CN109002419B - Dynamic analysis method and device for natural gas pipe network - Google Patents

Dynamic analysis method and device for natural gas pipe network Download PDF

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CN109002419B
CN109002419B CN201710421916.8A CN201710421916A CN109002419B CN 109002419 B CN109002419 B CN 109002419B CN 201710421916 A CN201710421916 A CN 201710421916A CN 109002419 B CN109002419 B CN 109002419B
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张劲军
苏怀
杨楠
张宗杰
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China University of Petroleum Beijing
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Abstract

The embodiment of the application provides a dynamic analysis method and a dynamic analysis device for a natural gas pipe network, wherein the method comprises the following steps: establishing a node dynamic equation of a specified natural gas pipe network based on a mass conservation equation, and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation; determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix, and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix; coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network; and dynamically analyzing the natural gas pipe network according to the state space model. The embodiment of the application can realize dynamic analysis of large-scale complex pipe networks and has high efficiency.

Description

Dynamic analysis method and device for natural gas pipe network
Technical Field
The application relates to the technical field of dynamic analysis of natural gas pipe networks, in particular to a dynamic analysis method and device of a natural gas pipe network.
Background
Disturbances generated by any unit in the natural gas pipeline network can cause large-scale state fluctuation in the system, thereby affecting normal gas supply. Due to the compressibility of natural gas, slow transient changes caused by disturbances are closely related to time and space; moreover, the natural gas pipe network is composed of a large number of units of different types, has different operation modes, control modes and limiting conditions, and has different responses to disturbances. In addition, the gas sources of the natural gas pipe network are various, and the operating modes of different gas sources are greatly different. The above characteristics of the natural gas pipe network bring great difficulties to the running state prediction and system characteristic analysis.
At present, the transient simulation technology of the natural gas pipeline is mature. Researchers have also published many papers on transient models of natural gas pipeline networks. However, most of the models in these articles are not "pipe network models" in the true sense, but are pieced together based on pipe models. The main focus of these models is on the processing of partial differential equations, simply taking into account the conservation relationships at the pipe-to-pipe connections.
Among them, a representative recent method is Mahmood Farzaneh-Gord, published by Hamid Reza Rahbari in 2016 in Journal of Natural Gas Science and Engineering, an analytical approach, and having a flow of biological gases. In this article, the authors first simplified the mass conservation equation and the momentum conservation equation using the Kolomogorov and Fomin transform; the reduced system of equations is then integrated (over time), converting the non-steady state equations into a "steady state system of equations". However, the key coefficients in the steady state system of equations are time dependent. And then combining the steady state equation sets of all the pipelines together by using the kirchhoff's law to form a pipe network equation set. The method is a typical 'piecing together' method, and is characterized in that the improvement of a pipeline model is emphasized, and then the coupling relation of the pipeline model is simply considered to form a pipe network model. The problem with this model is that: the formed pipe network model is very complex in form, and has great difficulty in being applied to large and complex pipe networks.
This problem has also been addressed by researchers attempting to model the system of the natural gas pipeline network from an overall perspective. An article entitled "a state space model for transportation flow in natural gas pipelines" was published in Journal of natural gas Science and Engineering in 2012 by r.alamian, m.behbahani-Nejad, a.ghanbarzadeh, and was established from a cybernetics perspective. Firstly, an author carries out Laplace transform on a mass conservation equation and a momentum conservation equation to establish a transfer function model of a pipeline; and then extracting state variables based on the transfer function, describing the action relation between each node and each pipeline in the pipe network, and then performing inverse Laplace transformation to establish a state space model of the pipe network. However, because the model is completely based on a control method, a logic block diagram is also constructed besides two laplace transformations in the modeling process, thereby causing a large burden on calculation. Therefore, this solution is not feasible for large-scale complex pipe networks. In other words, the existing models are only applicable to simple natural gas pipe networks.
Disclosure of Invention
An object of the embodiments of the present application is to provide a dynamic analysis method and apparatus for a natural gas pipe network, so as to implement dynamic analysis of a large-scale complex pipe network.
In order to achieve the above object, in one aspect, an embodiment of the present application provides a dynamic analysis method for a natural gas pipeline network, including:
establishing a node dynamic equation of a specified natural gas pipe network based on a mass conservation equation, and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation;
determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix, and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix;
coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network;
and dynamically analyzing the natural gas pipe network according to the state space model.
In the dynamic analysis method for a natural gas pipe network according to the embodiment of the present application, the node dynamic equation includes:
Figure BDA0001315171900000021
wherein, Δ piIs the pressure increase at node i, ρnIs fluid density, c is acoustic velocity, Ai,jIs the cross-sectional area of the conduit between node i and node j, Δ xi,jIs the discrete space step length, Δ Q, of the pipeline between node i and node ji,jDelta L for the flow increment of the pipe between node i and node jiIs the air supply increment or demand increment at node j.
