CN114936522B - Dynamic modeling method for natural gas system - Google Patents

Dynamic modeling method for natural gas system Download PDF

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CN114936522B
CN114936522B CN202210534573.7A CN202210534573A CN114936522B CN 114936522 B CN114936522 B CN 114936522B CN 202210534573 A CN202210534573 A CN 202210534573A CN 114936522 B CN114936522 B CN 114936522B
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王程
许康平
毕天姝
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North China Electric Power University
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Abstract

The invention discloses a dynamic modeling method for a natural gas system, belonging to the technical field of energy systems. The method comprises the following steps: step 1: acquiring the actual operation data of the air source flow, the node pressure and the load flow of the air network; step 2: establishing a dynamic two-port time domain model of the air network to obtain an air network associated parameter matrix; and step 3: determining a maximum time constant of the air network; and 4, step 4: segmenting actual operation data of the gas network according to the maximum time constant of the gas network; and 5: fitting the natural gas system dynamics by using a deep learning method, and extracting neural network parameters to construct a gas network dynamic agent model; step 6: the dynamic agent model of the air network is used in a rolling mode, and the purpose of describing the long-time dynamic process of the air network by using a small-scale model is achieved. Compared with a gas network dynamic physical model using a homogenization parameter, the precision of the method is higher; and a rolling mechanism is introduced, so that the scale of the proxy model and the model training cost are reduced, the model parameters are reduced, and the model fitting precision is improved.

Description

Dynamic modeling method for natural gas system
Technical Field
The invention relates to the technical field of energy systems, in particular to a dynamic modeling method for a natural gas system.
Background
As the biggest energy consumption country in China, the development of energy faces a plurality of challenges such as serious environmental pollution, low energy utilization efficiency, severe energy safety situation and the like, so that the transformation of the energy structure in China is imperative. Natural gas, the cleanest fossil energy source, can be transformed into other forms of energy by various coupling devices, such as: the natural gas hydrogen-doped transportation becomes a new research direction along with the concern of the country on hydrogen energy, and thus, the natural gas system has a very important position in an energy system.
The natural gas propagation dynamics along the pipeline can be described by a group of partial differential equations in a time domain, the calculation cost is high, and the time constant of the pipeline with the size of thousands of meters under typical parameters is in the order of minutes. If the natural gas system is assumed to be in a steady state at all times in the optimal energy flow problem, although the time domain partial differential equation can be avoided being solved, the model solving cost is reduced, but a larger modeling error is caused. Therefore, how to reasonably model the natural gas dynamics becomes the key point and difficulty of the optimal energy flow research.
In general, natural gas dynamics refers to the time-domain dynamic process of natural gas flow and gas pressure along a pipeline, and represents the conduction of state quantity (flow and gas pressure) at any end of the pipeline to the other end of the pipeline, and the natural gas dynamics is visually represented as the non-instantaneity of space-time propagation of state quantity change. In order to avoid the problem that the precision of the finite difference time domain model and the model resolving cost are difficult to balance, scholars at home and abroad adopt a signal transformation thought to transform the natural gas time domain partial differential dynamic equation into a frequency domain, a complex frequency domain and a Bernstein space. And working to perform different forms of finite difference time domain format approximation on the natural gas time domain partial differential dynamic equation to obtain a natural gas dynamic time domain two-port model by derivation.
The above natural gas dynamic model has two common points in the derivation process: firstly, the partial differential equation coefficients (the inclination angle of the pipeline, the friction coefficient of gas and the pipe diameter) of the same pipeline are regarded as constant; second, some terms of the partial differential equation (e.g., convection terms and elevation difference) are ignored. However, in actual engineering, a large number of pipelines with short lengths are spliced to form the natural gas pipeline, in order to adapt to terrains and existing public facilities in the construction process, an inclination angle may exist in the local part of the pipeline, meanwhile, the corrosion of the pipeline is mainly caused by internal corrosion, and the friction coefficient and the pipe diameter of different positions are different due to different conditions of the internal corrosion. Therefore, the assumption of the aforementioned model with respect to the homogenization of the pipe parameters and the model simplification condition may cause a large modeling error. Because the natural gas pipeline is buried underground, actual physical parameters of each section of pipeline are not easy to obtain, and the difficulty of the natural gas dynamic fine modeling is increased. Therefore, a completely new dynamic modeling method for natural gas systems is needed to solve the above problems.
