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                                                    K. Debnath

                                              School of Engineering
                                              University of Tasmania
                                              Hobart, Australia 7000


        The accuracy of CTs used for metering purposes are required to be very accurate as they are used
        in tariff calculations. Decades ago, the current flowing in distribution circuits could be considered
        more or less to be of a purely sinusoidal form. In recent times, however, such is not the case.
        Many loads such as rectifiers, inverters and a host of other electronic devices draw non-sinusoidal
        currents. A non-sinusoidal current waveform can be considered to be composed of a pure sinusoid
        of the fundamental power frequency and its harmonics. Since these harmonics are injected into
        the system the ammeters and energy meters read the composite current, not just the fundamental
        component. The measurements will, therefore, reflect the actual currents only if the CTs
        transform the harmonics in the same proportion as the fundamental component. This paper
        presents the results of an investigation on the accuracy of some commercial current transformers.

1.   INTRODUCTION                                           and the secondary were measured. The following two
                                                            types of instruments were used for the current
Current transformers used in measuring currents in          measurements:

high voltage and high current circuits need to have         1. HP digital oscilloscope (Model 54602A)
high accuracy since they may be used for tariff             2. Fluke 41 Power Harmonic Analyzer.
calculations. A sinusoidal primary current is expected      Both of the above meters can provide true rms current
to produce a similar secondary current wave shape           values.
with a high transformation accuracy. However, the
current may contain harmonic distortion due to              2.1 Harmonic sources
rectifying and other types of loads such as fluorescent
lamps [1]. The question therefore arises whether the        Two different types of sources were used. The first
CTs remain equally accurate in the presence of the          one is a single-phase half-controlled bridge rectifier
harmonics. It is the purpose of this paper to present the   fed from the mains power supply. The current drawn
results of an investigation performed on commercial         by the rectifying circuit was passed through the CT
current transformers to establish their behaviour in the    primary winding as shown in Figure 1. The harmonic
presence of harmonics. Although both protection and         contents of the current can be varied by varying the
metering type of CTs were used in the investigation,        firing angle of the thyristors. The advantage of this
the results of only the latter type are presented in this   type of source is that it is realistic and representative
paper.                                                      of the kind of non-sinusoidal currents experienced in
                                                            the real world [2]. The disadvantage is that the

In addition to some others, the following two CTs                      A       Secondary
were made available to us by a power utility for
investigation:                                                                             Half-controlled
Delle    Type TAT 1        15VA 50 Hz 150/5A                                    A
Delle    Type TAT 2        30VA 50 Hz 300/5A                          CT
                                                                             Primary                         Resistive
                                                                  Ac mains
                                                                             current                         load
Tests performed on both CTs yielded similar results.
Therefore, results of only the first one are presented in
this paper.
                                                                Figure 1 Test circuit with controlled rectifier as
The primary winding of the CT was excited by a                                 harmonic source
harmonic source and the currents in both the primary
magnitudes of the individual harmonics can not be                                Rp    Lp             Ls        Rs
controlled at will for test purposes.
The second type of source used is a programmable                                        Re     Ie
                                                                           Ip/ N                                       Ib
waveform generator [PWG]. The equipment consists
of computer software and hardware including a digital
to analog conversion circuit. Since the output of this
generator is very low, a power amplifier was used to                                    Le            Ics
deliver the required test current. This equipment is            1:N
capable of generating any arbitrary waveform by
specifying the order as well as the magnitude of the            Id eal
harmonics, in addition to the fundamental. An
additional advantage of this generator is that it could
generate a "pure" sinusoid in contrast to the somewhat    Figure 3 Frequency dependent equivalent circuit of a
distorted mains power supply. The test circuit with                      current Transformer.
this kind of harmonic source is shown in Figure 2.        current through the total secondary circuit impedance
                                                          including the burden. Since the secondary current may
                                                          vary over a wide range i.e. from zero to rated current.
                                                          The secondary current Ib can be expressed as
         Secondary current
                 A                                                    Ib =  − I e − I cs
                                                          For a practical CT, Ie is not zero. Also, at high
                                                          frequencies, the current Ics can be significant [5].
                      Primary current                     Therefore the secondary current Ib is different from the
                                                          nominal Ip/N.
                CT                                        2.3 Ratio correction factor
                                        Load              The transformation accuracy of a CT can be defined in
                                                          terms of its ratio correction factor (RCF). The turns
 Figure 2 Test circuit with programmable waveform         ratio N multiplied by the RCF equals the ratio of
       generator (PWG) as harmonic source.                primary current to secondary current. An ideal CT will
                                                          have an RCF of unity.
2.2 Equivalent circuit
                                                                      Ip         I b + I e + I cs    I + I cs
An equivalent circuit of the test CT was determined by    RCF =              =                    =1+ e
                                                                    N Ib               Ib               Ib
performing the open-circuit and short-circuit tests.
Since a frequency dependent model is considered, test
                                                          Using this RCF factor, CT accuracy may also be
voltages of varying frequencies were used. Figure 3
                                                          expressed as an error percentage as follows:
shows the kind of CT equivalent circuit considered [3]
in this investigation. Some authors use a slightly
                                                                                     I e + I cs                1 
different equivalent circuit [4]. The parameters of the   % error = 100 ×                         = 100 × 1 −     
equivalent circuit are as follows:                                               I b + I e + I cs             RCF 

