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ELECTRIC POWER DISTRIBUTION EQUIMPENT AND SYSTEMS
4
Transformer
s
Ac transformers are one of the keys to allowing widespread distribution of
electric power as we see it today. Transformers efficiently convert electricity
to higher voltage for long distance transmission and back down to low
voltages suitable for customer usage. The distribution transformer normally
serves as the final transition to the customer and often provides a local
grounding reference. Most distribution circuits have hundreds of distribu-
tion transformers. Distribution feeders may also have other transformers:
voltage regulators, feeder step banks to interface circuits of different volt-
ages, and grounding banks.
4.1 Basics
A transformer efficiently converts electric power from one voltage level to
another. A transformer is two sets of coils coupled together through a mag-
netic field. The magnetic field transfers all of the energy (except in an
autotransformer). In an ideal transformer, the voltages on the input and the
output are related by the turns ratio of the transformer:
V
=
N
N
1
V
1
2
2
where
N
1
and
N
2
are the number of turns and
V
1
and
V
2
are the voltage on
windings 1 and 2.
In a real transformer, not all of the flux couples between windings. This
flux creates a voltage drop between windings, so the voltage is more
accurately described by
V
=
N
N
1
VXI
L
−
1
2
1
2
159
Copyright © 2006 Taylor & Francis Group, LLC
leakage
160
Electric Power Distribution Equipment and Systems
where
X
L
is the leakage reactance in ohms as seen from winding 1, and
I
1
is
the current out of winding 1.
The current also transforms by the turns ratio, opposite of the voltage as
I
N
N
=
2
I
or
N I N I
=
1
2
1 1
2 2
1
The “ampere-turns” stay constant at ; this fundamental rela-
tionship holds well for power and distribution transformers.
A transformer has a magnetic core that can carry large magnetic fields.
The cold-rolled, grain-oriented steels used in cores have permeabilities of
over 1000 times that of air. The steel provides a very low-reluctance path for
magnetic fields created by current through the windings.
Consider voltage applied to the
NI NI
11
=
2 2
primary
side (source side, high-voltage
side) with no load on the
secondary
side (load side, low-voltage side). The
current from the system that sets up a sinusoidal
magnetic field in the core. The flux in turn creates a back emf in the coil that
limits the current drawn into the transformer. A transformer with no load
on the secondary draws very little current, just the exciting current, which
is normally less than 0.5% of the transformer’s full-load current. On the
unloaded secondary, the sinusoidal flux creates an open-circuit voltage equal
to the primary-side voltage times the turns ratio.
When we add load to the secondary of the transformer, the load pulls
current through the secondary winding. The magnetic coupling of the sec-
ondary current pulls current through the primary winding, keeping constant
ampere-turns. Normally in an inductive circuit, higher current creates more
flux, but not in a transformer (except for the leakage flux). The increasing
force from current in one winding is countered by the decreasing force from
current through the other winding (see
Figure 4.1
)
. The flux in the core on
a loaded transformer is the same as that on an unloaded transformer, even
though the current is much higher.
The voltage on the primary winding determines the flux in the transformer
(the flux is proportional to the time integral of voltage). The flux in the core
determines the voltage on the output-side of the transformer (the voltage is
proportional to the time derivative of the flux).
Figure 4.2
shows models with the significant impedances in a transformer.
The detailed model shows the series impedances, the resistances and the
reactances. The series resistance is mainly the resistance of the wires in each
winding. The series reactance is the leakage impedance. The shunt branch
is the magnetizing branch, current that flows to magnetize the core. Most of
the magnetizing current is reactive power, but it includes a real power
component. Power is lost in the core through:
exciting
•
— As the magnetic dipoles change direction, the core heats
up from the friction of the molecules.
Copyright © 2006 Taylor & Francis Group, LLC
winding draws
Hysteresis
Transformers
161
φ
L
1
φ
L
2
I
1
φ
core
I
2
Magnetic equivalent circuit
Electric circuit
R
0
L
1
L
2
N
1
I
1
φ
core
N
2
I
2
V
1
E
1
E
2
V
2
N
1
N
2
E
2
E
1
Since
R
0,
N
1
I
1
N
2
I
2
L
1
and
L
2
are from the leakage fluxes, φ
L
1
and φ
L
2
FIGURE 4.1
Transformer basic function.
