represent the transition rate of the compressor station by matrix A as:

[0136]

[0137] Then the matrix form of the Markov process can be expressed as:

[0138]

[0139] where P(t)=(P j (t)) represents the state probability vector of the compressor station at time t, and P j (t)=P{X i (t)=j}.

[0140] Step 1.3: Model the pipeline degradation process:

[0141] Since pipeline corrosion will greatly reduce the reliability and integrity of the pipeline and is one of the main factors restricting the continuous and stable operation of the pipeline, engineering practice shows that the depth of corrosion defects on the pipeline is the most important factor determining the pipeline state;

[0142] Therefore, represent the maximum corrosion depth of pipeline (i,j) at time t as: D i,j (t);

[0143] If maintenance measures are not considered, the change in corrosion depth shows a cumulative process with a monotonically increasing trend. The present invention assumes that the change in corrosion depth conforms to a Gamma process, and the expression of its probability density function is:

[0144]

[0145] where,

[0146] Step 1.4: Model the random capacity:

[0147] Since corrosion is a degradation mechanism with time dependence, as the maximum corrosion depth of the pipeline continuously increases, the pipeline wall thickness gradually decreases. Correspondingly, the maximum allowable operating pressure of the pipeline will also gradually decrease as the wall thickness thins; based on the finite element model, the arc-length method is adopted in ANSYS software in the present invention to obtain the maximum pressure value that the pipeline can withstand under different corrosion states, and the expression is:

[0148]

[0149] Among them, P i,j cor (t) represents the maximum pressure that the corroded pipeline (i, j) can withstand at time t. P0 is the maximum pressure that a sound pipeline can withstand. wt is the wall thickness of the pipeline, and a1 and a2 are undetermined constants. c2 = a1P0 - a2P0 is also a constant.

[0150] During the operation of the pipeline network, the degradation of compressor stations and pipelines jointly affects the inlet pressure of pipelines, thus determining the natural gas capacity of pipelines:

[0151] On the one hand, considering the economic benefits of pipeline network operation, the corroded pipeline can still undertake a certain gas transmission task, but the maximum pressure that the pipeline can withstand will gradually decrease with the corrosion degradation of the pipeline, as shown in formula (4);

[0152] On the other hand, during the transportation of natural gas, the compressor station compensates for the pressure drop caused by the friction between the inner surface of the pipeline and the gas. When the compressor station fails, the compressor station can only play a connecting role and cannot provide pressure compensation; therefore, the reliability of the compressor station also affects the inlet pressure of the pipeline, thereby affecting the natural gas capacity of the pipeline.

[0153] From Figure 2 it can be seen that if the compressor station at node i is operating normally, the maximum allowable pressure at the inlet of pipeline (i, j) is the maximum pressure P i,j cor (t) that it can withstand in the current corrosion state;

[0154] Connect the outlet of pipeline (i, j) to the compressor station, and its minimum allowable pressure at the outlet is the minimum inlet pressure P C , P C is a constant determined by the performance of the compressor station;

[0155] If the compressor station at node i fails, it is equivalent to directly connecting pipeline (i, j) to its upstream pipeline, that is, the compressor station only plays a connecting role. The calculation formula for the capacity ci,j(t) of pipeline (i, j) at time t is:

[0156]

[0157] Among them, F is a constant, P i,j cor (t) is the maximum pressure that pipeline (i, j) can withstand, but its value cannot be greater than the design pressure of the pipeline, P C is the minimum inlet pressure of the compressor station, D is the inner diameter of the pipeline, λ is the friction coefficient, Δ is the relative density of the gas, J is the gas compressibility factor, T0 is the average temperature of the pipeline, Li,j is the length of pipeline (i, j).

[0158] As Figure 3 shown, by combining Equation (4) and Equation (5), the pipeline capacity c i,j (t) and the maximum corrosion depth d i,j (t) have the following functional relationship:

[0159]

[0160] where c4 = P C 2 are all constants.

[0161] Due to the randomness of the corrosion state, the pressure that the pipeline can withstand is random, which further makes the pipeline capacity under the influence of pressure random. Combining the probability density function of the maximum corrosion depth d i,j (t) with the following formula, the expression of the probability density function of the pipeline capacity c i,j (t) can be deduced as:

[0162]

[0163] where is a constant.

