CA1335210C - Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signals - Google Patents
Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signalsInfo
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- CA1335210C CA1335210C CA000616683A CA616683A CA1335210C CA 1335210 C CA1335210 C CA 1335210C CA 000616683 A CA000616683 A CA 000616683A CA 616683 A CA616683 A CA 616683A CA 1335210 C CA1335210 C CA 1335210C
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Abstract
The voltage between two objects is measured utilizing an electro-optic crystal exhibiting birefringence in two axes (slow and fast) mutually orthoganal to an optic axis extending between the two objects. Two collimated light beams polarized at an angle to the slow and fast axes is passed through the crystal parallel to the optic axis with one of the collimated light beams retarded relative to the other by about 1/4 wave. The two beams emerging from the crystal are passed through a polarizer and converted to phase-shifted electrical signals by photo diodes in electric circuits which regulate the sources of the light beams to maintain the peak magnitudes of the two electric signals constant and equal.
As another feature of the invention, a stairstep output waveform representative of the measured waveform is generated in a digital computer from a bidirectional cumulative count of zero crossings of the two electric signals which is incremented or decremented depending upon which of the two electrical signals is leading. Improved accuracy of the output signal is achieved by adjusting the stairstep waveform by the magnitude of the smaller of the two electrical signals, with the sense of the adjustment determined by the relative polarities of the two electrical signals.
As another feature of the invention, a stairstep output waveform representative of the measured waveform is generated in a digital computer from a bidirectional cumulative count of zero crossings of the two electric signals which is incremented or decremented depending upon which of the two electrical signals is leading. Improved accuracy of the output signal is achieved by adjusting the stairstep waveform by the magnitude of the smaller of the two electrical signals, with the sense of the adjustment determined by the relative polarities of the two electrical signals.
Description
W.E. 54,510 ~3352~
Background of Invention Field of Invention Thls inventlon relates to an electro-optical system for accurately determining the electrical voltage between two spaced objects. More speclfically, the inventlon relates to a system which utilizes an electro-optlcal crystal with a fourfold axis of rotary inversion which exhiblts birefringence in proportion to the magnitude of an applied eleçtric field. In particular, it relates to generating two electrical signals in quadrature from parallel beams of collimated polarlzed light whlch are passed through the electro-optical crystal and retarded by fractlonal waveplates to produce a relative retardation of 1/4 wave. Finally, the invention relates to deriving a representation of the voltage waveform generating the fleld applied to the electro-optlc crystal from the two electrlcal slgnals in quadrature utilizing a digltal computer.
Background Information Electro-optical systems for measuring electric voltages are known. For instance, devices known as Pockel cells utilize certa1n crystals which exhibit birefringence, that is a difference in the index of refraction in two orthogonal planes, in the presence of an electric fleld.
Some of these crystals, such as, for example, KDP (potassium ~Qr -2- W.E. 54,510 dlhydrogen phosphate), have a fourfold axis of rotary inverslon. Such materials have the property that in the absence of an electrlc field the index of refraction for light propagating along the fourfold axls lS independent of the plane of polarization of the light. However, if an electric fleld is applied parallel to the direction of the llght, the index of refraction for light polarized in one direction transverse to the fourfold ax1s, known as the fast axls lncreases and that ln an orthogonal dlrection, also ~o transverse to the fourfold axis, and known as the slow axis, decreases by an amount which lS proportional to the strength of the electrlc field. In such Pockel cell devices, lf light is polarized in a plane whlch forms an angle to these transverse axes, the component of the polarized llght in the directlon of the slow axis wlth the decreased index of refraction is retarded with respect to the other component. If the crystal i8 aligned with its fourfold axis extendlng between the objects between which the voltage is to be measured, and the polarized light is directed parallel to the fourfold axis, the total retardation will be proportional to the total voltage differential between the two objects. This retardation is typically measured ln wavelengths. The retardation lS detected in an analyzer and converted to an electrical signal for producing an output representative of the magnitude of the voltage generatlng the field. Due to the cylic nature of this electrlcal slgnal, the output is only unambiguous for voltages producing a retardation which is less than the half wave voltage for the crystal. In RDP, this half wave voltage is about 11300 volts. This type of device is therefore not sultable for measuring transmission line voltages which can be 100,000 volts rms and more.
Other types of crystals used in Pockel cells respond to an electric field in a direction perpendicular to W.E. 54,510 the dlrectlon of propagatlon of light through the cell.
Such cells only provide an lndicatlon of the potential at the lntersectlon of the beam with the fleld. Thus, a slngle cell cannot integrate the potentlal over the full space between two objects, and therefore these devlces do not provlde an accurate measurement of the voltage between the two objects. Systems uslng this type of Pockel cell commonly either, (1) measure the potential at one polnt and assume that the potentlal at all other polnts between the two objects can be derived from thls single measurement, or ~2) provlde some sort of voltage dlvider and apply a fixed fraction of the line voltage to the cell in an arrangement whlch malntains the fleld within the cell constant. The problem wlth the first approach is that except for low impedance paths, the field along a path is sensitlve to the locatlon of any conducting or dielectric bodies in the viclnity of the path. Thus, if this type of Pockel cell is mounted on the surface of a conductor and the field measured, the reading would depend on the slze and shape of ~0 the conductor, on the distance from the conductor to ground, on the location and potential of any nearby conductors, on the location of any insulating or conducting bodies near the sensor or on the ground beneath the sensor, and on the presence of any birds, rain droplets or snow between the sensor and ground. Thus, only under very ideal circumstances would accurate measurements be possible with such a system. The problem with the second approach lS in provlding an accurate stable voltage divider.
Optical voltage measuring systems are deslrable because they provide good isolation from the voltage belng measured. Through the use of optic fiber cables, it is possible to easily and conveniently provide remote indicators which are not subject to the electrlcal disturbances which remote indicators fed by electrical s1gnals must contend with.
W.E. 54,510 There remalns, however, a need for an optlcal system for accurately measuring very large voltages such as, for example, those present in electrical transmission systems without the use of a voltage divider.
S~bordinate to this need lS a need for such an optical system whlch can integrate the field over the entire space between the objects, such as in the case of the electrlcal transmlssion system between line and ground.
Summary of the Invention 0 These and other needs are satisfled by the inventlon which is directed to a method and apparatus for measuring an electrlcal potential between two spaced apart objects utilizing a crystal having a fourfold axis of rotary inverslon extending between the spaced apart objects.
lS Collimated light polarized with a plane of polarization formlng an acute angle to the fast and slow axes of the crystal by first polarizing means is directed through the crystal parallel to the fourfold axis of rotary inversion.
Retardatlon, due to the electric field, of the polarlzed colllmated light passed through the crystal, is detected by addltional polarizing means. The llght emerging form the addltional polarizing means is converted to electrlcal signals by photodetectors. To ellminate ambiguities in the measurement of voltages which exceed the half-wave voltage of the crystal, a first portion of the polarized colllmated light is retarded wlth respect to a second portlon.
Preferably, this retardatlon is 1/4 wave so that the two electrical signals generated from the two portions of polarized collimated light are ln quadrature.
Preferably, the collimated light is generated by two separate light sources. The parallel collimated llght beams produced by these two sources are polarized by the first polarized means and pass through the electro-optic crystal to f~rm the first and second portions of the W.E. 54,510 polarlzed collimated llght which are converted lnto the two electrical slgnals. The intensities of these llght sources for the two beams are regulated by feedback circuits to malntaln the peak to peak values of the two electrlcal signals constant and equal.
One feature of the lnventlon is a method and apparatus for derivlng a waveform representative of an orlginal waveform, such as the voltage generating the fleld applied to the crystal in the voltage measuring system, from 0 two phase shifted electrical signals such as the two constant peak amplitude electrical signals generated by the photodetectors in the voltage measuring system. In one sense, the original waveform is reconstructed from selected segments of the two electrical signals with the segments selected in part as a function of the sequence of zero cross1ngs of the two electrical signals. At another level, the representative waveform can be constructed as a stairstep signal having discrete incremental values which increment or decrement with each zero crossing depending upon which of the two electrical signals is leading.
Reversal of direction of the measured waveform can be detected, for instance, from two zero crosslngs in succession by one of the two electrical signals.
While such a stairstep waveform may be adequate for many applications, the accuracy of such a signal does not reach the 0.1% desired in the measurement of transmission line voltages which, for example, can be 260,000 volts peak to peak or 93,000 volts rms.
Accordingly, the invention includes interpolating between steps of the stairstep waveform using the instantaneous value of a selected one of the two electrical signals. The value of the electrical signal which is smaller in magnltude is always selected for the interpolation. This results in utilization of portions of the component waveforms where the small angle approximation, that is where the sine of the angle is approximately equal to the angle, is valid, and hence the errors introduced by the interpolation are small.
In order to eliminate erratic indexing of the zero crossing count for random behavior of the electrical signals around zero, a dead band is centered on the zero axis of the electrical signals.
