AN IMPROVED TECHNIQUE OF MEASUREMENT OF HIGH A.C. VOLTAGE

Sirshendu Saha#1

#1 Department of Applied Electronics and Instrumentation Engineering, Academy of Technology, P.O.- Aedconagar,

Adisaptagram, Hooghly -712121, India #1sirshendueie@gmail.com,

Satish Chandra Bera*2

*2Instrumentation Engineering Section, Department of Applied Physics University of Calcutta, 92, A.P.C. Road,

Kolkata 700009, India *2scbera_cal52@rediffmail.com

Abstract—High a. c. voltage is generally measured by a potential transformer instead of an a.c. volt meter in order to avoid the hazards of high voltage. The conventional potential transformer is specially designed step down transformer where almost accurate voltage between primary and secondary is maintained to obtain output voltage directly proportional to input voltage. But this measurement suffers from ratio error and phase angle error, due to the effects of secondary current, magnetizing current and eddy current. In the present paper attempts have been made to reduce these currents by an improved design technique of the transformer. The technique has been utilized to fabricate a low voltage prototype unit. Its performance characteristics have been experimentally studied in a storage oscilloscope. The experimental results are reported in this paper. From these results a very good linear response with negligible phase angle error has been observed. Keywords— High A.C. voltage measurement, Ratio error, Phase angle error and Feedback technique

I. INTRODUCTION

High a.c. voltage and current are required to be measure very accurately in magnitude and phase by using accurate potential transformer and current transformer respectively so that high tension power measurement may become accurate. A small error in this power measurement may lead to huge loss of power supply authority. So design of accurate potential transformer and current transformer with negligible ratio error and phase angle error is always important in power system instrumentation. The conventional potential transformer [15]-[16] has output line voltage range from 0V to 110V and phase voltage range from 0V to 110/√3V with burden in the range from 15VA to 200 VA for classes like A, B and C and 10VA for higher classes like AL and BL. Thus in conventional potential transformer where output voltage is measured by an a.c voltmeter is always associated with secondary current as well as magnetizing current and eddy current components of no load current. These currents produce phase angle error and

ratio error of potential transformer and thus produce error in high tension voltage and power measurement. For ideal potential transformer having no ratio error and phase angle error, the actual voltage ratio of primary voltage to secondary voltage should be exactly equal to the nominal ratio of primary turns to secondary turns for no ratio error and secondary voltage should be exactly at 1800 phase angle with respect to the primary voltage for zero phase angle error. But due to the effects of the secondary current and no load current components, this ideal condition cannot be maintained in a potential transformer. Hence two types of measurement errors like ratio error and phase angle error are observed. The difference between the actual primary voltage to secondary voltage ratio and the primary turns to secondary turns ratio is called the ratio error whereas the phase angle between the applied primary voltage and the reversed secondary voltage is called the phase angle error. The recommended ratio error may vary from 0.5% to 2%, which may increase to 5% for class D transformer. The phase angle error may vary from 20 min to 30 min. Various research works are still being continued to analyze and reduce the above errors of a potential transformer. Slomovitz D.[1] has described a new electronic system to compensate the voltage drops in the series impedances of the instrument transformer, which are the main cause of errors at power frequency and avoiding the influence of nonlinear behavior of the magnetizing branch. Eren L. et al [2] have described Fourier based metering technique to compensate for the errors introduced by instrument transformers at each harmonic level. An online error correction method to correct for wound-type potential transformer measurement errors and its sensitivity analysis has been proposed by Hamrita T.K [4]. An on-line error correction method has been proposed by

