A modeling method for medium and low pressure gas distribution network of hydrogen-blended natural gas

Abstract

The present invention provides a method for modeling a medium- and low-pressure gas distribution network of hydrogen-blended natural gas, which comprises the following steps: S1, establishing a steady-state isothermal model of a hydrogen-blended natural gas network pipeline, wherein the steady-state isothermal model comprises parameter settings of density, Reynolds number, dynamic viscosity, and friction coefficient of the hydrogen-blended natural gas and a mathematical model description of nodes, pipelines, and loops of the hydrogen-blended natural gas network; S2, based on the mathematical model description in step S1, using an iteration method to establish a solution method for a medium- and low-pressure gas distribution network of hydrogen-blended natural gas; S3, according to the solution method in step S2, using a node method, a ring network method, and a ring energy method to respectively establish mathematical solution models of node pressure and pipeline flow of the network, analyzing and comparing the intrinsic connections between the mathematical solution models obtained by the three methods, and comparing and analyzing their respective characteristics and applicable occasions, and finally realizing a method for modeling a medium- and low-pressure gas distribution network of hydrogen-blended natural gas.

Description

Technical Field

[0001] The present invention belongs to the technical field of mathematical modeling of energy systems, and in particular relates to a method for modeling a medium- and low-pressure gas distribution network of hydrogen-blended natural gas. Background Art

[0002] With the continuous development of society, end users have higher standards for energy quality and higher requirements for energy efficiency and cleanliness. In recent years, with the country's vigorous promotion of electric energy and new energy technologies, especially the "two substitutions" - "electric energy substitution" and "clean substitution" policies, the pace of energy transformation has been further accelerated. How to improve the level of renewable energy consumption and how to improve the energy use structure are important research directions for future energy networks.

[0003] On the one hand, with the increasing public concern about environmental pollution and practical issues such as energy reserves, the consumption proportion of coal and oil in traditional fossil energy will continue to decline, while natural gas, as a clean fossil energy, will gradually increase its consumption proportion; on the other hand, with the development of clean energy use technology, hydrogen, as another clean energy, is also considered to be an important part of the future clean energy consumption structure. However, as an ideal clean energy, although hydrogen has the advantages of high energy density, wide flammability range, low minimum ignition energy, fast combustion rate, and no polluting emissions under the same weight, it also has problems such as affecting unit efficiency and difficult storage and transportation. Hydrogen can only be transported after being compressed, which is difficult and costly to transport. In addition, hydrogen is prone to gasification or ignition problems, the pure hydrogen gas engine technology is not mature, and the corresponding fuel infrastructure and fuel supply equipment are lacking, which greatly restricts the development of hydrogen fuel. Mixing hydrogen into natural gas to make hydrogen-blended natural gas will be a feasible way to transition to pure hydrogen energy. Compared with natural gas, hydrogen-blended natural gas has a higher combustion rate and less pollutant emissions. Compared with hydrogen, it can be transported using the existing natural gas pipeline network, has fewer usage restrictions, and a higher safety factor. It is a new type of hybrid clean energy that is more in line with current actual needs.

[0004] At the same time, hydrogen and natural gas have different physical and chemical properties, and their transportation conditions in the existing gas distribution network are also different. The original natural gas pipeline network model cannot accurately and effectively reflect the physical model of hydrogen-blended natural gas pipeline transportation. Studying the transportation characteristics of hydrogen-blended natural gas will be a very important task. Although existing literature has demonstrated the feasibility of hydrogen-blended natural gas transportation using existing natural gas pipelines, the mathematical modeling of the medium and low pressure gas distribution network for transporting hydrogen-blended natural gas is still in the exploratory stage. Therefore, the key to the problem is to propose an effective and accurate mathematical modeling method for the medium and low pressure gas distribution network of hydrogen-blended natural gas. Summary of the invention

[0005] In order to effectively characterize the pipeline transportation characteristics of hydrogen-blended natural gas, the present invention provides a method for modeling a medium- and low-pressure gas distribution network of hydrogen-blended natural gas, and provides the following technical solutions:

[0006] A method for modeling a medium- and low-pressure gas distribution network of hydrogen-blended natural gas comprises the following steps:

[0007] S1. Establishing a steady-state isothermal model of a hydrogen-blended natural gas network pipeline, wherein the steady-state isothermal model includes parameter settings of density, Reynolds number, dynamic viscosity, and friction coefficient of the hydrogen-blended natural gas and mathematical model descriptions of nodes, pipelines, and loops of the hydrogen-blended natural gas network;

[0008] S2. Based on the mathematical model described in step S1, an iterative method is used to establish a solution method for the medium and low pressure gas distribution network of hydrogen-blended natural gas;

[0009] S3. According to the solution method in step S2, the node method, ring network method and ring energy method are used to establish mathematical solution models of the node pressure and pipeline flow of the network respectively, and the internal connection between the mathematical solution models obtained by the three methods is analyzed and compared, and their respective characteristics and applicable occasions are compared and analyzed, and finally a modeling method of a medium and low pressure gas distribution network of hydrogen-blended natural gas is realized;

[0010] Furthermore, the specific process of setting the parameters of the density, Reynolds number, kinematic viscosity and friction coefficient of the hydrogen-blended natural gas is as follows:

[0011] The density ρ of the hydrogen-blended natural gas is the relative density Δ of the hydrogen-blended natural gas under standard conditions divided by the air density ρ 空气 The specific expression is:

[0012]

[0013] In formula (1), ρ0 represents the dry air density under standard conditions, where the temperature is 273.15 K, the pressure is 101.3 kPa, and the value is 1.293 kg / m 3 ; p represents the pressure of hydrogen-blended natural gas, in MPa; T represents the temperature of hydrogen-blended natural gas, in K;

[0014] Or the density ρ of the hydrogen-blended natural gas is obtained by formula (2), that is:

[0015]

[0016] In formula (2), represents the density of CH4, represents the volume of CH4, represents the density of H2, represents the volume of H2;

[0017] The hydrogen volume ratio σ is set to 10%, that is:

[0018]

[0019] The characterization formula of the Reynolds number Re of the hydrogen-blended natural gas is as follows:

[0020]

