8.1.1 Winding Arrangements

Because the secondary voltages must be a scaled representation of the associated primary potentials, voltage transformers are usually connected in a star‐star (wye‐wye) configuration, which allows both phase and line voltages to be measured. Occasionally a delta‐delta connection is used in situations where line voltages alone are sufficient for the intended application, particularly in ungrounded or high impedance grounded networks. In both these arrangements there is no significant phase shift introduced between the primary and secondary potentials.

There is also a third connection that is used in protection applications. This relates to the detection of residual or zero‐sequence voltages, arising during fault conditions. Residual voltage transformers have a grounded star connected primary; their secondary windings are connected in an open delta arrangement, across which the residual voltage appears (Figure 8.3). A residual VT may be constructed using three single‐phase transformers or alternatively it may be based on a three‐phase transformer. In the latter case a five‐limb core (i.e. a shell type core) must be used, so that a zero‐sequence flux can be supported, as required to generate the zero‐sequence voltage in each winding. The residual voltage developed across the open delta will thus be equal to three times the zero‐sequence voltage.

8.2.1 Voltage Transformer Standards

We shall confine our interest in voltage transformer standards to three documents, the first two of which are European standards: IEC61869‐3 Additional Requirements for Inductive Voltage Transformers and IEC61869‐5 Additional Requirements for Capacitor Voltage Transformers. The third is the American standard IEEE C57.13 IEEE Standard Requirements for Instrument Transformers, including its supplement, IEEE C57.13.6 IEEE Standard for High‐Accuracy Instrument Transformers. The last two documents apply to both voltage and current transformers. Both the European and American standards define the requirements of voltage transformers for both metering and protection applications. We will initially consider the requirements for metering class VTs as defined by each standard.

8.2.2 Magnitude and Phase Errors Defined under IEC 61869‐3 and IEC 61869‐5

IEC 61869‐3 and IEC61869‐5 define magnitude and phase error limits for VTs used in metering applications according to Table 8.2. Five classes of voltage transformer are defined. Class 0.1 applies to inductive laboratory grade instruments, and will not generally be found in metering applications. Classes 0.2 and 0.5 and 1.0 are prescribed for revenue metering applications, while class 3.0 is generally only used for panel instrumentation.

Table 8.3 defines the standard burden ratings for voltage transformers. Two ranges are prescribed: range I applies to very lightly loaded transformers, typical of modern metering or protection equipment: these burdens are assumed to be resistive. Range II applies to more traditional VTs where a heavier burden must be supported, one that is partially inductive. The error limits outlined in Table 8.2 apply for 0–100% of the rated burden for range I, and 25–100% of rated burden for range II. Burden ratings specified under IEC 61869‐3 apply to each winding on a voltage transformer.

Finally, the prescribed error limits must be maintained for voltages within the range 0.8–1.2 pu, and in the case of capacitive voltage transformers, over a frequency range of 99% to 101% of the nominal device frequency (50 or 60 Hz.)

8.2.3 Ratio and Phase Errors Defined under IEEE C57.13

The American standard IEEE C57.13 defines three standard classes of metering transformer (0.3, 0.6, 1.2) and its supplement IEEE C57‐13.6, defines a further high accuracy class, 0.15. This standard does not directly prescribe magnitude and phase errors, but rather places limits on a related quantity known as the transformer correction factor (TCF).

As mentioned above, any magnitude or phase errors inherent in the associated VT will introduce a small error into the measurement of the power or energy flowing. This error may be corrected using the transformer correction factor, which may be calculated from the ratio correction factor (RCF), the phase error γ of the associated VT, and the phase angle of the metered load ϕ, using:

(8.2)

(Note that this equation does not include the errors associated with the current transformers (CTs) used in the metering installation.)

The RCF is defined as the factor by which the stated ratio of an instrument transformer must be multiplied to obtain the actual ratio. Therefore the RCF can be used to correct the measured voltage presented by a VT for the effects of magnitude error, as follows:

where V_measured, is the voltage measured by the VT in question, and V_correct is this quantity corrected for the magnitude error introduced by the VT. The RCF is related to the magnitude error e, according to:

For example, if the magnitude error, e = +0.2%, then the associated RCF will be 0.998.

IEEE C57.13 prescribes limits on the TCF, which appear in Table 8.4. These must be maintained from 0% to 100% of the transformer’s rated burden, for metered loads with lagging power factors between 0.6 and 1.0. They must also be maintained over a range of applied voltages between 0.9 and 1.1 pu.

