Download - Lecture Transformers (2)11
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steam generator
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HASNAIN BASHIRKAMRAN ZEB WAQAR UDDIN
Group Members
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Introduction
DEF: A transformer is a static electrical device that transform ac electric power from one voltage level to another voltage level through the action of electromagnetic induction
Frequency Remains constant.
There are two or more stationary electric circuits that are coupled magnetically.
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Transformer Classification
In terms of number of windings1) Conventional transformer: two windings2) Autotransformer: one winding3) Others: more than two windings
In terms of number of phases1) Single-phase transformer2) Three-phase transformer
Depending on the voltage level at which the winding is operated1) Step-up transformer: primary winding is a low voltage (LV)
winding2) Step-down transformer : primary winding is a high voltage
(HV) winding
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Primary and Secondary Windings
A two-winding transformer consists of two windings interlinked by a mutual magnetic field. Primary winding – energized by connecting it to an input source Secondary winding – winding to which an electrical load is
connected and from which output energy is drawn.
Primary winding Secondary winding
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Ideal Transformers
No iron and copper losses No leakage fluxes A core of infinite magnetic permeability and of infinite
electrical resistivity winding resistances are negligible
An ideal transformer is a lossless device with an input winding and an output winding. It has the following properties:
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Ideal Transformers
aii
vv
p
s
s
p
An ideal transformer is a lossless device with an input winding and an output winding.
The relationships between the input voltage and the output voltage, and between the input current and the output current, are given by the following equations.
In instantaneous quantities
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Ideal Transformers
aII
VV
p
s
s
p
Np: Number of turns on the primary windingNs: Number of turns on the secondary windingvp(t): voltage applied to the primary sidevs(t): voltage at the secondary sidea: turns ratioip(t): current flowing into the primary sideis(t): current flowing into the secondary side
aNN
ii
vv
s
p
p
s
s
p
In rms quantities
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Power in an Ideal Transformer
outssppin
outsss
sppin
SIVIVS
QIVaIaVIVQ
inPpIpVpaIapV
ssIsVoutP
sp
ppIpVinP
sinsinsin
coscoscos
cos
Real powerReal power P supplied to the transformer by the primary circuit
Real power coming out of the secondary circuit
Thus, the output power of an ideal transformer is equal to its input power. Reactive PowerThe same relationship applies to reactive Q and apparent power S:
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Transformers
Leakage flux: flux that goes through one of the transformer windings but not the other one Mutual flux: flux that remains in the core and links both windings
LSMS
LPMP p: total average primary flux
M : flux linking both primary and secondary windingsLP: primary leakage fluxS: total average secondary fluxLS: secondary leakage flux
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Excitation Current
Excitation current.The current required to produce flux in the ferromagnetic core and is called excitation current. It consists of two components:
1. The magnetization current Im, which is the current required to produce the flux in the transformer core
2. The core-loss current Ih+e, which is the current required to make up for hysteresis and eddy current losses
E1
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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
Copper (I2R) losses. Copper losses are the resistive heating losses in the primary and secondary windings of the transformer. They are proportional to the square of the current in the windings.
Leakage flux. The fluxes which escape the core and pass through only one of the transformer windings are leakage fluxes. These escaped fluxes produce a self-inductance in the primary and secondary coils, and the effects of this inductance must be accounted for.
Eddy current losses. Eddy current losses are resistive heating losses in the core of the transformer. They are proportional to the square of the voltage applied to the transformer.
Hysteresis losses. Hysteresis losses are associated with the rearrangement of the magnetic domains in the core during each half-cycle. They are a complex, nonlinear function of the voltage applied to the transformer.
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Determining the Values of Components in the Transformer Model
It is possible to experimentally determine the parameters of the approximate the equivalent circuit. An adequate approximation of these values can be obtained with only two tests….
• open-circuit test
• short-circuit test
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Circuit Parameters: Open-Circuit Test
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Circuit Parameters: Short-Circuit Test
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Transformer Voltage Regulation
100
100
loadfullVloadfullVloadnoV
loadfullVloadfullVloadnoVgulationReVoltage%
p
pp
s
ss
The voltage regulation of a transformer is the change in the magnitude of the secondary terminal voltage from no-load to full-load.
Referred to the primary side
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Transformer Efficiency
cos1
1
sslosscorelosscopper
losscorelosscopper
IVPP
PPInputPower
LossesInputPower
LossesInputPowerInputPower
OutputPower
Usually the efficiency for a power transformer is between 0.9 to 0.99. The higher the rating of a transformer, the greater is its efficiency.
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Hysteresis losses
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Eddy Current loss
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Continue…
This loss can be reduced as follows when: a- using high resistive core material, few %
Si b- using a laminated core
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Skin Effect
Penetration depth (skin depth) is defined as the distance from the surface to where the current density is l/e times the surface current density:
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Ferrite Core
o Mixture of iron oxide with oxide or carbonate of manganese and zinc or nickel and zinc
o MnZn (1-2Mhz)o NiZn (1-several 100 MHz)o Resistivity of ferrite material (200-2000)ohm-
cmo Resistivity of metal alloy core (50-150)micro-
ohmo Used in SMPS
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Continue…
Advantages:Lower costlower losses.Disadvantages:Ceramic material (unacceptable in high shock)
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Application of Transformer
For voltage step up (electricity generation station)
Voltage Step down (Industrial machine, House hold appliances)
Impedance matching (loud speakers)For coupling (in different stage of
electronic circuit e.g. amplifying system)For Electrical Isolation
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steam generator
ALLAH NEGHABAN THE END