CN113591259B - Heat supply pipeline dynamic equivalent modeling method - Google Patents

Heat supply pipeline dynamic equivalent modeling method Download PDF

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CN113591259B
CN113591259B CN202110917198.XA CN202110917198A CN113591259B CN 113591259 B CN113591259 B CN 113591259B CN 202110917198 A CN202110917198 A CN 202110917198A CN 113591259 B CN113591259 B CN 113591259B
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胡阳
简睿妮
房方
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Abstract

The invention relates to a heat supply pipeline dynamic equivalent modeling method, which comprises the following steps: b1, heat supply pipeline steady state operation data extraction, B2, data-driven working domain division, B3 and mixed semi-mechanism modeling. The invention has the advantages that: the nonlinear space is reasonably divided into a plurality of working domains, and the nonlinear global characteristic is approximated by the linear model characteristic established by each working domain, so that the problem of complex nonlinear working conditions is solved well; the established linear low-order model can reasonably balance modeling precision and complexity, and can be widely applied to the fields of control design, rapid simulation, numerical optimization calculation and the like; a set of reasonable modeling method for the dynamic characteristics of the heat supply pipe network is researched, and the control performance of the heat supply process is improved in a more refined mode, so that the economical efficiency and the environmental value of electric heat cooperative utilization are guaranteed.

Description

Heat supply pipeline dynamic equivalent modeling method
Technical Field
The invention relates to the technical field of heating systems, in particular to a dynamic equivalent modeling method for a heating pipeline.
Background
In order to realize sustainable development of energy, Combined Heat and Power (CHP) units become the main centralized heat supply source in China. An electric heat cooperative utilization system based on the CHP unit is constructed, and high-proportion wind power grid-connected consumption can be greatly promoted. The electric heat coordinated supply process needs to fully utilize the heat supply flexibility, so the operation control level of the heat supply side needs to be improved urgently. Under the background, the deep research on the modeling of the dynamic characteristics of the heat supply pipe network and the optimization control of the modeling have important significance.
At present, a linear multi-model architecture is generally adopted for modeling a data-driven heat supply network to approximate actual nonlinear dynamics, and the commonly used linear model structure comprises an autoregressive moving average model, a conditional finite impulse response model and a subspace identification method. The autoregressive moving average modeling method and the subspace identification method can approximate the nonlinear dynamics of an actual system through the linear dynamics under multiple working conditions, however, the division of the multiple working conditions has empirical properties, and a single working condition model can only represent neighborhood characteristics; when the multi-level nodes in the heat supply network are dynamically transmitted, the model switching is interfered, and dynamic transmission accumulated errors are caused, so that the network integration modeling is not facilitated. The condition-limited impulse response model is a nonlinear fitting of the output temperature with respect to the input temperature and the water supply flow, has limited approximation capability to nonlinear dynamics, and can also generate dynamic accumulated errors during the dynamic transmission of the multi-stage nodes. By adopting the intelligent black box identification method, a nonlinear model of the key nodes can be directly established, however, the model has poor interpretability and is difficult to be used for convex optimization solution and stability analysis. In addition, all data modeling methods rely on identification test design and identification data acquisition, and implementation cost is high.
Disclosure of Invention
The technical problem to be solved by the invention is to solve the problems and provide a dynamic equivalent modeling method for the heat supply pipeline, which reasonably divides a nonlinear working domain and establishes a plurality of linear submodels to approximate global characteristics.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: a heat supply pipeline dynamic equivalent modeling method comprises the following steps:
b1, extracting steady-state operation data of the heat supply pipeline,
b2, data-driven work domain division,
b3, modeling of a mixing semi-mechanism.
Further, the step B1 includes determining actually required steady-state data by performing a random sampling consensus algorithm on the instantaneous flow data within a certain window, and fitting a curve model equation of the instantaneous flow within the window to be x ═ P by a least square method0+P1i1+P2i2+…+Pmim，P0Represents the mean size, P, within the window1Representing the slope of the variable over time.
