Upload
truongdung
View
219
Download
1
Embed Size (px)
Citation preview
1Week © Vocational Training Council, Hong Kong.
Basic Operating Principles Basic Operating Principles of Transformersof Transformers
EEE3441 Electrical MachinesDepartment of Electrical Engineering
││││ Lecture ││││
2Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Basic operating principles of following transformers
are introduced
� Single-phase Transformers
� Three-phase transformers
� Auto-transformers
� Instrument transformers
In this Lecture In this Lecture …………
3Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
• Transformer is a machine that has no moving parts
but is able to transform alternating voltages and
currents from high to low (step-up transformer )
and vice versa (step-down transformer).
• Transformers are used extensively in all branches of
electrical engineering from the large power
transformer employed in the T&D network to the
small transformer of an electronic amplifier.
Introduction
5Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Single-phase transformer
• A simple single-phase transformer consists of
two coils wound on a closed iron core as shown:
Secondary winding
Primary winding
6Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Construction of Single-phase transformer
Basically, a transformer has two windings:
• primary winding
• Secondary winding
Each winding consists of many turns and are wound
on a laminated iron core. The iron core is insulated
with the windings. The core itself forms a closed
iron magnetic circuit. Consequently, the windings
encircle the core and the core encircles the
windings.
7Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
• Core type
windings are wound around two legs of a magnetic core.
• Shell type
windings are wound around the center leg of a three-legged magnetic core
8Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Transformer action - Ideal Transformer
1. The winding resistances are negligible (R = 0)
2. All fluxes are confined to the core and link both windings (leakage flux = 0)
3. Permeability of the core is infinite (Iφ1= 0)
4. No eddy current and hysteresis losses
Assumptions:
9Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
When an A.C. voltage v1 applied to the primary winding:
The core flux also links the secondary winding, then:
From equations (1) and (2):
)1(1 −−−−−−−==dtdΦ
Ne 11v
)2(2 −−−−−−−==dtdΦ
Ne 22v
aNN
2
1 ==2
1
v
v
Transformer action - Ideal Transformer (cont)
10Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
• when a load is connected to the secondary winding, i2
will flow and will provide an mmf N2i2 for the core.
• i1 would immediately flow to establish another mmf
N1i1 to oppose N2i2 since no mmf is required to
establish a flux in the ideal core
a1
NN
1
2 ==2
1
i
i
02211 =− ii NN 2211 ii NN =
Then:
Transformer action - Ideal Transformer (cont)
⇒
11Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
If the supply voltage is sinusoidal, then in rms values:
2211 IVIV =∴
aNN
VV
2
1
2
1 ==a
1
N
N
I
I
1
2
2
1 ==
VAoutputVAinput =
Transformer action - Ideal Transformer (cont)
Since and
12Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Emf Equation of a Transformer (1/2)
Φ = Φm sin2πft instantaneous value of induced emf/turn
= − dΦ/dt volts
= − 2πfΦm cos2πft volts= 2πfΦm sin(2πft − π/2) volts
Transformer action - Ideal Transformer (cont)
13Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
rms value of induced emf / turn
= 0.707 x 2πfΦm volts
= 4.44 x fΦm volts
Hence E1 = 4.44N1fΦm volts
E 2 = 4.44N2fΦm volts
2
1
2
1
NN
EE =
Emf Equation of a Transformer (2/2)
Transformer action - Ideal Transformer (cont)
14Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Phasor Diagram of Ideal Transformer action under No-load
Φ
Im1
E1
E2=(N2 / N1) x E1
V1 = – E1
15Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Example 1
A 200kVA, 6600/400V, 50 Hz single-phase transformer has
80 turns on the secondary. Calculate:
a) the approximate values of the primary and secondary
currents;
b) the approximate number of primary turns; and
c) the maximum value of the flux.
Ans: 30.3A, 500A; 1320; 0.0225Wb
16Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Features of Practical Transformer
• the windings have resistances
• not all windings link the same flux
• permeability of the core material is not infinite, and
core losses occur when the core material is subjected
to time-varying flux
Losses in Practical Transformer
• Copper losses ( I2R losses )
• Iron losses ( Core losses )
17Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Transformer Losses
• Copper losses ( I2R losses )
Power losses due to the resistances in the primary and
secondary windings
PC = I12 R1 + I2
2 R2
• Iron losses ( Core losses )
a. Hysteresis loss
Power loss due to the alignment of magnetic dipoles
in the iron core
b. Eddy current loss
Power loss due to the induced eddy current
circulating in the iron core
18Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
In order to analyze transformer at different loading conditions,
based on the principles of transformer action, equivalent
circuit of practical transformer is worked out for calculation.
Parameters of Transformer
The four essential parameters of the transformer
equivalent circuit are then measured by
• Open-circuited test, and
• Short-circuited test on transformer
Req Xeq
RC Xm
Equivalent Circuit of Transformer
19Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
A set of three similar single phase transformers may be
connected to form a three-phase transformer (three-phase
transformer bank). The primary and secondary windings may be
connected in either star or delta configurations.
