WO2017000996A1 - Device and method for measuring capacitance of power cables - Google Patents
Device and method for measuring capacitance of power cables Download PDFInfo
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- WO2017000996A1 WO2017000996A1 PCT/EP2015/064886 EP2015064886W WO2017000996A1 WO 2017000996 A1 WO2017000996 A1 WO 2017000996A1 EP 2015064886 W EP2015064886 W EP 2015064886W WO 2017000996 A1 WO2017000996 A1 WO 2017000996A1
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- capacitance
- voltage
- cable
- reference capacitor
- power cable
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
- G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
- G01R27/26—Measuring inductance or capacitance; Measuring quality factor, e.g. by using the resonance method; Measuring loss factor; Measuring dielectric constants ; Measuring impedance or related variables
- G01R27/2605—Measuring capacitance
Definitions
- the technology disclosed herein relates generally to the field of power cables and in particular to a method and capacitance meter for measuring capacitance of power cables, and in particular of long power cables.
- High voltage cables are used for electric power transmission at high voltage and there are various types of such cables used in different applications, e.g. for alternating current (AC) power transmission and direct current (DC) power transmission.
- the cables should be designed and manufactured with care in view of safety and fulfilment of specifications.
- the cables should thus fulfil certain requirements, possibly to a more or less accurate degree of precision depending on location and application.
- An example on an electrical requirement of the cable is specification on its capacitance. It is important to ensure that the cable meets the capacitance specification e.g. for safety reasons and for ensuring proper operation. Cable manufacturers providing cables that fail to meet the capacitance specification may be required to pay penalties or to remanufacture a cable.
- the current available capacitance meters are based on using time varying currents or voltages for the measuring, and while functioning well for some applications, these meters give too poor accuracy for other applications, in particular for long power cables. There is thus a need for capacitance meters providing accurate measurements also on long power cables.
- the objective is according to a first aspect achieved by a method for determining capacitance of a power cable by using a capacitance meter.
- the method comprises charging a reference capacitor of the capacitance meter to a first voltage Vi, while discharging the power cable to zero voltage, wherein the reference capacitor has a first capacitance Ci; transferring charge from the reference capacitor to the power cable, the power cable obtaining a second capacitance C x ; measuring voltage over the reference capacitor to be a second voltage V2; and determining the capacitance, C x , of the power cable to be equal to the result of multiplying the first capacitance, Ci, with the ratio of the difference between the first and second voltages, Vi - V2, and the second voltage V2:
- the method provides a way of accurately measure power cables having considerable length, e.g. power cables being over 80 km long.
- the measuring on the principle of conservation of electric charge, instead of conventional frequency dependent measuring methods, the desired high accuracy for measuring long power cables is provided.
- the method is for measuring capacitance of a power cable that are longer than about 75 km, preferably longer than about 80 km, more preferably longer than about 82 km.
- the objective is according to a second aspect achieved by a capacitance meter for determining capacitance of a power cable.
- the capacitance meter comprises:
- - switching means arranged such as to:
- the switching means comprises:
- a first switch device arranged to allow charging of the reference capacitor to the reference voltage Vi, when being switched in a first position thereof, by connecting the power source to the reference capacitor such as to charge the reference capacitor to the reference voltage Vi,
- a second switch device arranged to allow discharging of the cable when being switched in a first position thereof, by providing an electrical path for such
- first switch device and the second switch device are arranged to be switched simultaneously to their respective first positions, and wherein the first switch device and the second switch device are, when being switched to their respective second positions, arranged such as to allow transfer of charge from the reference capacitor to the power cable, wherein the first switch device and the second switch device are arranged to be switched simultaneously to their respective second positions.
- the first switch device is arranged to allow transfer of charge from the reference capacitor to the power cable, when being switched to its second position by disconnecting the power source from the reference capacitor (15).
- the reference capacitor comprises a temperature stable capacitor having a nominal capacitance in the range of 9 ⁇ - n ⁇ , preferably about 10 ⁇ .
- Figure l illustrates a long cable as a transmission line.
- Figure 2 illustrates the principle and circuit based on which a meter for measurement of capacitance according to the invention is designed.
- Figure 3 illustrates schematically a capacitance meter according to an embodiment of the invention.
- Figure 4 illustrates an embodiment of a capacitance meter according to the present invention.
- Figure 5 illustrates connection of power cables used for measurement tests.
- Figure 6 is a flow chart of steps of a method for measuring power cables according to the present invention.
- a typical cable comprises, simplified, an inner conductor surrounded by an insulating layer, which in turn is surrounded by an outer conductive shield, also denoted metallic screen or conductive screen.
- the cable may also comprise further layers, such as e.g. further insulation layers, semiconducting layers and a protective jacket.
- the inner conductor and the outer conductive screen are isolated from each other, separated by the insulating layer, and may be seen as two conductors isolated from each other for the entire length of the cable.
- the far end of the cable is open.
- shorter cable lengths can be measured accurately by existing capacitance meters.
- the short length is treated by the meters as a lumped capacitance, i.e. the capacitance is represented by an idealized capacitor, and the accuracy of measurements is therefore acceptable.
- Figure ⁇ illustrates a long cable as a transmission line. That is, the pair of wires comprising the inner conductor and the outer screen are seen as circuit elements, as opposed to two conductors being completely insulated from each other.
- a long cable is in reality a transmission line with distributed capacitances (represented by capacitors C), inductances (represented by inductors L) and resistances (represented by resistors R) as illustrated in figure l. Measurement of the open line capacitance is hence in reality measurement of open end impedance. The impedance of the cable can be measured between the inner conductor and the conductive screen.
- a conventional LCR meter measuring inductance (L), capacitance (C) and resistance (R), uses sinusoidal voltage with frequency ⁇ rad/s for measurement of the
- the open line impedance measured with sinusoidal voltage is: eYd _
- the approximation of the impedance is acceptable for shorter cable lengths, but fails to hold for longer cables. Therefore the LCR meter measurement is acceptable up to about 75 km or possibly up to about 8o km. Measurements of longer lengths do not give acceptable accuracy, as will be shown by test results described later. Longer cables in this context are for instance cables longer than about 70 km, in particular longer than about 75 km or 80 km or 82 km.