[0021] In formula (4): γ represents the kinematic viscosity of the gas, in m 2 / s; μ represents dynamic viscosity, unit is N·s / m 2 ; v represents the gas velocity, in m / s; V represents the gas volume flow, in m 3 / s; M represents the gas mass flow rate, in kg / s; D represents the inner diameter of the pipeline, in m;

[0022] The calculation expression of dynamic viscosity μ is as follows:

[0023]

[0024] In formula (5), Δ represents the relative density of hydrogen-blended natural gas under standard conditions, that is, the ratio to the density of air under standard conditions; ρ represents the gas density of hydrogen-blended natural gas, in kg / m 3 ; T represents the gas temperature, the unit is K;

[0025] The friction coefficient λ of the hydrogen-blended natural gas is calculated using the Colebrook equation, namely:

[0026]

[0027] In formula (6): It represents the absolute roughness of the inner wall of the pipe, in mm; D represents the inner diameter of the pipe, in mm; Re represents the Reynolds number of hydrogen-blended natural gas.

[0028] Furthermore, in step S1, the mathematical model of the nodes, pipelines and loops of the hydrogen-blended natural gas network describes the specific process as follows:

[0029] Two basic equations are constructed to describe the network state: the node-pipeline association matrix A and the loop-pipeline association matrix Β;

[0030] The element a of the node-pipeline association matrix A ij According to Kirchhoff's first law, the construction condition is that the pressure of the reference node is known;

[0031]

[0032] The element b of the loop-pipe association matrix Bnj According to Kirchhoff's second law, the reference flow direction of the loop is assumed to be clockwise;

[0033]

[0034] Analogous to the node voltage solution method and the loop current solution method in the power system, the node-pipeline association matrix A and the loop-pipeline association matrix B are both matrices that describe the state of the pipeline network; according to graph theory, there is an orthogonal relationship between the node-pipeline association matrix A and the loop-pipeline association matrix B, that is, the inner product of the row vector of the node-pipeline association matrix A and the row vector of the loop-pipeline association matrix B is always equal to zero, and the specific expression is as follows:

[0035] A×B T =B×A T =0 (9)

[0036] For the hydrogen-blended natural gas network, assuming that the number of nodes is i, i includes the reference node, the number of pipelines is j, and the number of loops is n, the corresponding relationship between the number of nodes i, the number of pipelines j, and the number of loops n is:

[0037] j=n+i-1 (10)

[0038] The following equation is used to describe the hydrogen-blended natural gas network;

[0039] The node flow equation is derived from Kirchhoff's first law, where the flow into the node is equal to the flow out of the node, where the reference node pressure is known:

[0040] A (i -1) ×j V j×1 =q (i -1) ×1 (11)

[0041] In formula (11), q (i -1) ×1 represents the flow out of the node, A (i -1) ×j represents the node-pipeline association matrix without the reference node, V j×1 Represents the flow vector of each pipe section;

[0042] According to Kirchhoff's second law, the pressure drop equation of the circuit is obtained. The pressure drop along any closed circuit is 0:

[0043] B n×j Δp j×1 =0 (12)

[0044] In formula (12), B n×jrepresents the loop-pipe association matrix with n loops and j pipes, Δp j×1 Represents the pressure difference between the upper and lower ends of each pipe section;

[0045] According to the pipeline pressure drop equation, the relationship between the pipeline pressure drop and the pressure difference between the upper and lower ends of the pipeline is as follows:

[0046]

[0047] In formula (13): p (i -1) ×1 It is expressed as the pressure of each node relative to the reference node;

[0048] Because A×B T =B×A T =0, so Therefore, formula (12) can be expressed by formula (13), and either formula can be used;

[0049] When the pipe diameter is known, each pipe has two unknowns, the pressure drop Δp and the flow rate, i.e., a total of 2j unknown quantities. The number of equations that can be listed is j+(i-1)+n=2j for solution;

[0050] According to the quantitative relationship between pipeline pressure drop Δp and pipeline flow, the pipeline flow pressure drop equation is:

[0051] Δp=G|V|V (14)

[0052] In formula (14), G represents the diagonal element matrix of pipeline flow resistance coefficient, that is, the flow resistance coefficient of each pipe section is on the corresponding diagonal line, and the remaining elements of the matrix are 0; V represents the calculated flow vector of the pipeline, with the unit of m 3 / h;

[0053] For medium and low pressure pipe networks, the pipe pressure drop Δp between connection node a and connection node b ab The calculation formula for and the calculation formula for the pipeline flow resistance coefficient G are as follows:

[0054]

[0055] In formula (15): Δp ab Represents the pressure drop of the pipe connecting nodes a and b, in kPa 2 ;p a With p b represents the pressure at nodes a and b, in kPa; λ represents the hydraulic friction coefficient of the pipeline; Z n represents the compression factor of the gas under standard conditions, which is 1; D represents the inner diameter of the pipeline, in mm; ρ represents the density of hydrogen-blended natural gas, in kg / m 3 ; T nrepresents the standard state absolute temperature, which is 273.15K; T represents the pipeline temperature, in K; L represents the pipeline length, in km; Z represents the compression factor of hydrogen-blended natural gas, and the expression of Z is:

[0056]

[0057] In formula (16): T c Indicates the critical temperature of the gas, in K; p c Indicates the critical pressure of gas, in Pa; p av Indicates the average pressure of the pipeline mn, in Pa, p av The expression is:

[0058]

[0059] In formula (17), p m represents the node pressure at the beginning of the pipe segment, p n represents the node pressure at the end n of the pipe segment;

[0060] Let the element s in the j×j diagonal matrix S be jj satisfy:

[0061]

[0062] According to equations (11)-(14) and (18), the following relationship can be obtained:

[0063]

[0064] ASA T p=q (20)

[0065] B(G|V|V)=0 (21)

[0066] Furthermore, in step S2, the solution method for establishing a medium- and low-pressure gas distribution network of hydrogen-blended natural gas using an iterative method is specifically as follows:

[0067] Suppose there are N variables x1, x2, L, x N , given the equation:

[0068] F i (x1,x2,L,x N )=0, i=1,2,L,N (22)