Prescribing limits applicable to the TCF indirectly places limits on both the RCF and the phase error of a VT. The TCF is largest when the power factor of the metered load the lies at the lower end of the permitted range, i.e. when it equals 0.6. Under these conditions Equation (8.3) defines the relationship between these parameters. (This is fully discussed in Chapter 10.)

(8.3)

As a result, the ratio correction factor and the phase error are no longer independent of each other, and instead are constrained to lie within the parallelogram appropriate to the class of the VT, as shown in Figure 8.5.

IEEE C57.13 defines a list of standard burdens for voltage transformer accuracy testing, as shown in Table 8.5. For voltages different from those listed in the table, the burden impedance can be calculated according to . The accuracy class for a particular voltage transformer is specified in conjunction with a standard burden designation. For example, class 0.3ZZ implies that the transformer satisfies the 0.3 class accuracy requirements with a 400 VA burden of 0.85 pf. It will also be compliant with lower designations of the same power factor; however 0.3 class accuracy is not necessarily maintained for lower burden designations of a different power factor.

8.3.1 Turns Compensation in Voltage Transformers

Because the secondary voltage of any VT falls slightly when it is burdened, manufacturers generally apply some additional turns to the secondary winding, in order to slightly increase the magnitude of the secondary voltage. This permits an increase in the burden that can be applied before the magnitude error falls outside the lower class limit, at the expense of creating positive magnitude errors when small burdens are applied. This technique, called turns compensation, usually results in an actual turns ratio between 0.2% and 1.0% greater than the nominal ratio, depending on the class of the VT. Turns compensation has a marked effect on the magnitude error of the device, but makes no difference to the phase error.

8.3.2 VT Magnitude Error Equation

The voltage across the secondary terminals (S1, S2) depends on the actual turns ratio used (N_act), the short‐circuit impedance (r + jx) and the burden connected between S1 and S2. We will show that provided , then the magnitude error can be expressed to a very good approximation as:

(8.4)

where e = the magnitude error in %, N = the nominal turns ratio, E_1 rated/E_2 rated, N_act = the actual turns ratio, n₁/n₂, R_B = the resistive component of the burden, X_B = the inductive component of the burden, r = the resistive component of the short‐circuit impedance and x = the inductive component of the short‐circuit impedance.

The ratio is the normalised turns ratio, and typically lies between 1.002 and 1.01. Equation (8.4) may be derived from the secondary circuit phasor diagram shown in Figure 8.7. The burden voltage V₂ has been chosen as the reference phasor, and the inductive burden current I_B lags this by an angle ϕ_B. We resolve this current into an in‐phase component V₂/R_B and a quadrature component V₂/X_B.

The voltage drops across r and x due to each of these currents, when added to V₂, will yield the voltage developed across the secondary winding which, allowing for the application of turns compensation, will equal |V₁/N_act|, as shown in Figure 8.7. It is therefore apparent that:

Thus: 

Equation (8.1) can be re written as:

So:

which is the same as Equation (8.4).

It is interesting to consider the case where no burden is applied to the VT (i.e. when both ), the magnitude error then becomes:

In the unusual case where no turns compensation is applied, the zero burden magnitude error will be zero. However, in most cases, turns compensation is employed, and therefore e₀ generally lies between +0.2 and +1.0%. Note that the zero burden error is independent of the burden and therefore also of its power factor.

The RCF can also be expressed in terms of the equivalent circuit parameters as:

(8.4a)

8.3.3 VT Phase Error Equation

Figure 8.6 can also be used to obtain an expression for the phase error γ, in terms of the elements in the equivalent circuit, from which we may write:

And since for small γ (when expressed in radians), we may write:

(8.5)

Because , Equation (8.5) generally provides a very good approximation for γ. However, in the case when zero burden is applied, Equation (8.5) suggests that the phase error will be zero. While this is nearly so, we often find that γ takes small non‐zero values, determined largely by the small burden imposed by the magnetising impedance, R_M and X_M. We may therefore modify Equation (8.5) accordingly:

(8.5a)

where γ₀ is the zero burden phase error, expressed in Crad.

8.4.1 Properties of Error Lines

Before we can make full use of error lines it is necessary to understand some of their properties. We begin by plotting an error line for a VT from the magnitude and phase errors measured at two burden points. These are usually either 25% and 100%, or perhaps 0% and 100% of the applicable burden. Let us assume that we have data for the former. We plot the error line from this data, as shown in Figure 8.9.