When the value of the smaller electrical signal enters this dead band, indexing of the zero crossing count is suspended until the signal emerges from the band. If it exits on the opposite side of the band from which it entered, the zero crossing count is indexed. Whether it is incremented or decremented depends upon the direction in which the original waveform is moving, which is manifested by which of the quadrature electrical signals is leading. If the electrical signal of smaller magnitude exits on the same side of the dead band as it entered, the measured waveform has changed direction and the zero crossing count is not indexed. Preferably, the magnitude of the electrical signal required to exit the dead band is greater than that required to enter. This hystereses in the width of the dead band prevents erratic behavior at the boundaries.
While this reconstruction of a waveform from phase shifted electrical signals is particularly suitable for use in the opto-electrical system, which is also part of the invention, for generating waveforms representative of sinusoidal voltage waveforms of large magnltude, it also has applicability to reconstructing other types of waveforms in other applications.
- 6a -In accordance with a particular embodiment of the invention there is provided a method of constructing a waveform signal representative of an original waveform which has been resolved into first and second bipolar electrical waveform signals substantially in quadrature and having substantially constant and equal peak magnitudes comprising the steps of:
periodically generating data samples representative of the instantaneous value of said first and second electrical signalsi determining from said data samples zero crossings of said first and second electrical signals;
accumulating a bidirectional cumulative count of said zero crossings, with the direction of counting being determined by which of said first and second electrical signals is leading; and generating an output signal representative of the original waveform from said cumulative count of zero crossings.
Brief Description of the Drawinqs A full understanding of the invention can be gained from the following description of the preferred embodiment when read in conjunction with the accompanying drawings in which:
7 1 3352 1 ~W.E. 54,510 Figure 1 is a schematic diagram lllustratlng the prlnclple of operation of voltage measurlng systems which form a part of the invention.
Figure 2 is a schematic diagram of a voltage measuring &ystem in accordance with the invention.
Figures 3a, b and c are waveform dlagrams lllustrating respectlvely the line to ground voltage to be measured, the waveforms of the phase shifted electrical signals generated by the opto-electrical measurement system 0 of Figure 2, and the output waveform reconstructed from the phase shifted electrical waveforms.
Figure 4 is a dlagram illustrating how the output waveform is reconstructed from the phase shifted electrical waveforms.
Figure 5 is a flow chart illustrating the program used by the system of Figure 2 to construct the output waveform from the phase shifted electrical waveforms in the manner illustrated in Figure 4.
Figure 6 is an isometric view with part broken away of apparatus for measuring line to ground voltages in a hlgh voltage electric power transmission system in accordance with the inven~ion.
Figure 7 is an enlargement of a subassembly of Figure 6.
Figure 8 is a vertical section through a component which lS part of the subassembly of Figure 7.
Description of the Preferred Embodiments As is known, the voltage between two spaced points a and b is defined by the equation:
- Vab =r E(x) dx (Eq. 1) ~ ~ a .
W.E. 54,510 where E(x) lS the field gradient at x and the integral is lndependent of path. Thus, ln order to accurately measure the voltage between spaced polnts a and b, lt lS necessary that a sensor physically extend from a to b, lnteract with the fleld at every point along its length, and change some property so that some parameter varies in an addit~ve fashion allowing the integral to be evaluated. In the measurement of transmission line voltages, this requlres that one end of a sensor be electrically connected to the transmlssion line and - the other end be electrically connected to ground. Thus, the sensor must be of sufficient length to withstand normal line voltages and any surges whlch might be encountered.
The present invention utlllzes an electro-optlc crystal to measure the integral of the field gradient from point a to b and thus provides a true value for the voltage between a and b. As mentioned previously, certain crystaline materials having a fourfold axis of rotary lnversion, such as RDP (potassium dihydrogen phosphate), have the property that in the absence of an electrical fleld, the index of refraction for light propagating along the fourfold axis is independent of the direction of polarization of the light. However, if an electric field is applied parallel to the dlrection of propagation of the light, the index of refraction for light polarized in a given direction perpendicular to the fourfold axis increases while the index of refraction of light polarized in a perpendlcular direction decreases by an amount which is proportional to the field. In RDP, the direction parallel to the fourfold axis, which is also called the optic axis, is commonly deslgnated as the Z direction, and the orlentations of the polarlzation for whlch the maximum changes in refractive index with electric field are observed are commonly designated as the X and Y directions.
-9- 1 3352 1 o W.E. 54,510 To understand the prlnciple of operation of such an opto-electrical sensor, reference is made to Figure 1.
In the conventlonal Pockel cell device 1, a KDP crystal 3 lS
allgned wlth its fourfold axis of rotary inversion, Z, parallel tQ the field gradient, Fg to be measured. A slngle beam of unpolarlzed llght is incident on a first linear polarizer 7. The crystal 3 and first polarizer 7 are arranged such that collimated polarized light, 5p exiting the polarizer is propagating parallel to the Z axls of the 0 crystal and the plane of polarization of the light is at an angle of 45 degrees to the X and Y axes of the crystal.
The incident polarized beam 5p can be decomposed into two components of equal intensity, one polarized parallel to the X axis and the other polarized parallel to the Y axis. In the absence of an electric field, these two components will propagate with equal velocities and exit the crystal 3 ln phase with one another. When an electric field is applied along the Z axis of the crystal, the refractive indexes, and, as a result, the velocities of the two components will not be equal, and there will be a phase shlft or a retardation between the two components when they exit the crystal. Since the retardation in any small element along the crystal is proportional to the electric field acting on that element multiplied by the length of the element, and the total retardation is equal to the sum of the retardations in all of the elements along the crystal, retardation of the components exiting the crystal is proportional to r Edl, and thus the difference in voltage between the two ends of the crystal.
The retardation is usually expressed in wavelengths, that is a retardation of one means the optical path in the crystal ls one wavelength longer for one of the components of the beam 5p than for the other, and is given by the equation: y~
W.E. 54,510 1 3352 1 ~
s r = r63 n 3 x V (Eq. 2~
where r63 is an electro-optic coefficient, nz, is the refractlve index for light propagating along the Z axis, lS the wavelength of the light in vacuum, and V is the dlfference ln voltage in the two ends of the of the crystal. Whlle these parameters are known and the retardation can be calculated, it is usually more convenient to comblne them in a single parameter, the half-wave voltage, Vh, deflned by the equation:
Vh ~ (Eq. 3) 2 r63 n 3 and thus:
r = v (Eq. 4) 2vh Vh lS usually determined as part of the calibration of the sensor. If the two components of the beam 5p exltlng the crystal are passed through a second polarizer 9 oriented ~0 parallel to the first, the intensity of the beam I exiting the polarizer 9 is related to the retardation by equation:
I - Io Cos2 (~ r ) (Eq. 5) where Io is the intenslty of the exiting beam with zero retardation: That is, with no voltage difference between the ends of the crystal. If the second polarlzer 9 is rotated 90 degrees, then I is given by equation S in which the square of the sine function is substituted for the square of the cosine function.
It is common in such Pockel cell devices described to this point to insert a fractional wave plate 11 between the crystal dnd th~e second polarizer 9 to shlft the -11- 1 3352 1 0 W.E. 54,510 retardatlon to a linear point on the sine or cosine squared function.
Because of the periodic properties of the sine and cosine functions, a device as discussed to this point would only provide unambiguous results for voltages less than Vh. For KDP, at a wavelength of 800nm, Vh is roughly 11,300 volts, and thus such a device cannot be used to measure transmission line voltages which are typlcally around 100,000 volts rms line to ground or more.
In order to resolve the ambigulties inherent in the conventional Pockel cell arrangement, and allow measurements at transmlssion line voltages, the present lnventlon utilizes a second light beam 13 parallel to the beam 5. This second light beam 13 is polarized by the first polarizer 7 to form a second polarlzed light beam 13p which is passed through the crystal 3 parallel to the Z axis.
Thls second polarized light beam 13p can also be resolved lnto two components, one parallel to the Z axis and the other parallel to the Y axis. The second beam exiting the crystal 3 is also passed through the second polarizer 9 so that the intenqity of the second beam exitlng polarlzer 9 is also related to the retardation by equation 5 lf the second polarizer is oriented parallel to the first polarizer 7 or by the sine squared function if the second polarizer is orthogonal to the first polarizer. The second light beam 13 exitlng the crystal 3 lS also retarded by a fractlonal wave plate 15 before passing throùgh the second polarizer 9. The fractional wave plates 11 and 15 are selected so that one beam 1S retarded with respect to the other. In the preferred form of the invention, the one beam is retarded 1/4 wave with respect to the other so that the beams exltlng-the second polarizer are in quadrature. This retardation - may be accomplished by utilizing one-eighth wave plates for the fractiona~ wave ~lates 11 and 13 with their axes 17 and W.E. 54,510 19 respectlvely oriented 90 degrees wlth respect to one another. Other arrangements can be used to retard the one light beam 1/4 wave with respect to the other. For lnstance, one beam could be passed through a quarter wave plate while the other passes directly from the crystal to the second polarizer. Retarding one beam exactly 1/4 wave with respect to the other simplifies the calculation required, but as long as the retardation is about 1/4 wave, meanlng within about plus or minus 20~ of 1/4 wave, `0 satlsfactory results can- be achieved. In addition to 1/4 wave retardation, odd multiples of 1/4 wave can also be used i.e., 3/4, 5/4 et cetera.
