A semi-analytical modeling simulation method and system for heating network

Abstract

The present invention relates to the field of heating network modeling and simulation, and specifically discloses a method and system for semi-analytical modeling and simulation of a heating network. The method replaces the state variables of water in the pipeline transmission process with the state variables of water in the pipeline transmission process with the state variables of water in the pipeline transmission process. t and space x Two-dimensional function of the state variable with respect to time t and space x The partial derivative function of the state variable two-dimensional function and the partial derivative function are introduced into the PDE equation of the water transmission process in the pipeline to reconstruct the pipeline energy conservation equation and the node energy conservation equation; Combined with the initial value of the heating network and / or the boundary condition constraints in the dynamic process, the SAS model of the heating network quality regulation is solved to obtain the coefficients of the two-dimensional function of the state variable; According to the two-dimensional function of the state variable, the t and space x The present invention does not require the spatial discrete transformation of PDE, avoids the introduction of stability, convergence and error accumulation problems in the one-dimensional method, and improves the simulation accuracy.

Description

Technical Field

[0001] The present invention relates to the field of heating network modeling and simulation, and in particular to a heating network semi-analytical modeling and simulation method and system. Background Art

[0002] In the research framework of integrated energy system (IES), the heating network has attracted extensive attention as a key subsystem. Given the relatively slow transmission speed of the heating medium, the supply and demand balance in the heating system is not achieved instantly. Therefore, the dynamic transmission law of thermal energy needs to be described by a set of high-dimensional partial differential equations (PDE). However, in the actual analysis process, such models often find it difficult to effectively balance the modeling accuracy and solution efficiency while ensuring convergence and stability.

[0003] Given the difficulty of direct analysis of PDE models, existing studies generally use discrete difference methods to handle them. Specifically, the relevant technology uses the finite difference method (FDM) to discretize the model and approximate the PDE terms through the implicit Euler format. However, this format only has first-order convergence accuracy, and the choice of discrete step size is limited by the stability of the difference format.

[0004] Different from the discrete difference method, the related technology chooses another path, which is to convert the original PDE model to other spatial domains for analysis, which is called the spatial transformation method. For example, the PDE model is discretized in the Fourier domain. However, in the process of time domain-frequency domain / complex frequency domain conversion, it is usually difficult to explicitly consider the influence of initial conditions. In addition, the dynamic thermal model in the Fourier domain is composed of a set of linear combinations of different frequency components, and its modeling accuracy and complexity are directly related to the number of sinusoidal components.

[0005] Different from the discrete difference method and the space transformation method, the semi-analytical solution (SAS) method aims to obtain the approximate analytical expression (or SAS expression) of the state quantity expression based on the Taylor series approximation. The related technology applies the holomorphic embedding method to the dynamic energy flow calculation of the electrical thermal IES, and approximates the time-space PDE model into the time domain ODE model through the trapezoidal rule, and further transforms it into a time-domain continuous SAS model through the holomorphic embedding in the time domain, which meets the accuracy and real-time requirements of the digital twin. However, since this method uses the discrete difference method in the transformation process from PDE to ODE, the stability and convergence of the solution in different scenarios still need to be further resolved. At the same time, the process of quadratic approximation increases the risk of error accumulation, so there is still room for further improvement. Summary of the invention

[0006] To solve the above problems, the present invention provides a semi-analytical modeling and simulation method and system for a heating network, which does not require spatial discrete transformation of PDE, avoids the introduction of stability, convergence and error accumulation problems in one-dimensional methods, and improves simulation accuracy.

[0007] In a first aspect, the technical solution of the present invention provides a semi-analytical modeling simulation method for a heating network, wherein the heating network adopts a quality regulation control strategy, and the simulation method comprises the following steps:

[0008] Based on SAS expressions, the state variables of water in the pipeline are replaced by time t and space x Two-dimensional function of ;

[0009] Constructing state variables with respect to time based on two-dimensional functions of state variables t and space x The partial derivative function of

[0010] The two-dimensional function of state variables and partial derivative functions are introduced into the PDE equation of water transmission in pipelines to reconstruct pipeline energy conservation equations and node energy conservation equations; the two-dimensional function of state variables, partial derivative functions of state variables, reconstructed pipeline energy conservation equations and node energy conservation equations, and node mass conservation equations constitute a SAS model for heat supply network quality regulation based on time-space two-dimensional power series embedding;

[0011] Combined with the initial value of the heating network and / or the boundary condition constraints in the dynamic process, the SAS model of the heating network quality regulation is solved to obtain the coefficients of the two-dimensional function of the state variable;

[0012] According to the two-dimensional function of the state variable, any time is calculated t and space x The state variables at .

