Heat supply pipe network analytical solution method and system based on spectral decomposition

Abstract

The invention provides a heat supply pipe network analytical solution method and system based on spectral decomposition, and belongs to the technical field of heat supply simulation, and the method comprises the steps: building and solving a primary network water supply matrix operation model based on a heat supply pipe network topological structure, and obtaining a primary network water supply temperature; constructing an analysis response model based on a secondary network multi-node structure; performing spectral decomposition on the primary network water supply temperature to obtain a harmonic component serving as a sine boundary condition; obtaining the analytic solution temperature of the first node of the secondary network by using the characteristic equation of the analytic response model and the sine boundary condition; and on the basis of the primary network water supply temperature and the analytical solution temperature of the first node of the secondary network, a primary network return water and CHP inlet temperature calculation model is constructed and solved, and the primary network return water temperature and the CHP inlet temperature are obtained. According to the method, the whole process of primary network water supply, secondary network heat exchange and primary network water return is integrally solved from the perspective of heat flow, so that full-process efficient simulation of the heat supply network is realized.

Description

Technical Field

[0001] This invention relates to the field of heating simulation technology, and in particular to an analytical solution method and system for heating pipe networks based on spectrum decomposition. Background Technology

[0002] With the acceleration of urbanization and the transformation of energy structure, heating pipe networks play an important role in district heating. To ensure their efficient and stable operation, it is usually necessary to use computer simulation technology to simulate their thermodynamic dynamic processes to guide actual operation.

[0003] However, in existing heat network simulation frameworks, the dual dimensions of network topology and time step lead to an explosive increase in simulation overhead. In the primary water supply stage, independent temperature calculations are required for each heat exchange station node in the network within each discrete time step. In the secondary heat exchange stage, complex heat transfer coupling calculations are repeatedly performed on the multi-node network on the user side. In the return water stage, the return temperatures of each branch must be re-aggregated and progressively transferred back to the heat source to form a closed-loop iteration. Therefore, the entire simulation process generally adopts a multi-layered nested calculation method of "node-by-node – time-step-by-time step." This calculation method causes the scale of the simulation model and the depth of the computational loop to grow synchronously. When the number of heat exchange stations in the network increases or the required time resolution of the simulation increases, the total simulation time often shows a linear or even superlinear rapid increase, resulting in extremely low simulation efficiency. Summary of the Invention

[0004] This invention provides a method, system, electronic device, storage medium, and computer program product for analytical solving of heating pipe networks based on spectrum decomposition, in order to overcome the deficiencies in the prior art and achieve efficient simulation of the entire heating pipe network process.

[0005] This invention provides an analytical solution method for heating pipe networks based on spectral decomposition, comprising the following steps: Based on the heating network topology, a primary network water supply matrix calculation model is constructed. The primary network water supply matrix operation model is solved using a vectorized matrix operation method to obtain the primary network water supply temperature. Based on the multi-node structure of the secondary network, an analytical response model is constructed. The primary water supply temperature is subjected to spectral decomposition to obtain the harmonic components as sinusoidal boundary conditions; Using the characteristic equation and superposition principle of the analytical response model, and based on the sinusoidal boundary conditions, harmonic superposition is performed to obtain the analytical solution temperature of the first node of the quadratic network; Based on the primary network water supply temperature and the analytical solution temperature of the first node of the secondary network, a calculation model for the primary network return water and CHP inlet temperature is constructed. The primary network return water temperature and CHP inlet temperature are obtained by solving the calculation model of the primary network return water temperature and CHP inlet temperature using the flow weight mixing and pipeline heat leakage delay propagation algorithm.

[0006] According to the present invention, an analytical solution method for heating pipe networks based on spectral decomposition is provided, wherein the primary network water supply matrix operation model is constructed based on the heating pipe network topology, including: Identify the pipe connections from the CHP outlet to the inlet of each heat exchange station from the heating network topology; Based on the pipeline connection relationship, the heat transfer process of each pipeline segment is characterized as a temperature transfer relationship that includes heat loss and flow delay, wherein the pipeline outlet temperature is jointly determined by the pipeline inlet temperature, ambient temperature, pipeline leakage thermal resistance, and flow delay time. By combining the temperature transfer relationships of all pipelines, the primary network water supply matrix operation model is obtained.

[0007] According to the present invention, an analytical solution method for heating pipe networks based on spectral decomposition is provided, wherein the analytical response model is constructed based on a secondary network multi-node structure, including: The building heat dissipation process of heat users is equivalent to a thermal circuit network model composed of multiple thermal resistances and thermal capacities. The thermal circuit network model is provided with nodes that represent indoor air temperature, inner wall surface temperature, middle wall temperature and outer wall surface temperature respectively. Based on the thermal network model, the transient heat conduction differential equations of each node are obtained, and the differential equations are integrated into a single-degree-of-freedom high-order constant-coefficient non-homogeneous differential equation with respect to the temperature node of the outer surface of the wall, so as to establish the analytical response model.

[0008] According to the analytical solution method for heating pipe networks based on spectral decomposition provided by the present invention, the method utilizes a flow weighted mixing and pipeline heat leakage delay propagation algorithm to solve the calculation model of the primary network return water and CHP inlet temperature, thereby obtaining the primary network return water temperature and CHP inlet temperature, including: The primary return water temperature of the terminal heat exchange station, which is a leaf node, is used as the initial input, and the calculation is performed step by step from downstream to upstream along the return water network topology. At a confluence node where multiple downstream branches converge, the return water temperatures from the multiple downstream branches are weighted and mixed according to the mass flow rates of each of the multiple downstream branches to obtain the mixing temperature of the confluence node. The mixing temperature is used as the inlet temperature of the pipe connecting the manifold node to a higher-level node, and the outlet temperature of the pipe under the effects of heat leakage and delay is calculated. The outlet temperature is then used as the input for the return water temperature calculation of the higher-level node until the CHP inlet temperature is finally calculated.

[0009] According to the present invention, an analytical solution method for heating pipe networks based on spectral decomposition is provided. The method utilizes the characteristic equations and superposition principle of the analytical response model, and performs harmonic superposition based on the sinusoidal boundary conditions to obtain the analytical solution temperature of the first node of the secondary network, comprising: Solve the characteristic equation corresponding to the higher-order constant coefficient non-homogeneous differential equation to obtain multiple characteristic roots, and construct the transient general solution of the analytical response model based on the multiple characteristic roots. The transient general solution is a linear combination of multiple exponentially decaying terms containing undetermined constants. For each harmonic component, solve the higher-order constant-coefficient nonhomogeneous differential equation to obtain a steady-state particular solution; The transient general solution is superimposed with the steady-state particular solutions corresponding to all harmonics to form the complete temperature solution expression for each node in the thermal circuit network model; The initial temperatures of each node in the thermal network model are used as initial conditions and substituted into the complete temperature solution expression to determine the undetermined constants, thereby obtaining the analytical solution temperature of the first node of the secondary network.