With the two one-eighth wave plates oriented as indicated in Figure 2, the intensities of the two beams exiting the second polarizer can be determined as follows:
I1= Io Cos2 ( ~ r ~ ~ /8) (Eq. 6) and I2= Io Cos2 ( ~ r - ~/8) (Eq. 7) These two signals are in quadrature and, with the exceptlon of a constant, allow the unambiguous determination of the voltage applied to the crystal.
Figure 2 illustrates schematically a complete voltage measuring system in accordance with the invention.
This system 21 includes the sensor 1 comprising the crystal 3, the flrst and second polarizers 7 and 9 respectively, and the one-eighth wave plates 11 and 15. The system 21 also includes first and second light sources 23 and 25 which generate the two collimated light beams 5 and 13 respectively. The light source 23 includes a light emitting dlode (LED) 27. Light produced by the LED 27 is transmitted by OptlC fiber cable 29 and passed through collimating lens 31 to produce the fi~st collimated light beam 5. Similarly -13- 1 3352 1 0 W-E- 54,510 the LED 33 ln second light source 25 produces light which is transmltted by the optic fiber cable 35 and passed through colllmating lens 37 to produce the second collimated light beam 13. Light from the first beam 5 exiting the second S polarizer 9 is gathered by lens 39 and conducted through fiber optic cable 41 to a first electronic circuit 43.
Simllarly, the second beam exiting the second polarlzer 9 is focused by lens 45 on fiber optic cable 47 which directs the llght to a second electronic circuit 43.
The electronic circuits 43 are identical and include a photo diode 49 which converts the light beam carried by the optic fiber cables 41 or 47 respectively into an electrical current. The electronic circuits 43 include a transimpedance amplifier 51 which provides a low impedance lnpUt to a peak detector 53. Peak detector 53 includes a dlode 55 which feeds a capacitor 57 shunted by leak reslstor 59. The peak detector al~o includes a buffer amplifier 61 to prevent the peak detector from being loaded by the following stage. The following stage 63 acts as a summing ampllfier, integrator, and a driver for the respective LED
27 or 33. It includes a pair of resistors 65, and an operational amplifier 67 shunted by an integrating capacitor 69. An output circuit includes a pair of resistors 71 and 71' (equal to twice 71 in value), and an output ampllfier 73. A reference voltage -er is applied to the summlng circuits formed by the resistors 65 and 71-71'.
The electronic circuits 43 operate as follows:
Light exiting the second polarizer 9 and transmitted via the optic flber cable 41 or 47 respectively is converted to an electrlcal current signal by the photo diode 49. The peak detector 53 generates a signal which represents the peak value of this electrical current. The peak value s1gnal lS
compared with the reference signal through the resistors 65 connected to the ~verting input of the operatlonal W.E. 54,510 -14- 1 3352 1 ~
ampllfler 67. Since the diode 55 assures that the peak Slgnal lS posltlve, and since the reference signal -er lS
negative, these two signals are compared and the error between the two is applled to the lntegrator formed by the operatlonal amplifler 67 and the capacltor 69. Thls lntegrated error signal is used to drlve the LED 27 or 33 respectively of the llght sources for the first and second llght beams. Thus, the clrcuits 43 are feedback circults which regulate the lntensity of the respective llght beam so that the peak values of the current slgnals generated by these light beams through the photo detectors 49 remain constant and equal to the reference voltage and, hence, equal to each other. The summing amplifler 73 and voltage divlding reslstors 71 subtract the reference voltage from the unidirectional currents produced by the photodetectors 49 to produce blpolar voltage output signals el and e2 respectlvely in response to the field applied to the crystal 3. The analog signals el and e2 are periodically sampled by an analog to digital converter 75 for input into a digital computer 77. The digital computer 77 reconstructs the voltage waveform from the two signals el and e2 for Z5 presentation on an output device 79. The output device 79 can be, for instance, a digital readout, and/or can be a recorder which generates a permanent log of the measured voltage waveform.
Waveforms a, b and c of Figure 3 illustrate on a comparative time basis the voltage waveform VI to be measured, the quadrature electrical signals el and e2 generated ln response to the voltage waveform a by the system of Figure 2, and the output waveform V0 generated by the system of Flgure 2 whlch is representative of the voltage waveform a.
Figure 4 illustrates the manner in whlch the waveform c in Figure- 3 is constructed from the quadrature -15- 1 3352 1 0 W-E- 54,510 electrical signals el and e2 forming the waveform b in Flgure 3. Essentially the method comprises maintainlng a bldirectional count of the number of zero crosslngs of the two electrical signals e1 and e2. In the example given in Figure 4, the count, n of such zero crossings is shown across the top of the figure. The count n is incremented as the voltage waveform represented by e1 and e2 is becoming more positive (or less negative) and is decremented as the magnltude of the incremented waveform is becoming more o negatlve ~or less positive). The direction in which the waveform is moving is determined by which of the quadrature signals is leading. Reversal of the dlrection of the voltage waveform results in a switch in which signal el or e2 lS leading and can be detected by two successive zero crossings by the same signal el or e2.
A stairstep approximation of the voltage waveform indicated by the trace 81 in Figure 4 can be generated from the cumulative count n of the zero crossings. In the partlcular sample shown, the output stairstep waveform is generated as a function of twice the accumulated count n as shown by the scale on the left side of the trace 81 ln Figure 4.
This stairstep approximation 81 of the original voltage waveform generating the field applied to the opto-electrical sensor can be adequate for many purposes.However, where more accurate reproduction of the origlnal voltage waveform is required, such as in monitoring the voltage of high power transmission lines where an accuracy of 0.1 percent is required, interpolation must be made between the stairstep values of the output signals generated by the accumulated zero crossing count n. Thls smoothing of the output waveform is achieved by adding or subtracting the instantaneous value of a selected one of the quadrature sl~nals e~ and e2 to the stairstep value. The 1 3352 1 0 W.E. 54,510 selected signal is the one of the two signals, el and e2, WhlCh lS smaller in magnitude at the given instant. Thus, the magnitude of the signal el or e2 whlch is between the traces 83 and 85 in Figure 4 is selected. This results in utllization of portlons of the waveforms el and e2, where the small angle approxlmation, that is, where the slne of the angle is approximately equal to the angle, lS valid. As can be seen ln Figure 4, the technique essentially results in the stringing together of the segments of the quadrature signals el and e2 to reconstruct the original voltage waveform.
In order to avoid random indexing of the bidirectional cumulative count n of zero crossings which could occur with small signals, a band is created around the zero axis as indicated by the lines 89 and 91 in Figure 4.
Zero crossings are not counted while a signal el or e2 is in this dead band. Instead, a determination is made when the slgnal again leaves the dead band as to whether the zero crosslng n should be indexed. If the quadrature signal exits the dead band on the same side that it entered, then the target signal has changed direction and n should not be indexed. If the quadrature signal exits the dead band on the opposite side from which it entered, then there has been a zero crossing and n is indexed. While a quadrature slgnal lS within the dead band, its magnitude is continued to be used to interpolate between the stalrsteps. If the quadrature signal crosses the zero axis, the sign of the increment which is added or subtracted to the stairstep is changed to reflect this transition. This delay in the indexing of the zero crossing count n until the quadrature signal leaves the dead band results in a slight shlft in tlme of the stairstep signal, as indlcated at 93 in Figure 4. The width of the dead band should be set as wide as posslble wlthout having the instantaneous values of both -17- 1 3352 1 0 W.E. 54,510 el and e2 fall withln the band at anytime. Preferably, the boundarles of the dead band are expanded to 89'-91' once a signal is withln the band. This introduces hysteresis into the dead band which alds in assuring a positive transltlon lnto and out of the dead band.
Flgures 5a and 5b constitute a flow chart of the program employed by the digital computer 77 to reconstruct the voltage waveform sensed by the sensor from the quadrature electrical signals el and- e2, in the manner dlscussed in connection in Figure 4. As discussed previously, the analog quadrature signals el and e2 are applied to an analog to digital converter to generate digitaL samples of the instantaneous value of these waveforms for processing by the digital computer. The sampling rate should be sufficiently rapid that, at the maximum slew rate of the voltage signal being measured, which usually occurs at the its zero crossing, at least one data sample for el or e2 falls within he dead band. The sampling rate for the 60 hz voltage signal was 400 RHz in the exemplary system. As indicated at block 101 in Flgure 5a, the program waits for each new data sample. Two varlables, El and E2, are set equal to the current instantaneous value of the quadrature signals el and e2 respectively at 103 when each new data sample is acqulred.
Another variable S which indicates whether the signs of the current values of El and E2 are the same is set, and that indication is saved as an additional variable SS in block 105.
A flag Ql~ which has a value of 1 if the preceding El was inside the dead band defined by the lines 89-91 (entering) and 89'-91' (exiting) in Figure 4, is checked block 107. If the preceding El was inside the band and the present value of the first quadrature signal remains inslde the band as determined in block 109 (using the larger W.E. 54,510 boundary of llnes 89'-91' equal to 0.24 ER), then the varlable S, which wlll be recalled lS an indicatlon of whether the signs of El and E2 are the same, is set at 111 equal to S0 which is the value of S for the precedlng data polnt.
