A method, system, terminal and medium for dynamic simulation of regional heating network

Abstract

The present invention relates to the field of heating network simulation and specifically discloses a method, system, terminal, and medium for dynamic simulation of a district heating network. The method comprises constructing semi-analytical expressions for a hydraulic model and a semi-analytical expression for a thermal model of a pipeline in the district heating network, and constructing a set of linear equations with recursive relationships of semi-analytical coefficients based on the conservation of pipeline momentum and node mass. The semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical expression of the thermal model are calculated using the two sets of linear equations with recursive relationships based on the initial and boundary conditions of the pipeline segments, wherein the calculated semi-analytical coefficients satisfy a condition that a truncation error is no greater than a truncation error threshold. The semi-analytical coefficients are substituted into the semi-analytical expressions to obtain semi-analytical calculation results for each pipeline segment at all time steps. The present invention implements non-iterative calculation of PDAEs, reduces computational complexity, improves simulation efficiency, and ensures the continuity of the solution.

Description

Technical Field

[0001] The present invention relates to the field of heating network simulation, and in particular to a method, system, terminal and medium for dynamic simulation of a regional heating network. Background Art

[0002] District heating networks (DHNs) are systems designed to transport heat from one or more heat sources to multiple end users through infrastructure such as pipelines. Modeling and simulation are core tools for analyzing DHN operations. These techniques provide a numerical representation of the physical system, enabling prediction of the system's response under specific boundary conditions. This provides a critical basis for pre- and post-evaluation of control strategies and real-time verification of operational status. Due to the slow transport of heat media, the balance between supply and demand in DHNs is not achieved instantaneously. Therefore, the dynamic transport of heat energy must be described using high-dimensional partial differential equations (PDEs) for the heating pipelines and partial differential algebraic equations (PDAEs) for the network. However, solving complex dynamic models remains challenging, balancing accuracy and computational efficiency, limiting their scalability and real-time performance. Consequently, efficient methods for dynamic simulation of DHNs have become a research focus.

[0003] Due to the complexity of directly analyzing PDE models, existing research typically employs various discretization methods. For example, a related technique proposes an electrothermal system simulation method based on the method of characteristic lines (MOC), which identifies the characteristic equation of a partial differential equation and discretizes it into ordinary differential equations (ODEs) for subsequent simulation. In addition to discretization-based methods, some research transforms the original PDE model into other analysis domains for processing. These methods are referred to as transform-domain-based methods. Using appropriate approximations, researchers first solve the model in the other domain and then convert it back to the time domain using an inverse transform.

[0004] Discretization and transform-domain methods have made the simulation of district heating networks more efficient. With innovative fourth-generation district heating (4GDH) and fifth-generation district cooling and heating (5GDHC) systems becoming advanced design concepts for DHNs, the integration of alternative and renewable energy sources is increasing. The resulting fluctuations in heat source temperature and mass flow rate highlight the importance of mass-quantity regulation as a key trend in next-generation DHNs. (Regulation modes for district heating networks are generally categorized into three types: quantity regulation (also known as constant flow-variable temperature (CF-VT) strategy), quality regulation (also known as variable flow-constant temperature (VF-CT) strategy), and mass-quantity regulation (also known as variable flow-variable temperature (VF-VT) strategy). With the increase in system flexibility and regulation effectiveness, the computational complexity of the corresponding models also increases significantly. In this mode, DHN models transform into nonlinear PDAEs and exhibit intractable nonlinear characteristics. Existing simulation methods are either only applicable to linear systems (commonly seen in transform-domain methods) or require iterative root-finding, significantly reducing computational efficiency (commonly seen 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 a district heating network, which is suitable for a district heating network under a quality-quantity regulation mode, realizes non-iterative calculation of PDAEs, reduces computational complexity, improves simulation efficiency, and ensures the continuity of the solution.

