OPERATION UNDER ABNORMAL CONDITIONS
By definition, according to EN 60076, 'normal' service conditions for a power
transformer are at an altitude of not greater than 1000 m above sea level,
within an ambient temperature range of 25ºC to +40ºC, subjected to a wave
shape which is approximately sinusoidal, a threephase supply which is approximately
symmetrical and within an environment which does not require special provision
on account of pollution and is not exposed to seismic disturbance.
The inference, then, is that 'abnormal' means any conditions which fall out
side these boundaries. Some 'abnormalities' are, however, more likely to be
encountered in practice than others and, in this section, abnormal will be
taken to mean certain operating conditions which differ from those identified
on the transformer nameplate, namely:
• at other than rated power,
• at ambient temperatures which may not conform to the averages set out in
EN 60076,
• at other than rated frequency,
• at other than rated voltage,
• at unbalanced loading.
It is also increasingly common for transformers to be operated with wave shapes
which are not sinusoidal because of the large amount of equipment now installed
which utilizes thyristors or other semiconductor devices which generate high
levels of harmonics. Although such high levels of harmonics constitute abnormal
operating conditions in accordance with the above definition, the problem is
one which is particularly associated with rectifier transformers and is therefore
considered in Section 7.12 which covers these in detail.
Seismic withstand requirements are now also occasionally included in specifications
for transformers supplying strategically essential systems, for example, emergency
reactor cooling supplies for nuclear power stations. Transformers are normally
built with a high degree of ruggedness in order to withstand forces occurring
on short circuit, as explained in Section 4.7, so compliance with seismic requirements
mainly involves firmly anchoring the unit down and bracing the core to withstand
the lateral seismic forces. No generally accepted rules have, as yet, emerged
for the provision of measures to cater for these forces and it is not therefore
proposed to discuss this subject in greater detail.
The first two of the conditions listed above are the ones which are most frequently
encountered in practice and they are, of course, interrelated.
Transformers are rarely required to operate continuously at near constant
load and in the short to medium term ambients may differ significantly from
the annual averages on which EN 60076 ratings are based. Generally users recognize
that it is uneconomic to rate a transformer on the basis of the peak loading
which only occurs for limited periods each day and, in addition, in temper
ate climates where lighting and heating loads cause winter loading peaks to
be very much higher than those arising during the summer months, it is usually
considered desirable to expect to obtain a degree of overloading capability
during periods of low ambient temperature. Hence it is necessary to find a
means of assessing the extent to which recurring loads over and above the EN
rating might be permitted and of converting a cyclic loading pattern into an
equivalent continuous rating, or the extent of overload which a temporary reduction
in ambient might allow.
Operation at other than rated load or other than EN 60076 ambients
Operation at other than rated load will result in hot spot temperature rises
differing from those corresponding to rated conditions and, as explained in
Section 4.5, rated temperature rise is based on a hot spot temperature of 98ºC
with a 20ºC ambient. This hot spot temperature is considered to result in a
rate of ageing which will provide a satisfactory life expectancy. It has already
been stressed in the earlier section, and it is worth stressing again, that
there is no 'correct' value of hot spot temperature. The value of 98ºC has
been selected as a result of testing in laboratory conditions and any attempt
to draw too significant a conclusion as to true life expectancy from such laboratory
testing must be avoided because of the many other factors which also ultimately
affect service life. Consequently other values of hot spot temperature must
be equally tenable and other ratings besides the EN rating must be equally
permissible, particularly if it is anticipated that these ratings will not
be required to be delivered continuously and if it is recognized that 20ºC
may not always be representative of many ambients in which EN rated transformers
are required to operate.
The question then is to decide what variation from 98ºC should be permitted.
To do this it is necessary to revisit the conclusions concerning insulation
ageing which were discussed in Section 4.5. These were that for those periods
for which the hot spot temperature is above that corresponding to normal ageing,
insulation life is being used up at faster than the rate corresponding to normal
life expectancy. In order to obtain normal life expectancy, therefore, there
must be balancing periods during which insulation life is being used up less
rapidly. Expressed in quantitative terms the time required for insulation to
reach its end of life condition is given by the Arrhenius law of chemical reaction
rate:
where L is the time for the reaction to reach a given stage, but which might
in this case be defined as end of life
T is the absolute temperature
and a and ß are constants.
Within a limited range of temperatures this can be approximated to the simpler
Montsinger relationship
L = e^p theta
where p is a constant
theta is the temperature in degrees Celsius.
Investigators have not always agreed on the criteria for which L is representative
of end of life, but for the purposes of this evaluation this is not relevant
and of more significance is the rate of ageing. This is the inverse of the
lifetime, that is
v = Me e^p theta
where M is a constant which is dependent on many factors but principally moisture
content of the insulation and availability of oxygen. Additionally the presence
of certain additives such as those used for the production of thermally upgraded
paper (see Section 3.4) can have a significant effect on its value.