If El has emerged from the dead band, then the flag Ql is made equal to zero at 113 and it becomes necessary to determlne whether the zero crosslng count, n, should be indexed, and if so, in which direction. This is 0 accomplished by setting another variable A at 115 to lndicate whether the sign of the present El is equal to the sign of Eloo which lS the last value of El before El entered the dead band. For the purpose of this determination, the sign of El is +l if El has a positive value, or -1 if it has a negative value so that A can have a value of -2, +2 or zero. If the signs of El and Eloo are the same as determined in block 117, El has emerged from the same side of the dead band at which it entered and hence there has been no zero crossing. If these signs are not the same, then El has emerged from the opposite side of the dead band from which it entered and hence there was a zero crossing and n must be indexed. If the sign of A is the same as the sign of E2 as determined in block 119 then the voltage is golng up and a variable D is set equal to one at 121. If these signs are not equal, then the voltage is going down and D is set at equal to minus one at 123. The cumulative zero crossing count n is then indexed in the proper dlrection at block 125.
If it was determined back at block 107 that the precedlng instantaneous value of El was outside the dead band, then a check is made at 127 to determine if the present value of El is within the dead band (using the narrower boundary defined by lines 89-91 in Figure 4). If El ls now in the dead band, then the flag Ql is made equal -19- 1 3 3 5 2 1 0 W. E. 54,510 to one, Eloo which is a variable equal to the last value of El before the band was entered is made equal to Elo which lS
the precedlng value of El, and S which, lt will be recalled, lS an lndlcation of whether the slgns of El and E2 are the S same lS made equal to S0 which is the value of S for the last point, all as indicated at block 129. If El remains outslde of the dead band, then a determination is made at block 131 as to whether the preceding value of E2 was outside the band. If it was, and the present value of E2 lS
wlthln the band as determlned at block 133 (using the enterlng boundary lines 89-91 in Figure 4), then a flag Q2 is made equal to one, the last value of E2 before lt went lnto the band lS saved, and S is made equal to S0 all in block 135. If it was determined in block 133 that E2 was not within the band, then both El and E2 remain outside the dead band and the program proceeds ~to the calculation of the present value of the voltage signal~ in the manner discussed below. ~
If it was determined at 131 that E2 was inside the band at the previous data polnt, a determination is made at block 137 whether it is still within the band. If it lS, S
is set equal to S0 in 139. If E2 has now emerged from the band, then the flag Q2 is set equal to zero at 141. A
determination is then made in blocks 143 and 145 uslng the variable A in a manner similar to that described in connection with blocks llS and 117,`to determine whether the zero crossing count n should be indexed. If E2 has emerged from the opposlte side of the dead band from that from which it entered, then n is incremented or decremented in box 147, 149, 151 and 153 using the same technique as described ln connection wlth emergence of El from the dead band. That lS, n ~s incremented if waveform el leads e2 and hence the voltage belng measured is increasing, or n is decremented when the measured voltage is decreasing.
-20- 1 3352 1 o W.E. 54,510 Turnlng to Figure 5b, a determlnatlon is made in block 155 whether there has been a zero crossing by determinlng lf SS, which is the saved sign, lS equal to S, which was set equal to S for the preceding data polnt lf either El o-r E2 lS currently in the band. If there has been a zero crosslng, a variable P is set equal to mlnus one at 157, otherwlse P is set equal to plus onè at 159.
If El and E2 are not of the same sign as determined in block 161 and E2 is of smaller magnitude as 0 determined ln block 163, then a voltage EC is calculated uslng the cumulatlve zero crossing count n and the current magnitude E2 in the equation in block 165. However, if E
and E2 are not of the same sign but El is smaller than E2, then El is used with n to calculate EC using the formula ln block 167. When El and E2 are of the same sign, as determined at 161 and El lS smaller, as determined at 169, then El is used with n to calculate the value of EC in block 171. On the other hand, if E2 is the smaller of the two signals which are not of the same sign, then E2 is used with n to calculate EC in block 173. As will be noticed, the flrst term in the equations for EC in blocks 165 through 171 determlnes the stairstep value from the cumulative count of zero crossings n, and the second term provides the lnterpolation based upon the magnitude of the selected quadrature signal.
The calculated voltage EC is then multiplied by a scaling factor in block 173 to determine the instantaneous magnitude, E, of the measured voltage.
It is convenient to chose er, the reference voltage used in the electronic circuits, equal to 2.828 volts, so that that the quantity .3535 x er = 1 and 2 x 3535/er = 1/4 and hence the computations in blocks 165, 167, 171, 173 and 175 are simplified.
1 33521 0 W.E. 54,510 The measured voltage is unambiguously determlned by this procedure except for a constant error. This error ls the result of the uncertainty of the initial value of n when the program is started. It is noted that n is an 5 integer but otherwise arbitrary. If n can be set equal zero when the voltage is zero, then subsequent voltage measurements will be correct. In general this is not possible and one must adjust n in integer steps until the . average value of the calculated voltage over one cycle is o zero. After n is properly adjusted, the calculated voltages will be corcect until the program is interrupted.
The program is completed by storing the present values of S, El and E2 as the last value in block 177 in preparation for the next computation of E. The program then loops back to the beginning and waits for the next input of data.
Figures 6 through 8 illustrate a practical embodlment of a sensor 1, mounted in an insulation column 201 which is cut away to show the mounting of the sensor.
An upper supporting tube 203 is connected to a transmission line (not shown) and a lower supporting tube 205 is connected to ground. Both tubes are electrically c_nducting and provide contact between the ends to the sensor 1 and the line and ground respectively through mounting discs 207 constructed from electrically conducti~g transparent material such as NESA glass. Crystal 209 and the polarizers 211 and 213 are made with a circular cross section rather than square as in Figure 1 and 2 to reduce the electrical stresses.
As shown more clearly in Figure 7 for the second polarizer 213, two cylindrical collimators 215 are mounted on one flat end face of the cylindrical polarizer and rectangular one-eighth wave plates 217 and 219 are mounted against the opposite ~nd. The collimators 215, which focus -22- W.E. 54,510 the llght beams received from the second polarizer 213 on the OptlC fiber cables 221, are shown broken away in Figure 8. Each collimator 215 is formed from two pieces 223 and 225 of low refractive index glass, such as fused slllca and one plçce of hlgh index glass 227 such as SF59. The radius of the curved surface of 227, the thickness of 227 and the length of 225 are chosen so that a bundle of parallel llght entering 223 is focused on to the end of OptlC flber 221 and the rays from the edge of the bundle `0 strlke the fiber. More partlcularly, these parameters a chosen so that the radius of the bundle of light divided by the focal length of the lens is equal to or greater than the numerlcal aperture of the f1ber dlvided by the refractlve index of the lower refractive index glass. The collimators at the other end of the sensor are similarly designed, but operate in the reverse directlon to transform light received from the fiber optic cable into the bundle of parallel light whlch lS passed through the first polarizer 211. Thls form of a collimator is necessary since in order to withstand the ~0 hlgh electrical stresses during operation, and especlally lmpulse tests, the insulator 201 is filled with oil or pressurized sulfur hexafluroide (SF6), and thus the optical system cannot have any glass air interfaces.
While specific embodiments of the invention have been described in detail, it wlll be appreciated by those skilled - in the art that various modifications and alternatlves to those details could be developed in light of the overall teachings of the disclosure. Accordingly, the particular arrangements disclosed are meant to be illustratlve only and not limiting as to the scope of the lnvention which is to be given the full breadth of the appended clalms and any and all equivalents thereof.
Background of Invention Field of Invention Thls inventlon relates to an electro-optical system for accurately determining the electrical voltage between two spaced objects. More speclfically, the inventlon relates to a system which utilizes an electro-optlcal crystal with a fourfold axis of rotary inversion which exhiblts birefringence in proportion to the magnitude of an applied eleçtric field. In particular, it relates to generating two electrical signals in quadrature from parallel beams of collimated polarlzed light whlch are passed through the electro-optical crystal and retarded by fractlonal waveplates to produce a relative retardation of 1/4 wave. Finally, the invention relates to deriving a representation of the voltage waveform generating the fleld applied to the electro-optlc crystal from the two electrlcal slgnals in quadrature utilizing a digltal computer.
Background Information Electro-optical systems for measuring electric voltages are known. For instance, devices known as Pockel cells utilize certa1n crystals which exhibit birefringence, that is a difference in the index of refraction in two orthogonal planes, in the presence of an electric fleld.
