Transformer in Voltage and Current

Current or voltage instrument transformers are necessary for isolating the protection, control and measurement equipment from the high voltages of a power system, and for supplying the equipment with the appropriate values of current and voltage - generally these are 1A or 5Α for the current coils, and 120 V for the voltage coils.

The behavior of current and voltage transformers during and after the occurrence of a fault is critical in electrical protection since errors in the signal from a transformer can cause maloperation of the relays.

In addition, factors such as the transient period and saturation must be taken into account when selecting the appropriate transformer.

When only voltage or current magnitudes are required to operate a relay then the relative direction of the current flow in the transformer windings is not important. However, the polarity must be kept in mind when the relays compare the sum or difference of the currents.

1- Voltage transformers:

          With voltage transformers (VTs) it is essential that the voltage from the secondary winding should be as near as possible proportional to the primary voltage.

          In order to achieve this, VTs are designed in such a way that the voltage drops in the windings are small and the flux density in the core is well below the saturation value so that the magnetization current is small; in this way magnetization impedance is obtained which is practically constant over the required voltage range. The secondary voltage of a VT is usually 110 or 120 V with corresponding line-to-neutral values. The majority of protection relays have nominal voltages of 110 or 63.5 V, depending on whether their connection is line-to-line or line-to-neutral.

Voltage transformer equivalent circuits

Vector diagram for voltage transformer

1.1 Equivalent circuits

VT_s can be considered as small power transformers so that their equivalent circuit is the same as that for power transformers, as shown in Figure 1a. The magnetization branch can be ignored and the equivalent circuit then reduces to that shown in Fig 1b.

The vector diagram for a VT is given in Figure.2, with the length of the voltage drops increased for clarity. The secondary voltage V_s lags the voltage V_p/n and is smaller in magnitude. In spite of this, the nominal maximum errors are relatively small. VT_s have an excellent transient behaviour and accurately reproduce abrupt changes in. the primary voltage.

1.2 Errors

    When used for measurement instruments, for example for billing and control purposes, the accuracy of a VT is important, especially for those values close to the nominal system voltage.

    Notwithstanding this, although the precision requirements of a VT for protection applica­tions are not so high at nominal voltages, owing to the problems of having to cope with a variety of different relays, secondary wiring burdens and the uncertainty of system parameters, errors should he contained within narrow limits over a wide range of possible voltages under fault conditions.

     This range should be between 5 and 173% of the nominal primary voltage for VTs connected between line and earth.

   Referring to the circuit in Figure 1a, errors in a VT are clue to differences in magnitude and phase between V_p/n, and V_s. These consist of the errors under open-circuit conditions when the load impedance Ζ_B is infinite, caused by the drop in voltage from the circulation of the magnetization current through the primary winding, and errors due to voltage drops as a result of the load current I_L flowing through both windings. Errors in magnitude can be calculated from

Error _VT= {(n V_s - V_p) / V_p} x 100%. If the error is positive, then the secondary voltage exceeds the nominal value.

1.3 Burden

The standard burden for voltage transformer is usually expressed in volt-amperes (VΑ) at a specified power factor.

Table 1 gives standard burdens based on ANSI Standard C57.1 3. Voltage transformers are specified in IEC publication 186Α by the precision class, and the value of volt-amperes (VΑ).

The allowable error limits corresponding to different class values are shown in Table 2, where V_n is the nominal voltage. The phase error is considered positive when the secondary voltage leads the primary voltage. The voltage error is the percentage difference between the voltage at the secondary terminals, V₂, multiplied by the nominal transformation ratio, and the primary voltages V₁.

1.4 Selection of VTs

     Voltage transformers are connected between phases, or between phase and earth. The connection between phase and earth is normally used with groups of three single-phase units connected in star at substations operating with voltages at about 34.5 kV or higher, or when it is necessary to measure the voltage and power factor of each phase separately.