Most important, however, is the fact that the coefficient of temperature variation,
p, can be generally regarded as a constant over the temperature range 80140ºC
and it is widely agreed that its value is such that the rate of ageing doubles
for every 6 K increase in temperature for most of the materials currently used
in transformer insulation.
Relative aging rate
If 98ºC is then taken as the temperature at which normal ageing rate occurs,
then the relative ageing rate at any other temperature ?h is given by the expression
V = _ _ aging rate at /ageing rate at 98 C
(eqn. 61)
This expression may be rewritten in terms of a power of 10 to give
(eqn. 62)
This is represented in Fig. 130 and by Table 18.
Example. 10 hours at 104ºC and 14 hours at 86ºC would use (10 _ 2) _ (14 _
0.25) _ 23.5 hours life used in 24 hours operation.
FIG. 130 Life line Table 18
Equivalent life loss in a 24hour period
It may be required to find the time t hours per day for which the transformer
may be operated with a given hot spot temperature ?h, with the complement to
24 hours corresponding to a sufficiently low temperature for negligible life
loss; then the hours of life loss are given by tV and for tV to equal 24:
(eqn. 63)
Equation (eqn. 63) gives the number of hours per day of operation at any given
value of ?h that will use one days life per day. Table 19 gives values of
t for various values of ?h.
Table 19
It can happen that it is required, for limited periods of time, to operate
at higher temperatures than those associated with normal daily cyclic loading
and accept the more rapid use of life for those periods, for instance the loss
of a unit in a group. If a daily loss of life 2, 5, 10 … times the normal value
is assumed, the corresponding 'hot spot' temperatures will be 6ºC, 14ºC and
20ºC higher than given in Table 19, but ?h must not exceed 140ºC.
As a general rule, the transformer will be loaded in such a way that daily
operation with use of life higher than normal will not extend over periods
of time which are an appreciable proportion of normal expected life duration.
In these conditions it will not be necessary to keep a record of the successive
loads on the unit.
Determination of hot spot temperature for other than rated load In all of
the foregoing discussion load capability has been related to hot spot temperature.
The effect on hot spot temperature at rated load of variation in ambient is
simple to deduce; one degree increase or reduction in ambient will result,
respectively, in one degree increase or reduction in hot spot temperature.
The question which is less simple to answer is, how does hot spot temperature
vary with variation in load at constant ambient? To consider the answer to
this it is necessary to examine the thermal characteristics of a transformer,
which were discussed in Section 4.5.
Hot spot temperature is made up of the following components:
• Ambient temperature
• Top oil temperature rise
• Average gradient
• Difference between average and maximum gradient of the windings In EN 60076
the last two terms are on occasions taken together to represent maximum gradient.
Maximum gradient is then greater than average gradient by the 'hot spot factor.'
This factor is considered to vary between 1.1 for distribution transformers
to 1.3 for medium sized power transformers. The last term thus varies between
0.1 and 0.3 times the average gradient.
Effect of load on oil temperature rise Mean oil rise is determined by the
dissipation capability of the cooling surface and the heat to be dissipated.
The heat to be dissipated depends on the losses.
At an overload k times rated load the losses will be increased to:
Fe + k^2 Cu
where Fe and Cu are the rated noload and load losses respectively.
As the excess temperature of the cooling surface above its surroundings increases,
cooling efficiency will tend to be increased, that is the oil tempera ture
will increase less than prorata with the increased losses to be dissipated.
This relationship may be expressed in the form increased losses rated losses
where ?o is the oil temperature rise, with suffixes 1 and 2, respectively,
indicating the rated and the overload conditions.
EN 60076, Part 2, which deals with temperature rise, gives values for the
index x which are considered to be valid within a band of +/20 percent of
the rated power, these are:
0.8 for distribution transformers having natural cooling with a maximum rating
of 2500 kVA
0.9 for larger transformers with ON.. cooling 1.0 for transformers with OF..
or OD.. cooling
The inference to be drawn from the above values is that with OF.. and OD..
cooling, the coolers are already working at a high level of efficiency so that
increasing their temperature with respect to the surroundings cannot improve
the cooler efficiency further.