Three-Phase Transformer
20Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Ease of transportation
Inefficient magnetic circuit, less efficient
Higher capital cost than a single one
1-phase of the transformer at fault, the other two are not affected
Characteristics of Three-phase Transformer Bank
21Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Usually 3-limb core structure
5-limb core may be used to reduce the overall height
of a 3-limb core
Magnetic flux shares the magnetic circuit
Fault on one-phase very likely affects the other two
phases
Construction of Three-phase Transformer
22Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Three-phase Transformer
3 limb core structure 3-phase transformer
23Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
25kV Alternator
Customers
Three-phaseTransformers in T&D System
24Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
3-Ø 11kV/380V Tx
LV Side HV
Side
25Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Pole-mounted 3-Ø 11kV/380V Tx
11kV/380V 3-phase transformer fixed at a wooden pole
26Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
1. STAR/delta ( Yd )
1
2
2
1
2
1
2
1
.N3
N
.a3
1II
;N
.N3.a3
VV ====
Turn ratio/Voltage ratio/Current ratio of 3-phase transformer (1/4)
27Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
2. DELTA/star ( Dy )
1
2
2
1
2
1
2
1
N.N3
a3
II
;.N3
N
3
aVV ====
Turn ratio/Voltage ratio/Current ratio of 3-phase transformer (2/4)
28Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
3. DELTA/delta ( Dd )
1
2
2
1
2
1
2
1
NN
a1
II
;NN
aVV ====
Turn ratio/Voltage ratio/Current ratio of 3-phase transformer (3/4)
29Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
4. STAR/star ( Yy )
1
2
2
1
2
1
2
1
NN
a1
II
;NN
aVV ====
Turn ratio/Voltage ratio/Current ratio of 3-phase transformer (4/4)
30Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Auto-transformer
• transformer having a part of
its windings common to the
primary and secondary
• when a load is connected
across b and c, then a current
I2 will flow through the load.
The current I2 will produce an
m.m.f. in the core which will
be balanced by a current I1flowing in the complete
winding
31Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
The voltages and currents are
related by the same turns ratio
as in a two-winding transformer:
aNN
VV
2
1
2
1 ==
a1
NN
II
1
2
2
1 ==
Auto-transformer
32Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Single-phase Auto-transformer
33Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Three-phase Auto-transformer
34Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Example 2
A 1φ, 100 kVA, 2000/200 V two-winding transformer is
connected as an autotransformer as shown such that more than
2000 V is obtained at the secondary. The portion ab is the 200
V winding, and the portion bc is the 2000 V winding. Compute
the kVA rating as an autotransformer.
35Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Example 2 (cont)
The current rating of the winding are:
AIab 500200
000,100 ==
AIbc 50000,2
000,100 ==
Therefore, for full-load operation of the autotransformer, the terminal currents are:
AIH 500=
AIL 55050500 =+=
36Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Example 2 (cont)
Now, VL = 2000V and VH = 2200V
Therefore,
)ans(11001000
5002200|kVA H =×=
)ans(11001000
5502000|kVA L =×=
Note: A 1φ, 100 kVA, two-winding transformer when connected as an autotransformer can deliver 1100 kVA.
37Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Advantages of Auto-transformer
• It effects a saving in winding material (copper or aluminum), since the secondary winding is part of the primary current.
• Lower copper loss, therefore efficiency is higher than in the two winding transformer.
• Lower leakage reactances, lower exciting current.
• Variable output voltage can be obtained.
38Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Disadvantage of Auto-Transformer
• There is a direct connection between the primary and secondary sides.
• Should an open-circuit develop between points b andc, the full mains voltage would be applied to the secondary.
• The short-circuit current is much larger than for normal two-winding transformer
39Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Application of Auto-transformer
• Boosting or bucking of a supply voltage by a small amount. (The smaller difference voltage between the output and input voltages the greater is the saving of winding material.)
• Starting of a.c. machines, e.g. induction motor, where the voltage is raised in two or more steps from a small value to the full supply voltage.
• Continuously variable a.c. supply voltages, normally connected between a low voltage supply in and a high voltage supply out.
• Production of very high voltages, e.g. 275kV and 400kV grid system
40Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Instrument Transformers
� Instrument transformers are used to reduce the voltage or
current magnitudes so that the measuring ranges of
measuring instruments can be extended.
� Measuring Instruments are connected to the secondary of
the transformers.
� The measured values should then be multiplied by the
appropriate turns ratio to get the actual primary values.
1. Voltage Transformer VT (or PT)
– N1/N2 is large and standard 110 V at the secondary.
2. Current Transformer CT
– N1/N2 is small and standard 5 A or 1A at the secondary.
41Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Voltage Transformer (VT)
• Fundamentally similar in principle to power transformers
but with rated outputs in VA rather than kVA or MVA.
• Operating at full supply voltage, the secondary current is
very small so that the transformers may be regarded in the
same way as a power transformer on no load.
Current Transformer (CT)
• Transforms large primary current value in terms of its
magnitude and phase to a smaller secondary current value.
• the secondary value is directly proportional to the primary
value.
• Nominal CT ratio (60~3000A/5A, 30~1000A/1A)
42Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Protection CT
• Nominal CT ratio (1000/5, 100/5)
• Required to operate at many times full load current.
Linearity under these conditions is not of great importance.
• The essential point is that saturation must be high enough to
drive the magnetizing current and the secondary current
under fault condition.
Ring type CT terminal Markings
P1
P2
S1
S2
Ring type CT
Primary
Secondary
Insulation
Iron area
43Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Metering CT
• For non-protection purpose
• Metering CTs need perform very accurately but only over the
normal range of load up to about 120% full load current.
44Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
Reasons for using Instrument Transformer
• Do not require special designed instruments for h.v. or heavy current measurements (the instrument ranges could be standardized)
• Electrical isolation from the primary (h.v. side) is achievable
• For safety reason, one terminal of the secondary winding can be earthed
45Week © Vocational Training Council, Hong Kong.
EEE3441 Electrical Machines
About the Use of Instrument Transformer
• may have turns ratio error
• phase shift may exist between primary and secondary measuring quantities.
• CT is actually a step-up transformer with very large turns ratio (eg 500/1), excessive voltage will exist between the secondary terminals if they were left open.
� NEVER LET THE SECONDARY OF A C.T. OPEN-CIRCUITED