CN114021490A - A dynamic full analysis method for hot water network - Google Patents

A dynamic full analysis method for hot water network Download PDF

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CN114021490A
CN114021490A CN202111241203.6A CN202111241203A CN114021490A CN 114021490 A CN114021490 A CN 114021490A CN 202111241203 A CN202111241203 A CN 202111241203A CN 114021490 A CN114021490 A CN 114021490A
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顾伟
张苏涵
陆海
俞睿智
陆帅
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Abstract

本发明公开了一种热水网络动态全解析方法，属于能源系统建模与运行分析领域，包括以下步骤：10)根据热力学第一定律和热传导定律建立热水网络的动态模型，进一步建立以环境温度为基准值的热水网络动态等值模型；20)以空间轴为特征线，推导热水网络动态等值模型中由初始条件决定的温度解析式；30)以时间轴为特征线，推导热水网络动态等值模型中由边界条件决定的温度解析式；40)根据热水网络等值模型的可叠加特性，建立热水网络动态全解析模型。本发明直接建立了热水网络动态模型的解析解，相较于基于离散化的数值方法，避免了近似误差与数值色散耗散；在求解中避免了离散过程，提高了热水网络模型的计算效率与求解精度。

Figure 202111241203

The invention discloses a dynamic full analysis method for a hot water network, which belongs to the field of energy system modeling and operation analysis. 20) Taking the space axis as the characteristic line, deduce the temperature analytical formula determined by the initial conditions in the dynamic equivalent model of the hot water network; 30) Taking the time axis as the characteristic line, deduce The temperature analytical formula determined by the boundary conditions in the hot water network dynamic equivalent model; 40) According to the superimposed characteristics of the hot water network equivalent model, a dynamic full analytical model of the hot water network is established. The present invention directly establishes the analytical solution of the dynamic model of the hot water network, and compared with the numerical method based on discretization, the approximation error and numerical dispersion dissipation are avoided; the discrete process is avoided in the solution, and the calculation of the hot water network model is improved. Efficiency and solution accuracy.

