CN109284573B - Multi-loop cable steady-state temperature rise acquisition method considering nearby heat source conditions - Google Patents
Multi-loop cable steady-state temperature rise acquisition method considering nearby heat source conditions Download PDFInfo
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- 230000017525 heat dissipation Effects 0.000 claims description 6
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Abstract
The invention relates to a multi-loop cable steady-state temperature rise acquisition method under the condition of considering nearby heat sources, which comprises the following steps: 1) According to a thermal field superposition principle, a multi-loop cable steady-state temperature rise calculation model under the condition of considering nearby heat sources is established; 2) Under different working conditions, solving a transfer matrix A in a multi-circuit cable steady-state temperature rise model under the condition of a heat source nearby the filter; 3) And carrying out iterative computation according to the transfer matrix A to obtain the steady-state temperature rise of the multi-loop cable. Compared with the prior art, the method has the advantages of quick calculation, high calculation efficiency, accurate modeling and the like.
Description
Technical Field
The invention relates to the field of power distribution network cable monitoring, in particular to a multi-loop cable steady-state temperature rise acquisition method under the condition of considering nearby heat sources.
Background
With the development of modern cities, the heat transfer environment medium along the entire underground cable is in fact greatly affected by external environmental changes, especially the heat transfer pipes that exist with the trend of the cable. Because of the operational specificity of the power cable, it is generally impossible to obtain the core temperature of the power cable by direct measurement, and therefore, a plurality of methods are proposed by the technician to calculate the core temperature of the power cable, which are engineering formulas or approximate formulas based on numerical solutions and test results. For example, the method based on IEC60287 standard is a classical calculation method for calculating the core temperature of the power cable and a current-carrying capacity solving method based on numerical calculation. However, similar researches are mostly aimed at single-loop cables, numerical method is mostly adopted for solving the multi-loop cables in actual operation, and the complexity of working condition combination is considered, so that the required calculation amount is huge, and the efficiency in specific implementation is very low.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a multi-loop cable steady-state temperature rise acquisition method under the condition of considering a nearby heat source.
The aim of the invention can be achieved by the following technical scheme:
a multi-loop cable steady-state temperature rise acquisition method under the condition of considering nearby heat sources comprises the following steps:
1) According to a thermal field superposition principle, a multi-loop cable steady-state temperature rise calculation model under the condition of considering nearby heat sources is established;
2) Under different working conditions, solving a transfer matrix A in a multi-circuit cable steady-state temperature rise model under the condition of a heat source nearby the filter;
3) And carrying out iterative computation according to the transfer matrix A to obtain the steady-state temperature rise of the multi-loop cable.
In the step 1), the multi-loop cable steady-state temperature rise calculation model under the condition of considering the nearby heat source is specifically:
A*T＝Q
wherein A is a transfer matrix whose diagonal element a ii Element a on the off-diagonal line representing self-heating of the ith cable ij Representing the thermal effect of the ith cable on the jth cable, where i, j e n, n is the total number of cables, a i0 The heat conduction from the external heat source to the ith cable core is converted, T is a temperature rise matrix, and T i For the temperature rise of the ith cable, V 1 For the difference value of the heat source exceeding the heat dissipation boundary temperature, Q is a heat flow matrix, Q i Is the heat flow of the ith cable.
The step 3) specifically comprises the following steps:
31 Acquiring the ambient temperature T) 0 And calculates the ambient temperature T 0 Heat flow q of each cable 0 Obtaining the ambient temperature T 0 The lower initial heat flux matrix Q 0 ；
32 According to the initial heat flux matrix Q 0 Obtaining a temperature rise matrix T of the first iteration step by using a multi-loop cable steady-state temperature rise calculation model 1 The following steps are:
33 According to the temperature rise matrix T of the first step of iteration 1 Calculating a heat flux matrix Q of the first step of iteration 1 ；
34 Repeating the steps 32) -33) until the maximum difference between each element of the temperature rise matrix of the current step and the temperature rise matrix of the last step is not more than 0.1K, and the corresponding temperature rise matrix is the steady-state temperature rise.
In the steps 31) and 33), the calculation formula of the heat flow matrix is:
Q m ＝I*R*(1+kT m )*k 1
wherein Q is m For iterating the heat flow matrix of the m step, I is the cable current, R is the direct current resistance of the cable at 0 ℃, k is the temperature coefficient of resistance, k 1 To take into account the coupling effect, eddy current loss, etc. conversion coefficients, T m The temperature rise matrix of the m-th step is iterated.
