Lecture 12 EE 743 AC Machines Reluctance machines

Lecture 12 - EE 743 AC Machines Reluctance machines - Induction machines Professor: Ali Keyhani

Two-Pole reluctance machines bs axis r as’ r as' r as axis as Single phase r bs' bs as axis as Two phase 2

Two-Pole reluctance machines n n Stator windings are assumed to be sinusoidally distributed For single phase machines excited by an AC current source, the generated flux wave has two opposite rotating mmfs (These motors are used in clocks and some other turntables) 3

Two-Pole reluctance machines n term results in counterclockwise (positive) travelling wave n term results in clockwise (negative) travelling wave 4

Two-Pole reluctance machines n For reluctance machine (Fig. 1), 5

Two-Pole reluctance machines n For two-phase reluctance machines (see Fig. 1), only one constant-amplitude rotating air gap mmf is produced during balanced steady state conditions n Two-phase reluctance machines develop a constant torque at synchronous speed rather than a torque which pulsates about an average value as is the case with single-phase machines 6

Two-pole induction machines bs axis br axis as' r r as' r ar' ar as Single phase ar axis s as axis br' ar ar axis r br ar' bs' r r bs s as axis as Two phase 7

Cutaway Views of Squirrel-cage Induction Motor 8

Two-pole induction machines n n Single and two pole induction machines have identical equivalent orthogonal windings which are sinusoidally distributed (see Fig. 2) Rotor windings are short-circuited Single-phase induction machines are widely used (washers, dryers, furnace fans, etc. ) Recall: 9

Two-pole induction machines n Term #1: positive travelling flux wave n Term #2: negative travelling flux wave Recall: Single-phase induction machines do not develop a starting torque. At the start r=0, Te=0, i. e at start the rotor cannot follow either of the rotating mmfs since it develops as much torque to go in either direction Single-phase induction motors have two stator windings with provision to switch out one of the windings once the rotor accelerates to between 60 to 80 percent of synchronous speed n n n 10

Two-pole induction machines n To provide two phase power from one phase power supply, a capacitor is used during the starting. 11

Two-pole induction machines n For two-phase induction machines, stator n mmfs is a positive travelling flux wave which rotates around the air gap at a speed of e (see Fig. 2 b) Machine rotor windings are short-circuited 12

Two-pole induction machines n n Current flowing in the rotor windings will be due to induction with a frequency of e - r. The rotor currents, iar and ibr will produce an air gap mmf that travels at a speed of e - r relative to the rotor or e relative to a stationary observer. Interactions of mmfr due to rotor and mmfs due to stator will produce torque on the rotor. 13

Three-phase induction machines bs - axis br - axis as' cs ar' br bs bs' ar Te r ar - axis Tl r s cr br' r as - axis cr' cs' as cs - axis cr - axis 14

Three-phase induction machines n Three-phase induction machines have three identical sinusoidally distributed stator and rotor windings. The magnetic axes of the windings are displaced 120 o from each other and rotor windings are short-circuited (see Fig. 3) 15

Three-phase induction machines n n n mmfs is a positive travelling flux wave which rotates around the air gap at a speed of e. mmfr is a positive travelling flux wave which rotates around the air gap at a speed of e- r relative to the rotor. Interactions of mmfr due to rotor and mmfs due to stator will produce torque on the rotor. 16

Three-phase induction machines - dq axis bs - axis br - axis q - axis r ar - axis r s as - axis d - axis cs - axis cr - axis 17