[0164] Step two: For the evaluation of the gas supply reliability of the pipe network

[0165] The evaluation of the gas supply reliability of the pipe network mainly includes two aspects:

[0166] On the one hand, deduce the probabilities of various operating states of the pipe network, and these probabilities can be deduced based on Steps 2.2 - 2.3;

[0167] On the other hand, evaluate the supply - demand relationship of the pipe network in various states, which requires obtaining the maximum gas supply of the pipe network affected by the degradation of pipelines and compressor stations; therefore, determining the gas supply plan of the pipe network under the random capacity constraint of pipelines is also an important part of evaluating the gas supply reliability of the pipe network.

[0168] Step 2.1: For the evaluation of the reliability of the compressor station:

[0169] Define that if the state probability vector of the initial state of the compressor station satisfies then the reliability of compressor station i is the probability that the compressor station has been in normal operation until time t, that is, it satisfies:

[0170]

[0171] Meanwhile, P in Equation (8) j(t), j ∈ W satisfy the differential equation system shown in Equation (9):

[0172]

[0173] Among them, P W (t) = (P0(t), P1(t), …, P a (t)) represents the probability vector that the compressor station is in the working state at time t, is a block matrix of matrix A, and matrix B is in a block form in matrix A, indicating that the state of the compressor station is in the normal working state before and after the conversion. Its specific form is expressed as:

[0174]

[0175] Considering that it is rather cumbersome to solve Equation (9) by the general method, the Laplace transform can be performed on both sides of Equation (9) to obtain:

[0176]

[0177] Among them, I is the identity matrix;

[0178] Therefore, substituting Equation (11) into Equation (8), the calculation shows that:

[0179]

[0180] Among them, e W is an (a + 1)-dimensional column vector with all components being 1.

[0181] Furthermore, taking the inverse Laplace transform of in Equation (12), the system reliability of compressor station i at time t can be obtained

[0182] Step 2.2: Evaluate the pipeline reliability considering capacity:

[0183] Define that at t = 0, pipeline (i, j) is put into operation in a brand-new state, and the corrosion depth is denoted as d i,j (t) = 0, and the pipeline reliability at this time is denoted as As the pipeline operation time increases, the maximum corrosion depth of the pipeline continuously increases, resulting in a gradual decrease in the pipeline capacity, which makes the possibility of the pipeline completing the gas transmission task decrease, and the pipeline reliability also decreases accordingly; when the pipeline operates to time t, the pipeline corrosion depth is d i,j (t). From Equation (5), it can be seen that the maximum capacity c i,j (t) at this time means that when the transportation task of pipeline (i, j) is less than or equal to the capacity c i,j (t), the pipeline can maintain reliable operation.

[0184] Based on the above analysis, considering all cases of the corrosion depth d i,j (t), the expression for the reliability of the pipeline at time t is as follows:

[0185]

[0186] where L is the corrosion failure threshold of the pipeline.

[0187] Step 2.3: Evaluate the gas supply reliability of the pipe network:

[0188] In a "single-source and single-sink" flow network, the maximum flow problem is to find the maximum feasible flow that satisfies the capacity and flow conservation constraints. The actual natural gas pipeline network often has multiple gas sources and multiple users. If virtual source points and virtual sink points are added to the natural gas pipeline network, solving the problem of the maximum gas supply volume of the natural gas pipeline network can be transformed into a typical maximum flow problem. For this reason, a schematic diagram of the pipeline network structure with added virtual source point S and sink point E is given, as Figure 4 shown.

[0189] When solving the maximum flow of the pipeline network, the input is the capacity matrix C = (c i，j (t)) n×n , and its element c i,j (t) is the capacity of the pipeline (i, j) affected by the degradation of the pipeline and the compressor station, and its value can be calculated by Equation (5); if there is no pipeline connection between nodes i and j, record ci,j(t) = 0; the maximum flow G(t) of the pipeline network at time t can be solved by the following mathematical optimization model:

[0190] Objective:

[0191]

[0192] Constraints:

[0193] 0 ≤ Q i,j (t) ≤ c i，j (t) (5);

[0194]

[0195] where Qi,j(t) is the actual flow of the pipeline (i, j), S is the super source point of the pipeline network, and E is the super sink point of the pipeline network. Constraint Equation (15) means that the actual flow Qi,j(t) of the pipeline cannot exceed the pipeline capacity limit, constraint Equation (16) means that for the intermediate node i, all the flows flowing into node i are equal to all the flows flowing out of node i, and constraint Equation (17) means that in the pipeline network, all the flows flowing out of the super source point S are equal to all the flows flowing into the super sink point E. The basic algorithm of the maximum flow problem is used to solve the optimization model shown in Equations (14)-(17).