[0010] According to the analytical solution method for heating pipe networks based on spectral decomposition provided by the present invention, the spectral decomposition of the primary network water supply temperature includes: The time-series curve of the primary water supply temperature is sampled at equal intervals to obtain a time-series sequence containing multiple sampling points; A fast Fourier transform is performed on the time series to extract a DC component and the amplitude and phase information of each of the harmonic components.

[0011] The analytical solution method for heating pipe networks based on spectral decomposition provided by the present invention further includes: Perform an inverse fast Fourier transform on the amplitude and phase information of the DC component and each of the harmonic components to generate a reconstructed temperature curve; The reconstructed temperature curve is compared with the time series to verify the fidelity of the spectral decomposition.

[0012] This invention also provides an analytical solution system for heating pipe networks based on spectral decomposition, comprising the following modules: The first processing module is used to construct a primary network water supply matrix calculation model based on the heating network topology. The second processing module is used to solve the primary network water supply matrix operation model using a vectorized matrix operation method to obtain the primary network water supply temperature. The third processing module is used to construct an analytical response model based on the secondary network multi-node structure; The fourth processing module is used to perform spectral decomposition on the primary water supply temperature to obtain harmonic components as sinusoidal boundary conditions. The fifth processing module is used to obtain the analytical solution temperature of the first node of the quadratic network by utilizing the characteristic equation and superposition principle of the analytical response model and performing harmonic superposition according to the sinusoidal boundary conditions. The sixth processing module is used to construct a calculation model for the return water temperature of the primary network and the inlet temperature of CHP based on the analytical solution temperature of the primary network supply water temperature and the first node of the secondary network. The seventh processing module is used to solve the calculation model of the primary network return water and CHP inlet temperature by using the flow weight mixing and pipeline heat leakage delay propagation algorithm, so as to obtain the primary network return water temperature and CHP inlet temperature.

[0013] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the analytical solution method for heating pipe networks based on spectral decomposition as described above.

[0014] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the analytical solution method for heating pipe networks based on spectral decomposition as described above.

[0015] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the analytical solution method for heating pipe networks based on spectral decomposition as described above.

[0016] In summary, one or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: By constructing a primary network water supply matrix operation model based on the heating network topology and solving the model using vectorized matrix operations, the original double-nested loop calculations requiring node and time dimensions are simplified to single-layer matrix operations only in the time dimension, effectively improving the computational efficiency of the primary network water supply temperature. Next, an analytical response model is constructed based on the secondary network's multi-node structure, and the primary network water supply temperature is spectrally decomposed. Harmonic superposition is then used to solve the problem using characteristic equations and the superposition principle, transforming the complex transient thermal response problem of the secondary network from a costly numerical integration method to an efficient analytical solution. Finally, a primary network return water model is constructed based on the primary network water supply temperature and the secondary network analytical solution temperature. This model is solved using a flow weighted mixing and pipeline leakage delay propagation algorithm, decomposing the complex multi-stage confluence and transmission process in the return water network into a structured downstream-to-upstream propagation calculation, thus achieving efficient simulation of the entire heating network process. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the analytical solution method for heating pipe networks based on spectral decomposition provided by the present invention.

[0019] Figure 2 This is a model diagram of the topology of the primary water supply side provided by the present invention.

[0020] Figure 3 This is a heat flow model diagram of the primary water supply side provided by the present invention.

[0021] Figure 4 This is a curve showing the change of water supply temperature over time in the primary heat exchange station provided by the present invention.

[0022] Figure 5 This is a schematic diagram of a secondary network multi-node structure provided by the present invention.

[0023] Figure 6 This is a comparison chart of vectorization and FFT reconstruction of the primary network water supply temperature of the heat exchange station provided by the present invention.

[0024] Figure 7 This is the return water temperature curve of the primary heat exchange station provided by the present invention.

[0025] Figure 8 This is a heat flow model diagram of the primary network return water section provided by the present invention.

[0026] Figure 9 This is the CHP inlet temperature curve provided by the present invention.

[0027] Figure 10 This is a schematic diagram of the analytical solution system for heating pipe networks based on spectral decomposition provided by the present invention.

[0028] Figure 11 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0030] It should be noted that in the description of this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. The terms "upper," "lower," etc., indicating orientation or positional relationships according to the accompanying drawings, are only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the system or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0031] The terms "first," "second," etc., used in this invention are used to distinguish similar objects, not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class, without limiting the number of objects; for example, a first object can be one or more. Furthermore, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0032] The following is combined with Figures 1 to 11 This invention describes the analytical solution method, system, electronic device, storage medium, and computer program product for heating pipe networks based on spectrum decomposition provided by this invention.

[0033] Reference Figure 1 , Figure 1 This is a flowchart illustrating the analytical solution method for heating pipe networks based on spectral decomposition provided by the present invention, as shown below. Figure 1 As shown, steps 101 to 107 are included: Step 101: Based on the heating network topology, construct a primary network water supply matrix operation model.

[0034] To achieve efficient and accurate simulation of large-scale heating pipe networks, it is first necessary to establish a mathematical model that can completely describe the physical processes on the primary water supply side of the network. Traditional simulation methods are inefficient due to computational complexity and cannot meet the requirements of real-time control. Therefore, this invention provides a novel modeling approach to solve the aforementioned technical problems.

[0035] In a specific embodiment, this method first performs the step of constructing a primary network water supply matrix operation model based on the heating network topology. Here, the heating network topology refers to the connection relationships and layout of the various physical components within the heating network. The primary network water supply matrix operation model is a mathematical model used to describe the entire thermodynamic behavior of the primary network from the heat source outlet to the inlet of each heat exchange station. This model uniformly expresses the heat transfer and delay process of the entire water supply network in matrix form.

[0036] When constructing the primary water supply matrix operation model, key nodes such as pipeline nodes and heat exchange station inlets are interconnected through a sparse topology matrix to form an overall thermal model covering the entire process.

