CN110046322A - A kind of long cable voltage test core voltage Analytic Calculation Method - Google Patents
A kind of long cable voltage test core voltage Analytic Calculation Method Download PDFInfo
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- CN110046322A CN110046322A CN201910259942.4A CN201910259942A CN110046322A CN 110046322 A CN110046322 A CN 110046322A CN 201910259942 A CN201910259942 A CN 201910259942A CN 110046322 A CN110046322 A CN 110046322A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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- Y—GENERAL 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
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention discloses a kind of long cable voltages to test core voltage Analytic Calculation Method, based on and the equivalent-circuit model of cable sheath, list Kirchhoff's equation group, by carrying out Laplace transform to Kirchhoff's equation group, single-phase cable mode is established, single-phase cable mode is substituted by the way that cable voltage is tested boundary condition, obtains the formula for calculating cable core voltage-to-ground, by substituting into cable material parameter and structural parameters, the voltage-to-ground of cable core is obtained；Method of the invention is simple, without can be obtained the voltage-to-ground of cable core by in-site measurement, effectively evade and occur the excessively high potential danger for causing cable insulation to puncture of core voltage-to-ground in pressure test, to provide technological guidance to cable voltage plan design personnel.
Description
Technical field
The present invention relates to a kind of long cable voltages to test core voltage Analytic Calculation Method, belongs to transmission line of electricity measuring technology
Field.
Background technique
Long-distance cable rises phenomenon because holding when carrying out ac voltage withstanding test, and core is increased along line voltage, raised
Numerical value can threaten the major insulation of cable to hinder the progress of cable voltage test.Cable equivalent-circuit model is most at present
It is to ignore the influence of cable sheath based on the Two-port netwerk circuit model of equation for transmission line use, but calculating long-distance cable
When core voltage, cable sheath and cable core have stronger coupling, if ignoring cable sheath, are calculated
Long cable core voltage's distribiuting situation is not inconsistent with actual conditions.Therefore need it is a kind of meter and cable sheath acquisition cable core pair
The method of ground voltage distribution, certain guidance is provided for pressure test personnel.
Summary of the invention
The purpose of the present invention is to provide a kind of long cable voltages to test core voltage Analytic Calculation Method, existing to solve
One of caused above-mentioned defects or defect in technology.
In order to achieve the above objectives, the present invention adopts the following technical solutions realization:
In a first aspect, the present invention provides a kind of long cable voltages to test core voltage Analytic Calculation Method, method includes
Following steps:
According to meter and cable sheath distribution parameter equivalent circuit, Kirchhoff's equation group is listed；
Further, Kirchhoff's equation group includes KVL equation group, KCL equation group；
Laplace transform is taken to the both sides of Kirchhoff's equation group, obtain the first equation group and the first equation group is asked
Solution, according to the first solution of equations and inverse Laplace transform, obtains single-phase cable mode；
Further, single-phase cable mode structure are as follows:
Wherein, x indicates the distance apart from cable head；T (x) indicates transmission matrix；U1x、U2x、I1x、I2xRespectively indicate away from
It is cable core voltage-to-ground at x with a distance from cable head, apart from cable head distance is that cable sheath at x is electric over the ground
Pressure, be cable core electric current at x apart from cable head distance, apart from cable head distance be the cable sheath electric current at x；
U10、U20、I10、I20Respectively indicate voltage-to-ground at cable core head end, voltage-to-ground, cable core head at cable sheath head end
Electric current at end, electric current at cable sheath head end；
Cable voltage test boundary condition is substituted into single-phase cable mode, obtains the calculating of cable core voltage-to-ground
Formula；
The structural parameters and material parameter for obtaining cable use cable according to the structural parameters and material parameter of cable
Core voltage-to-ground calculation formula obtains the voltage-to-ground at cable core different location；The structural parameters and material parameter of cable
It include: radius, resistivity, the relative permeability of cable core, radius, resistivity, the relative permeability of cable sheath；Cable is exhausted
The radius of edge layer and oversheath, relative dielectric constant.
Further, cable voltage test boundary condition includes: to apply voltage in cable core head end；Cable sheath both ends
The voltage-to-ground of ground connection, cable sheath both ends is equal to zero；Cable core end is hanging, and cable end piece electric current is equal to zero.
A kind of long cable voltage provided by the invention tests core voltage Analytic Calculation Method, based on and cable sheath
Equivalent-circuit model proposes a kind of formula for calculating cable core voltage-to-ground, is joined by substituting into cable material parameter and structure
Number obtains the voltage-to-ground of the high cable core of accuracy, and the personnel to carry out pressure test to cable provide technological guidance.