[0006] In a first aspect, the technical solution of the present invention provides a method for dynamic simulation of a district heating network, which is applicable to a district heating network in a quality-quantity regulation mode, comprising the following steps:

[0007] Step 1: Construct a semi-analytical expression of the hydraulic model and the semi-analytical expression of the thermal model of the pipeline in the district heating network, and construct a linear equation system of the recursive relationship of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the semi-analytical expression of the thermal model based on the conservation of pipeline momentum and the conservation of node mass;

[0008] Step 2: Initialize the preset parameters, including the length of the pipeline and spatial step size Divide the pipeline into several segments and set the total simulation time and time step , set the truncation error threshold ;

[0009] Step 3: configuring the initial conditions of each pipe section of each pipeline and the boundary conditions of each pipe section of each pipeline at each time step, wherein 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;

[0010] Step 4: According to the initial conditions and boundary conditions of the pipe section, the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical expression of the thermal model are calculated respectively through two semi-analytical coefficient recursive linear equations. The calculated semi-analytical coefficients satisfy the truncation error not greater than the truncation error threshold. Substitute the semi-analytical coefficients into the semi-analytical expression to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

[0011] In an optional embodiment, step 4 specifically includes:

[0012] Step 4.1, obtain the boundary conditions of each pipe section of the current pipeline at the current time step;

[0013] Step 4.2, set the maximum order of the power series;

[0014] Step 4.3, starting from a power series of 1, calculate the semi-analytical coefficients of the hydraulic model semi-analytical expression using the recursive linear equations of the semi-analytical coefficients of the hydraulic model semi-analytical expression based on the current power series, the initial mass flow rate of the current pipe section, and the boundary pressure value. This is recorded as the first semi-analytical coefficient. Also, calculate the semi-analytical coefficients of the thermal model semi-analytical expression using the recursive linear equations of the semi-analytical coefficients of the thermal model semi-analytical expression based on the current power series, the initial temperature, the boundary temperature value, and the semi-analytical coefficients of the thermal model semi-analytical expression. This is recorded as the second semi-analytical coefficient.

[0015] Step 4.4, substitute any spatial position and time into the semi-analytical expression of the hydraulic model with the first semi-analytical coefficient 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 coefficient to obtain the second truncation error;

[0016] Step 4.5: Determine whether the first truncation error and the second truncation error are both less than the truncation error threshold If yes, output the semi-analytical calculation result of the current pipe segment. Otherwise, add 1 to the power series and return to step 4.3. Repeat this process until the semi-analytical calculation result of each pipe segment of each pipeline at the current time step is output.

[0017] In 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.

[0018] In an optional embodiment, the semi-analytical expression of the hydraulic model includes the mass flow rate Semi-analytical expressions and pressure The semi-analytical expressions of are expressed as,

[0019]

[0020]

[0021] Where, Represents space, Indicates time, represents the highest order of the power series, .

[0022] In an optional embodiment, the semi-analytical coefficient recursive relationship linear equation system of the semi-analytical expression of the hydraulic model is expressed as:

[0023]

[0024] Where, is the cross-sectional area of ​​the pipe, is the pipeline friction coefficient, is the inner diameter of the pipe, is the water density;

[0025] is the node-pipe association matrix of the inlet pipe, is the node-pipeline association matrix of the outlet pipeline, represents the node index, Indicates the pipeline index.

[0026] In an optional embodiment, the semi-analytical expression of the thermal model includes the temperature The semi-analytical expression of is expressed as,

[0027]

[0028] Where, Represents space, Indicates time, represents the highest order of the power series, .

[0029] In an optional embodiment, the semi-analytical coefficient recursive relationship linear equation system of the semi-analytical expression of the thermal model is expressed as:

[0030]

[0031] Where, is the water density, is the specific heat capacity of water, is the cross-sectional area of ​​the pipe, is the pipe heat dissipation coefficient, is the ambient temperature, Heating network node The load at

[0032] is the node-pipe association matrix of the inlet pipe, is the node-pipeline association matrix of the outlet pipeline, represents the node index, Indicates the pipeline index.

[0033] In an optional embodiment, 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 one time step is added; 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 one time step is added.

[0034] In a second aspect, the technical solution of the present invention provides a district heating network dynamic simulation system applicable to a district heating network in a quality-quantity regulation mode, comprising:

[0035] A model building module is used to construct semi-analytical expressions of the hydraulic model and the thermal model of the pipelines in the district heating network, and to construct a linear equation system of recursive relations of the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical coefficients of the semi-analytical expressions of the thermal model based on the conservation of pipeline momentum and the conservation of node mass;

[0036] Parameter initialization module, used to initialize preset parameters, including according to the pipeline length and spatial step size Divide the pipeline into several segments and set the total simulation time and time step , set the truncation error threshold ;

[0037] An initial condition configuration module is used to configure the initial conditions of each pipe section of each pipeline and the boundary conditions of each pipe section of each pipeline at each time step, wherein 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;