- the conventional LCR meters use either constant current or voltage to charge a cable being measured to a certain voltage. The time to reach this certain voltage is then a measure of the capacitance.
- the methods and meters used are not applicable for long cables, as described above. Due to the effects of capacitance and inductance distributed along the length of the cable, the cable's response to the (rapidly) changing sinusoidal voltages is such that it acts as a finite impedance, drawing current proportional to an applied voltage. These frequency dependent methods hence give too large errors on the long cables.
- Figure 2 illustrates a circuit 10 and also the principle based on which the meter for measurement of capacitance according to the present invention is designed. The measurement method according to the present invention is described in the following with reference to figure 2.
- a first switch 11 (also denoted first switch device 11) is in a first position 11a (left-hand position) a reference capacitor 15 having reference capacitance Ci (also denoted nominal capacitance or rated capacitance) is charged to a voltage Vi by a power source 13, for instance a DC power source 13, and in the following exemplified by a voltage source 13 and as measured by a voltmeter 14.
- a power source 13 for instance a DC power source 13
- the cable that is being measured is discharged to zero voltage by a second switch 12 (also denoted second switch device 12) being in its first position 12a (left-hand position).
- V 1 - C 1 V 2 - (C + C x ) (4)
- FIG 3 illustrates an embodiment of a capacitance meter 1 according to the invention.
- the capacitance meter 1 implements the above method of measuring capacitance e.g. by comprising a circuit 10 as described.
- the circuit 10 may be implemented using components available on the market, the first and second switches may, for instance, comprise conventional electronic switches.
- the first and second switches 11, 12 may be digitally controlled for switching them between their respective first positions 11a, 12a and second positions 11b, 12b.
- the capacitance meter 1 is to be connected to the cable, in particular to the inner conductor and conductive screen thereof.
- the capacitance meter 1 may comprise two test leads (also denoted measurement leads), which are schematically indicated at reference numeral 19. One of the test leads is connected to the inner conductor and the other to the conductive screen of the cable being measured.
- the first switch 11 When the first switch 11 (refer to figure 2) is in the first position 12a, an electric path is provided such that the voltage source 13 is connected to the terminals of the reference capacitor 15, thereby charging it to the voltage Vi. Simultaneously, the second switch 12, which is in its first position 12a, provides an electrical path for the cable to be discharged.
- first switch 11 and the second switch 12 When the first switch 11 and the second switch 12 are in their respective second positions 11b, 12b, they provide an electrical path between the two test leads 19 (connected to the conductor core and conductive screen of the cable), through the capacitance meter 1 and enables the cable measurement.
- the capacitance meter 1 may comprise or be connected to an electric power source 13, e.g. a DC voltage source, or to an AC mains supply through AC-DC converter(s). If being connected to such external electric power source, a suitable input/output device is provided.
- the capacitance meter 1 comprises such a DC voltage source within its encapsulation 17, as indicated by reference numeral 13.
- the capacitance meter 1 comprises a DC unit comprising e.g. AC- DC converters and an interface (e.g. a cable) for connection to an AC mains supply.
- the capacitance meter 1 may comprise processing circuitry 18 for determining the capacitance according to the method described herein.
- the processing circuitry 18 may be adapted to perform the various functions, e.g. estimating and determining, by using program code stored in memory.
- the capacitance meter 1 is connected to a computer (not illustrated) comprising such processing circuitry and/or computer programs executing a measurement algorithm according to what is described herein, e.g. with reference to figure 2.
- the capacitance meter 1 then comprises an interface 20 towards the computer, e.g. a Universal Serial Bus (USB) connection. Omitting such processing circuitry from the capacitance meter l, and instead connecting it to a computer, may render the capacitance meter 1 less expensive.
- USB Universal Serial Bus
- the capacitance meter l may further comprise a display unit 16 for displaying measurement results, e.g. a light emitting diode (LCD) display.
- a display unit 16 for displaying measurement results, e.g. a light emitting diode (LCD) display.
- the measurement results may instead be displayed on a screen of or connected to the computer.
- Figure 4 illustrates in more detail an embodiment of the meter according to the invention. Same reference numerals as used in figure 3 refer to same or similar elements also in figure 4, and description of these apply here as well and are therefore not repeated here.
- the capacitance meter 1 may, as mentioned in relation to figure 3, comprise AC-DC converters 21, 22 connected between an AC mains supply and the circuit 10 for providing different output DC voltages.
- the capacitance meter 1 may comprise a voltage meter 14.
- the voltage meter 14 may for instance comprise a voltage divider 24, 25 connected in parallel with the reference capacitor 15 and in series with an electronic amplifier circuit 23 (e.g. with feedback) for providing measurement values to a computer.
- the capacitance meter 1 may, as mentioned earlier, comprise e.g. an USB connection to the computer.
- An interface towards a computer is indicated at reference numeral 20.
- Such interface 20 may, as exemplified in figure 4, comprise an USB connection.
- An analog to digital converter (ADC) 26 may then be connected between the voltmeter 14 and the interface 20, for converting the continuous signals to discrete digital numbers to be displayed.
- ADC analog to digital converter
- the capacitance meter 1 may comprise still additional components, besides the described components.
- the capacitance meter 1 may for instance comprise additional components such as overvoltage protective devices. Further, means for automatic measuring and/or registering measurement results may also be provided.
- the power source 13 may comprise devices such as fuses and switches, and an interface device if connected to an external power source.
- the reference capacitance Ci of the reference capacitor 15 should be chosen to a value giving maximum accuracy for long cables. By testing and evaluation, the following exemplary data of the capacitance meter 1 were found to give high accuracy:
- the reference capacitor 15 could be selected to have a value within an interval of e.g. 8 ⁇ ⁇ 10 ⁇ ⁇ 12 ⁇ .
- the time constant is:
- the voltmeter 14 should have a high internal resistance to avoid discharge of the cable that is being measured or discharge through the voltage meter 14 that is used for determining the voltage V2.
- the DC voltage source 13 may, for simplicity reasons, be built in the DC encapsulation 17 of the capacitance meter 1.