Detailed description of the invention
Fig. 1 is a kind of meter provided according to embodiments of the present invention and the distribution parameter equivalent circuit of cable sheath.
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.
The present embodiment provides a kind of long cable voltages to test core voltage Analytic Calculation Method, and method includes:
Step 1: building Kirchhoff's equation group
According to the distribution parameter equivalent circuit of cable sheath and cable core referring to Fig.1, list comprising KVL equation, KCL
The Kirchhoff's equation group of equation, cable sheath are the metal sheath of metal material preparation；Δ x is one infinitesimal of cable in Fig. 1
Length, Δ U1xFor under infinitesimal length Δ x core terminal voltage and head end voltage it is poor, Δ U2xFor the sheath under infinitesimal length Δ x
Terminal voltage and head end voltage are poor, Δ I1xFor under infinitesimal length Δ x core end current and head end electric current it is poor, Δ I2xIt is micro-
Sheath end current and head end electric current under first length Δ x is poor.
The Kirchhoff's equation group such as formula (1) of building:
U1x、U2x、I1x、I2xRespectively indicate apart from cable head distance be x at cable core voltage-to-ground, apart from cable
Head end distance is cable sheath voltage-to-ground at x, apart from cable head distance is cable core electric current at x, apart from cable
Head end distance is the cable sheath electric current at x；Z1、Z2、Z12、Y12、YgRespectively indicate the distribution ginseng of cable sheath and cable core
The impedance of cable core equivalent unit length, the impedance of cable sheath equivalent unit length, cable core and the sheath of number equivalent circuit
Unit length is led between unit length admittance, cable sheath and the earth between the mutual impedance of equivalent unit length, cable core and sheath
It receives.
Z1、Z2、Z12、Y12、YgExpression formula such as formula (2):
Wherein cable sheath is the metal sheath of metal material preparation, and the partial parameters in formula (2) can be according to cable
Structural parameters and material parameter obtain: according to the core of cable, the radius of cable sheath, cable core resistivity, cable
Core relative permeability acquires cable core outer surface unit length internal impedance Z '1, according to cable core radius, insulating layer radius,
Insulating dielectric layer relative permeability acquires the unit length impedance Z to insulate between cable core and cable sheath '2, according to insulation
Layer radius, cable sheath radius, cable sheath resistivity, cable sheath relative permeability acquire the unit of cable sheath inner surface
Length internal impedance Z '3With cable sheath outer surface unit length internal impedance Z '4, according to cable sheath radius, oversheath radius and
The relative permeability of oversheath medium acquires the unit length impedance Z to insulate between cable sheath and the earth '5, according to the earth electricity
Resistance rate, the earth relative permeability, oversheath radius acquire the unit length internal impedance Z ' of ground return circuit6, according to core resistivity,
Core radius, core relative permeability acquire cable sheath unit length transfger impedance Z '12, normal with respect to dielectric according to insulating layer
Number, core radius, insulating layer radius acquire the equivalent capacity C to insulate between core and cable sheath12, it is situated between according to oversheath is opposite
Electric constant, cable sheath radius, oversheath radius acquire the equivalent capacity C to insulate between cable sheath and the earthg；
Solve the equation K of plural number K2The imaginary part of=- 1, j expression plural number K；ω is angular frequency, and the π of ω=2 f, f are experiment power supply
Frequency.
Step 2: obtaining single-phase cable mode
Laplace transform is taken to the both sides of formula (1), obtains the first equation group, shown in the first equation group such as formula (3):
Wherein, s is Laplace operator, U10、U20、I10、I20Respectively indicate voltage-to-ground, cable at cable core head end
Voltage-to-ground at sheath head end, electric current at cable core head end, electric current at cable sheath head end；U1(s), U2(s)、I1(s), I2
It (s) is U1x、U2x、I1x、I2xCorresponding image function after Laplace transform.
Solution formula (3), obtains U1(s), U2(s)、I1(s), I2(s) expression formula is as follows:
To the U of the solution as shown in above-mentioned formula1(s), U2(s)、I1(s), I2(s) equation carries out inverse Laplace transform,
And indicate the form of transformation results matrix, obtain single-phase cable mode, the matrix of single-phase cable transmission mathematical model
Indicate such as formula (4):
Wherein, T (x) is transmission matrix, shown in the structure of T (x) such as formula (5):
Wherein, the expression formula of coherent element is as follows in transmission matrix T (x):
Solve equation (s2-c)(s2- h)-ab=0, obtain Laplace operator s two solutions be expressed as λ1And λ2:
Wherein, the expression formula of parameter a, b, c, h is as follows:
Step 3: obtaining the calculation formula of cable core voltage-to-ground
The cable that length is l carries out pressure test boundary condition are as follows: applies voltage U in cable core head end10, cable sheath
The voltage-to-ground of two-terminal-grounding, cable sheath both ends is equal to zero, i.e. U20=U2l=0；Cable core end is hanging, cable end piece
Electric current is equal to zero, i.e. I1l=0.
