CN106646146B - A method of it calculating unloaded high voltage power cable highest and bears voltage location - Google Patents

A method of it calculating unloaded high voltage power cable highest and bears voltage location Download PDF

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Publication number
CN106646146B
CN106646146B CN201610842296.0A CN201610842296A CN106646146B CN 106646146 B CN106646146 B CN 106646146B CN 201610842296 A CN201610842296 A CN 201610842296A CN 106646146 B CN106646146 B CN 106646146B
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cable
sine wave
highest
wave
coefficient
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CN106646146A (en
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曹京荥
陈杰
李陈莹
胡丽斌
谭笑
周志成
朱孟周
颜彪
梁伟
陈平春
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/12Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00Details relating to the application field
    • G06F2113/16Cables, cable trees or wire harnesses
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses a kind of methods for calculating unloaded high voltage power cable highest and bearing voltage location, including calculate cable loop resistance per unit length, inductance, capacitor and admittance parameter according to construction of cable parameter;According to resistance, inductance, capacitor and admittance parameter, the attenuation coefficient and phase coefficient of cable unit length are calculated;By attenuation coefficient and phase coefficient in conjunction with sinusoidal wave function, sine wave propagation function is constructed;According to sine wave propagation function, voltage computation model is born with each point highest along sine wave propagation law building cable, cable highest is calculated and bears voltage location.The present invention solves the problems, such as to bear voltage location method currently without the unloaded high voltage power cable highest of calculating, it can be in long range non-loaded cable route, the cable transient state breakdown fault analysis of the appearance such as the operation of high pressure power frequency, frequency conversion pressure test, the test of damped vibration wave provides analysis and guidance, and can test for simulated failure cable run breakdown accident and provide data foundation.