In the dynamic analysis method for a natural gas pipe network according to the embodiment of the present application, the pipeline dynamic equation includes:
Figure BDA0001315171900000031
wherein, is Δ QiFor the pressure increase of the pipe i, Δ pkIs the pressure increase, Δ p, at the end k of the pipe ijIs the pressure increase at the end j of the pipe i, KqiIs a first coefficient, and
Figure BDA0001315171900000032
Kpkis a second coefficient, and
Figure BDA0001315171900000033
Kpjis a third coefficient, and
Figure BDA0001315171900000034
f(Q0,p0,p0) Is the value of the rate of change of the pipeline flow when the variable is in an equilibrium state.
In the dynamic analysis method for a natural gas pipe network according to the embodiment of the present application, the node directed adjacency matrix includes:
Figure BDA0001315171900000035
wherein the content of the first and second substances,
Figure BDA0001315171900000036
the vector is the derivative of the pressure variation at all the nodes in the natural gas pipe network to time, phi is a first coefficient matrix, AI is an adjacency matrix, delta Q vector is the flow variation of all the pipelines in the natural gas pipe network, and delta L vector is the natural gas inflow at all the demand points in the natural gas pipe network or the natural gas inflow at all the demand points in the natural gas pipe networkAnd the natural gas outflow at all gas supply points in the pipe network.
In the dynamic analysis method for a natural gas pipe network according to the embodiment of the present application, the pipe directed adjacency matrix includes:
Figure BDA0001315171900000037
wherein the content of the first and second substances,
Figure BDA0001315171900000038
the vector is the derivative of the flow variation of all the pipelines in the natural gas pipeline network to the time, KpIs a matrix of second coefficients, KQAnd the delta p vector is a third coefficient matrix and is the pressure increment of nodes at two ends of each control unit in the natural gas pipe network, and the delta Q vector is the flow variation of all pipelines in the natural gas pipe network.
In the dynamic analysis method for a natural gas pipe network according to the embodiment of the present application, the state space model includes:
Figure BDA0001315171900000039
wherein the content of the first and second substances,
Figure BDA00013151719000000310
a state space model of the natural gas pipe network is obtained;
a is the state matrix of the natural gas pipe network, and
Figure BDA00013151719000000311
x is a state variable matrix of the natural gas pipeline network, an
Figure BDA00013151719000000312
B is a control matrix of the natural gas pipeline network, and
Figure BDA00013151719000000313
u is stationA control variable matrix of the natural gas pipe network, and
Figure BDA0001315171900000041
m is the number of pipelines in the natural gas pipe network, n is the number of nodes in the natural gas pipe network, O is a zero matrix, CpIs a fourth coefficient matrix, CQIs a fifth coefficient matrix, the p vector is the pressure of the two end nodes of each control unit in the natural gas pipe network, QnAnd the vector is the flow of the non-pipeline part in the natural gas pipe network.
The dynamic analysis method for the natural gas pipe network according to the embodiment of the application, the dynamic analysis of the natural gas pipe network according to the state space model, includes:
receiving a disturbance event input to the state space model based on a preset rule, wherein the disturbance event is an adverse event causing the state space model to deviate from a normal operation state;
and simulating the propagation process of the disturbance event in the state space model according to a preset numerical solving method.
On the other hand, the embodiment of the application also provides a dynamic analysis device of the natural gas pipe network,
the method comprises the following steps:
the dynamic equation establishing module is used for establishing a node dynamic equation of the specified natural gas pipe network based on a mass conservation equation and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation;
the adjacency matrix establishing module is used for determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix;
the state space model obtaining module is used for coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network;
and the pipe network dynamic analysis module is used for dynamically analyzing the natural gas pipe network according to the state space model.
The dynamic analysis device of the natural gas pipe network of the embodiment of the application, the node dynamic equation comprises:
Figure BDA0001315171900000042
wherein, Δ piIs the pressure increase at node i, ρnIs fluid density, c is acoustic velocity, Ai,jIs the cross-sectional area of the conduit between node i and node j, Δ xi,jIs the discrete space step length, Δ Q, of the pipeline between node i and node ji,jDelta L for the flow increment of the pipe between node i and node jiIs the air supply increment or demand increment at node j.
The dynamic analysis device of natural gas pipe network of the embodiment of this application, pipeline dynamic equation includes:
Figure BDA0001315171900000043
wherein, is Δ QiFor the pressure increase of the pipe i, Δ pkIs the pressure increase, Δ p, at the end k of the pipe ijIs the pressure increase at the end j of the pipe i, KqiIs a first coefficient, and
Figure BDA0001315171900000051
Kpkis a second coefficient, and
Figure BDA0001315171900000052
Kpjis a third coefficient, and
Figure BDA0001315171900000053
f(Q0,p0,p0) Is the value of the rate of change of the pipeline flow when the variable is in an equilibrium state.
The dynamic analysis device of natural gas pipe network of the embodiment of the application, the directional adjacency matrix of node includes:
Figure BDA0001315171900000054
wherein the content of the first and second substances,
Figure BDA0001315171900000055
the vector is the derivative of the pressure variation of all the nodes in the natural gas pipe network to time, phi is a first coefficient matrix, AI is an adjacency matrix, delta Q vector is the flow variation of all the pipelines in the natural gas pipe network, and delta L vector is the natural gas inflow of all the demand points in the natural gas pipe network or the natural gas outflow of all the gas supply points in the natural gas pipe network.