At this stage, a summary of the important properties of error lines is useful.

1. For a particular VT, all the errors corresponding to fractions of a particular burden lie on the same error line.
2. The error at any fractional burden is distributed along the error line in direct proportion to the fraction concerned. For example, the errors corresponding to 50% of the rated burden lie half way between the zero burden point and the 100% point.
3. The zero burden point can therefore be found by extrapolating the error line to the right of the 25% point, by one third of the distance between the 25% and 100% points. Once the zero burden point ( has been found, the value of the normalised turns ratio N/N_act can be determined.
4. A unique error line exists for each particular burden power factor. The error line corresponding to a unity power factor burden is known as the base line.
5. All error lines for a particular VT must pass through the zero burden point, since this is independent of the burden power factor.
6. All error lines for a particular voltage transformer are the same length. Therefore the fractional burden errors from one error line can be easily transferred to another, by scribing arcs of appropriate radii, centred on the zero burden point.
7. The error line corresponding to a lagging burden of power factor pf, lags the base line by an angle of arcos(pf ). Thus the error line corresponding to a 0.8 pf burden lags the base line by 36.9°. Therefore once one error line has been plotted, others can be quickly constructed.

The following example will clarify these concepts.

8.4.2 Error Conversion between Burdens of Differing Power Factors

Occasionally it may become necessary to evaluate the magnitude and phase errors at a burden whose power factor is different from that at which it was originally tested. For example, if the error measurements were made with a 0.8 pf burden for a range II, 10 VA VT, which is subsequently to be used as a range I VT, it will be necessary to demonstrate compliance with the IEC standard when burdened at unity power factor. The steps outlined below demonstrate how the unity power factor errors can be graphically obtained from the 0.8 pf results.

Example: We will use the 0.8 pf test data from a 44 kV, Class 0.5, 100 VA VT presented in Table 8.6, to evaluate the errors at unity power factor. (Note that in this instance the test results are independent of the applied voltage over the range 0.8–1.2 pu. This is usually the case.)

We proceed as follows:

• Step 1: Plot the error line corresponding to the 0.8 power factor data for 25% and 100% burdens. This is the upper line in Figure 8.10.
• Step 2: Determine the zero burden point as described above. In this case, the zero burden error (e₀ , γ₀) is (0.36%, 0.02 Crad), thus the normalised turns ratio for this VT is 1.0036.
• Step 3: Since the unity pf line leads the 0.8 pf line by an angle equal to arcos(0.8) or 36.9°, this error line can be constructed by simply drawing a line that leads the 0.8 pf line by this angle, passing through the zero burden point (the lower line in Figure 8.10).
• Step 4: All error lines for a given VT have the same length, therefore the 100% error point can be scaled directly from the 0.8 pf line. Errors for any other fractional burden may also be similarly derived.

Since the unity pf error line was used constructed from the 0.8 pf data, the unity pf errors obtained from the graph should be compared with those in the Table 8.6. It can be seen from Figure 8.10 that this IEC 61869‐3 Class 0.5 VT does not quite satisfy the IEEE C57.13 Class 0.3 limits, particularly when a unity power factor burden is applied.

In summary, because of the linear nature of voltage transformers, if two sets of magnitude and phase errors are known for a particular burden, the magnitude and phase errors may be derived for any other burden. This simple graphical process does not require knowledge of any of the VT’s internal parameters, nor does it require complex computations. Annex ZA of IEC 61869‐3 includes a description of this process as well as an equivalent numerical approach to error conversion.

8.6.1 Voltage Factor (F_v)

The voltage factor depends on the magnitude of the over‐voltages that the VT may encounter as a result of faults on or near the bus to which it is connected. The maximum primary voltage that can be supported by a VT can be found by multiplying its rated voltage by the voltage factor F_v. Table 8.8 shows voltage factors for single and three‐phase VTs prescribed by IEC 61869‐3, for both effectively earthed and non‐effectively earthed systems. Together with the F_v values, the table also specifies the duration for which the over‐voltage may exist.

Voltage factors vary between 1.2 and 1.9 and are determined largely by the performance of the earthing system at the location of the VT in question. A voltage factor of 1.9 requires that the VT be capable of supporting almost twice its rated voltage. It must therefore be conservatively designed to operate at a relatively low flux density at its nominal voltage and be equipped with sufficient insulation to cope with the required over‐voltage.