[0038] The semi-analytical result simulation calculation module is used to calculate the semi-analytical coefficients of the hydraulic model semi-analytical expression and the thermal model semi-analytical expression respectively through two semi-analytical coefficient recursive linear equations according to the initial conditions and boundary conditions of the pipe section. The calculated semi-analytical coefficients meet the truncation error not greater than the truncation error threshold. Substitute the semi-analytical coefficients into the semi-analytical expression to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

[0039] In a third aspect, the technical solution of the present invention provides a terminal, including:

[0040] A memory for storing a district heating network dynamic simulation program;

[0041] A processor is used to implement the steps of the district heating network dynamic simulation method as described in any one of the above items when executing the district heating network dynamic simulation program.

[0042] In a fourth aspect, the technical solution of the present invention provides a computer-readable storage medium, on which a regional heating network dynamic simulation program is stored. When the regional heating network dynamic simulation program is executed by a processor, the steps of the regional heating network dynamic simulation method as described in any one of the above items are implemented.

[0043] It can be seen from the above technical solutions that this application has the following advantages:

[0044] 1) Support for Advanced Control Modes: Dynamic simulation of DHNs in mass-quantity control mode is enabled, while also being compatible with other control modes (mass and quantity). Furthermore, the model considers the hydraulic dynamics of DHNs, capturing the inertial effects of the heating medium as mass flow rates change.

[0045] 2) Achieving Efficient Simulation: The SAS (Semi-Analytical Solution) method enables non-iterative calculation of PDAEs. Compared with the traditional iterative root-finding process, this method significantly reduces the computational complexity and provides an efficient solution for real-time simulation of DHNs without sacrificing accuracy.

[0046] 3) Continuous Spatiotemporal Solution: Thanks to its semi-analytical nature, this method can provide explicit solutions at any spatiotemporal location within the target region, ensuring solution continuity. Its potential advantages include: i) Flexibility: Continuous solutions allow explicit determination of system states (e.g., pipe temperature distribution) between discrete time steps without rerunning the entire simulation; ii) Immediacy: The current state of the system (e.g., the instantaneous hydraulic conditions of the heating 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: This method allows different energy subsystems to evolve naturally within their own time steps, ensuring smooth integration of coupled processes and avoiding data alignment issues caused by inconsistent time steps, thereby improving the realism and accuracy of multi-system interactions. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for the description. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0048] Figure 1 A schematic flow chart of a method for dynamic simulation of a district heating network provided in an embodiment of the present invention.

[0049] Figure 2 Schematic diagram of mesh comparison between FDM and SAS boundary value problems, where Figure 2 (a) is the FDM grid, Figure 2 (b) in the figure is the SAS grid.

[0050] Figure 3 Schematic diagram of hydraulic boundary conditions.

[0051] Figure 4 Schematic diagram of thermal boundary conditions.

[0052] Figure 5 A schematic diagram of a SAS simulation process of an optional implementation method.

[0053] Figure 6 A schematic block diagram of the structure of a district heating network dynamic simulation system provided by an embodiment of the present invention.

[0054] Figure 7 A schematic diagram of the structure of a terminal provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to make the application objectives, features, and advantages of this application more obvious and easy to understand, the technical solutions protected by this application will be clearly and completely described below using specific embodiments and drawings. Obviously, the embodiments described below are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0056] Unless otherwise defined, all technical and scientific terms used in this application have the same meaning as those commonly understood by those skilled in the art to which the present invention pertains. The terms used in this application and in the specification of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention.

[0057] Figure 1 A flow chart of a method for dynamic simulation of a district heating network provided by an embodiment of the present invention. Figure 1The execution entity may be a district heating network dynamic simulation system. The district heating network dynamic simulation method provided in embodiments of the present invention is executed by a computer device. Accordingly, the district heating network dynamic simulation system runs on the computer device. The order of the steps in this flowchart may be changed, and some steps may be omitted, depending on different needs.

[0058] like Figure 1 As shown, the method includes the following steps.

[0059] S1. Construct the semi-analytical expressions of the hydraulic model and the thermal model of the pipeline in the district heating network, and construct the linear equation group of the recursive relationship of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the semi-analytical expression of the thermal model based on the conservation of pipeline momentum and node mass.