The dynamic analysis device of natural gas pipe network of the embodiment of the application, the directional adjacency matrix of pipeline includes:
Figure BDA0001315171900000056
wherein the content of the first and second substances,
Figure BDA0001315171900000057
the vector is the derivative of the flow variation of all the pipelines in the natural gas pipeline network to the time, KpIs a matrix of second coefficients, KQAnd the delta p vector is a third coefficient matrix and is the pressure increment of nodes at two ends of each control unit in the natural gas pipe network, and the delta Q vector is the flow variation of all pipelines in the natural gas pipe network.
The dynamic analysis device of natural gas pipe network of the embodiment of the application, the state space model includes:
Figure BDA0001315171900000058
wherein the content of the first and second substances,
Figure BDA0001315171900000059
a state space model of the natural gas pipe network is obtained;
a is the state matrix of the natural gas pipe network, and
Figure BDA00013151719000000510
x is a state variable matrix of the natural gas pipeline network, an
Figure BDA00013151719000000511
B is a control matrix of the natural gas pipeline network, and
Figure BDA00013151719000000512
u is a control variable matrix of the natural gas pipe network, and
Figure BDA00013151719000000513
m is the number of pipelines in the natural gas pipe network, n is the number of nodes in the natural gas pipe network, O is a zero matrix, CpIs a fourth coefficient matrix, CQIs a fifth coefficient matrix, the p vector is the pressure of the two end nodes of each control unit in the natural gas pipe network, QnAnd the vector is the flow of the non-pipeline part in the natural gas pipe network.
The dynamic analysis device of natural gas pipe network of the embodiment of this application, according to the state space model is right the natural gas pipe network carries out dynamic analysis, include:
receiving a disturbance event input to the state space model based on a preset rule, wherein the disturbance event is an adverse event causing the state space model to deviate from a normal operation state;
and simulating the propagation process of the disturbance event in the state space model according to a preset numerical solving method.
In yet another aspect, an embodiment of the present application further provides a computer storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the following steps:
establishing a node dynamic equation of a specified natural gas pipe network based on a mass conservation equation, and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation;
determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix, and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix;
coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network;
and dynamically analyzing the natural gas pipe network according to the state space model.
According to the scheme of the embodiment of the application, Laplace transformation is not needed in the modeling process of the embodiment of the application, and a logic block diagram is not needed to be constructed; and a node dynamic equation of the natural gas pipe network can be directly established based on the mass conservation equation to replace the traditional method of describing mass conservation by using a kirchhoff equation at a node, so that the equation quantity in the model is greatly reduced, the storage space is saved, and the calculation efficiency is improved. Therefore, theoretical basis is provided for online prediction, decision and early warning of the operation state of the large-scale complex natural gas pipeline network.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and for those skilled in the art, other drawings can be obtained according to the drawings without any creative effort. In the drawings:
fig. 1 is a flow chart of a dynamic analysis method of a natural gas pipeline network according to an embodiment of the present disclosure;
fig. 2 is a schematic view of a natural gas pipe network topology according to an embodiment of the present application;
FIG. 3 is a load curve (disturbance event) for the 50 th and 61 th demand nodes in the natural gas pipeline network of FIG. 2;
fig. 4 is a comparison graph of a flow fluctuation curve obtained by using the embodiment of the present application and a flow fluctuation curve obtained by using the existing TGNET software at an upstream node of the 2 nd pipeline in the natural gas pipeline network shown in fig. 2;
fig. 5 is a graph comparing a pressure fluctuation curve obtained by using the embodiment of the present application and a pressure fluctuation curve obtained by using the existing TGNET software at an upstream node of the 2 nd pipeline in the natural gas pipeline network shown in fig. 2;
fig. 6 is a comparison graph of a flow fluctuation curve obtained by using the embodiment of the present application and a flow fluctuation curve obtained by using the existing TGNET software at an upstream node of the 41 th pipeline in the natural gas pipeline network shown in fig. 2;
FIG. 7 is a graph comparing a pressure fluctuation curve obtained using the embodiment of the present application with a pressure fluctuation curve obtained using existing TGNET software at an upstream node of the 41 th pipeline in the natural gas pipeline network shown in FIG. 2;
FIG. 8 is a graph of a fluctuation in supply at the 59 th source node in the natural gas pipeline network of FIG. 2;
fig. 9 is a block diagram of a dynamic analysis apparatus for a natural gas pipeline network according to an embodiment of the present application.
Detailed Description
In order to make those skilled in the art better understand the technical solutions in the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Referring to fig. 1, a dynamic analysis method for a natural gas pipeline network according to an embodiment of the present disclosure may include the following steps:
s101, establishing a node dynamic equation of the specified natural gas pipe network based on a mass conservation equation, and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation.
In the embodiment of the present application, the mass conservation equation and the momentum conservation equation are respectively expressed by the following formula (1) and formula (2).
Figure BDA0001315171900000071
Figure BDA0001315171900000072
Where p is pressure, v is flow velocity, x is length, t is time, λ is coefficient of friction, ρnFor fluid density, g is gravitational acceleration, α is pipe inclination.