The nominal primary voltage of a VT is generally chosen with the higher nominal insulation voltage (kV) and the nearest service voltage in mind. The nominal secondary voltages are generally standardized at 110 and 120 V. In order to select the nominal power of a VT, it is usual to acid together all the nominal VΑ loadings of the apparatus connected to

 

Table 1 Standard burdens for voltage Transformer

Standard burden			Characteristics for 120 V and 60 Hz			Characteristics for 69.3 V and 60 Hz
design	Volt- amperes	power factor	resistance(Ω)	inductance (H)	impedance (Ω)	resistance (Ω)	inductance (H)	impedance (Ω)
W	12.5	0.10	115.2	3.040	1152	38.4	1.010	384
Χ	25.0	0.70	403.2	1.090	575	134.4	0.364	192
Υ	75.0	0.85	163.2	0.268	192	54.4	0.089	64
Ζ	200.0	0.85	61.2	0.101	72	20.4	0.034	24
ΖΖ	400.0	0.85	31.2	0.0403	36	10.2	0.0168	12
Μ	35.0	0.20	82.3	1.070	411	27.4	0.356	137

Table 2 Voltage transformers error limits

Class	Primary voltage	Voltage error (±%)	Phase error (±min)
0.1	0.8 Vn , 1.0 Vn and 1.2 Vn	0.1	0.5
0.2		0.2	10.0
0.5		0.5	20.0
1.0		1.0	40.0
0.1	0.5 Vn	1.0	40.0
0.2		1.0	40.0
0.5		1.0	40.0
1.0		2.0	80.0
0.1	Vn	0.2	80.0
0.2		2.0	80.0
0.5		2.0	80.0
1.0		3.0	120.0

 Vn = nominal voltage

      The VT secondary winding. In addition, it is important to take account of the voltage drops in the secondary wiring, especially if the distance between the transformers and the relays is large.
 

 1.5 Capacitor voltage transformers

In general, the size of an inductive VT is proportional to its nominal voltage and, for this reason, the cost increases in a similar manner to that of a high voltage transformer. One alternative, and a more economic solution, is to use a capacitor voltage transformer.

This device is effectively a capacitance voltage divider, and is similar to a resistive divider in that the output voltage at the point of connection is affected by the load - in fact the two parts of the divider taken together can be considered as the source impedance which produces a drop in voltage when the load is connected.

 Capacitor VT equivalent circuit

The capacitor divider differs from the inductive divider in that the equivalent impedance of the source is capacitive and the .fact that this impedance can be compensated for by connecting a reactance in series at the point of connection.

      With an ideal reactance there are no regulation problems - however, in an actual situation on a network, some resistance is always present. The divider can reduce the voltage to a value which enables errors to be kept within normally acceptable limits. For improved accuracy a high voltage capacitor is used in order to obtain a bigger voltage at the point of connection, which can be reduced to a standard voltage using a relatively inexpensive trans-former as shown in Figure 3.

          Α simplified equivalent circuit of a capacitor VT is shown in Figure 4 in which V_i is equal to the nominal primary voltage, C is the numerically equivalent impedance equal to ( C₁ + C₂ ), L is the resonance inductance, R_i represents the resistance of the primary winding of transformer Τ  plus the losses in C and L, and Z_e is the magnetization impedance of transformer Τ. Referred to the inter-mediate voltage, the resistance of the secondary circuit and the load impedance are represented by   and respectively, while and  represent the secondary voltage and current.

 

Capacitor VT vector diagram

It can be seen that, with the exception of C, the circuit in Figure 4.4 is the same as the equivalent circuit of a power transformer. Therefore, at the system frequency when C and L are resonating and canceling out each other, under stable system conditions the capacitor VT acts like a conventional transformer. R_i and R'_s are not large and, in addition, I_e is small compared to I'_s, so that the vector difference between V_i and V'_s which constitutes the error in the capacitor VT, is very small.

       This is illustrated in the vector diagram shown in Figure 4.5 which is drawn for a power factor close to unity. The voltage error is the difference in magnitude between V_i and V'_s, whereas the phase error is indicated by the angle θ. From the diagram it can be seen that, for frequencies different from the resonant frequency, the values of E_L and E_C predominate, causing serious errors in magnitude and phase.

          Capacitor VTs display better transient behaviour than electro-magnetic VTs as the inductive and capacitive reactance in series are large in relation to the load impedance referred to the secondary voltage, and thus, when the primary voltage collapses, the secondary voltage is maintained for some milliseconds because of the combination of the series and parallel resonant circuits represented by L, C and the transformer T.
 

 2 Current transformers

Although the performance required from a current transformer (CT) varies with the type of protection, high grade CTs must always be used. Good quality CTs are more reliable and result in less application problems and, in general, provide better protection.

