Get documents about "Current Transformer Specification & Steady State
Document Sample
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Learning guideline
After these lectures you should be able to understand and apply the following:
i. CT/VT specification and classes
ii. The effect of CT/VT error
iii. Proper testing method for CT
iii. Effect of CT magnetising current on earth leakage protection
iv. Selection of CT and relay secondary rating
v. Working principle of CVT
vi. Transient behaviour of VT/CVT
3.1 Introduction
In the power system, the two major electrical quantities that has to be measured are
current and voltage. These quantities has to be step down to a suitable value and to provide a
physical isolation between the primary and secondary instruments. A transducer, known as
the current or voltage transformer, is therefore needed between the primary system and the
secondary equipments. They are among the most commonly used electrical apparatus, and
yet, their performance are often neglected. Their characteristics in fact affects directly the
performance of equipments in the secondary. If they are not used properly, they may directly
led to inaccuracies in measurement, or malfunction of protective devices. Hence current and
voltage transformers should be treated as part of the measurement or protective system and
their performance should be carefully matched with the other measuring equipment or
protective relays in the system.
Current transformers are classified according to the role they play in the power
system. If it is used for metering and instrumentation, its essential role is to deliver in the
secondary a quantity accurately representing the primary current in magnitude (by a fixed
ratio) and phase angle. Its normal measuring range is normally from 10 % full load to 120 %
full load. If the C.T. is used for protection purposes, the role of a C.T. varies according to the
type of protective devices. Very often the C.T. is required to measure fault current which is
many times above normal full load current.
On the other hand, there is no great difference between a protective voltage
transformer and a measuring voltage transformer. Quite often, the same transformer can serve
both purposes reasonably well. This is because it does not have to handle a voltage which is
many times larger than its rating as that of a protective C.T.
3.2 Current Transformer (CT) Theory
The working principle of a C.T. is similar to that of a ordinary two winding
transformer. Its equivalent circuit is shown in Fig. 3.1. The flow of current in the primary
winding produces an alternating flux in the core and this flux induces an e.m.f. in the
secondary winding which results in the flow of secondary current. The magnetic effect of the
secondary current is opposite to the magnetic effect produced in the primary. The resultant
magnetic effect of the primary and secondary currents produce a flux in the iron core
required to induce the e.m.f. necessary to drive the secondary current against the impedance
of the circuit in which it flows. However, the flux produced by the primary current mainly
depends on the load current and cannot be affected by the burden connected in the secondary
of a C.T. This is the only difference between a C.T. and a V.T. The net flux level in the iron
core therefore is a function of the primary current and the impedance of burden connected to
32
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
the secondary. The C.T. secondary therefore should not be left open circuited when the
primary is connected to the system as the primary current would set up a large flux in the iron
core which is not counter balanced by flux set up by secondary current. This flux would in
turn produce large e.m.f. in the secondary. This e.m.f. can be a few thousand volts which may
damage the insulation of the
Fig. 3.1
The phasor diagram of the C.T. is shown in Fig. 3.2. It can be seen that the main Source of
error is the magnetising current and the core loss. Error can be reduced by:
i) using better magnetic material,
ii) reduce the mean length of magnetic path, and/or
iii) reduce the flux density in the iron core.
Fig. 3.2
According to BS 3938: 1973, the current error of a C.T. is defined as
K pIs − I p 3.1
CurrentError = x100%
Ip
Phase Error = θ
θ is +ve when Is' leads Ip
θ error = φ I − φ I 3.2
s p
33
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
When IP reduces, IS will also be reduced. The secondary voltage and flux will also be
reduced. However, due to the non-linear magnetizing characteristic of iron, Ie will not be
reduced in the same proportion. The result is a larger ratio of Ie at lower primary current. Fig.
3.3 shows the trend of ratio error and phase error of a C.T.
Fig. 3.3
The errors associated with C.T.s are the current ratio error and phase angle error. A
C.T. used for measurement purpose requires low core magnetising current as well as low core
loss. Range of measurement will not be very much larger than normal load range. It follows
that a high permeability core material with a low saturation level is most suitable. Nickel iron
alloy is the most suitable core material for measurement C.T. due to its low exciting ampere
turns and the knee points occurs at a relatively low flux density. On the other hand, a
protection C.T. requires a high saturation level. Grain orientated silicon steel are used as they
offer a very high knee point flux density although they exhibit a poorer exciting ampere
turns.
3.3 Classification of C.T.
C.T. is classified according to its percentage current error and phase error under
various conditions. Tables of limits of error for various classes of C.T. extracted from BS
3938: 1973 is shown in Table 3.1, 3.2, and 3.3.
