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@ipmishra
Basic Electrical Engineering KEE101/201
@ipmishra
Text Book
(1) I. J. Nagrath and D. P. Kothari
Basic Electrical Engineering- Tata McGraw Hill
Reference Books:
(2) Alexander S. Langsdorf
Theory of Alternating Current Machinery-TMGH
(3) D. P. Kothari , I. J. Nagrath
Electric Machines-Tata McGraw Hill
Transformers
@ipmishra
Km
We understand electrical machines as electro-mechanical energy conversion devices.
Transformer
Transformer is not really an electro-mechanical energy conversion device
β¦β¦β¦.. It basically converts Voltage!
So first we have to understandβ¦β¦.
β¦β¦β¦..why voltage transformation isnecessary??
@ipmishra
The power industry survives on the economics ofcost recovery.
The larger the power plant is, the more economicalpower generation is.
Large power plants may be built at the locationswhere resources like coal or water or gas etc areavailable in abundance.
These may be at very far places from the loadcenters.
So the power needs to be transported over the longdistances from generation stations to load centers.
Transformer
@ipmishra
Lines are designed to operate at constant current density J
π = β΄π
π= β΄
π
πΌπ½
πππππ πππ π πππ πππ€ππ πΏππ π ππ = πΌ2π
πππππ πππ π πππ πππ€ππ πΏππ π ππ = πΌ2β΄π
πΌπ½
πππππ πππ π πππ πππ€ππ πΏππ π ππ = πΌ β΄ π π½
πππππ πππ π πππ πππ€ππ πΏππ π ππ =π
πβ΄ π π½
ππ =π
ππ(πΆπππ π‘πππ‘)
So to reduce line loss ππ we need to increase Voltage.
Why need high Transmission Voltage
@ipmishra
It is not convenient to generate at high voltage say at 400 kV. Generation is normally done at 11 or 22 kV and not more than that.
Therefore Voltage needs to be stepped up for transmission.
It is not convenient and safe to design common load devices which operate at high voltages
So we need to step down the transmission voltage.
Thatβs why we need Transformer !!!!
Why need Transformer
@ipmishra
Of course the transformer losses come into picture.
But fortunately we have the transformer efficiency more than 85 % in normal cases.
So general conception is that we need to have a power system as:
Why need Transformer
@ipmishra
Transformer in Power System
@ipmishra
How to transform Voltage?
Simplest method is to use potential divider
How to transform Voltage ?
β’ But here we cannotstep up the voltage
β’ And there will behuge losses inresistance
@ipmishra
Next option is to use a coil (Inductor)β’ Now it is low loss
method We may stepup the voltage also ifwe interchange theposition of load andsource
β’ possibility of damageto the load duringshort circuit of A to Cor fault.
How to transform Voltage ?
@ipmishra
The circuit was basically known as auto transformer.
Now as magnetic circuits do not need physical connection, we may separate these two coils and couple them magnetically to do the same function.
Less Probability of Damage to the load during short circuit of two coil terminals.
How to transform Voltage ?
@ipmishra
Magnetic Circuits
AT any point P near to a wire carrying current i:
β’ The Magnetic Field intensity vector will be π»and
β’ Magnetic flux density vector will be π΅
π΅ = πππππ»
@ipmishra
Magnetic Circuits
The Magnetic flux density at the point P due to an incremental length of wire dl will be given by Biot Savartβs Law as :
ππ΅ =ππππ4Ο
ππΤ¦π π₯ Τ¦π
π3
The flux density due to wire of length l will be given by the integral over length l.
π΅ = ΰΆ»ππππ4Ο
ππΤ¦π π₯ Τ¦π
π3
@ipmishra
As solution of magnetic circuit using Biot Savart is not convenient we will use another method which is Amperes Circuital Law.
According to this law the Line integral of magnetic field intensity along a closed path will be sum of all the currents enclosed within the loop.
.π»Χ― πΤ¦π=I
Magnetic Circuits
@ipmishra
Magnetic Circuits
We have a core of regular shape on which some winding is put.
Here π. π = π». π or π» =ππ
π
@ipmishra
π» =ππ
π
Magnetic Circuits
β’ So finding out B is relatively easier in thisway.
β’ we have assumption that due to highpermeability of iron core all the flux isconfined to the core
β’ Hence leakage flux outside the core innegligible
π΅ = πππππ»
@ipmishra
Magnetic Circuits : Analogy with Electrical Circuit
π = π©.π¨
π = πππππ―.π¨
π = πππππ΅π
π. π¨
π =π΅ππ
πππππ¨
π =π΅π
π½
π =π΄π΄π
π½
π΄π΄π = π.π½ Compare with π½ = π°. πΉ (Elect Ckt)
@ipmishra
β’ If DC is applied fluxwill be dc. If ac isapplied it willalternate
β’ Faradayβs Law ofElectromagneticInduction:
Emf induced will beequal to the rate ofchange of flux.
If AC voltage is applied in a coil wound over a
core: π = ππ cosβ΅π‘
π = πππ
ππ‘π = πβ΅ππ sinβ΅π‘π = π2ππππ sinβ΅π‘πΈπ = π2ππππ
πΈπππ =π2ππππ
2πΈπππ = 4.44ππππ
@ipmishra
Ideal Transformer is a conceptual Device with following Assumptions:
Coil resistance is zero (Lossless)
Core material has infinite permeability
No flux Leakages (All flux is linked with the core)
No eddy current losses, No Hysteresis Losses.
Ideal Transformer
@ipmishra
Principle of Operation of a conceptual Ideal Transformer
Ideal Transformer
@ipmishra
We must understand that there is no such thing likeβIdeal Transformerβ. It is only a conceptual device.
If an ac voltage is applied at one side terminals oftransformer, This side is known as primary side.
Another side is called Secondary side.
Secondary side : if terminals are left openthen transformer is said to be at βNo Loadβ
Secondary side : If Load is connected acrossthe terminals the transformer is said to be βOn Loadβ
@ipmishra
π½π = π¨ππππππ ππ π½ππππππ(πΉπ΄πΊ)
π¬π = π. ππππππ΅π
π¬π = π. ππππππ΅π
π¬π = π°ππ ππππ π½ππππππ ππ π·ππππππ(πΉπ΄πΊ)
π¬π = π°ππ ππππ π½ππππππ ππ πΊπππππ πππ(πΉπ΄πΊ)
π½π = π»πππππππ ππ ππππππ πππ π½ππππππ(πΉπ΄πΊ)
π¬π
π¬π=
π΅π
π΅π=
π½π
π½π
Ideal Transformer on Load
@ipmishra
Excitation current is zero for primary Ni
π°π = πΊπππππ πππ πππππππ ππππ ππππ ππ πππππππππ
π΅ππ°π = πΊπππππ ππππππ
π΅ππ°π = π·ππππππ πππππππ πππ
π΅ππ°π = π΅ππ°π
π΅π
π΅π=
π°π
π°π
Draw Phasor Diagram
Ideal Transformer on Load
@ipmishra
Coil resistance is zero (Lossless)
Core material has infinite permeability
No flux Leakages (All flux is linked with the core)
No eddy current losses, No Hysteresis Losses.
Coil resistance is present though it is low.
Core material has finite permeability
Some Flux Leakages occur through air. Represented by Leakage reactance.
Eddy current and Hysteresis Losses are present. (core or Fixed Losses)
Ideal Vs Practical Transformer
@ipmishra
Practical 1-Phase Transformer: Construction
@ipmishra
Transformer: Construction
@ipmishra
Transformer: Construction
@ipmishra
3 Phase Transformer: Construction
@ipmishra