[0069] F i The function introduced by the iterative method, x1,x2,L,x N is the function F i The input variables are N at most. Let the variable matrix X = [x1 x2…x i]', the imbalance matrix δX = [δx1δx2…δx i ]', function matrix F = [F1 F2…F i ]', the imbalance square matrix δX 2 =[(δx1) 2 (δx2) 2 …(δx i ) 2 ]', then each F i Using Taylor series expansion, we can get:

[0070]

[0071] i is the number of nodes in the hydrogen-blended natural gas network, and j is the number of pipelines in the hydrogen-blended natural gas network;

[0072] Let the partial derivatives form the Jacobian matrix J, where the (i,j) element J ij for

[0073]

[0074] but:

[0075] F(X+δX)=F(X)+J×δX+O(δX 2 ) (25)

[0076] Ignore O(δX 2 ), and let F(X+δX)=0, we can get the linear equations about the unbalanced quantity δX:

[0077] J×δX=-F(X) (26)

[0078] In formula (25) and formula (26): δX makes each function approach zero at the same time,

[0079] The unbalance is added to the solution vector to continuously correct the initial value,

[0080] X k+1 =X k +δX k (27)

[0081] In formula (27): X k+1 represents the iterative result of the k+1th solution vector, X k represents the iterative result of the kth solution vector, δX k Represents the revised value of the k-th iteration solution vector.

[0082] Furthermore, in step S3, the specific process of using the node method to establish the mathematical solution model of the node pressure and pipeline flow of the network is as follows:

[0083] Transform formula (20) into:

[0084] ASA T pq=0 (28)

[0085] Formula (28) is written in equation form as:

[0086] F(p)=ASA T pq=0 (29)

[0087] First, the initial estimated value of each node pressure is given, and then the estimated value is continuously corrected to obtain the unbalanced amount of node pressure, which is the error correction amount:

[0088] J p ×δp k =-F(p k ) (30)

[0089] In formula (30): J p represents the Jacobian matrix formed by taking partial derivatives of the node pressure p; p k Represents the node pressure value solved at the kth iteration;

[0090]

[0091] The iterative process used to correct the estimated nodal pressure is:

[0092] p k+1 =p k +δp k (32)

[0093] In formula (32), p k+1 represents the node pressure value solved in the k+1th iteration; p k represents the node pressure value solved in the kth iteration; δp k Represents the node pressure correction value solved at the kth iteration;

[0094] The iteration termination condition is:

[0095] |δp k |≤ε (33)

[0096] In formula (33), ε is the calculation accuracy.

[0097] In each iteration, the value of S changes according to equation (13), equation (14), and equation (18), and the value of V needs to be continuously corrected according to the value of Δp.

[0098] Furthermore, in step S3, the specific process of using the ring network method to establish a mathematical solution model for the node pressure and pipeline flow of the network is as follows:

[0099] According to formula (21), it can be written in equation form:

[0100] F(V)=BG|V|V=0 (34)

[0101] Formula (34) can be converted into:

[0102] BGV+B T e|(V+B T e)=0 (35)

[0103] In formula (35), e represents a correction amount added to the branch flow to correct the estimated value of the branch flow;

[0104] but:

[0105] F(e)=BGV+B T e|(V+B T e)=0 (36)

[0106] First, the initial value of the loop flow is given, and then it is continuously iterated until the true solution is reached; in the iterative solution process of the ring network method, F(e) is not equal to zero, that is, a loop flow error is introduced for each loop, based on which the unbalanced amount of the loop flow can be obtained, which can be considered as the error correction amount:

[0107] J e ×δe k =-F(e k ) (37)

[0108] In formula (37): J e represents the Jacobian matrix formed by taking the partial derivative of the branch flow correction amount e; e k represents the branch flow correction value solved at the kth iteration; δe k represents the correction value of branch flow correction obtained at the kth iteration;

[0109]

[0110] The iterative process used to correct the loop flow estimate is:

[0111] e k+1 =e k +δe k (39)

[0112] The iteration termination condition is:

[0113] |δe k |≤ε (40)

[0114] In formula (40): ε is the calculation accuracy;

[0115] In this method, J eNeed to constantly combine with e to change.

[0116] Furthermore, the specific process of using the ring energy method to establish the mathematical solution model of the network node pressure and pipeline flow is as follows:

[0117] According to formula (11) and formula (21), it can be written in matrix form as:

[0118]

[0119] Then the iterative method is "count twice", and the solution is achieved through iterative approximation between the true value and the estimated value:

[0120]

[0121] In formula (42): V k ' represents the estimated value of the pipe flow calculated for the kth time; V k represents the true value of the flow rate of the pipe section calculated for the kth time; V k+1 represents the true value of the pipe flow calculated for the k+1th time; ω is the weight coefficient;

[0122] The iteration termination condition is:

[0123] |V k+1 -V k |≤ε (43)

[0124] In formula (43), ε is the calculation accuracy.

[0125] Beneficial Effects

[0126] The method for modeling a medium- and low-pressure gas distribution network for hydrogen-blended natural gas proposed in the present invention fully considers the differences in physical properties between hydrogen-blended natural gas and pure natural gas, establishes a method for modeling a medium- and low-pressure gas distribution network for hydrogen-blended natural gas, and uses three different methods, namely, a node method, a ring network method, and a ring energy method, to compare and analyze their respective characteristics and calculation results by utilizing the iterative solution principle, fully considering the differences in the physical and chemical properties of hydrogen-blended natural gas and the needs of actual projects, so that the pipeline modeling is more in line with the actual project needs while ensuring the simulation accuracy, and realizes the modeling of a medium- and low-pressure gas distribution network for hydrogen-blended natural gas that is more in line with the actual project needs while ensuring the simulation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0127] Figure 1 The figure is a flow chart of an implementation method in an embodiment of the present invention.

[0128] Figure 2 This is a diagram of an 11-node hydrogen-blended natural gas pipeline network system in an embodiment of the present invention.

[0129] Figure 3This is a simulation result diagram of the steady-state node method for an 11-node hydrogen-blended natural gas pipeline network in an embodiment of the present invention.

[0130] Figure 4 It is a comparison chart of the node pressure simulation results of three calculation methods in the embodiments of the present invention.