Effect of load on winding gradients The heat transfer between windings and
oil is considered to improve in the case of ON.. and OF.. transformers for
increased losses, that is the increased heat to be dissipated probably increases
the oil flow rate, so that the winding gradient also increases less than prorata
with heat to be dissipated, which is, of course, proportional to overload factor
squared. EN 600762, gives the following values
wo wo1 2
_ k y
where ??wo is the winding/oil differential temperature, or gradient, with
additional suffixes 1 and 2, respectively, to indicate the rated and overload
conditions. The index y is then
1.6 for ON.. and OF.. cooled transformers
2.0 for OD.. cooled transformers
EN 600762, places limits on the accuracy of the above as within a band of
_10 percent of the current at which the gradient is measured, however it does
state that this limitation, and that placed on the formula for extrapolation
for oil temperature indicated above, should be applied where the procedure
is used for the evaluation of test results subject to guarantee. In other circumstances
the method may give useful results over wider ranges.
Example 1. The above method may be used to estimate the hot spot temperature
of a 30/60 MVA 132/33 kV ONAN/ODAF transformer when operated at, say, 70 MVA.
The transformer has losses of 28 kW at no load and load losses of 374 kW on
minimum tapping at 60 MVA. On temperature rise test the top oil rise was 57.8ºC
and the rise by resistance was; LV, 69.2ºC; HV, 68.7ºC on minimum tapping.
The effect of changes in ambient can also be included. Let us assume that the
ambient temperature is 10ºC.
The transformer temperature rise test certificate should indicate the value
of the mean oil rise and the winding average gradients. If this information
is not available, for example if no temperature rise test was carried out,
these values will have to be estimated. Top oil rise at 60 MVA can be measured
by a thermometer placed in the top tank pocket. Oil temperature rise on return
from the cooler can be similarly measured at the tank oil inlet. Mean oil temperature
rise is the average of these two figures. Let us assume that either from the
test certificate or by measurement, mean oil rise is found to be 49.8ºC. Then,
LV winding gradient = 69.249.8 = 19.4ºC, and
HV winding gradient = 68.749.8 = 18.9ºC.
At 70 MVA, the overload factor is 70/60 = 1.167
New top oil rise 57.8
The critical gradient is the LV winding _ 19.4ºC, at 1.167 times rated load
this will become:
19.4 x 1.167^1.6 = 24.8
hence, hot spot temperature = 10 + 77.3 + 1.3 x 24.8 = 119.5ºC.
By reference to Table 19 it can be seen that this overload may be carried
for up to 2 hours/day with the remainder of the time at a load which is low
enough to cause minimal loss of life. Alternatively, provided this daily over
load is only imposed for a matter of a few weeks, normal load may be carried
for the remainder of the day with only negligible loss of life.
Normally a transformer such as the one in the above example would have pumps
and fans controlled from a winding temperature indicator which would mean that
these would not be switched in until a fairly high winding tempera ture was
reached, however if the overload is anticipated, pumps and fans can, with advantage,
be switched in immediately. This will delay the time taken to reach maximum
hot spot temperature and, although cooler losses will be incurred, these will
to some extent be offset by the lower transformer load loss resulting from
the reduction in winding copper temperature.
During any period of overloading there will be a time delay before the maximum
hot spot temperature is reached. This will have two components:
• The time for the windings to reach equilibrium with the oil at the new level
of gradient.
• The time taken for the complete transformer to reach equilibrium with its
surroundings.
The first of these, the winding time constant, is likely to be of the order
of minutes, say, between 5 and 20 minutes and it is normally neglected. The
second, the transformer oil time constant, or simply transformer time constant,
will be a great deal longer, probably between 1 and 3 hours. The hot spot temperature
variation for a daily loading duty of the form indicated in Fig. 131 will
be as shown, with an exponential increase at the commencement of the overloading
and a similar decay at the end of the overload period. In terms of use of life
the areas under these exponential curves are equal, so the times spent in the
heating and cooling phases will partly cancel out and may therefore be ignored.
This will not be entirely true however because rate of ageing is proportional
to 2 (or 10) raised to a power of temperature (see Eqs (eqn. 58) and (eqn. 59) above).
Ignoring the time delays results in the introduction of a small factor of pessimism
which is no bad thing. Recognition of the time delay can be particularly beneficial,
however, where the overload would take the final hot spot temperature above
140ºC. By definition, for an overloading period equal to the time constant
for the oil, the rise in top oil temperature at the end of this period will
be approximately 63 percent of its ultimate value. If the time constant for
the oil is 2 hours and its ultimate rise, say, 45ºC, 63 percent of this is
only 28.4ºC, some 16.6ºC lower, and this will not be reached until after 2
hours.
