ELECTRICAL MACHINES I Presented by CH BHARATHI Assoc

ELECTRICAL MACHINES – I Presented by CH. BHARATHI Assoc. Professor DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING VISAKHA INSTITUTE OF ENGINEERING & TECHNOLOGY

Hans Christian Oersted (1777 – 1851) X 1822 In 1820 he showed that a current produces a magnetic field.

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

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. A capacitance of 1 coulomb per volt is called a farad (F) Faraday’s electromagnetic induction ring

Joseph Henry (1797 – 1878) American scientist, Princeton University professor, and first Secretary of the Smithsonian Institution. Discovered selfinduction 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 a magnetic flux, , in webers, Wb. Bgd. A BA A B = magnetic flux density in Wb/m 2. B H H = magnetic field intensity in A/m. = magnetic permeability Ampere's Law: Hgdl Ñ i Magnetomotive force F Ni Hl Ni reluctance F R

Magnetic Flux Magnetic flux, , in webers, Wb. Current entering "dots" produce fluxes that add. 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 total flux in coil 1 12 2 total flux in coil 2 21 22

Faraday's Law i Total flux linking coil 1: 1 N 1 1 d 1 N d 1 Faraday's Law: induced voltage in coil 1 is v 1 (t) 1 dt dt Sign of induced voltage v 1 is such that the current i through an external resistor would be opposite to the current i 1 that produces the flux 1. Symbol L of inductance from Lenz Example of Lenz's law

Mutual Inductance Faraday's Law v 1 (t) N 1 d d N 1 11 N 1 12 dt dt dt In linear range, flux is proportional to current di 1 di 2 v 1 (t) L 11 L 12 dt dt self-inductance mutual inductance

Mutual Inductance di 1 di L 12 2 dt dt di di v 2 (t) L 21 1 L 22 2 dt dt v 1 (t) L 11 di 1 L di 2 v 2(t) M 2 dt dt Linear media L 12 L 21 M Let L 22 di 1 M di 2 v 1 (t) L 1 dt dt L 11

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.