[0131] Figure 5 It is a comparison chart of the pipe section flow simulation results of three calculation methods in the embodiments of the present invention. DETAILED DESCRIPTION

[0132] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0133] The simulated hydrogen-blended natural gas pipeline network system in the embodiment of the present invention is as follows: Figure 2 As shown in the figure, the system is a medium-pressure hydrogen-blended natural gas pipeline network in a certain area, with a total of 11 nodes and 12 pipeline sections. The gas source node is node 11, where the reference pressure is 1.8 MPa. The length, inner diameter, rated temperature, and relative density of the fluid in the system pipeline network are shown in Table 1, and the load flow of each node is shown in Table 2.

[0134] Table 1 Hydrogen-blended natural gas pipeline network data in the example

[0135] Serial number Beginning and End Length / km Inner diameter / mm Temperature / K Relative density 1 11-1 12.3 495 289.15 0.494 2 1-2 7.6 495 289.00 0.494 3 2-3 8.1 495 288.85 0.494 4 1-4 11.1 495 288.65 0.494 5 4-5 8.9 495 288.75 0.494 6 5-6 14.4 495 288.85 0.494 7 7-6 10.2 495 288.65 0.494 8 11-7 7.8 495 288.95 0.494 9 7-8 13.7 495 288.35 0.494 10 8-9 11.5 495 288.55 0.494 11 10-9 13.8 495 288.25 0.494 12 10-5 12.6 495 288.15 0.494

[0136] Table 2 Nodal load parameters in the example

[0137] Serial number 1 2 3 4 5 6 7 8 9 10 <![CDATA[Load flow / (m 3 / h)]]> 0 4500 4200 3630 4700 5500 2300 1150 3930 1600

[0138] The method for modeling a medium and low pressure gas distribution network of hydrogen-blended natural gas proposed in the embodiment of the present invention is referred to Figure 1 As shown, the following steps are included:

[0139] S1. Establish a steady-state isothermal model of the hydrogen-blended natural gas network pipeline. The model mainly includes two aspects: 1. Parameter settings of gas density, Reynolds number, dynamic viscosity, and friction coefficient of hydrogen-blended natural gas; 2. Mathematical model description of nodes, pipelines, and loops of the hydrogen-blended natural gas network;

[0140] S2. Based on the mathematical model description of the steady-state isothermal model of the network pipeline, the solution method for the medium and low pressure distribution pipeline network of hydrogen-blended natural gas was established by using the iterative method;

[0141] S3. According to the solution method, the node method, ring network method and ring energy method are used to establish the mathematical solution model of the node pressure and pipeline flow of the network. The internal connection between the mathematical solution models obtained by these three methods is analyzed and compared, and their respective characteristics and applicable occasions are compared and analyzed. Finally, the modeling method of the medium and low pressure distribution pipeline network of hydrogen-blended natural gas is realized.

[0142] In step S1, the specific process of setting the parameters of the density, Reynolds number, kinematic viscosity and friction coefficient of the hydrogen-blended natural gas is as follows:

[0143] 1) Density of hydrogen-blended natural gas

[0144] The density of hydrogen-blended natural gas ρ is the relative density Δ of hydrogen-blended natural gas under standard conditions and the density of air ρ 空气 The specific expression is:

[0145]

[0146] In formula (1), ρ0 represents the dry air density under standard conditions, where the temperature is 273.15 K, the pressure is 101.3 kPa, and the value is 1.293 kg / m 3 ; p represents the pressure of hydrogen-blended natural gas, in MPa; T represents the temperature of hydrogen-blended natural gas, in K.

[0147] The density of hydrogen-blended natural gas is

[0148]

[0149] In formula (2), represents the density of CH4, represents the volume of CH4, represents the density of H2, represents the volume of H2.

[0150] Considering the safety of pipeline transportation and related transformation projects of terminal equipment, the hydrogen blending ratio of hydrogen-blended natural gas is often limited, usually limited to the range of 5% to 20%. Therefore, the present invention uniformly sets the hydrogen volume ratio σ to 10%, that is:

[0151]

[0152] The density of hydrogen-blended natural gas is the product of relative density Δ and air density. The relative density of hydrogen-blended natural gas is:

[0153]

[0154] 2) Reynolds number

[0155] The Reynolds number is a similarity criterion number that characterizes the effect of viscosity in fluid mechanics. The smaller the Reynolds number, the more significant the effect of viscosity. The larger the Reynolds number, the greater the effect of fluid inertia on the flow of fluid in the circular tube. The characterization formula is as follows:

[0156]

[0157] In formula (4), γ represents the kinematic viscosity of the gas, m 2 / s; μ represents dynamic viscosity, N·s / m 2 ; v represents gas velocity, m / s; V represents gas volume flow, m 3 / s; M represents the gas mass flow rate, kg / s; D represents the inner diameter of the pipe, m.

[0158] 3) Dynamic viscosity μ

[0159] Dynamic viscosity characterizes the internal friction generated by the interaction of fluids, which can be obtained from the ratio of stress to strain rate. According to the pressure, temperature and relative density of hydrogen-blended natural gas under standard conditions, the calculation expression of dynamic viscosity can be obtained:

[0160]

[0161] In formula (5), Δ represents the relative density of hydrogen-blended natural gas under standard conditions, that is, the ratio to the density of air under standard conditions; ρ is the gas density, kg / m 3 ; T represents the gas temperature, K.

[0162] 4) Friction coefficient λ

[0163] The Colebrook equation is generally used to calculate the friction coefficient of hydrogen-blended natural gas pipelines, namely:

[0164]

[0165] In formula (6): It represents the absolute roughness of the inner wall of the pipe, mm. The steel pipe is generally 0.1-0.2mm, and the polyethylene pipe is generally 0.01mm; D represents the inner diameter of the pipe, mm; Re represents the Reynolds number.

[0166] According to formulas (1)-(6), the parameters of the simulated hydrogen-blended natural gas pipeline system in the embodiment of the present invention are calculated as shown in Table 3.