[0037] In one possible implementation, step 101 specifically includes the following steps: Step 201: Identify the pipe connections from the CHP outlet to the inlet of each heat exchange station from the heating network topology; Step 202: Based on the pipeline connection relationship, the heat transfer process of each pipeline segment is characterized as a temperature transfer relationship that includes heat loss and flow delay. The pipeline outlet temperature is determined by the pipeline inlet temperature, ambient temperature, pipeline leakage thermal resistance, and flow delay time. Step 203: Combine the temperature transfer relationships of all pipelines to obtain the primary network water supply matrix operation model.

[0038] Specifically, the first step is to identify the pipe connections from the CHP outlet to the inlet of each heat exchange station within the heating network topology. This step aims to clarify the path and sequence of heat transfer on the primary water supply side. Specifically, refer to... Figure 2 , Figure 2 This is a model diagram of the topology of the primary water supply network provided by this invention. For example... Figure 2 As shown, the heat originates from the heat source (CHP) outlet (node ​​0), travels through the main pipeline to heat exchange station 1, and then branches at this node, forming two parallel branches flowing to heat exchange stations 2 and 3 respectively. Simultaneously, a downstream branch extending from the outlet of heat exchange station 3 is identified, connecting in series with heat exchange station 4. This step provides a clear understanding of the complete topology of the entire water supply network, encompassing both parallel branches and series connections, providing a basis for subsequent overall model building.

[0039] Next, after clarifying the pipe connections, the heat transfer process of each pipe segment is characterized as a temperature transfer relationship including heat loss and flow delay, based on these connections. (Refer to...) Figure 3 , Figure 3 This invention provides a heat flow model diagram for the primary water supply side of a network. The step where the pipe outlet temperature is determined by the pipe inlet temperature, ambient temperature, pipe leakage thermal resistance, and flow delay time is crucial. This step aims to establish an accurate mathematical and physical model for each individual pipe segment. For any given pipe segment, its outlet temperature... With inlet temperature The relationship, taking into account the flow delay time Then, it can be described by the following formula: In the above formula, It is the outlet temperature of the pipe. It is the inlet temperature of the pipe. This is the moment when the fluid particle enters the pipe. It is the delay time of the flow in the pipe. It describes the thermodynamic potential caused by heat leakage along the pipeline, specifically: In the formula, It is the total heat loss of fluid elements flowing through the pipe. v ρ is the flow velocity, ρ is the density of water, and S is the cross-sectional area of ​​the pipe. It is the specific heat capacity of water.

[0040] Total heat loss The calculation further considers the pipe inlet temperature, ambient temperature, and the average heat transfer temperature change caused by heat leakage. Its expression is: in can be derived from formula Approximate calculations are performed, while the heat transfer resistance, which reflects the overall heat leakage characteristics of the pipeline, is used. Then by formula Sure.

[0041] Finally, the step of combining the temperature transfer relationships of all pipelines to obtain the primary network water supply matrix calculation model is performed. This step aims to integrate the multiple temperature transfer relationships established for single pipeline segments, based on the identified pipeline topology, into a unified model capable of describing the entire network. Specifically, the derived formulas are organized and written in a discrete-time vectorized expression. At any given time... The outlet temperature of a section of pipe It can be calculated from the following final vectorized expression: in, Representing the current moment, The temperature at the pipe inlet at the current moment. To account for flow delay time Then, in the future The pipe outlet temperature. This temperature is also affected by the current ambient temperature. With future ambient temperature The influence of the formula. All coefficients in the formula are predetermined by the physical properties of the pipe, such as heat transfer resistance. Flow velocity v, water density ρ, pipe cross-sectional area S, water specific heat capacity .

[0042] By constructing such a linear water supply matrix operation model, the complex thermodynamics problem of the pipeline network can be transformed into a structured mathematical model. This model lays the foundation for subsequent solutions using efficient vectorized matrix operation methods, thereby greatly improving the efficiency of simulation calculations and providing a prerequisite for achieving efficient simulation of the entire heating pipeline network process.

[0043] Step 102: Solve the primary network water supply matrix operation model using the vectorized matrix operation method to obtain the primary network water supply temperature.

[0044] After establishing the primary water supply matrix calculation model, it is necessary to solve the model to obtain the temperature dynamics of each node in the pipeline network. Traditional point-by-point iterative solution methods require nested calculations for each node and each time step, resulting in a huge computational load that is difficult to meet the efficiency requirements of real-time simulation. Therefore, this invention provides an efficient solution method to address the problem of low computational efficiency.

[0045] In a specific embodiment, the step of solving the primary water supply network matrix operation model using a vectorized matrix operation method to obtain the primary water supply temperature is performed. This vectorized matrix operation method refers to representing the temperature of all nodes in the primary water supply network as a temperature vector at the same time, and integrating the coefficients describing the heat transfer and delay characteristics of each pipe into an operation matrix. By iterating through time and performing matrix operations on the temperature vector at each time step, the future temperatures of all nodes are calculated synchronously.

[0046] At each simulation time step to set the inlet temperature of all pipes and ambient temperature , As a vector input, a single matrix operation can yield the corresponding delay times for all pipelines. Afterwards Exit temperature vector at time By repeating this process over time, a complete curve showing the change in primary water supply temperature at the inlet of each heat exchange station over time can be obtained. The format of the result can be referenced. Figure 4 , Figure 4 This is a curve showing the change of water supply temperature over time in the primary heat exchange station provided by the present invention.

[0047] By employing this vectorized matrix operation method, the previously required double-nested loop calculations in both the node and time dimensions are simplified to a single-layer loop in only the time dimension. This method avoids traversing and solving each network node individually, significantly reducing computational complexity and thus greatly improving the efficiency of determining the primary network water supply temperature.

[0048] Step 103: Construct an analytical response model based on the secondary network multi-node structure.

[0049] After calculating the primary network water supply temperature, it is necessary to further solve the thermal response of the secondary network under the combined effects of primary network heating and outdoor ambient temperature. The thermodynamic processes of the secondary network involve complex heat transfer and heat storage effects within the building envelope. Solving its transient behavior using traditional numerical integration methods results in extremely high computational costs, making efficient simulation difficult. To improve the computational efficiency and accuracy of the secondary network response, this invention provides a modeling approach based on analytical methods.