[0013] In an optional embodiment, the state variable of water in the pipeline transmission process is replaced by the state variable of water in the pipeline transmission process. t and space x The two-dimensional function consists of replacing the state variables with t and space x The two-dimensional polynomial of is expressed as;

[0014]

[0015] In the formula, is a state variable, are the coefficients of the two-dimensional polynomial, is the highest order of the polynomial.

[0016] In an optional implementation, constructing a state variable partial derivative function based on the state variable two-dimensional function specifically includes:

[0017] Constructing state variables about time t and space x Partial derivative polynomials,

[0018] .

[0019] In an optional embodiment, when the state variable is the temperature of water, the two-dimensional function and partial derivative function of the state variable are introduced into the PDE equation of the water transmission process in the pipeline, and the pipeline energy conservation equation and the node energy conservation equation are reconstructed, specifically including:

[0020] The reconstructed pipeline energy conservation equation is expressed as:

[0021]

[0022] In the formula, represents the density of water, represents the specific heat capacity of water, represents the heat dissipation coefficient of the pipe, represents the mass flow rate of water, represents the cross-sectional area of ​​the pipe, Represents the ambient temperature;

[0023] The reconstructed node energy conservation equation is expressed as:

[0024]

[0025] In the formula, , Represents the heating network node indicator set, represents the node association matrix at the head end of the pipeline, represents the node association matrix at the end of the pipeline, represents the length of the pipeline, Represents a heating network node The load at .

[0026] In an optional embodiment, the SAS model of quality regulation of the heating network is solved in combination with the initial value of the heating network and / or the boundary condition constraints in the dynamic process to obtain the coefficients of the two-dimensional function of the state variable, specifically including:

[0027] By comparing the two sides of the equation in the SAS model of heating network quality regulation , , , …, The coefficients of the terms are used to derive a set of linear equations;

[0028] Combining the initial value of the thermal network and / or the boundary condition constraints in the dynamic process, the derived set of linear equations are organized into a matrix form;

[0029] Solve the matrix to obtain the coefficients of the two-dimensional function of the state variable.

[0030] In an optional embodiment, when the heating network is a single-pipeline scenario, the initial value includes the temperature at the initial moment of the head end of the pipeline and the temperature at the initial moment at each step distance.

[0031] In an optional embodiment, when the heating network is a network scenario, the initial value includes the temperature at the initial moment of each pipeline head end and the temperature at the initial moment of each order distance, and the boundary condition constraints in the dynamic process are the change information of the source node temperature over time.

[0032] In a second aspect, the technical solution of the present invention provides a semi-analytical modeling simulation system for a heating network, wherein the heating network adopts a quality regulation control strategy, and the simulation system comprises:

[0033] State variable two-dimensional function building module: Based on SAS expression, the state variable of water in the pipeline transmission process is replaced by the state variable of water in the pipeline transmission process. t and space x Two-dimensional function of ;

[0034] State variable partial derivative function construction module: construct state variable partial derivative function with respect to time based on state variable two-dimensional function t and space x The partial derivative function of

[0035] Energy conservation equation reconstruction module: Bring the two-dimensional function of state variables and partial derivative function into the PDE equation of water transmission process in pipelines, and reconstruct the pipeline energy conservation equation and node energy conservation equation; the two-dimensional function of state variables, partial derivative function of state variables, reconstructed pipeline energy conservation equation and node energy conservation equation, and node mass conservation equation constitute a heating network quality regulation SAS model based on time-space two-dimensional power series embedding;

[0036] SAS model solving module: Combined with the initial value of the heating network and / or the boundary condition constraints in the dynamic process, the SAS model of the heating network quality regulation is solved to obtain the coefficients of the two-dimensional function of the state variable;

[0037] Real-time state variable calculation module: calculate the state variable two-dimensional function to obtain any time t and space x The state variables at .

[0038] A semi-analytical modeling and simulation method and system for a heating network provided by the present invention has the following beneficial effects relative to the prior art: in mathematical form, different from the one-dimensional holomorphic embedding adopted by the traditional SAS modeling and simulation method for the heating network, this method is based on the time-space two-dimensional power series embedding, does not require the spatial discrete transformation of the PDE, and avoids the introduction of stability / convergence / error accumulation problems in the one-dimensional method. In terms of simulation effect, this method has better comprehensive performance in terms of accuracy, complexity and stability than traditional methods. In terms of application prospects, this method shows the unique advantage of constructing an approximate analytical expression of the state quantity to accurately depict the continuous evolution process of slow dynamics in a specific time domain. For any time point in the time domain, there is a set of corresponding analytical expressions of the state quantity, which shows that this method is expected to avoid the common time step matching problem in the process of multi-energy flow joint modeling and simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 It is a flow chart of a semi-analytical modeling and simulation method for a heating network provided in an embodiment of the present invention.

[0041] Figure 2 It is a three-node two-pipeline topology diagram.

[0042] Figure 3 It is the temperature change curve at the beginning of the pipeline.