Boundary condition is substituted into the single-phase mode of cable obtained according to step 1 and step 2, acquires cable core over the ground
Shown in voltage computing formula such as formula (6):
Step 4: obtaining the voltage-to-ground at cable core different location
According to step 1 to step 3, calculating cable that length is l is being cable core at x apart from cable head distance
Voltage-to-ground.
The accuracy of the voltage-to-ground of the cable core obtained referring to above-mentioned steps is verified, the cable used is tested
It is the twisted polyethylene cable that rated line voltage is 220kV, length 100km, cable core radius 0.0242m, cable for test product
Insulating layer radius is 0.05355m, and cable sheath radius is 0.06085m, and cable sheath is metal material, cable jacket radius
For 0.06875m, cable core resistivity is 1.72 × 10-8Ω m, cable sheath resistivity are 2.2 × 10-7Ω m, cable
The relative dielectric constant of insulating layer is 2.3, and the relative dielectric constant of oversheath is 2.5, cable core and cable sheath it is opposite
Magnetic conductivity is all 1, head end core pressurization 1.7U0, U0=127kV, experiment power supply frequency are 300Hz, and cable sheath both ends directly connect
Ground；According to the above structure parameter and material parameter of cable, using the above method acquire apart from cable head distance be 10Km,
The voltage-to-ground value of cable core at 20Km, 30Km, 40Km, 50Km, and the cable core voltage-to-ground value that will acquire with
The result that PSCAD software emulation obtains compares, and comparing result is as shown in table 1；
Table 1
| Away from head end away from/km | 10 | 20 | 30 | 40 | 50 |
| Simulated measurement/kV | 260.3∠-7.39° | 304.8∠-12.78° | 346.7∠-16.5° | 384.8∠-19.64° | 417.8∠-21.8° |
| Formula calculating/kV | 261.6∠-7.44° | 306.1∠-12.69° | 347.9∠-16.6° | 386.0∠-19.56° | 419.1∠-21.6° |
Referring to table 1, a kind of long cable voltage provided according to embodiments of the present invention tests core voltage Analytic Calculation Method
The voltage-to-ground and simulation result repeatability of the cable core of acquisition are high, illustrate that the present embodiment provides schemes to obtain cable core
The accuracy of voltage-to-ground is high.
According to twisted polyethylene cable pressure test engineering test specification and possess more than ten years On-Site Testing experience
Engineer learn that 220kV twisted polyethylene cable highest withstanding voltage must not exceed 2.5U0=317.5kV, reference table 1, away from
Being greater than the voltage-to-ground of the cable core at 30km with a distance from cable head is more than 2.5U0, that is to say, distance when bright pressure test
The cable insulation that cable head distance is greater than at 30km can be breakdown, to damage cable, this seriously inhibits cable voltages
Test go on smoothly, it should Adjustment Tests scheme, until cable core along voltage magnitude all meet the requirements just can be carried out it is resistance to
Pressure test, referring to shown in the above method and table 1 as a result, without can be obtained the electric over the ground of cable core by in-site measurement
Pressure can effectively evade and occur the excessively high potential danger for causing cable insulation to puncture of core voltage-to-ground in pressure test, be right
Cable voltage plan design personnel provide technological guidance.
A kind of long cable voltage provided in an embodiment of the present invention tests core voltage Analytic Calculation Method, based on and cable
The equivalent-circuit model of sheath, propose it is a kind of calculate cable core voltage-to-ground formula, by substitute into cable material parameter and
Structural parameters obtain the voltage-to-ground of cable core, and method provided in an embodiment of the present invention is simple, pair of the cable core of acquisition
Ground voltage accuracy is high, and the personnel to carry out pressure test to cable provide technological guidance.
The above is only embodiments of the present invention, it is noted that those skilled in the art are come
It says, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations are also answered
It is considered as protection scope of the present invention.