[0050] In one specific embodiment, the step of constructing an analytical response model based on a secondary network multi-node structure is performed. Here, the secondary network multi-node structure refers to a physical network on the heat user side composed of thermal resistance and heat capacity, while the analytical response model is a mathematical model that accurately describes the dynamic temperature response of each node in the secondary network by deriving ordinary differential equations. The construction of this model aims to replace costly numerical iteration with analytical solutions, thereby directly obtaining a functional expression for temperature changing over time.

[0051] In constructing this model, the building heat dissipation process of heat users in the secondary network is first abstracted into a thermal network model composed of multiple thermal resistance and thermal capacity components. Next, based on this network model, a set of transient heat conduction differential equations is written for each temperature node. Through mathematical elimination, this set of equations is finally integrated into a high-order, constant-coefficient, non-homogeneous differential equation concerning the temperature of a specific node.

[0052] In one possible implementation, step 103 specifically includes the following steps: Step 301: Equivalently represent the building heat dissipation process of heat users as a thermal network model composed of multiple thermal resistances and thermal capacities, wherein the thermal network model is set with nodes representing indoor air temperature, inner wall surface temperature, middle wall temperature and outer wall surface temperature respectively. Step 302: Based on the thermal network model, obtain the transient heat conduction differential equations for each node, and integrate the differential equations into a single-degree-of-freedom high-order constant-coefficient nonhomogeneous differential equation for the temperature nodes of the outer surface of the wall, so as to establish an analytical response model.

[0053] Specifically, the first step involves modeling the building's heat dissipation process as an equivalent thermal network composed of multiple thermal resistances and capacities. This thermal network model includes nodes representing indoor air temperature, the inner surface temperature of the wall, the temperature at the center of the wall, and the outer surface temperature of the wall. This method analogizes the complex heat dissipation process of a building envelope to an electrical network. (Refer to...) Figure 5 , Figure 5 This is a schematic diagram of a secondary network multi-node structure provided by the present invention. Figure 5 As shown, the primary network water supply temperature input is defined as the high-temperature boundary. The ambient temperature is at the low temperature boundary. Four key temperature nodes were set up in the network. T 1- T 4, of which, Indoor air temperature T air , Temperature of the inner surface of the wall T w,in , Temperature in the middle of the wall T w,mid , External surface temperature of the wall T w,out These nodes are connected by a series of thermal resistance and thermal capacitance elements. Among them, The equivalent thermal resistance of the heat exchange process. and These represent the convective heat transfer resistances of the inner and outer sides of the building envelope, respectively. This represents the thermal resistance of half of the building envelope. Meanwhile, Represents the total heat capacity of indoor air. These represent the total heat capacity of the building envelope, which is then distributed accordingly to the individual nodes. This step simplifies a continuous-medium heat transfer problem into a thermal network consisting of discrete nodes and components, which is easier to analyze mathematically.

[0054] Based on the established thermal network model, the next step is to obtain the transient heat conduction differential equations for each node based on the thermal network model, and then integrate the differential equations into a single-degree-of-freedom high-order constant-coefficient nonhomogeneous differential equation concerning the temperature nodes of the outer surface of the wall, in order to establish the analytical response model. First, the external node method is used to... T 1- T4. Write the heat balance equations for the four nodes to obtain the following set of transient heat conduction differential equations: Then, by using the elimination method, the temperature variable is... , , use It is expressed in terms of its derivatives. Through derivation, we can obtain... , , The expressions are as follows: Among them, let: The above formula can then be expressed as: in, τ 1= R 1 C 1. τ 2= R 2 C 2, r ij = R i / R j This holds true for i, j = 0, 1, 2, 3.

[0055] Finally, , , Substituting the expression into the first differential equation and rearranging it, we obtain a result containing only variables. The fourth-order nonhomogeneous differential equation with constant coefficients: make: The above formula can then be expressed as: This equation is the final analytical response model. Through the above derivation, a coupled system of differential equations was successfully transformed into a standard single-degree-of-freedom high-order ordinary differential equation, providing a direct mathematical object for subsequent analytical solutions, thereby avoiding complex numerical integration and ensuring the solution efficiency and accuracy of the model.

[0056] Step 104: Perform spectral decomposition on the primary water supply temperature to obtain the harmonic components as sinusoidal boundary conditions.

[0057] After constructing the analytical response model, explicit boundary conditions need to be provided for solving the model. The primary network water supply temperature, as a key heat source input driving the secondary network thermal response, typically exhibits complex periodic fluctuations over time. Directly substituting it as a time-varying function into the differential equation would make the solution process exceptionally complex. To transform these complex boundary conditions into a form easily handled by the analytical model, this embodiment of the invention employs a frequency domain analysis method.

[0058] In one specific embodiment, a step is performed to perform spectral decomposition on the primary network water supply temperature to obtain harmonic components as sinusoidal boundary conditions. Spectral decomposition here is a mathematical processing technique that decomposes a complex time-domain signal (such as the primary network water supply temperature curve) into a superposition of a series of simple sine waves with different frequencies, amplitudes, and phases. The harmonic components refer to each sinusoidal wave component obtained after decomposition, and these harmonic components collectively constitute the sinusoidal boundary conditions driving the analytical response model.

[0059] The specific implementation involves processing the time-series curve of the primary water supply temperature obtained from the aforementioned steps using mathematical tools such as the Fast Fourier Transform (FFT). This processing converts the temperature fluctuation signal in the time domain into a series of discrete harmonic components in the frequency domain. Each harmonic component can be represented as a standard sine function.

[0060] In one possible implementation, step 104 specifically includes the following steps: Step 401: Sample the time-series curve of the primary water supply temperature at equal intervals to obtain a time-series sequence containing multiple sampling points; Step 402: Perform a Fast Fourier Transform on the time series to extract a DC component and the amplitude and phase information of each harmonic component.

[0061] Specifically, the first step involves sampling the time-series curve of the primary water supply temperature at equal intervals to obtain a time-series sequence containing multiple sampling points. This step aims to discretize the continuous temperature curve for digital processing. For example, to finely characterize the fluctuation of the water supply temperature over a complete cycle (e.g., 24 hours), 96 sampling points at equal time intervals can be obtained from the time-series curve of the primary water supply temperature, thus forming a discrete time-series sequence containing 96 temperature values.

[0062] After obtaining the time series, the next step is to perform a Fast Fourier Transform (FFT) on the time series to extract a DC component and the amplitude and phase information of each harmonic component. The Fast Fourier Transform (FFT) is an efficient algorithm used to transform discrete signals in the time domain to the frequency domain. After performing this transform, the original temperature time series is decomposed into multiple frequency components. These frequency components collectively constitute the high-temperature boundary condition of the primary network water supply temperature. and low temperature boundary Its mathematical form can be represented as the superposition of multiple harmonics: ; In the formula, , The angular frequency and phase corresponding to the high-temperature boundary side. , These represent the angular frequency and phase corresponding to the low-temperature boundary side.