[0043] Figure 4 is the temperature change curve at the end of the pipeline, where (a) is the temperature change curve at the end of the pipeline simulated using the FDM method when the spatial step is 10m, (b) is the temperature change curve at the end of the pipeline simulated using the FDM method when the spatial step is 20m, (c) is the temperature change curve at the end of the pipeline simulated using the FDM method when the spatial step is 50m, and (d) is the temperature change curve at the end of the pipeline simulated using the SAS method.

[0044] Figure 5 It is a six-node heating network topology diagram.

[0045] Figure 6 It is the water supply temperature variation curve of the heat source node.

[0046] Figure 7 It is the water supply temperature variation curve of load node 5.

[0047] Figure 8 It is the return water temperature variation curve of the heat source node.

[0048] Fig. 9 It is a schematic block diagram of the structure of a semi-analytical modeling and simulation system for a heating network provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] In order to enable those skilled in the art to better understand the scheme of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0050] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0051] Figure 1 This is a flow chart of a semi-analytical modeling and simulation method for a heating network provided by an embodiment of the present invention. Figure 1 The execution subject may be a semi-analytical modeling and simulation system for a heating network. The semi-analytical modeling and simulation method for a heating network provided in an embodiment of the present invention is executed by a computer device, and accordingly, the semi-analytical modeling and simulation system for a heating network runs in the computer device. According to different requirements, the order of the steps in the flowchart may be changed, and some may be omitted.

[0052] In this embodiment, Figure 1 As shown, the method includes the following steps.

[0053] S1, based on SAS expression, replaces the state variables of water in the pipeline transmission process with the state variables about time t and space x Two-dimensional function of .

[0054] For the mathematical model of the heating network, the state variable is a function of time and space. In this embodiment, the state variable is expressed as a two-dimensional function of time and space. Specifically, the heating network adopts a mass regulation control strategy, the hydraulic state is constant, and the pipeline mass flow Due to the incompressibility of water, when the flow rate is maintained, the pressure at the pipe inlet does not change, and the water pressure only changes with the space. x Therefore, based on SAS, the state variable can be replaced by the time t and space x The two-dimensional polynomial form of is expressed as:

[0055]

[0056] In the formula, is a state variable, are the coefficients of the two-dimensional polynomial, It is the highest order of the polynomial. The state variables of the heating network include temperature, flow, water pressure, etc. The target state variables can be processed and simulated as needed.

[0057] S2, constructs the state variable with respect to time based on the two-dimensional function of the state variable t and space x The partial derivative function of .

[0058] Considering time variables and space variables, the two-dimensional function of the state variable is analyzed with respect to time. t and space x The partial derivative of the state variable is calculated to obtain the partial derivative function of the state variable. In this embodiment, the two-dimensional function of the state variable is in polynomial form, and the partial derivative function is also in polynomial form, and the expression is:

[0059] .

[0060] S3, introduce the two-dimensional function of state variables and partial derivative function into the PDE equation of water transmission process in pipeline, and reconstruct the pipeline energy conservation equation and node energy conservation equation.

[0061] According to the basic principles of fluid dynamics, the pipeline flow process of water follows the law of conservation of energy. In the construction of the heating network, the node is a key component connecting each pipeline, and its function is to ensure the conservation of mass and energy in the network. Specifically, the node achieves the balance of flow and energy by adjusting the flow and energy of the import and export pipelines. Based on the above principles, the PDE equation of the water transmission process in the pipeline is constructed. This embodiment further introduces the two-dimensional function of the state variable and the partial derivative function into the PDE equation of the water transmission process in the pipeline to obtain the reconstructed pipeline energy conservation equation and node energy conservation equation.

[0062] Taking the water temperature as an example, the reconstructed pipeline energy conservation equation is expressed as follows:

[0063]

[0064] In the formula, represents the density of water, represents the specific heat capacity of water, represents the heat dissipation coefficient of the pipe, represents the mass flow rate of water, represents the cross-sectional area of ​​the pipe, Represents the ambient temperature.

[0065] The reconstructed node energy conservation equation is expressed as:

[0066]

[0067] In the formula, , Represents the heating network node indicator set, represents the node association matrix at the head end of the pipeline, represents the node association matrix at the end of the pipeline, represents the length of the pipeline, Represents a heating network node The load at .

[0068] The state variable two-dimensional function, state variable partial derivative function, reconstructed pipeline energy conservation equation and node energy conservation equation of this embodiment constitute a heating network quality regulation SAS model based on time-space two-dimensional power series embedding.

[0069] S4, combining the initial value of the heating network and / or the boundary condition constraints in the dynamic process, solving the SAS model of the heating network quality regulation, and obtaining the coefficients of the two-dimensional function of the state variable.

