A natural gas network analysis sensitivity calculation method

Abstract

The application discloses a natural gas network analysis sensitivity calculation method. The method comprises the following steps: step S1, obtaining a natural gas network operation state parameter; step S2, constructing a load node pressure relative to a reference node pressure analysis sensitivity; step S3, constructing a load node pressure relative to a ratio of a natural gas flow provided by a relaxation node and a reference node analysis sensitivity; and step S4, constructing a load node pressure relative to a natural gas flow consumed by a load node analysis sensitivity. The application can establish a state variable-control variable sensitivity analysis expression in the natural gas network, describe the correlation between the sensitivity and the natural gas network topological parameters and the operation state parameters in the form of an explicit expression, and provide strong support for determining a natural gas network planning scheme and an operation scheme.

Description

Technical Field

[0001] This invention belongs to the field of natural gas system applications, and particularly relates to a method for calculating the analytical sensitivity of a natural gas network. Background Technology

[0002] Given that natural gas can provide a clean alternative to high-carbon fossil fuels and offer flexibility for renewable energy sources with uncertainties, the scale and application scenarios of natural gas will continue to expand in the future, leading to more complex natural gas network structures and user types. Effectively analyzing the operational characteristics of natural gas networks is a crucial issue in the planning, design, and operation control of these networks. Sensitivity methods utilize the differential relationships between different physical quantities to describe the coupling relationships between variables, quantifying the degree of change in state parameters under disturbances and thus identifying weak links and key factors in the system. Current sensitivity methods are based on solving the Jacobian matrix in the energy flow equations; the sensitivity results are black-box results, meaning they cannot reflect the influence of topological data and current state parameters on the sensitivity results, and therefore cannot effectively guide the adjustment of coupling characteristics. Therefore, there is an urgent need to propose an analytical sensitivity calculation method for natural gas networks. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the analytical sensitivity of a natural gas network, so as to establish explicit expressions for the sensitivity of each state variable-control variable with respect to topology parameters and state parameters, providing strong guidance for changing the coupling characteristics of a natural gas network by adjusting topology parameters or state parameters.

[0004] To address the aforementioned technical problems, this invention provides a method for calculating the analytical sensitivity of a natural gas network, comprising the following steps:

[0005] Step S1: Obtain the operating status parameters of the natural gas network; the operating status parameters include the natural gas flow rate in the natural gas branch, the pressure of each node, and the pressure ratio of the compressor;

[0006] Step S2: Construct the analytical sensitivity of the load node pressure relative to the reference node pressure;

[0007] Step S3: Construct the analytical sensitivity of the ratio of the load node pressure to the natural gas flow provided by the slack node and the reference node;

[0008] Step S4: Construct the analytical sensitivity of the load node pressure relative to the natural gas flow consumed by the load node.

[0009] Furthermore, step S2 specifically includes the following steps:

[0010] Step S21: Define the node with a given pressure in the natural gas network as the reference node, denoted as Ref; define the node with a given injection flow rate ratio to the injection flow rate of the reference node as the relaxation node, and denote the set of all relaxation nodes as Ω1; define the remaining nodes as load nodes, and denote the set of all load nodes as Ω2.

[0011] Step S22, denoted as p at the pressure at the reference node Ref. Ref Let i be any load node in Ω2, and let p be the pressure at load node i. i , note p i Relative to p Ref The sensitivity is The construction steps are as follows:

[0012] When there is no compressor on the path from load node i to reference node Ref, The analytical expression is:

[0013]

[0014] When there is a compressor on the path from load node i to reference node Ref and the path first passes through the compressor's inlet node, The analytical expression is:

[0015]

[0016] In the above formula, ε is the pressure ratio of the compressor;

[0017] When there is a compressor on the path from load node i to reference node Ref and the path first passes through the compressor's outlet node, The analytical expression is:

[0018]

[0019] Furthermore, step S3 specifically includes the following steps:

[0020] Step S31: Denote the set consisting of all branches in the natural gas network as Ω3, and denote any branch in Ω3 as x1. Calculate the characteristic parameters of branch x1.

