CN105975690A - Construction method of transient state thermal circuit model of 10kV three-core cable on the basis of segmentation method - Google Patents
Construction method of transient state thermal circuit model of 10kV three-core cable on the basis of segmentation method Download PDFInfo
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- CN105975690A CN105975690A CN201610291532.4A CN201610291532A CN105975690A CN 105975690 A CN105975690 A CN 105975690A CN 201610291532 A CN201610291532 A CN 201610291532A CN 105975690 A CN105975690 A CN 105975690A
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Abstract
The invention discloses a construction method of a transient state thermal circuit model of a 10kV three-core cable on the basis of a segmentation method. The method comprises the following steps: S1: according to the radial section temperature distribution symmetry of the three-core cable, symmetrically segmenting the radial section of the three-core cable into the 1/3 radial section three-core cable, wherein each segmented part is provided with a cable core; S2: according to a heat transfer theory principle, establishing a transient state thermal circuit distribution parameter mathematic model of a cylindrical wall volume infinitesimal, expanding the model, inducing the transient state thermal circuit model of the 10kV three-core cable, carrying out analogy on the series-parallel connection calculation of resistance and capacitance in a circuit, and further simplifying the transient state thermal circuit model to obtain a transient state thermal circuit simplification model; S3: calculating the thermal resistance and the thermal capacity of each layer of material of the three-core cable; and S4: comparing a nodal method of analysis in the circuit, and inducing a calculation formula for solving the temperature of a conductor via the skin temperature of the cable under the transient state condition of the 10kV three-core cable. The construction method can accurately calculate the temperature of the conductor of the three-core cable so as to determine the carrying capacity of an operation cable.
Description
Technical field
The present invention relates to cable Transient Thermal Circuit modelling technique field, particularly relate to a kind of 10kV based on split-run tri-core electricity
The construction method of cable Transient Thermal Circuit model.
Background technology
Along with developing rapidly of China's economy, city need for electricity increases day by day, and this situation directly results in urban distribution network
Current-carrying capacity of cable is increasing.Therefore, it is more likely that occur that distribution network cable current-carrying capacity exceedes the upper limit, i.e. cable overload situations.Cable
When heavy overload runs, owing to cable core is overheated, make the temperature of insulating barrier exceed its highest tolerable temperature, cause insulating barrier
Insulating properties reduce, accelerate cable aging, even cause cable to break down, thus urban electricity supply reliability caused seriously
Threaten.Additionally, due to distribution network cable load fluctuation is relatively big, some period load is far from reaching its rated current-carrying capacity, does not has
Having the transmittability making full use of cable, this will result in the waste of cable resource, greatly reduces economy.Based on above-mentioned feelings
Condition, the method for the fully operation conditions of grasp distribution network cable, and measurement and calculating three-core cable conductor temperature seems and very must
Want.
The determination of power cable conductor temperature is significant to current-carrying capacity, and it determines that whether cable reaches specified load
The foundation of flow.In order to obtain operating three-core cable conductor temperature, according to the cable outer skin temperature measured, and can lead to
It is calculated cable conductor temperature after accordingly, is i.e. calculated cable conductor temperature by cable surface temperature.At present, by cable surface
Temperature calculates that the research method of cable conductor temperature is mainly Re Lufa, owing to upper three-core cable structure is special, utilizes Re Lufa
During calculating, except IEC standard, domestic scholars proposes again three cores according to its structural particularity and carries out setting up hot road with axiation method,
Although above method also can be extrapolated cable conductor temperature by cable skin temperature, but all right with whole three-core cable for research
As.Now, the shadow that mutually heat transfer and three cores the most externally conduct heat between internal three cores of three-core cable to be considered
Ring, considerably increase the complexity of research, also increase the difficulty that thermal circuit model is set up simultaneously, and then be difficult to accurately calculate three
Core cable is to conductor temperature, thus cannot correctly determine the current-carrying capacity size running cable.Thus, find a kind of simplicity by three
Core cable surface temperature calculates that the method for conductor temperature has and important has meaning.
Summary of the invention
The technical problem existed based on background technology, it is temporary that the present invention proposes a kind of 10kV three-core cable based on split-run
The construction method of state thermal circuit model.
