predictive capabilities of eqs (7) and (8) for the transformer under test. If a problem is discovered,
the error budget is adjusted accordingly.

‘The above discussion might enable customers of the voltage transformer calibration service to better
design their calibration requests. Using eqs (7) and (8), the customer might be able to reduce the
number of measurements required. A note of caution is in order. It is likely that using a zero burden
and a 10 volt-ampere burden result to predict the transformer’s behavior at a ZZ burden may lead
to large inaccuracies. The reasons are twofold. First, the differences RCF;— RCF, andl; — I’, are
likely to be small for a burden as small as 10 volt-amperes and extrapolations can cause large errors.
‘The second reason can be seen from figure 10. The higher current of the ZZ burden will cause Z, to
heat up and increase in value, leading to errors if eqs (7) and (8) are used. Somewhat better results
are likely if one used a ZZ burden result to predict a transformer’s behavior at 10 volt-amperes.
However, it is best to choose burden, 7’, to have a volt-ampere rating the same order of magnitude
as the burden of interest, C. Also, the values in eqs (7) and (8) are all to be measured at the same
frequency and at the same secondary voltage.

Harmonic Effects

The measurement of the ratio and phase angle of a voltage transformer can be affected by the
presence of harmonics in the voltage waveform. If a tuned null detector is not used, the balance
of a bridge circuit can be difficult in the presence of harmonics and often a precise balance is not
possible resulting in increased measurement uncertainties. Harmonics can also lead to errors in
measuring the magnitude of the secondary voltage. For example, if an average reading, rms scaled
voltmeter measured a 100-volt rms fundamental with an in-phase 3-volt rms third harmonic, the
meter would read 101 volts. Setting the voltage to read 100 volts on the meter would result in a one
volt discrepancy between the intended and actual voltage. Many transformers have large enough
voltage coefficients for this one-volt error in the voltage setting to have a non-negligible effect on
the measured ratio correction factor and phase angle. If instead, a true rms voltmeter were used
to measure this signal, the measured voltage would be 100.045 volts and the resulting error would
be negligible. At NBS three different steps are taken to lessen the effects of harmonics. The first
is to try to minimize the harmonic content of the power supply. The supply used for most of the
calibrations has a total harmonic distortion of order 0.2% of the fundamental. Second, a tuned
detector is used to assure that the balance conditions are for the fundamental component of the
voltage waveform. And third, all voltage measurements are made wita true-rms voltmeters.

Voltage Dependence of Standard Capacitor

An additional measurement concern is the voltage coefficient of the high-voltage standard capacitor
shown in figure 5. Although no absolute measurements are required to calibrate a voltage trans-
former, the ratio of the two standard capacitors must be known. The problem is that the low-voltage
standard capacitor typically has a maximum voltage rating of 500volts, and both the primary of
the transformer and the high-voltage standard capacitor might be energized to 100kV. Since the
capacitor ratio measurement must be done at less than 500volts, the voltage dependence of the
high-voltage capacitor is important. This problem was discussed in Section 3.2.

4 MEASUREMENT INSTRUMENTATION

‘The calibration of voltage transformers and high-voltage capacitors at NBS requires the combined
use of standard capacitors and the current comparator bridge. Standard capacitors have been
thoroughly discussed in the literature [5, 6, 9]. The care that must be taken with their use in these
types of measurements has been discussed above. The current comparator bridge will be discussed
in this section.

14


Table 2. Gas Density Dependence

GAS OC/OP at T = 22.8°C

(units of picofarads/pascal)

SFe | (2.012 + 0.022) x 10-5 + [(5.1+ 0.6) x 10-8 ]P
COz | (0.903 + 0.015) x 10-6 + [(1.4+ 0.4) x 10-19] P
He _| (0.075 + 0.004) x 10-€ + (0.2+ 0.1) x 10-13]P

surement process. The average value is then used in order to minimize the problem associated with
this thermal drift.

Gas-Density Dependence

Compressed gas standard capacitors can have an additional source of error associated with gas
leakage. Values of 8C/OP (to first order in pressure) measured at a temperature of 22.8°C are
shown in table 2 for three different gases [6].

The gas pressure, P, is in units of pascals and the capacitance in picofarads. For a 100-pF capacitor
with SF¢ as the dielectric gas, a 1-psi (6900-pascal) leak would cause the capacitance to decrease by
about 140 ppm. It must be stressed that this change is valid only if the pressure change is caused
by the loss of gas and not by the lowering of the gas temperature. As can be seen in table 2, the
gas density coefficient is largest for SFg. Customers using compressed gas capacitors for standards
might be advised to monitor the gas pressure with a good quality pressure gauge. Leaking SFe-filled
capacitors should be checked often against a good low-voltage standard.

3.3 Voltage Transformers

Information Necessary to Initiate Calibration

In order to calibrate a voltage transformer, several different parameters must be specified: frequency;
windings and/or range; secondary voltage; and burden or impedance across the secondary winding.
In some cases, for example when there is a tertiary winding, additional parameters may be required.

Labeling of Terminals

There are some standard conventions as to which of the primary and secondary taps are to be at
low or ground potential and which are to be at rated voltage. Some transformers have one tap of
the secondary and one tap of the primary winding marked by a “t”. These two taps are connected
together and to ground potential. Some transformers use the designators H1, H2 for the primary
taps, and X1, X2 (and Y1 and Y2 for the transformers with two secondaries) for the secondary taps.
Sometimes the secondary winding has a third tap, X3. By convention the primary and secondary
taps with the largest number are connected together and to ground. If the customer wants some
other arrangement, they should notify NBS prior to the calibration.

Load Imposed by NBS Measurement System

The basic measurement circuit is shown in figure 5. The two capacitors shown are three-terminal
standard capacitors. Their dissipation factors are typically less than 5 x 10-6. The capacitor
connected to the secondary usually has the nominal value of 1000 pF. Therefore, for 60-Hz measure-
ments, the capacitor imposes a negligible load (2.7 megohms or 0.005 volt-amperes at 120 volts) on
the voltage transformer. Negligible in this case means that the effect of this burden on the measured
ratio and phase angle can not be observed at the ppm level. The digital voltmeter (DVM) in figure 5


Cx Cs>n
t ak
e Ce"

ace Se

= Se pH

Figure 15. Current comparator bridge modified for 4-terminal capacitance measurements.

Table 4. Check Standard History
[Date Capacitance Ratio [ Date Capacitance Ratio |

6/80 1.000025 1/84 1.000032
6/81 1.000028 5/84 1.000033
9/81 1.000027 10/84 1.000032
1/82 1.000027 4/85 1.000041
4/82 1.000026 6/85 1.000042
7/82 1.000026 10/85 1.000041
9/82 1.000028 12/85 1.000042
1/83 1.000030 1/86 1.000041
3/83 1.000031 5/86 1.000044
6/83 1.000033 7/86 1.000044
8/83 1.000031 10/86 1.000044
12/83 1.000031 2/87 1.000044

18


CorIankw ne

11
12
13
14
15
16
17

18

List of Figures

Schering bridge. ......
Basic measurement circuit for the calibration of a high-voltage capacitor. .... . .
Basic measurement circuit for the calibration of a voltage transformer. .......
Basic measurement circuit for the 4-terminal calibration of large capacitors... . .
Correct measurement circuit for the calibration of a voltage transformer... ... . «

A voltage transformer measurement circuit with a wiring defect.

A voltage transformer measurement circuit with a wiring defect. . .
An improved measurement circuit for the calibration of voltage transformers. . . . .
Equivalent circuit of a voltage transformer.
Equivalent circuit of a voltage transformer with secondary burden. .........-

Capacitive burden box. .........

