Dynamic simulation method and system for regional heat supply network, terminal and medium

Abstract

The invention relates to the field of heat supply network analogue simulation, and particularly discloses a regional heat supply network dynamic simulation method and system, a terminal and a medium, the method comprises the following steps: constructing a hydraulic model semi-analytical expression and a thermal model semi-analytical expression of a pipeline in a regional heat supply network, and according to the pipeline momentum conservation and the node mass conservation, calculating the thermal model semi-analytical expression of the pipeline in the regional heat supply network; constructing semi-analytic coefficient recursive relation linear equations, and respectively calculating semi-analytic coefficients of a hydraulic model semi-analytic expression and a thermal model semi-analytic expression through the two semi-analytic coefficient recursive relation linear equations according to initial conditions and boundary conditions of the pipe section; the calculated semi-analytic coefficient meets the condition that the truncation error is not greater than a truncation error threshold value; and substituting the semi-analytic coefficient into the semi-analytic expression to obtain a semi-analytic calculation result of each pipe section of each pipeline under all time steps. According to the method, non-iterative calculation of the PDAEs is realized, the calculation complexity is reduced, the simulation efficiency is improved, and the solution continuity can be ensured.

Description

Technical Field

[0001] The present invention relates to the field of heat supply network simulation, and specifically relates to a dynamic simulation method, system, terminal and medium for a district heating network. Background Art

[0002] A district heating network (DHNs) is a system designed to transfer thermal energy from one or more heat sources to multiple end-users through infrastructure such as pipelines. Modeling and simulation are core tools for the operation analysis of DHNs. These technologies provide a numerical representation of the physical system, capable of predicting the system's response under specific boundary conditions, and providing a key basis for the pre- and post-evaluation of control strategies and the real-time verification of the operating state. Due to the slow transmission speed of the heat medium, the supply-demand balance in DHNs is not achieved instantaneously. Therefore, the dynamic transmission of thermal energy needs to be described by the high-dimensional partial differential equations (PDEs) of the heating pipelines and the partial differential-algebraic equations (PDAEs) of the network. However, there are still challenges in balancing the accuracy and computational efficiency of solving complex dynamic models, which limits their scalability and real-time performance. Therefore, efficient methods for DHNs dynamic simulation have become the focus of research.

[0003] Due to the complexity of directly analyzing the PDE model, existing research usually adopts various discretization methods for processing. For example, related technologies have proposed a simulation method for an electro-thermal system based on the method of characteristics (MOC), which identifies the characteristic equations of the partial differential equations and discretizes them into ordinary differential equations (ODEs) for subsequent simulation. In addition to the discretization-based methods, some research processes the original PDE model by transforming it into other analysis domains. Such methods are called transform-domain-based methods. With appropriate approximation conditions, researchers first solve the model in other domains and then transform it back to the time domain through inverse transformation.

[0004] Discretization and transform domain-based methods have made the simulation of district heating networks more efficient. With the gradual emergence of innovative fourth-generation district heating (4GDH) systems and fifth-generation district heating and cooling (5GDHC) systems as advanced design concepts for DHNs, there is an increasing practice of integrating alternative and renewable energy sources. The resulting fluctuations in heat source temperature and mass flow highlight the importance of the mass-quantity regulation mode as a key trend for next-generation DHNs. (The regulation modes of district heating networks are generally divided into three categories: quantity regulation mode (also known as constant flow variable temperature (CF-VT) strategy), quality regulation mode (also known as variable flow constant temperature (VF-CT) strategy), and mass-quantity regulation mode (also known as variable flow variable temperature (VF-VT) strategy)). As the system flexibility and regulation effect improve, the computational complexity of the corresponding models also increases significantly. In this mode, the DHNs model is transformed into a nonlinear PDAE and exhibits intractable nonlinear characteristics. Existing simulation methods are either only applicable to linear systems (commonly found in transform domain-based methods) or suffer from a significant reduction in computational efficiency due to iterative root finding (commonly found in discretization-based methods). Summary of the Invention

[0005] To solve the above problems, the present invention provides a dynamic simulation method, system, terminal, and medium for district heating networks, which is applicable to district heating networks in the mass-quantity regulation mode, realizes non-iterative calculation of PDAEs, reduces computational complexity, improves simulation efficiency, and can ensure the continuity of the solution.