[0021]

[0022] In the above formula, x 1,in and x 1,out These are the nodes at the starting and ending points of branch x1, respectively. The natural gas flow rate in branch x1, and They are nodes x 1,in and node x1,out Pressure at the location;

[0023] Step S32, let any relaxed node in Ω1 be k, and let R be the ratio of the injected flow at relaxed node k to the injected flow at reference node Ref. k , note p i Relative to R k The sensitivity is Let Sum be the sum of the flow consumed by each load node. load Let Sum1 be the sum of the ratios of the flow provided by all relaxed nodes and the reference node plus 1. Let t be any relaxed node in Ω1 except k, and let R be the ratio of the flow provided by relaxed node t to that provided by the reference node. t Let node m be the intersection of the path from relaxed node k to reference node Ref and the path from node i to reference node Ref; let node n be the intersection of the path from relaxed node t to reference node Ref and the path from node i to reference node Ref; and let the set of branches on the path from node m to reference node Ref be denoted as . remember Let x2 be any branch in the equation, and let the natural gas flow rate in branch x2 be denoted as x2. The characteristic parameters of branch x2 are denoted as Let the set of branches on the path from node n to reference node Ref be . remember Let x3 be any branch in the network, and let the natural gas flow rate in branch x3 be denoted as x3. The characteristic parameters of branch x3 are denoted as The construction steps are as follows:

[0024] When there are no compressors on the path from node m to reference node Ref and on the path from node n to reference node Ref, The analytical expression is:

[0025]

[0026] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's inlet node, and there is no compressor on the path from node n to reference node Ref, let the compressor's inlet node and outlet node be u, respectively. m and v m The compressor has a pressure ratio of ε. m Let the distance from node m to node u be recorded. m The set of branches on the path is remember Let x4 be any branch in the network, and let the natural gas flow rate in branch x4 be denoted as x4. The characteristic parameters of branch x4 are denoted as Let node v be a record.m The set of branches on the path to the reference node Ref is remember Let x5 be any branch in the network, and let the natural gas flow rate in branch x5 be denoted as x5. The characteristic parameters of branch x5 are denoted as: The analytical expression is:

[0027]

[0028] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's outlet node, and there is no compressor on the path from node n to reference node Ref, The analytical expression is:

[0029]

[0030] When there is no compressor on the path from node m to reference node Ref, but there is a compressor on the path from node n to reference node Ref and this path passes through the compressor inlet first, let the compressor inlet node and outlet node be u, respectively. n and v n The compressor has a pressure ratio of ε. n Let the distance from node n to node u be denoted as . n The set of branches on the path is remember Let x6 be any branch in the network, and let the natural gas flow rate in branch x6 be denoted as x6. The characteristic parameters of branch x6 are denoted as: Let node v be a record. n The set of branches on the path to the reference node Ref is remember Let x7 be any branch in the network, and let the natural gas flow rate in branch x7 be denoted as x7. The characteristic parameters of branch x7 are denoted as The analytical expression is:

[0031]

[0032] When there is no compressor on the path from node m to reference node Ref, and there is a compressor on the path from node n to reference node Ref, and this path passes through the compressor's outlet first, The analytical expression is:

[0033]

[0034] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's inlet node, and simultaneously there is a compressor on the path from node n to reference node Ref and this path first passes through the compressor's inlet node, The analytical expression is:

[0035]

[0036] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's inlet node, and simultaneously there is a compressor on the path from node n to reference node Ref and this path first passes through the compressor's outlet node, The analytical expression is:

[0037]

[0038] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's outlet node, and simultaneously there is a compressor on the path from node n to reference node Ref and this path first passes through the compressor's inlet node, The analytical expression is:

[0039]