Basic current comparator bridge.
Current comparator bridge with high-voltage resistor for in-phase current balance.
Current comparator with superior in-phase current balance. ......- seen

Current comparator bridge modified for 4-terminal capacitance measurements.

Current comparator bridge with external range extender.

Circuit for checking operation of dissipation factor measurement of current compara-
tor bridge. . 2.2... :

Circuit for determining correction to measurement shown in figure 17. .......-

vi


and

Xow (#24) [Co — TF) cos 6; + (RCF; — RCF,) sin |). (44)

Using eqs (37), (43), and (44) and the relations:

cos6, cos; + sin 9, sin 0; = cos(8; — Oc) (45)
080; sin 0 — sin 0, cos0; = sin(® — 42) (48)
one finds
RCF. & RCF. + (aan) (RCP, — RCF,) cos(0, — 0.) + (Tr —T'o)sin(@—6.)] (47)
B:RCF,

or B
RCF. &: ROP. + (2) (RGF, — RCP.) cos(0, — 0.) + (Pr —T)sin(@ —6.)) (48)

7

where B, = 1/2, is the burden in ohms~1 of the impedance Z.. Since the second term in eq (47)
represents a small correction to the first and since RCF, is approximately equal to one, RCF, has
been dropped from the second term of eq (48). Using eqs (32)-(34)

es Ie 058, — Ry sin) (49)
Using eqs (43)-(46) and (49)
Tem o+ (pepe) [Ps To)eos(6e ~ 8.) (REF, —RCF.)sin(®—0.)) (50)
or
TewTot (#) [(P: -T.) cos(0; — 6.) — (RCF; — RCF,) sin(; — 0.)] (51)
7

since RCF, is approximately equal to one.

The relations eqs (48) and (51) can be used to calculate the RCF and phase angle for some secondary
burden, C, if the ratio correction factors and phase angles are known at some other burden, 7’, and
at zero burden.

29


©)

\t
\I

~Cx ~Cs

Nx Ns

Figure 12. Basic current comparator bridge.

‘The current comparator bridge can be thought of as a voltage comparator transformer arm bridge
in which the detector and power source have been interchanged. Traditionally, the disadvantage of
the current comparator bridge versus the voltage comparator bridge is the signal-to-noise level. For
high-voltage measurement applications, this is no longer a problem. Kusters and Petersons were the
first to develop this bridge for the comparison of two capacitors at high voltage [3]. A basic current
comparator bridge is shown in figure 12. The current in the unknown capacitor, C,, is balanced
against the current in the standard capacitor, C,, by varying the turns ratios, N, and Nz.

Balance is achieved when the signal at the detector, D, is equal to zero. At balance IpNz = I, Ng
or:

V2nfCzNz = V2nfC,N, (9)
where f is the frequency. This balance equation can also be expressed as:
N,
Ce = HECe. (10)

The bridge shown in figure 12 has no means of balancing the in-phase current resulting from a
non-ideal unknown capacitor, Cz. The current comparator in figure 13 does have the capability of
balancing both the in-phase and quadrature components of the capacitive current. The difficulty
with the approach used in figure 13 is that the applied high voltage is across the variable resistance
R,. It is nearly impossible to design a stable high-voltage variable resistor with negligible phase
defect. Another means is necessary to balance the in-phase current, preferably at low voltage using
well-characterized components.

The current comparator shown in figure 14 provides a satisfactory means of achieving both the
in-phase and quadrature current balances. The quadrature current balauce is ideutical to that in
figures 12 and 13 above. The in-phase current balance is accomplished at low voltage with the aid
of an operational amplifier. The current from the standard capacitor after passing through the N,
winding goes to the inverting input of the operational amplifier. This point is at virtual ground
so the capacitive current balance, eq (10), is not affected. The feedback capacitor, Cy, causes the
output voltage of the operational amplifier to be a small fraction (C,/Cy where Cis approximately
10 pF) of the applied voltage and = radians out of phase with it. The inductive voltage divider allows
a known fraction, a, of this output signal to be applied across a standard resistor, R. As can be
seen from figure 14, the signal is first inverted before the resistor in order to have the correct phase
relationship with the unknown in-phase current. It is necessary that the non-inverted signal be

15


\}

~ Cx Cs7

R —— ~~
«| | CURRENT |

->{ COMPARATOR |=-—
| BRIDGE |
— BRIDGE __

Figure 18. Circuit for checking operation of dissipation factor measurement of current comparator
bridge. Input is grounded in order to measure € in eq (18).

Since e < V subtracting eq (19) from eq (18) one obtains:

DFp = DF - DF, = (20)

—o
Qn f RCL"
At NBS typical values of a are 0.003, 0.0003, -0.0003, -0.003. With a one-megohm resistor and a
1000-pF standard capacitor this enables a near full scale test of the dissipation factor on its four
ranges. Recent results are shown in table 5. The dissipation factor values are all in units of percent.

Agreement: between the calculated values in eq (20) and the corrected measurement DFim (the last
two columns) are well within 0.1% of the measured value. This check is performed at approxi-
mately six-month intervals.

It is further proposed that an additional check standard be obtained and measured quarterly. Specif-
ically, a voltage transformer measured regularly at a ratio of 10:1 would give an additional check on
the phase angle circuitry and on the bridge windings at something other than a 1:1 ratio.

5 MEASUREMENT UNCERTAINTIES

5.1 Voltage Transformers

The records of the National Bureau of Standards show examples of voltage transformers that have
been calibrated at five-year intervals over a period of thirty to forty years. Invariably the original
‘uncertainty statement covers.any variation in ratio correction factor and phase angle observed over
this period of time. Voltage transformers are often used by the customer in conjunction with other
equipment to measure some quantity. For example, used with a current transformer and watthour
meter, a voltage transformer can help provide a measure of the energy consumed by a large power

21


applied to an identical standard resistor as shown in figure 14 so that the current from the standard
winding, N,, reaching the operational amplifier has no phase defect. The in-phase current into the
standard winding, N,, is then equal to:

VC.
tin = ($24) pr (11)
Since the quadrature current Iour = V2xfC,, the dissipation factor is:
Dra in = 2VGs (12)

~ Tout 2nfRVC;C,

or

DF= (13)

@
QnfRCy
The resistor, R, can be chosen so that a is direct reading in percent or milliradians.

In some cases, particularly for larger capacitors, it is necessary to make a four-terminal measure-
ment. This is required when the lead and winding impedances become a significant fraction of the
impedance to be measured. Figure 15 shows a current comparator bridge with this capability. Be-
cause of the non-negligible lead and winding impedance, there is some voltage, e, at the low-voltage
terminal of the capacitor. This voltage signal is inverted as shown in figure 15 and connected to the
N, winding through a capacitor, C,,. The current through the unknown capacitor is:

I, = j2af(V —e)Cr (14)
The current reaching the N, winding is:
I, = j2nfVC, — j2mfeCy. (15)
If Cy. is adjusted prior to the measurement to be equal to C, then eq (15) reduces to:
I, = j2xf(V —e)C,. (16)

Comparing this with eq (14), the effect of the compensation circuit has been to place the same
voltage across both the standard and unknown capacitors. This is exactly what is required for lead
compensation.

Figure 16 shows the last. enhancement. of the bridge to be discussed. The National Bureau of
Standards’ current comparator bridge has an internal range of 1000:1 (i-e., the maximum value of
Na/Nz is 1000). The external current transformer shown in figure 16, referred to as a range extender,
increases the measurement range by a factor of 1000 allowing the comparison of two currents differing
in magnitude by as much as a factor of a million. As with the transformers internal to the current
comparator bridge, the accuracy requirements on the range extender are quite stringent. Further
details on the design of a ppm current comparator and the specifics of NBS’ current comparator
bridge are available in the literature [10, 11).