Detailed transformer model
Ideal
transformer
Magnetizing
branch
Simplified model
FIGURE 4.2
Transformer models.
Copyright © 2006 Taylor & Francis Group, LLC
162
Electric Power Distribution Equipment and Systems
TABLE 4.1
Common Scaling Ratios in Transformers
Quantity
Relative
to kVA
Relative to a Reference
Dimension,
l
Rating
kVA
l
Weight
K kVA
3/4
K
l
Cost
K KVA
3/4
K (% Total Loss)
–3
Length
K kVA
1/4
K
l
Width
K kVA
1/4
K
l
Height
K kVA
1/4
K
l
Total losses
K kVA
3/4
K
l
No-load losses
K kVA
3/4
K
l
Exciting current
K kVA
3/4
K
l
% Total loss
K kVA
–1/4
K
–1
% No-load loss
K kVA
–1/4
K
–1
% Exciting current
K kVA
–1/4
K
–1
% R
K kVA
–1/4
K
–1
% X
K kVA
1/4
K
l
Volts/turn
K kVA
1/2
K
l
Arthur D. Little, “Distribution Transformer Rulemak-
ing Engineering Analysis Update,” Report to U.S. Depart-
ment of Energy Office of Building Technology, State, and
Community Programs. Draft. December 17, 2001.
•
— Eddy currents in the core material cause resistive
losses. The core flux induces the eddy currents tending to oppose
the change in flux density.
The magnetizing branch impedance is normally above 5,000% on a trans-
former’s base, so we can neglect it in many cases. The core losses are often
referred to as iron losses or no-load losses. The load losses are frequently
called the wire losses or copper losses. The various parameters of transform-
ers scale with size differently as summarized in Table 4.1.
The simplified transformer model in
Figure 4.2
with series resistance and
reactance is sufficient for most calculations including load flows, short-circuit
calculations, motor starting, or unbalance. Small distribution transformers
have low leakage reactances, some less than 1% on the transformer rating,
and
X/R
ratios between 10 and 40.
The leakage reactance causes voltage drop on a loaded transformer. The
voltage is from flux that doesn’t couple from the primary to the secondary
winding. Blume et al. (1951) describes leakage reactance well. In a real
transformer, the windings are wound around a core; the high- and low-
voltage windings are adjacent to each other.
Figure 4.3
shows a configuration;
each winding contains a number of turns of wire. The sum of the current in
each wire of the high-voltage winding equals the sum of the currents in the
Copyright © 2006 Taylor & Francis Group, LLC
4
3
3
3
3
l
l
l
l
2
Source:
Eddy currents
ratios of 0.5 to 5. Larger power transformers used in distribution
substations have higher impedances, usually on the order of 7 to 10% with
X/R
Transformers
163
Side View of Windings
Top View of Windings
Insulation between the
primary and secondary windings
Current
Equivalent Circuit
h
r
Current in
a loop
w
w
Area determines
leakage inductance
FIGURE 4.3
Leakage reactance.
), so each winding is equivalent to a busbar.
Each busbar carries equal current, but in opposite directions. The opposing
currents create flux in the gap between the windings (this is called
N
1
I
1
= N
2
I
2
leakage
). Now, looking at the two windings from the top, we see that the wind-
ings are equivalent to current flowing in a loop encompassing a given area.
This area determines the leakage inductance.
The leakage reactance in percent is based on the coil parameters and
separations (Blume et al., 1951) as follows:
126
10
fNI rw
hS
kVA
2
X
=
%
11
where
f
= system frequency, Hz
N
= number of turns on one winding
I
= full load current on the winding, A
r
= radius to the windings, in.
w
= width between windings, in.
h
= height of the windings, in.
S
kVA
= transformer rating, kVA
Copyright © 2006 Taylor & Francis Group, LLC
low-voltage winding (
flux
()
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