[0070] In the constructed SAS model, at any selected distance x and time t Under all circumstances, it is necessary to ensure that the equations on both sides of the equation always hold. From the condition of equal series, it can be seen that the coefficients of the same-order terms in the equation must be equal. Based on the above principles, this embodiment combines the initial value of the heating network and / or the boundary condition constraints in the dynamic process to solve the SAS model to obtain the coefficients of the two-dimensional function of the state variable.

[0071] S4.1, by comparing the two sides of the equation in the SAS model for heat network quality regulation , , , …, The coefficients of the terms derive a set of linear equations.

[0072] S4.2, combining the initial values ​​of the thermal network and / or the boundary condition constraints in the dynamic process, the derived set of linear equations are organized into a matrix form.

[0073] S4.3, solve the matrix to obtain the coefficients of the two-dimensional function of the state variable.

[0074] When the heating network is a single-pipe scenario, the initial values ​​include the temperature at the initial end of the pipe and the temperature at the initial time of each order of distance. When the heating network is a network scenario, the initial values ​​include the temperature at the initial end of each pipe and the temperature at the initial time of each order of distance. The boundary condition constraints in the dynamic process are the changes in the source node temperature over time.

[0075] S5, calculate any time according to the two-dimensional function of the state variable t and space x The state variables at .

[0076] Through the above steps 1 to 4, the coefficients of the two-dimensional function of the state variable are obtained. The two-dimensional function of the state variable is about time t and space x A two-dimensional function, based on the known coefficients, converts time t and space x Input the two-dimensional function of the state variable to obtain the time t and space x The state variables below.

[0077] To further understand the present invention, the following describes in detail the process of constructing and solving a dynamic model based on SAS based on a general analytical formula of a dynamic model of a heating network.

[0078] (1) General analytical formula for the dynamic model of the heating network.

[0079] The heating network is mainly composed of pipelines, nodes and heat transfer media. This paper focuses on analyzing the dynamic changes of water state parameters (such as temperature, pressure, mass flow) during pipeline transmission. According to the basic principles of fluid dynamics, the pipeline flow process of water follows the three laws of conservation of mass, conservation of momentum and conservation of energy, and their mathematical expressions are:

[0080] (1)

[0081] (2)

[0082] (3)

[0083] Where: represents the density of water, ; represents the water flow rate, ; Represents the water pressure, ; represents the specific heat capacity of water, take ; represents the water temperature, ; represents the friction coefficient of the pipeline; represents the inner diameter of the pipe, ; represents the heat dissipation coefficient of the pipe, ; represents the ambient temperature, ; is the time variable; is a spatial variable.

[0084] As an incompressible fluid, the density of water can be considered constant in general. In a closed pipe, the mass flow rate of water is The relationship with water velocity is Therefore, substituting the above relationship into equations (1) to (3), we can obtain:

[0085] (4)

[0086] (5)

[0087] (6)

[0088] Where: is the cross-sectional area of ​​the pipe, .

[0089] In the construction of the heating network, nodes are key components that connect various pipelines. Their function is to ensure the conservation of mass and energy in the network. Specifically, nodes achieve the balance of flow and energy by adjusting the flow and energy of the inlet and outlet pipelines. This process can be described by the following mathematical equation:

[0090] (7)

[0091] (8)

[0092] Where: is the heating network node indicator set, is the heat supply network pipeline index set, is the node association matrix at the head end of the pipeline, is the node association matrix at the end of the pipeline, Heating network node The load at .

[0093] The node index refers to the node number. For example, there are 10 nodes in total. i The value range of is 1-10, and each node i needs to satisfy equations (7) and (8). Like the node index, the pipeline index refers to the sequence number of the pipeline, and any pipeline connects at least two nodes.

[0094] (2) Dynamic modeling and solving based on SAS.

[0095] (2.1) General expression of SAS model.

[0096] The SAS method first sets the solution to an analytical form in a piecewise multivariate polynomial format, and then determines the coefficients in the polynomial to approximate the solution of the PDE under study. This method was first applied to the calculation of steady-state power flow in power systems, expressing the voltage as a combination of multidimensional variables. For the mathematical model of the heating network, the state quantity is a function of time and space, and the state quantity can be expressed as a two-dimensional polynomial form in time and space.

[0097] For convenience, only the first-order constant coefficient PDE with a single function and two variables is discussed here to illustrate the construction process of the SAS model, which can also be extended to PDEs of other formats. Consider the time variable and spatial variables .set up is a function of at least Mth order continuously differentiable; let the function Known, is a constant. The PDE can be expressed as:

[0098] (9)

[0099] Will Represented by a two-dimensional polynomial, right and The partial derivatives can be written as:

[0100] (10)

[0101] In the formula Represents the highest order of the polynomial.

[0102] Both sides of the equation will contain Therefore, solving PDE has been transformed into solving a system of linear equations. The coefficients in the SAS model can be uniquely solved by matrix calculation. If the coefficients of the low-order polynomial are known, the linear equation can be decomposed into multiple smaller recursive problems, which is conducive to solving by computer programs and is more efficient.