- the registered voltage V2 should be frozen within some second to avoid discharge of the circuit 10 influencing the measured capacitance.
- Dipole relaxation phenomenon of polymeric insulation has very long time constants.
- the time constant is in order of 4 hours and cold cable more than 24 hours.
- the relaxation phenomenon may hence be disregarded.
- V2 is a variable. If the voltage is digitally registered then both voltages Vi and V2 and capacitance Cx may be presented on the same display.
- Leakage resistance of test leads and cable terminations of cable should have leakage resistance R > 5 Mohm.
- Figure 5 illustrates the connection of cable cores for the measurements that were performed on the long 3-core polymeric insulated (Cross-linked polyethylene, XLPE) submarine cable 30.
- the cable 30 comprises, as described earlier, an inner conductor 31, which may comprise, for instance, a three-core conductor or one three-phase group of single-core conductors.
- the inner conductor 31 is surrounded by an insulating layer 32, which in turn is surrounded by an outer conductive screen 33.
- the cable may also comprise further layers, such as e.g. a protective jacket.
- 3-core cables 30a, 30b, 30c were connected serially by connecting a first end of a first cable 30a with a first end of a second cable 30b, and a second end of the second cable 30b with a first end of a third cable 30c.
- the conductor cores of the first cable 30a were connected to corresponding conductor cores of the second cable 30b, as indicated at reference numeral 34
- the conductive screen of the first cable 30a was connected to the conductive screen of the second cable 30b, as indicated at reference numeral 35.
- a corresponding connection of the second cable 30b to the third cable 30c was done.
- each cable 30a, 30b, 30c was 82 km long.
- the capacitance meter 1 according to the invention is, as has been described, based principle conservation of electric charge.
- the capacitance measurement value of 82 km cable length was taken as a reference value.
- FIG. 6 is a flow chart of steps of a method for measuring power cables according to the present invention.
- a method 40 is provided for determining capacitance of a power cable 30 by using a capacitance meter 1, such as the capacitance meter 1 that has been described.
- the method 40 comprises charging 41 a reference capacitor 15 of the capacitance meter 1 to a first voltage Vi, while discharging the power cable 30 to zero voltage, wherein the reference capacitor 15 has a first capacitance Ci.
- the method 40 comprises transferring 42 charge from the reference capacitor 15 to the power cable 30, the power cable 30 thereby obtaining a second capacitance C x .
- the reference capacitor 15 is discharged through the power cable 30 by disconnecting it from a power source 13, which was used for charging it.
- a first switch device 11 and a second switch device 12, as described e.g. with reference to figures 2 and 3, may be used for accomplishing the charging 41, discharging and charge transferring 42.
- the method 40 comprises measuring 43 the voltage over the reference capacitor 15 to be a second voltage V2.
- the measuring 43 may be performed by a voltmeter 14.
- the method 40 comprises determining 44 the capacitance C x of the power cable 30 to be equal to the result of multiplying the first capacitance Ci with the ratio of the difference between the first and second voltages Vi - V2 and the second voltage V2:
- the method 40 for measuring capacitance of a power cable 30 gives high accuracy even for power cables 30 that are longer than about 75 km, preferably longer than about 80 km, more preferably longer than about 82 km.
- capacitance meters are not suitable for such cable lengths, as they give too large measurement errors.
- a capacitance meter 1 is also provided for determining capacitance of a power cable 30.
- the capacitance meter 1 comprises a reference capacitor 15 having a nominal first capacitance Ci.
- the capacitance meter 1 comprises switching means 11, 12 arranged such as to:
- the switching means 11, 12 comprises:
- first switch device 11 arranged to allow charging of the reference capacitor 15 to the reference voltage Vi, when being switched in a first position 11a thereof, by connecting the power source 13 to the reference capacitor 15 such as to charge the reference capacitor 15 to the reference voltage Vi
- second switch device 12 arranged to allow discharging of the cable 30 when being switched in a first position 12a thereof, by providing an electrical path for such discharging, wherein the first switch device 11 and the second switch device 12 are arranged to be switched simultaneously to their respective first positions 11a, 12a, and wherein the first switch device 11 and the second switch device 12 are, when being switched to their respective second positions 11b, 12b, arranged such as to allow transfer of charge from the reference capacitor 15 to the power cable 30, wherein the first switch device 11 and the second switch device 12 are arranged to be switched simultaneously to their respective second positions 11a, 12a (or essentially
- the means 18, 20 for determining the capacitance, C x may comprise processing circuitry 18 provided in the capacitance meter 1 and comprising e.g. computer program with computer program code, which, when executed on at least one processor of the capacitance meter 1 causes it to perform the method 40 according to any of the described embodiments thereof.
- processing circuitry is provided in a computer, and the means 20 for determining the
- capacitance may then comprise an interface 20 towards the computer.
- the first switch device 11 is arranged to allow transfer of charge from the reference capacitor 15 to the power cable 30, when being switched to its second position lib, by disconnecting the power source 13 from the reference capacitor 15.
- the reference capacitor 15 comprises a temperature stable capacitor having a nominal capacitance in the range of 9 ⁇ - n ⁇ , preferably about 10 ⁇ .
- the method 40 and capacitance meter 1 that have been described is useful for measuring long cables, for which accurate measurement methods are lacking.
- the method and capacitance meter 1 may be used for improving on
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Abstract
The invention relates to a method (40) for determining capacitance of a power cable (30) by using a capacitance meter (1). The method (40) comprises charging (41) a reference capacitor (15) of the capacitance meter (1) to a first voltage V1, while discharging the power cable (30) to zero voltage, wherein the reference capacitor (15) has a first capacitance Ci; transferring (42) charge from the reference capacitor (15) to the power cable (30), the power cable (30) obtaining a second capacitance Cx; measuring (43) voltage over the reference capacitor (15) to be a second voltage V2; and determining (44) the capacitance, Cx, of the power cable (30) to be equal to the result of multiplying the first capacitance, Ci, with the ratio of the difference between the first and second voltages, V1 - V2, and the second voltage Formula (I) The invention also relates to a corresponding capacitance meter (1).