Some of these crystals, such as, for example, KDP (potassium ~Qr -2- W.E. 54,510 dlhydrogen phosphate), have a fourfold axis of rotary inverslon. Such materials have the property that in the absence of an electrlc field the index of refraction for light propagating along the fourfold axls lS independent of the plane of polarization of the light. However, if an electric fleld is applied parallel to the direction of the llght, the index of refraction for light polarized in one direction transverse to the fourfold ax1s, known as the fast axls lncreases and that ln an orthogonal dlrection, also ~o transverse to the fourfold axis, and known as the slow axis, decreases by an amount which lS proportional to the strength of the electrlc field. In such Pockel cell devices, lf light is polarized in a plane whlch forms an angle to these transverse axes, the component of the polarized llght in the directlon of the slow axis wlth the decreased index of refraction is retarded with respect to the other component. If the crystal i8 aligned with its fourfold axis extendlng between the objects between which the voltage is to be measured, and the polarized light is directed parallel to the fourfold axis, the total retardation will be proportional to the total voltage differential between the two objects. This retardation is typically measured ln wavelengths. The retardation lS detected in an analyzer and converted to an electrical signal for producing an output representative of the magnitude of the voltage generatlng the field. Due to the cylic nature of this electrlcal slgnal, the output is only unambiguous for voltages producing a retardation which is less than the half wave voltage for the crystal. In RDP, this half wave voltage is about 11300 volts. This type of device is therefore not sultable for measuring transmission line voltages which can be 100,000 volts rms and more.
Other types of crystals used in Pockel cells respond to an electric field in a direction perpendicular to W.E. 54,510 the dlrectlon of propagatlon of light through the cell.
Such cells only provide an lndicatlon of the potential at the lntersectlon of the beam with the fleld. Thus, a slngle cell cannot integrate the potentlal over the full space between two objects, and therefore these devlces do not provlde an accurate measurement of the voltage between the two objects. Systems uslng this type of Pockel cell commonly either, (1) measure the potential at one polnt and assume that the potentlal at all other polnts between the two objects can be derived from thls single measurement, or ~2) provlde some sort of voltage dlvider and apply a fixed fraction of the line voltage to the cell in an arrangement whlch malntains the fleld within the cell constant. The problem wlth the first approach is that except for low impedance paths, the field along a path is sensitlve to the locatlon of any conducting or dielectric bodies in the viclnity of the path. Thus, if this type of Pockel cell is mounted on the surface of a conductor and the field measured, the reading would depend on the slze and shape of ~0 the conductor, on the distance from the conductor to ground, on the location and potential of any nearby conductors, on the location of any insulating or conducting bodies near the sensor or on the ground beneath the sensor, and on the presence of any birds, rain droplets or snow between the sensor and ground. Thus, only under very ideal circumstances would accurate measurements be possible with such a system. The problem with the second approach lS in provlding an accurate stable voltage divider.
Optical voltage measuring systems are deslrable because they provide good isolation from the voltage belng measured. Through the use of optic fiber cables, it is possible to easily and conveniently provide remote indicators which are not subject to the electrlcal disturbances which remote indicators fed by electrical s1gnals must contend with.
W.E. 54,510 There remalns, however, a need for an optlcal system for accurately measuring very large voltages such as, for example, those present in electrical transmission systems without the use of a voltage divider.
S~bordinate to this need lS a need for such an optical system whlch can integrate the field over the entire space between the objects, such as in the case of the electrlcal transmlssion system between line and ground.
Summary of the Invention 0 These and other needs are satisfled by the inventlon which is directed to a method and apparatus for measuring an electrlcal potential between two spaced apart objects utilizing a crystal having a fourfold axis of rotary inverslon extending between the spaced apart objects.
lS Collimated light polarized with a plane of polarization formlng an acute angle to the fast and slow axes of the crystal by first polarizing means is directed through the crystal parallel to the fourfold axis of rotary inversion.
Retardatlon, due to the electric field, of the polarlzed colllmated light passed through the crystal, is detected by addltional polarizing means. The llght emerging form the addltional polarizing means is converted to electrlcal signals by photodetectors. To ellminate ambiguities in the measurement of voltages which exceed the half-wave voltage of the crystal, a first portion of the polarized colllmated light is retarded wlth respect to a second portlon.
Preferably, this retardatlon is 1/4 wave so that the two electrical signals generated from the two portions of polarized collimated light are ln quadrature.
Preferably, the collimated light is generated by two separate light sources. The parallel collimated llght beams produced by these two sources are polarized by the first polarized means and pass through the electro-optic crystal to f~rm the first and second portions of the W.E. 54,510 polarlzed collimated llght which are converted lnto the two electrical slgnals. The intensities of these llght sources for the two beams are regulated by feedback circuits to malntaln the peak to peak values of the two electrlcal signals constant and equal.
One feature of the lnventlon is a method and apparatus for derivlng a waveform representative of an orlginal waveform, such as the voltage generating the fleld applied to the crystal in the voltage measuring system, from 0 two phase shifted electrical signals such as the two constant peak amplitude electrical signals generated by the photodetectors in the voltage measuring system. In one sense, the original waveform is reconstructed from selected segments of the two electrical signals with the segments selected in part as a function of the sequence of zero cross1ngs of the two electrical signals. At another level, the representative waveform can be constructed as a stairstep signal having discrete incremental values which increment or decrement with each zero crossing depending upon which of the two electrical signals is leading.
Reversal of direction of the measured waveform can be detected, for instance, from two zero crosslngs in succession by one of the two electrical signals.
While such a stairstep waveform may be adequate for many applications, the accuracy of such a signal does not reach the 0.1% desired in the measurement of transmission line voltages which, for example, can be 260,000 volts peak to peak or 93,000 volts rms.
Accordingly, the invention includes interpolating between steps of the stairstep waveform using the instantaneous value of a selected one of the two electrical signals. The value of the electrical signal which is smaller in magnltude is always selected for the interpolation. This results in utilization of portions of the component waveforms where the small angle approximation, that is where the sine of the angle is approximately equal to the angle, is valid, and hence the errors introduced by the interpolation are small.
In order to eliminate erratic indexing of the zero crossing count for random behavior of the electrical signals around zero, a dead band is centered on the zero axis of the electrical signals.
When the value of the smaller electrical signal enters this dead band, indexing of the zero crossing count is suspended until the signal emerges from the band. If it exits on the opposite side of the band from which it entered, the zero crossing count is indexed. Whether it is incremented or decremented depends upon the direction in which the original waveform is moving, which is manifested by which of the quadrature electrical signals is leading. If the electrical signal of smaller magnitude exits on the same side of the dead band as it entered, the measured waveform has changed direction and the zero crossing count is not indexed. Preferably, the magnitude of the electrical signal required to exit the dead band is greater than that required to enter. This hystereses in the width of the dead band prevents erratic behavior at the boundaries.
While this reconstruction of a waveform from phase shifted electrical signals is particularly suitable for use in the opto-electrical system, which is also part of the invention, for generating waveforms representative of sinusoidal voltage waveforms of large magnltude, it also has applicability to reconstructing other types of waveforms in other applications.
- 6a -In accordance with a particular embodiment of the invention there is provided a method of constructing a waveform signal representative of an original waveform which has been resolved into first and second bipolar electrical waveform signals substantially in quadrature and having substantially constant and equal peak magnitudes comprising the steps of:
periodically generating data samples representative of the instantaneous value of said first and second electrical signalsi determining from said data samples zero crossings of said first and second electrical signals;
accumulating a bidirectional cumulative count of said zero crossings, with the direction of counting being determined by which of said first and second electrical signals is leading; and generating an output signal representative of the original waveform from said cumulative count of zero crossings.
Brief Description of the Drawinqs A full understanding of the invention can be gained from the following description of the preferred embodiment when read in conjunction with the accompanying drawings in which:
7 1 3352 1 ~W.E. 54,510 Figure 1 is a schematic diagram lllustratlng the prlnclple of operation of voltage measurlng systems which form a part of the invention.
Figure 2 is a schematic diagram of a voltage measuring &ystem in accordance with the invention.
Figures 3a, b and c are waveform dlagrams lllustrating respectlvely the line to ground voltage to be measured, the waveforms of the phase shifted electrical signals generated by the opto-electrical measurement system 0 of Figure 2, and the output waveform reconstructed from the phase shifted electrical waveforms.
Figure 4 is a dlagram illustrating how the output waveform is reconstructed from the phase shifted electrical waveforms.
Figure 5 is a flow chart illustrating the program used by the system of Figure 2 to construct the output waveform from the phase shifted electrical waveforms in the manner illustrated in Figure 4.
Figure 6 is an isometric view with part broken away of apparatus for measuring line to ground voltages in a hlgh voltage electric power transmission system in accordance with the inven~ion.
Figure 7 is an enlargement of a subassembly of Figure 6.
Figure 8 is a vertical section through a component which lS part of the subassembly of Figure 7.
Description of the Preferred Embodiments As is known, the voltage between two spaced points a and b is defined by the equation:
- Vab =r E(x) dx (Eq. 1) ~ ~ a .
W.E. 54,510 where E(x) lS the field gradient at x and the integral is lndependent of path. Thus, ln order to accurately measure the voltage between spaced polnts a and b, lt lS necessary that a sensor physically extend from a to b, lnteract with the fleld at every point along its length, and change some property so that some parameter varies in an addit~ve fashion allowing the integral to be evaluated. In the measurement of transmission line voltages, this requlres that one end of a sensor be electrically connected to the transmlssion line and - the other end be electrically connected to ground. Thus, the sensor must be of sufficient length to withstand normal line voltages and any surges whlch might be encountered.