The construction method of a kind of based on split-run 10kV three-core cable Transient Thermal Circuit model that the present invention proposes, including with
Lower step:
S1, according to the symmetry of three-core cable radial section Temperature Distribution, is 1/3 3 by three-core cable radial section symmetry division
Core cable, and each part of segmentation is all with single line core；
S2, sets up the Transient Thermal Circuit distributed constant mathematical model of cylindrical wall differential element of volume, is expanded by this model according to heat transfer principle
The Transient Thermal Circuit model of three-core cable is derived after exhibition；In analogous circuit, resistance, the connection in series-parallel of electric capacity calculate, to Transient Thermal Circuit mould
Type simplifies and obtains Transient Thermal Circuit simplified model；
S3, calculates thermal resistance and the thermal capacitance of 1/3 three-core cable layers of material after segmentation；
S4, the nodal method of analysis in analogy circuit, set up the temperature equation of each node, derive under three-core cable transient condition
The computing formula of conductor temperature is solved by cable skin temperature.
Preferably, in described S2, set up the Transient Thermal Circuit distributed constant number of cylindrical wall differential element of volume according to heat transfer principle
Learn model, the Transient Thermal Circuit model of three-core cable will be derived after this model extension；The connection in series-parallel of resistance, electric capacity in analogous circuit
Calculate, Transient Thermal Circuit model simplification is obtained Transient Thermal Circuit simplified model, particularly as follows:
A, according to heat transfer principle, set up the Transient Thermal Circuit distributed constant mathematical model of cylindrical wall differential element of volume；
B, according to cylindrical wall Transient Thermal Circuit distributed parameter model, by this model extension to 10kV three-core cable layers of material, obtain
The Transient Thermal Circuit model of the whole cross-section of cable；
C, according to 10kV three-core cable Transient Thermal Circuit model, utilize resistance in circuit, the connection in series-parallel of electric capacity calculates, analogy to hot road
In model, model is simplified further, obtain Transient Thermal Circuit simplified model.
In the present invention, first split three-core cable according to the symmetry of three-core cable radial section Temperature Distribution, resettle circle
The Transient Thermal Circuit distributed constant mathematical model of barrel differential element of volume, and then derive the Transient Thermal Circuit model of 10kV three-core cable also
Simplify, by thermal resistance and the thermal capacitance of layers of material, derive and solved by cable skin temperature under 10kV three-core cable transient condition
The computing formula of conductor temperature, the present invention mainly uses split-run to build 10kV three-core cable Transient Thermal Circuit model, greatly
Simplifying greatly the complexity of research, thermal circuit model is set up and is become simple, can accurately calculate three-core cable to conductor temperature, enter
And determine the current-carrying capacity size running cable.
Accompanying drawing explanation
Fig. 1 is the construction method of a kind of based on split-run the 10kV three-core cable Transient Thermal Circuit model that the present invention proposes
/ 3rd cable longitudinal section view；
Fig. 2 is the cylinder of the construction method of a kind of based on split-run the 10kV three-core cable Transient Thermal Circuit model that the present invention proposes
Wall Transient Thermal Circuit distributed parameter model；
Fig. 3 is the 10kV of the construction method of a kind of based on split-run the 10kV three-core cable Transient Thermal Circuit model that the present invention proposes
Three-core cable Transient Thermal Circuit model；
Fig. 4 is the 10kV of the construction method of a kind of based on split-run the 10kV three-core cable Transient Thermal Circuit model that the present invention proposes
The simplified model of three-core cable Transient Thermal Circuit.
In figure: 1 packed layer, 2 insulation screens, 3 insulating barriers, 4 conductors, 5 conductor shields, 6 metal screen layers, protect in 7
Set, 8 armors, 9 oversheaths.
Detailed description of the invention
Below in conjunction with specific embodiment, the present invention is explained orally further.
The construction method of a kind of based on split-run 10kV three-core cable Transient Thermal Circuit model that the present invention proposes, including with
Lower step:
S1, according to the symmetry of three-core cable radial section Temperature Distribution, is 1/3 3 by three-core cable radial section symmetry division
Core cable, and each part of segmentation is all with single line core；
S2, sets up the Transient Thermal Circuit distributed constant mathematical model of cylindrical wall differential element of volume, is expanded by this model according to heat transfer principle
The Transient Thermal Circuit model of three-core cable is derived after exhibition；In analogous circuit, resistance, the connection in series-parallel of electric capacity calculate, to Transient Thermal Circuit mould
Type simplifies and obtains Transient Thermal Circuit simplified model；
S3, calculates thermal resistance and the thermal capacitance of 1/3 three-core cable layers of material after segmentation；
S4, the nodal method of analysis in analogy circuit, set up the temperature equation of each node, derive under three-core cable transient condition
The computing formula of conductor temperature is solved by cable skin temperature.