8.6.2 Earth Fault Factor and Effective Earthing

Put simply, the earth fault factor is the ratio of the highest phase to earth voltage on a healthy phase during an earth fault on a system, to the magnitude of the same voltage in the absence of such a fault.

The earth fault factor has a direct impact on the potential that voltage transformers must support near to a fault. It quantifies the maximum in potential experienced by the healthy phase(s) during fault conditions. The earthing system at the fault location is classified as either effectively earthed or non‐effectively earthed, according to the magnitude of the earth fault factor.

A three‐phase earthed neutral system is said to be effectively earthed at a given location, if the earth fault factor at that location does not exceed 1.4. On the other hand, a system is said to be non‐effectively earthed if the earth fault factor there exceeds 1.4.

The earth fault factor depends on the system impedances at the fault, and it can be shown that a system can be considered effectively earthed if the ratio of resistive component of the zero‐sequence impedance R₀, to the positive sequence reactance X₁, is less than one, and the ratio of the zero‐sequence reactance X₀, to the positive sequence reactance X₁, is less than three.

The over‐voltage problem occurs during faults to earth, when a potential difference arises between the neutral terminal of the supply transformer and the star point of the VT in question. This neutral shift voltage occurs as a result of the fault current flowing through an impedance between these points. This may be the resistance between the ground connections of the supply transformer and the star point of the VT, the impedance of the neutral conductor in MV systems when the neutral is distributed, or the impedance of the neutral connection where impedance earthing is used.

The potential difference between these terminals is generally small, and can usually be neglected. However, during earth faults, where substantial ground currents can flow, this potential may become significant. If the VT in question is near a phase‐to‐ground fault, the resulting potential rise appears as a neutral shift voltage, causing a reduction in the potential seen by the faulted phase, and an increase in the potential seen by at least one other.

This is illustrated in Figure 8.12, where a phase‐to‐ground fault near the VT causes a substantial rise in the local earth potential. In this case, it is assumed that the earth resistance between the remote earth and that of the supply transformer is dominant, and therefore most of the faulted phase potential is dropped between the two ground connections. As a result, the neutral potential at the VT rises, reducing the A phase voltage in proportion, and increasing both the B and C phase voltages seen by the VT.

If the earth fault factor at a particular location is 1.4 or less, then allowing for bus voltages of up to 1.1 pu, the maximum phase potential seen by a VT at that location under fault conditions, will be equal to . Therefore a voltage factor of 1.5 is appropriate.

The largest earth fault factor possible is , occurring when a phase‐to‐ground fault occurs at the VT and faulted phase potential is therefore zero. If the maximum bus voltage is 1.1 pu, then the voltage factor will be .

The duration associated with the voltage factor depends on the operating time of the earth fault protection equipment. In some cases, such as resonant or impedance earthing, the fault may exist for some time before being cleared, and therefore the VT may need to have a continuous over‐voltage capability. In other cases, the fault will be cleared relatively quickly, and the VT need only be short term over‐voltage rated.

8.6.3 IEEE C57.13 Over‐Voltage Ratings

IEEE C57.13 defines five groups of voltage transformers each with over‐voltage and exposure durations ratings, shown in Table 8.9.

8.8.1 Ferro‐Resonance

There is a danger of exciting a ferro‐resonant oscillation when VTs are connected between line and ground on ungrounded networks or networks grounded through a high impedance. As explained in Chapter 11, ungrounded networks tend to be loosely tied to ground through the action of the parasitic capacitances that exist between each phase and ground, as depicted in Figure 8.13. Because there is no firm ground connection, the source phase voltages can vary with respect to ground in response to a disturbance such as ferro‐resonance.

Ferro‐resonance is a highly non‐linear oscillation that arises between the magnetising inductance of a transformer and the stray system capacitance existing in parallel with it. It can be triggered by a temporary over‐voltage, possibly as a result of a switching transient, which drives the transformer deep into the saturated region of its magnetising characteristic. The large magnetising currents that result can generate very high oscillatory voltages, across a range of frequencies, both above and below the system frequency, due to the non‐linear nature of the transformer’s magnetising inductance. This may result in the destruction of the VT and possible damage to nearby equipment.