FIG. 131 Simplified load diagram for cyclic daily duty
IEC loading guide for oilfilled transformers
The principles outlined above have been used as a basis for compiling loading
guides for oilimmersed transformers, for example IEC 60354 (in the UK BS 7735)
Loading guide for oilimmersed transformers. Whilst the use of such guides
can greatly simplify the process of assessing loading capability, it is always
beneficial to have a good understanding of the theory involved. As well as
aiding an appreciation of the precise effect on the transformer of operating
at other than rated load, it is clearly preferable to be able to perform a
calculation for a particular transformer using loss values and gradients specific
to that transformer than to rely on guides which must of necessity make many
assumptions. It will be seen from the example worked above, that if a transformer
has high maximum gradients, say approaching 30ºC, which is not untypical of
many OD. type transformers (IEC 60354, 1991, assumes 29ºC), then its ability
to carry overloads will be considerably less than that of a transformer having
maximum gradients of, say 25ºC or less, since the effect of overloading for
OD.. transformers is to increase gradients in accordance with a square law.
For an overload of 25 percent, 1.252 _ 30 _ 46.8ºC, whereas 1.252 _ 25 _ 39.06,
so an OD.. transformer having the lower maximum gradient will have a rate of
using life of less than half that of the transformer with the higher gradient
at an overload of 25 percent.
It should also be noted that a transformer with a low ratio of load loss to
noload loss will also be capable of slightly greater overloading than one
for which this ratio is higher, since it is only the load loss which will increase
under overload, and this in proportion to the overload squared. Loading guides
must assume a typical value for the ratio of the load to noload loss. IEC
60354 assumes a ratio of 5 for ONAN distribution transformers and 6 for all
other types. Just how widely actual transformers can vary in practice will
be apparent from the example of the 30/60 MVA transformer used in the overload
calculation above. The figures are for an actual transformer and it can be
seen that the ratio is 374/28 _ 13.4 to 1. Variation of this ratio has less
an effect on top oil temperature, and hence hot spot temperature, than does
variation in gradient. If the transformer in the above example is assumed to
have the same total losses, that is 402 kW, but split so that the ratio is
the IEC assumed value, that is 57.4 and 344.6 kW, respectively, and the top
oil rise recalculated for a load of 70 MVA, it will be found that this equates
to 75.7ºC, only 1.6ºC lower.
Continuous loading at alternative ambients in accordance with IEC 60354 Table 20, reproduced from IEC 60354, gives factors for continuous loadings which
will result in a hot spot temperature of 98ºC for varying ambient temperatures
and for each type of cooling, thus enabling the continuous loading capability
for any ambient temperature to be calculated.
Table 20 Acceptable load factor for continuous duty K24 at different ambient
temperatures (ON, OF and OD cooling)
Cyclic loading in accordance with IEC 60354 IEC 354 may also be used to give
indication of permissible daily loading cycles. Loading patterns are deemed
to consist of a simplified daily cycle having the form shown in Fig. 131,
above. Symbols used in the guide have the following meanings:
K1 is the initial load power as a fraction of rated power K2 is the permissible
load power as a fraction of rated power (usually greater than unity)
t is the duration of K2, in hours
?A is the temperature of cooling medium, air or water
__ and where S1 is the initial load power
S2 is the permissible load power and
Sr is the rated power
The values of K1, K2 and t must be selected to obtain as close a match as
possible between the actual load cycle and the overload basic cycle of Fig. 131. This can be done on an area for area basis as shown in Fig. 132, reproduced
from IEC 60354. For the not uncommon case where there are two peaks of nearly
equal amplitude but different duration, the value of t is deter mined for the
peak of longer duration and the value of K1 is selected to correspond to the
average of the remaining load as shown in the example of Fig. 133. Where
the peaks are in close succession, the value of t is made long enough to enclose
both peaks and K1 is selected to correspond to the average of the remaining
load, as shown in Fig. 134.
FIG. 132 Load cycle with one peak
FIG. 133 Load cycle with two peaks of equal amplitude and different duration
FIG. 134 Load cycle with peaks in close succession
FIG. 135 Permissible cyclic loading duties for ONAN distribution transformers
for normal loss of life at 20 degr. C ambient
A series of loading curves for varying ambients, of which Fig. 135 is a
typical example, are then provided to enable permissible cyclic loading to
be deduced. The guide lists the thermal characteristics which have been assumed
in drawing up the curves and recommends that for normal cyclic loading the
load current should not exceed 1.5 times rated current and the hot spot temperature
should not exceed 140ºC. For large power transformers (over 100 MVA) it recommends
that these should not exceed 1.3 times rated current and 120ºC, respectively.
For all transformers it recommends that top oil temperature should not exceed
105ºC. The following examples shows how the tables may be used.
Example 2. A 2 MVA ONAN distribution transformer has an initial load of 1
MVA. To find the permissible load for 2 hours at an ambient temperature of
20ºC, assuming constant voltage:
?A _ 20ºC K1 _ 0.5 t _ 2 hour FIG. 135 gives K2 _ 1.56, but the guide
limit is 1.5. Therefore the permissible load for 2 hours is 3 MVA (then returning
to 1 MVA).
