AC MACINERY FUNDAMENTALS

Generators & Motors

Composition of an AC machine

Stator

Cylindrical Rotor Salient-Pole Rotor

Air Gap

CopperCoils

Magnetic field production by current in a coil

• An AC current flow in a coil produces an alternating magnetic field according to Ampere’s Law:

where

tIi pa ωsin=

ℜ=Φ p

p

NI

tpa ωφ sinΦ=

Induced voltage in a coil by a rotating magnetic field

• If a magnetic field Ф in rotated within a coil at an angular speed ω, it will induce a voltage at the coil terminals according to Faraday’s Law:

tN

tdtdN

dtdNe v

ωω

ω

sin

)cos(

Φ=

Φ−=

Φ−=

Rotating Magnetic Field• A set of balanced AC currents

• Produces a set of pulsating flux densities

The total stator flux density is constant and rotates with speed ω.

tIi pa ωsin=

)120sin( opb tIi −= ω

)120sin( opc tIi += ω

tBb pa ωsin=)120sin( o

pb tBb −= ω)120sin( o

pc tBb += ω

])(cos)[(sin5.1 ytxtBbbbb pcbanetrr ωω −=++=

Relation between electrical frequency and speed of magnetic field rotation

• In a 2-pole machine,

• In a 4-pole machine,

• In an a p-pole machine,

me ωω =

me ωω 2=

120,

2pnfp m

eme =⇒= ωω

Induced torque in an AC machine• Torque is produced by the

interaction of the stator magnetic field and rotor magnetic field.

• Torque may be computed by from the forces induced in the current carrying conductors in the rotor.

αsin2 srilBT = αsinsrBkBT =

Power flow diagram in an AC machine

GENERATOR

MOTOR

Machine efficiency, voltage and speed regulation

• Efficiency (motor and generator)

• Voltage regulation (generator)

• Speed regulation (motor)

%100*in

out

PP

=η

%100*fl

flnl

VVV

VR−

=

%100*fl

flnl

nnn

SR−

=