[0063] This transformation allows us to clearly extract a DC component representing the average temperature over the period from the frequency domain results. and And multiple harmonic components representing different frequency fluctuations. For each harmonic component, its corresponding amplitude can be extracted. , With phase information , .

[0064] It should be noted that, in the process of converting the time-domain signal into frequency-domain components using spectral decomposition, to ensure the accuracy of this conversion process and the reliability of the results obtained by subsequently using this frequency-domain information to drive the analytical model, this embodiment of the invention adds a verification step to the method. This step aims to verify whether the inverse conversion from the frequency domain to the time domain can accurately restore the original signal.

[0065] In one possible implementation, the method further includes the following steps: Step 501: Perform inverse fast Fourier transform on the amplitude and phase information of the DC component and each harmonic component to generate the reconstructed temperature curve; Step 502: Compare the reconstructed temperature curve with the time series to verify the fidelity of the spectral decomposition.

[0066] Specifically, the first step involves performing an inverse fast Fourier transform (IFFT) on the DC component and the amplitude and phase information of each harmonic component to generate a reconstructed temperature curve. The inverse fast Fourier transform (IFFT) here is a computational method that functions inversely to the fast Fourier transform (FFT), reconstructing the signal from the frequency domain back to the time domain. Specifically, the DC component extracted in the previous step, along with the amplitude and phase information of each harmonic component, is fed as input to an IFFT algorithm (e.g., implemented using NumPy's efficient FFT library). This algorithm synthesizes these frequency domain coefficients to generate a new reconstructed temperature curve represented in the time domain.

[0067] Next, the reconstructed temperature curve is compared with the time series to verify the fidelity of the spectral decomposition. Here, the time series refers to the discrete temperature point sequence obtained by sampling at equal intervals from the original primary water supply temperature curve before performing the FFT. The fidelity is used to measure the degree of consistency between the reconstructed temperature curve and the original time series. Specifically, the comparison is performed by plotting the reconstructed temperature curve and the original sampled curve on the same coordinate system, referring to… Figure 6 , Figure 6 This is a comparison chart of vectorized and FFT reconstructed primary network water supply temperature of the heat exchange station provided by this invention. Figure 6 As shown, the fidelity can be intuitively judged by observing the degree of agreement between the two curves. If the reconstructed curve is highly consistent with the original curve throughout the entire period, and the error between the two is much smaller than the preset accuracy threshold, it indicates that the spectral decomposition and inverse transform process has very high fidelity.

[0068] Step 105: Using the characteristic equation of the analytical response model and the superposition principle, and based on the sinusoidal boundary conditions, the harmonic superposition is performed to obtain the analytical solution temperature of the first node of the quadratic network.

[0069] After decomposing the primary network water supply temperature boundary conditions into a series of harmonic components, the previously established analytical response model needs to be solved to obtain the accurate temperature response of each node in the secondary network. Directly solving the high-order differential equations containing multiple harmonic inputs remains very difficult. Therefore, this embodiment of the invention utilizes linear system theory to provide an efficient and accurate solution strategy.

[0070] In a specific embodiment, the step involves using the characteristic equation of the analytical response model and the superposition principle, and performing harmonic superposition based on sinusoidal boundary conditions to obtain the analytical solution temperature of the first node of the quadratic network. Here, the characteristic equation refers to an algebraic equation derived from the homogeneous differential equation of the analytical response model, whose roots determine the transient decay characteristics of the system response. The superposition principle states that for a linear system, the total response produced by multiple inputs acting together is equal to the linear superposition of the responses produced by each input acting alone. This step utilizes this principle to decompose the problem of solving the response under complex boundary conditions into the problem of solving and summing the responses under multiple simple sinusoidal boundary conditions.

[0071] The specific implementation involves first solving the characteristic equation corresponding to the analytical response model to obtain a set of eigenvalues. These eigenvalues ​​are used to construct the general solution describing the transient behavior of the system. Next, for each harmonic component obtained in the previous step, the steady-state particular solution of its higher-order differential equation when used as a forcing term is solved. Finally, the transient general solution describing the system's own characteristics is superimposed with the steady-state particular solutions corresponding to all harmonic components to obtain a complete temperature solution expression containing undetermined constants. By substituting the initial temperature conditions of the system, all undetermined constants can be determined, ultimately obtaining the complete analytical solution temperature of the first node of the quadratic network.

[0072] In one possible implementation, step 105 specifically includes the following steps: Step 601: Solve the characteristic equation corresponding to the higher-order non-homogeneous differential equation with constant coefficients to obtain multiple characteristic roots, and construct the transient general solution of the analytical response model based on the multiple characteristic roots. The transient general solution is a linear combination of multiple exponentially decaying terms containing undetermined constants. Step 602: For each harmonic component, solve the higher-order constant-coefficient nonhomogeneous differential equation to obtain a steady-state particular solution; Step 603: Superimpose the transient general solution with the steady-state particular solutions corresponding to all harmonics to form the complete temperature solution expression for each node in the thermal circuit network model; Step 604: Substitute the initial temperature of each node in the thermal network model as the initial condition into the complete temperature solution expression to determine the undetermined constants and obtain the analytical solution temperature of the first node of the secondary network.

[0073] To efficiently obtain the accurate temperature response of each node in a quadratic network, this invention provides a specific method for analytically solving the aforementioned high-order non-homogeneous differential equation with constant coefficients. This method decomposes the complex solution process into a series of well-defined mathematical steps, thereby avoiding costly numerical integration.

[0074] Specifically, the process begins by solving the characteristic equation corresponding to the higher-order non-homogeneous differential equation with constant coefficients to obtain multiple characteristic roots. Then, based on these characteristic roots, a transient general solution for the analytical response model is constructed. The transient general solution is a linear combination of multiple exponentially decaying terms containing undetermined constants.

[0075] because This is a fourth-order nonhomogeneous differential equation with constant coefficients, containing a general solution and a particular solution, the particular solution being: The general solution is transformed into a homogeneous equation: The general solution should be in the form of: Will Substituting and simplifying, we get This is a quartic equation in one variable, also known as a characteristic root equation, which has four roots. μ i (i=1,2,3,4) is The solution is obtained by superimposing the general solution and the particular solution using the four characteristic roots: in is an undetermined constant.