[0040] When there is a compressor on the path from node m to reference node Ref and this path passes through the compressor's outlet node first, and simultaneously there is a compressor on the path from node n to reference node Ref and this path passes through the compressor's outlet node first, The analytical expression is:

[0041]

[0042] Furthermore, step S4 specifically includes the following steps:

[0043] Step S41, let any node in Ω2 be i, and let the natural gas flow rate consumed at node i be L. i Let f be any node on the path from node i to reference node Ref, and let p be the pressure at node f. f Let the set of all branches on the path from node f to reference node Ref be . Let any branch be denoted as x8, and the node on the side of branch x8 furthest from node i be y1. Let the sum of the ratios of the injected flow at all relaxed nodes after node y1 in the direction furthest from node i to the injected flow at the reference node be denoted as x8. Remember p f Compared to L i The sensitivity is The build process is as follows:

[0044] When there is no compressor on the path from node f to reference node Ref, The analytical expression is:

[0045]

[0046] When there is a compressor on the path from node f to reference node Ref, and the path first passes through the compressor's inlet, let the compressor's inlet and outlet be denoted as u. j and v j Let the pressure ratio of the compressor be ε. j Let the distance from node f to node u be recorded. j The set of all branches on the path is Let any branch be denoted as x9, and the node on the side of branch x9 furthest from node i be y2. Let the sum of the ratios of the injected flow at all relaxed nodes after node y2 in the direction furthest from node i to the injected flow at the reference node be denoted as... Let node v be a record. j The set of all branches on the path to node Ref is Let x be any branch in the path. 10 , note the branch x 10 Let y3 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y3 in the direction furthest from node i to the injected flow at the reference node is denoted as . The analytical expression is:

[0047]

[0048] When there is a compressor on the path from node f to reference node Ref and the path first passes through the compressor's outlet, The analytical expression is:

[0049]

[0050] Step S42: Let any relaxed node in Ω1 be k, let the intersection of the path from node i to relaxed node k and the path from node i to reference node Ref be w, let any node on the path from node w to relaxed node k be l, and let the pressure at node l be p. l Let the set of all branches on the path from node w to reference node Ref be . Let x be any branch in the path. 11 , note the branch x 11 Let y4 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y4 in the direction furthest from node i to the injected flow at the reference node is denoted as . Let the set of all branches on the path from node w to node l be . Let x be any branch in the path. 12 , note the branch x 12 Let y5 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y5 in the direction furthest from node i to the injected flow at the reference node is denoted as . Remember p l Compared to L i The sensitivity is The construction process is as follows:

[0051] When there is no compressor on the path from node w to reference node Ref, and also when there is no compressor on the path from node w to node l, The analytical expression is:

[0052]

[0053] When there is a compressor on the path from node w to reference node Ref and this path first passes through the compressor's inlet node, and there is no compressor on the path from node w to node l, denote the compressor's inlet node and outlet node on the path from node w to reference node Ref as u, respectively. w and v w Let the pressure ratio of the compressor be ε. w Let the distance from node w to node u be recorded. w The set of all branches on the path is Let x be any branch in the path. 13 , note the branch x 13 Let y6 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y6 in the direction furthest from node i to the injected flow at the reference node is denoted as [y6 is missing from the original text]. Let node v be a record. w The set of all branches on the path to node l is Let x be any branch in the path. 14 , note the branch x 14 Let y7 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y7 in the direction furthest from node i to the injected flow at the reference node is denoted as . The analytical expression is:

[0054]

[0055] When there is a compressor on the path from node w to reference node Ref and this path first passes through the compressor's outlet node, and there is no compressor on the path from node w to node l, The analytical expression is:

[0056]

