CN109446633B - Cable group steady-state temperature rise acquisition method considering heat conductivity coefficient and heat dissipation coefficient - Google Patents
Cable group steady-state temperature rise acquisition method considering heat conductivity coefficient and heat dissipation coefficient Download PDFInfo
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Abstract
The invention relates to a cable group steady-state temperature rise acquisition method considering a heat conduction coefficient and a heat dissipation coefficient, which comprises the following steps of: 1) Establishing a steady-state temperature rise calculation model of the cable group according to the structure of the section of the cable group; 2) Acquiring known steady-state temperature rises of the cable under a plurality of working conditions, and acquiring corresponding steady-state temperature rise transfer matrixes of the cable group under different working conditions; 3) Obtaining a cable group steady-state temperature rise transfer matrix A' taking the change of the soil heat conductivity coefficient and the convective heat dissipation coefficient into consideration after fitting through data fitting; 4) And acquiring an actual cable group steady-state temperature rise transfer matrix according to the soil heat conductivity coefficient and the convective heat dissipation coefficient measured on site during actual measurement, and acquiring the actual cable group steady-state temperature rise by combining with the on-site cable heat flow calculation. Compared with the prior art, the invention has the advantages of taking the heat conductivity coefficient and the heat dissipation condition into consideration, being convenient, rapid and accurate, and the like.
Description
Technical Field
The invention relates to the field of power cable monitoring, in particular to a cable group steady-state temperature rise acquisition method considering heat conductivity and heat dissipation coefficient.
Background
With the increasing use of power cables in cities, particularly the advancement of overhead line ground-entering projects, a large number of 10kV overhead lines are changed into cable ground-entering laying. Unlike conventional 35kV and above buried cables, the 10kV cable is limited to the surrounding environment, the laying depth of the 10kV cable is generally not more than 1m, and the surrounding soil property (heat conductivity coefficient) and heat dissipation condition are relatively easy to be influenced by factors such as seasons, rainwater, wind speed convection and the like, so that the 10kV cable has a certain degree of change. These variations all affect the accuracy of the steady-state temperature rise transfer matrix and need to be considered in the modeling effort. However, the number of the 10kV cable lines is large, a transfer matrix is established for each group of soil heat conductivity coefficient and convection heat dissipation, time and labor are wasted, the efficiency is low, and the method cannot be implemented in practice. Therefore, a method for quickly establishing a steady-state temperature rise transfer matrix of the cable group needs to be studied.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a cable group steady-state temperature rise acquisition method considering the heat conductivity coefficient and the heat dissipation coefficient.
The aim of the invention can be achieved by the following technical scheme:
a cable group steady-state temperature rise acquisition method considering heat conductivity coefficient and heat dissipation coefficient comprises the following steps:
1) Establishing a steady-state temperature rise calculation model of the cable group according to the structure of the section of the cable group;
2) Acquiring known steady-state temperature rises of the cable under a plurality of working conditions, and acquiring corresponding steady-state temperature rise transfer matrixes of the cable group under different working conditions;
3) Obtaining a cable group steady-state temperature rise transfer matrix A' taking the change of the soil heat conductivity coefficient and the convective heat dissipation coefficient into consideration after fitting through data fitting;
4) And acquiring an actual cable group steady-state temperature rise transfer matrix according to the soil heat conductivity coefficient and the convective heat dissipation coefficient measured on site during actual measurement, and acquiring the actual cable group steady-state temperature rise by combining with the on-site cable heat flow calculation.
In the step 1), the cable group steady-state temperature rise calculation model specifically comprises the following steps:
A*T＝Q
wherein A is a steady-state temperature rise transfer matrix of the cable group, and the element a on the diagonal line of the steady-state temperature rise transfer matrix ii Representing self-heating of the ith cable as a cable self-influencing factor, element a on off-diagonal line ij Representing the thermal influence of the ith cable on the jth cable as an inter-cable influence factor, where i, j E n, n is the total cable lengthNumber, a i0 The heat conduction from the external heat dissipation condition to the ith cable core is converted into the heat conduction from the external heat dissipation condition as an influence factor of the external heat dissipation condition, T is a temperature rise matrix, and T i For the temperature rise of the ith cable, V 1 Q is the heat flux matrix, Q is the temperature difference between boundary conditions i Is the heat flow of the ith cable.
In the step 2), the conditions corresponding to different working conditions comprise soil heat conductivity coefficient, boundary temperature and convection heat dissipation coefficient.
In the step 2), finite element calculation is adopted to obtain a steady-state temperature rise transfer matrix of the cable group corresponding to different working conditions, in the finite element calculation process, the cable is regarded as a cylindrical axisymmetric structure, the thermal resistances in all directions are the same, and the structures of all layers outside the conductors in the multi-layer cable are equivalent to an equivalent outer protective layer.