Rp = Primary winding resistance                           It is noted that the percent error approaches zero as the
Lp = Primary leakage inductance                           RCF approaches unity. RCF is a function not only of
Re = Resistive part of the magnetizing impedance Ze       Ie and Ics but also of the Ib i.e. the burden supplied by
Le. = Inductive part of the magnetizing impedance Ze      the CT. With a particular secondary current, Ics
Cs = Stray capacitance                                    increases with frequency and so does the percent error
Rs = Secondary winding resistance                         because the second term of the RCF increases.
Ls = Secondary leakage inductance
Rb = Resistive burden (not shown) through which the       A direct measurement of the currents in the primary
      current Ib flows.                                   and the secondary windings of the CT was performed
                                                          and the ratio correction factor determined. This was
The exciting current Ie is dependent on Ze and the        done at various frequencies and is shown in a later
secondary voltage required to drive the secondary         section.
2.4 Open circuit test

With the "primary winding" kept open, a voltage of
1 V rms was applied at the secondary. The magnitude
and phase angle of the current drawn at the secondary
were measured. This was repeated with a wide range
of frequencies (50 Hz to 400 kHz). Plotted on a
log-log paper, the open circuit impedance shows a
linear rise upto about 125 kHz and then falls off as
shown in Figure 4. Obviously, the impedance between
50 Hz and 125 kHz is due to Ze. The straight line can
be expressed as

        log (Zoc) = 0.372 log (f) + 0.615
                                                                                      Frequency (Hz)
from which
                                                              Figure 5 Phase angle of open circuit impedance of
         Z oc = 4.123 f   0.372
                                           for f < 125 kHz         15VA 150/5A Delle current transformer

Again, the equation of the straight line for the Zoc         2.5 Short circuit test
which can be considered due to Zcs, between 150 kHz
and 400 kHz is given by:                                     For the purpose of this test, the "primary" was hand-
                                                             wound with sufficient number of turns so that rated
        log (Zoc) = -0.999 log(f) + 7.669                    primary current was obtained. Short circuit test was
                                                             then performed for a wide range of frequencies.
         Z oc = Z cs = 46647112.32 f                         Voltage and current magnitudes as well as the phase
                                                             difference were noted. The short circuit impedance
         C s = 3.412 nF                                      curve is shown in Figure 6.