To simplify the modeling process, equation (2) can be converted into a differential equation that is derived only over time using a finite difference method without loss of accuracy:
Figure BDA0001315171900000081
wherein Q isiIs the flow of the pipe i, pjAnd pkPressure at nodes j and k at the two ends of the pipeline i, respectively, A is the cross-sectional area of the pipeline, c is the speed of sound, ηeFor pipe efficiency, Δ x is the discrete spatial step, D is the pipe internal diameter,
Figure BDA0001315171900000082
is the average pressure of conduit i, and:
Figure BDA0001315171900000083
in the prior art, an energy conservation and mass conservation equation is generally established for a pipeline, and then the pipeline equation is coupled into a pipe network model by using kirchhoff's law. In the embodiment of the present application, equation (1) is applied to a node (e.g., a pipeline connection point, a natural gas supply and demand point, etc.) of a natural gas pipeline network, so that a node dynamic equation can be directly established at the node, as shown in equation (5). The physical significance is as follows: the rate of change of pressure at a node is dependent on the change in flow at that node. The purpose of this is to replace the traditional method of using kirchhoff equation to describe the conservation of mass at the nodes, thereby greatly reducing the number of equations in the model, saving the storage space, and improving the calculation efficiency (wherein, the reduced number of equations is equivalent to the number of nodes). This is especially advantageous when building state space models for highly complex pipe networks.
Figure BDA0001315171900000084
Wherein p isiIs the pressure at node i, c is the speed of sound, Ai,jIs the cross-sectional area of the conduit between node i and node j, Δ xi,jIs the discrete space step length, Q, of the pipeline between node i and node ji,jFlow rate of the pipe between node i and node j, LiThe amount of gas supplied or required at node j.
To further simplify the model, taylor's formula can be used for linearization of equation (3), and a linearized relationship can be obtained:
Figure BDA0001315171900000085
wherein Q isi0,pk0,pj0Is the value of the corresponding physical quantity at the stable operating point;
ΔQi＝Qi-Qi0(7)
Δpk＝pk-pk0(8)
Δpj＝pj-pj0(9)
Figure BDA0001315171900000091
to make formula (6) simpler in form and because
Figure BDA0001315171900000092
Figure BDA0001315171900000093
Equation (6) is abbreviated as constant in the form of equation (11):
Figure BDA0001315171900000094
wherein, is Δ QiFor the flow increment of the pipe i, Δ pkIs the pressure increase, Δ p, at the end k of the pipe ijIs the pressure increase at the end j of the pipe i, KqiCoefficient calculated for equation (12), KpkCoefficient calculated for equation (13), KpjCoefficient calculated for equation (14), f (Q)i0,pk0,pj0) F is the value of the variable f at the equilibrium state, f is the simplified expression of the change of the pipeline flow, and:
Figure BDA0001315171900000095
Figure BDA0001315171900000096
Figure BDA0001315171900000097
in order to establish a unified state space model of the natural gas pipe network, the formula (5) can be transformed into the following form:
Figure BDA0001315171900000098
wherein, Δ piDelta L as the pressure increase at node iiIs the air demand increment or demand increment at node j, and:
Δpi＝pi-pi0(16)
ΔQi,j＝Qi,j-Qi,j0(17)
in the formula,. DELTA.pi0，ΔQi,j0Respectively, the values of the corresponding physical quantities at the stable operating points.
S102, determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix, and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix.
In the embodiment of the present application, the adjacency matrix may be used to describe the topology of the natural gas pipe network and the connection relationship or interaction between nodes and edges in the network. In order to couple the dynamic equations (equation (11) and equation (15)) of all the pipelines and nodes in the same natural gas pipeline network, the pipeline dynamic equations and the node dynamic equations can be expressed by using the adjacency matrix to facilitate the coupling. Wherein the adjacency matrix may be defined as:
Figure BDA0001315171900000101
based on the definition of equation (1), the state space model (equation (15)) of all nodes can be integrated into the form of equation (19):
Figure BDA0001315171900000102
wherein the content of the first and second substances,
Figure BDA0001315171900000103
the vector is a derivative of pressure variation quantity of all nodes in the natural gas pipeline network with respect to time calculated by an equation (16), AI is an adjacency matrix (which is established according to graph theory and embodies the connection relation between the nodes of the pipeline network), Δ Q vector is a flow variation quantity of all pipelines in the natural gas pipeline network calculated by an equation (17), Δ L vector is a natural gas inflow quantity of all demand points in the natural gas pipeline network or a natural gas outflow quantity of all gas supply points in the natural gas pipeline network, Φ is a coefficient matrix, and Φ is calculated by an equation (20), that is:
Φ＝diag(φ1,φ2,φ3…φn) (20)
Figure BDA0001315171900000104
when describing the dynamic process of the pipeline, it is necessary to resort to the transpose of AI, BI.
Figure BDA0001315171900000105
Meanwhile, embodiments of the present application may also express control units (i.e., non-duct units, such as pneumatic stations, valve chambers, etc.) in the form of edges in an adjoining matrix.
To facilitate differentiation from the pipeline, the BI is split into the form of formula (23):
BI＝[BIP|BIN](23)
wherein, BIPAn adjacency matrix transpose representing a pipe; BI (BI)NRepresenting the transpose of the adjacency matrix of non-pipe elements.