Description
DEVICE AND METHOD FOR MEASURING CAPACITANCE OF POWER CABLES
Technical field
The technology disclosed herein relates generally to the field of power cables and in particular to a method and capacitance meter for measuring capacitance of power cables, and in particular of long power cables.
Background
High voltage cables are used for electric power transmission at high voltage and there are various types of such cables used in different applications, e.g. for alternating current (AC) power transmission and direct current (DC) power transmission. The cables should be designed and manufactured with care in view of safety and fulfilment of specifications.
The cables should thus fulfil certain requirements, possibly to a more or less accurate degree of precision depending on location and application. An example on an electrical requirement of the cable is specification on its capacitance. It is important to ensure that the cable meets the capacitance specification e.g. for safety reasons and for ensuring proper operation. Cable manufacturers providing cables that fail to meet the capacitance specification may be required to pay penalties or to remanufacture a cable.
Accurate measurements of the cable capacitance are therefore needed. At installation, the capacitance of the cable should agree with the capacitance measured at sample tests in manufacturing sites on cable lengths before jointing to final length.
The current available capacitance meters are based on using time varying currents or voltages for the measuring, and while functioning well for some applications, these meters give too poor accuracy for other applications, in particular for long power cables. There is thus a need for capacitance meters providing accurate measurements also on long power cables.
Summary
An objective of the present disclosure is to solve the above mentioned problem.
The objective is according to a first aspect achieved by a method for determining capacitance of a power cable by using a capacitance meter. The method comprises charging a reference capacitor of the capacitance meter to a first voltage Vi, while discharging the power cable to zero voltage, wherein the reference capacitor has a first capacitance Ci; transferring charge from the reference capacitor to the power cable, the power cable obtaining a second capacitance Cx; measuring voltage over the reference capacitor to be a second voltage V2; and determining the capacitance, Cx, of the power cable to be equal to the result of multiplying the first capacitance, Ci, with the ratio of the difference between the first and second voltages, Vi - V2, and the second voltage V2:
The method provides a way of accurately measure power cables having considerable length, e.g. power cables being over 80 km long. By basing the measuring on the principle of conservation of electric charge, instead of conventional frequency dependent measuring methods, the desired high accuracy for measuring long power cables is provided.
In various embodiments, the method is for measuring capacitance of a power cable that are longer than about 75 km, preferably longer than about 80 km, more preferably longer than about 82 km.
The objective is according to a second aspect achieved by a capacitance meter for determining capacitance of a power cable. The capacitance meter comprises:
- a reference capacitor having a nominal first capacitance Ci,
- switching means arranged such as to:
- allow charging of the reference capacitor to a first voltage Vi by means of a power source, while discharging the power cable to zero voltage, when the switching means are switched in a first position, and
- allow transferring of charge from the reference capacitor to the power cable, whereby the power cable obtains a second capacitance Cx, when the switching means are switched in a second position,
- means for measuring a second voltage V2 over the reference capacitor, when the switching means are switched in the second position, and
- means for determining the capacitance Cx, of the power cable to be equal to the result of multiplying the first capacitance Ci, with the ratio of the difference between the first and second voltages, Vi - V2, and the second voltage V2:
In a variation of the above embodiment, the switching means comprises:
- a first switch device arranged to allow charging of the reference capacitor to the reference voltage Vi, when being switched in a first position thereof, by connecting the power source to the reference capacitor such as to charge the reference capacitor to the reference voltage Vi,
- a second switch device arranged to allow discharging of the cable when being switched in a first position thereof, by providing an electrical path for such
discharging, wherein the first switch device and the second switch device are arranged to be switched simultaneously to their respective first positions, and wherein the first switch device and the second switch device are, when being switched to their respective second positions, arranged such as to allow transfer of charge from the reference capacitor to the power cable, wherein the first switch device and the second switch device are arranged to be switched simultaneously to their respective second positions.
In some embodiments, the first switch device is arranged to allow transfer of charge from the reference capacitor to the power cable, when being switched to its second position by disconnecting the power source from the reference capacitor (15).
In various embodiments, the reference capacitor comprises a temperature stable capacitor having a nominal capacitance in the range of 9 μΡ - n μΡ, preferably about 10 μΡ.
Further features and advantages of the embodiments of the present teachings will become clear upon reading the following description and the accompanying drawings.
Brief description of the drawings
Figure l illustrates a long cable as a transmission line.
Figure 2 illustrates the principle and circuit based on which a meter for measurement of capacitance according to the invention is designed.
Figure 3 illustrates schematically a capacitance meter according to an embodiment of the invention.
Figure 4 illustrates an embodiment of a capacitance meter according to the present invention.
Figure 5 illustrates connection of power cables used for measurement tests.
Figure 6 is a flow chart of steps of a method for measuring power cables according to the present invention.
Detailed description
In the following description, for purposes of explanation and not limitation, specific details are set forth such as particular architectures, interfaces, techniques, etc. in order to provide a thorough understanding. In other instances, detailed descriptions of well-known devices, circuits, and methods are omitted so as not to obscure the description with unnecessary detail. Same reference numerals refer to same or similar elements throughout the description.
A typical cable comprises, simplified, an inner conductor surrounded by an insulating layer, which in turn is surrounded by an outer conductive shield, also denoted metallic screen or conductive screen. The cable may also comprise further layers, such as e.g. further insulation layers, semiconducting layers and a protective jacket. The inner conductor and the outer conductive screen are isolated from each other, separated by the insulating layer, and may be seen as two conductors isolated from each other for the entire length of the cable.
At measurement of the cable capacitance the far end of the cable is open. As will be described, shorter cable lengths can be measured accurately by existing capacitance meters. The short length is treated by the meters as a lumped capacitance, i.e. the
capacitance is represented by an idealized capacitor, and the accuracy of measurements is therefore acceptable.
The difficulties on measuring capacitance on long cables, e.g. cables longer than about 75 km, compared to shorter cables are elaborated on in the following.
