ACCURACY OF DISTRIBUTION CURRENT TRANSFORMERS UNDER NON-SINUSOIDEAL EXCITATION K. Debnath School of Engineering University of Tasmania Hobart, Australia 7000 Abstract 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 . 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 . The disadvantage is that the 2. TEST METHODS AND EQUIPMENT In addition to some others, the following two CTs A Secondary current were made available to us by a power utility for investigation: Half-controlled rectifier 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. Ip 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 Cs 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 Ip A Ib = − I e − I cs N For a practical CT, Ie is not zero. Also, at high frequencies, the current Ics can be significant . Primary current Therefore the secondary current Ib is different from the nominal Ip/N. A CT 2.3 Ratio correction factor PWG Resistive 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  in this investigation. Some authors use a slightly I e + I cs 1 different equivalent circuit . 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. −0.999 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 F 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 frequencies. 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.  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.  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  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  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  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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