With reference to Fig. 1, this three-core cable is sequentially provided with conductor 4, conductor shield 5, insulating barrier 3, insulation shielding from the inside to the outside
Layer 2, packed layer 1, metal screen layer 6, inner sheath 7, armor 8, oversheath 9.
Three-core cable transient state diabatic process refers to that cable internal heat transfer reaches the stage before dynamic equilibrium, its diabatic process
The thermal resistance of Rotating fields each with cable, thermal capacitance are relevant.Conduct heat law according to Fourier, whendQHeat passes through area within the unit interval
FordAInfinitesimal time, the thermograde of its size direct ratio and this infinitesimalWithdA.I.e.
(1)
Wherein,λFor the heat conductivity of this infinitesimal material, unit K m/W.
With a length of 1m, radius it isr, thickness isdrCylindrical wall as a example by, derivation three-core cable Transient Thermal Circuit model.If
In the timedτIn, this cylindrical wall flows into heat and isdQ i , flowing out heat isdQ o , self heat production isdQ p , volume isdV, this cylinder
Wall material specific heat capacity isc.According to law of conservation of energy, can obtain, in the timedτIn, the temperature rise of this cylindrical wallΔtFor:
(2)
From formula (1), this cylindrical wall flows out heat and is, whereindA=2πr.This cylindrical wall volumedV=2πr·dr, substitute into formula
(2) can obtain:
* MERGEFORMAT (3)
Formula (3) both sides simultaneously divided bydτ, and makedQ i /dτ=P i ,dQ p /dτ=P p , then it is:
* MERGEFORMAT (4)
Formula (4) is the Transient Thermal Circuit distributed constant mathematical model of taken cylindrical wall, wherein, \* MERGEFORMAT
For flowing through the heat flow of this cylindrical wall thermal resistanceP R ,* MERGEFORMAT for being stored in this cylindrical wall thermal capacitance
HeatP C , it is expressed as thermal circuit model to above-mentioned, as shown in Figure 2.
According to the cylindrical wall Transient Thermal Circuit distributed parameter model shown in Fig. 2, this model extension is each to 10kV three-core cable
Layer material, can obtain the Transient Thermal Circuit model of the whole cross-section of cable, as shown in Figure 3.
In Transient Thermal Circuit model, the definition of each parameter is:Q c The conductor losses produced for cable core；Q d For insulating barrier 3,
The dielectric loss sum of insulation screen 2 and conductor shield 5 three；λ 1 Loss factor for metal screen layer 6；λ 2 For armouring
The loss factor of layer 8；θ 1 For cable conductor 4 temperature；θ 2 For metal screen layer 6 temperature；θ 3 For armor 8 temperature；θ 0 For cable
Skin temperature；T 1 For insulating barrier 3, insulation screen 2 and the thermal resistance of conductor shield 5 three；T 2 For packed layer 1 thermal resistance；T 3 For
Inner sheath 7 thermal resistance；T 4 For oversheath 9 thermal resistance；* MERGEFORMAT be conductor 4 thermal capacitance； \* MERGEFORMAT
Thermal capacitance sum for insulating barrier 3, conductor shield 5 and insulation screen 2 three；* MERGEFORMAT be metallic shield
Layer 6 thermal capacitance；* MERGEFORMAT be packed layer 1 thermal capacitance；* MERGEFORMAT be inner sheath 7 thermal capacitance； \*
MERGEFORMAT is armor 8 thermal capacitance；* MERGEFORMAT be oversheath 9 thermal capacitance.
According to Fig. 3, utilize the connection in series-parallel calculating of resistance in circuit, electric capacity, in analogy to thermal circuit model, model is further
Simplify, Transient Thermal Circuit simplified model can be obtained, as shown in Figure 4.
Thermal resistance in the simplified model of Transient Thermal CircuitT 1 ’、T 2 ’、T 3 ’, thermal capacitanceC 1 、C 2 、C 3 And heating flow sourceQ 1 、Q 2 、Q 3 Size divide
It is not:
QUOTE (5)
In S3, to 1/3 three-core cable after segmentation, calculate thermal resistance and the thermal capacitance of layers of material.