Figure ι illustrates a long cable as a transmission line. That is, the pair of wires comprising the inner conductor and the outer screen are seen as circuit elements, as opposed to two conductors being completely insulated from each other. A long cable is in reality a transmission line with distributed capacitances (represented by capacitors C), inductances (represented by inductors L) and resistances (represented by resistors R) as illustrated in figure l. Measurement of the open line capacitance is hence in reality measurement of open end impedance. The impedance of the cable can be measured between the inner conductor and the conductive screen.
A conventional LCR meter, measuring inductance (L), capacitance (C) and resistance (R), uses sinusoidal voltage with frequency ω rad/s for measurement of the
capacitance. That is, the cable that is being measured is subjected to a sinusoidal voltage source and the LCR meter measures the voltage across and current through the cable. The response of the measured open line impedance depends on the time functions of currents and voltage used by the LCR meter. The open line impedance measured with sinusoidal voltage is: eYd _|_ e -yd
(°) = 0 eyd _ e -yd Ohm (1)
The impedance is, as mentioned, measured between the conductor and screen of the cable, and is in particular measured at distance x = o and at far end open at distance x = d.
The electrical conductance G for the cable may be treated as G = o because of the negligible leakage current through the insulation of the cable, i.e. conductance of the insulation between conductor and screen may be considered to be zero.
The propagation function is:
7 = J(R + j(t)V) · jCi) — (2)
m where:
R ohm/m conductor + screen resistance
L H/m inductance between conductor and screen
C F/m capacitance of the cable
G S/m conductance of insulation for cables, G = o
For shorter cables the expression of the open line impedance may be approximated with serial developments of the exponential expressions: l + yd + l - yd Z0 1
Z(0) * ZQ ' Λ . ' = -J = ~ Τ ohm (3)
1 + yd — 1 + yd yd jaiCd
The approximation of the impedance is acceptable for shorter cable lengths, but fails to hold for longer cables. Therefore the LCR meter measurement is acceptable up to about 75 km or possibly up to about 8o km. Measurements of longer lengths do not give acceptable accuracy, as will be shown by test results described later. Longer cables in this context are for instance cables longer than about 70 km, in particular longer than about 75 km or 80 km or 82 km.
The conventional LCR meters use either constant current or voltage to charge a cable being measured to a certain voltage. The time to reach this certain voltage is then a measure of the capacitance. The methods and meters used are not applicable for long cables, as described above. Due to the effects of capacitance and inductance distributed along the length of the cable, the cable's response to the (rapidly) changing sinusoidal voltages is such that it acts as a finite impedance, drawing current proportional to an applied voltage. These frequency dependent methods hence give too large errors on the long cables.
One problem that must be overcome is the self-discharge over cable over end terminations or through voltage meter used for determination of the voltage. In view
of this, the meter and method according to the invention are based on the principle conservation of electric charge as will be described next.
Figure 2 illustrates a circuit 10 and also the principle based on which the meter for measurement of capacitance according to the present invention is designed. The measurement method according to the present invention is described in the following with reference to figure 2.
When a first switch 11 (also denoted first switch device 11) is in a first position 11a (left-hand position) a reference capacitor 15 having reference capacitance Ci (also denoted nominal capacitance or rated capacitance) is charged to a voltage Vi by a power source 13, for instance a DC power source 13, and in the following exemplified by a voltage source 13 and as measured by a voltmeter 14. At the same time the cable that is being measured is discharged to zero voltage by a second switch 12 (also denoted second switch device 12) being in its first position 12a (left-hand position).
When the first and second switches 11, 12 are in their respective second positions 11b, 12b (right-hand positions), charge is allowed to be transferred from the reference capacitor 15, initially having reference capacitance Ci, to the cable capacitance Cx, which is the parameter being measured. The voltage over the reference capacitor 15 is then changed to V2 when being discharged.
Condition for conservation of charge is:
V1 - C1 = V2 - (C + Cx) (4)
The total load is kept according the above principle. The equation (4) gives the cable capacitance Cx:
Figure 3 illustrates an embodiment of a capacitance meter 1 according to the invention. The capacitance meter 1 implements the above method of measuring capacitance e.g. by comprising a circuit 10 as described. The circuit 10 may be implemented using components available on the market, the first and second switches may, for instance, comprise conventional electronic switches. The first and
second switches 11, 12 may be digitally controlled for switching them between their respective first positions 11a, 12a and second positions 11b, 12b.
The capacitance meter 1 is to be connected to the cable, in particular to the inner conductor and conductive screen thereof. To this end, the capacitance meter 1 may comprise two test leads (also denoted measurement leads), which are schematically indicated at reference numeral 19. One of the test leads is connected to the inner conductor and the other to the conductive screen of the cable being measured.
When the first switch 11 (refer to figure 2) is in the first position 12a, an electric path is provided such that the voltage source 13 is connected to the terminals of the reference capacitor 15, thereby charging it to the voltage Vi. Simultaneously, the second switch 12, which is in its first position 12a, provides an electrical path for the cable to be discharged.
When the first switch 11 and the second switch 12 are in their respective second positions 11b, 12b, they provide an electrical path between the two test leads 19 (connected to the conductor core and conductive screen of the cable), through the capacitance meter 1 and enables the cable measurement.
The capacitance meter 1 may comprise or be connected to an electric power source 13, e.g. a DC voltage source, or to an AC mains supply through AC-DC converter(s). If being connected to such external electric power source, a suitable input/output device is provided. In an embodiment, the capacitance meter 1 comprises such a DC voltage source within its encapsulation 17, as indicated by reference numeral 13. In other embodiments, the capacitance meter 1 comprises a DC unit comprising e.g. AC- DC converters and an interface (e.g. a cable) for connection to an AC mains supply.
The capacitance meter 1 may comprise processing circuitry 18 for determining the capacitance according to the method described herein. The processing circuitry 18 may be adapted to perform the various functions, e.g. estimating and determining, by using program code stored in memory. In other embodiments, the capacitance meter 1 is connected to a computer (not illustrated) comprising such processing circuitry and/or computer programs executing a measurement algorithm according to what is described herein, e.g. with reference to figure 2. The capacitance meter 1 then comprises an interface 20 towards the computer, e.g. a Universal Serial Bus (USB)
connection. Omitting such processing circuitry from the capacitance meter l, and instead connecting it to a computer, may render the capacitance meter 1 less expensive.