[0060] The purpose of this step is to construct semi-analytical expressions for the hydraulic and thermal models, as well as a linear system of equations that recursively relate the semi-analytical coefficients of these two semi-analytical expressions. This system of linear equations is used to derive the semi-analytical coefficients of the semi-analytical expressions. Once the semi-analytical coefficients are known, the semi-analytical results of the pipelines can be simulated and calculated using the semi-analytical expressions. The semi-analytical expressions for the hydraulic and thermal models are constructed based on a dynamic model of the district heating network under the mass-quantity regulation mode.

[0061] S2, initialize the preset parameters, including the length of the pipeline and spatial step size Divide the pipeline into several segments and set the total simulation time and time step , set the truncation error threshold .

[0062] This step initializes the preset parameters, including dividing the pipeline into multiple segments, setting the total simulation duration and time step, and setting the truncation error threshold. Subsequently, simulations are performed for each segment at each time step. The highest order of the power series affects the truncation error. Choosing an appropriate highest order of the power series ensures that the truncation error does not exceed the truncation error threshold.

[0063] S3, configuring the initial conditions of each pipe section of each pipeline and the boundary conditions of each pipe section of each pipeline at each time step, wherein the initial conditions include an initial mass flow rate and an initial temperature, and the boundary conditions include a boundary pressure value and a boundary temperature value.

[0064] Solving the linear equation system with semi-analytical coefficient recurrence requires initial and boundary conditions. The initial conditions include the initial mass flow rate and initial temperature, while the boundary conditions include boundary pressure and boundary temperature. Boundary pressures include the current inlet and outlet pressures and their values ​​at the next moment after one time step. Boundary temperature values ​​include the current inlet and outlet temperature and their values ​​at the next moment after one time step.

[0065] S4, according to the initial conditions and boundary conditions of the pipe section, the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical expression of the thermal model are calculated respectively through two semi-analytical coefficient recursive linear equations. The calculated semi-analytical coefficients satisfy the truncation error not greater than the truncation error threshold. Substitute the semi-analytical coefficients into the semi-analytical expression to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

[0066] 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 through the semi-analytical coefficient recursive relationship linear equation system, and 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 truncation error not greater than the truncation error threshold. Finally, the semi-analytical calculation results of each pipe segment in each pipeline at all time steps are obtained. The specific steps include the following.

[0067] S4.1, obtain the boundary conditions of each pipe segment of the current pipeline at the current time step.

[0068] S4.2, sets the maximum order of the power series.

[0069] S4.3, starting from a power series of 1, calculate the semi-analytical coefficients of the hydraulic model semi-analytical expression based on the current power series, the initial mass flow rate of the current pipe section, and the boundary pressure value through the linear equation group of the recursive relationship between the semi-analytical coefficients of the hydraulic model semi-analytical expression, and record it as the first semi-analytical coefficient; and calculate the semi-analytical coefficients of the thermal model semi-analytical expression based on the current power series, initial temperature, boundary temperature value, and the linear equation group of the recursive relationship between the semi-analytical coefficients of the thermal model semi-analytical expression, and record it as the second semi-analytical coefficient.

[0070] S4.4, substitute any spatial position and time into the semi-analytical expression of the hydraulic model of the first semi-analytical coefficient 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 coefficient to obtain the second truncation error.

[0071] S4.5, determine whether the first truncation error and the second truncation error are both less than the truncation error threshold If so, output the semi-analytical calculation result of the current pipe segment. Otherwise, add 1 to the power series and return to S4.3. Repeat this process until the semi-analytical calculation result of each pipe segment of each pipeline at the current time step is output.

[0072] 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.

[0073] Furthermore, as a refinement and extension of the specific implementation of the above embodiment, the specific implementation process in this embodiment is fully described below.

[0074] First, we introduce the dynamic model of the district heating network under the mass-quantity regulation mode. The pipeline model describes the hydraulic and thermal dynamic characteristics using spatiotemporal partial differential equations. Combined with the algebraic equations for the conservation of mass and momentum at the nodes, these equations together form the differential algebraic equations for the DHN.

[0075] Because the core goal of DHN simulation is to describe the overall state at the system level (such as the temperature and pressure distribution across the entire network), rather than characterizing the microscopic characteristics of the fluid at the element level, pipeline models typically only consider one spatial dimension. The one-dimensional flow characteristics of water flow in the pipeline are described by the pipeline mass conservation equation (Equation (1)) and the pipeline momentum conservation equation (Equation (2)), while the thermodynamic process is characterized by the pipeline energy conservation equation (Equation (3)).