Further, the steady state data defines a steady state criterion through a curve model, and includes:
a1, after the least square fitting of the instantaneous flow data, the difference value between the maximum value and the minimum value of the polynomial filtering value of the curve model is smaller than a given threshold value,
a2, screening the difference value between the maximum value and the minimum value of the instantaneous flow data to be less than a given threshold value by a random sampling consistency algorithm,
a 3, curve model P1The coefficient is less than a given threshold.
Further, the step B2 includes calculating feature vectors characterizing external characteristics of the model based on the extracted steady-state operation data, and then implementing working domain division through feature vector clustering and working domain boundary estimation, and the main steps are as follows:
b1, determining the number of the characteristic vectors and the working domains, establishing input vectors by referring to a piecewise affine autoregressive method, determining the input and output of the system and the corresponding order, and establishing a local data set C by taking a certain data point as a data center, the data center and adjacent C-1 data pointskCalculating Euclidean distance between each point input vector and input vector of data center, selecting C-1 point with minimum distance to form a local data set C, and based on CkThe parameter vector of the data is calculated by using a least square calculation formula and is combined with CkThe mean value of the medium input vector jointly forms a feature vector;
then, the feature vectors are regarded as random vectors which obey Gaussian distribution, the covariance of the feature vectors is estimated, the confidence coefficient of the mean value of the feature vectors is evaluated by using a unified standard according to the characteristics of the Gaussian distribution, finally, a high-dimensional clustering algorithm is selected to cluster each feature vector, the steady-state data set is divided into the corresponding number of working domains according to the clustering number, and the steady-state data in each working domain are stored;
b2, estimating scope boundaries, estimating the boundary characteristics of each work domain based on a pattern recognition algorithm of the data set, namely solving the hyperplane between the data sets, solving a hyperplane equation which is the scope boundary characteristics by adopting a soft interval support vector machine with better robustness and generalization capability, and thus forming the scope of each work domain together with other sub-planes, and facilitating the switching application after the dynamic sub-model is established.
Further, after the B3 includes reasonably dividing the working domains, establishing a dynamic equivalent model for each working domain, establishing a nonlinear ordinary differential equation according to the pipeline operation characteristics, selecting an appropriate state quantity for the nonlinear ordinary differential equation, establishing a continuous state space model of the heat supply pipeline, discretizing the continuous state space model, and obtaining a discrete state space expression; identifying and calculating data parameters in each working domain to obtain each parameter of each mechanism sub-model; because the low-order equivalent model has limited dynamic approximation accuracy, a machine learning algorithm is introduced to carry out deviation dynamic compensation on the mechanism model, and a mixed semi-mechanism model with arbitrary accuracy approximation capability is established.
After adopting the structure, the invention has the following advantages:
the nonlinear space is reasonably divided into a plurality of working domains, and the nonlinear global characteristic is approximated by the linear model characteristic established by each working domain, so that the problem of complex nonlinear working conditions is well solved;
the established linear low-order model can reasonably balance modeling precision and complexity, and can be widely applied to the fields of control design, rapid simulation, numerical optimization calculation and the like;
a set of reasonable modeling method for the dynamic characteristics of the heat supply pipe network is researched, and the control performance of the heat supply process is improved in a more refined mode, so that the economical efficiency and the environmental value of electric heat cooperative utilization are guaranteed.
Drawings
FIG. 1 is a flow chart of a heat supply pipeline dynamic equivalent modeling technique route of the heat supply pipeline dynamic equivalent modeling method of the present invention.
FIG. 2 is a flow chart of transient flow steady state data extraction of the heat supply pipeline dynamic equivalent modeling method of the present invention.
FIG. 3 is a working domain boundary characteristic a diagram of steady-state working condition 1 of the heat supply pipeline dynamic equivalent modeling method.
FIG. 4 is a working domain boundary characteristic b diagram of steady-state working condition 1 of the heat supply pipeline dynamic equivalent modeling method.
FIG. 5 is a working domain boundary characteristic diagram of steady-state condition 2 of the heat supply pipeline dynamic equivalent modeling method of the present invention.
FIG. 6 is a verification result diagram under multi-working-domain switching of the dynamic equivalent modeling method for heat supply pipelines of the present invention.