The current comparator bridge is quite straightforward to use and has proven to be rugged in
practice. In order to monitor the behavior of NBS’ current comparator bridge, a check standard is
maintained. In this case, the check standard consists of two high quality standard capacitors. ‘The
ratio of the two capacitors is measured quarterly. For the last seven years, this ratio has been stable
to within 20 ppm as can be seen in table 4.

The drift can readily be attributed to the two capacitors. The 9 ppm change between 10/84 and 4/85
occurred apparently after one of the capacitors had been used for another purpose. An independent
measurement of that capacitor verified the change. While the use of this check standard cannot.

7


REFERENCES

(1) F. K. Harris, Electrical Measurements, John Wiley & Sons, New York, pp. 576-577 (1966).
{2] F. K. Harris, Electrical Measurements, John Wiley & Sons, New York, pp. 687-738 (1966).

[3] N. L. Kusters and O. Petersons, “A ‘Transformer-Ratio-Arm Bridge for High-Voltage Capaci-
tance Measurements,” IEEE Trans. Commun, Electron., vol. CE-82, pp. 606-611, Nov. 1963.

[4] M. C. McGregor, J. F. Hersh, R. D. Cutkosky, F. K. Harris, and F. R. Kotter, “New Apparatus
at the National Bureau of Standards for Absolute Capacitance Measurement,” IRE Trans. on
Instrum., vol. I-7, no. 3 & 4, Dec. 1958.

[5] D. L. Hillhouse and A. E. Peterson, “A 300-kV Compressed Gas Standard Capacitor with
Negligible Voltage Dependence,” vol. IM-22, pp. 406-416, December 1973.

[6] W. E. Anderson, R. S. Davis, O. Petersons, and W. J. M. Moore, “An International Comparison
of High Voltage Capacitor Calibrations,” IEEE Trans. Power Appar. Syst., vol. PAS-97, no. 4,
pp. 1217-1223, July 1973.

[7] IEEE Standard Requirements for Instrument Transformers, American National Standards In-
stitute, ANSI/IEEE C57.13-1978, pp. 32, 1978.

[8] IEEE Standard Requirements for Instrument Transformers, American National Standards In-
stitute, ANSI/IEEE C57.13-1978, pp. 45, 46, 1978.

[9] F. K. Harris, Electrical Measurements, John Wiley & Sons, New York, pp. 673-687 (1966).

[10] O. Petersons and W. E. Anderson, “A Wide-Range High-Voltage Capacitance Bridge with One
PPM Accuracy,” IEEE ‘Trans. Instrum. Meas., vol. IM-24, no. 4, December 1975.

[11] O. Petersons, A Wide-Range High-Voltage Capacitance Bridge with One PPM Accuracy, D.

Sc. dissertation, School of Engineering and Applied Sciences, George Washington University,
Washington, DC, February 1974.

30


Table 3, ANSI Standard Burdens
[ANSI Burden | Volt-amperes | Power Factor (Lagging) |

Ww 12.5 0.10
».¢ 25 0.70
M 35 0.20
Y 7 0.85
Z 200 0.85
ZZ 400 0.85
Ej

© iw

Figure 9. Equivalent circuit of a voltage transformer.

The voltage transformer will be represented as an ideal transformer with some unknown series
output impedance, Z, , as shown in figure 9. The model has been shown to be sufficiently accurate

experimentally. The relationship between the input voltage, E; , and the output voltage with zero
burden, Eo, is:
Ei _ iT o
E NRCF.e =
where N is the nominal (or turns) ratio of the transformer, RCF is the ratio-correction factor
(NxRCF= actual ratio) at zero burden, I’, is the angle by which the secondary voltage vector leads
the primary voltage vector and j = /—1. A similar relationship exists between the input voltage,
F,, and the output voltage E., with secondary burden C (having impedance Z.) shown in figure 10:
Fi _ wrov,e-i¥- (6)
EL
where KC, is the ratio correction factor with secondary burden C and I’, is the corresponding
phase angle. If the transformer is measured at zero burden (RCF, and I’,) and at burden T (RCF;
and [;), the ratio correction factor and phase angle at burden C’ are approximately given by:

Ei

‘0

eiTo (6)

B .
ROF. © RCFs + F°[(RCF: — RCF,) cos(8: — 6) + (Ts — Po) sin(Or — 8-)], (7)
i
where B, = 1/Z¢ is the burden in ohms~! of the impedance Ze, and

Peete Fer, ~ Tp) cos(6; — 8) — (RCF, — RCF,)sin(6, — 6.)}- (8)

12


of sufficient quality to be considered transfer standards. Historically these transformers have shown
excellent long-term stability rarely changing by more than 100 ppm in ratio or 0.1 mrad in phase
(at or below rated burden) for periods as long as thirty years or more. In general the voltage and
burden dependence of these transformers are the major contributors to the measurement uncer-
tainties. These uncertainties (300 ppm for ratio, -40.8mrad for phase angle) meet the accuracy
requirements of most of our customers.

Voltage transformers of a higher accuracy class often serve as transfer standards for manufacturers
of voltage transformers and voltage transformer test sets (voltage comparators). The estimated
uncertainties for these transformers are +100 ppm in ratio, and 0.1 mrad in phase angle. They are
generally designed for use with very small burdens (< 15 volt-amperes).

The above discussion for voltage transformers assumes a voltage at a frequency of 60Hz. The
National Bureau of Standards has some capability to calibrate voltage transformers from about
50Hz to 400Hz (at the lower voltage and power ranges). Such calibrations are infrequent and
customers interested in these voltage ranges and measurement uncertainties should contact NBS
directly.

2.2 Capacitors

The maximum voltage for capacitor calibrations is presently 170kV at 60Hz. The restrictions is
imposed by the supply transformer and not by limitations in the measurement instrumentation.
Therefore, this constraint should not be considered time invariant and customers should contact
NBS about present physical limitations.

The maximum power available is 50kVA (i-e., C < 50, 000/{2760V?} where V is the applied voltage
and C is the capacitance). In order to energize the capacitors a resonant circuit is often required to
couple the necessary energy into the customer’s capacitor. Since this requires the availability of an
assortment of series and parallel inductors and capacitors, there are undoubtedly some capacitors
that, despite having a burden of less than 50 kVA, cannot be calibrated. The customer should contact
NBS before submitting a capacitor for calibration. As with voltage transformers, NBS restricts its
calibration services to those devices of sufficient quality to be used as the transfer standards. This
in general depends upon the stability of the capacitor (i.e., whether the measured capacitance and
dissipation factor are intrinsic properties of the device itself or. instead are largely a function of
conditions at the time of the calibration). For example, small two-terminal capacitors (less than
10,000 picofarads) may be significantly influenced by stray capacitance in the measurement circuit.
‘There are cases, however, where one component (capacitance or dissipation factor) is stable and the
other is not. For example, power factor capacitors often have relatively stable dissipation factors
but have capacitances that vary significantly with applied voltage (even demonstrating hysteresis
effects) and temperature. In this case a calibration of dissipation factor would be meaningful. It
also ic important that the capacitors have connectors? that are generally available, e.g., BNC, GR,

UHF, BPO, or Type'N.

The most accurate capacitor calibrations have an uncertainty of +25 ppm for capacitance and an
uncertainty of +5 x 107° for dissipation factor. For capacitors with large dissipation factors, the
dissipation factor uncertainty is generally at least -++1% of the measured value +5 x 10-®. The
uncertainty in the capacitance value and the dissipation factor can be largely a function of the
stability of the capacitor.

2Certain commercial products are identified. In no case does such identification imply recommendation by NBS,
nor does it imply the products are the best available.