3.4 Saturation and Non-linearity of Iron
The main departure from linearity in the shunt impedance Zm occurs when the core
flux reaches saturation. This is accompanied by a rapid reduction of Zm and a large increase
in errors. It is important to know the secondary current at which this departure from
reasonable accuracy occurs. It is often defined by Saturation Factor, which is the multiple of
rated current up to which the current transformer is accurate for a specified secondary burden.
Although saturation effects the greatest departure from linearity, most magnetic steels
are fairly non-linear over most of the working range, giving typical voltage/current
characteristics as shown in fig. 3.4. There is generally a region of low initial permeability
followed by a region of high permeability and finally the region of low permeability resulting
from saturation. Such non-linearity results in harmonic components of magnetizing currents
even in the unsaturated regions.
34
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Table 3.1 Limits of error for accuracy Classes 0.1 to 1
± phase displacement at percentage of
± percentage current (ratio) error at rated current shown below
percentage of rated current shown below
Class minutes
10 up to 20 up to 100 up to 10 up to 20 up to 100 up to
but not incl but not incl 120 but not incl but not incl 120
20 100 20 100
0.1 0.25 0.2 0.1 10 8 5
0.2 0.5 0.35 0.2 20 15 10
0.5 1.0 0.75 0.5 60 45 30
1.0 2.0 1.5 1.0 120 90 60
Table 3.2 Limits of error for accuracy Class 3 and Class 5
± percentage current (ratio) error at percentage of rated current
Class shown below
50 120
3 3 3
5 5 5
Table 3.3 Limits of error for accuracy Class 5P and Class 10P
Phase displacement at Composite error at
Current error at rated
Accuracy Class rated primary current rated accuracy limit
primary current %
primary current
minutes
5P ±1 ± 60 5
10P ±3 - 10
0
Fig. 3.4
35
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
3.5 Open Circuit Excitation Curves
These are used to define the volt/ampere characteristics of the shunt impedance Zm.
They may be obtained by actual measurement on the C.T. A typical C.T. characteristic is
shown in Fig. 3.5. The phase angle of the magnetizing impedance can also be shown on the
same sheet. The knee point voltage can also be shown.
Fig. 3.5 Typical C.T. excitation curve
Fig. 3.6 Open circuit excitation curves using various test methods
36
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
These curves are widely used for protective C.T.s as they contain all the necessary
information to assess the capabilities of a C.T. and its consistency with others of the same
nominal design. It is important to note that the form of this curve is affected by the method of
test, the instruments used, or the basic data curves. This is illustrated in Fig. 3.6, which gives
a series of excitation curves for the same C.T. for different test conditions.
Considering curves (1) and (2), the average value of voltage, regardless of waveform,
depends on the average flux-change, which depends on maximum flux and hence on peak
magnetizing current. The r.m.s. value of a quantity is very dependent on waveform, and this
is noticeable in curves (3) and (4). Taking the sinusoidal voltage case (3), the r.m.s. value of
the peaky magnetizing current will be greater than its average value but will still be less than
that of the sinusoidal current, and hence this curve will thus lie between (1) and (2).
It should be noted that all the curves coincides in the unsaturated region because both
current and voltage are approximately sinusoidal.
The curve normally used for protective relays is (3), i.e. sinusoidal voltage with r.m.s.
reading instruments, and most design data curves are given for this condition. This is valid in
most applications of low impedance schemes with linear burdens since the secondary current,
and thus voltage, is nearly sinusoidal. For high impedance schemes the voltage may become
very peaky on internal faults and curve (4) is more applicable. However, this is not generally
used even for high impedance schemes, the additional voltage obtained being considered as
an additional safety factor. In any case, the validity of using a curve would depend upon
whether the relay is responsive to r.m.s. values or average values.
3.6 Knee Point Voltage
The transition from the unsaturated region to the saturated region of the open circuit
characteristic is a rather gradual process in most of the core materials. It is generally defined
as:
The sinusoidal e.m.f. of rated frequency applied to the secondary terminals of
the current transformer with all other windings being open-circuited, which,
when increased by 10 %, causes the exciting current to increase by 50 %.
3.7 Composite Error
Composite error is mainly due to non-linearity of iron which causes Ze varies at
different load current conditions, particular near saturation region.
1 T
∫ (K i − i p ) dt
2
n s
3.3
T 0
Composite Error = • 100%
Ip
The secondary current waveform at high primary current is shown in Fig. 3.8.
37
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Fig. 3.7
Fig. 3.8
B-H curve of iron core
Partial saturation of iron core
3.8 Rated Saturation Factor (Rated Accuracy Limit Factor)
The maximum primary current expressed as a multiple of rated primary current,
which can still maintain its composite error accuracy limit.