Example 3. With ?A _ 20ºC, an ONAN distribution transformer is required to
carry 1750 kVA for 8 hours and 1000 kVA for the remaining 16 hours each day.
To find the optimum rating required to meet this duty. Assuming constant voltage,
we have K K 2 1 1750 1000 175 __ .
FIG. 136 Illustration of Example 3
On the curve of Fig. 135, first plot the line K2/K1 _ 1.75 (Fig. 136),
then at the point where this intersects the curve for t _ 8, the values of
K1 and K2 are K2 _ 1.15 and K1 _ 0.66 so that the rated power is
Sr
___ 1750 115 1000
066 1520
kVA Emergency cyclic loading
Example 3, above, enables the best rating of transformer to be selected to
meet a known cyclic duty. On occasions it may be necessary to overload a transformer
on a cyclic basis when it was not originally intended to be so loaded and even
though some shortening of life might be entailed. IEC 354 terms this 'Emergency
cyclic loading' and provides a series of tables covering all cooling types
for a range of loading duties. Table 21, which is Table 27 of the guide,
provides information relating to emergency loading of OD medium and large power
transformers for 2 hours.
Example 4. What is the daily loss of life and the hot spot temperature when
the 30/60 MVA transformer of Example 1, above, is loaded at 70 MVA for 2 hours
in an ambient of 10ºC?
K1 _ 1.0, K2 _ 1.167, ?A _ 10ºC, t _ 2 hours
Table 21 shows that V _ 2.4, ??h _ 103.7 for an ambient temperature of 20ºC.
(By linear interpolation between K2 _ 1.1 and K2 _ 1.2, which is reasonable
for hot spot temperature, somewhat optimistic for V). Taking account of the
actual ambient temperature of 10ºC we have:
Loss of life _ 2.4 _ 0.32 _ 0.77 'normal' days ?h _ 103.7 _ 10 _ 113.7ºC.
The above hot spot temperature is a little lower than the figure of 119.5
calculated in Example 1 which corresponds to exactly one days loss of life
per day.
It will be noted that there is a reference in Table 21 to a Table 1 which
gives a value of maximum permissible hot spot temperature. This is, of course,
Table 1 of IEC 60354. For completeness this is reproduced as Table 22, how
ever the reader should refer to IEC 60354 for a full explanation of its position
in relation to maximum hot spot temperature.
The above examples give some indication of the information which is available
in IEC 60354 and the way in which it can be used to determine the loading capability
of an oilfilled transformer. For a fuller explanation of over loading principles
for all sizes of transformers and types of cooling reference should be made
to the document itself.
Table 21 OD medium and large power transformers: t _ 2 hours. Permissible
duties and corresponding daily loss of life (In 'normal' days)
To determine whether a daily load diagram characterized by particular values
of K1 and K2 is permissible and to evaluate the daily loss of life entailed,
proceed as follows:
Hotspot temperature:
Add the hotspot temperature rise given in the table to the ambient temperature.
If the resulting hotspot temperature exceeds the limit stated in Table 1,
the duty is not permissible.
Limitations on overloading
Although in the previous paragraphs emphasis has been placed on the arbitrary
nature of 98ºC as a hot spot temperature for 'normal' rating in normal ambients
and the flexibility built into the rating of transformers designed on this
basis, before concluding it is appropriate to add a few words of caution.
Table 22 Current and temperature limits applicable to loading beyond nameplate
rating
Care should be taken, when increasing the load on any transformer, that any
associated cables and switchgear are adequately rated for such increases and
that any transformer ancillary equipment, for example tapchangers, bushings,
etc., do not impose any limitation. The voltage regulation will also increase
when the load on a transformer is increased.
The mineral oil in the transformer should comply with BS 148 and should be
maintained at least in accordance with BS 5730. Consideration should be given
to closer monitoring of the oil in accordance with the procedures out lined
in Section 6.7.
For normal cyclic duty, the current should not exceed 1.5 times rated value.
Hot spot temperature should never exceed 140ºC. For emergency duty, currents
in excess of 1.5 times rated value are permissible provided that the 140ºC
hot spot temperature is not exceeded, that the fittings and associated equipment
are capable of carrying the overload and that the oil temperature does not
exceed 115ºC. The limit of 115ºC for the oil temperature has been set bearing
in mind that the oil may overflow at oil temperatures above normal. Depending
on the provision made for oil expansion on a particular transformer, the oil
may overflow at temperatures lower than 115ºC.