[0076] Will Substitution , , From the expression, we can obtain the solutions for each temperature: when T h , T c When a sinusoidal change occurs, the step involves superimposing the transient general solution with the steady-state particular solutions corresponding to all harmonics to form the complete temperature solution expression for each node in the thermal network model. This step, based on the superposition principle of solutions to linear differential equations, linearly sums the general solution describing the transient behavior of the system with the particular solutions describing the system's response under all boundary condition forcings. For the temperature nodes on the outer surface of the wall... The complete temperature solution expression is in the form of: , , in T 4,s1 It is a steady-state term. T 4,s2 This is the general solution. T 4,c , T 41 , , The equilibrium value of the steady-state term, amplitude, angular frequency, and initial phase. (i=1-4) is a constant. Is with equation The root-consistent transient decay factor.

[0077] This patent studies the response at a fixed frequency, first assuming that the frequencies at the high and low temperature boundaries are all constant. , the formula ; , , , ,as well as Substitute into the formula In the middle, we get: in: in: The variables mentioned above are intermediate coefficients defined for simplified representation.

[0078] make: For the equation to always hold true, the following must be satisfied: Substituting the above equation into... , , as well as From the expression, we can obtain: Assumption T 1. T 2. T 3. T 4 in t The initial temperature at which = 0 is T 01 , T 02 , T 03 , T 04 Introducing initial conditions and substituting them into the above equation yields a formula regarding... c i A system of four linear equations in four variables (i=1,2,3,4,5): At this point, based on the four given initial values, the DC component of the sinusoidal boundary condition and the amplitude and phase of each harmonic are input: for the ambient temperature and the primary network water supply input, the magnitude and phase angle of their FFT results are extracted and converted into sinusoidal forced terms. Substituting these values ​​into the solved equations yields the temperature curves for each node. (Refer to...) Figure 7 , Figure 7 This is the return water temperature curve of the primary heat exchange station provided by the present invention.

[0079] Finally, the step of substituting the initial temperatures of each node in the thermal network model as initial conditions into the complete temperature solution expression is performed to determine the undetermined constants and obtain the analytical solution temperature of the first node of the quadratic network. The known initial temperatures of each node are then used as initial conditions. T 01 , T 02 , T 03 , T 04Substituting the values ​​into the complete temperature solution expression obtained in the previous step at time t=0 yields a system of four linear equations in four variables concerning the undetermined constant ci. Solving this system of equations uniquely determines the values ​​of all undetermined constants ci. Substituting the obtained constants back into the temperature solution expression yields the precise analytical solution temperature of the first node of the quadratic network (e.g., indoor air temperature T1) as a function of time.

[0080] By employing the method of superimposing characteristic equations and harmonics, the problem of solving a differential equation under a complex input is transformed into a combined problem of solving an algebraic equation and a series of differential equations for a standard sinusoidal input. This method is not only mathematically simpler but also accurately captures the amplitude attenuation and phase delay characteristics of the system under multi-frequency harmonic inputs. This step significantly improves the efficiency and accuracy of solving the dynamic response of the quadratic network.

[0081] Step 106: Based on the primary network supply water temperature and the analytical solution temperature of the first node of the secondary network, construct a calculation model for the primary network return water and CHP inlet temperature.

[0082] After calculating the primary network supply water temperature and the secondary network node temperatures, the return water temperature of the primary network needs to be solved to close the thermodynamic simulation loop of the entire heating network and ultimately obtain the inlet temperature of the heat source (CHP). The return water temperature of the primary network is determined by the outlet temperature of each heat exchange station, and the performance of the heat exchange station is simultaneously affected by the primary network supply water temperature and the secondary network heat load. Therefore, a model that couples these two calculation results must be established to accurately simulate the return water process.

[0083] In a specific embodiment, the step of constructing a calculation model for the primary network return water and CHP inlet temperature based on the primary network supply water temperature and the analytical solution temperature of the first node of the secondary network is performed. This calculation model for the primary network return water and CHP inlet temperature is a mathematical model used to describe the thermodynamic process on the primary network return water side. This model comprehensively utilizes the known primary network inlet temperature of the heat exchange station and the secondary network user-side temperature to first calculate the primary network outlet temperature of each heat exchange station, and then simulates the process of these return waters converging in the pipeline network and ultimately flowing back to CHP. (Refer to...) Figure 8 , Figure 8 This is a heat flow model diagram of the primary network return water section provided by the present invention.

[0084] When constructing this model, the first step is to establish a model describing the heat exchange process of a single heat exchange station. The return water temperature of the primary network at the heat exchange station... It can be determined by its water supply temperature The temperature drop is obtained by subtracting the heat transferred to the secondary network during the heat exchange process. The calculation formula is as follows: Among them, the heat flow rate of the primary network side of the heat exchange station The calculation requires the use of the primary network water supply temperature. and the temperature on the secondary network side ,Right now Temperature on the secondary network side With the first node of the secondary network (such as indoor air temperature) They are directly related, and their relationship can be expressed by the following formula: In the formula, G It is the heat capacity flow on the primary network side of the heat exchange station. R HES It is the thermal resistance of the heat exchange station. R h It is the thermal resistance of the heat sink.

[0085] Through this series of formulas, the calculation relationship from the primary network supply water temperature and secondary network node temperature to the primary network return water temperature of the heat exchange station is established. Subsequently, using the return water of each heat exchange station as input, a model describing the mixing, delay, and heat leakage of the return water in the pipeline is further established, ultimately forming a complete calculation model for the primary network return water and CHP inlet temperature.

[0086] This model successfully couples the calculation results of the primary water supply module and the secondary analytical response module. The model clearly defines the solution path from the upstream calculation results to the downstream return water temperature.

[0087] Step 107: Use the flow weight mixing and pipeline heat leakage delay propagation algorithm to solve the calculation model of primary network return water and CHP inlet temperature, and obtain the primary network return water temperature and CHP inlet temperature.

[0088] After constructing the calculation model for the primary return water and CHP inlet temperature, the model needs to be solved to obtain the temperature distribution of the entire return water network and ultimately determine the inlet temperature of the heat source. The return water network topology involves multiple branch convergences, and traditional solution methods struggle to efficiently handle this complex convergence and transmission process. Therefore, this invention provides a structured solution algorithm to achieve efficient and accurate calculation of the return water process.