3.9 Class X Protective C.T. for Special Purpose
It is a special C.T. whose characteristic cannot be expressed by 5 P or 10 P. Normally
used for cases where accurate current balance is required. The following of a class X C.T.
must be specified:
1) Rated primary current.
2) Turns ratio.
3) Rated knee point e.m.f. at maximum secondary turns.
4) Maximum exciting current at the rated knee point e.m.f.
5) Maximum resistance of the secondary winding corrected to 75 C or the
maximum service temperature, whichever is the greater.
6) Turns ratio error should not exceed ± 0.25 %.
3.10 Considerations Required in Choosing Protective C.T.
1. C.T. Ratio - The total secondary burden of a current transformer includes not only the
internal impedance of the secondary winding and the impedance of the instruments and
relays which are connected to it, but also that of the secondary leads. In outdoor sub-
station, the distance between the C.T.s and the relay panels may be considerable and with
a rated secondary current of 5 A, the impedance of these leads constitute a considerable
burden. In this cases, C.T.s of secondary rating of 1 A or less may have to be used.
2. C.T. burden - The normal practice is to express the burden in terms of VA and power
factor of the VA consumed in the burden at rated secondary current. However, as the
secondary current increases, the C.T. burden impedance decreases because of saturation
in the magnetic circuit of relays and other devices. At high saturation the impedance
approaches the resistance.
The VA burden of relays and instruments are usually given at the setting current. That is,
a 1 VA relay set at 20 % of rated current will have an effective burden on the C.T. at
rated current of 1 A equal to 25 VA. If the primary of an auxiliary C.T. (or interposing
C.T.) is to be connected into the secondary of a C.T. whose accuracy is being studied, one
38
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
must know the impedance of the auxiliary C.T. viewed from its primary with its
secondary short circuited. The lead resistance and the impedance of burden on the
secondary of auxiliary C.T. should also be considered when viewed from the primary of
auxiliary C.T.
3. Choice of C.T. Primary Current - The C.T. primary current rating is usually chosen to be
equal to or greater than the normal full load current of the protected circuit. Generally
speaking, the maximum ratio is about 3000/1. This is mainly due to : (i) size of core; and
(ii) more important, is the open circuit volts would be highly dangerous. For large turbo
alternators whose primary current approaches to 5000 A, it is a usual practice to use a
C.T. of ratio 5000/20 together with 20/1 interposing auxiliary C.T.
4. Class of C.T. - relates with nature of application (e.g. 5P, 10P, X, etc.).
5. Ratio error.
6. Phase error - Phase error is not important for relays which operates on current magnitudes
only. It is important to sensitive directional relays (e.g. Reverse Power Relay) and should
be taken into account.
7. Rated saturation factor - relates with the fault current on which the relay is expected to
work on.
e.g. 10 VA 5P 10 - with 10 VA burden, the C.T. gives 1 % error at rated current and 5 %
composite error at 10 times rated current.
To convert C.T. VA and Saturation Factor into knee point voltage, we may use the following
expression:
VA
Vk = • ( Saturation Factor ) 3.4
I rate
3.11 Relay Sensitivity at Different Settings for Electro-mechanical Relays
Assume : i) C.T. has no loss and relay burden is pure reactive; and
ii) The impedance of relay is inversely proportional to the square of its
current setting.
If the burden is pure reactive, the secondary e.m.f. will be leading the secondary
current by 90º. The secondary current and the magnetising current is then in phase as shown
in Fig. 3.9. Then
I p = ( Is + I e ) N
At 100 % Iset, Iop = ( Is + Ie ) N
Es = Is Zb
At 50 % Iset, Zb' = ( 1/0.5 )2 Zb = 4 Zb
Es' = 0.5 Is x 4 Zb = 2 Es
Ie' can then be obtained from magnetisation curve. If Es and Ie is proportional, then
I e' = 2 I e
, Iop = (0.5 Is + 2 Ie ) N
39
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Fig. 3.9 Fig. 3.10
Phasor of magnetizing Ideal and actual primary
current on reactive burden operating current
The operating current at other relay setting can be obtained in a similar manner. At
lower relay settings, it can be shown that although the relay sensitivity has been increased,
the actual primary current to operate the relay may not decrease due to the excessive
magnetising current. The setting with highest sensitivity may not be the one with lowest
setting. A typical actual relay operating current against its setting is shown in Fig. 3.10.