IEC 60354, 1991, states that for certain emergency conditions the hot spot
temperature may be allowed to reach 160ºC. The question then is what constitutes
such an emergency. It should be noted that when the hot spot temperature reaches
140160ºC, gas bubbles may develop which could hazard the electrical strength
of the transformer. It is clearly most undesirable to add to an existing emergency,
possibly caused by the failure of a transformer, by creating conditions which
might lead to the failure of a second unit.
Operation at other than rated voltage and frequency Considering initially
variation from rated frequency, it can be stated that it is not usually possible
to operate a transformer at any frequency appreciably lower than that for which
it was designed unless the voltage and consequently the output are correspondingly
reduced. The reason for this is evident if the expression connecting voltage,
frequency and magnetic flux given in Section 1.1, Eq. (1.4), is recalled. This
is
E/N _ 4.44 Bm Af _ 10_6
where E/N is the volts per turn, which is the same
in both windings
Bm is the maximum value of flux density in the core, Tesla
A is the net crosssectional area of the core, mm^2
f is the frequency of supply, Hz.
Since, for a particular transformer A and N are fixed, the only variables
are E, Bm and f, and of these Bm is likely to have been set at the highest
practicable value by the transformer manufacturer. We are therefore left with
E and f as the only permissible variables when considering using a transformer
on a frequency lower than that for which it was designed. The balance of the
equation must be maintained under all conditions, and therefore any reduction
in frequency f will necessitate precisely the same proportionate reduction
in the voltage E if the flux density Bm is not to be exceeded and the transformer
core not to become overheated. The lower the frequency the higher the flux
density in the core, but as this increase is relatively small over the range
of the most common commercial frequencies its influence on the output is very
slight, and therefore the reduction in voltage and output can be taken as being
the same as the reduction in frequency.
Operation at higher than rated frequency but at design voltage is less likely
to be problematical. Firstly, the danger of saturation of the core is no longer
a threat since increased frequency means a reduction in flux density. There
will be some increase in winding eddy current loss which will probably increase
as the square of the frequency. The impact of this will depend on the magnitude
of the eddy current losses at rated frequency but for transformers smaller
than 1 or 2 MVA and frequencies within about 20 percent of rated frequency,
this will probably be acceptable. Changes in hysteresis and eddy current components
of core loss, both of which increase with frequency, will probably be balanced
by the reduction in flux density as can be seen by reference to the expressions
for these quantities which were given in Section 3.2. These were Eqs (3.1)
and (3.2) respectively:
Hysteresis loss, Wh _ k1fBn max W/kg and Eddy current loss, We _ k2 f 2 t
2 B2 eff /? W/kg
where k1 and k2 are constants for the material
f is the frequency, Hz
t is thickness of the material, mm
? is the resistivity of the material
Bmax is maximum flux density, T
Beff is the flux density corresponding to the r.m.s. value of the applied
voltage.
n is the 'Steinmetz exponent' which is a function of the material.
Considering next the question of using a transformer on voltages different
from the normal rated voltage, it can be stated very definitely that on no
account should transformers be operated on voltages appreciably higher than
rated voltage. This is inadmissible not only from the point of view of electrical
clearances but also from that of flux density, as will be clear from Eq. (1.4)
which was recalled earlier. It should be noted, whilst considering this aspect
of operation at higher than rated voltage, that many specifications state that
the system voltage may be capable of increasing by 10 percent above its rated
value. It is important that in this circumstance the designer must limit the
design flux density to such a value as will ensure that saturation is not approached
at the overvoltage condition. This usually means that the nominal
flux density must not exceed 1.7 Tesla at any point in the core. If the transformer
has an onload tapchanger under automatic control and there is any possibility
that this might be driven to minimum tap position whilst system volts are high,
then the design flux density must be selected so as to ensure that saturation
is not approached under this fault condition, which might require that this
be kept as low as 1.55 Tesla.
FIG. 137 Current distribution due to a singlephase load on polyphase
transformers or transformer groups. Note: in all cases the dotted lines indicate
the phase angle of the singlephase load currents
FIG. 138 Current distribution due to singlephase load on polyphase transformer
groups. Note: in all cases the dotted lines indicate the phase angle of the
singlephase load currents
Operation with unbalanced loading
In considering the question of unbalanced loading it is easiest to treat the
subject from the extreme standpoint of the supply to one singlephase load
only, as any unbalanced threephase load can be split up into a balanced threephase
load and one or two singlephase loads. As the conditions arising from the
balanced threephase load are those which would normally occur, it is only
a question of superposing those arising from the singlephase load upon the
normal conditions to obtain the sum total effects. For the purpose of this
study it is only necessary to consider the more usual connections adopted for
supplying three phase loads. The value of current distribution is based upon
the assumption that the singlephase currents are not sufficient to distort
the voltage phasor diagrams for the transformers or transformer banks. This
assumption would approximate very closely to the truth in all cases where the
primary and secondary currents in each phase are balanced. In those cases,
however, where the primary current on the loaded phase or phases has to return
through phases unloaded on the secondary side, the distortion may be considerable,
even with relatively small loads; this feature is very pronounced where threephase
shelltype transformers and banks of singlephase transformers are employed.