Disclosure of Invention
The invention aims to provide a dynamic modeling method for a natural gas system, which is characterized by comprising the following steps of:
step 1: acquiring the actual operation data of the air source flow, the node pressure and the load flow of the air network;
step 2: establishing a gas network dynamic two-port time domain model based on a pipeline dynamic two-port physical model of an explicit difference method to obtain a gas network associated parameter matrix;
and step 3: determining the maximum time constant of the air network according to the air network associated parameter matrix obtained in the step 2;
and 4, step 4: segmenting actual operation data of the air network according to the maximum time constant of the air network;
and 5: fitting the natural gas system dynamics by using a deep learning method, and extracting neural network parameters to construct a gas network dynamic agent model;
step 6: and (5) rolling the dynamic agent model of the air network in the step 5 for use, so as to achieve the purpose of describing the long-time dynamic process of the air network by using a small-scale model.
The step 2 is specifically as follows:
the head end pressure and the tail end pressure of the pipeline p meet the following requirements:
Figure BDA0003647201260000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003647201260000022
respectively representing the head end flow, the tail end flow, the head end air pressure and the tail end air pressure of the pipeline; />
Figure BDA0003647201260000023
Is a two-port model coefficient matrix;
the deformation processing is carried out on the formula (1) and comprises the following steps:
Figure BDA0003647201260000024
further establishing a node-outflow pipeline incidence matrix A out Node-inflow pipe incidence matrix A in Pipeline head end-node incidence matrix A pn1 Pipeline end-node incidence matrix A pn2 (ii) a The network node injection flow is expressed as:
M n ＝A in M out -A out M in (3)
meanwhile, the node-pipeline pressure satisfies:
Γ in ＝A pn1 Γ n Γ out ＝A pn2 Γ n (4)
substituting formula (3) and formula (4) into formula (2) yields:
Figure BDA0003647201260000031
in the formula: m sr The injection flow rate of the gas source node; m int The vector is 0 known from KCL as the injection flow of the intermediate node; m ld The injection flow of the load node; gamma-shaped sr Is the pressure of the air source node; gamma-shaped int Is the pressure of the intermediate node; gamma-shaped ld For the pressure of the load node, the formula (5) is arranged to obtain:
Figure BDA0003647201260000032
Figure BDA0003647201260000033
thus, a dynamic two-port time domain model of the air network is constructed:
Figure BDA0003647201260000034
wherein, the matrix Y mm ,Y mp ,Y pm ,Y pp Is M ld 、Γ sr And M sr 、Γ ld The air network correlation parameter matrix.
The maximum time constant pi of the gas network in the step 3 net Is R net x.DELTA.T, wherein R net Is a matrix Y mm ,Y mp ,Y pm ,Y pp Element coordinate boundary, Δ T is the time bin length.
The invention has the beneficial effects that:
1. compared with a gas network dynamic physical model using a uniform parameter, the gas network dynamic proxy model provided by the invention has higher precision;
2. the invention introduces a rolling mechanism to reduce the scale of the proxy model and the model training cost, reduce the model parameters and improve the model fitting precision.
Drawings
FIG. 1 is a flow chart of a method of dynamic modeling of a natural gas system of the present invention;
FIG. 2 is a schematic diagram of inlet flow versus outlet flow;
FIG. 3 (a) is a graph showing the nth row and column number of the coefficient matrix A;
FIG. 3 (b) is a graph showing the n-th row and column number of the coefficient matrix A;
FIG. 4 is a diagram of a natural gas system topology for validating a dynamic proxy model of a gas network;
FIG. 5 (a) is a graph comparing the mass flow of a source gas in a sample set for a dynamic proxy model of a gas network and a full-time proxy model;
FIG. 5 (b) is a graph comparing the pressure at 3 nodes in the sample set of the dynamic proxy model of the air network and the full-time proxy model;
FIG. 5 (c) is a graph comparing the pressure at 4 nodes in the sample set for the dynamic proxy model of the air network and the full-time proxy model;
FIG. 6 (a) is a graph comparing the mass flow of the source outside the sample set for the dynamic proxy model of the air network and the full-time proxy model;
FIG. 6 (b) is a graph comparing the pressure of the gas network dynamic proxy model and the pressure of the 3 nodes outside the sample set in the full-time proxy model;
fig. 6 (c) is a graph comparing the pressure of the gas network dynamic proxy model and the pressure of the full-time proxy model at 4 nodes outside the sample set.