[0103] (2.2) SAS expression of heating network based on time-space two-dimensional power series embedding.

[0104] From equations (4) to (8), it can be seen that the model of the heating network is a two-dimensional PDE equation about time and space. This model can be expressed by a two-dimensional polynomial about time and space. When the heating network adopts the quality regulation control strategy, the hydraulic state is constant and the pipeline mass flow Due to the incompressibility of water, when the flow rate is maintained, the inlet pressure of the pipe does not change. Only with space Related. Based on SAS, time-varying parameters Can be replaced by about time and space Two-dimensional function of :

[0105] (11)

[0106] Where: is a two-dimensional polynomial Term coefficient, is the highest order of the polynomial.

[0107] At this time, the partial derivative of the state variable is also about and Polynomial of:

[0108] (12)

[0109] Substituting the state variables and partial derivative expressions (Formulas (11) and (12)) into the PDE equation, the pipeline energy conservation equation (Formula (3)) can be reconstructed as:

[0110] (13)

[0111] The node energy conservation equation (Formula (8)) can be reconstructed as:

[0112] (14)

[0113] Equations (7), (11)-(14) constitute the SAS model of heating network quality regulation based on time-space two-dimensional power series embedding.

[0114] At any chosen distance and time In all cases, we must ensure that the equations on both sides of the equation always hold. From the condition of equality of series, we know that the coefficients of the same-order terms in the equation must be equal. By comparing the two sides , , , …, By combining the coefficients of the terms, we can derive a set of linear equations. By combining the initial values ​​of the heating network and the boundary conditions in the dynamic process, we can organize these linear equations into matrix form and obtain the coefficients of the polynomials of various orders in the SAS model through matrix solution.

[0115] In formulas (7), (11)-(14), except for temperature Except for , the rest are known quantities. For example (this method can process equations with M of any high degree. In theory, the higher the M, the more accurate the calculated value, but the calculation time will also be longer. Therefore, in this embodiment, M is 3 in a single-pipeline scenario and 2 in a network scenario. The calculation time and accuracy are better than the traditional method). And its partial derivatives can be expressed as:

[0116] (15)

[0117] (16)

[0118] In a single-pipeline scenario, we only need to satisfy equation (13), which is:

[0119] (17)

[0120] The initial value is By comparing the two sides , , , …, The coefficients of the terms are calculated and the higher-order terms are ignored (this operation is for the convenience of calculation, so it will cause a certain error, but the error range is within the allowable range and is better than the traditional FDM method). The coefficients of the same-order terms in the equation are equal, so it can be sorted into the following linear equation:

[0121] (18)

[0122] make ,

[0123] , , then formula (18) can be organized into a matrix form:

[0124] (19)

[0125] Using Matrix Inversion Solving the matrix form of equation (19) yields the polynomial coefficients of temperature of various orders:

[0126] After obtaining the polynomial coefficients, we can get the temperature expression of the pipeline in time and space:

[0127]

[0128] Then substitute the corresponding and , we can get the specific temperature value at any position in the pipeline at any time. As time changes, if the boundary conditions (the temperature at the beginning of the pipeline) If the temperature changes, the above process can be repeated to obtain the latest expression of temperature.

[0129] The network scenario is similar to the single-pipe scenario, but the node energy conservation equation needs to be considered. For ease of understanding, , and the network form is three nodes and two pipelines, node 1 is the source node, and the load at node 2 is , Figure 2 It is a three-node two-pipeline topology diagram.

[0130] Temperature Its partial derivative can be expressed as:

[0131] (20)

[0132] (twenty one)

[0133] At this time, the mass conservation equation (7) can be expressed as:

[0134] (twenty two)

[0135] Both pipeline 1 and pipeline 2 must satisfy the energy conservation equation, that is,

[0136] (twenty three)

[0137] Node 2 needs to satisfy the node energy conservation equation (14):

[0138] (twenty four)

[0139] The boundary condition of the network is that the temperature of the source node changes with time Change and change, that is (The specific change value will be given in advance, i.e. is a known quantity). The initial condition is that pipes 1 and 2 are The initial temperature value at is known. The temperature at the pipe head end is known, and if the temperature at the pipe head end remains constant, then:

[0140]

[0141] The above equation can be organized into a linear equation:

[0142] (25)

[0143] make ,

[0144] in,

[0145] ,

[0146] ,

[0147] , , then equation (25) can be organized into a matrix form:

[0148] (26)

[0149] Using Matrix Inversion Solving the matrix form of equation (26) yields the polynomial coefficients of the temperature of each pipe: …

[0150] After obtaining the polynomial coefficients, we can get the temperature expressions of these pipes with respect to time and space:

[0151] (27)

[0152] Then substitute the corresponding and , we can get the specific temperature value at any position in the pipeline at any time. As time changes, if the boundary conditions (the temperature at the beginning of the pipeline) If the temperature changes, the above process can be repeated to obtain the latest expression of temperature.