APPENDIX

The voltage transformer will be represented as an ideal transformer with some unknown series
output impedance, Z,, as shown in figure 9. The model has been shown to be sufficiently accurate
experimentally. The relationship between the input voltage, E;, and the output voltage with zero
burden, Eo, is:
Ei i
Ez = NRCF,e~iF°

0

(21)

where N is the nominal (or turns) ratio of the transformer, RCF, is the ratio-correction factor
(N x RCF, = actual ratio) at zero burden, I’, is the angle by which the secondary voltage vector
leads the primary voltage vector and j = /—I. A similar relationship exists between the input
voltage, E;, and the output voltage ., with secondary burden C (having impedance Z,) shown in
figure 10:

Fie NRCF-,e7JFe (22)
Ee

where RCF, is the ratio correction factor with secondary burden C' and I’, is the corresponding
phase angle.

Equating the current through Z, and Z- in figure 10, one obtains

E,-E. _ Ee
Zo de (28)

or
E.

(24)

This can be rewritten in the following form:

BE Zo
Sot (1452).
BE (1+%) (25)

Setting Z, equal to Ro + jX» and Z, equal to Re + jXc, eq (25) becomes:

Ei _ [ Rot es)
Sta tly 4 —e el, 26
E. Eo Re t+ jXe (28)
‘Laking the absolute value of both sides of eq (26), one finds that:
E; E; RoR. + XoXe
lz ~[Elb RErx? | en

where it has been assumed that both R, and X, are much less than Z, so that terms of order
(RoR. + XoX-)/(R2 + X?)]? and higher have been neglected. Using eq (21) and (26), one obtains

E; ir, [ al
= °j14+—— 28
E. ° Ret+jXe (28)
“ (Ro + jXo)( )
Ey 5 Ro + jXo)(Re — jXe 5
= iT. Soha OR Sai A Sa a a 4
€ [i+ 2 3 (29)

This can also be expressed as

eWITof.. ]. (30)



{10 ppm for capacitance (1 x 107S for dissipation factor). The random error associated with the
© measurement is +1 ppm and +1 x 1076 for dissipation factor. Conservatively then,
NBS could calibrate a customer’s capacitor to an overall uncertainty of +15 ppm in capacitance and
tb x 10-© + 1% of the value for dissipation factor. In general, the quoted uncertainty is always
larger than this except for low-voltage standard capacitors similar to those used at the National
Bureau of Standards. (Low-voltage standard capacitors are in general calibrated by the National
Measurement Laboratory of NBS. The service described here provides higher voltage calibration of
these same capacitors).

capacit

The uncertainty statements for high-voltage standard capacitors and power-factor capacitors depend
on the stability of these devices during the course of the NBS’ measurements. The stability is
influenced by both the voltage dependence of the device and self-heating (i.e., the capacitance and
dissipation factors vary as the internal energy dissipated heats the device). Self-heating effects are
more important for power-factor capacitors. Some power-factor capacitors demonstrate significant
hysteresis effects. Assigning an uncertainty statement to these measurements depends on the specific
behavior of the capacitor. If self-heating is a problem the calibration report clearly must specify
the amount of time the capacitor was energized before the measurement was made. If hysteresis
effects are detected they are so noted. Because of the nature of most of these devices, the calibration
reports for capacitors usually include a statement of the form: “the estimated uncertainties quoted
apply to the above tabulated values and should not be construed as being indicative of the long-term
stability of the device under test.” This statement is also important for the compressed gas insulated
capacitors whose values might change significantly by handling during shipping.

The actual uncertainty quoted to the customer is derived by algebraically summing the systematic
uncertainties and adding three times the root mean sum of squares of the random uncertainties. For
the capacitance measurement of compressed ges insulated capacitors, the measurement uncertainty
will include a 20ppm contribution because of the possible one kelvin variation in temperature of
the NBS voltage transformer laboratory. For power-factor capacitors the self-heating variations will
dominate ambient temperature effects.

6 ACKNOWLEDGMENTS

The author would like to thank Oskars Petersons, Chief of the Electrosystems Division, who has
been the source of nearly all the author’s knowledge on the calibration of voltage transformers
and capacitors. The author would also like to acknowledge the work of Barbara Frey and Roberta
Cummings who helped prepare this manuscript. Lastly, but certainly not least, the author would
like to acknowledge both the “old-timers” here at the National Bureau of Standards, who began
the tradition of excellence in measurements, and the present calibration staff who are attempting to
carry on this tradition under vastly different constraints.

7 REPORT FORMAT

Examples of the calibration report format are shown on the next pages for both the voltage trans-
former and high-voltage capacitor calibration service. These formats are frequently modified in
order to deal with special circumstances pertaining to a particular calibration.

24


A Calibration Service for Voltage Transformers
and High-Voltage Capacitors

William E. Anderson

Abstract

The National Bureau of Standards calibration service for voltage transformers and high-voltage
capacitors is described. The service for voltage transformers supports the measurement of ratio
correction factors and phase angles at primary voltages up to 170kV and secondary voltages
as low as 10 volts at 60Hz. Calibrations at frequencies from 50-400 Hz are available over a
more limited voltage range. The service for high-voltage capacitors supports the measurement
of capacitances and dissipation factors at applied voltages ranging from 100V to 170kV at
60 Hz depending on the nominal capacitance. Calibrations over a reduced voltage range at
other frequencies are also available. As in the case with voltage transformers, these voltage
constraints are determined by the facilities at the National Bureau of Standards.

Key words: calibration; capacitors; dissipation factor; electric power; electric standards; NBS
services; voltage transformers

1 INTRODUCTION

The purpose of this report is to provide a description of the National Bureau of Standards (NBS)
methodology for calibrating high-voltage capacitors and transformers. It is hoped that this might
benefit the customers in several ways. First, by understanding how NBS makes these measurements,
the customers might be able to define weaknesses in their own measurement procedures and correct
them. Secondly, the customers might be able to make better use of the data in the calibration report
(e.g., to understand what is meant by the uncertainty statement). Thirdly, the customers might be
able to better specify the required test conditions so that information more pertinent to their needs
might be obtained at a lesser cost.

This report describes two different calibration services: high-voltage capacitors and voltage trans-
formers. At NBS these two services are performed using the same equipment. In fact, in order to
calibrate a voltage transformer, one of the steps is to measure the ratio of two capacitors. The two
services are therefore discussed in parallel.

There are several different ways to measure the ratio and phase angle of a voltage transformer. Har-
tis [1] categorizes them as the direct versus comparative methods and within these two classifications
either the deflection or null measurement technique. A direct measurement is defined here to mean
a measurement in which the quantity of interest can be determined without a comparison to ‘some
absolute standard.

In the “direct deflection method” the primary and secondary voltage vectors are each directly
measured. This approach ‘is, in general, of most value for lower voltage transformers (i.¢c., primary
voltages of order 100 volts). Even then more accurate, less difficult measurements can be made using
one of the other techniques.


Naan eo ne

List of Tables

Measurement Capability 2.6... ee ee eee 3
Gas Density Dependence... 06.0 cece ce eee nent eee eee 8
ANSI Standard Burdens «1... ee eee ee eee eee 12
Check Standard History ©... 11. ee ee ee ee ee 18
Dissipation Factor Check Standard «6... 1. eee eee ee ee 22
Contributions to Uncertainty ©... ee eee ee 23
Total Estimated Uncertainties ©... 1... ce eee ee eee 23

vii


OQ 3 Eyre
‘0

Zc

Figure 10. Equivalent circuit of a voltage transformer with secondary burden Z-.

| ur uF | 4uF

o

Figure 11. Capacitive burden box.