[0089] In a specific embodiment, the process involves executing a flow-weighted mixing and pipeline heat leakage delay propagation algorithm to solve the primary network return water and CHP inlet temperature calculation model, thereby obtaining the primary network return water temperature and CHP inlet temperature. The flow-weighted mixing and pipeline heat leakage delay propagation algorithm is an iterative algorithm that calculates the temperature of each node and pipe segment along the return water network path. This algorithm integrates two core operations: first, at the return water confluence node, it calculates the mixed temperature using the flow-weighted mixing principle; second, in the return water pipeline, it calculates the heat leakage and delay effects during the water flow process.

[0090] In one possible implementation, step 107 specifically includes the following steps: Step 701: Using the primary network return water temperature of the terminal heat exchange station (which is a leaf node) as the initial input, calculate step by step from downstream to upstream along the return water network topology. Step 702: At the confluence node where multiple downstream branches converge, the return water temperatures from the multiple downstream branches are weighted and mixed according to the mass flow rates of each downstream branch to obtain the mixing temperature of the confluence node. Step 703: Use the mixing temperature as the inlet temperature of the pipe connecting the confluence node and a previous node, and calculate the outlet temperature of the pipe under the effects of heat leakage and delay. The outlet temperature is then used as the input for the return water temperature calculation of the previous node until the CHP inlet temperature is finally calculated.

[0091] Specifically, the solution process first uses the primary return water temperature of the terminal heat exchange station (a leaf node) as the initial input, and then performs calculations step by step from downstream to upstream along the return water network topology. Here, a leaf node refers to the heat exchange station at the very end of the return water topology, without any downstream branches. Since it has no downstream child nodes, its return water originates solely from the outlet temperature of its own heat exchanger; therefore, this temperature is directly used as the inlet temperature of its upstream return water section, without the need for mixing.

[0092] When the calculation proceeds up the pipeline topology to a confluence node where multiple downstream branches converge, the step involves weighting and mixing the return water temperatures from these downstream branches according to their respective mass flow rates to obtain the mixing temperature at the confluence node. This mixing process follows the law of conservation of energy, and the resulting mixing temperature... It can be calculated using the following formula: in, and These represent the two branches that merge into this node at time [time]. temperature, This refers to the mass flow rate of each section of the return water network. It is the mass flow rate on the primary heat network side of the heat exchange station.

[0093] After obtaining the mixing temperature at the manifold, the next step involves using this mixing temperature as the inlet temperature of the pipe connecting the manifold to a higher-level node, and calculating the outlet temperature of the pipe under the effects of heat leakage and delay. This outlet temperature is then used as input for calculating the return water temperature at the higher-level node, until the final CHP inlet temperature is obtained. This step uses a vectorized expression similar to that on the supply side to calculate the heat leakage and delay effects of the pipe. The mixing temperature... As the inlet temperature of the pipe, then during the delay time After that, the pipe outlet temperature It can be obtained from the following formula: The calculated outlet temperature will be used as input for the next higher-level node. The algorithm will repeatedly perform mixing and pipeline transport calculations, progressing upwards level by level until the return water finally reaches the heat source, thus calculating the CHP inlet temperature. The result format can be referenced. Figure 9 The smooth hysteresis curve shown is Figure 9 This is the CHP inlet temperature curve provided by the present invention. The algorithm decomposes the complex return water network calculation into a series of structured hybrid and vectorized advancement steps, avoiding multiple nested loops, and significantly improving the calculation efficiency of the entire return water process while ensuring accuracy.

[0094] Reference Figure 10 , Figure 10 This is a schematic diagram of the analytical solution system for heating pipe networks based on spectral decomposition provided by the present invention. The system includes: The first processing module is used to construct a primary network water supply matrix calculation model based on the heating network topology. The second processing module is used to solve the primary network water supply matrix operation model using a vectorized matrix operation method to obtain the primary network water supply temperature. The third processing module is used to construct an analytical response model based on the secondary network multi-node structure; The fourth processing module is used to perform spectral decomposition on the primary water supply temperature to obtain harmonic components as sinusoidal boundary conditions. The fifth processing module is used to obtain the analytical solution temperature of the first node of the quadratic network by utilizing the characteristic equation and superposition principle of the analytical response model and performing harmonic superposition according to the sinusoidal boundary conditions. The sixth processing module is used to construct a calculation model for the return water temperature of the primary network and the inlet temperature of CHP based on the analytical solution temperature of the primary network supply water temperature and the first node of the secondary network. The seventh processing module is used to solve the calculation model of the primary network return water and CHP inlet temperature by using the flow weight mixing and pipeline heat leakage delay propagation algorithm, so as to obtain the primary network return water temperature and CHP inlet temperature.

[0095] It should be noted that the heating network analytical solution system based on spectrum decomposition provided by the present invention can execute the heating network analytical solution method based on spectrum decomposition of any of the above embodiments during specific operation, which will not be elaborated in this embodiment.

[0096] Figure 11This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 11 As shown, the electronic device may include: a processor 1110, a communication interface 1120, a memory 1130, and a communication bus 1140, wherein the processor 1110, the communication interface 1120, and the memory 1130 communicate with each other through the communication bus 1140. The processor 1110 can call logic instructions in the memory 1130 to execute an analytical solution method for heating pipe networks based on spectrum decomposition. This method includes: constructing a primary network water supply matrix operation model based on the heating pipe network topology; solving the primary network water supply matrix operation model using a vectorized matrix operation method to obtain the primary network water supply temperature; constructing an analytical response model based on the secondary network multi-node structure; performing spectrum decomposition on the primary network water supply temperature to obtain harmonic components as sinusoidal boundary conditions; using the characteristic equation and superposition principle of the analytical response model, and performing harmonic superposition according to the sinusoidal boundary conditions, to obtain the analytical solution temperature of the first node of the secondary network; constructing a calculation model for the primary network return water and CHP inlet temperature based on the primary network water supply temperature and the analytical solution temperature of the first node of the secondary network; and solving the calculation model for the primary network return water and CHP inlet temperature using a flow weighted mixing and pipeline heat leakage delay propagation algorithm to obtain the primary network return water temperature and CHP inlet temperature.

[0097] Furthermore, the logical instructions in the aforementioned memory 1130 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0098] On the other hand, the present invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by a computer, the computer is able to execute the analytical solution method for heating pipe networks based on spectrum decomposition provided in the above embodiments.

[0099] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, is implemented to perform the analytical solution method for heating pipe networks based on spectrum decomposition provided in the above embodiments.