The capacitance meter l may further comprise a display unit 16 for displaying measurement results, e.g. a light emitting diode (LCD) display. Alternatively, if the capacitance meter 1 is connected to a computer the measurement results may instead be displayed on a screen of or connected to the computer.
Figure 4 illustrates in more detail an embodiment of the meter according to the invention. Same reference numerals as used in figure 3 refer to same or similar elements also in figure 4, and description of these apply here as well and are therefore not repeated here.
The capacitance meter 1 may, as mentioned in relation to figure 3, comprise AC-DC converters 21, 22 connected between an AC mains supply and the circuit 10 for providing different output DC voltages.
The capacitance meter 1 may comprise a voltage meter 14. The voltage meter 14 may for instance comprise a voltage divider 24, 25 connected in parallel with the reference capacitor 15 and in series with an electronic amplifier circuit 23 (e.g. with feedback) for providing measurement values to a computer. For this end, the capacitance meter 1 may, as mentioned earlier, comprise e.g. an USB connection to the computer. An interface towards a computer is indicated at reference numeral 20. Such interface 20 may, as exemplified in figure 4, comprise an USB connection. An analog to digital converter (ADC) 26 may then be connected between the voltmeter 14 and the interface 20, for converting the continuous signals to discrete digital numbers to be displayed.
The capacitance meter 1 may comprise still additional components, besides the described components. The capacitance meter 1 may for instance comprise additional components such as overvoltage protective devices. Further, means for automatic measuring and/or registering measurement results may also be provided.
The power source 13 may comprise devices such as fuses and switches, and an interface device if connected to an external power source.
The reference capacitance Ci of the reference capacitor 15 should be chosen to a value giving maximum accuracy for long cables. By testing and evaluation, the following exemplary data of the capacitance meter 1 were found to give high accuracy:
E = 50 V DC
Ci = 10 μΡ temperature stable capacitor Cx = 1 - 100 μΡ capacitance of cable
It is however noted that the reference capacitor 15 could be selected to have a value within an interval of e.g. 8 μΡ < 10 μΡ < 12 μΡ.
Time constants of meter according to invention
If the voltage source 13 injects a minimum constant current Io = 10 mA, then the time to charge reference capacitor 15 to capacitance Ci is, with the above exemplary data for the capacitance meter 1:
- C 50■ 10■ 10~6
ti —— ;————— 7~—— = 50 ms (6)
1 /0 10■ 10-3 J
Data for determination of time to charge a 300 km cable: Cx = 50 μΡ cable capacitance between conductor and screen Rx = 180 ohm screen resistance
The time constant is:
Tx = Rx - Cx = 180■ 50■ 10"6 = 9 ms
The voltmeter 14 (V2) should have a high internal resistance to avoid discharge of the cable that is being measured or discharge through the voltage meter 14 that is used for determining the voltage V2.
Next, some further considerations are mentioned. The DC voltage source 13 may, for simplicity reasons, be built in the DC encapsulation 17 of the capacitance meter 1. The
registered voltage V2 should be frozen within some second to avoid discharge of the circuit 10 influencing the measured capacitance.
Dipole relaxation phenomenon of polymeric insulation has very long time constants. For hot cable the time constant is in order of 4 hours and cold cable more than 24 hours. The relaxation phenomenon may hence be disregarded.
In the equation (5) V2 is a variable. If the voltage is digitally registered then both voltages Vi and V2 and capacitance Cx may be presented on the same display.
Fault sources at measurement
Fault sources estimated when implementing the capacitance meter 1 using available standard components (accuracy is indicated as percentage of nominal value, i.e. accuracy < 1 % means that the error in measurement is less than 1 %):
1. Accuracy Vi < 1%
2. Accuracy V2 < 1%
3. Accuracy Ci < 1%
4. Accuracy difference (V1-V2) estimated 2%
5. Stray capacitances < 5 pF
6. Self-discharge of Cx depends of leakage resistance of measurement leads 19 and cable terminations.
Fault calculation through logarithmic derivation of (5) gives:
ACX Α(γ, - V2) AV2 AC-,
— =— - +— +— (7)
Cx Vi - V2 V2 d J
Maximum failure if all faults have same sign and coincident ACx < 3%, but in reality and in most cases the expected value is even lower.
Self-discharge of Cx at measurement
The voltage V2 over capacitance Cx parallel with reference capacitor 15 (Ci) decays exponential when discharged over leakage resistance R:
Error in measured voltage U2 if time constant T is large:
U20 - U2 t t
= 1 - e T « - (9)
If acceptable error is 1% minimum leakage resistance is determined R from:
1 t t
(10)
100 T R(C1 + Cx)
If time for measurement is t = 1 s and capacitance in order 10 μΡ, then minimum value of R is:
100 - 1
R = = 5■ 106 ohm (11)
2 - 10 - 10-6 J
Leakage resistance of test leads and cable terminations of cable should have leakage resistance R > 5 Mohm.
Test results
Comparison of measured capacitances obtained by using standard meters available on the market and the meter according to the invention was performed on a long 3- core high voltage alternating current (HVAC) submarine cable.
Figure 5 illustrates the connection of cable cores for the measurements that were performed on the long 3-core polymeric insulated (Cross-linked polyethylene, XLPE) submarine cable 30. The cable 30 comprises, as described earlier, an inner conductor 31, which may comprise, for instance, a three-core conductor or one three-phase group of single-core conductors. The inner conductor 31 is surrounded by an insulating layer 32, which in turn is surrounded by an outer conductive screen 33. The cable may also comprise further layers, such as e.g. a protective jacket.
For the testing, three such 3-core cables 30a, 30b, 30c were connected serially by connecting a first end of a first cable 30a with a first end of a second cable 30b, and a second end of the second cable 30b with a first end of a third cable 30c. In particular, the conductor cores of the first cable 30a were connected to corresponding conductor cores of the second cable 30b, as indicated at reference numeral 34, and the conductive screen of the first cable 30a was connected to the conductive screen of the second cable 30b, as indicated at reference numeral 35. A corresponding connection of the second cable 30b to the third cable 30c was done.