Hamrita T.K. et al [3] to correct for the resonance errors as well as possible saturation errors in existing substation instrument transformers designed for 60Hz. Skundric S. et al [5] have reported a new method of instrument transformer accuracy testing based on the measurement of two phase angles and on the use of a mathematical model for calculating amplitude and phase errors. A new compensating system has been described by Slomovitz D. [6] to reduce the ratio error and the phase error of inductive voltage dividers and standard voltage transformers operating at no load. Kadar L. et. al. [7] have proposed a method to correct for measurement error, which can be introduced by current and voltage transformers using compensation scheme implemented as a digital filter. Cox M.D. et al [8] have studied the performance of distribution potential transformers for non-sinusoidal waveform with ratio correction factor. Improved models for current transformers (CT), potential transformers (PT), and capacitive voltage transformers (CVT) for a relay software library have been reported by Lucas J.R et al [9]. A new digital data-acquisition method has been presented by Fuchs E.F. et al [10] for the separate measurement of iron-core and copper losses of transformers under any full or partial-load condition. D.A.Douglass [11] has analyzed potential transformer accuracy above and below the rated voltage at different frequencies above 60Hz. The effect of high frequency on the operation of a transformer has been studied by P.T.M. Vaessen[12]. A current comparator technique has been proposed by E.So. [13] for calibration of non-conventional instrument transformers. The parameter identification of a potential transformer model has been reported by J. Bak-Jensen et al [14]. In the present study the design of an accurate low cost potential transformer has been reported. The high value of the no load current due to the very high transmission line voltage on primary in combination with the secondary current passing through the display unit tends to produce larger amount of error components. In the present design a feedback technique is proposed where the no load current becomes very small and the current drawn from the secondary by the output device is reduced to a negligibly small or zero value so that the error components of the potential transformer may become very small. A theoretical analysis of the proposed technique has been described in this study and it has been shown that the feed back current is directly proportional to the primary

voltage and will have similar waveform as the primary voltage. These predictions from theoretical analysis have been verified experimentally on a low voltage prototype unit of the potential transformer. The experimental results are reported in the study.

II. METHOD OF APPROACH

Let the applied voltage across the primary of a conventional potential transformer be Vp, the secondary voltage be Vs, the ratio of primary to secondary turns be n, the secondary current through the display unit be Is, the resistance and reactance of the primary winding be respectively rp and xp and those of the secondary winding be rs and xs. Let magnetizing current and the eddy current in the transformer core be respectively Im and Ie, the phase angle between the secondary current Is and the secondary terminal voltage Vs be δ and the phase angle between reversed secondary voltage and the primary current Ip be β. Let the phase angle between the reversed secondary voltage and applied primary voltage be θ. Hence from the phasor diagram[15] of the transformer as shown in Fig.3 we have the following equation.

cos cos sin cos sinp s s s s s p p p pV nV nI r nI x I r I xθ δ δ β β= + + + + (1)

Since θ is usually very small, cosθ may be assumed to be very nearly equal to 1 and the reversed Vs and Vp are considered to be at right angles to Φ. So we have following equations.

cos cossp e

II In

β δ= + and sin sinsp m

II In

β δ= + (2)

Hence

( )cos sin cos sins sp s s s s p e p m

I IV nV nI r x r I x In n

δ δ δ δ⎛ ⎞ ⎛ ⎞= + + + + + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(3)

From this we can calculate the actual ratio error of the potential transformer which is given by the following

equation. Ratio error = p

s

V nV⎡ ⎤−⎢ ⎥⎣ ⎦

=

( ) ( ){ }2 2cos sins

s p s p e p m p

s

I n r r n x x I r I xn

V

δ δ⎡ ⎤⎛ ⎞ + + + + +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(4)

From the phasor diagram as shown in Fig.3, we also obtain the following equations

cos sin cos sinsin p p p p s s s s

p

I x I r nI x nI rV

β β δ δθ − + −=

= θ (radians) (5)