[0167] Table 3 Hydrogen-blended natural gas pipeline network data in the example

[0168] Serial number Beginning and End Relative density Δ Reynolds number Dynamic viscosity μ Friction coefficient λ 1 11-1 0.494 569777.37 0.01170 0.04889 2 1-2 0.494 339358.50 0.01170 0.04894 3 2-3 0.494 163902.49 0.01169 0.04906 4 1-4 0.494 230921.07 0.01169 0.04899 5 4-5 0.494 89149.85 0.01169 0.04926 6 5-6 0.494 112630.49 0.01169 0.04917 7 7-6 0.494 327462.64 0.01169 0.04894 8 11-7 0.494 659165.95 0.01170 0.04888 9 7-8 0.494 242711.14 0.01167 0.04899 10 8-9 0.494 197645.45 0.01168 0.04902 11 10-9 0.494 44180.47 0.01167 0.04969 12 10-5 0.494 18377.60 0.01167 0.05086

[0169] In step S1, the mathematical model of the nodes, pipelines and loops of the hydrogen-blended natural gas network describes the specific process as follows:

[0170] For the hydrogen-blended natural gas network, two basic equations can be constructed to describe the network status: the node-pipeline association matrix A and the loop-pipeline association matrix B.

[0171] Element a of the node-pipeline association matrix A ijIt can be deduced based on Kirchhoff's first law, and the construction condition is that the pressure of the reference node is known.

[0172]

[0173] Element b of the loop-pipe association matrix Β nj It can be deduced from Kirchhoff's second law, assuming that the reference flow direction of the loop is clockwise.

[0174]

[0175] The two matrices logically describe the relationship between nodes, pipelines, and loops, showing the relationship between pipelines and loops, and realizing the mutual conversion between node pressure, pipeline pressure drop, and loop pressure drop. By analogy with the node voltage solution method and loop current solution method in the power system, it can be considered that the node-pipeline association matrix A and the loop-pipeline association matrix B are both matrices that describe the state of the pipeline network. According to graph theory, there is an orthogonal relationship between the node-pipeline association matrix A and the loop-pipeline association matrix B, that is, the inner product of the row vector of the node-pipeline association matrix A and the row vector of the loop-pipeline association matrix B is always equal to zero:

[0176] A×B T =B×A T =0 (9)

[0177] For the hydrogen-blended natural gas network, assuming that the number of nodes is i, i includes the reference node, the number of pipelines is j, and the number of loops is n, the relationship between the three can be obtained as follows:

[0178] j=n+i-1 (10)

[0179] The hydrogen-blended natural gas network can be described using the following equation.

[0180] The node flow equation is derived from Kirchhoff's first law, where the flow into the node is equal to the flow out of the node (the reference node pressure is known):

[0181] A (i -1) ×j V j×1 =q (i -1) ×1 (11)

[0182] In formula (11), q (i -1) ×1 represents the flow out of the node, A (i -1) ×j represents the node-pipeline association matrix without the reference node, V j×1 Represents the flow vector of each pipe section.

[0183] According to Kirchhoff's second law, the pressure drop equation of the circuit is obtained. The pressure drop along any closed circuit is 0:

[0184] B n×j Δp j×1 =0 (12)

[0185] In formula (12), B n×j represents the loop-pipe association matrix with n loops and j pipes, Δp j×1 Represents the pressure difference between the upper and lower ends of each pipe section.

[0186] According to the pipeline pressure drop equation, the pipeline pressure drop is related to the pressure difference between the upper and lower ends of the pipeline:

[0187]

[0188] In formula (13): p (i -1) ×1 It is expressed as the pressure of each node relative to the reference node.

[0189] Because A×B T =B×A T =0, so Therefore, formula (12) can be expressed by formula (13), or either one can be used.

[0190] When the pipe diameter is known, each pipeline has two unknowns, namely pressure drop and flow rate, that is, a total of 2j unknown quantities. The number of equations that can be listed is j+(i-1)+n=2j, so the solution can be achieved.

[0191] Secondly, there is a corresponding quantitative relationship between pipeline pressure drop and pipeline flow, which is the pipeline flow pressure drop equation:

[0192] Δp=G|V|V (14)

[0193] In formula (14), G represents the diagonal element matrix of pipeline flow resistance coefficient, that is, the flow resistance coefficient of each pipe section is on the corresponding diagonal line, and the remaining elements of the matrix are 0; V represents the calculated flow vector of the pipeline, with the unit of m 3 / h.

[0194] For medium and low pressure pipelines (low pressure: 0 ~ 0.01MPa; medium pressure pipeline: 0.01 ~ 0.4Mpa), the following are uniformly adopted:

[0195]

[0196] In formula (15): Δp ab represents the pressure drop in the pipe connecting nodes a and b, kPa 2 ;p a With p brepresents the pressure at nodes a and b, kPa; λ represents the pipeline hydraulic friction coefficient, which is related to the Reynolds number Re, the relative density of hydrogen-blended natural gas Δ, etc.; Z n represents the compression factor of gas under standard conditions, which is 1; D represents the inner diameter of the pipeline, mm; ρ represents the density of hydrogen-blended natural gas, kg / m 3 ; T n Indicates the standard state absolute temperature, 273.15K; T indicates the pipeline temperature, K; L indicates the pipeline length, km;

[0197] Table 4 Flow resistance coefficient of hydrogen-blended natural gas pipeline network in the example

[0198]

[0199] Z represents the compression factor of hydrogen-blended natural gas, and the formula is:

[0200]

[0201] In formula (16): T c represents the critical temperature of the gas, K; p c Indicates the critical pressure of gas, Pa;

[0202] Table 5 Compression factor of hydrogen-blended natural gas in pipeline network in the example

[0203]

[0204] p av Represents the average pressure of the pipeline mn, Pa, expressed as:

[0205]

[0206] In formula (17), p m represents the node pressure at the beginning of the pipe segment, p n Represents the node pressure at the end n of the pipe segment.

[0207] Let the element s in the j×j diagonal matrix S be jj satisfy:

[0208]

[0209] According to equations (11)-(14) and (18), the following relationship can be obtained:

[0210]

[0211] ASA T p=q (20)

[0212] B(G|V|V)=0 (21)

[0213] Therefore, the node method, ring network method and ring energy method can be used to solve the problem respectively.

[0214] Further, in step S2, the process of establishing a solution method for a medium- and low-pressure gas distribution network of hydrogen-blended natural gas is as follows:

[0215] A common solution method is to introduce an unbalanced value in the iteration, perform a Taylor series expansion, and limit the unbalanced value to below a specified value, which can be considered an accurate solution.