[0006] In a first aspect, the technical solution of the present invention provides a dynamic simulation method for district heating networks, which is applicable to district heating networks in the mass-quantity regulation mode and includes the following steps: Step 1, construct semi-analytical expressions of the hydraulic model and the thermal model of the pipelines in the district heating network, and construct a linear equation set of the recurrence relation of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and a linear equation set of the recurrence relation of the semi-analytical coefficients of the semi-analytical expression of the thermal model according to the momentum conservation of the pipelines and the mass conservation of the nodes; Step 2, initialize preset parameters, including dividing the pipelines into several pipe segments according to the pipeline length and the space step , set the total simulation duration and the time step , and set the truncation error threshold ; Step 3, configure the initial conditions of each pipe segment of each pipeline and the boundary conditions of each pipe segment of each pipeline at each time step, where the initial conditions include the initial mass flow rate and the initial temperature, and the boundary conditions include the boundary pressure value and the boundary temperature value; Step 4: According to the initial conditions and boundary conditions of the pipe segments, calculate the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical expressions of the thermal model respectively through two linear equations of recurrence relations of semi-analytical coefficients, and the calculated semi-analytical coefficients meet the condition that the truncation error is not greater than the truncation error threshold; substitute the semi-analytical coefficients into the semi-analytical expressions to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

[0007] In an alternative embodiment, Step 4 specifically includes: Step 4.1: Obtain the boundary conditions of each pipe segment of the current pipeline at the current time step; Step 4.2: Set the maximum order of the power series; Step 4.3: Starting from the power series being 1, according to the current power series, the initial mass flow rate and the boundary pressure value of the current pipe segment, calculate the semi-analytical coefficients of the semi-analytical expression of the hydraulic model through the linear equations of recurrence relations of semi-analytical coefficients, denoted as the first semi-analytical coefficients; and according to the current power series, the initial temperature, and the boundary temperature value, calculate the semi-analytical coefficients of the semi-analytical expression of the thermal model through the linear equations of recurrence relations of semi-analytical coefficients, denoted as the second semi-analytical coefficients; Step 4.4: Substitute any spatial position and time into the semi-analytical expression of the hydraulic model of the first semi-analytical coefficients to obtain the first truncation error, and substitute any spatial position and time into the semi-analytical expression of the thermal model of the second semi-analytical coefficients to obtain the second truncation error; Step 4.5: Determine whether both the first truncation error and the second truncation error are less than the truncation error threshold , if so, output the semi-analytical calculation results of the current pipe segment, otherwise, add 1 to the power series and return to Step 4.3, and so on, until the semi-analytical calculation results of each pipe segment of each pipeline at the current time step are output; Step 4.6: Update the time step and return to Step 4.1, and so on, until the semi-analytical calculation results of each pipe segment of each pipeline at all time steps are output.

[0008] In an alternative embodiment, the semi-analytical expression of the hydraulic model includes the semi-analytical expression of the mass flow rate and the semi-analytical expression of the pressure , which are respectively expressed as,

[0009]

[0010] wherein, represents space, represents time, ​Represents the highest order of the power series, .

[0011] In an alternative embodiment, the linear equations of the recurrence relation of the semi-analytical coefficients of the hydrodynamic model semi-analytical expression are expressed as,

[0012] wherein, is the cross-sectional area of the pipeline, is the pipeline friction coefficient, is the inner diameter of the pipeline, is the water density; is the node-pipeline incidence matrix of the inlet pipeline, is the node-pipeline incidence matrix of the outlet pipeline, represents the node index, represents the pipeline index.

[0013] In an alternative embodiment, the semi-analytical expression of the thermal model includes the semi-analytical expression of the temperature and is expressed as,

[0014] wherein, represents space, represents time, represents the highest order of the power series, .

[0015] In an alternative embodiment, the linear equations of the recurrence relation of the semi-analytical coefficients of the thermal model semi-analytical expression are expressed as,

[0016] wherein, is the water density, is the specific heat capacity of water, is the cross-sectional area of the pipeline, is the heat dissipation coefficient of the pipeline, is the ambient temperature, is the heat supply network node at the load; is the node-pipeline incidence matrix of the inlet pipeline, is the node-pipeline incidence matrix of the outlet pipeline, represents the node index, represents the pipeline index.

[0017] In an alternative embodiment, the boundary pressure values include the pressure values at the inlet and outlet at the current moment, as well as the pressure values at the inlet and outlet at the next moment after adding one time step; the boundary temperature values include the temperature values at the inlet and outlet at the current moment, as well as the temperature values at the inlet and outlet at the next moment after adding one time step.

[0018] In a second aspect, the technical solution of the present invention provides a dynamic simulation system for a district heating network, which is applicable to the district heating network in the mass-flow regulation mode, and includes: A model construction module, configured to construct semi-analytical expressions of the hydraulic model and the thermal model of the pipelines in the district heating network, and construct a linear equation system of recurrence relations of semi-analytical coefficients of the semi-analytical expression of the hydraulic model and a linear equation system of recurrence relations of semi-analytical coefficients of the semi-analytical expression of the thermal model according to the conservation of momentum of the pipelines and the conservation of mass of the nodes; A parameter initialization module, configured to initialize preset parameters, including dividing the pipelines into several pipe segments according to the pipeline length and the space step , setting the total simulation duration and the time step , and setting the truncation error threshold ; An initial condition configuration module, configured to configure the initial conditions of each pipe segment of each pipeline, as well as the boundary conditions of each pipe segment of each pipeline at each time step, where the initial conditions include the initial mass flow rate and the initial temperature, and the boundary conditions include the boundary pressure values and the boundary temperature values; A semi-analytical result simulation calculation module, configured to calculate the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the semi-analytical expression of the thermal model respectively through two linear equation systems of recurrence relations of semi-analytical coefficients according to the initial conditions and boundary conditions of the pipe segments, and the calculated semi-analytical coefficients satisfy the condition that the truncation error is not greater than the truncation error threshold ; substituting the semi-analytical coefficients into the semi-analytical expressions to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