Description

A method of it calculating unloaded high voltage power cable highest and bears voltage location
Technical field
The present invention relates to a kind of methods for calculating unloaded high voltage power cable highest and bearing voltage location, belong to power technology Field.
Background technique
At present for long distance transmission line, sine voltage mostly uses steady-state distribution to join along the calculating of transmission line of electricity voltage Number circuits derive method, calculate the attenuation coefficient and phase coefficient of route, thus along calculating each point steady state voltage, but It is the computational problem that can not solve sinusoidal traveling wave transient voltage on the transmission line.For sinusoidal traveling wave along cable transmission line, Each point is most along there is presently no the sine traveling waves caused by maloperation and failure etc. in long-distance cable transmission line of electricity The calculation method for the transient voltage that height is born.
Summary of the invention
In order to solve the above-mentioned technical problems, the present invention provides a kind of unloaded high voltage power cable highests of calculating to bear voltage The method of position.
In order to achieve the above object, the technical scheme adopted by the invention is that:
A method of it calculating unloaded high voltage power cable highest and bears voltage location, comprising the following steps:
Cable loop resistance per unit length, inductance, capacitor and admittance parameter are calculated according to construction of cable parameter;
According to resistance, inductance, capacitor and admittance parameter, the attenuation coefficient and phase coefficient of cable unit length are calculated;
By attenuation coefficient and phase coefficient in conjunction with sinusoidal wave function, sine wave propagation function is constructed;
According to sine wave propagation function, voltage is born with each point highest along sine wave propagation law building cable and is calculated Model calculates cable highest and bears voltage location.
Cable resistance, inductance, capacitor and admittance parameter calculation formula be
Rθ=[R1+R2+(R1κ1+R2κ2)(θ-20)]/n
G=ω ' C × tan δ
Wherein, RθFor D.C. resistance of the cable loop at temperature θ, R1For in temperature θ, unit length cable core is led Body D.C. resistance, R2For in temperature θ, unit length cable cover(ing) conductor DC resistance, κ1Cable when for each absolute temperature θ The corresponding temperature coefficient of cable core conductor material, κ2Cable cover(ing) conductor material corresponding temperature coefficient when for each absolute temperature θ, N is route number in parallel in circuit;
L is cable loop unit length inductance, μ0For space permeability, mean geometrical distance of the s between cable core, Dco For cable conductor outer diameter;
C is cable loop capacitance per unit length, ε0For permittivity of vacuum, εrFor the relative dielectric constant of insulating materials, Di By examination cable metal sheath internal diameter, DnFor in cable loop with other parallel line distances, DcFor cable core outer diameter;
G is cable loop unit length conductance, and ω ' is power frequency angular frequency, and tan δ is the loss factor of material.
The calculation formula of attenuation coefficient and phase coefficient is,
Wherein, α, β respectively indicate attenuation coefficient and phase coefficient, and ω is angular frequency.
Sine wave propagation function U+(x, t) is,
0≤t≤tm
Wherein, t is propagation time, tmFor the time of waveform, A is waveforms amplitude, and x is sine wave since cable incidence end Displacement on cable termination direction,The initial phase of waveform is generated for sine wave sources, g (t-x/v) is the function of definition,V indicates velocity of wave.
Each point voltage is along cable,
U (x, t)=U-(x,t)+U+(x,t)
Wherein, U-(x, t) is reflection wave function,
Wherein, l is cable length.
Work as tmWhen >=(2l+ λ)/v:
Cable any point all undergoes sine wave and back wave at least a cycle simultaneously, then
0≤δ≤π
X '=l-x
Wherein, x ' is the distance of wave travel positional distance cable termination, and λ indicates wavelength,
When U (x, t) maximum, the x solved is that cable highest bears voltage location;
Work as tmWhen < (2l+ λ)/v:
When sine wave is transmitted to cable termination from cable head-end for the first time, wave function U is reflected_(x, t)=0;
0≤t≤tm
0≤x≤vt
Wherein,
If 0≤x '≤tmV/2- λ, section inner cable any point all undergo sine wave and at least one week of back wave simultaneously Phase;
0≤δ≤π
X '=l-x
Wherein,
If 0 < tmV/2- λ < x '≤tmV/2 or 0 < x '≤tmV/2 < λ, sine wave on the inner cable any point of section (the t less than 2 π is undergone with back wavemV-2x') the phase angle variations of β/2;
(l-x)/v+tm/2+x/v≤t≤tm+x/v
0≤δ≤π
X '=l-x
Wherein,
As max [U1(x,t),U2(x,t),U3(x, t)] it is maximum when, the x solved is that cable highest bears voltage location.
It is held advantageous effects of the invention: the present invention is solved currently without the unloaded high voltage power cable highest of calculating It the problem of by voltage location method, can be in long range non-loaded cable route, the operation of high pressure power frequency, be damped frequency conversion pressure test The cable transient state breakdown fault analysis of the appearance such as Sasser test provides analysis and guidance, and can puncture for simulated failure cable run Accident test provides data foundation.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 is cable distribution Simplified analysis figure.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.Following embodiment is only used for clearly illustrating the present invention Technical solution, and not intended to limit the protection scope of the present invention.
As shown in Figure 1, a kind of method for calculating unloaded high voltage power cable highest and bearing voltage location, including following step It is rapid:
1) cable loop resistance per unit length, inductance, capacitor and admittance parameter are calculated according to construction of cable parameter.
Specific formula for calculation is as follows:
Rθ=[R1+R2+(R1κ1+R2κ2)(θ-20)]/n
Wherein, RθFor D.C. resistance of the cable loop at temperature θ, R1For in temperature θ, unit length cable core is led Body D.C. resistance, R2For in temperature θ, unit length cable cover(ing) conductor DC resistance, κ1Cable when for each absolute temperature θ The corresponding temperature coefficient of cable core conductor material, κ2Cable cover(ing) conductor material corresponding temperature coefficient when for each absolute temperature θ, N is route number in parallel in circuit.