[0216] Suppose there are N variables x1, x2, L, x N , given the equation:

[0217] F i (x1,x2,L,x N )=0, i=1,2,L,N (22)

[0218] F i The function introduced by the iterative method, x1,x2,L,x N is the function F i The input variables are N at most. Let the variable matrix X = [x1 x2…x i ]', the imbalance matrix δX = [δx1δx2…δx i ]', function matrix F = [F1 F2…F i ]', the imbalance square matrix δX 2 =[(δx1) 2 (δx2) 2 …(δx i ) 2 ]', then each F i Using Taylor series expansion, we can get:

[0219]

[0220] i is the number of nodes in the hydrogen-blended natural gas network, and j is the number of pipelines in the hydrogen-blended natural gas network;

[0221] Let the partial derivatives form the Jacobian matrix J, where the (i,j) element J ij for:

[0222]

[0223] but:

[0224] F(X+δX)=F(X)+J×δX+O(δX 2 ) (25)

[0225] Ignore O(δX 2 ), and let F(X+δX)=0, we can get the linear equations about the unbalanced quantity δX:

[0226] J×δX=-F(X) (26)

[0227] In equations (25) and (26): δX allows each function to approach zero simultaneously.

[0228] Finally, the imbalance is added to the solution vector to continuously correct the initial value.

[0229] X k+1 =X k +δX k (27)

[0230] In formula (27): X k+1 represents the iterative result of the k+1th solution vector, X k represents the iterative result of the kth solution vector, δX k Represents the revised value of the k-th iteration solution vector.

[0231] The key to solving the problem is to construct a reversible Jacobian matrix.

[0232] Furthermore, in step S3, the specific process of using the node method to establish the mathematical solution model of the node pressure and pipeline flow of the network is as follows:

[0233] According to formula (20), it can be transformed into:

[0234] ASA T pq=0 (28)

[0235] Formula (28) is written in equation form as:

[0236] F(p)=ASA T pq=0 (29)

[0237] The node method is used to solve the problem. First, the initial estimated value of each node pressure is given, and then the estimated value is continuously corrected until the final result is obtained. Since the node pressure value is only an estimated value, F(p) is not actually equal to zero during the iteration process. Based on this, the unbalanced amount of the node pressure can be obtained, which can be considered as the error correction amount:

[0238] J p ×δp k =-F(p k ) (30)

[0239] In formula (30): J p represents the Jacobian matrix formed by taking partial derivatives of the node pressure p; p k Represents the node pressure value solved at the kth iteration.

[0240]

[0241] The iterative process used to correct the estimated nodal pressure is:

[0242] p k+1 =p k +δp k (32)

[0243] In formula (32), p k+1 represents the node pressure value solved in the k+1th iteration; p k represents the node pressure value solved in the kth iteration; δp k Represents the node pressure correction value solved at the kth iteration.

[0244] The iteration termination condition is:

[0245] |δp k |≤ε (33)

[0246] In formula (33), ε is the calculation accuracy and is small enough.

[0247] In each iteration, the value of S changes according to equation (13), equation (14), and equation (18), and the value of V needs to be continuously corrected according to the value of Δp.

[0248] Furthermore, in step S3, the specific process of using the ring network method to establish a mathematical solution model for the node pressure and pipeline flow of the network is as follows:

[0249] According to formula (21), it can be written in equation form:

[0250] F(V)=BG|V|V=0 (34)

[0251] The loop network method requires defining a set of closed loops in the pipe network, giving the initial estimated value of the flow of each pipe branch and ensuring the balance of the flow at each node. Since the flow of each pipe branch is given, the loop flow must also be introduced. The loop flow is a correction amount e added to the branch flow to correct the estimated value of the branch flow, and the direction is the same as the loop reference direction.

[0252] A specific natural gas pipeline may be affected by more than one loop flow rate. Generally speaking, the pipeline flow rate is a function of the initial estimate and all loop flows, that is, equation (34) can be converted to:

[0253] BGV+B T e|(V+B T e)=0 (35)

[0254] In formula (35), e represents a correction amount added to the branch flow to correct the estimated value of the branch flow;

[0255] but:

[0256] F(e)=BGV+B T e|(V+B T e)=0 (36)

[0257] First, the initial value of the loop flow is given, and then it is continuously iterated until the true solution is reached. In the iterative solution process of the ring network method, F(e) is not equal to zero, that is, a loop flow error is introduced for each loop. Based on this, the imbalance of the loop flow can be obtained, which can be considered as the error correction amount:

[0258] J e ×δe k =-F(e k ) (37)

[0259] In formula (37): J e represents the Jacobian matrix formed by taking the partial derivative of the branch flow correction amount e; e k represents the branch flow correction value solved at the kth iteration; δe k Represents the correction value of the branch flow correction amount solved at the kth iteration.

[0260] The iterative process used to correct the loop flow estimate is:

[0261] e k+1 =e k +δe k (39)

[0262] The iteration termination condition is:

[0263] |δe k |≤ε (40)

[0264] In formula (40), ε is the calculation accuracy and is small enough.

[0265] In this method, J e Need to constantly combine with e to change.

[0266] The specific process of using the ring energy method to establish the mathematical solution model of the network node pressure and pipeline flow is as follows:

[0267] According to formula (11) and formula (21), it can be written in matrix form as:

[0268]

[0269] Then the iterative method is "count twice", and the solution is achieved through iterative approximation between the true value and the estimated value:

[0270]

[0271] In formula (42): V k ' represents the estimated value of the pipe flow calculated for the kth time; V k represents the true value of the flow rate of the pipe section calculated for the kth time; V k+1 Represents the true value of the pipe section flow calculated for the k+1th time; ω is the weight coefficient, which is generally 0.5.

[0272] The iteration termination condition is:

[0273] |V k+1 -V k |≤ε (43)

[0274] Where: ε is the calculation accuracy and is small enough.

[0275] like Figure 3 As shown in the figure, the simulation results of the steady-state node method for the 11-node hydrogen-blended natural gas pipeline network are shown. Figure 4-5 As shown in the figure, it is a comparison chart of the simulation results of node pressure and pipe flow of three methods.