[0019] In a third aspect, the technical solution of the present invention provides a terminal, including: A memory, configured to store a dynamic simulation program for the district heating network; A processor, configured to implement the steps of the dynamic simulation method for the district heating network as described in any one of the above when executing the dynamic simulation program for the district heating network.

[0020] Fourthly, the technical solution of the present invention provides a computer-readable storage medium, on which a dynamic simulation program for district heating networks is stored. When the dynamic simulation program for district heating networks is executed by a processor, the steps of the dynamic simulation method for district heating networks as described in any one of the above are realized.

[0021] As can be seen from the above technical solutions, the present application has the following advantages: 1) Support for advanced regulation modes: The dynamic simulation of DHNs in the quality - quantity regulation mode is realized, and other regulation modes (quality regulation and quantity regulation) are also compatible. In addition, the hydraulic dynamic characteristics of DHNs are considered in the model, and the inertial effect of the heating medium when the mass flow rate changes can be captured.

[0022] 2) Realization of efficient simulation: The non-iterative calculation of PDAEs is realized through the SAS (Semi-Analytical Solution) method, which significantly reduces the computational complexity compared with the traditional iterative root-finding process, providing an efficient solution for the real-time simulation of DHNs without sacrificing accuracy.

[0023] 3) Continuous spatio-temporal solution: Thanks to the semi-analytical characteristics, the method can provide explicit solutions at any spatio-temporal position within the target area, ensuring the continuity of the solutions. Its potential advantages include: i) Flexibility: The continuous solution allows the explicit determination of the system state (such as the pipeline temperature distribution) between discrete time steps without re-running the entire simulation process; ii) Immediacy: The current state of the system (such as the instantaneous hydraulic condition of the heat network) can be obtained in real time without waiting for the next discrete time step, which is crucial for dynamic monitoring and decision-making; iii) Synergy: It supports the natural evolution of different energy subsystems at their respective time steps, ensuring the smooth integration of the coupling process, avoiding data alignment problems caused by inconsistent time steps, and thus improving the authenticity and accuracy of multi-system interaction. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the present application, the drawings required for description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0025] Figure 1 It is a schematic flow chart of a dynamic simulation method for district heating networks provided by an embodiment of the present invention.

[0026] Figure 2 It is a schematic diagram of grid comparison for the boundary value problems of FDM and SAS, where Figure 2 in (a) is the FDM grid, Figure 2 in (b) is the SAS grid.

[0027] Figure 3 It is a schematic diagram of hydraulic boundary conditions.

[0028] Figure 4 It is a schematic diagram of thermal boundary conditions.

[0029] Figure 5 It is a schematic diagram of the SAS simulation process of an optional implementation manner.

[0030] Figure 6 It is a schematic block diagram of the structure of a district heating network dynamic simulation system provided by an embodiment of the present invention.

[0031] Figure 7 It is a schematic diagram of the structure of a terminal provided by an embodiment of the present invention. Specific implementation manners

[0032] To make the application purpose, features, and advantages of the present application more obvious and understandable, the technical solutions protected by the present application will be clearly and completely described below by using specific embodiments and the accompanying drawings. Obviously, the embodiments described below are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0033] Unless otherwise defined, all technical and scientific terms used in the present application have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the specification of the present invention in the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present invention.

[0034] Figure 1 It is a schematic diagram of the process of a district heating network dynamic simulation method provided by an embodiment of the present invention. Among them, Figure 1 The execution subject can be a district heating network dynamic simulation system. The district heating network dynamic simulation method provided by the embodiment of the present invention is executed by a computer device. Correspondingly, the district heating network dynamic simulation system runs in the computer device. According to different requirements, the order of the steps in this flowchart can be changed, and some can be omitted.

[0035] Such as Figure 1 shown, the method includes the following steps.

[0036] S1. Construct semi-analytical expressions of the hydraulic model and the thermal model of the pipelines in the district heating network, and construct a linear equation system of the recurrence relationship of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and a linear equation system of the recurrence relationship of the semi-analytical coefficients of the semi-analytical expression of the thermal model according to the momentum conservation of the pipelines and the mass conservation of the nodes.