[0196] In addition, the gas demand of the pipe network is not only affected by the seasonal changes of temperature and other weather variables, but also by the daily gas consumption habits of users and the social and economic level, etc. Therefore, the total demand of the pipe network shows a high degree of randomness. Regarding it as a random variable can more objectively describe the supply-demand relationship in the pipe network and accurately evaluate the gas supply reliability of the pipe network. The present invention assumes that the total demand of the pipe network users follows a normal distribution.

[0197] The gas supply reliability of the pipe network should be the probability that the maximum gas supply of the pipe network is G(t) under each degradation state of the pipe network multiplied by the probability that the maximum gas supply G(t) is greater than or equal to the total demand Z(t):

[0198] First, the calculation formula for the probability that the maximum gas supply of the pipe network is G(t) is:

[0199]

[0200] Among them, the function represents the reliability considering the series-parallel relationship of pipelines, is the reliability of the compressor station at node i at time t, and the function represents the structural reliability considering the series-parallel relationship of compressor stations.

[0201] Secondly, assuming that the probability density function of the total demand Z(t) of the pipe network is f Z (z(t)), then the probability that the maximum gas supply G(t) is greater than or equal to the total demand Z(t) is:

[0202]

[0203] In summary, the expression for the gas supply reliability of the pipe network is:

[0204]

[0205] Step 2.4: Evaluation of the gas supply reliability of the pipe network considering degradation and renewal:

[0206] During the actual operation of the pipe network, due to the different operating environments of the same type of equipment, different degradation characteristics will be shown. And during the operation and maintenance of the pipe network, by detecting the degradation state of the pipe network, new degradation data of pipelines and compressor stations will be continuously obtained; using these data to update the parameters of the degradation model can significantly improve the accuracy of the evaluation results and avoid unnecessary maintenance costs; therefore, on the basis of Step 2.3, the gas supply reliability of the pipe network considering renewal can be modeled.

[0207] For pipelines, assuming that the degradation differences exhibited by pipelines in the actual environment only affect the scale parameter β of the Gamma process and have no effect on the shape parameter, the Bayesian update process is used to update the scale parameter β, and the conjugate distribution family is considered to simplify the analytical solution of the posterior distribution of the parameter; for this purpose, assume that the prior distribution of the parameter β is a Gamma distribution, denoted as Ga(u P ,v P ). At the detection time t = lT, l = 1, 2, …, the maximum corrosion depth data of the pipeline is obtained Then, combined with the state data D (l-1) of the pipeline (i, j) at the previous detection time t = (l - 1)T, the incremental data of the pipeline (i, j) can be obtained

[0208] Specifically, using the Bayesian update theorem, based on the prior distribution f(β (l) ) of β and the corresponding maximum likelihood function (l) , the posterior distribution of β can be obtained, and the expression is: (l)

[0209]

[0210] where, when l = 1, f(β (l) ) is the prior distribution Ga(u P ,v P ) of β. When l > 1, f(β (l) ) is also the posterior distribution of β (l-1) . It can be seen from the conclusion of the above formula (21) that the posterior distribution of β (l) is:

[0211]

[0212] Assuming that the corrosion degradation of each pipeline is independent of each other, combined with formula (21), the predicted reliability of the pipeline (i, j) at time t is:

[0213]

[0214] For compressor stations, their failure rates will change with the change of operating conditions, and new detection data needs to be introduced to update the parameters of the degradation model. The repair technology of compressors is relatively mature, and its repair rate can be estimated using the historical data of similar equipment without updating; since the number of newly added compressor failures in the compressor station during the detection period follows a Poisson distribution with parameter λ, and the Poisson distribution and the Gamma distribution are conjugate distributions, so assume that the prior distribution of λ is Ga(u C ,v C ).​

[0215] At the moment k=1,2,…get status data of compressor station in, represents the number of compressor failures at the i-th compressor station at the k-th detection; combined with the last detection time Status data of compressor stations X (k-1) , the number of newly added failure units in compressor station i can be obtained as