‘The power factor of burden C is cos6., RCF, is the ratio correction factor calculated for burden C,
and I, is the angle by which the secondary voltage leads the primary voltage for burden C.

The equations (7) and (8) can be used to calculate the RCF and phase angle for some secondary
burden, C, if the ratio correction factors and phase angles are known at some other burden, T, and
at zero burden. In practice, at NBS, capacitive burdens are used for the “TJ” or known burdens in
eqs (7) and (8). The main reason is their stability. The heat generated in a large resistive burden,
for example, is likely to cause the burden’s impedance value to vary. Capacitors, in addition, are
compact so even the ZZ burden in table 3 is easy to handle. At NBS, capacitive burden boxes have
been constructed in a binary layout (figure 11) so that capacitors from 1 to 32 microfarads can be
switched in and out allowing any capacitance value from zero to 63 microfarads. Since a ZZ burden
is equivalent to a 74 microfarad capacitor at 120 volts, two such burden boxes are sufficient for nearly
all the calibrations at NBS.

Several approximations were made to derive eqs (7) and (8). The approximations relate to the
relative ratio of the transformer’s output impedance, Zo, to the impedance of the secondary burden
Z; or Ze. The smaller this ratio, the more accurate are eqs (7) and (8). This ratio also affects
the differences, RCF; — RCF, and I’; —T,. If the ratio correction factor difference is 0.001 or less,
and if the phase angle difference is 1 milliradian or less than eqs (7) and (8) should be accurate to
within +10 ppm for the ratio correction factor and to within +10 microradians for the phase angle
if it is assumed that the ratio of the burdens is known with no more than a +1 percent uncertainty.
Data over the years has indicated that eqs (7) and (8) are always at least that accurate. In order
to identify any problems, an extra measurement is made at a different secondary burden to test the

13


‘The main limitation of the Schering bridge is a result of the fact that the low side of the unknown
and standard capacitors are not at ground potential at bridge balance. Therefore, without care-
ful guarding of the bridge components, stray currents can affect the bridge accuracy. The voltage
applied to the shields to eliminate these stray currents must be adjusted for both magnitude and
phase. Unfortunately this procedure ic not perfect and bridge accuracy is consequently affected.
Another limitation of the Schering bridge is the inherent inaccuracy of the resistance ratio of the
two low-voltage arms.

‘The current comparator bridge developed by Kusters and Petersons [3] allows the intercomparison
of two capacitors with their low-voltage terminals at ground potential, thereby eliminating the
main objection in using the Schering bridge. This bridge used in both the voltage transformer
and capacitor calibrations will be described in some detail in Section 4. There is an important.
distinction between the calibration of voltage transformers and capacitors at NBS. The voltage
transformer calibration is of the direct null type, and the capacitor calibration is of the comparative
null type. In other words, the accuracy of the capacitance measurements ultimately depends on the
uncertainty in assigning a value to a standard capacitor. The standard capacitor used in this service
is directly traceable to the calculable cross capacitor [4] which, in turn, is known in terms of the
fundamental unit of length.

The remainder of this document is divided into the following subject areas: voltage transformers
and capacitors covered by this service, measurement methodology, measurement instrumentation,
analysis of uncertainties, and calibration report format. The contents of this document plus the cited
references should provide the reader with a fairly complete description of the voltage transformer
and high-voltage capacitor calibration service at NBS.

2 RANGE OF SERVICES

The NBS measurement capabilities are summarized in table 1 and discussed in more detail below.

Table 1. Measurement Capability

Voltage ‘Transformers - 60 Hz
Primary Voltage Secondary Voltage Phase Angle
50-170,000 V rms > 50 Vrms < 11 mrad
Capacitors - 60 Hz
Applied Voltage! Capacitance Dissipation Factor
50-170,000 Vrms 10pF — 0.001F < 0.011

2.1 Voltage Transformers

Presently, voltage transformers (assuming they are of sufficient quality to be used as laboratory
standards) with primary voltages up to 170kV at a frequency of 60 Hz can be calibrated at NBS. This
maximum voltage is imposed by the supply transformer and not by limitations in the measurement
instrumentation. Therefore, this constraint should not be considered rigid and customers should
contact the NBS about present physical limitations.

‘The largest portion of the voltage transformers submitted to NBS are calibrated with a total esti-
mated uncertainties of +300 ppm in ratio, and +0.3mrad in phase angle. These transformers are

1 Total power must be less than 50kVA.


L

~Cs

\I

Figure 16. Current comparator bridge with external range extender.

19



NBS MEASUREMENT SERVICES:
A Calibration Service for

Voltage Transformers and
High-Voltage Capacitors

William E. Anderson

Electrosystems. Division

Center for Electronics and Electrical Engineering
National Engineering Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

yt OF
co Poy

sn
x Xn,

‘a

Ne a
Mths sO

Ry

% .
“Ureay of

June 1988

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary
NATIONAL BUREAU OF STANDARDS, Emest Ambler, Director


Vp
N Vs

ay!

~ Cp Cs

(YYY\V SY VV VS
Nx Ns

Figure 3. Basic measurement circuit for the calibration of a voltage transformer.

3.2. Capacitors

General Measurement Technique

Capacitors are measured by balancing the current through the capacitor under test against the
current through a standard air or compressed gas capacitor as shown in figure 2. Large capacitors
(> 1 microfarad) necessitate’a four-terminal measurement as shown in figure 4. A discussion of this
measurement will be discussed in Section 4. The four-terminal measurement does eliminate the
effect of the leads in the measurement of the capacitance and dissipation.

Information Necessary to Initiate Calibration

The customer usually only needs to specify the voltage and the frequency. For small capacitors
(10,000 picofarads or less), it is essential that the low-voltage electrode and the conductor leading
to the measurement instrumentation be shielded by a grounded conductor. Otherwise, the stray
capacitance may cause significant measurement error. The National Bureau of Standards requires
some sort of standard connector (BNC, UHF, GR, BPO, or Type N) at the low-voltage terminal
in order to connect to the measurement system. Larger capacitors do not need to be shielded but
must be measured as a four terminal admittance because of the non-negligible lead impedance.
A description of how this measurement is done will be covered in Section 4. Capacitors must be
stable and reproducible in order to be considered standards, and, hence, warrant an NBS calibration.
Power factor capacitors (large capacitors used to tune distribution lines, etc.) are often special cases.
‘Their dissipation factors (in-phases component of the current divided by quadrature component)
are often quite stable but their capacitance values are often not. Because of the importance of these
capacitors to the electrical industry, they are often acceptable for calibration even though they do
not mect normal stability requirements.

Although the instrumentation has been used to calibrate a million-volt standard capacitor at rated
voltage, the instrumentation does impose some limitations on the voltage applied to the capacitor.
The only limitation on the maximum voltage is that the current through the standard capaci-
tor should be no larger than 10 milliamperes. In order to have reasonable sensitivity, the current


(D) |

= Cx ~Cs

ay
ay!

Y Ix Is

Nx Ns

Figure 2. Basic measurement circuit for the calibration of a high-voltage capacitor.

3 MEASUREMENT METHODOLOGY

3.1 Basic Measurement Circuits

The current comparator bridge used to calibrate voltage transformers and high-voltage capacitors
will be discussed in considerable detail in Section 4. A brief discussion of this bridge will be presented
here in order to facilitate understanding of the NBS measurement methodology. A simplified circuit
for measuring the ratio of two capacitors is shown in figure 2. (The active circuitry to achieve
dissipation factor balance is not included). At balance

V2afCrNz _ V2afC.Ns qa
Np ~ Np ’

where f is the frequency. This can be rewritten

(2)

The simplified circuit for measuring the ratio of voltage transformers is shown in figure 3. At balance
Vp2xfO>Nz _ Vs2nfC,N, @)
Na ~ Ne
or,
Vp _ NC
Pus 4
V, NeCp ®
The ratio of the two capacitors in (2) can be measured using the circuit discussed above in figure 2.