The present invention utlllzes an electro-optlc crystal to measure the integral of the field gradient from point a to b and thus provides a true value for the voltage between a and b. As mentioned previously, certain crystaline materials having a fourfold axis of rotary lnversion, such as RDP (potassium dihydrogen phosphate), have the property that in the absence of an electrical fleld, the index of refraction for light propagating along the fourfold axis is independent of the direction of polarization of the light. However, if an electric field is applied parallel to the dlrection of propagation of the light, the index of refraction for light polarized in a given direction perpendicular to the fourfold axis increases while the index of refraction of light polarized in a perpendlcular direction decreases by an amount which is proportional to the field. In RDP, the direction parallel to the fourfold axis, which is also called the optic axis, is commonly deslgnated as the Z direction, and the orlentations of the polarlzation for whlch the maximum changes in refractive index with electric field are observed are commonly designated as the X and Y directions.
-9- 1 3352 1 o W.E. 54,510 To understand the prlnciple of operation of such an opto-electrical sensor, reference is made to Figure 1.
In the conventlonal Pockel cell device 1, a KDP crystal 3 lS
allgned wlth its fourfold axis of rotary inversion, Z, parallel tQ the field gradient, Fg to be measured. A slngle beam of unpolarlzed llght is incident on a first linear polarizer 7. The crystal 3 and first polarizer 7 are arranged such that collimated polarized light, 5p exiting the polarizer is propagating parallel to the Z axls of the 0 crystal and the plane of polarization of the light is at an angle of 45 degrees to the X and Y axes of the crystal.
The incident polarized beam 5p can be decomposed into two components of equal intensity, one polarized parallel to the X axis and the other polarized parallel to the Y axis. In the absence of an electric field, these two components will propagate with equal velocities and exit the crystal 3 ln phase with one another. When an electric field is applied along the Z axis of the crystal, the refractive indexes, and, as a result, the velocities of the two components will not be equal, and there will be a phase shlft or a retardation between the two components when they exit the crystal. Since the retardation in any small element along the crystal is proportional to the electric field acting on that element multiplied by the length of the element, and the total retardation is equal to the sum of the retardations in all of the elements along the crystal, retardation of the components exiting the crystal is proportional to r Edl, and thus the difference in voltage between the two ends of the crystal.
The retardation is usually expressed in wavelengths, that is a retardation of one means the optical path in the crystal ls one wavelength longer for one of the components of the beam 5p than for the other, and is given by the equation: y~
W.E. 54,510 1 3352 1 ~
s r = r63 n 3 x V (Eq. 2~
where r63 is an electro-optic coefficient, nz, is the refractlve index for light propagating along the Z axis, lS the wavelength of the light in vacuum, and V is the dlfference ln voltage in the two ends of the of the crystal. Whlle these parameters are known and the retardation can be calculated, it is usually more convenient to comblne them in a single parameter, the half-wave voltage, Vh, deflned by the equation:
Vh ~ (Eq. 3) 2 r63 n 3 and thus:
r = v (Eq. 4) 2vh Vh lS usually determined as part of the calibration of the sensor. If the two components of the beam 5p exltlng the crystal are passed through a second polarizer 9 oriented ~0 parallel to the first, the intensity of the beam I exiting the polarizer 9 is related to the retardation by equation:
I - Io Cos2 (~ r ) (Eq. 5) where Io is the intenslty of the exiting beam with zero retardation: That is, with no voltage difference between the ends of the crystal. If the second polarlzer 9 is rotated 90 degrees, then I is given by equation S in which the square of the sine function is substituted for the square of the cosine function.
It is common in such Pockel cell devices described to this point to insert a fractional wave plate 11 between the crystal dnd th~e second polarizer 9 to shlft the -11- 1 3352 1 0 W.E. 54,510 retardatlon to a linear point on the sine or cosine squared function.
Because of the periodic properties of the sine and cosine functions, a device as discussed to this point would only provide unambiguous results for voltages less than Vh. For KDP, at a wavelength of 800nm, Vh is roughly 11,300 volts, and thus such a device cannot be used to measure transmission line voltages which are typlcally around 100,000 volts rms line to ground or more.
In order to resolve the ambigulties inherent in the conventional Pockel cell arrangement, and allow measurements at transmlssion line voltages, the present lnventlon utilizes a second light beam 13 parallel to the beam 5. This second light beam 13 is polarized by the first polarizer 7 to form a second polarlzed light beam 13p which is passed through the crystal 3 parallel to the Z axis.
Thls second polarized light beam 13p can also be resolved lnto two components, one parallel to the Z axis and the other parallel to the Y axis. The second beam exiting the crystal 3 is also passed through the second polarizer 9 so that the intenqity of the second beam exitlng polarlzer 9 is also related to the retardation by equation 5 lf the second polarizer is oriented parallel to the first polarizer 7 or by the sine squared function if the second polarizer is orthogonal to the first polarizer. The second light beam 13 exitlng the crystal 3 lS also retarded by a fractlonal wave plate 15 before passing throùgh the second polarizer 9. The fractional wave plates 11 and 15 are selected so that one beam 1S retarded with respect to the other. In the preferred form of the invention, the one beam is retarded 1/4 wave with respect to the other so that the beams exltlng-the second polarizer are in quadrature. This retardation - may be accomplished by utilizing one-eighth wave plates for the fractiona~ wave ~lates 11 and 13 with their axes 17 and W.E. 54,510 19 respectlvely oriented 90 degrees wlth respect to one another. Other arrangements can be used to retard the one light beam 1/4 wave with respect to the other. For lnstance, one beam could be passed through a quarter wave plate while the other passes directly from the crystal to the second polarizer. Retarding one beam exactly 1/4 wave with respect to the other simplifies the calculation required, but as long as the retardation is about 1/4 wave, meanlng within about plus or minus 20~ of 1/4 wave, `0 satlsfactory results can- be achieved. In addition to 1/4 wave retardation, odd multiples of 1/4 wave can also be used i.e., 3/4, 5/4 et cetera.
With the two one-eighth wave plates oriented as indicated in Figure 2, the intensities of the two beams exiting the second polarizer can be determined as follows:
I1= Io Cos2 ( ~ r ~ ~ /8) (Eq. 6) and I2= Io Cos2 ( ~ r - ~/8) (Eq. 7) These two signals are in quadrature and, with the exceptlon of a constant, allow the unambiguous determination of the voltage applied to the crystal.
Figure 2 illustrates schematically a complete voltage measuring system in accordance with the invention.
This system 21 includes the sensor 1 comprising the crystal 3, the flrst and second polarizers 7 and 9 respectively, and the one-eighth wave plates 11 and 15. The system 21 also includes first and second light sources 23 and 25 which generate the two collimated light beams 5 and 13 respectively. The light source 23 includes a light emitting dlode (LED) 27. Light produced by the LED 27 is transmitted by OptlC fiber cable 29 and passed through collimating lens 31 to produce the fi~st collimated light beam 5. Similarly -13- 1 3352 1 0 W-E- 54,510 the LED 33 ln second light source 25 produces light which is transmltted by the optic fiber cable 35 and passed through colllmating lens 37 to produce the second collimated light beam 13. Light from the first beam 5 exiting the second S polarizer 9 is gathered by lens 39 and conducted through fiber optic cable 41 to a first electronic circuit 43.
Simllarly, the second beam exiting the second polarlzer 9 is focused by lens 45 on fiber optic cable 47 which directs the llght to a second electronic circuit 43.
The electronic circuits 43 are identical and include a photo diode 49 which converts the light beam carried by the optic fiber cables 41 or 47 respectively into an electrical current. The electronic circuits 43 include a transimpedance amplifier 51 which provides a low impedance lnpUt to a peak detector 53. Peak detector 53 includes a dlode 55 which feeds a capacitor 57 shunted by leak reslstor 59. The peak detector al~o includes a buffer amplifier 61 to prevent the peak detector from being loaded by the following stage. The following stage 63 acts as a summing ampllfier, integrator, and a driver for the respective LED
27 or 33. It includes a pair of resistors 65, and an operational amplifier 67 shunted by an integrating capacitor 69. An output circuit includes a pair of resistors 71 and 71' (equal to twice 71 in value), and an output ampllfier 73. A reference voltage -er is applied to the summlng circuits formed by the resistors 65 and 71-71'.
The electronic circuits 43 operate as follows:
Light exiting the second polarizer 9 and transmitted via the optic flber cable 41 or 47 respectively is converted to an electrlcal current signal by the photo diode 49. The peak detector 53 generates a signal which represents the peak value of this electrical current. The peak value s1gnal lS
compared with the reference signal through the resistors 65 connected to the ~verting input of the operatlonal W.E. 54,510 -14- 1 3352 1 ~
ampllfler 67. Since the diode 55 assures that the peak Slgnal lS posltlve, and since the reference signal -er lS
negative, these two signals are compared and the error between the two is applled to the lntegrator formed by the operatlonal amplifler 67 and the capacltor 69. Thls lntegrated error signal is used to drlve the LED 27 or 33 respectively of the llght sources for the first and second llght beams. Thus, the clrcuits 43 are feedback circults which regulate the lntensity of the respective llght beam so that the peak values of the current slgnals generated by these light beams through the photo detectors 49 remain constant and equal to the reference voltage and, hence, equal to each other. The summing amplifler 73 and voltage divlding reslstors 71 subtract the reference voltage from the unidirectional currents produced by the photodetectors 49 to produce blpolar voltage output signals el and e2 respectlvely in response to the field applied to the crystal 3. The analog signals el and e2 are periodically sampled by an analog to digital converter 75 for input into a digital computer 77. The digital computer 77 reconstructs the voltage waveform from the two signals el and e2 for Z5 presentation on an output device 79. The output device 79 can be, for instance, a digital readout, and/or can be a recorder which generates a permanent log of the measured voltage waveform.