Thus, the linearized pipeline dynamics equation (11) can be integrated into the form of equation (24) by equation (23):
Figure BDA0001315171900000106
wherein the content of the first and second substances,
Figure BDA0001315171900000111
the vector is the derivative of the flow variation of all the pipelines in the natural gas pipeline network to the time, KpIs a coefficient matrix representing the physical properties of the nodes, represented by BI in formula (13), formula (14) and formula (23)PSynthesizing, namely putting the calculation results of the formula (13) and the formula (14) into the BI in a one-to-one correspondence mannerPThe corresponding position.
KQIs a coefficient matrix, embodies the physical properties of the pipeline, and
Figure BDA0001315171900000112
in the formula (25), the diagonal element corresponding to the non-pipe unit is 0.
In the embodiment of the present application, for the control unit (such as the air compression station, the valve chamber, etc.), the control modes can be summarized as follows:
cp,j,ipi+cp,j,kpk+cQ,jpi＝Ej(26)
wherein, cp,j,i，cp,j,k，cQ,jAnd EjIs a coefficient set according to the requirements of the cell; j is the number of the cell; i, k are the numbers of the nodes at the two ends of the control unit.
Based on equations (23) and (26), the control unit may be integrated as:
Figure BDA0001315171900000113
the p vector is the pressure of nodes at two ends of each control unit, the Q vector is the flow of the control units, and the elements corresponding to the pipeline units in the p vector and the Q vector are 0; cpIs a matrix of coefficients, and CpDetermined by the coefficients in equation (20) and put in one-to-one correspondence with the BI's in equation (23)NThe corresponding position of the element.
CQIs a coefficient matrix, is determined according to the coefficient value in the formula (26),
Figure BDA0001315171900000114
wherein, the diagonal element corresponding to the pipeline is 0.
Additionally, units such as pipeline gas sources, gas storage reservoirs, consumers, liquefied natural gas (L NG) stations, etc. are embodied as nodes in the model of the present application for these nodes, the control scheme can be described uniformly as equation (29):
Kp,ipi+KL,iLi＝Si(29)
wherein, Kp,iAnd KL,iFor the control coefficient, values are taken according to the actual control situation, SiA target value set for node i.
When a certain node in the model is a control point, for example, a certain gas source is in a pressure control mode, the node dynamic equation corresponding to the node is replaced by the form of equation (23), and the pressure or gas supply (demand) of the node is assigned as a constant.
S103, coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network.
The integrated formula (19), formula (24), formula (27), formula (29) can be represented by the following formula (30), and formula (30) is the final form of the model:
Figure BDA0001315171900000121
wherein m is the number of pipelines in the natural gas pipe network (i.e. the total number of communicating units including pipelines and control units), n is the number of nodes in the natural gas pipe network, O is a zero matrix, and
Figure BDA0001315171900000122
elements corresponding to the control unit in the vector and the delta Q vector are both 0; qnVector is the flow of non-pipe components (e.g., valves, pneumatic stations, etc.), and QnThe vector and the element corresponding to the pipe are both 0.
Further, equation (30) may be written in the form of equation (31):
Figure BDA0001315171900000123
according to the definition of a state space model in a control theory, A is a state matrix of the natural gas pipe network; x is a state variable matrix of the natural gas pipeline network; b is a control matrix of the natural gas pipeline network; u is the control variable matrix of natural gas pipe network, wherein:
Figure BDA0001315171900000124
Figure BDA0001315171900000125
Figure BDA0001315171900000126
Figure BDA0001315171900000127
the method comprises the steps of establishing a state space model of the natural gas pipe network, wherein the state space model comprises the topological structure of the natural gas pipe network, the pipeline parameters, the natural gas supply and demand parameters and the characteristics of pipe network control. The topological structure of the natural gas pipe network can be represented by an adjacency matrix, the pipeline parameters are contained in an equation (32), the natural gas supply and demand parameters are contained in equations (33) and (35), and the pipe network control is also contained in equations (33) and (35). That is to say, the embodiment of the present application considers the main dynamic components (the pipeline, the connection node of the pipeline, the gas source, and the user) inside the natural gas pipeline network, so that the system change caused by various disturbances can be captured, and when the natural gas pipeline network changes, only the parameters of the corresponding part in the formula (31) need to be adjusted. Therefore, no matter how complex the actual natural gas pipe network is, the state evolution process can be expressed by the corresponding state space model.
And S104, dynamically analyzing the natural gas pipe network according to the state space model.
In an embodiment of the present application, the dynamically analyzing the natural gas pipeline network according to the state space model may include the following steps:
firstly, a disturbance event input to the state space model based on a preset rule is received, wherein the disturbance event is an adverse event causing the state space model to deviate from a normal operation state.
The occurrence of most accidents (fluctuation of gas consumption of users, closing of valves, deliberate attack, equipment failure and the like) finally causes the change of the operation state (such as pressure, flow and the like) of the pipeline, and finally influences the gas supply capacity of a natural gas pipeline network. Thus, an adverse event may be defined in embodiments of the present application as a failure of one or more conduits. The failure of the pipeline is reflected by the loss of gas transmission capacity, and the weight value of the edge in the directional adjacency matrix is changed into 0. When the number of the failed pipelines is different, it may be considered that "disturbance force" applied to the state space model is different, in this embodiment of the application, the preset rule may include: randomly selecting an adverse event from a preset adverse event set by a Monte Carlo method and the like until each adverse event in the adverse event set is traversed; each adverse event in the adverse event set is different and comprises a rule that the weight of at least one pipeline connecting line is zero.
