EN 206
1/19
Prof. Doolla
Introduction
Votlage
Regulation
EN 206 - Power Electronics and Machines
Transformers
Efficiency
Auto
Transformer
Three Phase
Transformer
Suryanarayana Doolla
Department of Energy Science and Engineering
Indian Institute of Technology, Bombay
suryad@iitb.ac.in
Lecture Organization - Modules
EN 206
2/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Introduction and Power Semiconductor Switches
Module 1: Transformers
Module 2: AC/DC converter / Rectifier
Module 3: DC machines and Drives
Module 4: DC/DC converter
Module 5: Induction Machine
Module 6: DC/AC converter / Inverter
Module 7: AC/AC converter / Cyclo converter
Module 8: Synchronous Machine
Module 9: Special Topics: Machines, HVDC, APF
Review of Last Class
EN 206
3/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Transformers
Phasor diagram for ideal transformer and no load
condition, impedance transformation
Equivalent circuit
SC and OC Test of a Transformer
Voltage Regulation
EN 206
4/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Definition:
It is defined as change in voltage from no load to full load,
as a percentage of rated terminal voltage at full load.
FL
Voltage Regulation = VNLV−V
FL
Problem-1
EN 206
5/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Short circuit measurements done on a 2200/220V transformer
rated 500 kVA provide the following values of equivalent
resistance and reactance, respectively, referred to low-voltage
(secondary) side:
Re2 = 2mΩ, xe2 = 6mΩ
Calculate
(a) Rated secondary current
(b) Full-load equivalent resistance voltage drop I2 Re2 , Full load
equivalent reactance voltage drop I2 Re2 .
(c) Induced voltage when the transformer is delivering rated
current to a unity PF load.
(d) Voltage regulation at UPF. (e) Voltage regulation for rated
load at 0.8pf lagging. (f) Voltage regulation for rated load at
0.8pf leading.
VR - Analysis
EN 206
6/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
It is practically impossible to determine voltage regulation
for a transformer. In such case the results of SC test shall
be used to determine the voltage regulation.
It is possible to have zero percent or negative voltage
regulation depending on magnitude of leading pf.
Losses in a Transformer
EN 206
7/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Constant loss:
Core loss: Assumed to be constant for rated voltage and
frequency. Depends on flux density of the core, magnetic
properties of the material, resistivity of core material,
volume of core material.
Stray load loss: Leakage flux present in a transformer
induce eddy currents in the conductors, tanks, channels,
bolts etc. These eddy currents give rise to stray load loss.
Dielectric loss: This loss occurs in the insulating materials
(transformer oil, solid insulation of HV transformers)
Variable losses: These are due to ohmic losses in the
primary and secondary of transformer when it is loaded
(no load neglected).
Under normal operating conditions, the variation of mutual flux
is not more than 2 to 3%, consequently, core losses are
assumed to be constant throughout.
Efficiency
EN 206
8/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Both SC and OC test data is required to calculate efficieny
of a transformer.
Efficiency (η):
OutputPower (kW )
OutputPower (kW )+Losses(kW )
=
Po
Po +Losses
=
V2 I2 cosθ2
V2 I2 cosθ2 +(Pc +I22 Re2 )
Maximum efficieny of a transformer occurs at load when
fixed losses are equal to variable losses. “Try the proof at
home”.
q
Pc = I22 Re2 =⇒ I2 =
Pc
Re2
All Day Efficiency: In a transformer where the load
changes continuously with time (ex. distribution
transformer), all day efficieny is defined as
DailyLosses(kWh)
ADE=1- DailyOutput(kWh)+Dailylosses(kWh)
Autotransformer
EN 206
9/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
A transformer in which a part of winding is common to
both the primary and secondary circuits, is called an
auto-transformer.
In an autotransformer primary and secondary winding are
not isolated.
Working mmf in a transformer remains substantially
constant at its no load value. The primary must draw
additional current from the source, in order to neutralize
the effect of load current.