The measurement of a voltage transformer or a capacitor both involve the measurement of the ratio
of two standard capacitors. The measurement of capacitors will be discussed below followed by 2
discussion on the measurement of voltage transformers.


U.S. DEPARTMENT OF COMMERCE
NATIONAL BUREAU OF STANDARDS
GAITHERSBURG, MD 20899

REPORT OF CALIBRATION
STANDARD CAPACITOR
XXXXX, Serial No. 7277777

Submitted by

Customer Name
Customer Address

Capacitance and dissipation factor were measured on February 29, 1987, at a frequency of 60 Hz.
The results are tabulated below.

Voltage Capacitance
(kilovolts-rms) (picofarads)
2.5 1000.98
5 1000.98
10 1000.98

Ambient Temperature: 21.5 °C
The dissipation factor was measured to be less than 5 x 10~6.
Estimated Uncertainties

Capacitance: £0.05 pF
Dissipation Factor: +5 x 10-6
‘Temperature: +1°C

‘The estimated uncertainties quoted apply to the above tabulated values and should not be construed
as being indicative of the long-term stability of the device under test.

For the Director
National Engineering Laboratory

Group Leader
Applied Electrical Measurements
Electrosystems Division

26


U.S. DEPARTMENT OF COMMERCE
NATIONAL BUREAU OF STANDARDS
GAITHERSBURG, MD 20899

REPORT OF CALIBRATION
VOLTAGE TRANSFORMER.
120-14,400 to 120 Volts, 60 Hertz, 4.4 Volt-Amperes
XXXXX, Serial No. 777777?

Submitted by

Customer Name
Customer Address

Secondary
Frequency Secondary Voltage Phase Angle
(hertz) Burden — (volts) ‘Voltage Ratio (milliradian)
60 A 120 1x 1.00001 -0.12
B 1.00051 -0.16

Date of Test: February 29, 1987
Temperature: 20°C

The phase angle is positive when the secondary voltage leads the primary voltage of the same
polarity. The characteristics of the burdens designated above are given in the following table:

Impedance
Burden (ohms) Power Factor

A 1x 104 1.00
B 576 1.00

Estimated Uncertainties

Voltage Ratio: +0.01%
Phase Angle: +0.1 mrad
Temperature: +1°C

The results given in this report apply to the fundamental frequency components of the voltages.

For the Director
National Engineering Laboratory

Group Leader
Applied Electrical Measurements
Electrosystems Division

25


Cs Cx

~ {\-
LY
DETECTOR

Figure 1. Schering bridge.

In the past NBS had used a “comparative null method” to calibrate voltage transformers. The
unknown transformer was compared to an NBS reference transformer using a voltage comparator
consisting of a variable resistive divider and a mutual inductor. Reference transformers were available
with ratios ranging from 1/1 up to 2000/1. Measurement uncertainties in the comparison of the
unknown transformer with the reference transformer were +0.01% for ratio and £0.3 minutes for
phase angle. The ratio and phase angle of the reference transformers were known to about the
same accuracy. There are several disadvantages tu this approach. Since the comparator has a
limited range, several reference transformers must be available to cover the anticipated users’ needs.
The ratio and phase angles of each one of these transformers must be carefully determined over
the secondary voltage range of interest. These transformers then have to be rechecked at regular
intervals to determine if the ratios and phase angles have changed.

Ifa direct measurement method were available that was sufficiently accurate and straightforward to
make the calibration of these reference transformers a simple task, then that method could be used
to measure the customer’s transformer directly. At NBS, the “direct null method” in use originally
involved balancing the secondary of the reference transformer against the output of a resistive
divider used in conjunction with a variable mutual inductor to provide phase angle balance. Such a
measurement was difficult because the resistive divider ratio changed with heating. Since the late
1960’s a “direct null method” has been available that is straightforward and accurate and is now
used at NBS in place of comparative methods using reference transformers.

Capacitors are invariably measured by balancing the unknown capacitor against a known standard
using some type of bridge arrangement. ‘There are a variety of such bridges described in the lit-
erature [2]. ‘The one most used in high-voltage applications in the last sixty years is the Schering
bridge (figure 1). Two high-voltage arms of this bridge consist of the standard and unknown capac-
itors. The two low voltage arms are resistors (one has a parallel capacitor for phase angle balance).


4 ao
~~ >nC.
Cx Np $s Ake

Ix
LY VY i Ae e'
Nx [- Ns Is

Figure 13. Current comparator bridge with high-voltage resistor for in-phase current balance.

aR Cx (0) =Cs

Figure 14. Current comparator with superior in-phase current balance.

16


Table 5. Dissipation Factor Check Standard

Measured Correction

Corrected Theoretical

Date @ (DF) (DF.) (DFm) __(a/2xfRCz)
7/82 0.0003 =—-0.08003 0.0002 0.07983 0.07977
6.003 0.7982 0.0002 0.7980 0.7977
—0.003 = -0.7979 0.0002 —0.7981 —0.7977
0.0003 —0.07959 0.0002 —0.07979 — —-0.07977
3/83 0.0003 = 0.08135 —0.00014 0.08149 0.08147
0.003 0.81455 —0.00015 0.8147 0.8147
—0.003 —0.81475 —0.00015 -—0.8146 0.8147
—0.0003  —0.08160 —0.00014 -—0.08146 —0.08147
10/83 0.0003 0.07952 —0.0001 0.07962 0.07959
0.003 0.7959 = —0.0001 0.7960 0.7959
—0.003 —0.7960 —0.0001 0.7959 —0.7959
—0.0003 —0.07965 _—0.0001 —0.07955 —0.07959
1/84 0.0003 0.08174 0.00029 0.08145 0.08143
0.003 0.8148 0.00029 0.8145 0.8143
—0.003 = —0.8140 0.00029 = —0.8143. —0.8143
0.0003 —0.08110 0.00029 —-0.08139 _— —0.08143
5/84 0.0003 —-0.08090 0.0002 0.08070 0.08071
0.003 0.8076 0.0002 0.8074 0.8071
—0.003 = —0.8071 0.0002 —0.8073 —0.8071
~—0.0003  —0.08050 0.0002 ~0.08070 — —0.08071
11/84 0.0003 0.08000 0.0000 0.08000 0.07997
0.003 0.8000 0.0000 0.8000 0.7997
—0.003 —0.8000 0.0000 —0.8000 —0.7997
—0.0003 ——0.08000 0.0000 0.08000 — —0.07997
4/85 0.0003 —-0.08060 0.0000 0.08060 0.08059
0.003 0.8056 0.0000 0.8056 0.8059
—0.003 = —0.8055 0.0000 —0.8055 —0.8059
—0.0003 —0.08050 0.0000 0.08050 —0.08059
12/85 0.0003 (0.08070 = —-0.0001 0.08080 0.08071
0.003 0.8076 =—0.0001 0.8077 0.8071
—0.003 —0.8076 —0.0001 —0.8075 —0.8071
—0.0003 —0.08070 —0.0001 —0.08060  —0.08071
11/86 0.0003 0.08029 —0.00022 0.08051 0.08046
0.003 0.8049 —0.00022 0.8051 0.8046
—0.003 —0.8054 -0.00022 —0.8052 —0.8046
—0.0003 —0.08067_ —0.00022 —0.08045 — —0.68046

22



7

Table of Contents

INTRODUCTION

RANGE OF SERVICES
2.1. Voltage Transformers

2.2 Capacitors... ........0000-

MEASUREMENT METHODOLOGY

3.1 Basic Measurement Circuits... 2... 2. eee eee
3.2 Capacitors ..... ee eee eee eee eee eect eee ett e eee’

3.3. Voltage Transformers... 2... 2 eee eee ee

MEASUREMENT INSTRUMENTATION

MEASUREMENT UNCERTAINTIES

5.1 Voltage Transformers........---.---.... Loc ee eee
5.2 Capacitors... eee eee teen eee neces

ACKNOWLEDGMENTS

REPORT FORMAT

APPENDIX

REFERENCES

i

Caan

14

21
21
23

24

24

27

30


~Cp

ay

(3)

Ce)
yi
7f
(2)
a

BURDEN| | DVM | CURRENT |
\_-| COMPARATOR [=~
| BRIDGE |

Soop

Figure 5. Basic measurement circuit for the calibration of a voltage transformer with a digital
voltmeter (DVM) and secondary burden.

has an estimated uncertainty of less than +0.5% of the reading and measures true-rms ac volts.
The internal impedance of the DVM is equal to or greater than a megohm.