[0153] In order to verify the simulation performance of the SAS method proposed in this embodiment, two typical scenarios, a single-pipeline and a six-node heating network, were selected for computational analysis, and the calculation results of SAS were compared with the FDM method (using the cutting-edge central difference quotient implicit difference format) with different degrees of spatial discretization. All simulation experiments were performed on a computer equipped with an Intel(R) Core(TM) i7-13700CPU @ 2.10GHz and 32.0 GB RAM, using the MATLAB R2020a programming environment.

[0154] 1. Single pipeline case test.

[0155] The parameters of the heating pipeline in the single-pipeline example are shown in Table 1, and the simulation time is set to 900s.

[0156] Table 1: Thermodynamic parameters of heating pipelines

[0157] parameter Numeric unit Pipe length 100 m Working fluid flow rate 1 m / s Cross-sectional area 1.54 m² Thermal conductivity 0.67 W / (m*K) Ambient temperature 263.15 K

[0158] The settings of the comparative example are as follows:

[0159] 1) Benchmark value. Since the simulation results of the highly discretized FDM model are very close to those of the PDE, the spatial step size Δ x = 0.1 m, time step Δ t = 0.1 s FDM simulation results are the benchmark values.

[0160] 2) FDM (central difference quotient implicit difference format). Select the spatial step size Δ x The FDM calculation results of 10m, 20m and 50m are used for comparative analysis, and the time step Δ t = 0.1 s.

[0161] 3) SAS (the method proposed in this paper). The highest order initial value of the space-time two-dimensional power series is 3, and the spatial step length of the grid is Δ x = 1m, time step Δ t = 1 s. Since SAS can depict the continuous evolution of slow dynamics in a specific time domain, Δ t =0.1 s is the actual output step size of the simulation results.

[0162] The temperature change at the beginning of the pipeline is set as follows Figure 3 The response of the pipe end temperature is calculated by different methods, such as Figure 4 shown.

[0163] Depend on Figure 4 It can be seen that with the increase of the spatial step size, the oscillation of the temperature response curve at the end of the FDM pipe becomes increasingly obvious. This is a phenomenon caused by the excessive size of the space-time microelement in the traditional finite difference method. In contrast, the SAS temperature response curve is highly consistent with the benchmark value, effectively avoiding the numerical stability problem caused by the traditional finite difference method, thus showing higher accuracy.

[0164] In order to more comprehensively compare the performance of FDM and SAS methods in terms of accuracy and computational efficiency, Table 2 shows the calculation error values ​​of different simulation methods for a single pipeline example (three indicators are selected: mean absolute percentage error (MAPE), maximum absolute percentage error (MaxAPE), and mean absolute error (MAE)), and Table 3 compares the calculation time of different simulation methods.

[0165] Table 2: Simulation calculation errors of different methods for single pipeline example

[0166]

[0167] The data in Table 2 show that the calculation error of FDM increases significantly with the increase of spatial step size. The calculation error of SAS is smaller than that of all FDM models involved in the comparison. In addition, the difference between MaxAPE and MAPE of SAS is small; while for all FDM models, the difference between MaxAPE and MAPE is relatively large, indicating that the error caused by the oscillation phenomenon of its response curve is more significant and the numerical stability problem is more prominent.

[0168] Table 3: Simulation calculation time of different methods for single pipeline model

[0169]

[0170] According to the data in Table 3, SAS only needs 0.0376 s to complete the 900 s time domain simulation calculation, which is better than FDM with any spatial step length in the table. In addition, under similar computational costs (FDM (Δ x = 100m) and SAS (Δ x =1m), SAS can achieve more than 100 times improvement in accuracy compared to FDM (compare with MAPE index in Table 2), highlighting the significant comprehensive advantages of the method proposed in this embodiment in terms of accuracy / computational efficiency.

[0171] 2. Six-node heating network example test.

[0172] The topology of the six-node heating network example is as follows: Figure 5 As shown, the simulation time is set to 3600s.

[0173] The settings of the comparative example are as follows:

[0174] 1) Baseline value. Select the spatial step length Δ x = vΔ t , time step Δ t = 1 s FDM simulation results are the benchmark values.

[0175] 2) FDM (central difference quotient implicit difference format). Select the spatial step size Δ x The FDM calculation results for 15 m are used for comparative analysis, and the time step Δ t = 1 s.

[0176] 3) SAS (the method proposed in this paper). The highest order initial value of the space-time two-dimensional power series is 3, and the spatial step length of the grid is Δ x = vΔ t , time step Δ t= 10s. Since SAS can depict the continuous evolution of slow dynamics in a specific time domain, Δ t = 1 s is the actual output step size of the simulation results.