Detailed Description
The invention provides a dynamic modeling method of a natural gas system, which is further explained by combining an attached drawing and a specific embodiment.
As shown in fig. 1, the implementation process of the present invention specifically includes the following steps:
step 1: and acquiring actual operation data of the air network, including air source flow, node pressure, load flow and the like.
Step 2: and deducing a pipeline dynamic two-port physical model to a gas network two-port time domain model based on an explicit difference method to obtain a gas network associated parameter matrix.
The head end pressure and the tail end pressure of the pipeline p meet the following requirements:
Figure BDA0003647201260000041
and setting the total duration of the dynamic model as T, the length of the time infinitesimal as delta T and the number of the time infinitesimals as N = T/delta T. In the formula (9), the reaction mixture is,
Figure BDA0003647201260000042
respectively representing the head end flow, the tail end flow, the head end air pressure and the tail end air pressure of the pipeline;
Figure BDA0003647201260000043
is a two-port model coefficient matrix.
And generating matrixes A, B, C and D according to the natural gas pipeline parameters, wherein the matrixes are all strict lower triangular matrixes and take precedence near the main diagonal. Wherein A matrix is M in And M out And the correlation coefficient matrix, because the matrix A is a lower triangular matrix which is close to the dominant diagonal and takes the dimensionality of the matrix A into consideration, the model training cost is reduced. As shown in figure 2 of the drawings, in which,
Figure BDA0003647201260000044
is equal to M out The nth row of the multiplication A matrix and B gamma in Is compared with the sum of corresponding elements in FIG. 3 (a), it can be easily seen from FIG. 3 (a) that the number of l to n columns in the n-th row of the A matrix is much greater than that of the other columns (the value is 0 or close to 0), i.e. < >>
Figure BDA0003647201260000045
Mainly by/or>
Figure BDA0003647201260000046
To>
Figure BDA0003647201260000047
Neglecting the influence of M out Influence of other dimensions, where l is the nth row and the values in the 1 st to nth columns areξ% maximum corresponds to the ordinal number of the column. The nth list of the A matrix characterizes M in Is paired and/or matched>
Figure BDA0003647201260000051
FIG. 3 (b) shows that the n-th column of the A-matrix has a greater value in the number of rows n to m than in the other rows (a value of 0 or close to 0), i.e. < >>
Figure BDA0003647201260000052
Is mainly received by
Figure BDA0003647201260000058
To>
Figure BDA0003647201260000053
Neglecting the influence of M in Other row pairs->
Figure BDA0003647201260000054
Wherein m is the nth column, and the value in the N to N rows is the ordinal number of the row corresponding to the maximum value of ξ%. And the (n-l, m-n) dimensional compressed correlation coefficient matrix corresponding to the nth time element represents the approximate relation between the state quantity of the nth time element and the state quantities of other dimensions of the air network. Sequentially calculating the matrix dimension of the compressed correlation coefficient of each infinitesimal according to the sequence of the infinitesimal time from low to high, wherein the general formula is R A,n = max (n-l, m-n). Furthermore, the maximum dimension ^ of the correlation coefficient matrix after compression of each infinitesimal is taken>
Figure BDA0003647201260000059
Namely obtaining M under the condition of meeting the precision in And M out The dimension of the compressed correlation coefficient matrix can be obtained by the same method as R B 、R C 、R D . According to the definition of the maximum time constant, the element coordinate boundary R = max (R) of the dynamic correlation coefficient matrix of the influence pipeline can be calculated A ,R B ,R C ,R D ) And the maximum time constant pi of the single pipeline is R multiplied by delta T.