                                                                                      Frequency (Hz)

                                                                 Figure 6 Short circuit impedances (referred to
                               Frequency (Hz)                          secondary side) of 15VA 150/5A
                                                                           Delle current transformer
 Figure 4 Open circuit impedance of 15VA 150/5A
            Delle current transformer                        Upto a certain maximum frequency,

The phase angle of this impedance remains almost
                                                             Z p + Z s << Z e
constant at 450 for a frequency upto 4 kHz as shown in
Figure 5.
                                                             and therefore the short circuit impedance can be
                                                             considered to equal to Z p + Z s .
The secondary winding resistance can be measured                         3. MEASURED DATA
directly by using a suitable measuring device (a bridge
circuit or a digital meter). The leakage inductance of                   Using the test circuit shown in Figure 1, the primary
the secondary winding can be estimated by the                            current was adjusted to 51 amps (about 33% of rated
following methods:                                                       current) corresponding to a firing angle of 900. The
                                                                         expected secondary current is 1.7 amps. The actual
1.      A maximum value for Ls can be estimated by                       measured current was 1.73 amps. With the same
        noticing any lack of resonance in the short circuit              primary current but at a firing angle of 1260, the
        impedance curve.                                                 secondary current was measured to be 1.72 amps. The
                                                                         same procedure was repeated with 80% of rated
2.      The RCF of the CT can be measured as a function                  current (120 amps). The results are shown in Table 1.
        of frequency and the value of Ls that gives the                     Table 1 Measured currents of the CT excited by
        best fit for the RCF calculated from the CT                                       rectifier current.
        equivalent circuit and the measured RCF.
                                                                              Firing        Primary         Secondary
The slope of the short circuit impedances gives an                            Angle         Current          Current
approximation of the primary leakage inductance (Lp)                           (α)             (A)             (A)
of the hand-wound primary. It may be noticed in                                90°             51             1.73
Figure 6 that the portion between 200 Hz and 30 kHz                           126°             51             1.72
is straight which can be expressed as                                          90°            120             4.05
                                                                              126°            120             4.04
               Log (Zsc) = 0.936 log(f) -2.96
                                                                         The maximum errors here are 1.8% (1.73 amps instead
               ω ( L′p + Ls ) = 1.097 × 10 −3 f        0.936
                                                                         of 1.7) and 1.3% (4.05 amps instead of 4). It may be
                                                                         noted from the measured data that the error tends to
where L ′p is the primary leakage inductance referred                    decrease as the current approaches the rated value.
to the secondary side and Ls is the secondary leakage                    The above measurements were repeated with the
inductance. This total inductance as calculated from                     second harmonic source i.e. the programmable
the above equation is 1.94 mH.                                           waveform generator. Primary current consisting of the
                                                                         fundamental and any one of the odd harmonics
As there is no sign of any resonance up to 30 kHz, Ls                    between 3 to 11 were injected at one time. The
may be calculated as                                                     magnitude of the harmonic was 20% of the
                         1                                               fundamental. The secondary current was measured to
     Ls ≤                                = 8.249 mH
          (2 π × 30,000) × 3.412 × 10 −9
                        2                                                be 1.71 or 1.72 amps for a primary current of 51 amps
                                                                         as shown in Table 2. The secondary current does not
Using MATLAB, the value of Ls that gives the best fit                    change when all of this frequency components are
for the RCF is found to be 0.56 mH. The resistance of                    added so long as their combined magnitude remains
the secondary winding Rs was found to be 0.1 ohm.                        within 20%. The theoretical transformation ratio of
With all these values the equivalent circuit of the CT                   30:1 is not available even for the pure 50 Hz input (for
was constructed and is shown in Figure 7.                                a primary current of 120 amps, the secondary current
                                                                         is 3.99 amps instead of 4). However, it is noted with
                          Rp          Lp       0 . 5 6 mH      0.1 ohm   interest that exactly 4 amps is measured in
                                                                            Table 2 Measured secondary currents of the CT
                               2.91 f 0.37                                  excited by a programmable waveform generator.
                                               3 . 4 1 nF                                   Secondary          Secondary
                                                                            Harmonic       Current with       Current with
                               0.47 / f 0.63                                 order          Ip = 51 A          Ip = 120 A
                                                                                               (A)                 (A)
                                                                                 1             1.71                3.99
            1:N                                                                 1,3            1.71                3.99
     I d e al T r a n s f o r m e r                                             1,5            1.72                4.01
                                                                                1,7            1.72                4.02
 Figure 7 Frequency dependent equivalent circuit for                           1,11            1.71                4.02
             the CT under investigation                                     1,3,5,7,11         1.71                4.00
the secondary when the primary consisted of many                         Table 3 Phase angle error
                                                                                Burden, Ohms
The ratio correction factor curves for the current               f     0.2      1.0     3.0       5.0   10.0
transformer with various burden resistances are                (Hz)       Phase angle error, deg
shown in Figure 8. It may be noted from this figure             50     0.58    0.20     0.67     1.64   2.34
that for a burden of 1 ohm or less, the ratio correction        100    0.77    0.79     1.31     1.32   2.03
factor is very close to unity for frequencies upto              150    1.20    0.54     1.17     1.42   2.11
2 kHz. As the burden increases, the transformation              200    0.86    1.35     1.32     1.29   1.85
error increases for the same frequency range                    250    1.34    1.15     1.28     1.68   1.89
(≤ 2 kHz). Beyond this frequency range of 2 kHz                 300    1.51    1.31     1.36     1.77   1.93
(40th harmonic) the transformation accuracy                     350    1.19    1.54     1.17     2.05   1.78
deteriorates regardless of the burden value.
                                                                400    0.59    1.24     1.40     1.82   2.04
                                                                450    1.35    1.06     1.20     1.63   2.38
                                                                500    2.10    1.23     1.24     1.93   2.23
                                                                550    1.67    1.62     1.18     1.80   2.09
                                                                600    1.72    1.55     1.58     1.73   2.37
                                                                650    1.21    1.37     1.85     1.79   2.43
                                                                700    1.15    1.43     1.47     1.96   2.28
                                                                800    1.66    1.69     1.92     1.88   2.19
                                                                900    1.61    1.63     1.62     1.48   2.07
                                                                1k     1.53    1.66     1.37     1.95   2.27
                                                               1.2k    1.30    1.75     1.44     2.19   2.18
                                                               1.4k    1.45    1.58     1.59     2.04   2.25
                                                               2.0k    1.33    1.47     1.57     1.89   2.17