[0276] The initial value of the node method is the node pressure, and the requirements for the initial value are not high. The number of equations is 10 nodes with unknown pressure, the number of iterations is the largest, which is 49 times, and the convergence speed is the slowest. Because the pipeline flow is determined by the pressure difference, when the pipeline diameter is large, the pressure difference is small, and the sensitivity to the node pressure is different from that of the adjacent pipeline, the accuracy requirements of the pipeline flow will not be guaranteed, thereby affecting the convergence speed. According to the simulation results, the calculation accuracy and complexity of the node method are between the ring network method and the ring energy method. The initial value of the ring network method is the pipeline flow, which is required to satisfy the node flow balance equation. The number of equations is the least, which is equal to the number of network loops 2, the number of iterations is the lowest, which is 4 times, and the solution speed is the fastest. However, the algorithm has extremely high requirements for the selection of the initial pipeline flow, and the selection of the initial value directly affects the solution result, and the result error fluctuates greatly. The initial value of the ring energy method is the pipeline flow, and the requirements for the initial value are not high. The number of equations is the sum of the number of nodes and the number of loops with unknown network pressure, that is, the number of pipelines 12, and the number of iterations is 45 times. The ring energy method needs to consider both the node flow and the loop pressure drop equations at the same time, and the result is the most accurate. Literature research generally uses the results of this algorithm as the standard value. However, the number of equations in the ring energy method increases by 2 compared to the node method and by 10 compared to the ring network method. If it involves large-scale urban complex natural gas distribution network flow calculations, the calculation complexity will be greatly increased.

[0277] As shown in Tables 6 and 7, the simulation results of node pressure and pipeline flow of the three algorithms are compared with the algorithm complexity and error.

[0278] Table 6 Comparison of simulation results of three algorithms

[0279]

[0280]

[0281] Table 7 Comparison of complexity and error of three algorithms

[0282]

[0283] From the data in Table 7, it can be seen that the ring network method has the least number of equations and the least number of iterations, but its simulation results are the worst, with a larger relative error than the ring energy method and the node method. The ring energy method and the ring network method directly iterate the flow and can directly identify the correctness of the initial pipeline flow direction. Although the node method cannot directly solve the pipeline flow, it can also better identify the correctness of the initial pipeline flow direction through the sign of Δp. In terms of calculation accuracy, there is no obvious error in the results of the node method and the ring energy method, and a higher accuracy is obtained. At the same time, for the gas distribution network operation control platform, the node pressure monitoring points are generally dense and accurate, and the number of pipeline flow monitoring points is small and the accuracy is not high, so it is more advantageous to use the node method for flow calculation. From the analysis of application scenarios, considering that the gas distribution network control platform generally monitors the node pressure, the node method has more practical application advantages.

[0284] It should also be noted that the various specific technical features of the embodiments described in the above specific implementation manners, as well as the addition of other nodes in the system, can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not further describe other possible combinations.