[0177] The water supply temperature change setting of the heat source node is as follows: Figure 6 The water supply temperature of load node 5 and the return water temperature of heat source node are calculated by different methods. Some curves are shown as follows: Figure 7 and Figure 8 shown.

[0178] Depend on Figure 7 and Figure 8 It can be seen that the temperature response curve of FDM shows obvious oscillation when compared with the reference value, especially when the temperature changes. In contrast, the temperature response curve of SAS is highly consistent with the reference value, and no oscillation is observed even when the temperature changes, which verifies that this method still maintains relatively higher stability and accuracy when processing network models.

[0179] In order to more comprehensively compare the performance of FDM and SAS methods in terms of accuracy and computational efficiency in the six-node heating network example, Table 4 shows the computational errors of different simulation methods in the six-node heating network example, and Table 5 compares the computational time of different simulation methods in the six-node heating network example.

[0180] Table 4: Simulation calculation errors of different methods in the six-node heating network example

[0181]

[0182] According to the data in Table 4, it can be observed that with the increase of the spatial step size, the calculation error of FDM shows a significant growth trend. In contrast, SAS shows extremely low MAPE and MaxAPE values ​​in the simulation results, which are much lower than the corresponding results of FDM under any of the above spatial step sizes, highlighting the significant advantages of the method proposed in this embodiment in terms of simulation accuracy.

[0183] Table 5: Simulation time of different methods in the six-node heating network example

[0184]

[0185] The data in Table 5 show that the SAS method proposed in this embodiment can complete the 3600 s time domain simulation calculation in only 3.382 s, which is faster than the FDM with any spatial step length. In addition, under similar computational costs (FDM (Δ x =25m) and SAS (Δ x = vΔ t)), SAS can achieve tens of thousands of times improvement in accuracy compared to FDM (compare the MAPE index in Table 4), which highlights that the comprehensive advantages of the method proposed in this embodiment in terms of accuracy / computational efficiency are more significant in network scenarios.

[0186] An embodiment of a semi-analytical modeling and simulation method for a heating network is described in detail above. Based on the semi-analytical modeling and simulation method for a heating network described in the above embodiment, an embodiment of the present invention also provides a semi-analytical modeling and simulation system for a heating network corresponding to the method.

[0187] Fig. 9 is a schematic block diagram of the structure of a semi-analytical modeling and simulation system for a heating network provided in an embodiment of the present invention. In this embodiment, the semi-analytical modeling and simulation system for a heating network can be divided into multiple functional modules according to the functions it performs, such as Fig. 9 As shown. The functional modules may include: a state variable two-dimensional function construction module, a state variable partial derivative function construction module, an energy conservation equation reconstruction module, a SAS model solving module, and a real-time state variable calculation module. The module referred to in the present invention refers to a series of computer program segments that can be executed by at least one processor and can complete fixed functions, which are stored in a memory.

[0188] State variable two-dimensional function building module: Based on SAS expression, the state variable of water in the pipeline transmission process is replaced by the state variable of water in the pipeline transmission process. t and space x Two-dimensional function of .

[0189] State variable partial derivative function construction module: construct state variable partial derivative function with respect to time based on state variable two-dimensional function t and space x The partial derivative function of .

[0190] Energy conservation equation reconstruction module: introduce the two-dimensional function of state variables and partial derivative function into the PDE equation of water transmission process in pipeline, reconstruct the pipeline energy conservation equation and node energy conservation equation; the two-dimensional function of state variables, partial derivative function of state variables, reconstructed pipeline energy conservation equation and node energy conservation equation, and node mass conservation equation constitute a SAS model of heating network quality regulation based on time-space two-dimensional power series embedding.

[0191] SAS model solving module: Combined with the initial value of the heating network and / or the boundary condition constraints in the dynamic process, the SAS model of the heating network quality regulation is solved to obtain the coefficients of the two-dimensional function of the state variable.

[0192] Real-time state variable calculation module: calculate the state variable two-dimensional function to obtain any time t and space x The state variables at .

[0193] The heating network semi-analytical modeling and simulation system of the present embodiment is used to implement the aforementioned heating network semi-analytical modeling and simulation method. Therefore, the specific implementation method of the system can be seen in the embodiment part of the heating network semi-analytical modeling and simulation method in the previous text. Therefore, its specific implementation method can refer to the description of the corresponding embodiments of each part, which will not be elaborated here.

[0194] In addition, since the heating network semi-analytical modeling and simulation system of this embodiment is used to implement the aforementioned heating network semi-analytical modeling and simulation method, its function corresponds to that of the aforementioned method and will not be repeated here.

[0195] The above disclosure is only a preferred embodiment of the present invention, but the present invention is not limited thereto. Any non-creative changes that can be thought of by a person skilled in the art, as well as several improvements and modifications made without departing from the principle of the present invention, should fall within the protection scope of the present invention.