[0216] Using the Bayesian update theorem, from λ (k) The prior distribution f(λ (k) ) and the corresponding maximum likelihood function We can get λ (k) The posterior distribution of is expressed as:

[0217]

[0218] When k = 1, f(λ (k) ) is the prior distribution of λ is Ga(u C ,v C ), when k>1, f(λ (k) ) is also λ (k-1) From the conclusion of formula (23), we can see that λ (k) The posterior distribution of is:

[0219]

[0220] The updated failure rate λ (k) Substituting into equation (10), we can get the updated transfer rate block matrix, which is expressed as:

[0221]

[0222] According to the updated transfer rate block matrix B (k) and the current state The predicted reliability of compressor station i at time t can be derived as It can be expressed as:

[0223]

[0224] in, is the inverse Laplace transform, P W (t) is the state probability vector of compressor station i at time t.

[0225] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the reliability of natural gas pipeline network supply based on pipeline network degradation model, characterized in that: The evaluation steps include: Step 1: Considering the impact of the random degradation factors of compressor stations and pipelines on the natural gas pipeline network system, the random degradation processes of compressor stations and pipelines are modeled separately according to the different impacts of the degradation of the two on the gas supply of the natural gas pipeline network system; Step 2: Analyze and calculate the probability of various operating states of the pipeline network, and based on the maximum gas supply of the pipeline network under the influence of pipeline and compressor station degradation, evaluate the supply and demand relationship of the pipeline network under various states, so as to evaluate the gas supply reliability of the pipeline network, specifically including: Step 2.1: Conduct reliability assessment for compressor stations; Step 2.2: Conduct reliability assessment for pipelines with considered capacity; Step 2.3: Evaluate the reliability of gas supply in the pipeline network; Step 2.4: Evaluate the reliability of the gas supply network considering the renewal of compressor stations and pipeline degradation by: The degradation difference reflected in the pipeline in the actual environment is set, which only affects the scale parameter β of the Gamma process and has no effect on the shape parameter. The scale parameter β is updated using the Bayesian update process, and the conjugate distribution family is considered to simplify the analytical solution of the posterior distribution of the parameters: The prior distribution of the scale parameter β is set to Gamma distribution, denoted as Ga(u P ,v P ), where u P ,v P are the shape and scale parameters of the Gamma distribution, the pipeline detection period is T, at the detection time t = lT, l = 1, 2, ..., the maximum corrosion depth data of the pipeline is obtained as is the maximum corrosion depth of pipeline (i, j) at the lth detection cycle, m is the number of pipelines, and then combined with the status data D of pipeline (i, j) at the last detection time t = (l-1)T (l-1) , get the incremental data of pipeline (i,j) The specific calculation steps are: Using the Bayesian update theorem, based on β (l) The prior distribution f(β (l) ) and the corresponding maximum likelihood function β can be obtained (l) The posterior distribution of is expressed as: Among them, α, β are the shape and scale parameters of the Gamma process. When l = 1, f(β (l) ) is the prior distribution Ga(u P ,v P ), when l>1, f(β (l) ) is also β (l-1) The posterior distribution of β is obtained based on the above formula. (l) The posterior distribution of is: In the formula, m is the number of pipelines, and the corrosion degradation of each pipeline is assumed to be independent of each other. (l) The expression of the posterior distribution, which gives the prediction reliability of pipeline (i, j) at time t for: Where L is the corrosion failure threshold of the pipeline, c i，j (t) is the capacity of pipeline (i, j) at time t; The number of newly added compressor failures in the compressor station within the detection period τ follows the Poisson distribution with parameter λ. The Poisson distribution and the Gamma distribution are conjugate distributions, so the prior distribution of λ is set to Ga(u C , V C ),u C , v C are the shape and scale parameters of the Gamma distribution; At time t = kτ, k = 1, 2, ..., the status data of the compressor station is obtained, which is recorded as in, represents the number of compressor failures at the i-th compressor station at the k-th detection, and N is the number of compressor stations; Combined with the status data X of the compressor station at the last detection time t = (k-1)τ (k-1) , the number of newly added faulty compressors at compressor station i is obtained as Using the Bayesian update theorem, according to λ (k) The prior distribution f(λ (k) ) and the corresponding maximum likelihood function We can get λ (k) The posterior distribution of is expressed as: When k = 1, f(λ (k) ) is the prior distribution of λ is Ga(u C , v C ), when k>1, f(λ (k) ) is also λ (k-1) The posterior distribution of (k) The posterior distribution of is: Where N is the number of compressor stations; The updated failure rate λ (k) Substitute into matrix B to get the updated transfer rate block matrix B (k) , the expression is: According to the updated transfer rate block matrix B(k) and the current state Further calculate the predicted reliability of compressor station i at time t The calculation formula is: in, is the inverse Laplace transform, P W (t) is the state probability vector of compressor station i at time t, e w is an a+1-dimensional column vector whose components are all 1, and I is the identity matrix.