[0057] When there is no compressor on the path from node w to reference node Ref, but there is a compressor on the path from node w to node l, and this path first passes through the compressor's inlet node, denote the compressor's inlet node and outlet node on the path from node w to node l as u, respectively. l and v lLet the pressure ratio of the compressor be ε. l Let the distance from node w to node u be recorded. l The set of all branches on the path is Let x be any branch in the path. 15 , note the branch x 15 Let y8 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y8 in the direction furthest from node i to the injected flow at the reference node is denoted as . Let node v be a record. l The set of all branches on the path to node l is Let x be any branch in the path. 16 , note the branch x 16 Let y9 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y9 in the direction furthest from node i to the injected flow at the reference node is denoted as . The analytical expression is:

[0058]

[0059] When there is no compressor on the path from node w to reference node Ref, but there is a compressor on the path from node w to node l and this path passes through the compressor's outlet node first, The analytical expression is:

[0060]

[0061] The beneficial effects of this invention are:

[0062] The analytical sensitivity calculation method for natural gas networks proposed in this invention establishes analytical expressions for the sensitivity of load node pressure relative to reference node pressure, the ratio of natural gas flow provided by slack nodes and the reference node, and the natural gas flow consumed by load nodes. This method can intuitively reflect the influence of topology parameters and state parameters on the sensitivity results, and identify the topology parameters and state parameters that have the greatest impact on sensitivity. The analytical sensitivity results obtained by this method can provide theoretical support for improving the operating characteristics of natural gas networks by changing topology parameters and state parameters. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating the implementation of the natural gas network analytical sensitivity calculation method. Detailed Implementation

[0064] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0065] like Figure 1As shown, this invention provides a method for calculating the analytical sensitivity of a natural gas network, comprising the following steps:

[0066] Step S1: Obtain the operating status parameters of the natural gas network; the operating status parameters include the natural gas flow rate in the natural gas branch, the pressure of each node, and the pressure ratio of the compressor;

[0067] Step S2: Construct the analytical sensitivity of the load node pressure relative to the reference node pressure;

[0068] Step S3: Construct the analytical sensitivity of the ratio of the load node pressure to the natural gas flow provided by the slack node and the reference node;

[0069] Step S4: Construct the analytical sensitivity of the load node pressure relative to the natural gas flow consumed by the load node.

[0070] Step S2 specifically includes the following steps:

[0071] Step S21: Define the node with a given pressure in the natural gas network as the reference node, denoted as Ref; define the node with a given injection flow rate ratio to the injection flow rate of the reference node as the relaxation node, and denote the set of all relaxation nodes as Ω1; define the remaining nodes as load nodes, and denote the set of all load nodes as Ω2.

[0072] Step S22, denoted as p at the pressure at the reference node Ref. Ref Let i be any load node in Ω2, and let p be the pressure at load node i. i , note p i Relative to p Ref The sensitivity is The construction steps are as follows:

[0073] When there is no compressor on the path from load node i to reference node Ref, The analytical expression is:

[0074]

[0075] When there is a compressor on the path from load node i to reference node Ref and the path first passes through the compressor's inlet node, The analytical expression is:

[0076]

[0077] In the above formula, ε is the pressure ratio of the compressor;

[0078] When there is a compressor on the path from load node i to reference node Ref and the path first passes through the compressor's outlet node, The analytical expression is:

[0079]

[0080] Step S3 specifically includes the following steps:

[0081] Step S31: Denote the set consisting of all branches in the natural gas network as Ω3, and denote any branch in Ω3 as x1. Calculate the characteristic parameters of branch x1.