[0037] The purpose of this step is to construct semi - analytical expressions for the hydraulic model and the thermal model, as well as a system of linear equations for the recurrence relationship of semi - analytical coefficients of the two semi - analytical expressions. The system of linear equations for the recurrence relationship of semi - analytical coefficients is used to derive the semi - analytical coefficients of the semi - analytical expressions. After obtaining the semi - analytical coefficients, the semi - analytical results of the pipeline are simulated and calculated through the semi - analytical expressions. Among them, based on the dynamic model of the district heating network under the mass - quantity regulation mode, semi - analytical expressions for the hydraulic model and the thermal model are constructed.

[0038] S2, Initialize preset parameters, including dividing the pipeline into several pipe segments according to the pipeline length and the spatial step size setting the total simulation duration and the time step size , and setting the truncation error threshold .

[0039] The purpose of this step is to initialize the preset parameters, including dividing the pipeline into multiple pipe segments, setting the total simulation duration and the time step size, and setting the truncation error threshold. Subsequently, simulation calculations are performed for each pipe segment at each time step. The highest order of the power series affects the truncation error. Select an appropriate highest order of the power series to control the truncation error not exceeding the truncation error threshold.

[0040] S3, Configure the initial conditions for each pipe segment of each pipeline, and the boundary conditions for each pipe segment of each pipeline at each time step. The initial conditions include the initial mass flow rate and the initial temperature, and the boundary conditions include the boundary pressure value and the boundary temperature value.

[0041] The solution of the system of linear equations for the recurrence relationship of semi - analytical coefficients requires initial conditions and boundary conditions. The initial conditions include the initial mass flow rate and the initial temperature, and the boundary conditions include the boundary pressure value and the boundary temperature value. Among them, the boundary pressure value includes the pressure values at the inlet and outlet at the current moment, and the pressure values at the inlet and outlet at the next moment after adding one time step; the boundary temperature value includes the temperature values at the inlet and outlet at the current moment, and the temperature values at the inlet and outlet at the next moment after adding one time step.

[0042] S4, According to the initial conditions and boundary conditions of the pipe segment, calculate the semi - analytical coefficients of the semi - analytical expressions for the hydraulic model and the thermal model respectively through the two systems of linear equations for the recurrence relationship of semi - analytical coefficients. The calculated semi - analytical coefficients meet the condition that the truncation error is not greater than the truncation error threshold ; Substitute the semi - analytical coefficients into the semi - analytical expressions to obtain the semi - analytical calculation results for each pipe segment of each pipeline at all time steps.

[0043] This step is used to output the semi - analytical simulation calculation results. First, based on the initial conditions and boundary conditions, the semi - analytical coefficients are calculated by solving a system of linear equations of the semi - analytical coefficient recurrence relation. Then, the semi - analytical coefficients are substituted into the semi - analytical expression to obtain the semi - analytical calculation results. It should be noted that by changing the highest order of the power series, the semi - analytical coefficients satisfy the condition that the truncation error is not greater than the truncation error threshold. Finally, the semi - analytical calculation results of each pipe segment of each pipeline at all time steps are obtained. The specific steps are as follows.

[0044] S4.1, Obtain the boundary conditions of each pipe segment of the current pipeline at the current time step.

[0045] S4.2, Set the maximum order of the power series.

[0046] S4.3, Starting from the power series of 1, according to the current power series, the initial mass flow rate and the boundary pressure value of the current pipe segment, calculate the semi - analytical coefficients of the semi - analytical expression of the hydraulic model by solving a system of linear equations of the semi - analytical coefficient recurrence relation, denoted as the first semi - analytical coefficients; and according to the current power series, the initial temperature and the boundary temperature value, calculate the semi - analytical coefficients of the semi - analytical expression of the thermal model by solving a system of linear equations of the semi - analytical coefficient recurrence relation, denoted as the second semi - analytical coefficients.

[0047] S4.4, Substitute any spatial position and time into the semi - analytical expression of the hydraulic model with the first semi - analytical coefficients to obtain the first truncation error, and substitute any spatial position and time into the semi - analytical expression of the thermal model with the second semi - analytical coefficients to obtain the second truncation error.

[0048] S4.5, Determine whether both the first truncation error and the second truncation error are less than the truncation error threshold , if so, output the semi - analytical calculation results of the current pipe segment; otherwise, add 1 to the power series and return to S4.3, and so on, until the semi - analytical calculation results of each pipe segment of each pipeline at the current time step are output.

[0049] S4.6, Update the time step and return to S4.1, and so on, until the semi - analytical calculation results of each pipe segment of each pipeline at all time steps are output.

[0050] Furthermore, as a refinement and extension of the specific implementation of the above - mentioned embodiment, the following fully describes the specific implementation process in this embodiment.

[0051] First, introduce the dynamic model of the district heating network in the mass - quantity regulation mode. The pipe model describes the hydraulic and thermal dynamic characteristics with a spatio - temporal partial differential equation, combined with the algebraic equations of mass conservation and momentum conservation at the nodes, jointly constituting the differential - algebraic equation system of DHNs.