Waveforms a, b and c of Figure 3 illustrate on a comparative time basis the voltage waveform VI to be measured, the quadrature electrical signals el and e2 generated ln response to the voltage waveform a by the system of Figure 2, and the output waveform V0 generated by the system of Flgure 2 whlch is representative of the voltage waveform a.
Figure 4 illustrates the manner in whlch the waveform c in Figure- 3 is constructed from the quadrature -15- 1 3352 1 0 W-E- 54,510 electrical signals el and e2 forming the waveform b in Flgure 3. Essentially the method comprises maintainlng a bldirectional count of the number of zero crosslngs of the two electrical signals e1 and e2. In the example given in Figure 4, the count, n of such zero crossings is shown across the top of the figure. The count n is incremented as the voltage waveform represented by e1 and e2 is becoming more positive (or less negative) and is decremented as the magnltude of the incremented waveform is becoming more o negatlve ~or less positive). The direction in which the waveform is moving is determined by which of the quadrature signals is leading. Reversal of the dlrection of the voltage waveform results in a switch in which signal el or e2 lS leading and can be detected by two successive zero crossings by the same signal el or e2.
A stairstep approximation of the voltage waveform indicated by the trace 81 in Figure 4 can be generated from the cumulative count n of the zero crossings. In the partlcular sample shown, the output stairstep waveform is generated as a function of twice the accumulated count n as shown by the scale on the left side of the trace 81 ln Figure 4.
This stairstep approximation 81 of the original voltage waveform generating the field applied to the opto-electrical sensor can be adequate for many purposes.However, where more accurate reproduction of the origlnal voltage waveform is required, such as in monitoring the voltage of high power transmission lines where an accuracy of 0.1 percent is required, interpolation must be made between the stairstep values of the output signals generated by the accumulated zero crossing count n. Thls smoothing of the output waveform is achieved by adding or subtracting the instantaneous value of a selected one of the quadrature sl~nals e~ and e2 to the stairstep value. The 1 3352 1 0 W.E. 54,510 selected signal is the one of the two signals, el and e2, WhlCh lS smaller in magnitude at the given instant. Thus, the magnitude of the signal el or e2 whlch is between the traces 83 and 85 in Figure 4 is selected. This results in utllization of portlons of the waveforms el and e2, where the small angle approxlmation, that is, where the slne of the angle is approximately equal to the angle, lS valid. As can be seen ln Figure 4, the technique essentially results in the stringing together of the segments of the quadrature signals el and e2 to reconstruct the original voltage waveform.
In order to avoid random indexing of the bidirectional cumulative count n of zero crossings which could occur with small signals, a band is created around the zero axis as indicated by the lines 89 and 91 in Figure 4.
Zero crossings are not counted while a signal el or e2 is in this dead band. Instead, a determination is made when the slgnal again leaves the dead band as to whether the zero crosslng n should be indexed. If the quadrature signal exits the dead band on the same side that it entered, then the target signal has changed direction and n should not be indexed. If the quadrature signal exits the dead band on the opposite side from which it entered, then there has been a zero crossing and n is indexed. While a quadrature slgnal lS within the dead band, its magnitude is continued to be used to interpolate between the stalrsteps. If the quadrature signal crosses the zero axis, the sign of the increment which is added or subtracted to the stairstep is changed to reflect this transition. This delay in the indexing of the zero crossing count n until the quadrature signal leaves the dead band results in a slight shlft in tlme of the stairstep signal, as indlcated at 93 in Figure 4. The width of the dead band should be set as wide as posslble wlthout having the instantaneous values of both -17- 1 3352 1 0 W.E. 54,510 el and e2 fall withln the band at anytime. Preferably, the boundarles of the dead band are expanded to 89'-91' once a signal is withln the band. This introduces hysteresis into the dead band which alds in assuring a positive transltlon lnto and out of the dead band.
Flgures 5a and 5b constitute a flow chart of the program employed by the digital computer 77 to reconstruct the voltage waveform sensed by the sensor from the quadrature electrical signals el and- e2, in the manner dlscussed in connection in Figure 4. As discussed previously, the analog quadrature signals el and e2 are applied to an analog to digital converter to generate digitaL samples of the instantaneous value of these waveforms for processing by the digital computer. The sampling rate should be sufficiently rapid that, at the maximum slew rate of the voltage signal being measured, which usually occurs at the its zero crossing, at least one data sample for el or e2 falls within he dead band. The sampling rate for the 60 hz voltage signal was 400 RHz in the exemplary system. As indicated at block 101 in Flgure 5a, the program waits for each new data sample. Two varlables, El and E2, are set equal to the current instantaneous value of the quadrature signals el and e2 respectively at 103 when each new data sample is acqulred.
Another variable S which indicates whether the signs of the current values of El and E2 are the same is set, and that indication is saved as an additional variable SS in block 105.
A flag Ql~ which has a value of 1 if the preceding El was inside the dead band defined by the lines 89-91 (entering) and 89'-91' (exiting) in Figure 4, is checked block 107. If the preceding El was inside the band and the present value of the first quadrature signal remains inslde the band as determined in block 109 (using the larger W.E. 54,510 boundary of llnes 89'-91' equal to 0.24 ER), then the varlable S, which wlll be recalled lS an indicatlon of whether the signs of El and E2 are the same, is set at 111 equal to S0 which is the value of S for the precedlng data polnt.
If El has emerged from the dead band, then the flag Ql is made equal to zero at 113 and it becomes necessary to determlne whether the zero crosslng count, n, should be indexed, and if so, in which direction. This is 0 accomplished by setting another variable A at 115 to lndicate whether the sign of the present El is equal to the sign of Eloo which lS the last value of El before El entered the dead band. For the purpose of this determination, the sign of El is +l if El has a positive value, or -1 if it has a negative value so that A can have a value of -2, +2 or zero. If the signs of El and Eloo are the same as determined in block 117, El has emerged from the same side of the dead band at which it entered and hence there has been no zero crossing. If these signs are not the same, then El has emerged from the opposite side of the dead band from which it entered and hence there was a zero crossing and n must be indexed. If the sign of A is the same as the sign of E2 as determined in block 119 then the voltage is golng up and a variable D is set equal to one at 121. If these signs are not equal, then the voltage is going down and D is set at equal to minus one at 123. The cumulative zero crossing count n is then indexed in the proper dlrection at block 125.
If it was determined back at block 107 that the precedlng instantaneous value of El was outside the dead band, then a check is made at 127 to determine if the present value of El is within the dead band (using the narrower boundary defined by lines 89-91 in Figure 4). If El ls now in the dead band, then the flag Ql is made equal -19- 1 3 3 5 2 1 0 W. E. 54,510 to one, Eloo which is a variable equal to the last value of El before the band was entered is made equal to Elo which lS
the precedlng value of El, and S which, lt will be recalled, lS an lndlcation of whether the slgns of El and E2 are the S same lS made equal to S0 which is the value of S for the last point, all as indicated at block 129. If El remains outslde of the dead band, then a determination is made at block 131 as to whether the preceding value of E2 was outside the band. If it was, and the present value of E2 lS
wlthln the band as determlned at block 133 (using the enterlng boundary lines 89-91 in Figure 4), then a flag Q2 is made equal to one, the last value of E2 before lt went lnto the band lS saved, and S is made equal to S0 all in block 135. If it was determined in block 133 that E2 was not within the band, then both El and E2 remain outside the dead band and the program proceeds ~to the calculation of the present value of the voltage signal~ in the manner discussed below. ~
If it was determined at 131 that E2 was inside the band at the previous data polnt, a determination is made at block 137 whether it is still within the band. If it lS, S
is set equal to S0 in 139. If E2 has now emerged from the band, then the flag Q2 is set equal to zero at 141. A
determination is then made in blocks 143 and 145 uslng the variable A in a manner similar to that described in connection with blocks llS and 117,`to determine whether the zero crossing count n should be indexed. If E2 has emerged from the opposlte side of the dead band from that from which it entered, then n is incremented or decremented in box 147, 149, 151 and 153 using the same technique as described ln connection wlth emergence of El from the dead band. That lS, n ~s incremented if waveform el leads e2 and hence the voltage belng measured is increasing, or n is decremented when the measured voltage is decreasing.
-20- 1 3352 1 o W.E. 54,510 Turnlng to Figure 5b, a determlnatlon is made in block 155 whether there has been a zero crossing by determinlng lf SS, which is the saved sign, lS equal to S, which was set equal to S for the preceding data polnt lf either El o-r E2 lS currently in the band. If there has been a zero crosslng, a variable P is set equal to mlnus one at 157, otherwlse P is set equal to plus onè at 159.