2. According to claim 1, a natural gas pipeline network gas supply reliability assessment method based on a pipeline network degradation model is characterized by: The specific method for modeling the compressor station degradation process in step 1 is: Step 1.1: Describe the pipeline network system and use the following formula to express the simplified natural gas pipeline network topology: G≡(V, S); Where V = {1, 2, ..., N} is the set of all N nodes in the pipeline network, each node represents a compressor station, S = {(i, j)|, j, j∈V} is the set of all m edges in the pipeline network, each edge represents a section of natural gas pipeline; Step 1.2: Define that each compressor station consists of n identical compressors connected in parallel, including na operating compressors and a cold standby compressors. Each compressor has two states: normal and faulty. Specifically, the state of the entire station is defined by the number of faulty compressors in the compressor station: Using the random process {X i (t), t ≥ 0} represents the degradation process of compressor station i; Among them, X i (t) represents the state of compressor station i at time t, satisfying X i (t)∈{0, 1, 2,…,n}; When the number of failed compressors increases from 0 to a, it is considered as the normal working state of the compressor station, which is recorded as: W = {0, 1, ..., a}; When the number of failed compressors is greater than the number of standby compressors, that is, the number of failed compressors from a+1 to n is regarded as the failure state of the compressor station, which is recorded as: F = {a+1, a+2, ..., n}; Assume that the failure time and repair time of each compressor satisfy the exponential distribution, and represent the failure rate and repair rate by λ and μ respectively. The state evolution of the compressor station is described using a Markov process, and the conversion rate of the compressor station is represented by the matrix A as follows: The matrix form of the Markov process is expressed as: Where P(t)=(P j (t)) represents the state probability vector of the compressor station at time t, and P j (t) = P{X i (t) = j}.

3. The method for evaluating the reliability of natural gas pipeline network supply based on pipeline network degradation model according to claim 2 is characterized in that: The specific method for modeling the random degradation process of the pipeline in step 1 is: Step 1.3: Model the pipeline degradation process: The maximum corrosion depth D of pipeline (i, j) at time t i，j (t) is a random variable, the maximum corrosion depth D i，j (t) follows the probability density function Gamma process, at the time of detection, the maximum corrosion depth of pipeline (i, j) at time t is recorded as d i，j (t), the expression of its probability density function is: Among them, α, β are the shape and scale parameters of the Gamma process, and Γ(α) is defined as the Gamma function, defined as Γ(α) = ∫0 ∞ z α-1 e -z dz; Step 1.4: Model for random capacity: Using the finite element model and the arc length method in ANSYS software, the maximum pressure value that the pipeline can withstand under different corrosion conditions is obtained. The expression is: Among them, P i，j cor (t) represents the maximum pressure that the corroded pipeline (i, j) can withstand at time t, P0 is the maximum pressure that the intact pipeline can withstand, wt is the wall thickness of the pipeline, a1, a2 are unknown constants, c2=a1P0-a2P0 is also a constant; When the compressor station at node i is working normally, the maximum allowable pressure at the inlet of pipeline (i, j) is the maximum pressure it can withstand under the current corrosion state, denoted as P i，j cor (t); Connect the outlet of pipeline (i, j) to the compressor station. The minimum allowable pressure of its outlet is the minimum inlet pressure P of compressor station j. C , where P C is a constant determined by the performance of the compressor station; Define the capacity c of pipeline (i, j) at time t i，j The calculation formula of (t) is: Among them, F is a constant, P i，j cor (t) is the maximum pressure that the pipeline (i, j) can withstand, but its value cannot be greater than the design pressure of the pipeline, P C is the minimum inlet pressure of the compressor station, D is the inner diameter of the pipeline, λ is the friction coefficient, Δ is the relative density of the gas, J is the gas compression factor, T0 is the average temperature of the pipeline, L i，j is the length of pipeline (i, j); According to the maximum pressure value and capacity calculation, the pipeline capacity c can be obtained. i，j (t) and maximum corrosion depth d i，j The functional relationship between (t) is: in, c4=P C 2 are all constants; Combined maximum corrosion depth d i，j The probability density function of (t) is used to obtain the pipeline capacity c i，j The probability density function of (t) is expressed as: in, is a constant.