Wherein, L is cable loop unit length inductance, μ0For space permeability, geometric average of the s between cable core away from From DcoFor cable conductor outer diameter.
Wherein, C is cable loop in capacitance per unit length, ε0For permittivity of vacuum, εrFor the opposite dielectric of insulating materials Constant, DiBy examination cable metal sheath internal diameter, DnFor in cable loop with other parallel line distances, DcFor cable core Outer diameter.
G=ω ' C × tan δ
Wherein, G is cable loop unit length conductance, and ω ' is power frequency angular frequency, and tan δ is the loss factor of material.
2) according to resistance, inductance, capacitor and admittance parameter, attenuation coefficient and the phase system of cable unit length are calculated Number.
It is derived from according to the calculating of distributed constant circuit principle:
Wherein, α, β respectively indicate attenuation coefficient and phase coefficient, and ω is angular frequency.
3) by attenuation coefficient and phase coefficient in conjunction with sinusoidal wave function, sine wave propagation function is constructed.
Sinusoidal wave function f (t) are as follows:
0≤t≤tm
Wherein, t is propagation time, tmFor the time of waveform, A is waveforms amplitude,The first of waveform is generated for sine wave sources Beginning phase.
Therefore sine wave propagation function U+(x, t) are as follows:
0≤t≤tm
Wherein, x is displacement of the sine wave since cable incidence end on cable termination direction, and g (t-x/v) is definition Function,V=ω/β indicates velocity of wave.
4) according to sine wave propagation function, potentiometer is born with each point highest along sine wave propagation law building cable Model is calculated, cable highest is calculated and bears voltage location.
Sine wave is propagated have a characteristic that in the cable
1, the sinusoidal waveform time was less than at the propagation time of double length cable, and cable zero load is believed that cable two Terminal impedance is infinitely great, and multiple reflections can occur in cable for sine wave, due to there are waveform attenuating, when cable attenuation coefficient is big, Cable ceiling voltage point possibly is present at the head end position of cable;And when cable attenuation coefficient is small, cable ceiling voltage point may There is the overlapping portion of incidence wave and back wave, since there are waveform attenuating, incidence wave and back wave maximum superimposed voltages At the beginning of appearing in cable termination when secondary reflection, the superposition section of incidence wave and back wave on cable termination to incident extreme direction.
2, it is greater than when the sinusoidal waveform time in the propagation time of double length cable, cable any point is all undergone just simultaneously String wave and back wave at least a cycle, cable end piece are unloaded, it is believed that impedance is infinitely great, and incidence end connects power supply, impedance It is believed that being zero, therefore, sine wave is propagated in the cable, when voltage reflection wave reflects again from terminal arrival cable incidence end, Voltage reflection coefficient is 0, so maximum voltage need to only consider that sine wave passes to terminal from incidence end along cable, back wave is from terminal Pass to maximum voltage along the cable in incidence end this period.
To sum up, maximum voltage bears point and possibly is present at cable incidence end or cable termination to incidence end side along cable The superposition section of upward incidence wave and back wave.
Definition cable length is l, and cable distribution Simplified analysis figure is as shown in Fig. 2, due to cable end piece zero load, it is believed that resistance Anti- infinity, therefore terminal voltage refraction coefficient is 0, voltage reflection coefficient 1.Therefore, wave function U is reflected_(x, t) are as follows:
Wherein, 0≤x≤l.
Each point voltage along cable are as follows:
U (x, t)=U_(x,t)+U+(x,t)
Work as tmWhen >=(2l+ λ)/v:
Cable any point all undergoes sine wave and back wave at least a cycle simultaneously, then
0≤δ≤π
X '=l-x
Wherein, x ' is the distance of wave travel positional distance cable termination, and λ indicates wavelength, T is the period,
When U (x, t) maximum, the x solved is that cable highest bears voltage location.
Work as tmWhen < (2l+ λ)/v:
When sine wave is transmitted to cable termination from cable head-end for the first time, wave function U is reflected_(x, t)=0;
0≤t≤tm
0≤x≤vt
Wherein,
If 0≤x '≤tmV/2- λ, section inner cable any point all undergo sine wave and at least one week of back wave simultaneously Phase;
0≤δ≤π
X '=l-x
Wherein,
If 0 < tmV/2- λ < x '≤tmV/2 or 0 < x '≤tmV/2 < λ, sine wave on the inner cable any point of section (the t less than 2 π is undergone with back wavemV-2x') the phase angle variations of β/2;
(l-x)/v+tm/2+x/v≤t≤tm+x/v
0≤δ≤π
X '=l-x
Wherein,
As max [U1(x,t),U2(x,t),U3(x, t)] it is maximum when, the x solved is that cable highest bears voltage location.
In order to further illustrate the above method, following case is analyzed.
Target cable structural parameters are as shown in Table 1;
One target cable structural parameters of table
Wherein, D1And D2Tried cable is respectively indicated in circuit at a distance from other two shunt cables.
Following parameter can be solved according to the formula in method, specific as shown in Table 2:
Table two is according to the parameter of construction of cable gain of parameter
Sinusoidal wave function f (t) are as follows:
F (t)=1.28 × 103sin(2000πt+90°)
0≤t≤1.5×10-3
According to sinusoidal wave function:
0≤x≤5.3×104
tmThe v/2- λ of λ=- 0.25 < 0, there is no need to calculate U2(x,t);
As 0 < x'≤tmWhen v/2=0.75 λ, then
max[U1(x,t),U2(x,t),U3(x, t)]=1.28 × 105
The above method is the attenuation coefficient and phase coefficient by calculating cable unit length route, in conjunction with cable sine Waveform parameter establishes the propagation function that sinusoidal traveling wave is propagated in the cable, establishes with trigonometric function operation method about cable axis To the mathematical model of voltage is born, to calculate the position that cable highest bears electrical voltage point.
The above method solves the problems, such as to bear voltage location method currently without calculating unloaded high voltage power cable highest, It can be the cable of the appearance such as the operation of high pressure power frequency, frequency conversion pressure test, the test of damped vibration wave in long range non-loaded cable route The analysis of transient state breakdown fault provides analysis and guidance, and can test for simulated failure cable run breakdown accident and provide data foundation.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations Also it should be regarded as protection scope of the present invention.