(very nearly, since θ is very small) Otherwise,

cos sin cos sintan

cos sin cos sinp p p p s s s s

s s s s s p p p p

I x I r nIx nIrnV nIr nIx I r I x

β β δ δθδ δ β β

− + −=+ + + + (6)

or

cos sin cos sintan p p p p s s s s

s

I x I r nI x nI rnV

β β δ δθ − + −= (7)

since the terms in the denominator involving Is and Ip are very small compared to nVs. As θ is very small, the value of tan θ may be assumed to be nearly equal to θ. Hence the phase angle error of the potential transformer i.e. the phase angle between the reversed secondary voltage phasor and applied primary voltage phasor is given by the following equation. { }2 2 p( )cos ( )sin xs

s p s p e m p

s

I n x x n r r I I rn

nV

δ δθ

⎡ ⎤⎛ ⎞ + − + + −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦=

(8)

From (4) and (8) it is found that both ratio error and phase angle error in a potential transformer are mainly dependent on the secondary current Is, magnetizing current Im and eddy current Ie. In the conventional potential transformer, the material with high permeability like mumetal is used to decrease the magnetizing current and laminated core material with higher resistivity is used to decrease the eddy current and thus the error components are reduced. But since the output display unit like ac voltmeter draws a considerable amount of current from the secondary winding, the ratio error as high as 2-5% and the phase angle error as high as 20-30 min may exist in a conventional potential transformer. One of the conventional methods of measurement of ratio error and phase angle error is absolute method of measurement. In this absolute method [15] of measurement, the voltage of the transformer secondary winding is compared with a suitable fraction of the voltage applied to the primary winding. This fraction is being obtained by the use of non-inductive and non-capacitive resistance potential divider with a variable tapping. The magnitude and phase of the difference between these two voltages are measured and the transformer errors are obtained

there from. The burden with which the transformer is to be tested is connected across the secondary winding and the normal primary voltage at normal frequency is applied to the primary winding as shown in Fig.1. A non-inductive and non-capacitive potential divider is connected across the primary winding in series with an inductance L. A condenser C shunts a small part r of the resistance of the potential divider, which has two adjustable contacts b and c as shown. In carrying out the test, the positions of these contacts are adjusted until the vibration galvanometer produces no deflection. Let I is the current passing from the supply through the potential divider. When the vibration galvanometer indicates zero deflection, the current through the section co is the same as that through section dc. Then the secondary terminal voltage Vs = voltage drop across co = IZco where Zco is the impedance of the section co. The primary terminal voltage Vp=IZdo where Zdo is the impedance of the section d to o. Now we have Zco = (R2-r) + jωL + Zba where Zba is the impedance of r and C parallel. In evaluating Zba we have,

1 1 1 1b a

j CjZ r r

C

= + = + ω−ω

2 2 2(1 )H ence

1 1ba

r r j C rZj C r C r

=− ω=

+ ω + ω (9)

22 2 2 2 2 2 2

22 2 2 2 2 2 2

Now ( )1 1

1 1

cor j CrZ R r j LC r C r

r CrR r j LC r C r

ω= − + ω + −+ ω + ω

⎡ ⎤= − + + ω −⎢ ⎥

+ ω + ω⎢ ⎥⎣ ⎦

(10)

22 2 2 2 2 2 2

Again

1 1

do co dc co 1

1

Z Z Z Z R

r CrR R r j LC r C r

= + = +

⎡ ⎤= + − + + ω −⎢ ⎥

+ω +ω⎢ ⎥⎣ ⎦

(11)

Fig.1: Absolute method of measurement of potential transformer

Fig.2: Phasor diagram for absolute method of measurement

22 2 2 2 2 2 2

22 2 2 2 2 2 2

1 1Hence =

1 1

1p do

s co

r CrR R r j LC r C rV IZ

V IZ r CrR r j LC r C r

⎡ ⎤+ − + + ω −⎢ ⎥

+ω +ω⎣ ⎦=⎡ ⎤

− + + ω −⎢ ⎥+ω +ω⎣ ⎦

(12)

since 2 2 2C rω is small compared to unity, we have

2 2 2 (approximately)1

r rC r

=+ ω

and also 2

2 2 21CrL

C r

⎡ ⎤ω −⎢ ⎥

+ ω⎢ ⎥⎣ ⎦

is

small compared with R1 and R2.