Current transformer equivalent circuits

The quality of CTs is very important for differential protection schemes where the operation of the relays is directly related to the accuracy of the CTs under fault conditions as well as under normal load conditions.

        CTs can become saturated at high current values caused by nearby faults; to avoid this, care should be taken to ensure that under the most critical faults the CT operates on the linear portion of the magnetization curve. In all these cases the CT should be able to supply sufficient current so that the relay operates satisfactorily.

 2.1 Equivalent circuit

An approximate equivalent circuit for a CT is given in Figure 4.6a,

          Where n²Z_H represents the primary impedance Z_H referred to the secondary side, and the secondary impedance is, Z_L, R_m and X_m represent the losses and the excitation of the core.

          The circuit in Figure 4.6a can be reduced to the arrangement shown in figure 4.6b where Z_H can be ignored, since it does not influence either the current I_H/n or the voltage across X_m. The current flowing through X_m is the excitation current Ι_e.

The vector diagram, with the voltage drops exaggerated for clarity, is shown in Figure 4.7. In general, Z_L, is resistive and Ι_e lags V_s by 90°, so that I_e is the principal source of error. Note that the net effect of I_e is to make I lag and be much smaller than Ι_H /n, the primary current referred to the secondary side.

Vector diagram for the CT equivalent circuit

2.2 Errors

          The causes of errors in a CT are quite different to those associated with VTs. In effect, the primary impedance of a CT does not have the same influence

On the accuracy of the equipment  it only adds an impedance in series with the line, which can be ignored. The errors are principally due to the current which circulates through the magnetizing branch.

          The magnitude error is the difference in magnitude between Ι_H / n and I_L and is equal to I_r the component of I_e in line with k (see Figure 7).

The phase error, represented by θ, is related to I_q the component of I_e which is in quadrature with I_L. The values of the magnitude and phase errors depend on the relative displacement between I_e and I_L, but neither of them can exceed the vectorial error it should be noted that a moderate inductive load, with I_e and I_L approximately in phase, has a small phase error and the excitation component results almost entirely in an error in the magnitude.

2.3 AC saturation

CΤ errors result from excitation current, so much so that, in order to check if a CT is functioning correctly, it is essential to measure or calculate the excitation curve. The magnetization current of a CT depends on the cross section and length of the magnetic circuit, the number of turns in the windings, and the magnetic characteristics of the material.

Thus, for a given CT, and referring to the equivalent circuit of Figure 4.6b, it can be seen that the voltage across the magnetization impedance, Es, is directly proportional to the secondary current. From this it can be concluded that, when the primary current and therefore the secondary current is increased, these currents reach a point where the core commences to saturate and the magnetization current becomes sufficiently high to produce an excessive error.

       When investigating the behaviour of a CT, the excitation current should he measured at various values of voltage  the so-called secondary injection test. Usually, it is more convenient to apply a variable voltage to the secondary winding, leaving the primary winding open-circuited. Figure 4.8a shows the typical relationship between the secondary voltage and the excitation current determined in this way.

       In European standards the point Κp on the curve is called the saturation or knee point and is defined as the point at which an increase in the excitation voltage of ten per cent produces an increase of 50 % in the excitation current. This point is referred to in the ANSI / IEEE standards as the intersection of the excitation curves with a 45° tangent line, as indicated in Figure 4.8b. The European knee point is at a higher voltage than the ANSI/IEEE Knee point.

2.4 Burden

          The burden of a CT is the value in ohms-of the impedance on the secondary side of the CT due to the relays and the connections between the CT and the relays. By way of example, the standard burdens for CTs with a nominal secondary current of 5 A are shown in Table 3, based on ANSI Standard C57.13.

IEC Standard Publication 185(1987) specifies CTs by the class of accuracy followed by the letter Μ or P, which denotes whether the transformer is suitable for measurement or protection purposes, respectively. The current and phase-error limits for measurement and protection CTs are given in Tables 4a and 4.4b. The phase error is considered positive when the secondary current leads the primary current.

        The current error is the percentage deviation of the secondary current, multiplied by the nominal transformation ratio, from the primary current, i.e. {(CTR x Ι2) – I1} ÷ I1 (%), where I1 = prim­ary current (A), I2 = secondary current (A) and CTR = current transformer transformation ratio. Those CT classes marked with `ext' denote wide range (extended) current transformers with a rated continuous current of 1.2 or 2 times the nameplate current rating.