[0076] (1)

[0077] (2)

[0078] (3)

[0079] Where, and Representing time and space respectively; 、 、 represent the density, flow rate and pressure of water respectively; the specific heat capacity of water is given by Given; the pipe parameters in DHNs include the friction coefficient , inner diameter ,inclination and heat dissipation coefficient ;also, Indicates the temperature of water, Indicates the ambient temperature, is the acceleration due to gravity.

[0080] In district heating networks, water is usually treated as an incompressible fluid, i.e. its density can be considered constant. Pipeline mass flow and flow rate The relationship is , where is the cross-sectional area of ​​the pipeline. This application does not consider the influence of the horizontal inclination of the pipeline. Based on the above assumptions, equations (1), (2) and (3) can be simplified to:

[0081] (4)

[0082] (5)

[0083] (6)

[0084] In addition to the partial differential equations describing the pipeline dynamics mentioned above, the mass flow at each connection node in the heating network must satisfy the node mass conservation equation, which is mathematically expressed as:

[0085] (7)

[0086] Where, represents the node index, is the node index set of the heating network; Indicates the pipeline index, is the pipeline index collection of the heating network; in addition, and is the node-pipe association matrix of the inlet and outlet pipes.

[0087] The energy flow carried by hot water flowing into or out of each connection node must satisfy the node energy conservation equation, which is mathematically expressed as Equation (8):

[0088] (8)

[0089] Where, Heating network node The load at.

[0090] When the pipeline is divided into N segments, Equations (7) and (8) can also express the mass / energy conservation relationship between all segments. Therefore, based on Equations (7) and (8), the model derivation from a single segment to the entire pipeline and then to the complete DHNs can be achieved.

[0091] In summary, the hydraulic and thermal dynamic coupling model of the district heating network is defined by Equations (4) to (8).

[0092] The semi-analytical expression is explained below. Unlike traditional discretization methods (such as the finite difference method), which discretize partial differential equations into a system of algebraic equations and solve them, the semi-analytical solution aims to represent the spatiotemporal state variables by approximate analytical expressions. , its expression is as follows:

[0093] (9)

[0094] Where, For a two-dimensional power series The coefficient of the term, Represents the highest order of the power series ( ). The core goal of the semi-analytical method is to solve these power series coefficients. Then, by and time Substituting the above approximate expression, we can get a truncation error of Approximate state .

[0095] In online simulation, since boundary conditions are usually obtained through discrete measurement points, SAS is similar to FDM (Finite Difference Method) in that both require discrete grids to represent the boundary value problem (BVP) of partial differential equations. However, there are essential differences between the grids used by FDM and SAS, such as Figure 2 As shown, Figure 2 (a) is the FDM grid, Figure 2 (b) in the figure is the SAS grid.

[0096] exist Figure 2 In (a), FDM requires that the constraints of the PDE be satisfied only at specific locations within the grid (such as the corners in the figure), and generates numerical solutions only at these discrete points. Figure 2 (b) in the figure shows that the SAS method requires that the constraints of the PDE be satisfied throughout the entire grid domain (as shown in the highlighted area in the figure), thus generating an explicit solution at any spatial and temporal location within the grid. Furthermore, the SAS method's stringent constraints give it theoretically higher accuracy.

[0097] The following SAS expression of the hydraulic model is constructed based on the above semi-analytical expression.

[0098] From the SAS perspective, pressure Can be expressed as time and space Due to the incompressibility of water, the mass flow rate Just for time function, does not depend on space . and The semi-analytical expression of is as follows:

[0099] (10)

[0100] (11)

[0101] Where, and They are respectively and In this case, and The partial derivative of is:

[0102] (12)

[0103] (13)

[0104] (14)

[0105] By substituting the above partial derivatives into the partial differential equations, the pipeline momentum conservation equation (Equation 5) and the node mass conservation equation (Equation 7) can be reconstructed as follows:

[0106] (15)

[0107] (16)

[0108] When both sides of the above equation are expanded into a power series, to ensure that the equality holds for any and If both sides are established, the coefficients of the same order terms on both sides must be exactly equal. , , ,…, The coefficients of the terms can be used to obtain a set of linear equations that represent the recursive relationship, namely the semi-analytical coefficient recursive relationship linear equations of the semi-analytical expression of the hydraulic model (Equation 17).