[0052] Since the core objective of DHNs simulation is to describe the overall state at the system level (such as the temperature / pressure distribution across the network), rather than to characterize the microscopic properties at the fluid micro-element scale, the pipe model usually only considers the one-dimensional spatial dimension. The one-dimensional flow characteristics of the water in the pipe are described by the pipe mass conservation equation (Equation (1)) and the pipe momentum conservation equation (Equation (2)), while the thermodynamic process is characterized by the pipe energy conservation equation (Equation (3)).

[0053] (1) (2) (3) In the equations, and represent time and space respectively; , , represent the density, flow velocity and pressure of water respectively; the specific heat capacity of water is given by ; the pipe parameters in DHNs include the friction coefficient , the inner diameter , the inclination angle and the heat dissipation coefficient ; in addition, represents the temperature of water, represents the ambient temperature, is the acceleration due to gravity.

[0054] In a district heating network, water is usually regarded as an incompressible fluid, that is, its density can be regarded as a constant. The relationship between the pipe mass flow rate and the flow velocity is , where is the cross-sectional area of the pipe. The influence of the horizontal inclination angle of the pipe is not considered in this application. Based on the above assumptions, Equations (1), (2) and (3) can be simplified as: (4) (5) (6) In addition to the above partial differential equations describing the pipe dynamics, the mass flow rate at each connection node in the heating network needs to satisfy the node mass conservation equation, and its mathematical expression is: (7) In the equations, represents the node index, is the set of node indices of the heating network; represents the pipe index, is the set of pipe indices of the heating network; in addition, and is the node - pipe incidence matrix of the inlet pipe and the outlet pipe.

[0055] The energy flow carried by the hot water flowing into or out of each connected node needs to satisfy the node energy conservation equation, and its mathematical expression is Equation (8): (8) In the formula, is the load at the node of the heating network.

[0056] When the pipe is divided into N segments, Equations (7) and (8) can also represent the mass / energy conservation relationships between all segments. Therefore, based on Equations (7) and (8), the model derivation from a single pipe segment to the entire pipeline and then to the complete DHNs can be realized.

[0057] In summary, the hydraulic and thermal dynamic coupling model of the district heating network is jointly defined by Equations (4) to (8).

[0058] The following explains the semi - analytical expression. Different from the traditional discretization method (such as the finite - difference method, which discretizes the partial differential equation into a system of algebraic equations and solves it), the semi - analytical solution aims to represent the spatio - temporal state variables through an approximate analytical expression, and its expression form is as follows: (9) In the formula, is the coefficient of the term in the two - dimensional power series, represents the highest order of the power series ( ). The core goal of the semi - analytical method is to solve these power - series coefficients. Subsequently, by substituting any spatial position and time into the above approximate expression, an approximate state with a truncation error of can be obtained.

[0059] In online simulation, since the boundary conditions are usually obtained through discrete measurement points, SAS is similar to FDM (finite - difference method) in that both need to characterize the boundary - value problem (BVP) of the partial differential equation through a discrete grid. However, there are essential differences between the grids used by FDM and SAS. As Figure 2 shown, where Figure 2 in (a) is the FDM grid, and Figure 2 in (b) is the SAS grid.

[0060] In Figure 2In (a) therein, FDM requires that the constraint conditions of the PDE be satisfied only at specific positions (such as the corner points in the figure) within the grid, and the numerical solution is generated only at these discrete points. In contrast, Figure 2 In (b) therein shows that the SAS method requires that the constraint conditions of the PDE be satisfied throughout the entire grid domain (such as the highlighted area in the figure), so that the explicit solution can be generated at any spatio-temporal position within the grid. In addition, the strictness of the constraint conditions of the SAS method makes it theoretically have higher accuracy.

[0061] The following constructs the SAS expression of the hydraulic model based on the above semi-analytical expressions.

[0062] From the perspective of SAS, the pressure can be expressed as a two-dimensional power series of time and space . Due to the incompressibility of water, the mass flow rate is only a function of time and does not depend on space . And The semi-analytical expressions are as follows: (10) (11) In the formula, and are the coefficients of the and terms in the two-dimensional power series respectively. In this case, the partial derivatives of and are: (12) (13) (14) By substituting the above partial derivatives into the partial differential equation, the pipe momentum conservation equation (Equation 5) and the node mass conservation equation (Equation 7) can be reconstructed into the following form: (15) (16) When expanding both sides of the above equation into a power series, to ensure that the equation holds for any and , it is necessary to ensure that the coefficients of the same-order terms on both sides are exactly equal. By comparing the , , , …, By obtaining the coefficients of each term, a system of linear equations characterizing the recurrence relation can be obtained, namely, the system of linear equations for the recurrence relation of the semi-analytical coefficients in the semi-analytical expression of the hydraulic model (Equation 17).