                                                            2 degrees has been found for a burden of 10 ohms at a
                       Frequency (Hz)                       frequency of 2 kHz.

Figure 8 Ratio correction factor curves for the current     Considerable time has been devoted in developing a
         transformer with different burden.                 frequency dependent equivalent circuit of the CT.
                                                            Such a circuit can be utilized for the computation of
The phase error of the current transformer has been         actual current transformation ratio at any frequency.
determined for 50 Hz and its harmonics up to 2 kHz
for burdens of 0.2 ohm, 1 ohm, 3 ohms, 5 ohms and
                                                            5. REFERENCES
10 ohms respectively. Phase angle errors can exceed
20 even at 50 Hz with high burden say 10 ohms.              [1] P. G. Kendall, "Harmonics in Power System",
However, this error remains well within the bound of            The Electricity Council, Power System
20 for upto the 40th harmonic if the burden is 3 ohms           Engineering Series, 1981.
or less. Even with a burden of 5 ohms, the phase error
is very close to 20 as shown in Table 3.                    [2] J. Arrillaga, D.A. Bradley and P.S. Bodger.
                                                                "Power System harmonics", 1985, Wiley, New
4. SUMMARY & CONCLUSIONS                                        York.
Measured data on CT accuracy has been reported in           [3] D.A.Douglass, "Current Transformer Accuracy
this paper. Two different types of harmonic sources             with Asymmetric and High Frequency Fault
were used with varying degrees of representation of             Currents", IEEE Transactions on Power
practical situations.                                           Apparatus and Systems, Vol. PAS-100 No. 3,
                                                                March 1981.
It has been seen that the ratio correction factor is very
close to unity for low burden (1 ohm or less) for a         [4] V.J. Gosbell and G.J. Sanders, "Frequency
frequency range of upto about 2 kHz i.e. 40th                   Response of distribution CTs", Proceedings of
harmonic. There is a sharp deterioration of the RCF             AUPEC96, pp. 77-82.
beyond the 40th harmonic even with very low burden.
It has also been observed that the phase angle error        [5] Wright, "Current Transformers: Their transient
increases, in general, with frequency for a particular          and Steady State Performance", 1968, Chapman
burden. A maximum phase error of slightly above                 and Hall.

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