All day efficiency & Auto-transformer & Parallel transformer connection

all-day efficiency

the ordinary or commercial efficiency of
a transformer is given by the ratio
output in watts
input in watts
.
but there are certain types of transformers
whose performance cannot be judged by this
efficiency. transformers used for supplying
lighting and general network i.e., distribution
transformers have their primaries energised all
the twenty-four hours, although their
secondaries supply little or no-load much of
the time during the day except during the house
lighting period. it means that whereas core
loss occurs throughout the day, the cu loss
occurs only when the transformers are loaded. hence, it is considered a good practice to design such
transformers so that core losses are very low. the cu losses are relatively less important, because they
depend on the load. the performance of such is compared on the basis of energy consumed during a
certain time period, usually a day of 24 hours.
? ?all-day = output in kwh
input in kwh
(for 24 hours)
this efficiency is always less than the commercial efficiency of a transformer.
to find this all-day efficiency or (as it is also called) energy efficiency, we have to know the load cycle
on the transformer i.e., how much and how long the transformer is loaded during 24 hours. practical
calculations are facilitated by making use of a load factor.


auto-transformer

it is a transformer with one winding only, part of this being common to both primary and
secondary. obviously, in this transformer the primary and secondary are not electrically isolated from
each other as is the case with a 2-winding transformer. but its theory and operation are similar to those
of a two-winding transformer. because of one winding, it uses less copper and hence is cheaper. it is
used where transformation ratio differs little from unity. fig. 32.60 shows both step down and step-up
auto-transformers.

the current in section cb is vector
difference* of i2 and i1. but as the two
currents are practically in phase opposition,
the resultant current is (i2 ? i1)
where i2 is greater than i1.
as compared to an ordinary 2-
winding transformer of same output, an
auto-transformer has higher efficiency
but smaller size. moreover, its voltage
regulation is also superior.
saving of cu
volume and hence weight of cu, is
proportional to the length and area of
the cross-section of the conductors.
now, length of conductors is proportional to the number of turns and cross-section depends on current.
hence, weight is proportional to the product of the current and number of turns.
with reference to fig. 32.60,
wt. of cu in section ac is ? (n1 ? n2) i1 wt. of cu in section bc is ? n2 (i2 ? i1).
? total wt. of cu in auto-transformer ? (n1 ? n2) i1 + n2 (i2 ? i1)
if a two-winding transformer were to perform the same duty, then
wt. of cu on its primary ? n1i1 wt. of cu on secondary ? n2i2
total wt. of cu ?n1i1 + n2i2
? wt. of cu in auto-transformer
wt. of cu in ordinary transformer
= 1 2 1 2 2 1
1 1 2 2
(n n ) i n (i i )
n i n i
? + ?
+
= i ?
2
1 1 2
2 2 1 1
1 1
2
2 1
1 1
2
1
n
n k n i
k k
n i n i k
n i
= ? = ? ? = = ? ? ?
+ × ? ?

wt. of cu in auto-transformer
(wa) = (1 ? k) × (wt. of cu in ordinary
transformer w0)
? saving = w0 ? wa
= w0 ? (1 ? k) w0 = kw0
? saving = k × (wt. of cu in ordinary
transformer)
hence, saving will increase as k approaches
unity.
it can be proved that power transformed
inductively is input (1 ? k).
the rest of the power = (k × input) is
conducted directly from the source to the
load i.e., it is transferred conductively to
the load.

uses

as said earlier, auto-transformers are used when k is nearly equal to unity and where there is no
objection to electrical connection between primary and secondary. hence, such transformers are
used :
1. to give small boost to a distribution cable to correct the voltage droping.
2. as auto-starter transformers to give upto 50 to 60 % of full voltage to an induction motor during
starting.
3. as furnace transformers for getting a convenient supply to suit the furnace winding from a 230-v
supply
4. as interconnecting transformers in 132 kv/330 kv system.
5. in control equipment for 1-phase and 3-phase electrical locomotives


parallel operation of single-phase transformers


for supplying a load in excess of the rating of
an existing transformer, a second transformer may
be connected in parallel with it as shown in fig.
32.68. it is seen that primary windings are
connected to the supply bus bars and secondary
windings are connected to the load bus-bars. in
connecting two or more than two transformers in
parallel, it is essential that their terminals of similar
polarities are joined to the same bus-bars as in fig.
32.68. if this is not done, the two e.m.fs. induced
in the secondaries which are paralleled with incorrect
polarities, will act together in the local secondary
circuit even when supplying no load and will hence
produce the equivalent of a dead short-circuit as
shown in fig. 32.69.
there are certain definite conditions which
must be satisfied in order to avoid any local circulating currents and to ensure that the transformers share the
common load in proportion to their kva ratings. the conditions are :
1. primary windings of the transformers should be suitable for the supply system voltage and frequency.
2. the transformers should be properly connected with regard to polarity.
3. the voltage ratings of both primaries and secondaries should be identical. in other words, the
transformers should have the same turn ratio i.e. transformation ratio.
4. the percentage impedances should be equal in magnitude and have the same x/r ratio in order to
avoid circulating currents and operation at different power factors.
fig. 32.68
1194 electrical technology
5. with transformers having different kva ratings, the equivalent impedances should be
inversely proportional to the individual kva rating if circulating currents are to be avoided.
of these conditions, (1) is easily comprehended condition (2) is absolutely essential (otherwise
paralleling with incorrect polarities will result in dead short-circuit). there is some lattitude possible
with conditions (3) and (4). if condition (3) is not exactly satisfied i.e. the two transformers have
slightly different transformation or voltage ratios, even then parallel operation is possible. but due to
inequality of induced e.m.fs. in secondaries, there will be even on no-load, some circulating current between
them (and therefore between the primary windings also) when secondary terminals are connected in parallel.
when secondaries are loaded, this localized circulating current will tend to produce unequal loading condition.
hence, it may be impossible to take full kva output
from the parallel connected group without one of the
transformers becoming over-heated.