Current and voltage transformers

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.

Figure 1 Voltage transformer equivalent circuits


 Figure 2 Vector diagram for voltage transformer

1.1 Equivalent circuits

VTs 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 Vs lags the voltage Vp/n and is smaller in magnitude. In spite of this, the nominal maximum errors are relatively small. VTs 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 Vp/n, and Vs. These consist of the errors under open-circuit conditions when the load impedance ΖB 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 IL flowing through both windings. Errors in magnitude can be calculated from

Error VT= {(n Vs - Vp) / Vp} 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 Vn 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 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 







































































Table 2 Voltage transformers error limits


Primary voltage

Voltage error (±%)

Phase error




0.8 Vn , 1.0 Vn and 1.2 Vn















0.5 Vn



























 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.

Figure 4 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 Vi is equal to the nominal primary voltage, C is the numerically equivalent impedance equal to ( C1 + C2 ), L is the resonance inductance, Ri represents the resistance of the primary winding of transformer Τ  plus the losses in C and L, and Ze 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.

Figure 5 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. Ri and R's are not large and, in addition, Ie is small compared to I's, so that the vector difference between Vi 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 Vi 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 EL and EC 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.

Figure 6 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 n2ZH represents the primary impedance ZH referred to the secondary side, and the secondary impedance is, ZL, Rm and Xm 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 ZH can be ignored, since it does not influence either the current IH/n or the voltage across Xm. The current flowing through Xm is the excitation current Ιe.

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

Figure 7  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 ΙH / n and IL and is equal to Ir the component of Ie in line with k (see Figure 7).

The phase error, represented by θ, is related to Iq the component of Ie which is in quadrature with IL. The values of the magnitude and phase errors depend on the relative displacement between Ie and IL, but neither of them can exceed the vectorial error it should be noted that a moderate inductive load, with Ie and IL 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

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