In the step 3), if the iteration exceeds the maximum step number setting and does not converge, the calculation is considered to be failed.
In the step 2), different working conditions correspond to different heat flows, different temperature rises and different heat sources.
Compared with the prior art, the invention has the following advantages:
1. and (3) calculating quickly: the invention establishes a transfer matrix with lumped parameters to reflect thermal characteristics of heat sources around and nearby the cable through finite element calculation, and can adapt to rapid calculation of multi-working-condition steady-state temperature rise of the multi-loop cable under the condition of nearby heat sources.
2. The calculation efficiency is high: after a plurality of finite element calculations, the thermal characteristics of the section where the cable and the heat source are positioned can be comprehensively mastered, and the subsequent calculations only need simple matrixes and iterations, and satisfactory results can be obtained by using common tools such as a calculator and the like.
3. Modeling is accurate: the model is basically irrelevant to the loss and the heat source temperature value, only reflects the thermal characteristics of the section, has clear physical meaning and provides a direct basis for subsequent analysis and improvement.
Drawings
Fig. 1 is a structural diagram of a soil buried cable group arrangement.
Fig. 2 is a thermal field distribution cloud of a cable plant.
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 rapid calculation method capable of establishing a transfer matrix of lumped parameters to reflect thermal characteristics of heat sources around and nearby a cable through finite element calculation and adapting to multi-working-condition steady-state temperature rise of a multi-loop cable under the condition of nearby heat sources.
1. The principle of the method is as follows:
the superposition principle of the thermal field is utilized, the combined action of the multi-loop cables is discretized into the combination of the independent actions of the plurality of cables, the mutual influence between the cables is described by transfer coefficients, and further a transfer matrix formed by lumped parameters is formed, so that the rapid calculation of the steady-state temperature rise of the multi-loop cables under the multi-working conditions can be realized.
The following description will take 6 independent single-core cables and a nearby constant-temperature heat source as an example.
Transfer matrix a:
wherein a is 11 For self-heating, a 12 For the influence of cable 1 on cable 2, according to the dual principle, a 12 ＝a 21 The rest are similar; a, a 10 ～a 60 To convert the thermal conductance to each cable core corresponding to the external heat source.
Temperature rise matrix T:
heat flux matrix Q:
the matrix equation is:
wherein V is 1 Indicating the difference in the temperatures of the nearby heat sources beyond the heat dissipation boundary.
The determination of the model is independent of the heating value or the current of the cable, is only related to the relative position of the thermal characteristics of materials around the cable and nearby heat sources, but the material characteristics in the general operating temperature range can be considered to be basically unchanged, so that the satisfied result can be obtained directly through a simple matrix and iteration without repeating finite element or other numerical calculation when the cable current and the heat source temperature are transformed.
2 calculation flow
(1) Determination of transfer matrices
The transfer matrix A is considered to be unchanged in operation under the condition of boundary condition determination because the transfer matrix A is only related to thermal factors such as the heat conductivity coefficient of surrounding media, the environmental heat conductivity coefficient and the like and relative physical positions, but is not related to cable current and heat source temperature. Developing formula (1) to:
as can be seen from equation (2), if a Q matrix with enough elements and a corresponding T matrix can be obtained, a can be obtained by solving equation (2) 1，1 ，a 1，2 ，………，a 5，6 ，a 6，6 Etc., thereby forming a transfer matrix a. The definition of 'enough' is orthogonalization of the design working condition, and the number of equations is not less than the number of unknowns.
By means of a general numerical calculation tool (such as ANSYS, COMSOL or ANSOFT) or special calculation software (such as CYMCAP), a corresponding model is established, and a Q matrix under a certain working condition is set, so that a corresponding T matrix can be obtained. Through this process, a set of corresponding Q and T matrices can be obtained. And (3) changing working conditions, repeatedly calculating for a plurality of times (meeting enough requirements), and obtaining a new Q matrix and a corresponding T matrix of certain data. And (3) establishing an equation set shown in the equation (2) and then solving to obtain a transfer matrix A.
(2) Calculation of temperature rise of cable core
After the transfer matrix A is obtained, the relation between the heat flow matrix Q and the temperature rise matrix T can be obtained by using the formula (2). Considering that the heat flow is the heat per unit of time passing through a unit of cross-sectional area, its magnitude is a function of temperature, and generally a certain iteration is also required.