Figure 202111241203

Description

Dynamic full-analysis method for hot water network
Technical Field
The invention belongs to the field of energy system modeling and operation analysis, and particularly relates to a dynamic full-analysis method for a hot water network.
Background
The gradual increase of energy consumption and environmental pressure promote the change of low-carbon green energy network technology, and cities serve as main bodies of energy consumption and change, and forward multi-energy-flow and multi-dynamic complex energy networks are changed. The centralized heat supply power system serves as an important component of the urban energy network, and the comprehensive utilization efficiency of the energy system and the consumption capacity of renewable energy can be remarkably improved through interconnection and intercommunication and energy optimization management of the centralized heat supply power system, the power system and the natural gas system. The time scales of operation and management of different energy networks are greatly different, real-time, reliable and consistent network information needs to be acquired based on an accurate simulation model and technology, however, as the multi-energy network belongs to management and operation of different companies, interactive information is very limited, and attention needs to be paid to information protection in the process of joint simulation and operation optimization.
The simulation calculation of the heat supply pipe network is essentially to define a group of state variables to describe the key characteristics of the system, and then to analyze the system mechanism to obtain the change process of all the state variables under given excitation. Because the heat supply pipe network model is a group of nonlinear partial differential equations, the existing mainstream method is to differentiate the pipe model by space-time segmentation, and to perform recursive calculation on the state distribution in the system according to boundary conditions and initial conditions. However, to ensure the computational efficiency, the number of segments required on each pipeline is generally large, so that the whole recursion process is low in computational efficiency, and it is difficult to visually and quantitatively characterize the response degree of the state quantity in the thermodynamic system to the external excitation.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method is based on a dynamic equivalent model of the hot water network, and models an initial condition action component taking a spatial axis as a characteristic line and a boundary condition action component taking a time axis as the characteristic line respectively so as to obtain the dynamic full analytic model of the hot water network. And a model basis is provided for the operation analysis of the electric heating comprehensive energy system.
In order to solve the technical problem, the technical scheme adopts a dynamic full-analysis method of the hot water network, and the establishment of the model comprises the following steps:
step 10) establishing a dynamic model of the hot water network according to a first law of thermodynamics and a heat conduction law, and further establishing a dynamic equivalent model of the hot water network with the environmental temperature as a reference value;
step 20) deducing a temperature analytic expression determined by initial conditions in the dynamic equivalent model of the hot water network by taking the spatial axis as a characteristic line;
step 30) deriving a temperature analytic expression determined by boundary conditions in the dynamic equivalent model of the hot water network by taking a time axis as a characteristic line;
and step 40) establishing a dynamic full-analytic model of the hot water network according to the superposable characteristics of the equivalent model of the hot water network.
As a further introduction of the present invention, the step 10) specifically includes:
step 101) enabling the fluid to flow in the pipeline in a one-dimensional mode, enabling fluid parameters in the pipeline to be uniformly distributed in the whole cross section, and not counting axial heat loss. Establishing a conservation equation of hot water flowing in a pipe network according to a first thermodynamic law:
Figure RE-GDA0003455198650000021
in the formula, dx represents the infinitesimal length in the pipe, QxRepresenting heat through the conduit infinitesimal dx, h (x) and h (x + dx) being heat of the transverse input and output infinitesimal dx, dQlThe radial heat loss of the infinitesimal dx is shown, T' is the absolute temperature of the flowing working medium, and x is a space variable;
and 102) establishing a dynamic model analytic expression of the hot water network according to the Taylor approximate expansion. In heat transfer in a pipe, the heat per unit time passing through a given cross section is proportional to the rate of change of temperature and the cross sectional area in the direction perpendicular to the interface, as shown in equation (2),
Figure RE-GDA0003455198650000022
in the formula, maMass of working medium being infinitesimal dx, hsIs the specific enthalpy, t is the time variable. The rate of change of enthalpy with length at the infinitesimal dx can be obtained by the taylor expansion formula:
Figure RE-GDA0003455198650000023
the radial heat loss formula is shown in formula (4).
Figure RE-GDA0003455198650000024
In the formula, TaIs the ambient temperature, c is the specific heat capacity of the working medium, lambdahIs the thermal resistance of the pipeline, S is the sectional area of the pipeline, and is the density of the working medium. Mass m of infinitesimal dxaSpecific enthalpy hsAnd the calculation formulas of the enthalpy h are respectively shown as formulas (5) to (7),
ma＝ρSdx (5)
hs＝cT' (6)
h(x)＝mhs＝cmT' (7)