Claims (3)

1. a kind of method for calculating unloaded high voltage power cable highest and bearing voltage location, it is characterised in that: include the following steps,
Cable loop resistance per unit length, inductance, capacitor and admittance parameter are calculated according to construction of cable parameter;
According to resistance, inductance, capacitor and admittance parameter, the attenuation coefficient and phase coefficient of cable unit length are calculated;
By attenuation coefficient and phase coefficient in conjunction with sinusoidal wave function, sine wave propagation function is constructed;
According to sine wave propagation function, voltage is born with each point highest along sine wave propagation law building cable and calculates mould Type calculates cable highest and bears voltage location;
Sine wave propagation function U+(x, t) is,
0≤t≤tm
Wherein, t is propagation time, tmFor the time of waveform, A is waveforms amplitude, and x is for sine wave to electricity since cable incidence end The upward displacement of cable terminal side,The initial phase of waveform is generated for sine wave sources, g (t-x/v) is the function of definition,V indicates velocity of wave, and α, β respectively indicate attenuation coefficient and phase Potential coefficient;
Each point voltage is along cable,
U (x, t)=U-(x,t)+U+(x,t)
Wherein, U-(x, t) is reflection wave function,
Wherein, l is cable length;
Work as tmWhen >=(2l+ λ)/v:
Cable any point all undergoes sine wave and back wave at least a cycle simultaneously, then
0≤δ≤π
X '=l-x
Wherein, x ' is the distance of wave travel positional distance cable termination, and λ indicates wavelength,When U (x, t) most When big, the x solved is that cable highest bears voltage location;
Work as tmWhen < (2l+ λ)/v:
When sine wave is transmitted to cable termination from cable head-end for the first time, reflect wave function U- (x, t)=0;
0≤t≤tm
0≤x≤vt
Wherein,
If 0≤x '≤tmV/2- λ, section inner cable any point all undergo sine wave and back wave at least a cycle simultaneously;
0≤δ≤π
X '=l-x
Wherein,
If 0 < tmV/2- λ < x '≤tmV/2 or 0 < x '≤tmV/2 < λ, sine wave and anti-on the inner cable any point of section Ejected wave undergoes the (t less than 2 πmV-2x') the phase angle variations of β/2;
(l-x)/v+tm/2+x/v≤t≤tm+x/v
0≤δ≤π
X '=l-x
Wherein,
As max [U1(x,t),U2(x,t),U3(x, t)] it is maximum when, the x solved is that cable highest bears voltage location.
2. a kind of method for calculating unloaded high voltage power cable highest and bearing voltage location according to claim 1, special Sign is: cable resistance, inductance, capacitor and admittance parameter calculation formula be,
Rθ=[R1+R2+(R1κ1+R2κ2)(θ-20)]/n
G=ω ' C × tan δ
Wherein, RθFor D.C. resistance of the cable loop at temperature θ, R1For in temperature θ, unit length cable core conductor is straight Leakage resistance, R2For in temperature θ, unit length cable cover(ing) conductor DC resistance, κ1Cable core when for each absolute temperature θ The corresponding temperature coefficient of conductor material, κ2Cable cover(ing) conductor material corresponding temperature coefficient when for each absolute temperature θ, n are Route number in parallel in circuit;
L is cable loop unit length inductance, μ0For space permeability, mean geometrical distance of the s between cable core, DcoFor electricity Cable conductor diameter;
C is cable loop capacitance per unit length, ε0For permittivity of vacuum, εrFor the relative dielectric constant of insulating materials, DiFor institute Try the internal diameter of cable metal sheath, DnFor in cable loop with other parallel line distances, DcFor cable core outer diameter;
G is cable loop unit length conductance, and ω ' is power frequency angular frequency, and tan δ is the loss factor of material.
3. a kind of method for calculating unloaded high voltage power cable highest and bearing voltage location according to claim 1, special Sign is: the calculation formula of attenuation coefficient and phase coefficient is
Wherein, ω is angular frequency.
CN201610842296.0A 2016-09-22 2016-09-22 A method of it calculating unloaded high voltage power cable highest and bears voltage location Active CN106646146B (en)

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CN110161381B (en) * 2019-04-29 2021-04-13 云南电网有限责任公司电力科学研究院 Transformer bushing insulation damp state evaluation method based on oscillation waves
CN112432587A (en) * 2020-09-22 2021-03-02 国网江西省电力有限公司电力科学研究院 Method for judging length section of whole-disc cable conductor

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JPH09257849A (en) * 1996-03-18 1997-10-03 Mitsubishi Electric Corp Diagnosing method for insulation of cable
US6567955B1 (en) * 1997-09-02 2003-05-20 Hitachi Chemical Company, Ltd. Method and system for approximating distributed constant line
CN102565634A (en) * 2012-01-10 2012-07-11 广东电网公司电力科学研究院 Power cable fault location method based on transfer function method
CN103941147A (en) * 2013-12-05 2014-07-23 国家电网公司 Distribution network cable single-phase ground fault distance measuring method utilizing transient main frequency component
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