Thus the ratio 2

2 = (verynearly)p 1

s

V R RV R

+ (13)

The phasor diagram at balanced condition is shown in Fig.2. Ic and Ir are the two components of I flowing through the condenser C and resistance r respectively. θ is the phase angle of the transformer. The phasors representing the voltage drops across the parts of the circuit oa, ab, cb and cd are marked as voa, vab, vcb and vcd respectively. Now in the triangle whose sides are Vp, Vs and vcd we have

=sin sin

cd sv Vθ α

or =sin sin

1 sIR Vθ α

Hencesinsin = 1

s

IRV

θ α (14)

The angle α is the phase angle of the whole circuit d to o i.e. the angle between Vp and I.

2

2 2 21Now sin =

do

CrLC r

Z

⎡ ⎤ω −⎢ ⎥

+ ω⎣ ⎦α (15)

2

2 2 21H en ce s in = .

su b sti tu tin g fo r w e h ave ,

1

s d o

p

d o

C rLC rIR

V ZV IZ

θ

⎡ ⎤ω −⎢ ⎥

+ ω⎣ ⎦ (16)

2

2

2 2 2 2

2 2 21

sin = . .1

p 1 p 1

do s do s do

CrLC rV R V R CrL

Z V Z V Z C rθ

⎡ ⎤ω −⎢ ⎥ ⎡ ⎤+ ω⎣ ⎦ = ω −⎢ ⎥

+ ω⎢ ⎥⎣ ⎦

(17)

Now, 2

2 =p 1

s

V R RV R

+ and taking R1+R2=Zdo, since the other

terms involved in Zdo are small compared with R1+R2 we have

2

222 2 22 2

2

2 2 22 2

sin = .( ) 1

.( ) 1

1 1

1

1

1

R R R CrLR R R C r

R CrLR R R C r

θ⎡ ⎤+ ω −⎢ ⎥+ + ω⎢ ⎥⎣ ⎦

⎡ ⎤= ω −⎢ ⎥+ + ω⎢ ⎥⎣ ⎦

(18)

2 2( )1

1

RR R R+

may be written as2 2

1 11R R R

−+

and also

2 2 2C rω may be neglected in comparison with unity. Thus

( )2

2 2

1 1sin =1

L CrR R R

θ ⎡ ⎤ω − −⎢ ⎥+⎣ ⎦ (19)

Equations (13) and (19) are utilized to find out ratio and phase angle error of the potential transformer in the conventional method of measurement. In the present investigation, a modified design of the potential transformer has been proposed as shown in Fig.4. In this figure, Np denotes the number of turns of the primary winding, Ns denotes the number of the turns of the secondary winding of the proposed modified design of the potential transformer, Ns1 denotes the usual number of turns of another secondary winding so that output voltage across this winding may vary from 0V to 110V. Nf denotes the number of turns of a feedback winding. The conventional secondary winding Ns1 is used to find the ratio error and phase angle error of the transformer without feedback by using absolute method. The number of turns in the secondary winding Ns is selected to have very small so that the output voltage across this winding may be very small of the order of few volts. This small induced voltage is amplified by an instrumentation amplifier having very high input impedanceOPAMPs so that the current drawn from the secondary may be negligible and the secondary winding may be maintained in almost open circuit condition. The instrumentation amplifier consists of OPAMPs A1, A2 and A3 with very high input impedance and resistors R4, R5, R6, R7, R8, R9 and R10. The secondary winding is connected with this instrumentation amplifier through very high value