 2.5 Selection of CTs

When selecting a CT, it is important to ensure that the fault level and normal load conditions do not result in saturation of the core and that

 CT magnetization curves

CT magnetization curves

·        a Defining the knee point in a CT excitation curve according to  European standards

·        b Typical excitation curves for a multi ratio class C CT (From IEEE Standard C57.13-1978; reproduced by permission of the IEEE).

Table 4.3 Standard burdens for protection
            CTs with 5 Α secondary current

Designation	Resistance (Ω)	Inductance (mH)	Impedance (Ω)	Volt-amps (at 5 A)	Power factor
B-1	0.5	2.3	1.0	25	0.5
B-2	1.0	4.6	2.0	50	0.5
B-4	2.0	9.2	4.0	100	0.5
B-8	4.0	18.4	8.0	200	0.5

The errors do not exceed acceptable limits. These factors can be assessed from:

·   formulae;

·   CT magnetization curves;

·   CT classes of accuracy.

The first two methods provide precise facts for the selection of the CT. The third only provides a qualitative estimation. The secondary voltage Ε in Figure 4.6U has to be determined for all three methods. If the impedance of the magnetic circuit, Xm is high, this can be removed from the equivalent circuit with little error' giving Es=Vs and thus:

                                                      

                                   Vs=IL (ZL+ZC+ZB)    (1)

Where

Vs = r.m.s. voltage induced in the secondary winding

I_L       =maximum secondary current in amperes;
  this can be determined by dividing the maximum
  Fault current on the system by the transformer
 turns ratio selected

ZB = external impedance connected

ZL = impedance of the secondary winding

ZC =impedance of the connecting wiring

Use of the formula

This method utilizes the fundamental transformer equation:

              Vs = 4.44.f. Α. N. Bmax.10^-8 V      (2)

Where

       f    =frequency in Hz,

        Α    =cross-sectional area of core (cm²)
       Ν   =number of turns

       B_max =flux density (lines/cm²)

Table 4α   Error limits for measurement current transformers

Class	% current error at the given proportion of rated current shown below							% phase error at the given proportion of the  rated current shown below
	2.0*	1.2	1.00	0.50	0.20	0.10       0.05		2.0*	1.2	1.0	0.5	0.2	0.1	0.05
0.1		0.1	0.1		0.2	0.25			5	5		8	10
0.2		0.2	0.2		0.35	0.50			10	10		15	20
0.5		0.5	0.5		0.75	1.00			30	30		45	60
1.0		1.0	1.0		1.5	2.00			60	60	-	90	120	-
3.0		3.0		3.0	-	-       -	-	_	120	-	120	-	-	-
0.1	0.1		0.1		0.2	0.25	0.4	5	-	5		8	10	15
0.2 ext	0.2		0.2		0.35	0.50	0.75	10	-	10		15	20	30
0.5 ext	0.5		0.5		0.75	1.00	1.5	30	-	30		45	60	90
1.0 ext	1.0		1.0		1.5	2.00		60	-	60	-	90	120	-
3.0 ext	3.0	-	-	3.0	-	-	-	120	-	-	120	-	-	-

*ext = 200 %

Table 4b  Error limits for protection current transformers
 

Accuracy Class		+/- percentage Current ratio error				+/- Phase error (minutes)
	% Current	5	20	100	120	5	20	100	120
0.1		0.4	0.2	0.1	0.1	15	8	5	5
0.2		0.75	0.35	0.2	0.2	30	15	10	10
0.5		1.5	0.75	0.5	0.5	90	45	30	30
1.0		3	1.5	1.0	1.0	180	90	60	60

Total error for nominal error limit current and nominal load is five per cent for 5P and 5Ρ ext CTs and ten per cent for 10P and 10P ext CTs.

          The cross-sectional area of metal and the saturation flux density are sometimes difficult to obtain.

          The latter can be taken as equal to 100 000 lines/Cm², which is a typical value for modern transformers. To use the formula, V is determined from eqn. 4.1 and Bmax. is then calculated using eqn. 2. If Bmax.