[0082]

[0083] In the above formula, x 1,in and x 1,out These are the nodes at the starting and ending points of branch x1, respectively. The natural gas flow rate in branch x1, and They are nodes x 1,in and node x 1,out Pressure at the location;

[0084] Step S32, let any relaxed node in Ω1 be k, and let R be the ratio of the injected flow at relaxed node k to the injected flow at reference node Ref. k , note p i Relative to R k The sensitivity is Let Sum be the sum of the flow consumed by each load node. load Let Sum1 be the sum of the ratios of the flow provided by all relaxed nodes and the reference node plus 1. Let t be any relaxed node in Ω1 except k, and let R be the ratio of the flow provided by relaxed node t to that provided by the reference node. t Let node m be the intersection of the path from relaxed node k to reference node Ref and the path from node i to reference node Ref; let node n be the intersection of the path from relaxed node t to reference node Ref and the path from node i to reference node Ref; and let the set of branches on the path from node m to reference node Ref be denoted as . remember Let x2 be any branch in the equation, and let the natural gas flow rate in branch x2 be denoted as x2. The characteristic parameters of branch x2 are denoted as Let the set of branches on the path from node n to reference node Ref be . remember Let x3 be any branch in the network, and let the natural gas flow rate in branch x3 be denoted as x3. The characteristic parameters of branch x3 are denoted as The construction steps are as follows:

[0085] When there are no compressors on the path from node m to reference node Ref and on the path from node n to reference node Ref, The analytical expression is:

[0086]

[0087] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's inlet node, and there is no compressor on the path from node n to reference node Ref, let the compressor's inlet node and outlet node be u, respectively. m and v m The compressor has a pressure ratio of ε. m Let the distance from node m to node u be recorded. m The set of branches on the path is remember Let x4 be any branch in the network, and let the natural gas flow rate in branch x4 be denoted as x4. The characteristic parameters of branch x4 are denoted as Let node v be a record. m The set of branches on the path to the reference node Ref is remember Let x5 be any branch in the network, and let the natural gas flow rate in branch x5 be denoted as x5. The characteristic parameters of branch x5 are denoted as: The analytical expression is:

[0088]

[0089] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's outlet node, and there is no compressor on the path from node n to reference node Ref, The analytical expression is:

[0090]

[0091] When there is no compressor on the path from node m to reference node Ref, but there is a compressor on the path from node n to reference node Ref and this path passes through the compressor inlet first, let the compressor inlet node and outlet node be u, respectively. n and v n The compressor has a pressure ratio of ε. n Let the distance from node n to node u be denoted as . n The set of branches on the path is remember Let x6 be any branch in the network, and let the natural gas flow rate in branch x6 be denoted as x6. The characteristic parameters of branch x6 are denoted as: Let node v be a record. n The set of branches on the path to the reference node Ref is remember Let x7 be any branch in the network, and let the natural gas flow rate in branch x7 be denoted as x7. The characteristic parameters of branch x7 are denoted as The analytical expression is:

[0092]

[0093] When there is no compressor on the path from node m to reference node Ref, and there is a compressor on the path from node n to reference node Ref, and this path passes through the compressor's outlet first, The analytical expression is:

[0094]

[0095] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's inlet node, and simultaneously there is a compressor on the path from node n to reference node Ref and this path first passes through the compressor's inlet node, The analytical expression is:

[0096]

[0097] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's inlet node, and simultaneously there is a compressor on the path from node n to reference node Ref and this path first passes through the compressor's outlet node, The analytical expression is:

[0098]

[0099] When there is a compressor on the path from node m to reference node Ref and this path first passes through the compressor's outlet node, and simultaneously there is a compressor on the path from node n to reference node Ref and this path first passes through the compressor's inlet node, The analytical expression is:

[0100]

[0101] When there is a compressor on the path from node m to reference node Ref and this path passes through the compressor's outlet node first, and simultaneously there is a compressor on the path from node n to reference node Ref and this path passes through the compressor's outlet node first, The analytical expression is:

[0102]

[0103] Step S4 specifically includes the following steps:

[0104] Step S41, let any node in Ω2 be i, and let the natural gas flow rate consumed at node i be L.i Let f be any node on the path from node i to reference node Ref, and let p be the pressure at node f. f Let the set of all branches on the path from node f to reference node Ref be . Let any branch be denoted as x8, and the node on the side of branch x8 furthest from node i be y1. Let the sum of the ratios of the injected flow at all relaxed nodes after node y1 in the direction furthest from node i to the injected flow at the reference node be denoted as x8. Remember p f Compared to L i The sensitivity is The build process is as follows:

[0105] When there is no compressor on the path from node f to reference node Ref, The analytical expression is:

[0106]

[0107] When there is a compressor on the path from node f to reference node Ref, and the path first passes through the compressor's inlet, let the compressor's inlet and outlet be denoted as u. j and v j Let the pressure ratio of the compressor be ε. j Let the distance from node f to node u be recorded. j The set of all branches on the path is Let any branch be denoted as x9, and the node on the side of branch x9 furthest from node i be y2. Let the sum of the ratios of the injected flow at all relaxed nodes after node y2 in the direction furthest from node i to the injected flow at the reference node be denoted as... Let node v be a record. j The set of all branches on the path to node Ref is Let x be any branch in the path. 10 , note the branch x 10 Let y3 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y3 in the direction furthest from node i to the injected flow at the reference node is denoted as . The analytical expression is:

[0108]

[0109] When there is a compressor on the path from node f to reference node Ref and the path first passes through the compressor's outlet, The analytical expression is:

[0110]

[0111] Step S42: Let any relaxed node in Ω1 be k, let the intersection of the path from node i to relaxed node k and the path from node i to reference node Ref be w, let any node on the path from node w to relaxed node k be l, and let the pressure at node l be p. l Let the set of all branches on the path from node w to reference node Ref be . Let x be any branch in the path. 11 , note the branch x 11 Let y4 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y4 in the direction furthest from node i to the injected flow at the reference node is denoted as . Let the set of all branches on the path from node w to node l be . Let x be any branch in the path. 12 , note the branch x 12 Let y5 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y5 in the direction furthest from node i to the injected flow at the reference node is denoted as . Remember p l Compared to L i The sensitivity is The construction process is as follows:

[0112] When there is no compressor on the path from node w to reference node Ref, and also when there is no compressor on the path from node w to node l, The analytical expression is:

[0113]

[0114] When there is a compressor on the path from node w to reference node Ref and this path first passes through the compressor's inlet node, and there is no compressor on the path from node w to node l, denote the compressor's inlet node and outlet node on the path from node w to reference node Ref as u, respectively. w and v w Let the pressure ratio of the compressor be ε. w Let the distance from node w to node u be recorded. w The set of all branches on the path is Let x be any branch in the path. 13 , note the branch x 13 Let y6 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y6 in the direction furthest from node i to the injected flow at the reference node is denoted as [y6 is missing from the original text]. Let node v be a record. w The set of all branches on the path to node l is Let x be any branch in the path. 14 , note the branch x 14Let y7 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y7 in the direction furthest from node i to the injected flow at the reference node is denoted as . The analytical expression is:

[0115]

[0116] When there is a compressor on the path from node w to reference node Ref and this path first passes through the compressor's outlet node, and there is no compressor on the path from node w to node l, The analytical expression is:

[0117]

[0118] When there is no compressor on the path from node w to reference node Ref, but there is a compressor on the path from node w to node l, and this path first passes through the compressor's inlet node, denote the compressor's inlet node and outlet node on the path from node w to node l as u, respectively. l and v l Let the pressure ratio of the compressor be ε. l Let the distance from node w to node u be recorded. l The set of all branches on the path is Let x be any branch in the path. 15 , note the branch x 15 Let y8 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y8 in the direction furthest from node i to the injected flow at the reference node is denoted as . Let node v be a record. l The set of all branches on the path to node l is Let x be any branch in the path. 16 , note the branch x 16 Let y9 be the node furthest from node i. The sum of the ratios of the injected flow at all relaxed nodes after node y9 in the direction furthest from node i to the injected flow at the reference node is denoted as . The analytical expression is:

[0119]