Possible Errors Caused by Improper Wiring

The wiring of the circuit shown in figure 5 is critical. For example, it is important that the two
capacitors be connected directly to the primary and secondary terminals of the transformer. Consider
instead figure 6. The capacitor C’ is connected to the burden and the DVM instead of directly to
the secondary terminal of the transformer. If the secondary burden were an ANSI standard burden
2Z (36 ohms at 120 volts, see table 3) and the resistance of the lead connecting the burden to the
transformer were 10 milliohms, the incorrect wiring shown in figure 6 would cause an error in the
transformer ratio measurement of about 0.03%. For higher impedance burdens this becomes less
of a problem but, in general, one must take precautions to avoid including the voltage drop in the
lead connecting the transformer to the burden as part of the voltage on the transformer secondary
winding to be measured.

Another major concern in the measurement of the ratio and phase angle of a voltage transformer
is the proper definition of the ground point and the avoidance of ground loops. This can best be
illustrated by the presentation of a few examples. In figure 7, some common mistakes are shown.
The transformer is energized in such a manner that significant current is forced to flow between
the transformer ground and the circuit ground. The resulting voltage drop in the lead connecting
the transformer and ground will be part of the ratio and phase angle measured. The high-voltage
capacitor is not connected directly to the primary of the transformer under test. The measurement
of the ratio and phase angle, therefore, includes the effect of the voltage drop in the lead between
the point where the capacitor is connected to the power source and the transformer. In addition,
as there are three different “ground” points in the circuit and it is not, in general, possible to know
the voltages and impedances between these points, a measurement error is probable.

In figure 8 the problem has been eliminated by defining the low-voltage terminal of the transformer
as ground. Although this point may significantly differ from the building or utility ground, from
the measurement point of view this is the correct ground. It is important that the shields of the


KH

e3¢ 1 lL Fr :

BURDEN| | DVM | CURRENT |
] | COMPARATOR |

| BRIDGE |
2 I J

Figure 8. Measurement circuit for the calibration of a voltage transformer. Measurement ground is
defined. Transformer excitation current flows from the measurement ground to building ground.

three-terminal capacitors, the bridge detector ground, and all other measurement grounds each be
connected directly to this point.

In figure 5 the preferred method of wiring a voltage transformer calibration circuit is shown. The
customer’s transformer is connected in such a way that the energizing current does not flow between
the transformer and the measurement ground. All measurement grounds are connected to the
transformer ground point. The two capacitors are connected directly to the primary and secondary
terminals of the transformer. Only one ground is used in the circuit. While it is not always possible
to connect the transformer as in figure 5, this is the best choice. Otherwise tests are required to
ensure that systematic crrore are not compromising the measurement results.

Burdens

The burden attached to the secondary of the customer’s transformer (as shown in figure 5) is
specified by the customer. In general this would not be the burden corresponding to the maximum
volt-ampere rating of the transformer but instead would be equal to the burden attached to the
transformer in its intended use. For example, if the transformer will only have a digital voltmeter
attached to its secondary, a calibration with a secondary impedance of a megohm would be more
useful than one with an ANSI ZZ burden attached. Since the ANSI burdens are often requested,
they are summarized in table 3 [7]. By convention these burdens are defined for a frequency of 60 Hz
only.

Substitute Burdens

If the customer does not send the secondary burden with the transformer, the National Bureau of
Standards will provide the burden. It is not practical to have available and adequately characterized
all of the anticipated burdens. Fortunately this is not necessary. If the ratio and phase angle of a
transformer is known for two different burden values, the ratio and phase angle at any other burden
can be calculated (with certain limitations) [8]. A derivation of the formulas relating the ratios and
phase angles at zero and some other known burden value are given in the appendix and presented
in abbreviated form below.

u


— PREFACE —

Calibrations and related measurement services of the National Bureau of Standards (NBS) provide
the means for industry, government agencies, academia, and others to relate the measurements
they make to national standards and, by extension, to the measurement systems of other countries
throughout the world. It is of crucial importance to improving U.S. productivity, efficiency, and
quality—in short our competitive stance—that measurements of appropriate accuracy can be made
at all stages of product development, production, and marketing and that it is possible to refer the
results of these measurements to each other in a meaningful way. NBS services provide essential
support for satisfying these needs, as well as measurement needs arising from societal concerns such
as health, safety, natural resources, and defense. The requirements of NBS clientele range from the
highest levels of accuracy realizable from advanced science and technology to the practical levels of
accuracy needed to support routine production. A reference-level measurement may be the result
of days of painstaking individual effort or may be provided by a semi-automatic measuring system

in minutes. The variation in customer needs and hence in NBS services responsive to those needs is
great.

The more than 300 different calibration services, measurement assurance services, and special tests
that are offered by NBS are described in NBS Special Publication 250, NBS Calibration Services
Users Guide. The Guide provides essential technical details of NBS calibration and related mea-
surement services, such as levels of accuracy provided by NBS and the requirements to be met
by customers’ transfer standards. It also provides information needed for placing orders for these
services and identifies technical and administrative contacts for each service.

Technical descriptions in the Users Guide are intended to be restricted to the material needed
by a potential customer to decide if a given service will meet that customer’s needs. Frequently, a
customer may be interested in more detailed and extensive information, such as the way in which the
errors associated with a measurement are assessed. Beginning in 1987, NBS established a Special
Publication 250 series which supplements the Guide. Each publication in this series provides a

detailed technical description of a specific NBS calibration service, or closely related set of services,
and includes: .

© specifications for the service

« design philosophy and theory

« description of NBS measurement system used to provide service
NBS operational procedures

measurement uncertainty assessment, including error budget, identification of systematic and
random errors

¢ NBS internal quality control procedures

Special Publication 250-33, A Calibration Service for Voltage Transformers and High-
Voltage Capacitors, describes services offered under NBS Test Numbers 54510C through 54513C
(voltage transformers) and 52400C (high-voltage capacitors at power frequency). These services are
provided by the Applied Electrical Measurements Group in the Electrosyslems Division as pact of
a series of services offered by the Division in support of the transmission and distribution of electric
power,

be
pe
fe


~Cx Cs75

“CURRENT |
|_| COMPARATOR x—
| BRIDGE !

Figure 17. Circuit for checking operation of dissipation factor measurement of current comy ‘ator
bridge.

prove that the bridge is still working to the ppm level, it can alert the user of changes large enough
to affect calibration results. Of course, since the two capacitive currents are largely balanced using
stable passive components (i.e., transformer windings), one expects that. the bridge should be stable.
It should be noted that if a transformer winding were to become open or short circuited the result
would be dramatic and readily observed by the operator.