In the step 3), the expression of the cable group steady-state temperature rise transfer matrix A' taking the change of the soil heat conductivity coefficient and the convective heat dissipation coefficient into consideration after fitting is as follows:
wherein the superscript' indicates the element after fitting.
In the step 3), the cable is used as a self-influencing factor a' ii The calculation formula of (2) is as follows:
a′ ii ＝k 1 *α
wherein k is 1 And (3) fitting a constant by itself, wherein alpha is the thermal conductivity of soil.
In the step 3), the cable-to-cable influencing factor a' ij The calculation formula of (2) is as follows:
a′ ij ＝k 2 *α
wherein k is 2 And alpha is the soil heat conductivity coefficient, which is a mutual fitting constant.
In the step 3), the heat dissipation factor a 'is used as an external heat dissipation condition influence factor' i0 The calculation formula of (2) is as follows:
wherein k is 3 、k 4 The external heat dissipation fitting constants are respectively, alpha is the soil heat conductivity coefficient, and beta is the convection heat dissipation coefficient.
Compared with the prior art, the invention has the following advantages:
aiming at the characteristic that the soil property (heat conductivity coefficient) and the heat dissipation condition around the shallow buried cable are relatively easy to be influenced by factors such as seasons, rainwater, wind speed convection and the like, the invention has a certain degree of change, and the fitting rule between matrix parameters and soil characteristic parameters and convection heat dissipation coefficients is sought through the parameter analysis of the transfer matrix under multiple working conditions, thereby realizing the quick estimation method for establishing the matrix parameters, further completing the quick establishment of the transfer matrix and being convenient for quickly solving the steady-state temperature rise of the cable group under different working conditions.
Drawings
Fig. 1 is a finite element computation model.
FIG. 2 is a finite element calculation result under the working conditions of the embodiment.
Fig. 3 is a flow chart of the method of the present invention.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples.
The invention provides a cable group steady-state temperature rise acquisition method considering a heat conduction coefficient and a heat dissipation coefficient, which comprises the following steps of:
1) For a certain section, a cable group steady-state temperature rise calculation model is established (finite element calculation is adopted herein, and other numerical calculation or mature commercial software can be adopted in practical application).
2) And randomly selecting a plurality of groups of soil heat conductivity coefficients, boundary temperatures and convection heat dissipation coefficients, and calculating the steady-state temperature rise of the cable under each working condition.
3) And obtaining a transfer matrix under each working condition according to the steady-state temperature rise of the cable group.
4) And (3) obtaining an estimation formula of the relation between the transfer matrix parameters, the soil characteristic parameters (heat conductivity coefficients) and the convection heat dissipation coefficients by utilizing data fitting.
5) When the heat conductivity coefficient and the convection heat dissipation coefficient change, a new transfer matrix is obtained by using an estimation formula, so that the rapid calculation of the steady-state temperature rise is realized, and the steady-state temperature rise of the cable group is calculated.
Example 1:
1) Finite element modeling
Finite element computation requires consideration of orthogonality of the selected computation conditions and the number of computation conditions, depending on the number of loops of the same cross-section cable. The finite element calculation model in the embodiment is shown in figure 1, wherein A1-A6 are cable sections, and the current-carrying capacity is arbitrary; it is contemplated that high voltage power cables often comprise a multi-layer structure, and that some of the structural layers are thin. Because the cable is a cylindrical axisymmetric structure, the thermal resistances in all directions are the same, the multi-layer cable structure can be equivalent by adopting a harmonic averaging method, each layer of structure outside the conductor in the multi-layer cable is equivalent to an equivalent outer protective layer, and the harmonic thermal conductivity coefficient in the above example is set to be 23.3W/m < 2 >. K.
2) Solving steady-state temperature rise of cable under conditions of different heat conductivity coefficients, convective heat dissipation and boundary temperature difference of soil
Taking boundary 1 as a convection heat dissipation coefficient rand (0, 1) 15W/m 2K, and the temperature is 30+rand (0, 1) 20 ℃, so as to meet a third class boundary condition; the boundaries 2, 3 and 4 are all set to be at 30 ℃ and meet the first class of boundary conditions, and the calculation result of a certain working condition is shown in fig. 2.
Under the condition of ensuring the orthogonalization of the working condition, the following results are summarized as shown in table 1.
Table 1 summary of steady state calculations
3) And obtaining a transfer matrix under each working condition according to the steady-state temperature rise of the cable group.
The calculation of the transfer matrix is illustrated by the condition of ring temperature difference=16.94K, thermal conductivity=0.7W/m 2K, and heat dissipation=6.86W/m 2K.