By connecting cable cores serially, as illustrated in figure 5, three different lengths were made available for the measurements, wherein each cable 30a, 30b, 30c was 82 km long.
Besides the capacitance meter 1 according to the invention, a standard portable LCR meter was used for comparison. By the mentioned connection of cables, the available lengths were 82 km, 164 km and 246 km. Nominal capacitance according design report is C = 0,165 μΡ/km.
Measurements with a conventional LCR meter were performed at 60 Hz. The capacitance meter 1 according to the invention is, as has been described, based principle conservation of electric charge.
Table 1.
In the above table 1, the capacitance measurement value of 82 km cable length was taken as a reference value. The capacitance measurement value (capacitance μΡ /km) for cable lengths 164 km and 246 km were then expected to be the same, which would indicate accurate measurements. That is, AC in table 1 is deviation of capacitance per
km from the measured 82 km length data. For instance, for the conventional LCR- meter a capacitance of 11,97 uF was measured at 82 km length, which is equal to 0,145976 μΡ/km. The same value (0,145976 μΡ/km) was expected also at length 246 km, but the actually measured capacitance was instead 47 μΡ, i.e. 0,191057 μΡ/km, which translates to AC = 30,9 %.
From the result values obtained during the testing, indicated in the above table 1, it is clear that LCR meter results were unacceptable, showing, for instance, a deviation of almost 31 % for the longest cable length (246 km), while the inventive capacitance meter 1 provided excellent accuracy. The inventive meter showed the same value of μΡ /km irrespective of cable length.
The various features and embodiments that have been described may be combined in different ways, examples of which are given in the following.
Figure 6 is a flow chart of steps of a method for measuring power cables according to the present invention. A method 40 is provided for determining capacitance of a power cable 30 by using a capacitance meter 1, such as the capacitance meter 1 that has been described.
The method 40 comprises charging 41 a reference capacitor 15 of the capacitance meter 1 to a first voltage Vi, while discharging the power cable 30 to zero voltage, wherein the reference capacitor 15 has a first capacitance Ci.
The method 40 comprises transferring 42 charge from the reference capacitor 15 to the power cable 30, the power cable 30 thereby obtaining a second capacitance Cx. The reference capacitor 15 is discharged through the power cable 30 by disconnecting it from a power source 13, which was used for charging it. A first switch device 11 and a second switch device 12, as described e.g. with reference to figures 2 and 3, may be used for accomplishing the charging 41, discharging and charge transferring 42.
The method 40 comprises measuring 43 the voltage over the reference capacitor 15 to be a second voltage V2. The measuring 43 may be performed by a voltmeter 14.
The method 40 comprises determining 44 the capacitance Cx of the power cable 30 to be equal to the result of multiplying the first capacitance Ci with the ratio of the difference between the first and second voltages Vi - V2 and the second voltage V2:
The method 40 for measuring capacitance of a power cable 30 gives high accuracy even for power cables 30 that are longer than about 75 km, preferably longer than about 80 km, more preferably longer than about 82 km. Currently used capacitance meters are not suitable for such cable lengths, as they give too large measurement errors.
A capacitance meter 1 is also provided for determining capacitance of a power cable 30. The capacitance meter 1 comprises a reference capacitor 15 having a nominal first capacitance Ci.
The capacitance meter 1 comprises switching means 11, 12 arranged such as to:
- allow charging of the reference capacitor 15 to a first voltage Vi by means of a power source 13, while discharging the power cable 30 to zero voltage, when the switching means 11, 12 are switched in a first position 11a, 12a, and
- allow transferring of charge from the reference capacitor 15 to the power cable 30, whereby the power cable 30 obtains a second capacitance Cx, when the switching means 11, 12 are switched in a second position 11b, 12b,
- means 14 for measuring a second voltage V2 over the reference capacitor 15, when the switching means 11, 12 are switched in the second position 11b, 12b, and
- means 18, 20 for determining the capacitance, Cx, of the power cable 30 to be equal to the result of multiplying the first capacitance, Ci, with the ratio of the difference between the first and second voltages, Vi - V2, and the second voltage V2:
In an embodiment, the switching means 11, 12 comprises:
- a first switch device 11 arranged to allow charging of the reference capacitor 15 to the reference voltage Vi, when being switched in a first position 11a thereof, by connecting the power source 13 to the reference capacitor 15 such as to charge the reference capacitor 15 to the reference voltage Vi, and
- a second switch device 12 arranged to allow discharging of the cable 30 when being switched in a first position 12a thereof, by providing an electrical path for such discharging, wherein the first switch device 11 and the second switch device 12 are arranged to be switched simultaneously to their respective first positions 11a, 12a, and wherein the first switch device 11 and the second switch device 12 are, when being switched to their respective second positions 11b, 12b, arranged such as to allow transfer of charge from the reference capacitor 15 to the power cable 30, wherein the first switch device 11 and the second switch device 12 are arranged to be switched simultaneously to their respective second positions 11a, 12a (or essentially
simultaneously).
The means 18, 20 for determining the capacitance, Cx, may comprise processing circuitry 18 provided in the capacitance meter 1 and comprising e.g. computer program with computer program code, which, when executed on at least one processor of the capacitance meter 1 causes it to perform the method 40 according to any of the described embodiments thereof. In other embodiments, such processing circuitry is provided in a computer, and the means 20 for determining the
capacitance may then comprise an interface 20 towards the computer.
In some embodiments, the first switch device 11 is arranged to allow transfer of charge from the reference capacitor 15 to the power cable 30, when being switched to its second position lib, by disconnecting the power source 13 from the reference capacitor 15.
In various embodiments, the reference capacitor 15 comprises a temperature stable capacitor having a nominal capacitance in the range of 9 μΡ - n μΡ, preferably about 10 μΡ.
The method 40 and capacitance meter 1 that have been described is useful for measuring long cables, for which accurate measurement methods are lacking. In an aspect, the method and capacitance meter 1 may be used for improving on
impregnation of mass impregnated (MI) cables, in particular by allowing longer lengths to be more reliably impregnated. The measurement of the capacitance is a key measurement indicating the progress of the impregnating process and the present invention is hence a very valuable aid in obtaining a reliable impregnation by enabling accurate capacitance measurements.