The method comprises the following specific steps:
1) Assuming ambient temperature T 0 The lower heat flow is q i,r ＝I i 2 *R i,r *(1+kT 0 ) K1, wherein I i For the current flowing through the ith return cable, R i,r The direct current resistance of the ith return cable at 0 ℃, k is the temperature coefficient of the resistance, k 1 This is true for the remaining cables in order to take into account the coupling effects, eddy current losses, etc. conversion factors. Thus, the ambient temperature T can be formed 0 Lower heat flux matrix Q 0 。
2) Solving to obtain a temperature rise matrix T by using the transfer matrix 1 。
3) By means of a temperature rise matrix T 1 Obtaining a heat flux matrix Q 1 Thereby obtaining a corresponding temperature rise matrix T 2 。
4) Such as temperature rise matrix T 2 And T is 1 The maximum difference between the corresponding elements is not more than 0.1K, calculation convergence is considered, and the temperature rise at the moment is the steady-state temperature rise.
5) Otherwise repeating the steps 3) and 4), and considering the calculation failure after the iteration exceeds the maximum step number setting and does not converge.
Examples:
the method mainly comprises the following steps:
(1) Solving of transfer matrices
1) Finite element computation
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. Hereinafter, a description will be given of practical application using six direct-buried soil cable groups, with an external heat source as a constant heat source.
As shown in FIG. 1, A 1 ～A 6 The cross section of each cable is six, and the current-carrying capacity flowing through each cable is arbitrary. Wherein, the third class boundary condition: the convection heat dissipation coefficient corresponding to boundary 1 is 15W/m 2 * K, wherein the temperature is 30 ℃; first type of boundary conditions: the boundaries 2, 3, 4 are each set to a temperature of 30 ℃. Since the single-core cable is an axisymmetric structure, the thermal resistance in all directions is the same. Considering that the high-voltage power cable often comprises a multi-layer structure, the harmonic mean method is adopted for simplification, each layer of structure outside the conductor in the multi-layer cable is equivalent to an equivalent outer protective layer, and the harmonic heat conductivity coefficient in the embodiment is set to be 23.3W/m 2 * K, the soil heat exchange coefficient is 1.0W/m 2 *K。
Fig. 2 shows the calculation result of a certain working condition, so that the temperature rise value of each cable can be obtained.
The temperature rise of each cable under the given heating value condition can be obtained by repeating the calculation for a plurality of times, and the results are summarized in the table 1.
Table 1 finite element calculations
2) Transfer matrix acquisition
The transfer matrix a can be solved from the data of equation (2) and table 1 as:
the diagonal elements in the comparison matrix are substantially equal, and one side also illustrates the correctness of the method.
3) Checking and calculating a transfer matrix:
the initial heat flow rate was set to q= [62.8,39.39,68.27,13.45,42.61,45.83], v1=20, and the temperature rise matrix was obtained by finite element and transfer matrix, respectively, as shown in table 2.
Table 2 comparison of finite element and transfer matrix calculations
| Calculation result | T1 | T2 | T3 | T4 | T5 | T6 |
| Finite element | 28.41 | 22.45 | 32.80 | 15.18 | 25.24 | 27.97 |
| Transfer matrix | 28.41 | 22.45 | 32.81 | 15.17 | 25.23 | 27.97 |
| Error of | 0.00 | 0.00 | -0.01 | 0.01 | 0.01 | 0.00 |
As can be seen from table 2, the accuracy of the transfer matrix was demonstrated based on the substantial agreement between the transfer matrix and the finite element based calculation results.
(2) Current capacity solution
After the transfer matrix is obtained, the relation between the heat flow matrix Q and the temperature rise matrix T can be obtained by using the formula (2). After definition of Q or T, the corresponding T or Q can be obtained. Considering the heat flow as a function of temperature, it is also generally necessary to find it by a certain iteration.