Claims (6)
1. a kind of long cable voltage tests core voltage Analytic Calculation Method, which is characterized in that described method includes following steps:
Step 1: according to meter and cable sheath distribution parameter equivalent circuit, listing Kirchhoff's equation group；
Step 2: Laplace transform being taken to the both sides of Kirchhoff's equation group, the first equation group is obtained and the first equation group is asked
Solution, according to the first solution of equations and inverse Laplace transform, obtains single-phase cable mode；
Step 3: cable voltage test boundary condition being substituted into single-phase cable mode, obtains the meter of cable core voltage-to-ground
Calculate formula；
Step 4: obtaining cable using cable core voltage-to-ground calculation formula according to the structural parameters and material parameter of cable
Voltage-to-ground at core different location.
2. a kind of long cable voltage according to claim 1 tests core voltage Analytic Calculation Method, which is characterized in that institute
The method of stating further includes the structural parameters and material parameter for obtaining cable.
3. a kind of long cable voltage according to claim 1 or 2 tests core voltage Analytic Calculation Method, feature exists
In the structural parameters and material parameter of the cable include: radius, resistivity, the relative permeability of cable core, cable sheath
Radius, resistivity, relative permeability, radius, the relative dielectric constant of cable insulation and oversheath.
4. a kind of long cable voltage according to claim 1 tests core voltage Analytic Calculation Method, which is characterized in that institute
State single-phase cable mode structure are as follows:
Wherein, x indicates the distance apart from cable head；T (x) indicates transmission matrix；U1x、U2x、I1x、I2xRespectively indicate distance electricity
Cable head end distance be cable core voltage-to-ground at x, be apart from cable head distance cable sheath voltage-to-ground at x, away from
It is cable core electric current at x with a distance from cable head, apart from cable head distance is the cable sheath electric current at x；U10、U20、
I10、I20Respectively indicate voltage-to-ground at cable core head end, voltage-to-ground at cable sheath head end, electricity at cable core head end
Electric current at stream, cable sheath head end.
5. a kind of long cable voltage according to claim 1 tests core voltage Analytic Calculation Method, which is characterized in that institute
Stating cable voltage test boundary condition includes: to apply voltage in cable core head end；Cable sheath two-terminal-grounding, cable sheath two
The voltage-to-ground at end is equal to zero；Cable core end is hanging, and cable end piece core electric current is equal to zero.
6. a kind of long cable voltage according to claim 1 tests core voltage Analytic Calculation Method, which is characterized in that institute
Stating Kirchhoff's equation group includes KVL equation group, KCL equation group.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110456133A (en) * | 2019-08-27 | 2019-11-15 | 河海大学 | Method is determined based on the cable data of phase-model transformation |
| CN113281552A (en) * | 2021-04-13 | 2021-08-20 | 上海电机学院 | Zero-contact cable voltage measurement method |
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| US20070124093A1 (en) * | 2005-11-05 | 2007-05-31 | Myongji University Industry And Academia Cooperation Foundation | Method for locating line-to-ground fault point of underground power cable system |
| CN104007354A (en) * | 2013-02-27 | 2014-08-27 | 上海宝钢工业技术服务有限公司 | Whole-group test circuit and method for 10 kV zinc oxide lightning arrester and cable |
| CN108469562A (en) * | 2018-03-27 | 2018-08-31 | 国网山东省电力公司潍坊供电公司 | High-voltage cable metal sheath Circulation Model and method for establishing model |
| CN109254189A (en) * | 2018-11-02 | 2019-01-22 | 江苏方天电力技术有限公司 | A kind of submarine cable pressure test terminal voltage calculation method |
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2019
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20070124093A1 (en) * | 2005-11-05 | 2007-05-31 | Myongji University Industry And Academia Cooperation Foundation | Method for locating line-to-ground fault point of underground power cable system |
| CN104007354A (en) * | 2013-02-27 | 2014-08-27 | 上海宝钢工业技术服务有限公司 | Whole-group test circuit and method for 10 kV zinc oxide lightning arrester and cable |
| CN108469562A (en) * | 2018-03-27 | 2018-08-31 | 国网山东省电力公司潍坊供电公司 | High-voltage cable metal sheath Circulation Model and method for establishing model |
| CN109254189A (en) * | 2018-11-02 | 2019-01-22 | 江苏方天电力技术有限公司 | A kind of submarine cable pressure test terminal voltage calculation method |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110456133A (en) * | 2019-08-27 | 2019-11-15 | 河海大学 | Method is determined based on the cable data of phase-model transformation |
| CN110456133B (en) * | 2019-08-27 | 2021-11-09 | 河海大学 | Cable parameter determination method based on phase-mode transformation |
| CN113281552A (en) * | 2021-04-13 | 2021-08-20 | 上海电机学院 | Zero-contact cable voltage measurement method |
| CN113281552B (en) * | 2021-04-13 | 2023-02-10 | 上海电机学院 | Zero-contact cable voltage measurement method |
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