substituting the formulas (2) to (7) into the formula (1), and substituting the formula (8) to obtain a dynamic model describing the temperature distribution of the hot water network pipeline, as shown in the formula (9), wherein v is the working medium flow rate and gamma iswCoefficient of heat transfer in radial direction of working medium
m＝vρS (8)
Figure RE-GDA0003455198650000031
And 103) constructing a dynamic equivalent model of the hot water network by taking the ambient temperature as a reference value. The relative temperature of the working fluid is defined as:
T＝T'-Ta (10)
the second order term of the internal heat transfer of the water flow is reflected on the right side of the medium sign in the neglected formula (9), and the formula (10) is taken into the formula (9), so that the following can be obtained:
Figure RE-GDA0003455198650000032
as a further introduction of the present invention, the step 20) specifically includes:
step 201) constructs a fully differential version of the relative temperature T with respect to the time vector T, resulting in a characteristic line equation for the initial condition. The full differential of the relative temperature with respect to time t can be expressed as:
Figure RE-GDA0003455198650000033
comparing equation (12) with equation (11), a characteristic line equation with respect to the initial condition can be obtained as shown in equation (13), where C1Is an arbitrary constant, determined by initial conditions,
x(t)＝vt+C1 (13)
step 202) converting the original partial differential equation into a local ordinary differential equation about the initial condition according to the characteristic line equation, which can be expressed as:
Figure RE-GDA0003455198650000034
in the formula, T0(x) Is the initial condition of the temperature profile of the pipeline. Solving equation (14) yields:
Figure RE-GDA0003455198650000035
as a further introduction of the present invention, the step 30) specifically includes:
step 301) constructs a fully differential form of the relative temperature T with respect to the space vector x, resulting in a characteristic line equation for the initial condition, the fully differential of the relative temperature with respect to time x can be expressed as:
Figure RE-GDA0003455198650000041
comparing equation (16) with equation (11), a characteristic line equation with respect to the boundary condition can be obtained, as shown in equation (17), where C2Is an arbitrary constant, determined by initial conditions,
Figure RE-GDA0003455198650000042
step 302) converting the original partial differential equation into a local ordinary differential equation related to the boundary condition according to the characteristic line equation, which can be expressed as:
Figure RE-GDA0003455198650000043
in the formula, T0(x) For the initial conditions of the pipeline temperature profile, solving equation (18) yields:
Figure RE-GDA0003455198650000044
as a further introduction of the present invention, the step 40) specifically includes:
step 401) the solution of the dynamic model of the hot water network depends on both a set of initial conditions and boundary conditions, which can be expressed as:
Figure RE-GDA0003455198650000045
step 402), according to the formula (21) and the formula (22), the equivalent model of the hot water network has certain superposition characteristics,
Figure RE-GDA0003455198650000046
Figure RE-GDA0003455198650000047
defining delta (t) as a step function, and combining the formula (15) and the formula (19), a dynamic full-analytic model of the hot water network can be established, as shown in the formula (23).
Figure RE-GDA0003455198650000051
Advantageous effects
Compared with the prior art, the invention has the following beneficial effects: the method directly establishes an analytic solution of the hot water network dynamic model, and completely avoids approximation errors, numerical dispersion and dissipation compared with the traditional numerical method based on discretization; meanwhile, the discrete process is avoided in the solving process, and the calculation efficiency and the solving precision of the hot water network model are greatly improved.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention;
FIG. 2 is a block diagram of a thermodynamic system employed in an embodiment of the present invention;
FIG. 3 is a comparison of an analytical model and a conventional numerical model in accordance with an embodiment of the present invention;
Detailed Description
The technical solution of the embodiment of the present invention is further described below with reference to examples and drawings.
Taking the system shown in fig. 2 as an example, the system has 51 nodes, which include 1 heat source node and 25 heat load nodes, the transmission process from the heat source to each heat load is unique, the initial conditions are distributed in each pipeline in the system, and the boundary conditions are distributed on the heat source side.
As shown in fig. 1, an embodiment of the present invention provides a method for dynamically analyzing a hot water network, including the following steps:
step 10) establishing a dynamic model of the hot water network according to a first law of thermodynamics and a heat conduction law, and further establishing a dynamic equivalent model of the hot water network with the environmental temperature as a reference value;
step 20) deducing a temperature analytic expression determined by initial conditions in the dynamic equivalent model of the hot water network by taking the spatial axis as a characteristic line;
step 30) deriving a temperature analytic expression determined by boundary conditions in the dynamic equivalent model of the hot water network by taking a time axis as a characteristic line;
and step 40) establishing a dynamic full-analytic model of the hot water network according to the superposable characteristics of the equivalent model of the hot water network.