And then simulating the propagation process of the disturbance event in the state space model according to a preset numerical solving method. Because the problem of a troublesome numerical algorithm exists in the dynamic simulation of the natural gas pipe network, if the dynamic simulation is not properly processed, the iteration times are multiple, the fluctuation of the simulation process is large, and the results of long time consumption and low precision are further caused. In view of this problem, in an exemplary embodiment of the present application, an implicit high-order variable step size Numerical Differential Formula (NDF) may be used to simulate the dynamic process, and the simulation object is Formula (2). Therefore, compared with the widely adopted Runge-Kutta method (namely R-K method) and the like, the NDF algorithm has the advantages of less iteration times and higher precision.
The state space model of the embodiment of the application can be used for observing the inherent properties of the natural gas pipe network system. For example, the stability of the natural gas pipe network can be judged by calculating the eigenvalue of the state matrix a in the equation (25) by using the lyapunov first method (i.e., linear approximation method); for example, based on the controllability criterion, the state matrix a and the state matrix B may be used to construct the controllability matrix, so that the controllability of the natural gas pipe network may be determined, and the like.
In order to verify the applicability of the embodiment of the present application to a real and complex natural gas pipeline network, the embodiment of the present application is applied to a natural gas pipeline network in reality (as shown in fig. 2). The total mileage of the natural gas pipe network is 1100km, and the pipe diameter range is 950-1014 mm. The nodes with outward tips in fig. 2 represent demand nodes (i.e., customers) and the nodes with inward tips represent gas sources. Wherein, the gas source 1 (the normal daily gas supply amount is 3453 ten thousand Nm)3Air supply pressure 7MPa) and 59 (normal daily air supply amount 762 ten thousand Nm)3Air supply pressure of 6.5MPa) as pipeline air supply, and air supply 32 as L NG station (normal daily air supply of 130 ten thousand Nm)3) (ii) a The gas source 13 is an underground gas storage reservoir (normal daily peak regulation capacity 389 ten thousand Nm)3)。
Disturbance is applied to two demand nodes (50 and 61) in the natural gas pipe network shown in fig. 2 (as shown in fig. 3), and the method and the special software TGNET of the embodiment of the application are respectively adopted to simulate the pressure and flow change of each unit of the pipe network within 0-24 hours. Finally, the time for completing the whole simulation process is 5.8s by adopting the TGNET, and the time for completing the whole simulation process by adopting the method of the embodiment of the application is only 0.533 s.
In order to analyze the applicability of the embodiment of the present application to the pipe network as a whole, simulation results at the pipe 2, the upstream node of the pipe 41, and the gas source 59 are collected and compared with simulation results of TGNET, as shown in fig. 4 to 8. The three analysis objects represent the pipeline farthest from the disturbance, the connection point of the plurality of pipelines, and the gas source closest to the disturbance respectively. Through comparison, the calculation time is short by adopting the embodiment of the application, and the simulation result is basically consistent with the TGNET.
Referring to fig. 9, a dynamic analysis apparatus for a natural gas pipeline network according to an embodiment of the present disclosure may include:
the dynamic equation establishing module 91 may be configured to establish a node dynamic equation of a specified natural gas pipe network based on a mass conservation equation, and establish a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation;
the adjacency matrix establishing module 92 may be configured to determine a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix, and determine a pipe directed adjacency matrix according to the pipe dynamic equation and a transpose matrix of the adjacency matrix;
a state space model obtaining module 93, configured to couple the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network;
and a pipe network dynamic analysis module 94, which may be configured to perform dynamic analysis on the natural gas pipe network according to the state space model.
The apparatus of the embodiment of the present application corresponds to the method of the embodiment, and therefore, for details of the apparatus of the present application, please refer to the method of the embodiment, which is not described herein again.
