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ΜΕΤΑΣΧΗΜΑΤΙΣΤΕΣ
TRANSFORMERS
Reference : http://www.osha.gov/SLTC/etools/electric_power/images/transformer2.jpg
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DEFINITION
• Device used to transfer energy from
primary winding to secondary winding by
electromagnetic induction.
• Based on Faraday’s Law of induction
Where:-
ε – EMF (V)
ΦB – Magnetic flux (Wb)
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TRANSFORMER USES
• Impedance matching
• Electrical Isolation
• AC power transmission
 STEP-UP
Transformer
 STEP-DOWN
Transformer
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HISTORY
• 1831 – Michael Faraday invented the
Induction Ring.
• 1881 – Lucien Gaulard and John Gibbs
exhibited a device called secondary
generator.
• 1885 – William Stanley developed the fist
commercially used practical device while
working for Westinghouse Electric
Company in US.
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INDUCTION THEORY
• Transformers behaviour is based
on Faraday’s Law of Induction
Where:-
ε – EMF (V)
N – No of turns of wire
ΦB – Magnetic flux (Wb)
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INDUCTION THEORY
Reference:
http://www.tpub.com/doeelecscience/electrical%20science2_files/image1053.jpg
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TRANSFORMER MODELS
Ideal Transformer
ip(t)
Np
Ns
is(t)
+
+
Vp(t)
Vs(t)
-
-
Np = No of windings on the primary
ip = Current into the primary
Vp = Voltage across the primary
Ns = No of windings on the secondary
is = Current out from the secondary
Vs = Voltage across the secondary
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Primary and Secondary
Relationship
VP = NP = a = iS
VS
NS
iP
Note;
a < 1 = Step up transformer
a > 1 = Step down transformer
Voltage and current angles are NOT affected
hence, θP = θS = θ
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LOSSES
• Transformers have losses and these
losses must come into consideration.
• Copper losses (I^2 R)
• Leakage Flux losses
• Core losses
 Eddy
currents
 Hysteresis
losses
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REAL TRANSFORMER LOSSES
ip(t)
Lp
Rp
Vp(t)
Ls
jXm
Rc
Np
Ns
is(t)
Rs
Vs(t)
• Copper losses (I^2 R)
• Leakage Flux losses
• Core losses
 Eddy
currents
 Hysteresis losses
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EQUIVALENT CIRCUIT
Leqp
Vp
Rc
Is/a
Reqp
jXm
aVs
Approximate Transformer Model referred
to the primary side
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TYPES
Auto-Transformer
– Used to change a desirable voltage by only a small
amount. For example: 120/132 V
IH
VSE
+
VL
+
ISE
NSE
IL
VH
NC
-
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TYPES
Three Phase Transformers
Three phase transformers
can be constructed in two
different ways i.e. :1. A three phase bank consists
of three single phase
transformers.
2. Three windings wrapped
around a common core.
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THREE PHASE TRANSFORMER
CONNECTIONS
Delta – wye (Δ – Y)
Wye – delta (Y- Δ)
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Delta – delta (Δ – Δ)
Wye – wye (Y – Y)
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TYPES
•
Two types of special purpose transformers
used in power systems for taking
measurements.
– Potential Transformer
– Current Transformer
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EFFICIENCY
• Efficiency (η) is the ratio of the power out to
the power in of a transformer.
– η in an Ideal transformer, no power losses
• PIN = VPIP cos θP
• POUT = VSIS cos θS
• PIN = POUT = VPIP cos θP = VSIS cos θS
• SOUT = SIN = VPIP = VSIS
• ηIdeal = 100%
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Efficiency for a single phase
real transformer
• As mentioned previously, losses occur in a real
transformer and these losses must be taken into
count.
• Hence, ηReal = POUT x 100%
PIN
=
POUT
x 100%
POUT + PLOSS
=
VSIS cos θS_________
VSIS cos θS + i2R + (VP/a)2
RC
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VOLTAGE REGULATION
• Voltage regulation (VR) is the ability of a system
to provide near constant voltage over a wide
range of load conditions. Also it compares the VO
at no load to VO at full load.
• An Ideal transformer has a voltage regulation,
VR = 0%
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