4. The method for evaluating the reliability of natural gas pipeline network supply based on pipeline network degradation model according to claim 3 is characterized by: The specific method for performing reliability assessment on the compressor station in step 2.1 is: Define that if the state probability vector of the initial state of the compressor station satisfies The reliability of compressor station i is is the probability that the compressor station is in normal working condition until time t, that is, it satisfies: P in the formula j (t), j∈W satisfies the following differential equations: Among them, P W (t)=(P0(t),P1(t),…,P a (t)) represents the probability vector of the compressor station being in working state at time t, is the block matrix of matrix A, and matrix B is the block form of matrix A, indicating that the state of the compressor station is in normal working state before and after the conversion. The specific form of matrix B is expressed as: Perform Laplace transform on both ends of the above differential equations and solve them: in, represents the Laplace transform of Pw(t), where I is the unit matrix; Substituting the above formula into the reliability of compressor station i In the calculation formula, we can get: Among them, e W is an a+1-dimensional column vector whose components are all 1; For the above formula By performing inverse Laplace transform, we can get the system reliability of compressor station i at time t, which is expressed as:

5. The method for evaluating the reliability of natural gas pipeline network supply based on pipeline network degradation model according to claim 4 is characterized in that: The specific method for performing reliability assessment on the pipeline with considered capacity in step 2.2 is: Defined as: At time t = 0, the pipeline (i, j) is put into operation in a brand new state, and the corrosion depth is d i，j (t) = 0, and the pipeline reliability at this time is recorded as When the pipeline runs to time t, the pipeline corrosion depth is d i，j (t), the maximum capacity of the pipeline is c i，j (t), that is, when the transport task of pipeline (i, j) is less than or equal to capacity c i，j (t), the pipeline can maintain reliable operation, then the corrosion depth d i，j (t), the calculation formula of pipeline (i, j) reliability at time t is: Where L is the corrosion failure threshold of the pipeline.

6. The method for evaluating the reliability of natural gas pipeline network supply based on pipeline network degradation model according to claim 5 is characterized in that: The specific method for evaluating the reliability of gas supply in the pipeline network in step 2.3 is: The maximum flow of the pipe network is calculated, and the input is the capacity matrix of each pipe section, denoted as C = (c i，j (t)) n×n ; Among them, the element c i，j (t) is the capacity of pipeline (i, j) under the influence of pipeline and compressor station degradation; If there is no pipeline connection between nodes i and j, it is recorded as: c i，j (t) = 0; Calculate the maximum flow G(t) of the pipe network at time t, which is solved by the following mathematical optimization model: Target: constraint: 0≤Q i，j (t)≤c i，j (t); Among them, Q i，j (t) is the actual flow rate of pipeline (i, j), S is the super source point of the pipeline network, and E is the super sink point of the pipeline network; The constraints are: the actual flow rate Q i，j (t) The pipeline capacity limit cannot be exceeded; For an intermediate node i, all flows into node i are equal to all flows out of node i; All flows out of the super source point S in the pipe network are equal to all flows into the super sink point E; The gas supply reliability of the pipeline network to be evaluated is defined as follows: under each degradation state of the pipeline network, the probability that the maximum gas supply of the pipeline network is G(t) multiplied by the probability that the maximum gas supply G(t) is greater than or equal to the total demand Z(t). The specific calculation steps are: The calculation formula for the probability that the maximum gas supply of the pipeline network is G(t) is: Among them, the function Indicates the reliability of considering the series and parallel relationship of pipelines. is the reliability of the compressor station at node i at time t, function It represents the structural reliability considering the series and parallel relationship of the compressor stations; Assume the probability density function of the total demand Z(t) of the pipeline network is f Z (z(t)), then the probability that the maximum gas supply G(t) is greater than or equal to the total demand Z(t) is expressed as: P(G(t)≥Z(t))=∫0 G(t) f Z (z(t))dz(t); In summary, the expression for the reliability of gas supply in the pipeline network is:

Images