Figures 6.1376.139 show the current distribution on the primary and secondary
sides of three to threephase transformers or banks with different arrangements
of singlephase loading and different transformer connections. These diagrams
may briefly be explained as follows.
FIG. 139 Phasor diagrams showing unbalanced loadings on a delta/star,
threephase, stepdown transformer.
(a) Star/star; singlephase load across two lines
With this method of singlephase loading the primary load current has a free
path through the two primary windings corresponding to the loaded secondary
phases, and through the two line wires to the source of supply. There is, there
fore, no choking effect, and the voltage drops in the transformer windings
are those due only to the normal impedance of the transformer. The transformer
neutral points are relatively stable, and the voltage of the open phase is
practically the same as at noload. The secondary neutral point can be grounded
with out affecting the conditions.
The above remarks apply equally to all types of transformers.
(b) Star/star; singlephase load from one line to neutral With this method
of singlephase loading the primary load current corresponding to the current
in the loaded secondary must find a return path through the other two primary
phases, and as load currents are not flowing in the secondary windings of these
two phases, the load currents in the primaries act as magnetizing currents
to the two phases, so that their voltages considerably increase while the voltage
of the loaded phase decreases. The neutral point, therefore, is considerably
displaced. The current distribution shown on the primary side is approximate
only, as this will vary with each individual design.
The above remarks apply strictly to threephase shelltype transformers and
to threephase banks of singlephase transformers, but threephase coretype
transformers can, on account of their interlinked magnetic circuits, supply
consider able unbalanced loads without very severe displacement of the neutral
point.
(c) Star/star with generator and transformer primary neutrals joined; single
phase load from one line to neutral
In this case the connection between the generator and transformer neutral
points provides the return path for the primary load current, and so far as
this is concerned, the other two phases are short circuited. There is therefore
no choking effect, and the voltage drops in the transformer windings are those
on the one phase only, due to the normal impedance of the transformer. The
transformer neutral points are relatively stable, and the voltages of the above
phases are practically the same as at noload. The secondary neutral point
can be grounded without affecting the conditions.
The above remarks apply equally to all types of transformers.
(d) Delta/delta; singlephase load across two lines
With this connection the loaded phase carries twothirds of the total current,
while the remainder flows through the other two phases, which are in series
with each other and in parallel with the loaded phase. On the primary side
all three windings carry load currents in the same proportion as the secondary
windings, and two of the line wires only convey current to and from the generator.
There is no abnormal choking effect, and the voltage drops are due to the normal
impedance of the transformer only. The type of transformer does not affect
the general deductions.
(e) Star/delta; singlephase load across two lines On the delta side the distribution
of current in the transformer windings is exactly the same as in the previous
case, that is, twothirds in the loaded phase and onethird in each of the
other two. On the primary side the corresponding load currents are split up
in the same proportions as on the secondary, and in value they are equal to
the secondary currents of the different phases multiplied by _3 and multiplied
or divided by the ratio of transformation, according to whether the transformer
is a stepup or stepdown. The primary neutral point is stable.
The above remarks apply equally to all types of transformers.
(f ) Delta/star; singlephase load across two lines Singlephase loading across
lines of this connection gives a current distribution somewhat similar to that
of (a), except that the currents in the two primary windings are 1/_3 times
those occurring with the star primary, while all the three lines to the generating
source carry currents in the proportions shown instead of two lines only carrying
currents as in the case of the star primary.
There is no choking effect, and the voltage drops in the windings are due
only to the normal impedance of the transformer. The transformer secondary
neutral point is relatively stable and may be grounded. The voltage of the
open phase is practically the same as at noload.
The above remarks apply equally to all types of transformers.
(g) Delta/star; singlephase load from line to neutral With this connection
and singlephase loading the neutral, primary and secondary windings on one
phase only carry load current, and on the primary side this is conveyed to
and from the generating source over two of the lines only. There is no choking
effect, and the voltage drops in the transformer windings are those corresponding
only to the normal impedance of the transformer. The secondary neutral point
is stable and may be grounded without affecting the conditions. The voltages
of the open phase are practically the same as at noload. The type of transformer
construction does not affect the general deductions.