3.12 Selection of CT and Relay Secondary Rating
The secondary current rating of a CT depends on the location of relays and the relay
rating. 1A rating relay normally has higher impedance than a 5 A rating relay. The relay
rating of mechanical relays can be proportional to the square of the rating. For instance, if the
impedance of a 5A relay is 0.1Ω , then the typical impedance of a 1A relay can be (5/1)2 =
2.5Ω . If the relay is located very near to the CT, the lead resistance is low and then a 5A CT
and relay rating is preferred as the total burden of CT will be lower. If the relay is located
very far away from the CT, the lead resistance is high. In order to reduce the total burden
consumed by the CT, 1A secondary rating is preferred.
The total VA consumed by the CT should take the lead resistance into account.
C.T .Burden = I 2 ( Rlead + Z relay )
For example, take the VA rating of CT is 15 VA and the VA rating of relay is 10 VA
irrespective of the relay rating. The lead resistance is 0.1Ω when the relay is located near the
CT and 3Ω when it is far away from CT. Based on the above equation, the CT burden for
various relay location and relay rating can be calculated as shown in the following table.
Relay location
Relay rating
Near CT Far away from CT
5A 12.5VA 85VA
1A 10.1VA 13VA
40
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
The above table clearly shows that for relays near CT, both 1 or 5 A relay may be used and
there is not much difference between them, all is within the CT burden limit. For CT far away
from CT, only relay with 1A rating can consume VA within the VA burden limit of CT.
3.13 Electromagnetic Voltage Transformer (VT)
A V.T. seldom has an output exceeding a few hundred VAs and, therefore, the heat
generated is not sufficient to present any serious cooling problems. In many instances, ten
time normal rated output can be carried and the unit remains within the permissible
temperature rise. This is largely due to the size of the primary and secondary conductors
being determined by the small values of regulation necessary. The physical size of a V.T. is
largely dependent upon insulation and hence determined by system voltage.
Air cooled voltage transformers are usual up to 11 kV, whilst the systems above this
voltage oil is the most common cooling medium. At EHV system, the oil filled porcelain clad
cascade type of electromagnetic V.T. is more economical than the conventional bushing/tank
type of construction. This style breaks away from the single core and primary winding
principle by having the latter in several sections connected in series by stepping the voltage
down in stages. Each stage has a separate core. SF6 is also used as an insulation medium to
high voltage electromagnetic voltage transformers, in both single stage and cascade forms.
This medium has been used mainly for the V.T.s in SF6 Metalclad switchgears.
Voltage transformers may be either three-phase, single-phase for connection between
lines, or single-phase connected from line to earth. Three-phase units are common up to and
including 33 kV. However, for economical reasons, above this system voltage three single-
phase units connected as a three-phase Star/Star bank are more popular.
Protection is normally provided by HV fuses for V.T.s up to 66 kV. Above this
voltage, a gas actuated relay may be used.
3.14 Error Specification of VT
The equivalent circuit of a V.T. is exactly the same as a ordinary two winding
transformer and hence is not shown here. Its phasor diagram is shown in Fig. 3.11.
Fig. 3.11
Phasor diagram of V.T.
41
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
According to BS 3941: 1985, the error is defined as follows.
K nV s − V p
Ratio error = • 100%
Vp
Phase Error = γ
γ is +ve when (-Vs) leads Vp.
Table 3.4 shows the limits of error for measurement voltage transformers to BS 3941:
1985.
For protective purposes, accuracy of voltage measurement may be important during
fault conditions, as the system voltage might be reduced by the fault to a low value. Voltage
transformers for such types of service must comply with the extended range of requirements
set in Table 3.5.
Table 3.4 Limits of error for measurement voltage transformers to BS 3941 : 1985
± Percentage ± Phase
Class Application Voltage (Ratio) Displacement in
Error Minutes
Precision testing, or as a standard for testing
0.1 0.1 5
other voltage transformers
Precision Measurements (indicating
0.2 instrument, recorders and electronic 0.2 10
integrating meters)
As for Class 0.2 also meters of precision
0.5 0.5 20
grade in accordance with BS 37
Meters of commercial grade in accordance
with BS 37. General industrial
1.0 1.0 40
measurements (indicating instrument and
recorders)
Approximate measurement. General
3.0 industrial measurements (indicating 3.0 Not specified
instruments and recorders)
* Note : These error limits apply at rated frequency at any voltage between 80% and 120%
of rated voltage and with burdens of between 25% and 100% of rated burden, at a
power factor of 0.8 lagging.
42
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Table 3.5 Additional limits for protective voltage transformers
0.25 to 1.0 times rated burden at unity power factor
0.05 to 0.9 times rated primary
Class 1.1 to Vf times rated primary voltage
voltage
Phase Phase error
Voltage error % Voltage error %
error (minutes) (minutes)
E ±3 ± 120 ±3 ± 120
F ±5 ± 250 ± 10 ± 300
3.15 Voltage Factors
The quantity Vf in Table 5 is an upper limit of operating voltage, expressed per unit
of rated voltage, which may by important for correct relay operation and may also be
important when the ability of the V.T. to withstand the condition is being considered. Earth
faults cause a displacement of the system neutral, particularly in the case of unearthed or
impedance earthed systems, resulting in a rise in the voltage on the un-faulted phases.