The situation with the dissipation factor (or in-phase current) balance is different as active compo-
nents play an important role. Also, it is difficult to design a stable dissipation factor standard to act
as a check standard. This problem has been overcome by using the circuit in figure 17. Standard
capacitors are connected to the standard and unknown sides of the bridge. The known in-phase
current is applied with the use of the inductive voltage divider and a resistor as shown. The advan-
tage of this circuit is that the voltage across the resistor is small (~ 0.3 volt). However, because of
the small voltage, any error voltage, €, at the low side of the resistor, R, becomes important. The
in-phase current entering the N, winding is:

av.

(17)

Tin =

where a is the ratio of the inductive voltage divider (a < 1). The dissipation factor Iin/Tout is then

equal tu:
aV—e | (18)

DF =|—>————
lw —€)R2n fC,
The effect of € can be significant at the ppm level and needs to be eliminated. The circuit in figure 18

is identical to that in figure 17 except that the input of the inductive voltage divider is grounded.
The dissipation factor in this case is then:

nF, =

[w=sieerecl: (19)

20


Library of Congress Catalog Card Number: 88-600542

National Bureau of Standards Special Publication 250-33
Natl. Bur. Stand. (U.S.), Spec. Publ. 250-33, 37 pages (June 1988)
CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 1988

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325



Both exponentials have arguments much less than one so that discarding quadratic and higher order
terms and equating the imaginary components of the left and right sides of eq (30) one obtains

E; XeRo— XoRe
E.|te* ral [r+ eae (1)
or from eq (25) assuming Z. < Ze
wp, _ XoRe—XeRo
TeaTo RETA? (32)

The resistive and reactive components of the burden C' can be expressed as

Re = VRE X? cos, (33)

and
X, = JR2 +X? sind, (34)

where cos@, is the power factor of the burden C. From eqs (21) and (22)

(35)
and
(36)
Using eqs (27) and (33)-(36) one obtains
RCF, = RGF, [1 + Pal cos0, + Xosin 0)| . (37)

For the purposes of this discussion, it will be assumed that burden C (having impedance Z.) above
is the burden for which the ratio correction factor and phase angle are to be calculated. The ratio-
correction factor and phase angle must be known for some other burden, ‘1’, which shall be designated
as having impedance, Z;. Using eq (25) and substituting burden T for burden C:

y [BL Ee .
= [Big] % @)
or using eq (22)
Zo = Zy[RCF,e~1 FF) — RCF,]/RCF.. (39)
Neglecting second order and higher terms
Zq % Z[RCF; — RCF, + j(Po —Tt)]/RCFo. (40)
Using the facts that
Zr = |Z;| (cos 0; + j sin 0) (41)
and
Zo = Rot jXo (42)
one finds
Rot ( a ) [(RCF, — RCF,) cos + (Ts ~ T's) sin 8] (43)
RCF,

28


Table 6. Contributions to Uncertainty

Uncertainties
Random _ Systematic
Bridge measurement £2 (£2) £75 (£25
Secondary voltage setting £50 (+10)
Burden setting £50 (+10)
‘Transformer self-heating +75 (+20)
Capacitance ratio measurement +2 (+2) + 5 (+ 5)

Table 7. Total Estimated Uncertainties

Ratio correction factor 40.03% (£0.01 %)
Phase Angle +£0.3mrad (40.1 mrad)

transformer. Thus it is important to the customers of this calibration service to obtain a meaningful
uncertainty statement that reflects the contribution the voltage transformer would make to their
total error budget.

As mentioned earlier in this report, voltage transformers calibrated at NBS generally fall into two
accuracy classes: +0.03% uncertainty for ratio correction factor, -+0.3 mrad for phase angle; and
+£0.01 % for ratio correction factor, +0.1 mrad for phase angle. While it would be possible in some
cases to report smaller uncertainties to the customers by more thorough determinations of such
parameters as voltage coefficients, proximity effects, and burden dependencies, the present service
provides an economical way to present meaningful error statements to the customers and meets their
needs.

The analysis of the uncertainties for the ratio correction factor measurements are summarized in
table 6. The units are in ppm. The values in parentheses apply to the higher accuracy voltage
transformers described in Section 2.1 above. The uncertainties for the phase angle measurement of
voltage transformers are the same as is shown in table 6 except the units are microradians instead
of ppm.

To calculate the uncertainties reported to the customer, the systematic uncertainties tabulated
above are algebraically summed and added to three times the root sum of squares of the random
uncertainties. The results are shown in table 7.

The values in table 6 are approximate. Some transformers demonstrate stronger voltage dependences
than others or stronger burden dependences. In some cases the values in table 7 must be adjusted
for such transformers. The purpose of the above tables is to give the users an idea of the sources of
errors and how they are used to calculate an uncertainty statement.

Since most of the sources of error presented in table 6 originate from the transformer under te
NBS could in principle measure a nearly ideal voltage transformer to much better accuracy than
shown in table 7. Such a test would be expensive because of the time-consuming care that. would
be required.

5.2 Capacitors
The National Bureau of Standards has the capability to measure the ratio of two capacitors to an

estimated systematic error of +1 ppm and +1 x 10-§ + 1% of the measured value for the relative
dissipation factor. The values of the standard capacitors used for these comparisons are known to

23


Cc ~
T xX > ; Cs

LVN LSVYY)\
Nx Ns

Figure 4. Basic measurement circuit for the 4-terminal calibration of large capacitors.

should be at least 10 microamperes. The current through the customer’s capacitor can range from
10 microamperes to.1000 amperes.

Voltage Dependence

For the calibration of both capacitors and voltage transformers, the voltage coefficient of the standard
capacitor is important. The unit of capacitance at NBS is maintained at low voltage. This value
must be transferred to the high-voltage standard capacitors at their working voltages. At NBS,
considerable work was done to modify a commercial high-voltage standard capacitor to minimize
its voltage coefficient and to determine the magnitude of that voltage coefficient [5]. The National
Bureau of Standards was able to demonstrate that, if care were taken, a well-designed standard
capacitor should change capacitance by only a few ppm from 0 to 300kV. A more recent paper also
discusses the problem of the voltage dependence of standard capacitors and describes an international
comparison of high-voltage capacitor measurements [6]. (This paper also discusses the effect of
shipping and handling on the measured capacitance of a commercial standard capacitor.) The
voltage dependence of a compressed gas capacitor principally arises from the coulombic attraction
of the two electrodes and is hence quadratic in nature. The capacitor should be expected to vary
only slightly at lower voltages. Therefore, a capacitor rated at 200kV should be quite effective in
measuring the voltage dependence of another capacitor rated at 20kV.

Temperature Dependence

Another concern is the temperature dependence of the high-voltage standard capacitor. The typical
dependence is about +20ppm/°C. This dependence arises solely from the thermal expansion of the
components of the capacitor. Since C is directly proportional to the electrode area and inversely
proportional to the electrode separation, the thermal coefficient of the standard capacitor is pro-
portional to the linear coefficient of expansion. Although the laboratories at NBS are fairly stable
in temperature, the comparison of the high-voltage standard capacitor to the low-voltage standard
(which has a thermal coefficient of 2ppm/°C) is done at the beginning and conclusion of the mea-


BURDEN

DVM

i
1,
| aan a
| CURRENT |!
| COMPARATOR

! BRIDGE !
a

Figure 6. Measurement circuit for the calibration of a voltage transformer. Connection of low-voltage

capacitor as shown is incorrect.

©

BURDEN

DVM |

T

rd

a
~
4
| qq
| CURRENT |
_-! COMPARATOR --—
| BRIDGE |
LH

t~

Figure 7. Measurement circuit for the calibration of a voltage transformer. Grounds are poorly

defined.

10