Autotransformer - Analysis
EN 206
10/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
mmf of winding AB= I1 (N1 − N2 ) = (I2 − I1 )N2 = ICB N2
= mmf of winding CB
Transformer action takes place between winding AB and
BC
Transformed VA = VAB IAB = (V1 − V2 )I1 .
Transformed VA/Input VA =
V1 −V2
V1
=1−k
Autotransformer - Advantages & Disadvantages
EN 206
11/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Advantages
High efficiency
Low leakage impedance and has superior voltage
regulation when compared to a two winding transformer of
same output
Requires less conductor compared to a two winding
transformer (k < 1).
Disadvantages
Isolation or direct electrical connection
If the ratio of transformation is far from unity, the
economic advantages of auto transformer over two
winding transformer decreases.
Three Phase Transformer
EN 206
12/19
Prof. Doolla
Three phase supply for rectifiers, less ripple occurs in the
rectified output
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Simplicity, low cost, reliability, efficiency and safety
Three phase to two phase is mutually convertible.
Six and twelve phase circuits are obtained from Z circuits.
Most commonly used circuits ∆ or Y . Others include inter
connected Y arrangement, Open Delta (V connection), Tee
connections, Scott-Connection.
Delta - Delta connection
EN 206
13/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
The transformation ratio of all the transformers must be
the same, otherwise circulating currents round the winding
will be present even under no load condition
The impedance of all the units should be the same to
ensure equal load sharing
Secondary voltages are in phase with primary
Delta - Delta connection
EN 206
14/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
The voltages does not get unbalanced due to unbalancing
in the loads.
Cross section of the wire is reduced as Iph =
IL
√
3
If one of the three transformers gets burnt, the delta-delta
system continues functioning uninterrupted.
Star - Star connection
EN 206
15/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Line voltage =
phase current
√
3× phase voltage and line current =
No phase shift between primary and secondary voltages
With an unbalanced load on the secondary winding, the
phase voltage on the load side changes unless the neutral
point is earthed.
The neutral is also unstable because of third harmonic
component in the exciting currents, and also due to
unequal magnetizing currents for the three units.
Star - Delta connection
EN 206
16/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
The coil in star winding will carry full current but voltage
across them will be √13 of line voltage
Delta coils, carry only
line voltage
√1
3
of the line current but whole of
Generally used at substation end of the transmission line
where the incoming voltage is to be stepped down for
consumption purposes.
30o phase shift is observed between corresponding primary
and secondary terminal voltages.
Cannot be paralleled with ∆ − ∆ and Y-Y.
Delta - Star connection
EN 206
17/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Generally used for step-up the voltages
Most generally employed (both single phase and three
phase circuits)
Low voltage distribution systems.
300 phase shift is observed between corresponding primary
and secondary terminal voltages.
Cannot be paralleled with ∆ − ∆ and Y-Y.
Open Delta and Scott Connection
EN 206
18/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Open Delta:
It is extensively used in distribution systems
Initial stages of rural electrification
The two transformers will carry an overload of 15.5% as a
whole which is acceptable.
Scott Connection:
A poly phase system may be transformed to another
polyphase system.
General application of Scott connection involves 3∅ to 2∅
and 2∅ to 3∅ transformation.
Summary
EN 206
19/19
Prof. Doolla
Introduction
Votlage
Regulation
Efficiency
Auto
Transformer
Three Phase
Transformer
Transformers
Voltage regulation and efficiency of a transformer. All day
efficiency of a distribution transformer.
Auto Transformer (principle of operation, equivalent
circuit, advantages and disadvantages)
Three Phase Transformer
Next Class
AC/DC Converter
Thank you!!
For Further Reading:
Transformer Engineering: Design and Practice Authors:
S.V. Kulkarni and S.A. Khaparde Publisher: Marcel
Dekker (Taylor & Francis Group), New York, May 2004
ISBN: 0-8247-5653-3
Electric Machinery: A. E. Fitzgerald, C. Kingsley, S. D.
Umans. Publisher: TMH, New Delhi, India, 2009