Q matrix:
t matrix:
transfer matrix:
different transfer matrices are also available, as follows.
Transfer matrix (thermal conductivity=0.9W/m 2 x K, thermal conductivity=6.11W/m 2 x K):
transfer matrix ring (thermal conductivity=1.1W/m 2 x K, thermal conductivity=14.7W/m 2 x K):
transfer matrix ring (thermal conductivity=1.3W/m 2 x K, thermal conductivity=4.72W/m 2 x K):
transfer matrix ring (thermal conductivity=1.5W/m 2 x K, thermal conductivity=0.5W/m 2 x K):
4) And (3) obtaining an estimation formula of the relation between the transfer matrix parameters, the soil characteristic parameters (heat conductivity coefficients) and the convection heat dissipation coefficients by utilizing data fitting.
Parameters are divided into three classes according to the definition of the transfer matrix: factors affecting the cable itself (e.g. a 11 ) Factors affecting cable spacing (e.g. a 12 ) With external heat dissipation conditions influencing factors (e.g. a 10 )。
a. Self influencing factors (in a 11 For example
From the transfer matrix, the consolidated data is available:
| coefficient of thermal conductivity (W/ |
Heat dissipation factor (W/ |
a11 |
| 0.7 | 6.86 | 2.06 |
| 0.9 | 6.11 | 2.646 |
| 1.1 | 14.7 | 3.237 |
| 1.3 | 4.72 | 3.817 |
| 1.5 | 0.5 | 4.39 |
According to the principle of heat transfer, it is proposed: a11 Thermal conductivity coefficient =k1
Using least squares, it is possible to: k1 = 2.9353.
| No | Calculated | Fitting value | |
| 1 | 2.06 | 2.0545488 | |
| 2 | 2.646 | 2.6415628 | |
| 3 | 3.237 | 3.2285767 | |
| 4 | 3.817 | 3.8155907 | |
| 5 | 4.39 | 4.4026047 |
b. Factors affecting cable-to-cable (shown in a 12 For example
From the transfer matrix, the consolidated data is available:
| coefficient of thermal conductivity (W/ |
Heat dissipation factor (W/ |
a12 |
| 0.7 | 6.86 | -0.007 |
| 0.9 | 6.11 | -0.01 |
| 1.1 | 14.7 | -0.012 |
| 1.3 | 4.72 | -0.014 |
| 1.5 | 0.5 | -0.016 |
According to the principle of heat transfer, it is proposed: a12 Thermal conductivity coefficient =k2
Using least squares, it is possible to: k2 = -0.0107.
| No | Calculated value | Fitting value |
| 1 | -0.007 | -0.007521 |
| 2 | -0.01 | -0.00967 |
| 3 | -0.012 | -0.011819 |
| 4 | -0.014 | -0.013967 |
| 5 | -0.016 | -0.016116 |
c. External heat dissipation condition influencing factor (shown in a 10 For example
From the transfer matrix, the consolidated data is available:
according to the principle of heat transfer, it is proposed: a10 =1/(k 3/thermal conductivity+k4/thermal conductivity)
Using least squares, it is possible to: k3 -4.698, k4= -11.306.
| No | Calculated value | Fitting value |
| 1 | -0.12 | -0.116826 |
| 2 | -0.142 | -0.137975 |
| 3 | -0.199 | -0.196003 |
| 4 | -0.164 | -0.178473 |
| 5 | -0.039 | -0.036984 |
By integrating the above processes, the fitting formula of each factor of the transfer matrix can be obtained as follows:
a11 Heat conductivity = 2.9353; a22 Heat conductivity = 2.9353; a33 Heat conductivity = 3.0262;
a44 Heat conductivity = 2.6229; a55 Heat conductivity = 2.6232; a66 Heat conductivity = 2.7400;
a12 -0.0107 coefficient of thermal conductivity; a13 -0.2875 coefficient of thermal conductivity; a14 -0.5179 coefficient of thermal conductivity;
a15 -0.0126 heat conductivity; a16 -0.1445 coefficient of thermal conductivity;
a23 -0.2877 coefficient of thermal conductivity; a24 -0.0128 heat conductivity; a25 -0.5280 coefficient of thermal conductivity;
a26 -0.1442 coefficient of thermal conductivity;
a34 -0.1445 coefficient of thermal conductivity; a35 -0.1446 coefficient of thermal conductivity; a36 -0.4116 coefficient of thermal conductivity;
a45 -0.0236 coefficient of thermal conductivity; a46 -0.3842 coefficient of thermal conductivity;
a56 -0.3840 coefficient of thermal conductivity;
a10 -1/(4.6769/thermal conductivity + 11.3660/heat dissipation coefficient); a20 -1/(4.5935/thermal conductivity + 12.1736/heat dissipation coefficient);
a30 -1/(6.9629/thermal conductivity + 27.6160/heat dissipation coefficient); a40 -1/(0.5522/thermal conductivity + 1.6590/heat dissipation coefficient);
a50 -1/(0.5521/thermal conductivity + 1.6582/heat dissipation coefficient); a60 = -1/(0.6005/thermal conductivity + 2.0779/heat dissipation coefficient)
5) When the heat conductivity and the heat dissipation coefficient change, a new matrix parameter is obtained by using an estimation formula.