resistors R2 and R3 as shown in the Fig.4.The output of the instrumentation amplifier is connected with the feedback winding through a buffer amplifier consisting of the OP-AMP A4 and the ac current indicator mA. The winding direction of the feedback winding is such that the flux produced by this winding inside the core material is at 1800 phase opposition with respect to the flux produced by the primary winding. As a result the net flux inside the core decreases and so the induced voltage in the secondary winding also decreases. This will continue until the feedback current If increases to such a value so that the flux produced by the primary winding is completely nullified by the flux produced by the feedback winding and the voltage across the secondary becomes zero. Hence the effective magnetization current will be zero or negligible. Again the eddy current in the core material produced by the primary current will also be opposed by the eddy current produced by the feedback current. Hence the effective value of eddy current will also be zero or minimum and the ratio error and the phase angle error as shown in (4) and (8) will also be negligible.

Fig. 3. Phasor diagram of conventional potential transformer

Fig.4. Modified design of a potential transformer

If Ip and If be the value of primary and the secondary current under this balanced condition then, 0p p f fI N I N− = (20)

or p pf

f

N IIN

= (21)

Since the net flux inside the core becomes almost zero so the effective inductance of the primary winding becomes almost zero. Hence the primary winding behaves as a pure resistive element. As a result the current in the primary winding tends to increase. In order to reduce this current a resistance of value R1 is connected in series with the primary winding as shown in Fig.4. If rp be the value of the resistance of primary winding, Vp1 be the voltage measured across the primary winding for the supply voltage Vp and Ip be the primary current as shown in Fig.3 and Fig.4, then I p and Vp1 are given by,

1( )p

pp

VIR r

=+

(22)

and ( )

11

p pp

p

r VVR r

=+

(23)

Combining (21) and (22) we get,

( )1

p pf

f p

N VIN R r

=+

(24)

So the voltage Vf across the standard resistance Rf connected in series with the feedback winding is given by,

( )1

f p pf

f p

R N VVN R r

=+

(25)

Thus the feedback current or the feedback voltage Vf is proportional to the supply voltage Vp and will be in the same phase as the supply voltage. Hence an ac current meter measuring feedback current If or an ac voltmeter measuring feedback voltage Vf may be calibrated in terms of the supply voltage Vp since each of If and Vf is directly proportional to Vp. Thus the calibration will be free from ratio error and phase angle error.

III. DESIGN Let Bm be the operating flux density in the linear zone of the magnetization curve of the core material, A be the effective cross-sectional area of the core and Vs be the secondary voltage. So, for sinusoidal supply voltage Vp at the primary at a frequency f, s s mV 4.44N AB f= (26)

Similarly the induced primary voltage Vp1 is given by 1p p mV 4.44N AB f= (27)

From the magnetization characteristic of the core material, Bm can be selected in the linear zone, Vs and Vp1 may be selected

at some arbitrary lower values. The cross-sectional area (A) of the torroidal core can be selected from the available cores in the market and may be selected to be small since core loss in the proposed design is very small. Hence the secondary turns (Ns) and primary turns (Np) may be determined from (26) and (27) respectively. In the present investigation Vs and Vp1 are selected to be 2V and 5V respectively for the supply voltage of 230V. The feedback winding is selected to have identical number of turns as the primary winding. The operational amplifiers A1, A2, A3 and A4 are selected to be OP07. The actual ratio error and phase angle error of the above transformer without feedback has been measured by using absolute method with the usual secondary winding (Ns1). This secondary winding (Ns1) gives output voltage in the range 0-110V for primary voltage in the range 0-230V with the value of nominal ratio as 2. This winding is used to measure actual ratio error and phase angle error by absolute method as discussed earlier.