Claims

1. A method for modeling a medium- and low-pressure gas distribution network of hydrogen-blended natural gas, characterized in that: The steps include: S1. Establishing a steady-state isothermal model of a hydrogen-blended natural gas network pipeline, wherein the steady-state isothermal model includes parameter settings of density, Reynolds number, dynamic viscosity, and friction coefficient of the hydrogen-blended natural gas and mathematical model descriptions of nodes, pipelines, and loops of the hydrogen-blended natural gas network; S2. Based on the mathematical model described in step S1, an iterative method is used to establish a solution method for the medium and low pressure gas distribution network of hydrogen-blended natural gas; S3. According to the solution method in step S2, a mathematical solution model of the node pressure and pipeline flow of the network is established by using the node method to realize a modeling method of a medium and low pressure gas distribution network of hydrogen-blended natural gas; The specific process of setting the parameters of the density, Reynolds number, kinematic viscosity and friction coefficient of the hydrogen-blended natural gas is as follows: The density ρ of hydrogen-blended natural gas is the relative density Δ of hydrogen-blended natural gas under standard conditions and the density ρ of air. 空气 The specific expression is: In formula (1), ρ0 represents the dry air density under standard conditions, where the temperature is 273.15 K, the pressure is 101.3 kPa, and the value is 1.293 kg / m 3 ; p represents the pressure of hydrogen-blended natural gas, in MPa; T represents the temperature of hydrogen-blended natural gas, in K; Or the density ρ of the hydrogen-blended natural gas is obtained by formula (2), that is: In formula (2), represents the density of CH4, represents the volume of CH4, represents the density of H2, represents the volume of H2; The hydrogen volume ratio σ is set to 10%, that is: The characterization formula of the Reynolds number Re of the hydrogen-blended natural gas is as follows: In formula (4): γ represents the kinematic viscosity of the gas, in m 2 / s; μ represents dynamic viscosity, unit is N·s / m 2 ; v represents the gas velocity, in m / s; V represents the gas volume flow, in m 3 / s; M represents the gas mass flow rate, in kg / s; D represents the inner diameter of the pipeline, in m; The calculation expression of dynamic viscosity μ is as follows: In formula (5), Δ represents the relative density of hydrogen-blended natural gas under standard conditions, that is, the ratio to the density of air under standard conditions; ρ represents the gas density of hydrogen-blended natural gas, in kg / m 3 ; T represents the gas temperature, the unit is K; The friction coefficient λ of the hydrogen-blended natural gas is calculated using the Colebrook equation, namely: In formula (6): It represents the absolute roughness of the inner wall of the pipe, in mm; D represents the inner diameter of the pipe, in mm; Re represents the Reynolds number of hydrogen-blended natural gas; The mathematical model of the nodes, pipelines and loops of the hydrogen-blended natural gas network describes the specific process as follows: Two basic equations are constructed to describe the network state: the node-pipeline association matrix A and the loop-pipeline association matrix Β; The element a of the node-pipeline association matrix A ij According to Kirchhoff's first law, the construction condition is that the pressure of the reference node is known; The element b of the loop-pipe association matrix B nj According to Kirchhoff's second law, the reference flow direction of the loop is assumed to be clockwise; Analogous to the node voltage solution method and the loop current solution method in the power system, the node-pipeline association matrix A and the loop-pipeline association matrix B are both matrices that describe the state of the pipeline network; according to graph theory, there is an orthogonal relationship between the node-pipeline association matrix A and the loop-pipeline association matrix B, that is, the inner product of the row vector of the node-pipeline association matrix A and the row vector of the loop-pipeline association matrix B is always equal to zero, and the specific expression is as follows: A×B T =B×A T =0 (9) For the hydrogen-blended natural gas network, assuming that the number of nodes is i, i includes the reference node, the number of pipelines is j, and the number of loops is n, the corresponding relationship between the number of nodes i, the number of pipelines j, and the number of loops n is: j=n+i-1 (10) The following equation is used to describe the hydrogen-blended natural gas network; The node flow equation is derived from Kirchhoff's first law, where the flow into the node is equal to the flow out of the node, where the reference node pressure is known: A (i-1)×j V j×1 =q (i-1)×1 (11) In formula (11), q (i-1)×1 represents the flow out of the node, A (i-1)×j represents the node-pipeline association matrix without the reference node, V j×1 Represents the flow vector of each pipe section; According to Kirchhoff's second law, the pressure drop equation of the circuit is obtained. The pressure drop along any closed circuit is 0: B n×j Δp j×1 =0 (12) In formula (12), B n×j represents the loop-pipe association matrix with n loops and j pipes, Δp j×1 Represents the pressure difference between the upper and lower ends of each pipe section; According to the pipeline pressure drop equation, the relationship between the pipeline pressure drop and the pressure difference between the upper and lower ends of the pipeline is as follows: In formula (13): p (i-1)×1 It is expressed as the pressure of each node relative to the reference node; Because A×B T =B×A T =0, so Therefore, formula (12) can be expressed by formula (13), and either formula can be used; When the pipe diameter is known, each pipe has two unknowns: pressure drop Δp and flow rate, i.e., a total of 2j unknowns. The number of equations that can be listed is j+(i-1)+n=2j for solution; Secondly, according to the quantitative relationship between the pipeline pressure drop Δp and the pipeline flow rate, the pipeline flow pressure drop equation is: Δp=G|V|·V(14) In formula (14), G represents the diagonal element matrix of pipeline flow resistance coefficient, that is, the flow resistance coefficient of each pipe section is on the corresponding diagonal line, and the remaining elements of the matrix are 0; V represents the calculated flow vector of the pipeline, with the unit of m 3 / h; For medium and low pressure pipe networks, the pipe pressure drop Δp between connection node a and connection node b ab The calculation formula for and the calculation formula for the pipeline flow resistance coefficient G are as follows: In formula (15): Δp ab Represents the pressure drop of the pipe connecting nodes a and b, in kPa 2 ;p a With p b represents the pressure at nodes a and b, in kPa; λ represents the hydraulic friction coefficient of the pipeline; Z n It represents the compression factor of gas under standard conditions, which is 1; D represents the inner diameter of the pipeline, in mm; ρ represents the density of hydrogen-blended natural gas, in kg / m 3 ; T n represents the standard state absolute temperature, which is 273.15K; T represents the pipeline temperature, in K; L represents the pipeline length, in km; Z represents the compression factor of hydrogen-blended natural gas, and the expression of Z is: In formula (16): T c Indicates the critical temperature of the gas, in K; p c Indicates the critical pressure of gas, in Pa; p av Indicates the average pressure of the pipeline mn, in Pa, p av The expression is: In formula (17), p m represents the node pressure at the beginning of the pipe segment, p n represents the node pressure at the end n of the pipe segment; Let the element s in the j×j diagonal matrix S be jj satisfy: According to equations (11)-(14) and (18), the following relationship can be obtained: ASA T p=q (20) B(G|V|V)=0 (21) The specific solution method for establishing the medium and low pressure gas distribution network of hydrogen-blended natural gas using the iterative method is as follows: Suppose there are N variables x1, x2, L, x N , given the equation: F i (x1,x2,L,x N )=0,i=1,2,L,N (22) F i The function introduced by the iterative method, x1,x2,L,x N is the function F i The input variables are N at most. Let the variable matrix X = [x1 x2 … x i ]', the imbalance matrix δX=[δx1 δx2 … δx i ]', function matrix F = [F1 F2…F i ]', the imbalance square matrix δX 2 =[(δx1) 2 (δx2) 2 …(δx i ) 2 ]', then each F i Using Taylor series expansion we get: i is the number of nodes in the hydrogen-blended natural gas network, and j is the number of pipelines in the hydrogen-blended natural gas network; Let the partial derivatives form the Jacobian matrix J, where the (i,j) element J ij for but: F(X+δX)=F(X)+J×δX+O(δX 2 )(25) Ignore O(δX 2 ), and let F(X+δX)=0, we can get the linear equations about the unbalanced quantity δX: J×δX=-F(X)(26) In formula (25) and formula (26): δX makes each function approach zero at the same time, The unbalance is added to the solution vector to continuously correct the initial value, X k+1 =X k +δX k (27) In formula (27): X k+1 represents the iterative result of the k+1th solution vector, X k represents the iterative result of the kth solution vector, δX k Represents the revised value of the k-th iteration solution vector; The specific process of using the node method to establish the mathematical solution model of the network node pressure and pipeline flow is as follows: Transform formula (20) into: ASA T pq=0(28) Formula (28) is written in equation form as: F(p)=ASA T pq=0(29) First, the initial estimated value of each node pressure is given, and then the estimated value is continuously corrected to obtain the unbalanced amount of node pressure, which is the error correction amount: J p ×δp k =-F(p k )(30) In formula (30): J p represents the Jacobian matrix formed by taking partial derivatives of the node pressure p; p k Represents the node pressure value solved at the kth iteration; The iterative process used to correct the estimated nodal pressure is: p k+1 =p k +δp k (32) In formula (32), p k+1 represents the node pressure value solved in the k+1th iteration; p k represents the node pressure value solved in the kth iteration; δp k Represents the node pressure correction value solved at the kth iteration; The iteration termination condition is: |δp k |≤ε(33) In formula (33): ε is the calculation accuracy; In each iteration, the value of S changes according to equation (13), equation (14), and equation (18), and the value of V needs to be continuously corrected according to the value of Δp.

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