Claims

1. A semi-analytical modeling and simulation method for a heating network, characterized in that: The heating network adopts a quality regulation control strategy, and the simulation method comprises the following steps: Replace the state variables of water in the pipeline with the variables related to time t and space x A two-dimensional function of t and space x The two-dimensional polynomial of is expressed as: In the formula, is a state variable, are the coefficients of the two-dimensional polynomial, is the highest order of the polynomial; Constructing state variables with respect to time based on two-dimensional functions of state variables t and space x The partial derivative function of The two-dimensional function of state variables and partial derivative functions are introduced into the PDE equation of water transmission in pipelines to reconstruct pipeline energy conservation equations and node energy conservation equations; the two-dimensional function of state variables, partial derivative functions of state variables, reconstructed pipeline energy conservation equations and node energy conservation equations, and node mass conservation equations constitute a SAS model for heat supply network quality regulation based on time-space two-dimensional power series embedding; Combined with the initial value of the heating network and / or the boundary condition constraints in the dynamic process, the SAS model of the heating network quality regulation is solved to obtain the coefficients of the two-dimensional function of the state variable; According to the two-dimensional function of the state variable, any time is calculated t and space x The state variables at .

2. The semi-analytical modeling and simulation method for a heating network according to claim 1, characterized in that: The partial derivative function of the state variable is constructed based on the two-dimensional function of the state variable, including: Constructing state variables about time t and space x Partial derivative polynomials, 。 3. The semi-analytical modeling and simulation method for a heating network according to claim 2 is characterized in that: When the state variable is the temperature of water, the two-dimensional function and partial derivative function of the state variable are brought into the PDE equation of the water transmission process in the pipeline, and the pipeline energy conservation equation and the node energy conservation equation are reconstructed, including: The reconstructed pipeline energy conservation equation is expressed as: In the formula, represents the density of water, represents the specific heat capacity of water, represents the heat dissipation coefficient of the pipe, represents the mass flow rate of water, represents the cross-sectional area of ​​the pipe, Represents the ambient temperature; The reconstructed node energy conservation equation is expressed as: In the formula, , Represents the heating network node indicator set, represents the node association matrix at the head end of the pipeline, represents the node association matrix at the end of the pipeline, represents the length of the pipeline, Represents a heating network node The load at .

4. The semi-analytical modeling and simulation method for a heating network according to claim 3 is characterized in that: Combined with the initial value of the heating network and / or the boundary condition constraints in the dynamic process, the SAS model of the heating network quality regulation is solved to obtain the coefficients of the two-dimensional function of the state variable, including: By comparing the two sides of the equation in the SAS model of heating network quality regulation , , , …, The coefficients of the terms are used to derive a set of linear equations; Combining the initial value of the thermal network and / or the boundary condition constraints in the dynamic process, the derived set of linear equations are organized into a matrix form; Solve the matrix to obtain the coefficients of the two-dimensional function of the state variable.

5. The semi-analytical modeling and simulation method for a heating network according to claim 4, characterized in that: When the heating network is a single-pipe scenario, the initial values ​​include the temperature at the initial moment of the pipe head end and the temperature at the initial moment of each order distance.

6. The semi-analytical modeling and simulation method for a heating network according to claim 5, characterized in that: When the heating network is a network scenario, the initial values ​​include the temperature at the initial moment of each pipeline head end and the temperature at the initial moment of each order distance. The boundary condition constraints in the dynamic process are the change information of the source node temperature over time.

7. A semi-analytical modeling and simulation system for a heating network, characterized in that: The heating network adopts a quality regulation control strategy, and the simulation system includes: State variable two-dimensional function building block: replace the state variable of water in the pipeline with the state variable of time t and space x Two-dimensional function of ; State variable partial derivative function construction module: construct state variable partial derivative function with respect to time based on state variable two-dimensional function t and space x The partial derivative of t and space x The two-dimensional polynomial of is expressed as: In the formula, is a state variable, are the coefficients of the two-dimensional polynomial, is the highest order of the polynomial; Energy conservation equation reconstruction module: Bring the two-dimensional function of state variables and partial derivative function into the PDE equation of water transmission process in pipelines, and reconstruct the pipeline energy conservation equation and node energy conservation equation; the two-dimensional function of state variables, partial derivative function of state variables, reconstructed pipeline energy conservation equation and node energy conservation equation, and node mass conservation equation constitute a heating network quality regulation SAS model based on time-space two-dimensional power series embedding; SAS model solving module: Combined with the initial value of the heating network and / or the boundary condition constraints in the dynamic process, the SAS model of the heating network quality regulation is solved to obtain the coefficients of the two-dimensional function of the state variable; Real-time state variable calculation module: calculate the state variable two-dimensional function to obtain any time t and space x The state variables at .

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