In the above embodiment, the step 10) specifically includes:
step 101) enabling the fluid to flow in the pipeline in a one-dimensional mode, enabling fluid parameters in the pipeline to be uniformly distributed in the whole cross section, and not counting axial heat loss. Establishing a conservation equation of hot water flowing in a pipe network according to a first thermodynamic law:
Figure RE-GDA0003455198650000052
in the formula, dx represents the infinitesimal length in the pipe, QxRepresenting heat through the conduit infinitesimal dx, h (x) and h (x + dx) being heat of the transverse input and output infinitesimal dx, dQlT' is the absolute temperature of the flowing working medium, and x is a space variable.
And 102) establishing a dynamic model analytic expression of the hot water network according to the Taylor approximate expansion. In heat transfer through a pipe, the amount of heat per unit time passing through a given cross-section is directly proportional to the rate of change of temperature and the cross-sectional area in the direction perpendicular to the interface, as shown in equation (2).
Figure RE-GDA0003455198650000061
In the formula, maMass of working medium being infinitesimal dx, hsIs the specific enthalpy, t is the time variable. The variation rate of enthalpy at the infinitesimal dx along with the length is generalThe equation of Taylor expansion yields:
Figure RE-GDA0003455198650000062
the radial heat loss formula is shown in formula (4).
Figure RE-GDA0003455198650000063
In the formula, TaIs the ambient temperature, c is the specific heat capacity of the working medium, lambdahIs the thermal resistance of the pipeline, S is the sectional area of the pipeline, and is the density of the working medium. Mass m of infinitesimal dxaSpecific enthalpy hsAnd the calculation formulas of the enthalpy h are respectively shown as formulas (5) to (7).
ma＝ρSdx (5)
hs＝cT' (6)
h(x)＝mhs＝cmT' (7)
Substituting the formulas (2) to (7) into the formula (1), and substituting the formula (8) to obtain a dynamic model describing the temperature distribution of the hot water network pipeline, as shown in the formula (9), wherein v is the working medium flow rate and gamma iswCoefficient of heat transfer in radial direction of working medium
m＝vρS (8)
Figure RE-GDA0003455198650000064
And 103) constructing a dynamic equivalent model of the hot water network by taking the ambient temperature as a reference value. The relative temperature of the working fluid is defined as:
T＝T'-Ta (10)
the second order term of the internal heat transfer of the water flow is reflected on the right side of the medium sign in the neglected formula (9), and the formula (10) is taken into the formula (9), so that the following can be obtained:
Figure RE-GDA0003455198650000071
in the above embodiment, the step 20) specifically includes:
step 201) constructs a fully differential version of the relative temperature T with respect to the time vector T, resulting in a characteristic line equation for the initial condition. The full differential of the relative temperature with respect to time t can be expressed as:
Figure RE-GDA0003455198650000072
comparing equation (12) with equation (11), a characteristic line equation with respect to the initial condition can be obtained as shown in equation (13), where C1Is an arbitrary constant, determined by initial conditions.
x(t)＝vt+C1 (13)
Step 202) converting the original partial differential equation into a local ordinary differential equation about the initial condition according to the characteristic line equation, which can be expressed as:
Figure RE-GDA0003455198650000073
in the formula, T0(x) Is the initial condition of the temperature profile of the pipeline. Solving equation (14) yields:
Figure RE-GDA0003455198650000074
in the above embodiment, the step 30) specifically includes:
step 301) constructs a fully differential form of the relative temperature T with respect to the space vector x, resulting in a characteristic line equation for the initial condition. The full differential of the relative temperature with respect to time x can be expressed as:
Figure RE-GDA0003455198650000075
comparing equation (16) with equation (11), a characteristic line equation with respect to the boundary condition can be obtained, as shown in equation (17), where C2Is an arbitrary constantDepending on the initial conditions.
Figure RE-GDA0003455198650000076
Step 302) converting the original partial differential equation into a local ordinary differential equation related to the boundary condition according to the characteristic line equation, which can be expressed as:
Figure RE-GDA0003455198650000081
in the formula, T0(x) Is the initial condition of the temperature profile of the pipeline. Solving equation (18) yields:
Figure RE-GDA0003455198650000082
in the above embodiment, the step 40) specifically includes:
step 401) the solution of the dynamic model of the hot water network depends on both a set of initial conditions and boundary conditions, which can be expressed as:
Figure RE-GDA0003455198650000083
and step 402), according to the formula (21) and the formula (22), the equivalent model of the hot water network has certain superposition characteristics.
Figure RE-GDA0003455198650000084
Figure RE-GDA0003455198650000085
Defining delta (t) as a step function, and combining the formula (15) and the formula (19), a dynamic full-analytic model of the hot water network can be established, as shown in the formula (23).
Figure RE-GDA0003455198650000086
The temperature method determined by the method is compared with the conventional numerical method (node method, finite element method) for the node 51 in the system shown in fig. 2, as shown in fig. 3.
It will be appreciated by those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the spirit and scope of the invention, and any equivalents thereto, such as those skilled in the art, are intended to be embraced therein.