IV.EXPERIMENT A low voltage potential transformer has been fabricated according to the above design and some preliminary experiments have been performed with this potential transformer with the experimental set up as shown in Fig.4. Firstly the percentage ratio error and phase angle error of the above transformer with the usual secondary winding NS1 without feedback technique have been measured by using conventional absolute method and the experimental results are shown in Fig.5(a) and Fig.5(b). In the second phase, with the modified design the supply voltage Vp is varied in steps by an auto-transformer and in each step the supply voltage (Vp) at the output of the auto-transformer, the voltage (Vp1) across the primary, the voltage(Vs) across the secondary, the feedback current (If) and the feedback voltage (Vf) across the feedback resistance (Rf) are measured. The voltages are measured by digital multimeters and the feedback current is measured by a Weston ac milli-ammeter. Now characteristic graphs are drawn by plotting feedback current (If) against the supply voltage (Vp) and almost perfect straight-line graphs as shown in Fig.6(a) and Fig.6(c) have been obtained for two values of feedback resistors. The ideal best-fit straight-line graph from the experimental data are also shown in the same figure (Fig.6(b) and Fig.6(d)). The standard deviation curves of the experimental data from this ideal best-fit linearity graph is shown in Fig.7(a) and Fig.7(b).

(a)

(b)

Fig.5. Percentage ratio error and phase angle error curves of the potential transformer without feedback

(a)

(b)

(c)

(d) Fig.6. Characteristic graph of the proposed potential Transformer

(a)

(b)

Fig.7. Standard deviation curve of the proposed potential transformer.

In order to know the phase relationship between the feedback current and the supply voltage, both the primary voltage waveform (Vp1) and feedback voltage waveform (Vf) are observed in a storage oscilloscope and some of the recorded waveforms for supply voltage 20V, 40V, 60V, 80V, 100V, 120V, 140V, 160V 180V, 200V and 220V are as shown in Fig.8(a) to Fig.8(k), where the upper waveform in channel–1 denotes the feedback voltage wave and the lower wave form in channel-2 denotes the supply voltage wave not to the same scale.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

Fig.8(a)-(k): Feedback current wave and the supply voltage wave in the proposed potential transformer for supply voltages of 20V, 40V, 60V, 80V, 100V, 120V, 140V, 160V, 180V, 200V, 220V respectively

V. DISCUSSION From the characteristic graph as shown in Fig.6, it is found that the characteristic graph obtained by plotting feedback current against supply voltage shows almost a linear relationship. Hence the feedback current may be taken as a measure of the supply voltage as proposed in (23). From the recorded wave as shown in Fig.8 it is found that the feedback voltage wave is in the same phase as the supply voltage wave. It may be mentioned here that very small phase departure between these two waves may not be detectible from the waveforms in storage oscilloscope as shown in this figure. It may be possible to measure the exact phase departure between these two waves by using a microprocessor-based program, which will be taken up when a commercial unit according to

the above design will be manufactured. However this will be taken up in the second phase of the present investigation. Comparing the characteristic graphs of the transformer with feedback shown in Fig.6, Fig.7 and Fig.8, with the ratio error and phase angle error of the transformer without feedback shown in Fig.5(a) and Fig.5(b) it is noticed that the proposed technique may be assumed to give more accurate results than the conventional techniques. It was also observed that throughout the whole operating zone, the voltmeter reading across the secondary winding was always found to be maintained at zero value. Hence the basic assumption of the zero flux condition inside the core by the feedback winding appears to be true. Since the eddy current and magnetizing current are negligible so the heating effect of the core material due to these two currents are also very small and the core may be designed to be of smaller size than the conventional units. Hence the cost and size of the potential transformer may be reduced.

The experimental graphs in Fig.8 only show that the primary voltage Vp and feedback voltage Vf are in phase. An idea about the ratio error can be obtained from the linearity of the graph as shown in Fig.6. If the linearity and in phase relations between Vp and Vf are maintained then the basic purpose of the potential transformer may be assumed to be satisfied and Vf may be taken as a measure of the primary voltage both in magnitude and phase. It may be mentioned here that since the magnetization current and secondary current for which the ratio error and phase angle error are produced, are made negligible by using feedback technique, so the said errors may be assumed to be negligible in the proposed technique. REFERENCES

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