The invention has mainly been described herein with reference to a few embodiments. However, as is appreciated by a person skilled in the art, other embodiments than the particular ones disclosed herein are equally possible within the scope of the invention, as defined by the appended patent claims.
Claims
Claims l. A method (40) for determining capacitance of a power cable (30) by using a capacitance meter (1), the method (40) comprising:
- charging (41) a reference capacitor (15) of the capacitance meter (1) to a first voltage Vi, while discharging the power cable (30) to zero voltage, wherein the reference capacitor (15) has a first capacitance Ci,
- transferring (42) charge from the reference capacitor (15) to the power cable (30), the power cable (30) obtaining a second capacitance Cx,
- measuring (43) voltage over the reference capacitor (15) to be a second voltage V2, and
- determining (44) the capacitance, Cx, of the power cable (30) to be equal to the result of multiplying the first capacitance, Ci, with the ratio of the difference between the first and second voltages, Vi - V2, and the second voltage V2:
2. The method (40) as claimed in claim 1, wherein the method (40) is for measuring capacitance of a power cable (30) longer than about 75 km, preferably longer than about 80 km, more preferably longer than about 82 km.
3. A capacitance meter (1) for determining capacitance of a power cable (30), the capacitance meter (1) comprising:
- a reference capacitor (15) having a nominal first capacitance Ci,
- switching means (11, 12) arranged such as to:
- allow charging of the reference capacitor (15) to a first voltage Vi by means of a power source (13), while discharging the power cable (30) to zero voltage, when the switching means 11, 12 are switched in a first position (11a, 12a), and
- allow transferring of charge from the reference capacitor (15) to the power cable (30), whereby the power cable (30) obtains a second capacitance Cx, when the switching means 11, 12 are switched in a second position (lib, 12b),
- means (14) for measuring a second voltage V2 over the reference capacitor (15), when the switching means (11, 12) are switched in the second position (lib, 12b), and
- means (18, 20) for determining the capacitance, Cx, of the power cable (30) to be equal to the result of multiplying the first capacitance, Ci, with the ratio of the difference between the first and second voltages, Vi - V2, and the second voltage V2:
4. The capacitance meter (1) as claimed in claim 3, wherein the switching means (11, 12) comprises:
- a first switch device (11) arranged to allow charging of the reference capacitor (15) to the reference voltage Vi, when being switched in a first position (11a) thereof, by connecting the power source (13) to the reference capacitor (15) such as to charge the reference capacitor (15) to the reference voltage Vi,
- a second switch device (12) arranged to allow discharging of the cable (30) when being switched in a first position 12a thereof, by providing an electrical path for such discharging, wherein the first switch device (11) and the second switch device (12) are arranged to be switched simultaneously to their respective first positions (11a, 12a), and wherein the first switch device (11) and the second switch device (12) are, when being switched to their respective second positions (11b, 12b), arranged such as to allow transfer of charge from the reference capacitor (15) to the power cable (30) wherein the first switch device (11) and the second switch device (12) are arranged to be switched simultaneously to their respective second positions (11a, 12a).
5. The capacitance meter (1) as claimed in claim 3 or 4, wherein the first switch device (11) is arranged to allow transfer of charge from the reference capacitor (15) to the power cable (30), when being switched to its second position (lib) by disconnecting the power source (13) from the reference capacitor (15).
6. The capacitance meter (l) as claimed in claim 3, 4 or 5, wherein the reference capacitor (15) comprises a temperature stable capacitor having a nominal capacitance in the range of 9 μΡ - n μΡ, preferably about 10 μΡ.
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PCT/EP2015/064886 WO2017000996A1 (en) | 2015-06-30 | 2015-06-30 | Device and method for measuring capacitance of power cables |
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PCT/EP2015/064886 WO2017000996A1 (en) | 2015-06-30 | 2015-06-30 | Device and method for measuring capacitance of power cables |
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Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
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CN110598160A (en) * | 2019-08-05 | 2019-12-20 | 北京全路通信信号研究设计院集团有限公司 | Method and system for calculating distributed capacitance in multi-core cable |
EP4012926A1 (en) * | 2020-12-09 | 2022-06-15 | Siemens Aktiengesellschaft | Direct current switch |
CN115267348A (en) * | 2022-07-11 | 2022-11-01 | 江苏亨通高压海缆有限公司 | Submarine cable armored loss factor test system and test calculation method thereof |
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US5446392A (en) * | 1993-02-10 | 1995-08-29 | Fujitsu Limited | Submarine equipment and fault locating method for a submarine communication system |
US20100181180A1 (en) * | 2009-01-16 | 2010-07-22 | Microchip Technology Incorporated | Capacitive touch sensing using an internal capacitor of an analog-to-digital converter (adc) and a voltage reference |
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US5446392A (en) * | 1993-02-10 | 1995-08-29 | Fujitsu Limited | Submarine equipment and fault locating method for a submarine communication system |
US20100181180A1 (en) * | 2009-01-16 | 2010-07-22 | Microchip Technology Incorporated | Capacitive touch sensing using an internal capacitor of an analog-to-digital converter (adc) and a voltage reference |
Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN110598160A (en) * | 2019-08-05 | 2019-12-20 | 北京全路通信信号研究设计院集团有限公司 | Method and system for calculating distributed capacitance in multi-core cable |
CN110598160B (en) * | 2019-08-05 | 2023-03-14 | 北京全路通信信号研究设计院集团有限公司 | Method and system for calculating distributed capacitance in multi-core cable |
EP4012926A1 (en) * | 2020-12-09 | 2022-06-15 | Siemens Aktiengesellschaft | Direct current switch |
US11601124B2 (en) | 2020-12-09 | 2023-03-07 | Siemens Aktiengesellschaft | DC switch |
CN115267348A (en) * | 2022-07-11 | 2022-11-01 | 江苏亨通高压海缆有限公司 | Submarine cable armored loss factor test system and test calculation method thereof |
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