If El and E2 are not of the same sign as determined in block 161 and E2 is of smaller magnitude as 0 determined ln block 163, then a voltage EC is calculated uslng the cumulatlve zero crossing count n and the current magnitude E2 in the equation in block 165. However, if E
and E2 are not of the same sign but El is smaller than E2, then El is used with n to calculate EC using the formula ln block 167. When El and E2 are of the same sign, as determined at 161 and El lS smaller, as determined at 169, then El is used with n to calculate the value of EC in block 171. On the other hand, if E2 is the smaller of the two signals which are not of the same sign, then E2 is used with n to calculate EC in block 173. As will be noticed, the flrst term in the equations for EC in blocks 165 through 171 determlnes the stairstep value from the cumulative count of zero crossings n, and the second term provides the lnterpolation based upon the magnitude of the selected quadrature signal.
The calculated voltage EC is then multiplied by a scaling factor in block 173 to determine the instantaneous magnitude, E, of the measured voltage.
It is convenient to chose er, the reference voltage used in the electronic circuits, equal to 2.828 volts, so that that the quantity .3535 x er = 1 and 2 x 3535/er = 1/4 and hence the computations in blocks 165, 167, 171, 173 and 175 are simplified.
1 33521 0 W.E. 54,510 The measured voltage is unambiguously determlned by this procedure except for a constant error. This error ls the result of the uncertainty of the initial value of n when the program is started. It is noted that n is an 5 integer but otherwise arbitrary. If n can be set equal zero when the voltage is zero, then subsequent voltage measurements will be correct. In general this is not possible and one must adjust n in integer steps until the . average value of the calculated voltage over one cycle is o zero. After n is properly adjusted, the calculated voltages will be corcect until the program is interrupted.
The program is completed by storing the present values of S, El and E2 as the last value in block 177 in preparation for the next computation of E. The program then loops back to the beginning and waits for the next input of data.
Figures 6 through 8 illustrate a practical embodlment of a sensor 1, mounted in an insulation column 201 which is cut away to show the mounting of the sensor.
An upper supporting tube 203 is connected to a transmission line (not shown) and a lower supporting tube 205 is connected to ground. Both tubes are electrically c_nducting and provide contact between the ends to the sensor 1 and the line and ground respectively through mounting discs 207 constructed from electrically conducti~g transparent material such as NESA glass. Crystal 209 and the polarizers 211 and 213 are made with a circular cross section rather than square as in Figure 1 and 2 to reduce the electrical stresses.
As shown more clearly in Figure 7 for the second polarizer 213, two cylindrical collimators 215 are mounted on one flat end face of the cylindrical polarizer and rectangular one-eighth wave plates 217 and 219 are mounted against the opposite ~nd. The collimators 215, which focus -22- W.E. 54,510 the llght beams received from the second polarizer 213 on the OptlC fiber cables 221, are shown broken away in Figure 8. Each collimator 215 is formed from two pieces 223 and 225 of low refractive index glass, such as fused slllca and one plçce of hlgh index glass 227 such as SF59. The radius of the curved surface of 227, the thickness of 227 and the length of 225 are chosen so that a bundle of parallel llght entering 223 is focused on to the end of OptlC flber 221 and the rays from the edge of the bundle `0 strlke the fiber. More partlcularly, these parameters a chosen so that the radius of the bundle of light divided by the focal length of the lens is equal to or greater than the numerlcal aperture of the f1ber dlvided by the refractlve index of the lower refractive index glass. The collimators at the other end of the sensor are similarly designed, but operate in the reverse directlon to transform light received from the fiber optic cable into the bundle of parallel light whlch lS passed through the first polarizer 211. Thls form of a collimator is necessary since in order to withstand the ~0 hlgh electrical stresses during operation, and especlally lmpulse tests, the insulator 201 is filled with oil or pressurized sulfur hexafluroide (SF6), and thus the optical system cannot have any glass air interfaces.
While specific embodiments of the invention have been described in detail, it wlll be appreciated by those skilled - in the art that various modifications and alternatlves to those details could be developed in light of the overall teachings of the disclosure. Accordingly, the particular arrangements disclosed are meant to be illustratlve only and not limiting as to the scope of the lnvention which is to be given the full breadth of the appended clalms and any and all equivalents thereof.
Claims (8)
1. A method of constructing a waveform signal representative of an original waveform which has been resolved into first and second bipolar electrical waveform signals substantially in quadrature and having substantially constant and equal peak magnitudes comprising the steps of:
periodically generating data samples representative of the instantaneous value of said first and second electrical signals;
determining from said data samples zero crossings of said first and second electrical signals;
accumulating a bidirectional cumulative count of said zero crossings, with the direction of counting being determined by which of said first and second electrical signals is leading; and generating an output signal representative of the original waveform from said cumulative count of zero crossings.
periodically generating data samples representative of the instantaneous value of said first and second electrical signals;
determining from said data samples zero crossings of said first and second electrical signals;
accumulating a bidirectional cumulative count of said zero crossings, with the direction of counting being determined by which of said first and second electrical signals is leading; and generating an output signal representative of the original waveform from said cumulative count of zero crossings.
2. The method of claim 1 including:
freezing said cumulative count of zero crossings when the magnitude of the current data sample of either of said electrical signals falls within a band representative of a magnitude less than a preselected value; and unfreezing said cumulative count of zero crossings in response to the magnitude of the current data sample of either of said electrical signals exiting said band and indexing the cumulative count in response thereto, but only when the electrical signal which exits the band, exits with a plurality which is opposite the polarity of that electrical signal when it entered the band.
freezing said cumulative count of zero crossings when the magnitude of the current data sample of either of said electrical signals falls within a band representative of a magnitude less than a preselected value; and unfreezing said cumulative count of zero crossings in response to the magnitude of the current data sample of either of said electrical signals exiting said band and indexing the cumulative count in response thereto, but only when the electrical signal which exits the band, exits with a plurality which is opposite the polarity of that electrical signal when it entered the band.
3. The method of claim 2 wherein the rate at which said data samples are generated is such that the data sample from only one electrical signal at a time can be within said band.
4. The method of claim 2 wherein said band is representative of a magnitude less than a preselected first value when freezing said cumulative count and is representative of a magnitude less than a preselected second value which is greater than said preselected first value when unfreezing said cumulative count.
5. The method of claim 3 including adjusting the magnitude of the output signal generated from said cumulative count of zero crossings by the magnitude of the current data sample of a selected one of said electrical signals.
6. The method of claim 5 wherein the magnitude of the output signal generated from said cumulative count of zero crossings is adjusted by the magnitude of the current data sample of the electrical signal which is currently smaller in magnitude.
7. The method of claim 6 wherein the magnitude of the output signal generated from said cumulative count of zero crossings is adjusted by the magnitude of the data sample of the electrical signal which is smaller in magnitude applied in a sense which is determined by he relative polarities of the current data samples of the electrical signals.
8. The method of claim 7 including:
freezing the cumulative count of zero crossings when the magnitude of the current data sample of either of said electrical signals falls with a band representative of a magnitude less than a preselected value; and reversing the sense of adjusting the magnitude of the output signal by the magnitude of the smaller electrical signal when the smaller electrical signal makes a zero crossing while said cumulative count is frozen, and unfreezing said cumulative count in response to the magnitude of the current data sample of either of said electrical signal exiting the band, and indexing the cumulative count in response thereto, but only when the electrical signal which exits the band, exits the band from the side opposite to that at which it entered.
freezing the cumulative count of zero crossings when the magnitude of the current data sample of either of said electrical signals falls with a band representative of a magnitude less than a preselected value; and reversing the sense of adjusting the magnitude of the output signal by the magnitude of the smaller electrical signal when the smaller electrical signal makes a zero crossing while said cumulative count is frozen, and unfreezing said cumulative count in response to the magnitude of the current data sample of either of said electrical signal exiting the band, and indexing the cumulative count in response thereto, but only when the electrical signal which exits the band, exits the band from the side opposite to that at which it entered.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA000616683A CA1335210C (en) | 1988-09-28 | 1993-06-30 | Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signals |
Applications Claiming Priority (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US250,289 | 1988-09-28 | ||
| US07/250,289 US4904931A (en) | 1988-09-28 | 1988-09-28 | Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signals |
| CA000614172A CA1328482C (en) | 1988-09-28 | 1989-09-28 | Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signals |
| CA000616683A CA1335210C (en) | 1988-09-28 | 1993-06-30 | Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signals |
Related Parent Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000614172A Division CA1328482C (en) | 1988-09-28 | 1989-09-28 | Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signals |
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| Publication Number | Publication Date |
|---|---|
| CA1335210C true CA1335210C (en) | 1995-04-11 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000616683A Expired - Fee Related CA1335210C (en) | 1988-09-28 | 1993-06-30 | Electro-optical voltage measuring system incorporating a method and apparatus to derive the measured voltage waveform from two phase shifted electrical signals |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1335210C (en) |
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1993
- 1993-06-30 CA CA000616683A patent/CA1335210C/en not_active Expired - Fee Related
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