[0100] The system embodiments described above are merely illustrative. 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 the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0101] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of embodiments.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analytically solving heating network problems based on spectral decomposition, characterized in that, include: Based on the heating network topology, a primary network water supply matrix calculation model is constructed. The primary network water supply matrix operation model is solved using a vectorized matrix operation method to obtain the primary network water supply temperature. Based on the multi-node structure of the secondary network, an analytical response model is constructed. The primary water supply temperature is subjected to spectral decomposition to obtain the harmonic components as sinusoidal boundary conditions; Using the characteristic equation and superposition principle of the analytical response model, and based on the sinusoidal boundary conditions, harmonic superposition is performed to obtain the analytical solution temperature of the first node of the quadratic network; Based on the primary network water supply temperature and the analytical solution temperature of the first node of the secondary network, a calculation model for the primary network return water and CHP inlet temperature is constructed. The primary network return water temperature and CHP inlet temperature are obtained by solving the calculation model of the primary network return water temperature and CHP inlet temperature using the flow weight mixing and pipeline heat leakage delay propagation algorithm.

2. The analytical solution method for heating pipe networks based on spectral decomposition according to claim 1, characterized in that, The primary network water supply matrix calculation model based on the heating pipe network topology includes: Identify the pipe connections from the CHP outlet to the inlet of each heat exchange station from the heating network topology; Based on the pipeline connection relationship, the heat transfer process of each pipeline segment is characterized as a temperature transfer relationship that includes heat loss and flow delay, wherein the pipeline outlet temperature is jointly determined by the pipeline inlet temperature, ambient temperature, pipeline leakage thermal resistance, and flow delay time. By combining the temperature transfer relationships of all pipelines, the primary network water supply matrix operation model is obtained.

3. The analytical solution method for heating pipe networks based on spectral decomposition according to claim 1, characterized in that, The analytical response model constructed based on the secondary network multi-node structure includes: The building heat dissipation process of heat users is equivalent to a thermal circuit network model composed of multiple thermal resistances and thermal capacities. The thermal circuit network model is provided with nodes that represent indoor air temperature, inner wall surface temperature, middle wall temperature and outer wall surface temperature respectively. Based on the thermal network model, the transient heat conduction differential equations of each node are obtained, and the differential equations are integrated into a single-degree-of-freedom high-order constant-coefficient non-homogeneous differential equation with respect to the temperature node of the outer surface of the wall, so as to establish the analytical response model.

4. The analytical solution method for heating pipe networks based on spectral decomposition according to claim 1, characterized in that, The calculation model for the primary network return water and CHP inlet temperature is solved using the flow weight mixing and pipeline heat leakage delay propagation algorithm, resulting in the primary network return water temperature and CHP inlet temperature, including: The primary return water temperature of the terminal heat exchange station, which is a leaf node, is used as the initial input, and the calculation is performed step by step from downstream to upstream along the return water network topology. At a confluence node where multiple downstream branches converge, the return water temperatures from the multiple downstream branches are weighted and mixed according to the mass flow rates of each of the multiple downstream branches to obtain the mixing temperature of the confluence node. The mixing temperature is used as the inlet temperature of the pipe connecting the manifold node to a higher-level node, and the outlet temperature of the pipe under the effects of heat leakage and delay is calculated. The outlet temperature is then used as the input for the return water temperature calculation of the higher-level node until the CHP inlet temperature is finally calculated.

5. The analytical solution method for heating pipe networks based on spectral decomposition according to claim 3, characterized in that, The method of obtaining the analytical solution temperature of the first node of the quadratic network by utilizing the characteristic equation and superposition principle of the analytical response model, and performing harmonic superposition according to the sinusoidal boundary conditions, includes: Solve the characteristic equation corresponding to the higher-order constant coefficient non-homogeneous differential equation to obtain multiple characteristic roots, and construct the transient general solution of the analytical response model based on the multiple characteristic roots. The transient general solution is a linear combination of multiple exponentially decaying terms containing undetermined constants. For each harmonic component, solve the higher-order constant-coefficient nonhomogeneous differential equation to obtain a steady-state particular solution; The transient general solution is superimposed with the steady-state particular solutions corresponding to all harmonics to form the complete temperature solution expression for each node in the thermal circuit network model; The initial temperatures of each node in the thermal network model are used as initial conditions and substituted into the complete temperature solution expression to determine the undetermined constants, thereby obtaining the analytical solution temperature of the first node of the secondary network.

6. The analytical solution method for heating pipe networks based on spectral decomposition according to claim 1, characterized in that, The spectral decomposition of the primary water supply temperature includes: The time-series curve of the primary water supply temperature is sampled at equal intervals to obtain a time-series sequence containing multiple sampling points; A fast Fourier transform is performed on the time series to extract a DC component and the amplitude and phase information of each of the harmonic components.

7. The analytical solution method for heating pipe networks based on spectral decomposition according to claim 6, characterized in that, Also includes: Perform an inverse fast Fourier transform on the amplitude and phase information of the DC component and each of the harmonic components to generate a reconstructed temperature curve; The reconstructed temperature curve is compared with the time series to verify the fidelity of the spectral decomposition.

8. A system for analytically solving heating network problems based on spectral decomposition, characterized in that, include: The first processing module is used to construct a primary network water supply matrix calculation model based on the heating network topology. The second processing module is used to solve the primary network water supply matrix operation model using a vectorized matrix operation method to obtain the primary network water supply temperature. The third processing module is used to construct an analytical response model based on the secondary network multi-node structure; The fourth processing module is used to perform spectral decomposition on the primary water supply temperature to obtain harmonic components as sinusoidal boundary conditions. The fifth processing module is used to obtain the analytical solution temperature of the first node of the quadratic network by utilizing the characteristic equation and superposition principle of the analytical response model and performing harmonic superposition according to the sinusoidal boundary conditions. The sixth processing module is used to construct a calculation model for the return water temperature of the primary network and the inlet temperature of CHP based on the analytical solution temperature of the primary network supply water temperature and the first node of the secondary network. The seventh processing module is used to solve the calculation model of the primary network return water and CHP inlet temperature by using the flow weight mixing and pipeline heat leakage delay propagation algorithm, so as to obtain the primary network return water temperature and CHP inlet temperature.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the analytical solution method for heating pipe networks based on spectral decomposition as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the analytical solution method for heating pipe networks based on spectral decomposition as described in any one of claims 1 to 7.

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