[0109] (17)

[0110] For the hydraulic BVP of the heating pipes, each pipe in the district heating network is divided into N segments with a time step of , the spatial step length is ,like Figure 3 shown.

[0111] Pipe segment For example, the solution of the linear equation system (17) still requires additional initial conditions and boundary conditions. The required boundary conditions are as follows:

[0112] (18)

[0113] (19)

[0114] (20)

[0115] (twenty one)

[0116] like Figure 3 As shown, the given pipe segment Initial mass flow rate and its boundary pressure value ( , , , ), by solving the linear equations, we can get the pipe section Power series components of mass flow rate , ,…, From this, the semi-analytical expression of Equation (10) can be derived, which can be used to calculate and visualize the spatiotemporal hydraulic dynamic characteristics of each pipe section in the district heating network.

[0117] The following SAS expression of the thermal model is constructed based on the above semi-analytical expression.

[0118] Based on SAS, temperature It can be expressed as time and space The two-dimensional power series of :

[0119] (twenty two)

[0120] Where, It is a two-dimensional power series Term coefficient. The partial derivative of is:

[0121] (twenty three)

[0122] (twenty four)

[0123] like Figure 4 As shown in the thermal BVP of the heating pipe, each pipe in the district heating network is discretized into N segments, with time and space steps of and .

[0124] Pipe segment For example, solving the thermal BVP of this pipe section requires both initial conditions and boundary conditions. The necessary boundary conditions are as follows:

[0125] (25)

[0126] (26)

[0127] (27)

[0128] (28)

[0129] Substituting equations (23)-(28) into the pipeline energy conservation equation (Equation 6) and the node energy conservation equation (Equation 8), we obtain the following reconstructed form:

[0130] (29)

[0131] (30)

[0132] Expand both sides of the above equation into a series form. The equation can be applied to all terms only when the coefficients of the same order terms are consistent. and Established. By comparison , , ,…, The coefficients of the terms can be derived to derive the linear equations consisting of equations (31) and (32).

[0133] (31)

[0134] (32)

[0135] Correspondingly, the semi-analytical coefficient recursive relationship linear equation group of the semi-analytical expression of the thermal model is derived for all pipe sections and is expressed as follows:

[0136]

[0137] like Figure 4 As shown, the given pipe segment Initial temperature and its boundary temperature values ​​( , , , ), by solving the linear equations, the power series components of the temperature distribution of the pipe section can be determined , ,…, From this, the semi-analytical expression of Equation (22) can be derived, which can be used to calculate and visualize the spatiotemporal thermodynamic evolution of the temperature of each pipe section in the district heating network.

[0138] In some optional implementations, based on the SAS construction of the district heating network hydraulic and thermal model, the entire SAS simulation process is as follows Figure 5 The simulation process is divided into the preset value initialization and four decision cycles.

[0139] 1) Truncation error loop: Due to the inherent truncation error of the spatiotemporal 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 the highest order of the power series in the simulation of this application is set to 3, and the preset truncation error threshold is In practice, it's extremely rare for a third-order power series to fail to meet accuracy requirements, and the time consumed by this loop is negligible compared to the total simulation time. Therefore, this loop serves only as a safety mechanism for SAS accuracy, and does not significantly increase computational cost due to excessive iterations.

[0140] 2) Space step loop: This loop is for each space step of the pipeline Generate SAS expressions until the total length of the pipeline is covered .

[0141] 3) Pipeline iteration loop: After the current pipeline completes the SAS simulation of all spatial steps, this loop traverses each pipeline in the pipeline network until all pipelines complete the simulation of the current time step.

[0142] 4) Time stepping loop: This loop is for each time step Generate SAS expressions until the total simulation time is reached .

[0143] An embodiment of a method for dynamic simulation of a regional heating network is described in detail above. Based on the method for dynamic simulation of a regional heating network described in the above embodiment, an embodiment of the present invention further provides a system for dynamic simulation of a regional heating network corresponding to the method.

[0144] Figure 6 This is a schematic block diagram of the structure of a district heating network dynamic simulation system according to an embodiment of the present invention. In this embodiment, the district heating network dynamic simulation system 600 can be divided into multiple functional modules based on their functions. System 600 is suitable for district heating networks operating in a quality-quantity regulation mode. A module, as used herein, refers to a series of computer program segments that can be executed by at least one processor and perform fixed functions, and is stored in a memory.