FIG. 7 is a multi-working-domain internal model local verification result diagram of the heat supply pipeline dynamic equivalent modeling method of the present invention.
FIG. 8 is a multi-domain model performance index table of the dynamic equivalent modeling method for heat supply pipeline of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
With reference to the attached figure 1, a heat supply pipeline dynamic equivalent modeling method comprises the following steps:
b1, extracting steady-state operation data of the heat supply pipeline,
b2, data-driven work domain division,
b3, modeling of a mixing semi-mechanism.
Further, the step B1 includes determining actually required steady-state data by performing a random sampling consensus algorithm on the instantaneous flow data within a certain window, and fitting an instantaneous flow curve model equation within the window by a least square method, where x is P0+P1i1+P2i2+…+Pmim，P0Represents the mean size, P, within the window1Representing the slope of the variable over time.
Further, the steady state data defines a steady state criterion through a curve model, and includes:
a1, after the least square fitting of the instantaneous flow data, the difference value between the maximum value and the minimum value of the polynomial filtering value of the curve model is smaller than a given threshold value,
a2, screening out that the difference value between the maximum value and the minimum value of the instantaneous flow data is less than a given threshold value by a machine sampling consistency algorithm,
a 3, curve model P1The coefficient is less than a given threshold.
Further, the step B2 includes calculating feature vectors characterizing external characteristics of the model based on the extracted steady-state operation data, and then implementing working domain division through feature vector clustering and working domain boundary estimation, and the main steps are as follows:
b1, determining the number of the characteristic vectors and the working domains, establishing input vectors by referring to a piecewise affine autoregressive method, determining the input and output of the system and the corresponding order, and establishing a local data set C by taking a certain data point as a data center, the data center and adjacent C-1 data pointskCalculating Euclidean distance between each point input vector and input vector of data center, selecting C-1 point with minimum distance to form a local data set C, and based on CkThe parameter vector of the data is calculated by using a least square calculation formula and is combined with CkThe mean value of the medium input vector jointly forms a feature vector;
then, the feature vectors are regarded as random vectors which obey Gaussian distribution, the covariance of the feature vectors is estimated, the confidence coefficient of the mean value of the feature vectors is evaluated by using a unified standard according to the characteristics of the Gaussian distribution, finally, a high-dimensional clustering algorithm is selected to cluster each feature vector, the steady-state data set is divided into the corresponding number of working domains according to the clustering number, and the steady-state data in each working domain are stored;
b2, estimating scope boundaries, estimating the boundary characteristics of each work domain based on a pattern recognition algorithm of the data set, namely solving the hyperplane between the data sets, solving a hyperplane equation which is the scope boundary characteristics by adopting a soft interval support vector machine with better robustness and generalization capability, and thus forming the scope of each work domain together with other sub-planes, and facilitating the switching application after the dynamic sub-model is established.
Further, after the B3 includes reasonably dividing the working domains, establishing a dynamic equivalent model for each working domain, establishing a nonlinear ordinary differential equation according to the pipeline operation characteristics, selecting an appropriate state quantity for the nonlinear ordinary differential equation, establishing a continuous state space model of the heat supply pipeline, discretizing the continuous state space model, and obtaining a discrete state space expression; identifying and calculating data parameters in each working domain to obtain each parameter of each mechanism sub-model; because the low-order equivalent model has limited dynamic approximation accuracy, a machine learning algorithm is introduced to carry out deviation dynamic compensation on the mechanism model, and a mixed semi-mechanism model with arbitrary accuracy approximation capability is established.
