CN114021490A - Dynamic full-analysis method for hot water network - Google Patents

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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Southeast University
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Abstract

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 and comprises the following steps: 10) establishing a dynamic model of the hot water network according to a first law of thermodynamics and a law of heat conduction, and further establishing a dynamic equivalent model of the hot water network with the ambient temperature as a reference value; 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; 30) deducing 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; 40) and 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. The invention directly establishes the analytical solution of the hot water network dynamic model, and avoids approximation error and numerical dispersion dissipation compared with a numerical method based on discretization; in the solving process, a discrete process is avoided, and the calculation efficiency and the solving precision of the hot water network model are improved.

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. A dynamic full analysis method for a hot water network is characterized by comprising 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.
2. The dynamic full analysis method for the hot water network according to claim 1, wherein the step 10) specifically comprises the following steps:
step 101) setting the flow of fluid in a pipeline as one-dimensional flow, wherein fluid parameters in the pipeline are uniformly distributed in the whole cross section, axial heat loss is not counted, and a conservation equation of hot water flowing in a pipe network is established according to a first thermodynamic law;
Figure RE-FDA0003455198640000011
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;
step 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-FDA0003455198640000012
in the formula, maMass of working medium being infinitesimal dx, hsThe specific enthalpy, t is a time variable, and the change rate of the enthalpy at the infinitesimal dx along with the length can be obtained by a Taylor expansion formula:
Figure RE-FDA0003455198640000013
the radial heat loss formula is shown in equation (4):
Figure RE-FDA0003455198640000014
in the formula, TaIs the ambient temperature, c is the specific heat capacity of the working medium, lambdahIs thermal resistance of the pipeline, S is the sectional area of the pipeline, and is a working mediumDensity, 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 iswThe radial heat conduction coefficient of the working medium;
m＝vρS (8)
Figure RE-FDA0003455198640000021
step 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-FDA0003455198640000022
3. the dynamic full analysis method for the hot water network according to claim 2, wherein the step 20) specifically comprises the following steps:
step 201) constructing a full differential form of the relative temperature T with respect to a time vector T, thereby obtaining a characteristic line equation with respect to an initial condition;
the full differential of the relative temperature with respect to time t can be expressed as:
Figure RE-FDA0003455198640000023
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-FDA0003455198640000031
in the formula, T0(x) For the initial conditions of the pipeline temperature profile, solving equation (14) yields:
Figure RE-FDA0003455198640000032
4. a method for dynamically analyzing the full hot water network according to claim 3, wherein the step 30) comprises the following steps:
step 301) constructing a full differential form of the relative temperature T with respect to the space vector x, thereby obtaining a characteristic line equation with respect to an initial condition;
the full differential of the relative temperature with respect to time x can be expressed as:
Figure RE-FDA0003455198640000033
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-FDA0003455198640000034
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; can be expressed as:
Figure RE-FDA0003455198640000035
in the formula, T0(x) For the initial conditions of the pipeline temperature profile, solving equation (18) yields:
Figure RE-FDA0003455198640000036
5. a method for dynamically analyzing the full hot water network according to claim 3, wherein the step 40) comprises the following steps:
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-FDA0003455198640000037
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-FDA0003455198640000041
Figure RE-FDA0003455198640000042
defining delta (t) as a step function, combining the formula (15) and the formula (19), establishing a dynamic full-analytic model of the hot water network, as shown in the formula (23),
Figure RE-FDA0003455198640000043
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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
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