The method comprises the following specific steps:
1) Assuming ambient temperature T 0 Lower heat flow, Q i ＝I i 2 *R*(1+kT 0 )*k 1 Wherein Ii is the ith return cableThe current amount, R is the direct current resistance of the ith return cable at 0 ℃, k is the temperature coefficient of the resistance, k1 is the conversion coefficient considering the loss such as eddy current, and the rest of the return cables are all the same, so that a heat flow matrix Q is formed 0 . Form a conversion Q after considering the influence of different heat dissipation boundary conditions 0 ”。
2) Solving to obtain a temperature rise matrix T by using the transfer matrix 1 。
3) Such as temperature rise matrix T 0 And temperature rise matrix T 1 The maximum difference between the corresponding elements is greater than 0.1K, T is utilized 1 Instead of T 0 A new heat flux matrix is formed. Wherein the parts representing the differences of the different heat dissipation boundaries are not converted.
4) Repeating the steps until the maximum difference between the corresponding elements in the temperature rise matrix is smaller than 0.1K, and considering the calculation convergence, wherein the temperature rise at the moment is the steady-state temperature rise.
Table 3 is iterative solution process data.
TABLE 3 iterative process data
Claims (1)
1. The multi-loop cable steady-state temperature rise acquisition method under the condition of considering nearby heat sources is characterized by comprising the following steps of:
1) According to a thermal field superposition principle, a multi-loop cable steady-state temperature rise calculation model under the condition of considering nearby heat sources is established;
2) Under different working conditions, solving a transfer matrix A in a multi-circuit cable steady-state temperature rise model under the condition of a heat source nearby the filter;
3) Performing iterative computation according to the transfer matrix A to obtain steady-state temperature rise of the multi-loop cable;
in the step 1), the multi-loop cable steady-state temperature rise calculation model under the condition of considering the nearby heat source is specifically:
A*T＝Q
wherein A is a transfer matrix whose diagonal element a ii Element a on the off-diagonal line representing self-heating of the ith cable ij Representing the thermal effect of the ith cable on the jth cable, where i, j e n, n is the total number of cables, a i0 The heat conduction from the external heat source to the ith cable core is converted, T is a temperature rise matrix, and T i For the temperature rise of the ith cable, V 1 For the difference value of the heat source exceeding the heat dissipation boundary temperature, Q is a heat flow matrix, Q i The heat flow of the ith cable;
the step 3) specifically comprises the following steps:
31 Acquiring the ambient temperature T) 0 And calculates the ambient temperature T 0 Heat flow q of each cable 0 Obtaining the ambient temperature T 0 The lower initial heat flux matrix Q 0 ；
32 According to the initial heat flux matrix Q 0 Obtaining a temperature rise matrix T of the first iteration step by using a multi-loop cable steady-state temperature rise calculation model 1 The following steps are:
33 According to the temperature rise matrix T of the first step of iteration 1 Calculating a heat flux matrix Q of the first step of iteration 1 ；
34 Repeating the steps 32) -33) until the maximum difference between each element of the temperature rise matrix of the current step and each element of the temperature rise matrix of the last step is not more than 0.1K, and the corresponding temperature rise matrix is the steady-state temperature rise;
in the steps 31) and 33), the calculation formula of the heat flow matrix is:
Q m ＝I*R*(1+kT m )*k 1
wherein Q is m For iterating the heat flow of the mth stepMatrix, I is cable current, R is direct current resistance of cable at 0 ℃, k is resistance temperature coefficient, k 1 To consider the coupling effect, the conversion coefficient of eddy current loss, T m The temperature rise matrix is iterated in the m step;
in the step 3), if the iteration exceeds the maximum step number setting and does not converge, the calculation is considered to be failed;
in the step 2), different working conditions correspond to different heat flows, different temperature rises and different heat sources.
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| CN106021189A (en) * | 2016-05-13 | 2016-10-12 | 国网上海市电力公司 | Multi-loop cable steady-state temperature rise acquisition method adapting to various boundary conditions |
| WO2018045721A1 (en) * | 2016-09-08 | 2018-03-15 | 东南大学 | Thermal analysis method for motors having directly coupled temperature field and thermal circuit |
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| CN106021189A (en) * | 2016-05-13 | 2016-10-12 | 国网上海市电力公司 | Multi-loop cable steady-state temperature rise acquisition method adapting to various boundary conditions |
| WO2018045721A1 (en) * | 2016-09-08 | 2018-03-15 | 东南大学 | Thermal analysis method for motors having directly coupled temperature field and thermal circuit |
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| 基于转移矩阵的土壤直埋电缆群稳态温升;傅晨钊;《高压电器》;20171216;第53卷(第12期);全文 * |
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