electrical machines – i

ELECTRICAL MACHINES – I

Hans Christian Oersted (1777 – 1851)

1822

In 1820 he showed that a current produces a magnetic field.

X

André-Marie Ampère (1775 – 1836)

French mathematics professor who only a week after learning of Oersted’s discoveries in Sept. 1820 demonstrated that parallel wires carrying currents attract and repel each other.

attract

repel

A moving charge of 1 coulomb per second is a current of 1 ampere (amp).

Michael Faraday (1791 – 1867)Self-taught English chemist and physicist discovered electromagnetic induction in 1831 by which a changing magnetic field induces an electric field.

Faraday’s electromagneticinduction ring

A capacitance of 1 coulomb per voltis called a farad (F)

Joseph Henry (1797 – 1878)American scientist, Princeton University professor, and first Secretary of the Smithsonian Institution.

Discovered self-induction

Built the largest electromagnets of his day

Unit of inductance, L, is the “Henry”

Magnetic Fields and Circuits

A current i through a coil produces amagnetic flux, , in webers, Wb.

BA A

d B A

H = magnetic field intensity in A/m.

v

i

+

-

NB = magnetic flux density in Wb/m2.

B H

= magnetic permeability

Ampere's Law: d iH l

Hl Ni

NiFMagnetomotive force F R

reluctance

Magnetic Flux

Magnetic flux, , in webers, Wb.

1v 2v

2i1i

+ +

- -2N1N

11 flux in coil 1 produced by current in coil 1

12 flux in coil 1 produced by current in coil 2

21 flux in coil 2 produced by current in coil 1

22 flux in coil 2 produced by current in coil 2

1 11 12 total flux in coil 1

2 21 22 total flux in coil 2

Current entering "dots" produce fluxes that add.

Faraday's Law

1v 2v

2i1i

+ +

- -2N1N

1 1 1N

Faraday's Law: induced voltage in coil 1 is

Sign of induced voltage v1 is such that the current i through an external resistor would be opposite to the current i1 that produces the flux 1.

Total flux linking coil 1:

1 11 1( )

d dv t N

dt dt

i

Example of Lenz's law Symbol L of inductance from Lenz

Mutual Inductance

1v 2v

2i1i

+ +

- -2N1N

1 11 121 1 1 1( )

d d dv t N N N

dt dt dt

Faraday's Law

1 21 11 12( )

di div t L L

dt dt

In linear range, flux is proportional to current

self-inductance mutual inductance

Mutual Inductance

1v 2v

2i1i

+ +

- -2N1N

1 21 11 12( )

di div t L L

dt dt

1 22 21 22( )

di div t L L

dt dt

12 21L L M Linear media

1 21 1( )

di div t L M

dt dt

1 22 2( )

di div t M L

dt dt

2 22L L 1 11L LLet

Core losses

Hysteresis losses

Hysteresis losses

Hysteresis losses

Eddy current losses

Eddy current losses

How do we reduce Eddy current losses

SOLID

LAMINATED

Eddy current losses

Eddy current losses in windings

Can be a problem with thick wires- Low voltage machines- High speed machines

Force, torque and power

Universal modeling of terminal characteristic of electro-magnetic devices based on energy balance

Induced EMF

Induced emf could be classified into

two types

Dynamically induced EMF.

Statically induced EMF.

Statically induced emf

In statically induced emf, conductor is stationary with respect to the magnetic field.

Transformer is an example of statically induced emf. Here the windings are stationary,magnetic field is moving around the conductor and produces the emf.

Statically induced emf

• The emf produced in a conductor due to the change in magnetic field is called statically induce emf .It could be classified into two

• 1)self induced emf and 2)mutual induced emf

Dynamically induced emf

This is the EMF induced due to the motion of conductor in a magnetic field.

Mathematically e = Blv volts• e-induced emf• B – flux density of magnetic field in Tesla• l = length of conductor in meters• v- velocity of conductor in m/s

Dynamically induced emf

If the conductor moves in an angle θ,the induced emf could be represented as

e= Blvsinθ

the direction of induced emf is given by

flemmings right hand rule.

Generator is an example of dynamically induced emf.