Voltage factors, with the permissible duration of the maximum voltage, are given in Table
3.6.
Table 3.6 Voltage factors, with the permissible duration of the maximum voltage
Voltage Factor Earthing Conditions
Duration
Vf
VT primary windings System
1.1 Not limited Non-earthed Effectively or non-
effectively earthed
1.5 30 s Earthed Effectively earthed
1.9 30 s or 8 hours Earthed Non-effectively earthed
3.16 Residually Connected Voltage Transformers
The three voltages of a balanced system summate to zero, but this is not so when the
system subject to a single-phase earth fault. The residual voltage which exists in this case is
of great value for protective gear practice as a means of detecting or discriminating between
earth fault conditions. The residual voltage of a system is measured by connecting the
primary windings of a three-phase V.T. between the three phases and earth and connecting
the secondary windings in series or 'open delta' as shown in Fig. 3.12.
43
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Fig. 12
Residually connected voltage transformers
The output of the secondary windings connected in open delta is zero when balanced
sinusoidal voltages are applied but under conditions of imbalance any residual voltage of the
system will be developed. The residual voltage is three times the zero sequence voltage. In
order to measure this component, it is necessary for a zero sequence flux to be set up in the
V.T., and for this to be possible there must be a return path for the residual summated flux. It
is therefore necessary to use a five limb V.T. core or to use three single phase V.T.s. It is
equally necessary for the primary winding neutral to be earthed, for without an earth zero
sequence exciting current cannot flow.
The possible increase of the voltage of unfaulted phases during earth faults should
also be borne in mind and a V.T. to be used in this way should be rated to have an
appropriate voltage factor as described in Table 4. Voltage transformers are often provided
with a normal star-connected secondary winding and an open delta connected tertiary
winding. Alternatively the residual voltage can be extracted by using a star/open-delta
connected group of auxiliary voltage transformers energized from the secondary winding of
the main unit. The main voltage transformer must fulfil all the requirements for handling a
zero sequence voltage. The star points of the main V.T. secondary winding and the auxiliary
V.T. primary winding must be interconnected to complete the zero sequence circuit, and the
auxiliary V.T. must also be suitable for the appropriate voltage factor.
It should be noted that third harmonics in the primary voltage wave, which are of zero
sequence, summate in the open-delta winding.
3.17 Transient Performance of VT
If a voltage is suddenly applied, an inrush transient will occur, as with power
transformers. The effect will, however, be less severe than for power transformers because of
the lower flux density for which the V.T. is designed. An error will appear in the first few
cycles of the output current in proportion to the inrush transient that occurs.
When the supply to a voltage transformer is interrupted, the core flux will not readily
collapse; the secondary winding will tend to maintain the magnetizing force to sustain this
flux, and will circulate a current through the burden which will decay more or less
44
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
exponentially, possibly with a superimposed audio-frequency oscillation due to the
capacitance of the winding.
3.18 Capacitive Voltage Transformer (CVT)
` As system voltages rise, the cost of providing wound voltage transformers for
measurement and protection function increases, principally because of the cost of achieving
the requisite insulation levels.
It is possible to obtain a voltage output of given accuracy from a capacitance divider
connected between earth and the high voltage conductor. In this case the appropriate
insulation strength may be made inherent in the design of the capacitor thus optimizing
manufacturing costs. It can also be used as the coupling path for the power line carrier signal.
Under present day conditions, about 200 VA are required from the output of the
C.V.T. at an accuracy better than 1 % for frequencies in the range 47 to 51 Hz. A straight
capacitive divider cannot meet this requirement. This problem can be solved by tuning the
circuit to resonant at mid-frequency by a series reactor. A further alleviation is obtained if the
capacitance divider reduces the line voltage to some intermediate value (10 to 22 kV) and is
then stepped down to standard voltage (110 V between phases) in a conventional wound V.T.
For practical reasons the tuning reactor is on the high voltage side of the electro-magnetic
unit; alternatively in some modern designs the wound V.T. is design with high primary
leakage reactance and this is designed for series resonance. The complete circuit diagram of a
capacitance voltage transformer is shown in Fig. 3.13.
Ferroresonance
suppression
circuit
Fig. 13
Capacitive voltage transformer
The performance of a capacitance voltage transformer is virtually dictated by two
parameters:-
(1) The upper capacitance C1.
(2) The magnitude of the intermediate voltage determined by the ratio of C1 to C2.