[0063] (17) For the hydraulic BVP of the heating pipeline, each pipeline in the district heating network is divided into N segments, with a time step of , and a space step of , as shown in Figure 3 .

[0064] Taking the pipeline segment as an example, the solution of the system of linear equations (17) still requires the supplementation of initial conditions and boundary conditions. The required boundary conditions are as follows: (18) (19) (20) (21) As shown in Figure 3 , given the initial mass flow rate of the pipeline segment and its boundary pressure values ( , , , ), by solving the system of linear equations, the power series components of the mass flow rate of the pipeline segment , ,…, can be obtained. From this, the semi-analytical expression of Equation (10) can be derived, so as to calculate and visualize the spatio-temporal hydrodynamic characteristics of each pipeline segment in the district heating network.

[0065] The following constructs the SAS expression of the thermal model based on the above semi-analytical expression.

[0066] Based on SAS, the temperature can be expressed as a two-dimensional power series with respect to time and space : (22) In the formula, is the coefficient of the term of the two-dimensional power series. At this time, the partial derivative of is: (23) (24) As shown in Figure 4As shown, in the thermal BVP of the heating pipeline, each pipeline in the district heating network is discretized into N segments, and the time and space steps are and .

[0067] Taking the pipeline segment as an example, to solve the thermal BVP of this pipeline segment, the initial conditions and boundary conditions need to be given simultaneously. The necessary boundary conditions are as follows: (25) (26) (27) (28) Substituting equations (23)-(28) into the pipeline energy conservation equation (Equation 6) and the node energy conservation equation (Equation 8), the following reconstructed form is obtained: (29) (30) Expanding both sides of the above equations into series forms, the equation can hold for all and only when the coefficients of the same order terms are consistent. By comparing the coefficients of , , ,…, terms, a linear equation system composed of equations (31) and (32) can be deduced.

[0068] (31) (32) Correspondingly, when deduced to all pipeline segments, the linear equation system representing the recurrence relationship of the semi-analytical coefficients of the semi-analytical expression of the thermal model is expressed as

[0069] As Figure 4 shown, given the initial temperature of the pipeline segment and its boundary temperature values ( , , , ), by solving the linear equation system, the power series components , ,…, of the temperature distribution of this pipeline segment can be determined. From this, the semi-analytical expression of Equation (22) can be deduced, so as to calculate and visualize the spatio-temporal thermodynamics evolution process of the temperature of each pipeline segment in the district heating network.

[0070] In some alternative embodiments, based on the construction of the SAS for the hydraulic and thermal models of the district heating network, the entire SAS simulation process is as follows Figure 5 shown in the flowchart. This simulation process is divided into preset value initialization and four decision-making loop phases.

[0071] 1) Truncation error loop: Due to the inherent truncation error in the spatio-temporal power series expansion in the SAS method, this loop gradually increases the highest order of the series until the truncation error is lower than the preset threshold. It should be noted that in the simulation of this application, the highest order of the power series is set to 3, and the preset truncation error threshold is . In actual cases, it is extremely rare that the third-order power series cannot meet the accuracy requirements, and the time consumed by this loop is almost negligible compared to the total simulation time. Therefore, this loop is only used as a safety guarantee mechanism for the SAS accuracy and will not cause a significant increase in the computational cost due to excessive iteration.

[0072] 2) Spatial stepping loop: This loop generates SAS expressions for each spatial step of the pipeline until the total length of the pipeline is covered.

[0073] 3) Pipeline iteration loop: After the SAS simulation for all spatial steps of the current pipeline is completed, this loop traverses each pipeline in the pipe network until the simulation for all pipelines at the current time step is completed.

[0074] 4) Temporal stepping loop: This loop generates SAS expressions for each time step until the total simulation duration is reached.

[0075] The embodiments of a dynamic simulation method for a district heating network are described in detail above. Based on the dynamic simulation method for a district heating network described in the above embodiments, an embodiment of the present invention also provides a district heating network dynamic simulation system corresponding to this method.

[0076] Figure 6 FIG. is a schematic block diagram of the structure of a district heating network dynamic simulation system provided by an embodiment of the present invention. In this embodiment, the district heating network dynamic simulation system 600 can be divided into multiple functional modules according to the functions it performs. The system 600 is applicable to the district heating network in the mass-flow regulation mode. The module referred to in the present invention means a series of computer program segments that can be executed by at least one processor and can complete fixed functions, and are stored in the memory.

[0077] The model construction module 610 is used to construct the semi-analytical expressions of the hydraulic model and the thermal model for the pipelines in the district heating network, and construct the linear equations of the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the linear equations of the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the thermal model according to the momentum conservation of the pipelines and the mass conservation of the nodes.

[0078] The parameter initialization module 620 is used to initialize the preset parameters, including dividing the pipelines into several pipe segments according to the pipeline length and the space step , setting the total simulation duration and the time step , and setting the truncation error threshold .