 Exceeds the saturation density, there could be appreciable errors in the secondary current and the CT selected would not be appropriate.

Example 1.

          Assume that a CT with a ratio of 2000/5 is available, having a steel core of high permeability, a cross-sectional area of 3.25 In cm² and a secondary winding with a resistance of 0.31 Ω. The impedance of the relays, including connections, is 2 Ω. Determine whether the CT would be saturated by a fault of 35 000 A at 50 Hz.

Solution

If the CT is not saturated, then the secondary current, IL, is

35 000x 5/2000=87.5 A. N= 2000/5 = 400 turns

And Vs=87.5x (0.31+2) =202.1 V. Using eqn. 4.2, Bmax, can now be calculated:

Bmax = 202.1X10⁸/4.44X50X3.25X400=70 030 lines/ cm²

Since the transformer in this example has a steel core of high permeability, this relatively low value of flux density should not result in saturation.

 Using the magnetization curve

          Typical CT excitation curves which are supplied by manufacturers state the r.m.s. current obtained on applying an r.m.s. voltage to the secondary winding, with the primary winding open-circuited.

          The curves give the magnitude of the excitation current required order to obtain a specific secondary voltage.

          The method consists of producing a curve which shows the relationship between the primary and secondary currents for one tap and specified load conditions, such as shown in Figure 4.9.

          Starting with any value of secondary current, and with the help of the magnetisation curves, the value of the corresponding primary current can be determined. The process is summarized in the following steps:

(a) Assume a value for I_L.

(b) Calculate V_s in accordance with eqn. 4.1.

(c)  Locate the value of V_s on the curve for the tap selected, and find the associated value of the magnetization current, I_e.

(d) Calculate I_H/n (=I_L + I_e) and multiply this value by n to refer it to the primary side of the CT.

(e)  This provides one point on the curve of I_L against I_H, and the process is then repeated to obtain other values of I_L and the resultant values of I_H. By joining the points together the curve of I_L against I_H  is obtained.

using the magnetization curve

a- assume a value for I_L.        

  b-V_s = I_L (Z_L +Z_C+Z_B)

   c - find I_e from the curve

  d - I_H=n(I_1,+I_e )

   e - draw the point on the curve

This method incurs an error in calculating I_H /n by adding I_e and I_L together arithmetically and not vectorially, which implies not taking account of the load angle and the magnetizations branch of the equivalent circuit. However, this error is not great and the simplifica­tion snakes it easier to carry out the calculations.

After construction, the curve should be checked to confirm that the maximum primary fault current is within the transformer saturation zone. If not, then it will be necessary to repeat the process, changing the tap until the fault current is within the linear part of the characteristic.

In practice it is not necessary to draw the complete curve because it is sufficient to take the known fault current and refer to the secondary winding, assuming that there is no saturation for the tap selected.

This converted value can be taken as I_L initially for the process described earlier. If the tap is found to be suitable after finishing the calculations, then a value of I_H can be obtained which is closer to the fault current.

Accuracy classes established by the ANSI standards

The ANSI accuracy class of a CT (Standard C57.13) is described by two symbols — a letter and a nominal voltage; these define the capability of the CT.

C indicates that the transformation ratio can be calculated, and T indicates that the transformation ratio can be determined by means of tests. The classification C includes those CTs with uniformly distributed windings and other CTs with a dispersion flux which has a negligible effect on the ratio, within defined limits.

The classification T includes those CTs with a dispersion flux which considerably affects the transformation ratio.

For example, with a CT of class C—100 the ratio can be calculated, and the error should not exceed ten per cent if the secondary current does not go outside the range of 1 to 20 times the nominal current and if the load does not exceed 1Ω (1Ω x 5 Ax 20=100 V) at a minimum power factor of 0.5.

These accuracy classes are only applicable for complete windings. When considering a winding provided with taps, each tap will have a voltage capacity proportionally smaller, and in consequence it can only feed a portion of the load without exceeding the ten per cent error limit. The permissible load is defined as Z_B= (N_P  Vc) / 100, where Z_B, is the permissible load for a given tap of the CT, N_P, is the fraction of the total number of turns being used and Vc is the ANSI voltage capacity for the complete CT.

 2.6 DC saturation

Up to now, the behavior of a CT has been discussed in terms of a steady state, without considering the DC transient component of the

DC saturation is particularly significant in complex protection schemes since, in the case of external faults, high fault currents circulate through the CTs.