The exact analysis of the performance of a C.V.T. is rather complex because the
losses in series and shunt electromagnetic elements must be taken into account as well as the
effect of loads of variable magnitude and power factor. Its equivalent circuit is shown in Fig.
3.14.
45
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Fig. 3.14
Equivalent circuit of capacitor voltage transformer
It is possible however to specify the main requirements of the capacitance elements
by disregarding the shunt effect of the wound V.T. inductance L2 and considering the steady
state response for resistive burdens only.
If only simple analysis is required, Thevenin's theorem can be applied to the
capacitance section C1 and C2 and the load resistance is referred to the primary of the wound
V.T. (assumed to be ideal), while disregarding losses in the inductance L1. The equivalent
circuit is shown in Fig. 3.15.
Fig. 15
Simplified equivalent circuit of capacitor voltage transformer
where Vp is the phase/neutral system voltage
K = C1 / (C1 + C2) is the capacitance divider ratio
C1 + C2 is the effective source capacitance
Req is the equivalent value of resistance reflected into the primary
circuit.
It is evident from this circuit that there will be no error at resonance. Maximum errors
will occur for maximum frequency deviation and also for minimum Req (maximum output
power).
KV p Req
V out = 3.5
1
Req + j ωL1 −
ω (C1 + C 2 )
46
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
At resonance,
1
ω 0 L1 =
ω 0 (C1 + C 2 )
KV p
Vout =
1 ω ω0
1+ j
ω 0 (C1 + C 2 )R eq
ω − ω
0
Vout 1
=
KV p 1 + jD
where
1 ω ω0
D=
ω − ω
ω 0 (C1 + C 2 )R eq 0
δ
=
ω 0 (C1 + C 2 )R eq
(KV ) p
2
W max =
R eq
K 2V p2 Dω 0 (C1 + C 2 )
=
δ
Dω 0 C1 KV p2
=
δ
D, ωo, Vp, and δ are fixed parameters. Therefore the maximum burden is
proportional to C1 K. For reason of cost, it is desirable to keep C1 small. For ease of design
of electromagnetic unit, it is desirable to keep K small. Therefore a compromise design is
required.
3.19 Transient Behaviour of Capacitive Voltage Transformer
The introduction of the electromagnetic transformer between the intermediate voltage
and the output makes possible further resonance involving the exciting impedance of this unit
and the capacitance of the divider stack. When a sudden voltage step is applied, oscillations
in line with these different modes take place, and will persist for a period governed by the
total resistive damping that is present. Any increase in resistive burden reduces the time
constant of a transient oscillation, although the chance of a larger initial amplitude is
increased.
While a resistive burden helps to damp out transient oscillations, a compensated
reactive burden constitutes a further tuned circuit and introduce new modes of oscillation,
which can persist for several cycles of the system frequency. It is now standard practice,
when using the modern larger capacitor voltage transformers which do not require adjustment
according to burden, not to compensate for any inductive burdens which may be applied.
3.19.1 Ferro-resonance of capacitive voltage transformers
The exciting impedance Ze of the auxiliary transformer and the capacitance of the
potential divider together form a resonant circuit which will usually oscillate at a sub-normal
47
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
frequency. If this circuit is subjected to a voltage impulse, which may be no more than the
switching on of the supply voltage, some degree of oscillation will occur, which, because of
the non-linear nature of the inductance, may pass through a range of frequencies. If the basic
frequency of this circuit is slightly less than one-third of the system frequency, it is possible
for energy to be absorbed from the system and cause the oscillation to build up. As this
happens, increasing flux density in the transformer core reduces the inductance, bringing the
resonant frequency nearer to the one-third value of the system frequency. The result is a
progressive build-up until the oscillation stabilizes as a third sub-harmonic of the system,
which can be maintained indefinitely. Depending on the values of components, oscillations at
fundamental frequency or at other sub-harmonic or multiples of the supply frequency are
possible but the third sub-harmonic is the one most likely to be encountered. The principle
manifestation of such an oscillation is a rise in output voltage, the r.m.s. value being perhaps
25 to 50 % above the normal value. A typical secondary voltage waveform with third sub-
harmonic oscillation is shown in Fig. 3.16.
Such oscillations are less likely to occur when the circuit losses are high, as is the
case with a resistive burden, and if trouble of this nature is encountered it can be prevented
by increasing the resistive burden.
Special anti-ferro-resonance devices that use a parallel-tuned circuit are sometimes
built into the V.T. Although such arrangements help to suppress ferro-resonance, they tend to
impair the transient response, so that the design is a matter of compromise.