[0079] The initial condition configuration module 630 is used to configure the initial conditions of each pipe segment of each pipeline and the boundary conditions of each pipe segment of each pipeline at each time step. The initial conditions include the initial mass flow rate and the initial temperature, and the boundary conditions include the boundary pressure value and the boundary temperature value.

[0080] The semi-analytical result simulation calculation module 640 is used to calculate the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the semi-analytical expression of the thermal model respectively through two linear equations of the recurrence relations of the semi-analytical coefficients according to the initial conditions and the boundary conditions of the pipe segments. The calculated semi-analytical coefficients meet the condition that the truncation error is not greater than the truncation error threshold ; Substitute the semi-analytical coefficients into the semi-analytical expressions to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

[0081] The district heating network dynamic simulation system of this embodiment is used to implement the aforementioned district heating network dynamic simulation method. Therefore, the specific implementation manners in this system can be seen in the embodiment part of the district heating network dynamic simulation method in the previous text. Therefore, its specific implementation manners can refer to the descriptions of the corresponding individual part embodiments and will not be elaborated here.

[0082] In addition, since the district heating network dynamic simulation system of this embodiment is used to implement the aforementioned district heating network dynamic simulation method, its functions correspond to those of the above method and will not be repeated here.

[0083] Figure 7 FIG. 700 is a schematic structural diagram of a terminal 700 provided by an embodiment of the present invention, including: a processor 710, a memory 720, and a communication unit 730. The processor 710 is used to implement the process steps of the district heating network dynamic simulation method in the above embodiment when implementing the district heating network dynamic simulation program stored in the memory 720.

[0084] The terminal 700 includes a processor 710, a memory 720, and a communication unit 730. These components communicate via one or more buses. Those skilled in the art can understand that the structure of the server shown in the figure does not limit the present invention. It can be a bus structure, a star structure, and can also include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0085] Among them, the memory 720 can be used to store the execution instructions of the processor 710. The memory 720 can be implemented by any type of volatile or non-volatile storage terminal or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk, or optical disk. When the execution instructions in the memory 720 are executed by the processor 710, the terminal 700 can execute some or all of the steps in the above method embodiments.

[0086] The processor 710 is the control center of the storage terminal, connecting various parts of the entire electronic terminal through various interfaces and lines. By running or executing the software programs and / or modules stored in the memory 720, and by calling the data stored in the memory, it executes various functions of the electronic terminal and / or processes data. The processor can be composed of an integrated circuit (IC). For example, it can be composed of a single packaged IC, or can be composed of multiple packaged ICs with the same or different functions connected. For example, the processor 710 can only include a central processing unit (CPU). In the embodiment of the present invention, the CPU can be a single operation core or can include multiple operation cores.

[0087] The communication unit 730 is used to establish a communication channel so that the storage terminal can communicate with other terminals. It receives user data sent by other terminals or sends user data to other terminals.

[0088] The present invention also provides a computer storage medium. The storage medium here can be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), etc.

[0089] The present invention also provides a computer storage medium, which may be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), or the like.

[0090] The computer storage medium stores a dynamic simulation program for a district heating network. When the dynamic simulation program for the district heating network is executed by a processor, the method flow steps of the dynamic simulation method for the district heating network in the above embodiments are implemented.

[0091] Those skilled in the art can clearly understand that the technologies in the embodiments of the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solutions in the embodiments of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product is stored in a storage medium such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., which can store program codes, and includes several instructions for causing a computer terminal (which may be a personal computer, a server, or a second terminal, a network terminal, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0092] In several embodiments provided by the present invention, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some interfaces. The indirect coupling or communication connection of the devices or units can be in an electrical, mechanical, or other form.

[0093] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0094] In addition, in each embodiment of the present invention, the functional units can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit.