If the thermal conductivity is 1.0W/m2 x K and the convective heat dissipation is 9.46W/m2 x K, the transfer matrix is obtained according to the fitting formula summarized in 4):
the transfer matrix obtained by finite element direct calculation is as follows:
and calculating the steady-state temperature rise under two different working conditions by using the finite element and the two transfer matrixes respectively, wherein the results are shown in the following table. The result of the fitting matrix is reliable, and the error of the result of the fitting matrix is less than 2K compared with that of a finite element and direct matrix method. The comparison result shows that the rapid estimation method and the result of the parameters are reliable, which improves the adaptability of the transfer matrix to the change of the heat conductivity coefficient and the heat dissipation coefficient of the soil and creates conditions for the development of subsequent work.
Claims (1)
1. The cable group steady-state temperature rise acquisition method taking the heat conductivity coefficient and the heat dissipation coefficient into consideration is characterized by comprising the following steps of:
1) Establishing a steady-state temperature rise calculation model of the cable group according to the structure of the section of the cable group;
2) Acquiring known steady-state temperature rises of the cable under a plurality of working conditions, and acquiring corresponding steady-state temperature rise transfer matrixes of the cable group under different working conditions;
3) Obtaining a cable group steady-state temperature rise transfer matrix A' taking the change of the soil heat conductivity coefficient and the convective heat dissipation coefficient into consideration after fitting through data fitting;
4) Acquiring an actual cable group steady-state temperature rise transfer matrix according to the soil heat conductivity coefficient and the convective heat dissipation coefficient measured on site during actual measurement, and acquiring an actual cable group steady-state temperature rise by combining with on-site cable heat flow calculation;
in the step 1), the cable group steady-state temperature rise calculation model specifically comprises the following steps:
A*T＝Q
wherein A is a steady-state temperature rise transfer matrix of the cable group, and the element a on the diagonal line of the steady-state temperature rise transfer matrix ii Representing self-heating of the ith cable as a cable self-influencing factor, element a on off-diagonal line ij Representing the thermal influence of the ith cable on the jth cable as an inter-cable influence factor, where i, j e n, n is the total number of cables, a i0 The heat conduction from the external heat dissipation condition to the ith cable core is converted into the heat conduction from the external heat dissipation condition as an influence factor of the external heat dissipation condition, T is a temperature rise matrix, and T i For the temperature rise of the ith cable, V 1 Q is the heat flux matrix, Q is the temperature difference between boundary conditions i The heat flow of the ith cable;
in the step 2), the conditions corresponding to different working conditions comprise soil heat conductivity coefficient, boundary temperature and convection heat dissipation coefficient;
in the step 2), finite element calculation is adopted to obtain a steady-state temperature rise transfer matrix of the cable group corresponding to different working conditions, in the finite element calculation process, the cable is regarded as a cylindrical axisymmetric structure, the thermal resistances in all directions are the same, and the structures of all layers of the outer conductor layers in the multi-layer cable are equivalent to form an equivalent outer protection layer;
in the step 3), the expression of the cable group steady-state temperature rise transfer matrix A' taking the change of the soil heat conductivity coefficient and the convective heat dissipation coefficient into consideration after fitting is as follows:
wherein the superscript' represents the element after fitting;
in the step 3), the cable is used as a self-influencing factor a' ii The calculation formula of (2) is as follows:
a′ ii ＝k 1 *α
wherein k is 1 The self-fitting constant is adopted, and alpha is the soil heat conductivity coefficient;
in the step 3), the cable-to-cable influencing factor a' ij The calculation formula of (2) is as follows:
a′ ij ＝k 2 *α
wherein k is 2 Is a mutual fitting constant, and alpha is a soil heat conductivity coefficient;
in the step 3), the heat dissipation factor a 'is used as an external heat dissipation condition influence factor' i0 The calculation formula of (2) is as follows:
wherein k is 3 、k 4 The external heat dissipation fitting constants are respectively, alpha is the soil heat conductivity coefficient, and beta is the convection heat dissipation coefficient.
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| CN107944079A (en) * | 2017-10-25 | 2018-04-20 | 国网上海市电力公司 | Comb laying threephase cable group's temperature rise fast acquiring method based on transfer matrix |
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