The deformation processing is carried out on the formula (9) and comprises the following steps:
Figure BDA0003647201260000055
further establishing a node-outflow pipeline incidence matrix A out Node-inflow pipe incidence matrix A in Pipeline head end-node incidence matrix A pn1 Pipeline end-node incidence matrix A pn2 . The network node injection flow is expressed as:
M n ＝A in M out -A out M in (11)
meanwhile, the node-pipeline pressure satisfies:
Γ in ＝A pn1 Γ n Γ out ＝A pn2 Γ n (12)
by substituting formula (11) and formula (12) for formula (10), the following are obtained:
Figure BDA0003647201260000056
in the formula: m sr The injection flow rate of the gas source node; m int The vector is 0 as known from KCL for the injection flow of the intermediate node; m ld The injection flow of the load node; gamma-shaped sr Is the pressure of the air source node; gamma-shaped int Is the pressure at the intermediate node, and may be represented by other known quantities; gamma-shaped ld Is the pressure at the load node. The formula (13) can be arranged:
Figure BDA0003647201260000057
Figure BDA0003647201260000061
thus, a dynamic time domain two-port model of the gas network is constructed:
Figure BDA0003647201260000062
and 3, step 3: and (3) determining the maximum time constant of the air network according to the air network correlation parameter matrix obtained in the step (2).
Matrix Y mm ,Y mp ,Y pm ,Y pp Is M ld 、Γ sr And M sr 、Γ ld The correlation coefficient matrix Y is composed of one or more than one of Y 1 ,Y 2 ,…,Y n The square matrix is composed, each square matrix is also a lower triangular matrix and is dominant near the main diagonal, similar to the single-pipeline dynamic coefficient matrix, and the description needs to be given
Figure BDA0003647201260000063
Therefore, Y influencing the dynamic state of the air network can be calculated according to the maximum time constant definition of the air network mm ,Y mp ,Y pm ,Y pp Matrix element coordinate boundaries
Figure BDA0003647201260000064
Maximum time constant pi of air net net Is namely R net ×ΔT。
And 4, step 4: and segmenting actual operation data of the air network according to the maximum time constant of the air network so as to increase the number of samples.
And 5: and fitting the natural gas system dynamics by using a deep learning method, and extracting neural network parameters to construct a gas network dynamic agent model.
If the time resolution of the gas network load flow calculation is delta t, then: (1) connecting the air net with the neural network output layer dynamically and fully
Figure BDA0003647201260000065
The vector dimension is ceiling (delta T/delta T) + R net (ii) a (2) At Δ t + R net And dividing historical operation data of the air network at time intervals by using the xDeltaT to construct a training sample library.
Step 6: and (5) rolling and using the agent model in the step 5 to achieve the purpose of using a small-scale model to depict a long-time air network dynamic process.
In the above steps, the key step is to form a single-pipeline correlation parameter matrix based on an explicit difference method, obtain the connection relation between the pipelines from the gas network topological graph, deduce the gas network correlation parameter matrix, and estimate the maximum time constant of the gas network from the correlation parameter matrix.
The key parameter is the maximum time constant of the gas network, and the maximum time constant of the gas network determines how to segment actual operation data of the gas network and the dimensions of the input layer and the output layer of the neural network.
The process of the invention is illustrated below by means of a specific example. As shown in fig. 4, the lengths of the 1# -3# pipelines are all 2000m, the node 1 is an air source node, the air pressure is kept constant at 0.4MPa, and the nodes 3 and 4 are load nodes. And selecting 10 working conditions outside the training sample set to generate 10 test sample sets (different from the scenes in the training sample set), selecting 10 groups of data in the training sample set of the model I (the full-time surrogate model) to jointly form the test sample set, and comparing the precision, model parameters and solving time of the model I and the model II (the model provided by the method).
The results of comparing the model accuracy of model I and model II are summarized in table 1. The model I has high fitting precision on the training samples, the average error of the mass flow and the node pressure is not more than 0.4% and the maximum error is not more than 2%, the fitting precision on new samples outside the training sample set is low, the average fitting error of the node pressure is close to 5%, the maximum fitting error is close to 10%, and the maximum fitting error of the mass flow is more than 1%; and the model II has higher fitting precision for the air network state quantities of the training sample and the new sample, and the maximum error does not exceed five per ten thousandth. On one hand, the parameters needing fitting from the model I are more, on the other hand, the segmentation of the training samples is realized by introducing the maximum time constant of the air network into the model II, the number of the model training samples is indirectly increased, and the fitting precision is improved.
TABLE 1 comparison of dynamic proxy model for air network with full-time proxy model
Figure BDA0003647201260000071
Meanwhile, one working condition is selected from the training sample set and the new sample, and the fitting dynamic curve of the model I and the model II to the air network state quantity is drawn in fig. 5 (a), fig. 5 (b), fig. 5 (c), fig. 6 (a), fig. 6 (b) and fig. 6 (c). It can be seen that the mass flow and pressure curves fitted by the model I have burrs and are not smooth, and the dynamic depiction of the air network is rough. Compared with the prior art, the average error and the maximum error of the model II in and out of the training sample set are less than 0.05%, the model has high precision and strong generalization capability, and the mass flow and pressure curves of the model II are smoother and are close to the actual working condition, so that the dynamic process of the air network is accurately described.