[0095] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A dynamic simulation method for a district heating network, characterized in that This method is applicable to district heating networks in the mass-flow regulation mode and includes the following steps: Step 1: Construct semi-analytical expressions for the hydraulic model and the thermal model of the pipes in the district heating network, and construct linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the thermal model according to the pipe momentum conservation and node mass conservation; Step 2, initialize the preset parameters, including according to the pipeline length and the spatial step size divide the pipeline into several pipe segments, set the total simulation duration and the time step size , set the truncation error threshold ; Step 3: Configure the initial conditions for each pipe segment of each pipe, and the boundary conditions for each pipe segment of each pipe at each time step. The initial conditions include the initial mass flow rate and the initial temperature, and the boundary conditions include the boundary pressure value and the boundary temperature value; Step 4: According to the initial conditions and boundary conditions of the pipe segments, calculate the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical expressions of the thermal model respectively through two linear equations of recurrence relations of semi-analytical coefficients, and the calculated semi-analytical coefficients meet the condition that the truncation error is not greater than the truncation error threshold; substitute the semi-analytical coefficients into the semi-analytical expressions to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps. ​ 2. The dynamic simulation method of the district heating network according to claim 1, wherein Step 4 specifically includes: Step 4.1: Obtain the boundary conditions for each pipe segment of the current pipe at the current time step; Step 4.2: Set the maximum order of the power series; Step 4.3: Starting from the power series of 1, calculate the semi-analytical coefficients of the semi-analytical expression of the hydraulic model through the linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model according to the current power series, the initial mass flow rate of the current pipe segment, and the boundary pressure value, denoted as the first semi-analytical coefficients; and calculate the semi-analytical coefficients of the semi-analytical expression of the thermal model through the linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the thermal model according to the current power series, the initial temperature, and the boundary temperature value, denoted as the second semi-analytical coefficients; Step 4.4: Substitute any spatial position and time into the semi-analytical expression of the hydraulic model with the first semi-analytical coefficients to obtain the first truncation error, and substitute any spatial position and time into the semi-analytical expression of the thermal model with the second semi-analytical coefficients to obtain the second truncation error; Step 4.5, determine whether both the first truncation error and the second truncation error are less than the truncation error threshold , if so, output the semi-analytical calculation result of the current pipe segment; otherwise, increment the power series by 1 and return to Step 4.3, and so on, until the semi-analytical calculation results of each pipe segment of each pipeline at the current time step are output; Step 4.6: Update the time step and return to Step 4.1, and so on, until the semi-analytical calculation results for each pipe segment of each pipe at all time steps are output.

3. The dynamic simulation method for district heating network according to claim 1 or 2, characterized in that, The semi-analytical expressions of the hydraulic model include the semi-analytical expression of the mass flow rate and the semi-analytical expression of the pressure which are respectively expressed as In the formula, represents space, represents time, represents the highest order of the power series, .

4. The dynamic simulation method of a district heating network according to claim 3, characterized in that The linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model are expressed as Wherein, is the cross-sectional area of the pipeline, is the pipeline friction coefficient, is the inner diameter of the pipeline, is the water density; is the node-pipeline incidence matrix of the inlet pipeline, is the node-pipeline incidence matrix of the outlet pipeline, represents the node index, represents the pipeline index.

5. The dynamic simulation method for district heating network according to claim 1 or 2, characterized in that The semi-analytical expression of the thermal model includes the semi-analytical expression of temperature which is expressed as wherein, represents space, represents time, represents the highest order of the power series, .

6. The dynamic simulation method for a district heating network according to claim 5, characterized in that The linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the thermal model are expressed as Wherein, is the water density, is the specific heat capacity of water, is the cross-sectional area of the pipeline, is the heat dissipation coefficient of the pipeline, is the ambient temperature, is the heat supply network node at the load; is the node-pipeline incidence matrix for the inlet pipeline, is the node-pipeline incidence matrix for the outlet pipeline, represents the node index, represents the pipeline index.

7. The dynamic simulation method for a district heating network according to claim 1, characterized in that The boundary pressure value includes the pressure values at the inlet and outlet at the current moment, and the pressure values at the inlet and outlet at the next moment after adding one time step; the boundary temperature value includes the temperature values at the inlet and outlet at the current moment, and the temperature values at the inlet and outlet at the next moment after adding one time step.

8. A dynamic simulation system for a district heating network, characterized in that, Applicable to district heating networks in the mass-flow regulation mode, including: A model construction module for constructing semi-analytical expressions for the hydraulic model and the thermal model of the pipes in the district heating network, and constructing linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the linear equations for the recurrence relations of the semi-analytical coefficients of the semi-analytical expression of the thermal model according to the pipe momentum conservation and node mass conservation; A parameter initialization module for initializing preset parameters, including dividing a pipeline into several pipe segments according to the pipeline length and the spatial step size setting the total simulation duration and the time step size , and setting the truncation error threshold ; An initial condition configuration module for configuring the initial conditions for each pipe segment of each pipe, and the boundary conditions for each pipe segment of each pipe at each time step. The initial conditions include the initial mass flow rate and the initial temperature, and the boundary conditions include the boundary pressure value and the boundary temperature value; The semi-analytical result simulation calculation module is used to calculate the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical expressions of the thermal model respectively through two linear equations of the recurrence relations of the semi-analytical coefficients according to the initial conditions and boundary conditions of the pipe segments. The calculated semi-analytical coefficients meet the condition that the truncation error is not greater than the truncation error threshold. Substitute the semi-analytical coefficients into the semi-analytical expressions to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

9. A terminal, characterized in that, Including: A memory for storing the district heating network dynamic simulation program; A processor for implementing the steps of the dynamic simulation method of the district heating network according to any one of claims 1 to 7 when executing the dynamic simulation program of the district heating network.

10. A computer-readable storage medium, characterized in that, A dynamic simulation program of the district heating network is stored on the readable storage medium, and when the dynamic simulation program of the district heating network is executed by a processor, the steps of the dynamic simulation method of the district heating network according to any one of claims 1 to 7 are implemented.

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