Claims (5)

1.一种热水网络动态全解析方法，其特征在于，该方法包括以下步骤：1. a hot water network dynamic full analysis method, is characterized in that, the method comprises the following steps: 步骤10)根据热力学第一定律和热传导定律建立热水网络的动态模型，进一步建立以环境温度为基准值的热水网络动态等值模型；Step 10) establish a dynamic model of the hot water network according to the first law of thermodynamics and the law of heat conduction, and further establish a dynamic equivalent model of the hot water network with the ambient temperature as the reference value; 步骤20)以空间轴为特征线，推导热水网络动态等值模型中由初始条件决定的温度解析式；Step 20) take the space axis as the characteristic line, deduce the temperature analytical formula determined by the initial condition in the dynamic equivalent model of the thermal water network; 步骤30)以时间轴为特征线，推导热水网络动态等值模型中由边界条件决定的温度解析式；Step 30) take the time axis as the characteristic line, deduce the temperature analytical formula determined by the boundary condition in the dynamic equivalent model of the thermal water network; 步骤40)根据热水网络等值模型的可叠加特性，建立热水网络动态全解析模型。Step 40) According to the superimposable characteristics of the equivalent model of the hot water network, a dynamic full analytical model of the hot water network is established. 2.根据权利要求1所述的一种热水网络动态全解析方法，其特征在于，所述步骤10)具体包括以下步骤：2. a kind of hot water network dynamic full analysis method according to claim 1, is characterized in that, described step 10) specifically comprises the following steps: 步骤101)将流体在管道内的流动设定为一维流动，管道内流体参数在整个截面均匀分布，不计轴向的热损失，根据热力学第一定律建立热水在管网中流动的守恒方程；Step 101) Set the flow of the fluid in the pipeline as one-dimensional flow, the fluid parameters in the pipeline are evenly distributed in the entire section, ignoring the axial heat loss, and establish a conservation equation for the flow of hot water in the pipeline network according to the first law of thermodynamics ;
Figure RE-FDA0003455198640000011
Figure RE-FDA0003455198640000011
 式中，dx表示管道内的微元长度，Qx表示通过管道微元dx的热量，h(x)和h(x+dx)为横向输入和输出微元dx的热量，dQl为微元dx的径向热量损失，T'为流动工质的绝对温度，x为空间变量；In the formula, dx represents the length of the micro-element in the pipeline, Q x represents the heat passing through the micro-element dx in the pipeline, h(x) and h(x+dx) are the heat of the lateral input and output micro-element dx, and dQ l is the micro-element The radial heat loss of dx, T' is the absolute temperature of the flowing working medium, and x is the spatial variable; 步骤102)根据泰勒近似展开式，建立热水网络动态模型解析式；Step 102) according to Taylor approximate expansion formula, establish hot water network dynamic model analytical formula; 在管道传热中，单位时间内通过给定截面的热量，正比例于垂直于该界面方向上的温度变化率和横截面积，如式(2)所示，In pipe heat transfer, the heat passing through a given section in unit time is proportional to the temperature change rate and cross-sectional area perpendicular to the interface direction, as shown in formula (2),
Figure RE-FDA0003455198640000012
Figure RE-FDA0003455198640000012
 式中，ma为微元dx的工质的质量，hs为比焓，t为时间变量，微元dx处的焓随长度变化率可通过泰勒展开公式得到：In the formula, m a is the mass of the working fluid of the micro-element dx, h s is the specific enthalpy, t is the time variable, and the rate of change of the enthalpy at the micro-element dx with the length can be obtained by the Taylor expansion formula:
Figure RE-FDA0003455198640000013
Figure RE-FDA0003455198640000013
 径向热量损失公式如式(4)所示：The radial heat loss formula is shown in formula (4):
Figure RE-FDA0003455198640000014
Figure RE-FDA0003455198640000014