In terms of model fitting burden, because the output quantity of the model I is the unknown state quantity of the gas network of the total time of the samples, the input quantity and the output quantity of the corresponding proxy model are also larger, so that the dimensions of the parameter matrix W and B are increased, the number of parameters of the model I is 15,151,920, while the number of parameters of the model II is only 346,860, which is 2.29 percent of the number of parameters to be fitted of the model I. If the sample time length is increased, such as the time length is increased from 120 minutes to day level, the output dimension of the model I is continuously increased, the number of parameters to be fitted is increased along with the increase of the output dimension, and the training burden of the model is large; the model II can segment the sample according to the maximum time constant of the air network, so the number of parameters to be fitted is irrelevant to the sample duration, and the time advantage is more obvious. Therefore, the method disclosed by the invention is based on the historical operating data of the natural gas system and the deep learning technology, the natural gas dynamic proxy model is fitted, the assumption of homogenization of pipeline parameters is cancelled, and the model precision is improved; the method can effectively reduce the scale of the agent model, improve the reuse rate of the historical operating data of the natural gas system, and indirectly improve the number of effective samples in the model training stage.
The present invention is not limited to the above embodiments, and any changes or substitutions that can be easily made by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (1)

1. A dynamic modeling method for a natural gas system is characterized by comprising the following steps:
step 1: acquiring the actual operation data of the air source flow, the node pressure and the load flow of the air network;
step 2: establishing a gas network dynamic two-port time domain model based on a pipeline dynamic two-port physical model of an explicit difference method to obtain a gas network correlation parameter matrix;
the step 2 is specifically as follows:
the head end pressure and the tail end pressure of the pipeline p meet the following requirements:
Figure FDA0004026206260000011
in the formula (I), the compound is shown in the specification,
Figure FDA0004026206260000012
respectively representing the head end flow, the tail end flow, the head end air pressure and the tail end air pressure of the pipeline; />
Figure FDA0004026206260000013
Is a two-port model coefficient matrix;
the deformation treatment is carried out on the formula (1) and comprises the following steps:
Figure FDA0004026206260000014
further establishing a node-outflow pipeline incidence matrix A out Node-inflow pipe incidence matrix A in Pipeline head end-node incidence matrix A pn1 Pipeline end-node incidence matrix A pn2 (ii) a The network node injection flow is expressed as:
M n ＝A in M out -A out M in (3)
meanwhile, the node-pipeline pressure satisfies:
Γ in ＝A pn1 Γ n Γ out ＝A pn2 Γ n (4)
substituting formula (3) and formula (4) into formula (2) yields:
Figure FDA0004026206260000015
in the formula: m sr The injection flow rate of the gas source node; m is a group of int The vector is 0 known from KCL as the injection flow of the intermediate node; m ld The injection flow of the load node; gamma-shaped sr Is the pressure of the air source node; gamma-shaped int Is the pressure of the intermediate node; gamma-shaped ld For the pressure of the load node, the formula (5) is arranged to obtain:
Figure FDA0004026206260000021
Figure FDA0004026206260000022
thus, a dynamic two-port time domain model of the air network is constructed:
Figure FDA0004026206260000023
/>
wherein, the matrix Y mm ,Y mp ,Y pm ,Y pp Is M ld 、Γ sr And M sr 、Γ ld The gas network associated parameter matrix;
and step 3: determining the maximum time constant of the air network according to the air network associated parameter matrix obtained in the step 2;
the maximum time constant pi of the air network in the step 3 net Is R net x.DELTA.T, wherein R net Is a matrix Y mm ,Y mp ,Y pm ,Y pp Element coordinate boundary, Δ T is time bin length;
and 4, step 4: segmenting actual operation data of the air network according to the maximum time constant of the air network;
and 5: fitting the natural gas system dynamics by using a deep learning method, and extracting neural network parameters to construct a gas network dynamic agent model;
step 6: and (5) rolling the dynamic agent model of the air network in the step 5 for use, so as to achieve the purpose of describing the long-time dynamic process of the air network by using a small-scale model.
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