[0145] The model construction module 610 is used to construct a semi-analytical expression of the hydraulic model and a semi-analytical expression of the thermal model of the pipeline in the district heating network, and based on the conservation of pipeline momentum and the conservation of node mass, construct a linear equation group of recursive relations of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and a linear equation group of recursive relations of the semi-analytical coefficients of the semi-analytical expression of the thermal model.

[0146] Parameter initialization module 620 is used to initialize the preset parameters, including the parameters according to the pipeline length. and spatial step size Divide the pipeline into several segments and set the total simulation time and time step , set the truncation error threshold .

[0147] The initial condition configuration module 630 is used 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. The initial conditions include initial mass flow and initial temperature, and the boundary conditions include boundary pressure values ​​and boundary temperature values.

[0148] 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 semi-analytical coefficient recursive linear equations according to the initial conditions and boundary conditions of the pipe section. The calculated semi-analytical coefficients meet the truncation error not greater than the truncation error threshold. Substitute the semi-analytical coefficients into the semi-analytical expression to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

[0149] 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 methods of 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 methods can refer to the descriptions of the corresponding embodiments of each part and will not be elaborated here.

[0150] 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 function corresponds to that of the aforementioned method and will not be described in detail here.

[0151] Figure 7 The present invention provides a schematic diagram of a terminal 700, comprising a processor 710, a memory 720, and a communication unit 730. The processor 710 is configured to implement the steps of the method for dynamic simulation of a district heating network according to the above embodiment when executing the district heating network dynamic simulation program stored in the memory 720.

[0152] 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 will appreciate that the server structure shown in the figure does not limit the present invention; it may be a bus structure or a star structure, and may include more or fewer components than shown, or combine certain components, or arrange the components differently.

[0153] The memory 720 can be used to store 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 perform some or all of the steps in the following method embodiments.

[0154] The processor 710 is the control center of the storage terminal. It uses various interfaces and lines to connect various parts of the entire electronic terminal. It executes various functions of the electronic terminal and / or processes data by running or executing software programs and / or modules stored in the memory 720, and calling data stored in the memory. The processor can be composed of an integrated circuit (IC), for example, it can be composed of a single packaged IC, or it can be composed of multiple packaged ICs with the same or different functions. 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 computing core or multiple computing cores.

[0155] The communication unit 730 is configured to establish a communication channel so that the storage terminal can communicate with other terminals, receive user data sent by other terminals, or send user data to other terminals.

[0156] The present invention also provides a computer storage medium, wherein the storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0157] The present invention also provides a computer storage medium, wherein the storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0158] The computer storage medium stores a district heating network dynamic simulation program, and when the district heating network dynamic simulation program is executed by the processor, the process steps of the district heating network dynamic simulation method of the above embodiment are implemented.

[0159] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software plus a necessary general-purpose hardware platform. Based on this understanding, the technical solutions in the embodiments of the present invention, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, among other media capable of storing program code, and includes instructions for causing a computer terminal (which can 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 various embodiments of the present invention.

[0160] In the 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 merely a logical function division. In actual implementation, there may be other division methods, such as 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 mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0161] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0162] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0163] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement 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. Therefore, the present invention is not limited to the embodiments shown herein, but is intended to be construed in the widest manner consistent with the principles and novel features disclosed herein.

Claims

1. A method for dynamic simulation of a district heating network, characterized in that: The method is applicable to a district heating network in a quality-quantity regulation mode and comprises the following steps: Step 1: Construct a semi-analytical expression of the hydraulic model and the semi-analytical expression of the thermal model of the pipeline in the district heating network, and construct a linear equation system of the recursive relationship of the semi-analytical coefficients of the semi-analytical expression of the hydraulic model and the semi-analytical expression of the thermal model based on the conservation of pipeline momentum and the conservation of node mass; Step 2: Initialize the preset parameters, including the length of the pipeline and spatial step size Divide the pipeline into several segments and set the total simulation time and time step , set the truncation error threshold ; Step 3: configuring the initial conditions of each pipe section of each pipeline and the boundary conditions of each pipe section of each pipeline at each time step, wherein 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 section, the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical expression of the thermal model are calculated respectively through two semi-analytical coefficient recursive linear equations. The calculated semi-analytical coefficients satisfy the truncation error not greater than the truncation error threshold. Substitute the semi-analytical coefficients into the semi-analytical expression to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