If saturation occurs in different CTs associated with a particular relay arrangement, this could result in the circulation of unbalanced secondary currents which would cause the system to malfunction.

 2.7 Precautions when working with CTs

Working with CTs associated with energized network circuits can be extremely hazardous. In particular, opening the secondary circuit of a CT could result in dangerous over voltages which might harm operational staff or lead to equipment being damaged, because the current transformers are designed to be used in power circuits which have impedance much greater than their own.

As a consequence, when secondary circuits are left open, the equivalent primary-circuit impedance is almost unaffected but a high voltage will be developed by the primary current passing through the magnetizing impedance Thus, secondary circuits associated with CTs must always he kept in a closed condition or short-circuited in order to prevent these adverse situations occurring. To illustrate this, an example is given next using typical data for a CT and a 13.2 kV feeder.

The c. t. primary rating is usually chosen to be equal to or greater than the normal full load current o f the protected circuit. Standard primary ratings are given in B.S. 3938:1973. Generally speaking, the maximum ratio of CT’s is usually limited to about 3000/1. This is due to

(I) limitation of size of CT’s and more importantly

(II) the fact that the open circuit volts would be dangerously high for large CT’s Primary ratings, such as those encountered on large turbo alternators, e.g. 5,000 amperes. It is standard practice in such applications to use a cascade arrangement of say 5,000/20A together with 20/1A interposing auxiliary CT’s

Instantaneous over current relays

Class P method of specification will a suffice. A secondary accuracy limit current greatly in excess of the value t o cause relay operation serves no useful purpose and a rated accuracy limit of 5 will usually be adequate.

When such relays are set to operate at high values of over current, say from 5 to 15 times the rated current o f the transformer, the accuracy limit factor must be at least as high as the value of the setting current used in order to ensure fast relay operation.

Rated outputs higher than 15VA and rated accuracy limit factors higher than 10 are not recommended for general purposes. It is possible, however, to combine a higher rated accuracy limit factor with a lower rated output and vice versa. But when the product of these two exceeds 150 the resulting current transformer may be uneconomical, and/or of unduly large dimensions.

Over current relays with Inverse and Definite Minimum Time

(IDMT) lag characteristic

In general, for both directional and non-directional relays class 10P current transformers should be used

Earth fault relays with inverse time characteristic

(1) Schemes in which phase fault current stability and accurate time grading are not required.
     Class 10P current transformers are generally recommended in which the product of rated
     output and rated accuracy limit fact or approaches 150 provided that the earth fault relay is
     not set below 20% of the rated current of the associated current transformer and that the
     burden of the relay at its setting current does not exceed 4VA.

(2) Schemes in which phase fault stability and/or where time grading is critical.
     Class 5P current transformers in which the product of rated output and accuracy
     limit factor approaches 150 should be used.

They are in general suitable for ensuring phase fault stability up to 10 times the rated primary current and for maintaining time grading of the earth f a u l t relays, up to current values of the order of 10 times the earth fault setting provided t h a t the phase burden effectively imposed on each current transformer does not exceed 50% of it s rated burden.

The rated accuracy limit factor is not less than 10 the earth fault relay is not set below 30 % The burden of the relay at its setting does not exceed 4VA

The use of a higher relay setting the use of an earth fault relay having a burden of less than 4VA at its setting The use of current transformers having a product of rated output and rated accuracy factor in excess of 150.

Class “X” Current Transformer
 

Protection current transformers specified in terms of complying with Class ' X I

Specification is generally applicable to unit systems where balancing of outputs from each end of the protected plant is vital.

This balance, or stability during through fault conditions, is essentially of a transient nature and thus the extent of the unsaturated (or linear) zone is of paramount importance. Hence a statement of knee point voltage is the parameter of prime importance and it is normal to derive, from heavy current test results, a formula stating the lowest permissible value of V_K if stable operation is to be guaranteed, e.g.

V_k = K I_n (R_CT + 2R_L + R₀)
 

Where

          K - Is a constant found by realistic heavy current tests?

          I_n - rated current of C.T. and relay

          R_CT - secondary winding resistance of the line current transformers

          R_L - lead burden (route length) in ohms

          R_o - any other resistance (or impedance) in circuit