From the thermal circuit model of the 10kV three-core cable set up, thermal resistance specifically includes that insulating barrier 3 thermal resistance, packed layer
1 thermal resistance, inner sheath 7 thermal resistance and oversheath 9 thermal resistance.In 1/3rd 10kV three-core cables after singulation, the horizontal stroke of insulating barrier 3
Cross section is the annulus of rule, and the cross section of inner sheath 7 and oversheath 9 is also 1/3rd annulus of rule, therefore, according to heat transfer
The knowledge learned, the thermal resistance of this three part can be tried to achieve by following formula:
(6)
In formula, d2For the outside diameter of annulus, d1For the interior circular diameter of annulus,For cable length, λ is the heat conductivity of material.
For packed layer 1, it is also possible to calculate its thermal resistance by formula (6), but owing to the cross section of packed layer 1 is not the circle of rule
Ring-shaped, therefore can not directly calculate, and according to the knowledge of thermal conduction study, can be with the d in modus ponens (6)2For in inner sheath 7
Circular diameter, takes d1For the center of circle of three-core cable cross circular section to the distance of points of tangency between adjacent both threads core, then can by formula (6)
To calculate thermal resistance value R ', then the ratio of 1/3rd packed layer 1 areas and inner sheath 7 inner circle area it is multiplied by by this value,
To required packed layer 1 thermal resistance.
According to the definition of thermal capacitance, the thermal capacitance of Heat Conduction Material is multiplied by quality equal to its specific heat capacity, and quality is equal to its density
It is multiplied by volume.Therefore, for the thermal capacitance of each Rotating fields of the 10kV three-core cable of unit length, its computing formula such as formula (7) institute
Show:
(7)
In formula,cFor the specific heat capacity of material, unitJ/kg·K；ρFor density of material, unitkg/m 3 ；VUnit length for material
Volume, unitm 3 。
Above-mentioned Transient Thermal Circuit simplified model row are write the nodal voltage equation group in similar circuit, can obtain:
(8)
(9)
(10)
By above-mentioned three formula composition equation group, expressing with matrix form, can obtain, transient state cable each layer temperature expression formula is:
(11)
Wherein, t=t is worked as0Time, there is QUOTE, ε is initial temperature θ of each layer of cable1、θ2、θ3The matrix of composition.And
And:
(12)
(13)
(14)
(15)
(16)
Formula (11) is 10kV three-core cable when being in transient process, by the formula of cable surface temperature computation conductor temperature.?
In this formula, first draw matrix A according to thermal capacitance and the thermal resistance value of each Rotating fields of three-core cable, further according to the conductor electricity of three-core cable
Stream size calculates the loss of each Rotating fields, recently enters cable surface temperature sequence in transient process, can form matrix B, E
For unit matrix, cable each layer temperature θ under transient state finally can be tried to achieve1、θ2、θ3Time dependent temperature sequence, specifically solves square
The process of battle array equation can be directly by mathematical softwares such as Matlab.Therefore can realize under 10kV three-core cable transient state by surface temperature
Degree calculates conductor temperature in real time.
The above, the only present invention preferably detailed description of the invention, but protection scope of the present invention is not limited thereto,
Any those familiar with the art in the technical scope that the invention discloses, according to technical scheme and
Inventive concept equivalent or change in addition, all should contain within protection scope of the present invention.
Claims (2)
1. the construction method of a 10kV three-core cable Transient Thermal Circuit model based on split-run, it is characterised in that include following
Step:
S1, according to the symmetry of three-core cable radial section Temperature Distribution, is 1/3 3 by three-core cable radial section symmetry division
Core cable, and each part of segmentation is all with single line core；
S2, sets up the Transient Thermal Circuit distributed constant mathematical model of cylindrical wall differential element of volume, is expanded by this model according to heat transfer principle
The Transient Thermal Circuit model of three-core cable is derived after exhibition；In analogous circuit, resistance, the connection in series-parallel of electric capacity calculate, to Transient Thermal Circuit mould
Type simplifies and obtains Transient Thermal Circuit simplified model；
S3, calculates thermal resistance and the thermal capacitance of 1/3 three-core cable layers of material after segmentation；
S4, the nodal method of analysis in analogy circuit, set up the temperature equation of each node, derive under three-core cable transient condition
The computing formula of conductor temperature is solved by cable skin temperature.