For convenience of description, the above devices are described as being divided into various units by function, and are described separately. Of course, the functionality of the units may be implemented in one or more software and/or hardware when implementing the present application.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The application may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
The above description is only an example of the present application and is not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims (5)

1. A dynamic analysis method for a natural gas pipe network is characterized by comprising the following steps:
establishing a node dynamic equation of a specified natural gas pipe network based on a mass conservation equation, and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation;
determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix, and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix;
coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network;
performing dynamic analysis on the natural gas pipe network according to the state space model; wherein the content of the first and second substances,
the node dynamic equation comprises:
Figure FDA0002455348440000011
wherein, Δ piIs the pressure increase at node i, ρnIs fluid density, t is time, c is speed of sound, Ai,jIs the cross-sectional area of the conduit between node i and node j, Δ xi,jIs the discrete space step length, Δ Q, of the pipeline between node i and node ji,jDelta L for the flow increment of the pipe between node i and node jiThe increment of the air supply quantity or the increment of the air demand quantity at the node i;
the pipeline dynamic equation comprises:
Figure FDA0002455348440000012
wherein, is Δ QiFor the pressure increase of the pipe i, Δ pkIs the pressure increase, Δ p, at the end k of the pipe ijIs the pressure increase at the end j of the pipe i, KqiIs a first coefficient, and
Figure FDA0002455348440000013
Kpkis a second coefficient, and
Figure FDA0002455348440000014
Kpjis a third coefficient, and
Figure FDA0002455348440000015
f(Qi0,pk0,pj0) The value of the change rate of the pipeline flow when the variable is in the equilibrium state;
the node directed adjacency matrix includes:
Figure FDA0002455348440000016
wherein the content of the first and second substances,
Figure FDA0002455348440000017
the vector is the derivative of the pressure variation of all the nodes in the natural gas pipe network to time, phi is a first coefficient matrix, AI is an adjacency matrix, delta Q vector is the flow variation of all the pipelines in the natural gas pipe network, and delta L vector is the natural gas inflow at all the demand points in the natural gas pipe network or the natural gas outflow at all the gas supply points in the natural gas pipe network;
the pipe directional adjacency matrix includes:
Figure FDA0002455348440000021
wherein the content of the first and second substances,
Figure FDA0002455348440000022
the vector is the derivative of the flow variation of all the pipelines in the natural gas pipeline network to the time, KpIs a matrix of second coefficients, KQA third coefficient matrix is formed, the delta p vector is the pressure increment of nodes at two ends of each control unit in the natural gas pipe network, and the delta Q vector is the flow variation of all pipelines in the natural gas pipe network;
the state space model includes:
Figure FDA0002455348440000023
wherein the content of the first and second substances,
Figure FDA0002455348440000024
a state space model of the natural gas pipe network is obtained;
a is the state matrix of the natural gas pipe network, and
Figure FDA0002455348440000025
x is a state variable matrix of the natural gas pipeline network, an
Figure FDA0002455348440000026
B is a control matrix of the natural gas pipeline network, and
Figure FDA0002455348440000027
u is a control variable matrix of the natural gas pipe network, and
Figure FDA0002455348440000028
m is the number of pipelines in the natural gas pipe network, n is the number of nodes in the natural gas pipe network, O is a zero matrix, CpIs a fourth coefficient matrix, CQIs a fifth coefficient matrix, the p vector is the pressure of the two end nodes of each control unit in the natural gas pipe network, QnAnd the vector is the flow of the non-pipeline part in the natural gas pipe network.
2. The dynamic analysis method of a natural gas pipe network of claim 1, wherein the dynamically analyzing the natural gas pipe network according to the state space model comprises:
receiving a disturbance event input to the state space model based on a preset rule, wherein the disturbance event is an adverse event causing the state space model to deviate from a normal operation state;
and simulating the propagation process of the disturbance event in the state space model according to a preset numerical solving method.
3. A dynamic analysis device of a natural gas pipe network is characterized by comprising:
the dynamic equation establishing module is used for establishing a node dynamic equation of the specified natural gas pipe network based on a mass conservation equation and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation;
the adjacency matrix establishing module is used for determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix;
the state space model obtaining module is used for coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network;
the pipe network dynamic analysis module is used for carrying out dynamic analysis on the natural gas pipe network according to the state space model; wherein the content of the first and second substances,
the node dynamic equation comprises:
Figure FDA0002455348440000031
wherein, Δ piIs the pressure increase at node i, ρnIs fluid density, t is time, c is speed of sound, Ai,jIs the cross-sectional area of the conduit between node i and node j, Δ xi,jIs the discrete space step length, Δ Q, of the pipeline between node i and node ji,jDelta L for the flow increment of the pipe between node i and node jiThe increment of the air supply quantity or the increment of the air demand quantity at the node i;
the pipeline dynamic equation comprises:
Figure FDA0002455348440000032
wherein, is Δ QiFor the pressure increase of the pipe i, Δ pkIs the pressure increase, Δ p, at the end k of the pipe ijIs the pressure increase at the end j of the pipe i, KqiIs a first coefficient, and
Figure FDA0002455348440000033
Kpkis a second coefficient, and
Figure FDA0002455348440000034
Kpjis a third coefficient, and
Figure FDA0002455348440000035
f(Qi0,pk0,pj0) The value of the change rate of the pipeline flow when the variable is in the equilibrium state;
the node directed adjacency matrix includes:
Figure FDA0002455348440000036
wherein the content of the first and second substances,
Figure FDA0002455348440000037
the vector is the derivative of the pressure variation of all the nodes in the natural gas pipe network to time, the phi vector is a first coefficient matrix, the AI is an adjacency matrix, the delta Q vector is the flow variation of all the pipelines in the natural gas pipe network, and the delta L vector is the natural gas inflow of all the demand points in the natural gas pipe network or the natural gas outflow of all the gas supply points in the natural gas pipe network;
the pipe directional adjacency matrix includes:
Figure FDA0002455348440000038
wherein the content of the first and second substances,
Figure FDA0002455348440000039
the vector is the derivative of the flow variation of all the pipelines in the natural gas pipeline network to the time, KpIs a matrix of second coefficients, KQA third coefficient matrix is formed, the delta p vector is the pressure increment of nodes at two ends of each control unit in the natural gas pipe network, and the delta Q vector is the flow variation of all pipelines in the natural gas pipe network;
the state space model includes:
Figure FDA0002455348440000041
wherein the content of the first and second substances,
Figure FDA0002455348440000042
a state space model of the natural gas pipe network is obtained;
a is the state matrix of the natural gas pipe network, and
Figure FDA0002455348440000043
x is a state variable matrix of the natural gas pipeline network, an
Figure FDA0002455348440000044
B is a control matrix of the natural gas pipeline network, and
Figure FDA0002455348440000045
u is a control variable matrix of the natural gas pipe network, and
Figure FDA0002455348440000046
m is the number of pipelines in the natural gas pipe network, n is the number of nodes in the natural gas pipe network, O is a zero matrix, CpIs a fourth coefficient matrix, CQIs a fifth coefficient matrix, the p vector is the pressure of the two end nodes of each control unit in the natural gas pipe network, QnThe vector is the flow of the non-pipeline component in the natural gas pipe network, the phi vector is a first coefficient matrix, the AI is an adjacency matrix, and the delta L vector is the natural gas inflow at all demand points in the natural gas pipe network or the natural gas outflow at all gas supply points in the natural gas pipe network.