In the particular practice of the present invention,
extracting steady-state operation data of the heat supply pipeline: the general flow of steady-state data extraction for the heat supply pipeline is shown in fig. 2. Firstly, determining the initial length of a window to be 120, and determining the number of 'interior points' by carrying out a random sampling consistent algorithm on all instantaneous flow data; and fitting an instantaneous flow curve model in the window by a least square method. Determining the maximum and minimum difference C of the model polynomial filter values1Less than 25; determining the maximum and minimum difference C of the screened 'inner point' instantaneous flow data2Less than 20; determining P of a flow curve model1<And 3 delta, delta is the standard deviation of the instantaneous flow data selected by least square fitting. Extracting the steady-state flow data meeting the three conditions, and finding the input according to the steady-state label
Figure GDA0003553820470000041
And output
Figure GDA0003553820470000042
The corresponding steady state data is divided into two steady state conditions according to the range of the instantaneous flow data. Wherein the content of the first and second substances,
Figure GDA0003553820470000043
is a primary water supply input temperature, Tam(t) ambient temperature is the primary feed water outlet temperature.
Data-driven working domain partitioning: and determining the input order and the output order of the heat supply pipeline model to be 1 according to the operating characteristics of the heat supply pipeline. Input temperature by one-time water supply
Figure GDA0003553820470000044
As a control input, the ambient temperature Tam(t) disturbance input, primary water supply outlet temperature
Figure GDA0003553820470000045
Is the system output. Selecting model output according to the input vector structure
Figure GDA0003553820470000046
Model input vector
Figure GDA0003553820470000047
Firstly, taking steady-state data points (x (k), y (k)) as data centers, and respectively selecting adjacent data points c for two steady-state working conditions1＝55，c 225, establishing local data sets C of respective working conditionsk. Calculating a parameter vector PVk＝(Gk TGk)-1Gk TyCkWherein G isk＝[xj(k)1]，xj(k) Is a member of CkInput vector of, yCkIs CkThe output sample vector of (1). Binding of CkMiddle input vector
Figure GDA0003553820470000048
Figure GDA0003553820470000049
Mean value M ofkTogether forming a feature vector FVk＝[(PVk)TMk]T。
Taking the feature vector as the mean value FVkFor confidence of
Figure GDA00035538204700000410
To measure. Selecting a K-Means algorithm to cluster each feature vector, and determining the number of data division working domains of two steady-state working conditions to be S respectively1＝3，S2The total steady state operating condition is 5 working domains. And recording the data of each work domain as D1、D2、…、D5. And (3) a soft interval support vector machine with better robustness and generalization capability is adopted to calculate the boundary characteristic wx + b of each scope to be 0, wherein w is a slope and b is an intercept. The working domains of the two working conditions are divided as shown in fig. 3, fig. 4 and fig. 5.
Mixed semi-mechanism modeling: and after the working domains are reasonably divided, establishing a dynamic equivalent model for each working domain. The nonlinear ordinary differential equation can be established according to the pipeline operation characteristics as follows:
Figure GDA0003553820470000051
in the formula: heat capacity C of water in pipe sectionw＝Fdcwρw(J/. degree. C.), F is the cross-sectional area of the pipe (m)2)；cwThe specific heat capacity of water (J/(kg. DEG C)); rhowIs the density of water (kg/m)3) (ii) a d is the pipe length (m); t is time(s);
Figure GDA0003553820470000052
the water temperature (DEG C) of a primary water supply outlet of the pipeline;
Figure GDA0003553820470000053
the temperature (DEG C) of a primary water supply inlet of the pipeline; mass flow rate Qm＝Fdcwρwuw(kg/s)，uwThe water flow velocity (m/s); alpha is the convective heat transfer coefficient between water flow in the pipeline and the environment (J/(m)2C. s)); heat transfer area S of pipelinet＝Ld(m2)；Tam(t) is the ambient temperature (. degree. C.) and L is the pipe circumference (m).
Selecting proper state quantity for the formula (1), establishing a state space model of the heat supply pipeline, and discretizing the state space model to obtain a discrete state space expression of the heat supply pipeline. And identifying and calculating the data parameters in each working domain to obtain each parameter of each mechanism submodel.
Figure GDA0003553820470000054
U(kT)+eATP(kT) (2)
In the formula:
Figure GDA0003553820470000055
u2＝Tam(kT)；A＝-cwuw-αL/Fcwρw；U(kT)＝[u1(kT)u2(kT)](ii) a T is the sampling time.
And (3) introducing a machine learning algorithm to compensate the deviation dynamic of the model due to the lack of a compensation item of the low-order equivalent model, and establishing a mixed semi-mechanism model as shown in (3).