The construction method of a kind of 10kV three-core cable Transient Thermal Circuit model based on split-run the most according to claim 1,
It is characterized in that, in described S2, set up the Transient Thermal Circuit distributed constant mathematical modulo of cylindrical wall differential element of volume according to heat transfer principle
Type, will derive the Transient Thermal Circuit model of three-core cable after this model extension；The connection in series-parallel meter of resistance, electric capacity in analogous circuit
Calculate, Transient Thermal Circuit model simplification is obtained Transient Thermal Circuit simplified model, particularly as follows:
A, according to heat transfer principle, set up the Transient Thermal Circuit distributed constant mathematical model of cylindrical wall differential element of volume；
B, according to cylindrical wall Transient Thermal Circuit distributed parameter model, by this model extension to 10kV three-core cable layers of material, obtain
The Transient Thermal Circuit model of the whole cross-section of cable；
C, according to 10kV three-core cable Transient Thermal Circuit model, utilize resistance in circuit, the connection in series-parallel of electric capacity calculates, analogy to hot road
In model, model is simplified further, obtain Transient Thermal Circuit simplified model.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106339575A (en) * | 2016-08-15 | 2017-01-18 | 华南理工大学 | Method for establishing steady-state thermal circuit model of 10kV three-core cable based on segmentation method |
| CN107194027A (en) * | 2017-04-18 | 2017-09-22 | 华南理工大学 | Aluminium hydraulic pressed connecting pipe Heat Transfer Calculation at a kind of cable intermediate joint |
| CN108107256A (en) * | 2017-12-21 | 2018-06-01 | 国网冀北电力有限公司唐山供电公司 | A kind of three core power cable Circumferential field Equivalent analysis methods |
| CN109633334A (en) * | 2018-12-29 | 2019-04-16 | 广东电网有限责任公司 | A kind of electric heating combines thermal cycling ageing method, apparatus, equipment and storage medium |
| WO2019144657A1 (en) * | 2018-01-29 | 2019-08-01 | 华南理工大学 | Method for dynamically determining optimal number of insulating layers in transient thermal path of high-voltage cable |
| CN113190972A (en) * | 2021-04-08 | 2021-07-30 | 广东电网有限责任公司广州供电局 | Conductor temperature calculation method of cable joint and body based on micro-elements |
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| CN104636555A (en) * | 2015-02-06 | 2015-05-20 | 华南理工大学 | 10kV three-core cable temperature field model establishing method |
| CN104731898A (en) * | 2015-03-18 | 2015-06-24 | 华南理工大学 | 10-kV three-core cable finite element thermal analysis method |
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| CN104636555A (en) * | 2015-02-06 | 2015-05-20 | 华南理工大学 | 10kV three-core cable temperature field model establishing method |
| CN104731898A (en) * | 2015-03-18 | 2015-06-24 | 华南理工大学 | 10-kV three-core cable finite element thermal analysis method |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106339575A (en) * | 2016-08-15 | 2017-01-18 | 华南理工大学 | Method for establishing steady-state thermal circuit model of 10kV three-core cable based on segmentation method |
| CN107194027A (en) * | 2017-04-18 | 2017-09-22 | 华南理工大学 | Aluminium hydraulic pressed connecting pipe Heat Transfer Calculation at a kind of cable intermediate joint |
| CN107194027B (en) * | 2017-04-18 | 2020-05-22 | 华南理工大学 | Heat transfer calculation method for crimping pipe at cable intermediate joint |
| CN108107256A (en) * | 2017-12-21 | 2018-06-01 | 国网冀北电力有限公司唐山供电公司 | A kind of three core power cable Circumferential field Equivalent analysis methods |
| WO2019144657A1 (en) * | 2018-01-29 | 2019-08-01 | 华南理工大学 | Method for dynamically determining optimal number of insulating layers in transient thermal path of high-voltage cable |
| CN109633334A (en) * | 2018-12-29 | 2019-04-16 | 广东电网有限责任公司 | A kind of electric heating combines thermal cycling ageing method, apparatus, equipment and storage medium |
| CN113190972A (en) * | 2021-04-08 | 2021-07-30 | 广东电网有限责任公司广州供电局 | Conductor temperature calculation method of cable joint and body based on micro-elements |
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