Correct design will prevent a C.V.T. that supplies a resistive burden from exhibiting
this effect, but it is possible for non-linear inductive burdens, such as auxiliary voltage
transformers, to induce ferro-resonance. Auxiliary voltage transformers for use with
capacitive voltage transformers should be designed with a low value of flux density (about
0.4 webers/sq. m. in silicon steel cores), which prevents transient voltage from causing core
saturation, which in turn would bring high exciting currents.
Fig. 16
Secondary voltage waveform with third sub-harmonic oscillation
3.19.2 Effect of CVT to protective relays
(a) Frequency relay - depends upon speed of operation, normally a time delay is required.
(b) Undervoltage / overvoltage relay - cannot respond to instant voltage changes, a time
delay is preferrable.
(c) Solid state (including digital) distance relays - CVT transients can cause errors in
measurement, both over-reach and under-reach. Slower responding relays are not
affected.
48
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
(d) Directional relays - momentary directional error possible for relays without time delay.
3.20 Further Reading:
1. A. Wright, “Current Transformers – Their Transient and Steady State Performance”,
Chapman and Hall, 1968.
2. Denis Robertson (Editor), “Power System Protection Reference Manual”, Reyrolle
Protection, 1982.
3. A. Sweetana, “Transient Response Characteristics of Capacitive Potential Devices”,
IEEE Transaction on Power Apparatus and Systems, Vol., PAS-89, Nov/Dec 1970,
pp.1989-1997.
3.21 Self Evaluation
i. Do you underatand the classification of CT and VT?
ii. Why CT has to be classified into measurement and protection CT but such a
classification is not needed in VT?
iii. What is the effect of CT and VT error on power and energy measurement? Can you
calculate the error involved?
iv. What instrument should be used to test CT and why?
v. The reason of when to use a CT of 1A or 5A rating.
vi. Why it is not practical to set the current setting of an earth fault overcurrent relay too
low?
vii. What is the difference between electromagnetic and capacitive VT?
viii. How to calculate the error introduced by CVT when the system frequency deviates
from its tuned frequency?
3.22 Tutorials
Q1. (a) Explain why an instrument C.T. is not suitable for protection use.
(b) An instrument C.T. of turns ratio 500/1 has the following parameters:
secondary current rating : 1A
primary winding resistance : negligible
primary leakage inductance : 0.1 uH
secondary winding resistance : 1W
secondary leakage inductance : 15 mH
magnetising inductance : 1.2 H (referred to sec.)
coreloss resistance : 1000 ohms (referred to sec.)
Calculate the percentage current error and phase error of the C.T. under rated
secondary current at 50Hz with a 15 VA burden of 0.8 pf lagging. Sketch the corresponding
phasor diagram. ( - 4.72%, 1.1º)
Q2. A 500/1 ring C.T. has an equivalent shunt impedance of 1000/70º W referred to the
secondary and a secondary winding resistance of 1.1 W. Neglect leakage and fringing.
(a) Calculate the percentage current and phase error of the C.T. under rated
secondary current at 50 Hz with a burden of 0.8 p.f. lagging at 15 VA. ( - 1.28%, 0.52º)
(b) The above C.T. is used in a 3 phase wattmeter which consumes 15 VA 0.8p.f.
lagging at rated secondary current. If the secondary current of C.T. is 1 A and the wattmeter
49
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
reads 540 W, determine the actual power of the load and the load p.f. if the load voltage is
346 V. Assume a balanced 3 phase condition. (272.29kW, 0.8971)
Q3. The power and VA consumed by a consumer at 380V, 3 phase are measured through
three 400/5 CTs of Class 0.2. The CTs used has an error specification as shown in Table Q3.
The power and VA indicated by the meters on a typical working day are shown in Fig. Q3.
Calculate:
i) the actual power and VA consumption of the consumer at different time
periods on that typical working day; and (96.65kW, 120.42kVA, 240.89kW, 280.6kVA)
ii) the overall error in energy measurement per day. (170.25WHr)
Table Q3 Limits of error of CT
Percentage current (ratio) error at Phase displacement (in minutes) at
percentage of rated current shown percentage of rated current shown
Class below below
10 up to 20 up to 100 up to 10 up to 20 up to 100 up to
but not incl but not incl 120 but not incl but not incl 120
20 100 20 100
0.2 - 0.5 - 0.35 - 0.2 - 20 - 15 - 10
Fig. Q3
Q4. (a) Give a brief description on the main features of the Measurement Current
Transformer (CT) and the Protection CT.
(b) The secondary current rating of a CT is normally 1A or 5A. What are the
major considerations in choosing the secondary current rating of the CT?