(h) Interconnected star/star; singlephase load across two lines With this
connection and method of loading, all the primary windings take a share of
the load, and although in phase C there is no current in the secondary winding,
the load currents in the two halves of the primary windings of that phase flow
in opposite directions, so that their magnetic effects cancel. There is no
choking effect, and the voltage drops in the transformer windings are those
due to the normal impedance of the transformer only. With threephase shell
type transformers and threephase banks of singlephase transformers the secondary
neutral is not stable and should not be grounded unless the flux density is
sufficiently low to permit this. With threephase coretype transformers, how
ever, the neutral is stable and could be grounded. The voltage of the open
phase is practically that occurring at noload.
(i) Interconnected star/star; singlephase load from one line to neutral With
this connection and method of loading a partial choking effect occurs, due
to the passage of load current in each half of the primary windings corresponding
to the unloaded secondary windings. The voltage of the two phases in question,
therefore, becomes increased on account of the high saturation in the cores
and the voltage of the windings corresponding to the loaded phase drops. Both
primary and secondary neutrals are therefore unstable and should not be grounded.
The above remarks apply strictly to threephase shelltype transformers and
to threephase banks of singlephase transformers. With threephase coretype
transformers the deflection of the neutral point is not so marked, and considerable
outofbalance loads can be supplied without any excessive deflections of the
neutral points.
(j) Star/interconnected star; singlephase load across two lines With this
connection and method of loading the secondary windings on all three limbs
carry load currents, and therefore all the primary windings carry corresponding
balancing load currents. The current distribution is clearly shown on the diagram,
from which it will be seen there is no choking effect, and the transformer
neutral points are stable if threephase coretype transformers are used, and
so may be grounded. On the secondary side the voltage of the open phase is
practically the same as at noload. The voltage drops in the transformer windings
are those due only to the normal impedance of the transformer.
(k) Star/interconnected star; singlephase load from one line to neutral With
this method of loading there is similarly no choking effect, as the primary
windings corresponding to the loaded secondaries carry balancing load currents
which flow simply through two of the line wires to the generating source.
The voltage drops in the transformer windings are those due only to the normal
impedance of the transformer, and the voltages of the above phases are practically
the same as at noload. The secondary neutral is stable and can be grounded.
The primary neutral can only be grounded, however, if the transformer unit
is of the threephase core type of construction.
(l) Delta/interconnected star; singlephase load across two lines With this
connection and loading the general effect is similar to the star/inter connected
star connection. That is, there is no choking effect, as the primary windings
corresponding to the loaded secondaries take balancing load currents, although
the primary current distribution is slightly different from that occurring
with a star primary. The voltage drops in the transformer windings are those
due only to the normal impedance of the transformer, while the volt age of
the open phase is practically the same as at noload. The secondary neutral
is stable and can be grounded.
(m) Delta/interconnected star; singlephase load from one line to neutral
With this connection and method of loading the results are similar to those
obtained with the star/interconnected star, that is the primary windings corresponding
to the loaded secondaries carry balancing load currents so that there is no
choking effect. The voltage drops in the transformer windings are those due
only to the normal impedance of the transformer, while the voltages of the
open phases are practically the same as at noload. The secondary neutral point
is stable and can be grounded.
(n) Vee/vee With this connection and method of loading there is clearly no
choking effect, as this is simply a question of supplying a singlephase transformer
across any two lines of a threephase generator. The voltage drops are comparable
to those normally occurring, and the voltages of the open phases are practically
the same as at noload. The connection is, however, electrostatically unbalanced,
and should be used only in emergency.
(o) Tee/tee; singlephase load across two lines, embracing the teaser and
half the main windings With this connection and method of loading there is
no choking effect, as the balancing load current in the corresponding primary
windings has a perfectly free path through those windings and the two line
wires to the generating source. The voltage drops in the windings are those
due only to the normal impedance of the transformer, and the voltages of the
open phases are practically the same as at noload. The neutral points are
stable and may be grounded.
It should always be remembered that it is impossible to preserve the current
balance on the primary side of a polyphase transformer or bank and in the line
wires and source of supply when supplying an unbalanced polyphase load or a
pure singlephase load. In most cases the voltage balance is maintained to
a reasonable degree, and the voltage drops are only greater than those occurring
with a balanced load on account of the greater phase differences between the
voltages and the unbalanced polyphase currents or the pure singlephase currents. The voltage drops become accentuated, of course, by the reactance of
the circuit when the power factors are low.
FIG. 139 shows the phasor diagrams for typical unbalanced loading conditions
on a delta/star threephase stepdown transformer where one, two and three
separate singlephase loads are connected from lines to neutral. Voltage drops
include transformer and cable or line drops. The triangles constructed on V'
A, V' B and V' C show the resistive and reactive components of the total voltages
across the respective loads. In diagram 1 the current IN in the neutral is
the same as the load current IA; in diagram 2 the neutral current IN is the
phasor sum of the load currents IA and IB, while in diagram 3, IN is the phasor
sum of IA, IB and IC.