2. The method for dynamic simulation of a district heating network according to claim 1, characterized in that: Step 4 specifically includes: Step 4.1, obtain the boundary conditions of each pipe section 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 a power series of 1, calculate the semi-analytical coefficients of the hydraulic model semi-analytical expression using the recursive linear equations of the semi-analytical coefficients of the hydraulic model semi-analytical expression based on the current power series, the initial mass flow rate of the current pipe section, and the boundary pressure value. This is recorded as the first semi-analytical coefficient. Also, calculate the semi-analytical coefficients of the thermal model semi-analytical expression using the recursive linear equations of the semi-analytical coefficients of the thermal model semi-analytical expression based on the current power series, the initial temperature, the boundary temperature value, and the semi-analytical coefficients of the thermal model semi-analytical expression. This is recorded as the second semi-analytical coefficient. Step 4.4, substitute any spatial position and time into the semi-analytical expression of the hydraulic model with the first semi-analytical coefficient 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 coefficient to obtain the second truncation error; Step 4.5: Determine whether the first truncation error and the second truncation error are both less than the truncation error threshold If yes, output the semi-analytical calculation result of the current pipe segment. Otherwise, add 1 to the power series and return to step 4.

3. Repeat this process until the semi-analytical calculation result of each pipe segment of each pipeline at the current time step is output. In 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.

3. The method for dynamic simulation of a district heating network according to claim 1 or 2, characterized in that: The semi-analytical expression of the hydraulic model includes the mass flow rate Semi-analytical expressions and pressure The semi-analytical expressions of are expressed as, Where, Represents space, Indicates time, represents the highest order of the power series, .

4. The method for dynamic simulation of a district heating network according to claim 3, characterized in that: The semi-analytical coefficient recursive relationship linear equation group of the semi-analytical expression of the hydraulic model is expressed as follows: Where, is the cross-sectional area of ​​the pipe, is the pipeline friction coefficient, is the inner diameter of the pipe, is the water density; is the node-pipe association matrix of the inlet pipe, is the node-pipeline association matrix of the outlet pipeline, represents the node index, Indicates the pipeline index.

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

6. The method for dynamic simulation of a district heating network according to claim 5, characterized in that: The semi-analytical coefficient recursive relationship linear equation system of the semi-analytical expression of the thermal model is expressed as: Where, is the water density, is the specific heat capacity of water, is the cross-sectional area of ​​the pipe, is the pipe heat dissipation coefficient, is the ambient temperature, Heating network node The load at is the node-pipe association matrix of the inlet pipe, is the node-pipeline association matrix of the outlet pipeline, represents the node index, Indicates the pipeline index.

7. The method for dynamic simulation of 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, as well as the pressure values ​​at the inlet and outlet at the next moment after one time step is added; the boundary temperature value includes 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 one time step is added.

8. A district heating network dynamic simulation system, characterized in that: Applicable to district heating networks in quality-quantity regulation mode, including: A model building module is used to construct semi-analytical expressions of the hydraulic model and the thermal model of the pipelines in the district heating network, and to construct a linear equation system of recursive relations of the semi-analytical coefficients of the semi-analytical expressions of the hydraulic model and the semi-analytical coefficients of the semi-analytical expressions of the thermal model based on the conservation of pipeline momentum and the conservation of node mass; Parameter initialization module, used to initialize preset parameters, including according to the pipeline length and spatial step size Divide the pipeline into several segments and set the total simulation time and time step , set the truncation error threshold ; An initial condition configuration module is used to configure the initial conditions of each pipe section of each pipeline and the boundary conditions of each pipe section of each pipeline at each time step, wherein 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 hydraulic model semi-analytical expression and the thermal model semi-analytical expression respectively through two semi-analytical coefficient recursive linear equations according to the initial conditions and boundary conditions of the pipe section. The calculated semi-analytical coefficients meet the truncation error not greater than the truncation error threshold. Substitute the semi-analytical coefficients into the semi-analytical expression to obtain the semi-analytical calculation results of each pipe segment of each pipeline at all time steps.

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

10. A computer-readable storage medium, characterized in that The readable storage medium stores a district heating network dynamic simulation program, which, when executed by a processor, implements the steps of the district heating network dynamic simulation method according to any one of claims 1 to 7.

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