As with any resonant condition, the amplitude of a ferro‐resonant oscillation is influenced by the degree of damping present, and therefore a resistive burden on the VT can play an important role in suppressing ferro‐resonance. In cases where star connected VTs are used on ungrounded networks, a sufficiently resistive burden must be applied to avoid the possibility of ferro‐resonance. This may impose a significant thermal burden on a VT, beyond that permitted for metering purposes. Therefore in addition to the reasons cited above, this connection will generally only be used for residual voltage (ground fault) detection.

8.8.2 Ferro‐Resonance in Capacitive VTs

While all VTs are subject to ferro‐resonance in adverse circumstances, capacitive VTs are slightly more so, given that they already contain both capacitive and inductive elements. In order to prevent sustained ferro‐resonance, damping components are generally included in parallel with the secondary winding, as shown in Figure 8.14. The damping system chosen should not load the VT excessively at the fundamental frequency, since this will reduce its available VA capacity. Circuits like that shown in Figure 8.14a are often used in the secondary circuit of the inductive voltage transformer. Here a low impedance resistive path exists across the secondary winding at frequencies away from the system frequency. Since ferro‐resonance usually generates energy at many harmonic frequencies, the damping so provided will help to reduce the oscillation. Figure 8.14b shows an alternative arrangement where a spark gap connected resistor is connected across the VT secondary. This will consume no energy under normal circumstances, but will provide damping when the gap breaks down under high voltage conditions. This circuit also includes a saturable inductor L which will present a low impedance when saturated by large secondary voltages.

In addition to these techniques, non‐linear devices such as metal oxide varistors (MOVs) are also used as damping elements. These devices are made from a crystalline zinc oxide structure, the crystal boundaries of which form p‐n junctions that pass very little current under low voltage conditions. At high applied voltages these junctions break down in an avalanche mode, and the device impedance falls to a low value. However, they can only dissipate a certain amount of energy before permanent damage occurs, and therefore the energy rating should be carefully matched to the intended application.

IEC 61869‐5 deals with capacitive voltage transformers, and specifies that for any burden up to the device rating that once triggered, a ferro resonance condition shall not be sustained. This is generally satisfied by the provision of adequate damping of the types described above. This standard defines a maximum instantaneous error , defined by:

(8.6)

where is the maximum instantaneous error, is the peak secondary voltage, U_P is the primary voltage (r.m.s), U_Pr is the rated primary voltage (r.m.s), k_R is the transformation ratio and T_F is the duration of ferro‐resonance (seconds).

The maximum instantaneous error , shall fall to a value less than 10% after the duration T_F, as defined in Tables 8.10 and 8.11. Note that it is possible that the effects of ferro‐resonance may have entirely disappeared by time T_F, or that the oscillation may still be decaying. In either event the value of shall be less that 10%.

8.8.3 Earthing the LV Star Point

The LV star point should always be earthed, although this is more for reasons of safety. If the secondary star point was permitted to float, then it is possible that a substantial voltage could develop between the secondary star point and ground. This occurs because of the capacitive coupling between each HV winding and the associated LV winding, and between the each LV winding and ground, as is illustrated in Figure 8.15.

Provided that corresponding capacitances are equal, the secondary star point will remain close to ground potential, but if there is a mismatch between these capacitances then a neutral shift voltage will be generated which may pose a safety risk to both personnel and equipment. For this reason, the LV star point must be earthed so that such a potential cannot exist.

In the case of line connected VTs, where the secondary windings have no star point, it is customary to ground the white phase terminal, for the same reasons.

8.8.4 VT Protection

Voltage transformers are expensive and deserve some degree of protection, on both the primary side and the secondary side. Primary fusing is normally selected to protect the VT in the event of internal faults or short circuits close to the secondary terminals. It should be capable of carrying the inrush current of the device without causing nuisance tripping. Similarly, secondary fusing or magnetic circuit breakers should also be provided to protect the secondary from downstream faults and to provide a convenient method of isolating the VT. It is always preferable for the secondary protection to operate before the primary fuse, and therefore the secondary protection should be chosen accordingly.

Figure 8.16 shows what can go wrong when a VT fails internally, where the fault is not cleared by a primary fuse. The right‐hand VT in the figure shows a solid copper connection to the HV terminal; this link would normally be replaced with an HV fuse. In this case the left‐hand VT failed internally, and since it was not fuse protected the fault progressed to the stage where carbon condensate damage occurred throughout the cubicle in which it was housed. Where a VT is connected to an incoming feeder, such a fault can only be cleared by tripping the associated circuit breaker or by a bus zone protection operation, neither of which is desirable.