DEFINITIONDevice 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)
TRANSFORMER USESImpedance matching
Electrical Isolation
AC power transmission STEP-UP Transformer STEP-DOWN Transformer
HISTORY1831 – 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.
INDUCTION THEORYTransformers behaviour is based on
Faraday’s Law of Induction
Where:-
ε – EMF (V)
N – No of turns of wire
ΦB – Magnetic flux (Wb)
INDUCTION THEORY
Reference: http://www.tpub.com/doeelecscience/electrical%20science2_files/image1053.jpg
TRANSFORMER MODELSIdeal Transformer
-
Vs(t)
Np Ns+
Vp(t)
ip(t)
-
+
is(t)
Np = No of windings on the primary Ns = No of windings on the secondary
ip = Current into the primary is = Current out from the secondary
Vp = Voltage across the primary Vs = Voltage across the secondary
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
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
REAL TRANSFORMER LOSSES
Vp(t) jXm
Rp
Vs(t)Rc
is(t)Lp Ls
Np
Rsip(t)
Ns
Copper losses (I^2 R) Leakage Flux losses Core losses
Eddy currents Hysteresis losses
EQUIVALENT CIRCUIT
jXm aVsRc
Is/aLeqp Reqp
Vp
Approximate Transformer Model referred to the primary side
TYPESAuto-Transformer
Used to change a desirable voltage by only a small amount. For example: 120/132 V
IH+
-
+
-
VL
VSE
NC
NSE
VH
ISE
IL
TYPES
Three phase transformerscan be constructed in twodifferent ways i.e. :-1. A three phase bank consists
of three single phase transformers.
2. Three windings wrapped around a common core.
Three Phase Transformers
Reference : Electric Machinery and Power System Fundamentals, Stephen J. Chapman
THREE PHASE TRANSFORMER CONNECTIONS
Delta – wye (Δ – Y)
Wye – delta (Y- Δ)
Delta – delta (Δ – Δ)
Wye – wye (Y – Y)
Reference : Electric Machinery and Power System Fundamentals, Stephen J. Chapman
TYPES Two types of special purpose
transformers used in power systems for taking measurements. Potential Transformer Current Transformer
Reference : Electric Machinery and Power System Fundamentals, Stephen J. Chapman
EFFICIENCYEfficiency (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%
Efficiency for a single phase real transformerAs 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
• 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.
VOLTAGE REGULATION
• An Ideal transformer has a voltage regulation, VR = 0%Reference : http://en.wikipedia.org/wiki/Voltage_regulation
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