Figure GDA0003553820470000056
U(kT)+eATP(kT)+f(kT) (3)
In the formula: f (kT) is the dynamic compensation term for the deviation.
Convective heat transfer coefficient alpha and instantaneous water velocity u for each working domain modelwAnd respectively identifying parameters, calculating the other corresponding parameters of each model, and finally applying a machine learning algorithm to carry out dynamic compensation to obtain the piecewise affine-mixed semi-mechanism model with 5 working domains.
After the mixed semi-mechanism model is established, a section of actual operation data which does not participate in modeling is selected for verification, the verification result is shown in attached figures 6 and 7, and the related performance index evaluation is shown in figure 8.
The present invention and its embodiments have been described above, but the description is not limitative, and the actual structure is not limited thereto. It should be understood that those skilled in the art should understand that they can easily make various changes, substitutions and alterations herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A heat supply pipeline dynamic equivalent modeling method is characterized in that: the method comprises the following steps:
b1, extracting steady-state operation data of the heat supply pipeline, including determining actually required steady-state data by carrying out random sampling consistent algorithm on instantaneous flow data in a window, and fitting out an instantaneous flow curve model formula in the window by a least square method, wherein x is P0+P1i1+P2i2+…+Pmim，P0Represents the mean size, P, within the window1Representing the slope of the variable over time,
the steady state data defines a steady state discrimination indicator through a curve model, and comprises the following steps:
a1, after the least square fitting of the instantaneous flow data, the difference value between the maximum value and the minimum value of the polynomial filtering value of the curve model is smaller than a given threshold value,
a2, screening the difference value between the maximum value and the minimum value of the instantaneous flow data to be less than a given threshold value by a random sampling consistency algorithm,
a 3, curve model P1The coefficient is less than a given threshold;
b2, data-driven working domain division, including calculating the characteristic vector of the external characteristics in the characterization model based on the extracted steady-state operation data, and then realizing the working domain division through characteristic vector clustering and working domain boundary estimation, the main steps are as follows:
b1, determining the number of the characteristic vectors and the working domains, establishing input vectors by referring to a piecewise affine autoregressive method, determining the input and output of the system and the corresponding order, and establishing a local data set C by taking a certain data point as a data center, the data center and adjacent C-1 data pointskCalculating Euclidean distance between each point input vector and input vector of data center, selecting C-1 point with minimum distance to form a local data set C, and based on CkThe parameter vector of the data is calculated by using a least square calculation formula and is combined with CkThe mean value of the medium input vector jointly forms a feature vector;
then, the feature vectors are regarded as random vectors which obey Gaussian distribution, the covariance of the feature vectors is estimated, the confidence coefficient of the mean value of the feature vectors is evaluated by using a unified standard according to the characteristics of the Gaussian distribution, finally, a high-dimensional clustering algorithm is selected to cluster each feature vector, the steady-state data set is divided into the corresponding number of working domains according to the clustering number, and the steady-state data in each working domain are stored;
b2, estimating scope boundaries, estimating the boundary characteristics of each work domain based on a pattern recognition algorithm of a data set, namely solving the hyperplane between the data sets, solving a hyperplane equation which is the scope boundary characteristics by adopting a soft interval support vector machine with better robustness and generalization capability, and thus forming the scope of each work domain together with other sub-planes and facilitating the switching application after the dynamic sub-model is established;
b3, modeling by a mixed semi-mechanism, wherein after working domains are reasonably divided, dynamic equivalent models are established for each working domain, nonlinear ordinary differential equations can be established according to the operating characteristics of the pipeline, state quantities are selected for the nonlinear ordinary differential equations, a continuous state space model of the heat supply pipeline can be established, and the continuous state space model is discretized to obtain a discrete state space expression; identifying and calculating data parameters in each working domain to obtain each parameter of each mechanism sub-model; because the low-order equivalent model has limited dynamic approximation accuracy, a machine learning algorithm is introduced to carry out deviation dynamic compensation on the mechanism model, and a mixed semi-mechanism model with arbitrary accuracy approximation capability is established.
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