[0120] When there is no compressor on the path from node w to reference node Ref, but there is a compressor on the path from node w to node l and this path passes through the compressor's outlet node first, The analytical expression is:

[0121]

Claims

1. A method for calculating the sensitivity of natural gas network analysis, characterized in that, Includes the following steps: Step S1: Obtain the operating status parameters of the natural gas network; the operating status parameters include the natural gas flow rate in the natural gas branch, the pressure of each node, and the pressure ratio of the compressor; Step S2: Construct the analytical sensitivity of the load node pressure relative to the reference node pressure; Step S3: Construct the analytical sensitivity of the ratio of the load node pressure to the natural gas flow provided by the slack node and the reference node; Step S4: Construct the analytical sensitivity of load node pressure relative to the natural gas flow rate consumed by the load node; Step S2 specifically includes the following steps: Step S21: Define the node with a given pressure in the natural gas network as a reference node, denoted as... A node whose injected flow is equal to the ratio of injected flow to the reference node is defined as a relaxed node, and the set of all relaxed nodes is denoted as . The remaining nodes are defined as load nodes, and the set consisting of all load nodes is denoted as . ; Step S22, record the reference node The pressure at the point is ,remember Any load node in the middle is Load nodes The pressure at the point is recorded as ,remember Compared to The sensitivity is ; The construction steps are as follows: When load node To the reference node When there is no compressor in the passage, The analytical expression is: When load node To the reference node When there is a compressor in the passage and the passage first passes through the compressor's inlet node, The analytical expression is: In the above formula, This refers to the pressure ratio of the compressor; When load node To the reference node When there is a compressor in the passage and the passage first passes through the compressor's outlet node, The analytical expression is: ； Step S3 specifically includes the following steps: Step S31, denote the set consisting of all branches in the natural gas network as ,remember Any branch in the middle is Calculate branches characteristic parameters : In the above formula, and Branch roads The node at the starting point and the node at the ending point. branch road Natural gas flow rate in and They are nodes and nodes Pressure at the location; Step S32, record Any relaxed node in the middle is Record relaxation nodes Injected traffic and reference node The ratio of injected flow to ,remember Compared to The sensitivity is Let the sum of the flow consumed by each load node be ; Let the sum of the ratios of the flow provided by all relaxed nodes and the reference node plus 1 be the result. ,remember Except Any relaxed node other than Record relaxation nodes The ratio of the traffic provided by the reference node to the total traffic provided by the reference node is Record relaxation nodes To the reference node Pathways and nodes To the reference node The intersection of the paths is a node. Record relaxation nodes To the reference node Pathways and nodes To the reference node The intersection of the paths is a node. , record nodes To the reference node The set of branches on the path is ,remember Any branch in the middle is branch road The natural gas flow rate in the middle is recorded as branch road The characteristic parameters are denoted as , record nodes To the reference node The set of branches on the path is ,remember Any branch in the middle is branch road The natural gas flow rate in the middle is recorded as branch road The characteristic parameters are denoted as ; The construction steps are as follows: When node To the reference node Pathways and nodes To the reference node When there are no compressors in the passageway, The analytical expression is: When node To the reference node The passage contains a compressor and the passage first passes through the compressor's inlet node, and the node... To the reference node When there is no compressor in the path, denote the compressor's inlet and outlet nodes as follows: and The compressor's pressure ratio is , record nodes To the node The set of branches on the path is ,remember Any branch in the middle is branch road The natural gas flow rate in the middle is recorded as branch road The characteristic parameters are denoted as , record nodes To the reference node The set of branches on the path is ,remember Any branch in the middle is branch road The natural gas flow rate in the middle is recorded as branch road The characteristic parameters are denoted as , The analytical expression is: When node To the reference node The passage contains a compressor and the passage first passes through the compressor's outlet node, while the node... To the reference node When there is no compressor in the passage, The analytical expression is: When node To the reference node There is no compressor on the path, and the node To the reference node If a compressor is located in a passageway and the passageway first passes through the compressor's inlet, then the compressor's inlet node and outlet node are denoted as follows: and The compressor's pressure ratio is , record nodes To the node The set of branches on the path is ,remember Any branch in the middle is branch road The natural gas flow rate in the