(c) An earth fault overcurrent protection relay is supplied from a 1000/1 CT
connected in the neutral of the incoming transformer winding. The relay used has a burden of
5 VA at a power factor of 0.8 lagging at rated secondary current. The total resistance of the
CT winding and the lead used is 1.5 W. If saturation of the CT iron core should not occur at
10 times the CT rated current, calculate the minimum knee point voltage requirement of the
50
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
CT used. Assume the relay burden remains constant throughout the whole range of fault
current expected. (63 V)
Q5. An earth fault overcurrent relay has a rating of 1 A, with setting range from 20% to
80% at 10% steps. The burden of relay at setting current is 5 VA and the impedance of relay
may be assumed pure reactive. The relay is supplied from a 100/1 C.T. with a magnetisation
curve as shown below. Neglect the effect of lead resistance, plot the relay sensitivity (primary
operating current refering to secondary) against the relay setting.
Vm (V) 1.5 5 11.5 17 22.5 24 25
Im (A) 0.02 0.05 0.08 0.1 0.15 0.2 1
Q6. (a) Explain why an intermediate voltage is required in a capacitive voltage
transformer.
(b) A 160 KV / 63.5 V capacitive voltage transformer is designed to work in a
frequency range of 48 to 51 Hz with its resonant frequency tuned at 49.5 Hz. The upper
capacitance of the C.V.T. is 50 pF and the intermediate voltage is 6.35 KV. Calculate:
(i) the accuracy of the C.V.T. at nominal frequency if the burden has a resistance
of 60 W; and (error = 0.36%)
(ii) the minimum burden resistance so that the maximum error of the C.V.T. is
0.5% over the entire frequency range. (157 W)
Q7. An industrial consumer is drawing a load of 250 kVA 0.8 p.f. lagging at 380V. The
load may be assumed constant for 12 hours per day and for 360 days per year. The power and
energy consumption are measured through three 400/1 current transformers (CT). Two types
of CTs are proposed. The first proposal to is use three separate special measurement CTs of
class 0.2 with error limits as shown in Table Q7(a). The second proposal is to share the
three protection CT of class 5P with error limit as shown in Table Q7(b) so that the same CT
can be shared between protection and measurement devices. Calculate the possible reading of
the wattmeter in CT secondary and the error in energy measurement per year for both
proposals.
(496.6W, error = 5.848MWHr per year)
Comment on why it is not preferable to use protection CT for measurement purposes.
Table Q7(a) Limits of error of Measurement CT of Class 0.2
Percentage current (ratio) error at Phase displacement (in minutes) at
percentage of rated current shown percentage of rated current shown
Class below below
10 up to 20 up to 100 up to 10 up to 20 up to 100 up to
but not incl but not incl 120 but not incl but not incl 120
20 100 20 100
0.2 - 0.5 - 0.35 - 0.2 - 20 - 15 - 10
51
HONG KONG POLYTECHNIC UNIVERSITY
Department of Electrical Engineering
Modern Power System Protection
Chapter 3 – Current Transformer and Voltage Transformer
Specification and Steady State Performances
Table Q7(b) Limits of error of Protection CT of Class 5P
Current error at rated Phase displacement at Composite error at
Accuracy primary current % rated primary current rated accuracy limit
Class primary current %
minutes
5P -1 - 60 5
Q8. (a) Explain why different design on Current Transformer (CT) is required for
instrumentation and protection purposes but similar requirement is not required for Voltage
Transformer (VT).
(b) The full load rating of an industrial consumer is 3000 kVA 0.8 p.f. lagging at
11 kV 3 phase. The consumer is drawing full load for 8 hours per day and half load at the
same power factor for 4 hours per day. The power and energy consumption are measured
through three 150/1 CTs and three 11kV/110V VTs. The CTs and VTs used both have
accuracy class of 0.5 and the error limits are shown in Table Q9(a) and Table Q9(b). Calculate
(i) the power consumption indicated by the instruments under various load
conditions; and (158.75 W, 79.44 W)
(ii) the error in energy measurement per day. (- 12.24 Whr)
Table Q8(a) Limits of error of Measurement CT of Class 0.5
Percentage current (ratio) error at Phase displacement (in minutes) at
percentage of rated current shown percentage of rated current shown
Class below below
10 up to but 20 up to but 100 up 10 up to but 20 up to but 100 up
not incl 20 not incl 100 to 120 not incl 20 not incl 100 to 120
0.5 - 1.0 - 0.75 - 0.5 60 45 30
Table Q8(b) Limits of error for Measurement VT of Class 0.5*
± Phase
± Percentage
Displacement in
Class Voltage (Ratio)
Minutes
Error
20
0.5 - 0.5
* Note : These error limits apply at rated frequency at any voltage between 80% and 120%
of rated voltage and with burdens of between 25% and 100% of rated burden, at a
power factor of 0.8 lagging.
52