 式中，Ta为环境温度，c为工质的比热容，λh为管道热阻，S为管道的截面积，为工质密度，微元dx的质量ma、比焓hs、和焓h的计算公式分别如式(5)至式(7)所示，In the formula, T a is the ambient temperature, c is the specific heat capacity of the working medium, λ h is the thermal resistance of the pipe, S is the cross-sectional area of the pipe, and is the density of the working medium, the mass m a , the specific enthalpy h s , and the enthalpy of the microelement dx The calculation formulas of h are shown in equations (5) to (7), respectively, ma＝ρSdx (5)m a = ρSdx (5) hs＝cT' (6)h s = cT' (6) h(x)＝mhs＝cmT' (7)h(x)= mhs =cmT' (7) 将式(2)至式(7)代入式(1)中，并将式(8)代入，可得到描述热水网络管道温度分布的动态模型，如式(9)所示，其中，v为工质流速，γw为工质径向的热传导系数；Substituting equations (2) to (7) into equation (1), and substituting equation (8) into equation (8), a dynamic model describing the temperature distribution of hot water network pipes can be obtained, as shown in equation (9), where v is Working fluid flow rate, γ w is the thermal conductivity coefficient of working fluid in radial direction; m＝vρS (8)m=vρS (8)
Figure RE-FDA0003455198640000021
Figure RE-FDA0003455198640000021
 步骤103)以环境温度为基准值，构建热水网络的动态等值模型；Step 103) taking the ambient temperature as the reference value, constructing a dynamic equivalent model of the hot water network; 定义工质的相对温度为：The relative temperature of the working fluid is defined as: T＝T'-Ta (10)T=T'-T a (10) 忽略式(9)中等号右侧反映水流内部传热的二阶项，并将式(10)带入式(9)，可得到：Ignoring the second-order term on the right side of the equal sign in equation (9) that reflects the internal heat transfer of the water flow, and substituting equation (10) into equation (9), we can get:
Figure RE-FDA0003455198640000022
Figure RE-FDA0003455198640000022
 3.根据权利要求2所述的一种热水网络动态全解析方法，其特征在于，所述步骤20)具体包括以下步骤：3. a kind of hot water network dynamic full analysis method according to claim 2, is characterized in that, described step 20) specifically comprises the following steps: 步骤201)构建相对温度T关于时间向量t的全微分形式，从而得到关于初始条件的特征线方程；Step 201) constructing the total differential form of the relative temperature T with respect to the time vector t, thereby obtaining the characteristic line equation about the initial condition; 相对温度关于时间t的全微分可表示为：The total differential of relative temperature with respect to time t can be expressed as:
Figure RE-FDA0003455198640000023
Figure RE-FDA0003455198640000023
 对比式(12)和式(11)，可得到关于初始条件的特征线方程，如式(13)所示，其中，C1为任意常数，由初始条件决定，Comparing Equation (12) and Equation (11), the characteristic line equation about the initial conditions can be obtained, as shown in Equation (13), where C 1 is an arbitrary constant, determined by the initial conditions, x(t)＝vt+C1 (13)x(t)=vt+C 1 (13) 步骤202)根据特征线方程，将原始偏微分方程转换为局部的关于初始条件的常微分方程，可表示为：Step 202) According to the characteristic line equation, the original partial differential equation is converted into a local ordinary differential equation with respect to the initial conditions, which can be expressed as:
Figure RE-FDA0003455198640000031
Figure RE-FDA0003455198640000031
 式中，T0(x)为管道温度分布的初始条件，求解式(14)可得：In the formula, T 0 (x) is the initial condition of the temperature distribution of the pipeline, and by solving the formula (14), we can get:
Figure RE-FDA0003455198640000032
Figure RE-FDA0003455198640000032
 4.根据权利要求3所述的一种热水网络动态全解析方法，其特征在于，所述步骤30)具体包括以下步骤：4. a kind of hot water network dynamic full analysis method according to claim 3, is characterized in that, described step 30) specifically comprises the following steps: 步骤301)构建相对温度T关于空间向量x的全微分形式，从而得到关于初始条件的特征线方程；Step 301) construct the total differential form of the relative temperature T with respect to the space vector x, thereby obtaining the characteristic line equation about the initial condition; 相对温度关于时间x的全微分可表示为：The total differential of relative temperature with respect to time x can be expressed as:
Figure RE-FDA0003455198640000033
Figure RE-FDA0003455198640000033
 对比式(16)和式(11)，可得到关于边界条件的特征线方程，如式(17)所示，其中，C2为任意常数，由初始条件决定；Comparing Equation (16) and Equation (11), the characteristic line equation about the boundary conditions can be obtained, as shown in Equation (17), where C 2 is an arbitrary constant, determined by the initial conditions;
Figure RE-FDA0003455198640000034
Figure RE-FDA0003455198640000034
 步骤302)根据特征线方程，将原始偏微分方程转换为局部的关于边界条件的常微分方程；可表示为：Step 302) According to the characteristic line equation, the original partial differential equation is converted into a local ordinary differential equation about boundary conditions; it can be expressed as:
Figure RE-FDA0003455198640000035
Figure RE-FDA0003455198640000035
 式中，T0(x)为管道温度分布的初始条件，求解式(18)可得：In the formula, T 0 (x) is the initial condition of the temperature distribution of the pipeline, and by solving the formula (18), it can be obtained:
Figure RE-FDA0003455198640000036
Figure RE-FDA0003455198640000036
 5.根据权利要求3所述的一种热水网络动态全解析方法，其特征在于，所述步骤40)具体包括以下步骤：5. a kind of hot water network dynamic full analysis method according to claim 3, is characterized in that, described step 40) specifically comprises the following steps: 步骤401)热水网络动态模型的求解同时依赖于一组初始条件和边界条件，可表示为：Step 401) The solution of the dynamic model of the hot water network depends on a set of initial conditions and boundary conditions at the same time, which can be expressed as:
Figure RE-FDA0003455198640000037
Figure RE-FDA0003455198640000037
 步骤402)根据式(21)和式(22)，可知热水网络等值模型具有一定的叠加特性，Step 402) According to formula (21) and formula (22), it can be known that the equivalent model of the hot water network has certain superposition characteristics,
Figure RE-FDA0003455198640000041
Figure RE-FDA0003455198640000041
Figure RE-FDA0003455198640000042
Figure RE-FDA0003455198640000042
 定义δ(t)为阶跃函数，结合式(15)和式(19)，可建立热水网络动态全解析模型，如式(23)所示，Defining δ(t) as a step function, combined with Equation (15) and Equation (19), the dynamic full analytical model of the hot water network can be established, as shown in Equation (23),
Figure RE-FDA0003455198640000043
Figure RE-FDA0003455198640000043
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115906587A (en) * 2022-12-28 2023-04-04 南京聚润信息科技有限公司 Method for establishing dynamic coupling model of heat supply pipe network of comprehensive energy system

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112257279A (en) * 2020-10-28 2021-01-22 东南大学 Method for constructing feasible domain of electric heating comprehensive energy system
CN113486532A (en) * 2021-07-22 2021-10-08 东南大学 Dynamic safety control method for electric heating comprehensive energy system

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112257279A (en) * 2020-10-28 2021-01-22 东南大学 Method for constructing feasible domain of electric heating comprehensive energy system
CN113486532A (en) * 2021-07-22 2021-10-08 东南大学 Dynamic safety control method for electric heating comprehensive energy system

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
姜瑛;: "管网系统动态仿真数学模型的建立及求解", 石油天然气学报, no. 02, 15 April 2010 (2010-04-15) *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115906587A (en) * 2022-12-28 2023-04-04 南京聚润信息科技有限公司 Method for establishing dynamic coupling model of heat supply pipe network of comprehensive energy system
CN115906587B (en) * 2022-12-28 2024-02-20 南京聚润信息科技有限公司 Method for establishing dynamic coupling model of heat supply pipe network of comprehensive energy system

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