4. The dynamic analysis device for a natural gas pipe network according to claim 3, wherein the dynamic analysis of the natural gas pipe network according to the state space model comprises:
receiving a disturbance event input to the state space model based on a preset rule, wherein the disturbance event is an adverse event causing the state space model to deviate from a normal operation state;
and simulating the propagation process of the disturbance event in the state space model according to a preset numerical solving method.
5. A computer storage medium having a computer program stored thereon, the computer program, when executed by a processor, performing the steps of:
establishing a node dynamic equation of a specified natural gas pipe network based on a mass conservation equation, and establishing a pipeline dynamic equation of the natural gas pipe network based on a momentum conservation equation;
determining a node directed adjacency matrix according to the node dynamic equation and the adjacency matrix, and determining a pipeline directed adjacency matrix according to the pipeline dynamic equation and a transposed matrix of the adjacency matrix;
coupling the node directed adjacency matrix and the pipeline directed adjacency matrix to obtain a state space model of the natural gas pipe network;
performing dynamic analysis on the natural gas pipe network according to the state space model; wherein the content of the first and second substances,
the node dynamic equation comprises:
Figure FDA0002455348440000051
wherein, Δ piIs the pressure increase at node i, ρnIs fluid density, t is time, c is speed of sound, Ai,jIs the cross-sectional area of the conduit between node i and node j, Δ xi,jIs the discrete space step length, Δ Q, of the pipeline between node i and node ji,jDelta L for the flow increment of the pipe between node i and node jiThe increment of the air supply quantity or the increment of the air demand quantity at the node i;
the pipeline dynamic equation comprises:
Figure FDA0002455348440000052
wherein, is Δ QiFor the pressure increase of the pipe i, Δ pkIs the pressure increase, Δ p, at the end k of the pipe ijIs the pressure increase at the end j of the pipe i, KqiIs a first coefficient, and
Figure FDA0002455348440000053
Kpkis a second coefficient, and
Figure FDA0002455348440000054
Kpjis a third coefficient, and
Figure FDA0002455348440000055
f(Qi0,pk0,pj0) The value of the change rate of the pipeline flow when the variable is in the equilibrium state;
the node directed adjacency matrix includes:
Figure FDA0002455348440000056
wherein the content of the first and second substances,
Figure FDA0002455348440000057
the vector is the derivative of the pressure variation of all the nodes in the natural gas pipe network to time, phi is a first coefficient matrix, AI is an adjacency matrix, delta Q vector is the flow variation of all the pipelines in the natural gas pipe network, and delta L vector is the natural gas inflow at all the demand points in the natural gas pipe network or the natural gas outflow at all the gas supply points in the natural gas pipe network;
the pipe directional adjacency matrix includes:
Figure FDA0002455348440000058
wherein the content of the first and second substances,
Figure FDA0002455348440000059
the vector is the derivative of the flow variation of all the pipelines in the natural gas pipeline network to the time, KpIs a matrix of second coefficients, KQA third coefficient matrix is formed, the delta p vector is the pressure increment of nodes at two ends of each control unit in the natural gas pipe network, and the delta Q vector is the flow variation of all pipelines in the natural gas pipe network;
the state space model includes:
Figure FDA0002455348440000061
wherein the content of the first and second substances,
Figure FDA0002455348440000062
a state space model of the natural gas pipe network is obtained;
a is the state matrix of the natural gas pipe network, and
Figure FDA0002455348440000063
x is a state variable matrix of the natural gas pipeline network, an
Figure FDA0002455348440000064
B is a control matrix of the natural gas pipeline network, and
Figure FDA0002455348440000065
u is a control variable matrix of the natural gas pipe network, and
Figure FDA0002455348440000066
m is the number of pipelines in the natural gas pipe network, n is the number of nodes in the natural gas pipe network, O is a zero matrix, CpIs a fourth coefficient matrix, CQIs a fifth coefficient matrix, the p vector is the pressure of the two end nodes of each control unit in the natural gas pipe network, QnAnd the vector is the flow of the non-pipeline part in the natural gas pipe network.
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