middle is recorded as branch road The characteristic parameters are denoted as , record nodes To the reference node The set of branches on the path is ,remember Any branch in the middle is branch road The natural gas flow rate in the middle is recorded as branch road The characteristic parameters are denoted as , The analytical expression is: When node To the reference node There is no compressor on the path, and the node To the reference node When there is a compressor in the passage and the passage first passes through the compressor's outlet, The analytical expression is: When node To the reference node The passage contains a compressor, and the passage first passes through the compressor's inlet node, while the node... To the reference node When there is a compressor in the passage and the passage first passes through the compressor's inlet node, The analytical expression is: When node To the reference node The passage contains a compressor, and the passage first passes through the compressor's inlet node, while the node... To the reference node When there is a compressor in the passage and the passage first passes through the compressor's outlet node, The analytical expression is: When node To the reference node The passage contains a compressor and the passage first passes through the compressor's outlet node, while the node... To the reference node When there is a compressor in the passage and the passage first passes through the compressor's inlet node, The analytical expression is: When node To the reference node The passage contains a compressor and the passage first passes through the compressor's outlet node, while the node... To the reference node When there is a compressor in the passage and the passage first passes through the compressor's outlet node, The analytical expression is: ； Step S4 specifically includes the following steps: Step S41, record Any node in the middle is , record nodes The natural gas flow rate consumed is , record nodes To the reference node Any node on the path is , record nodes The pressure at the point is recorded as , record nodes To the reference node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . ,remember Compared to The sensitivity is , The build process is as follows: When node To the reference node When there is no compressor in the passage, The analytical expression is: When node To the reference node When a compressor is located in a passageway and the passageway first passes through the compressor's inlet, the compressor's inlet and outlet are denoted as _____ and _____, respectively. and Let the pressure ratio of the compressor be . , record nodes To the node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . , record nodes To the node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . , The analytical expression is: When node To the reference node When there is a compressor in the passage and the passage first passes through the compressor's outlet, The analytical expression is: Step S42, record Any relaxed node in the middle is , record nodes To the relaxation node Pathways and nodes To the reference node The intersection of the paths is , denote the node To the relaxation node Any node on the path is , record nodes The pressure at the point is recorded as , record nodes To the reference node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . , record nodes To the node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . ,remember Compared to The sensitivity is , The construction process is as follows: When node To the reference node There is no compressor on the path, and the node To the node When there is no compressor in the passage, The analytical expression is: When node To the reference node The passage contains a compressor, and the passage first passes through the compressor's inlet node, while the node... To the node When there is no compressor on the path, record the node. To the reference node The compressor's inlet and outlet nodes on the path are respectively and Let the pressure ratio of the compressor be . , record nodes To the node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . , record nodes To the node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . , The analytical expression is: When node To the reference node The passage contains a compressor and the passage first passes through the compressor's outlet node, while the node... To the node When there is no compressor in the passage, The analytical expression is: When node To the reference node There is no compressor on the path, and the node To the node If a compressor is present in the passageway and the passageway first passes through the compressor's inlet node, then the node is denoted as Node 1. To the node The compressor's inlet and outlet nodes on the path are respectively and Let the pressure ratio of the compressor be . , record nodes To the node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . , record nodes To the node The set of all branches on the path is , Any branch in the middle is denoted as , record the branch road Far from the node One side node is Following the path away from the node Direction node The sum of the ratios of the injected flow at all relaxed nodes to the injected flow at the reference node is denoted as . , The analytical expression is: When node To the reference node There is no compressor on the path, and the node To the node When there is a compressor in the passage and the passage first passes through the compressor's outlet node, The analytical expression is: 。

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