13.1 ELEMENTARY CONCEPTS OF ROTATING MACHINES 559the motor. The rotor winding is usually short-circuited through external resistances that can be
varied. A squirrel-cage rotor has a winding consisting of conducting bars of copper or aluminum
embedded in slots cut in the rotor iron and short-circuited at each end by conducting end rings.
The squirrel-cage induction machine is the electromagnetic machine most widely used as a motor
because of its extreme simplicity and ruggedness. Although the induction machine in the motor
mode is the most common of all motors, the induction machine has very rarely been used as
a generator because its performance characteristics as a generator are not satisfactory for most
applications; however, it has recently been used as a wind-power generator. The induction machine
with a wound rotor is also used as afrequency changer.
The polyphase induction motor operates with polyphase alternating current applied to the
primary winding, usually located on the stator of the polyphase machines. Three-phase motors are
most used commercially in practice, whereas two-phase motors are used in control systems. The
induction machine has emf (and consequently current) induced in the short-circuited secondary
(or rotor) winding by virtue of the primary rotating mmf. Such a machine is then singly excited.
The induction machine may be regarded as a generalized transformer in which energy conversion
takes place, and electric power is transformed between the stator and the rotor along with a change
of frequency and a flow of mechanical power.
Let us assume that the rotor is turning at a steady speed ofnr/min in the same direction as
the rotating stator field. Let the synchronous speed of the stator field ben 1 r/min, as given by
Equation (12.2.9), corresponding to the applied stator frequencyfsHz, orωsrad/s. It is convenient
to introduce the concept ofper-unit slipSgiven by
S=synchronous speed−actual rotor speed
synchronous speed=n 1 −n
n 1=ωs−ωm
ωs(13.1.6)The rotor is then traveling at a speed ofn 1 −norn 1 Sr/min in the backward direction with
respect to the stator field. The relative motion of the flux and rotor conductors induces voltages
of frequencySfs, known as theslip frequency,in the rotor winding. Thus, the induction machine
is similar to a transformer in its electrical behavior but with an additional feature of frequency
change. The frequencyfrHz of the secondary (or rotor) currents is then given by
fr=ωr
2 π=Sfs (13.1.7)At standstill,ωm=0, so that the slipS=1 andfr=fs; that is, the machine then acts as a simple
transformer with an air gap and a short-circuited secondary winding. A steady starting torque is
produced because the condition for energy conversion at constant torque is satisfied; hence the
polyphase induction motor is self-starting. At synchronous speed, however,ωm=ωs, so that the
slipS=0 andfr=0; no induction takes place because there is no relative motion between flux
and rotor conductors. Thus, at synchronous speed, the value of the secondary mmf is zero, and
no torque is produced; that is, the induction motor cannot run at synchronous speed. The no-load
speed of the induction motor is usually on the order of 99.5% of synchronous speed so that the
no-load per-unit slip is about 0.005, and the full-load per-unit slip is on the order of 0.05. Thus,
the polyphase induction motor is effectively a constant-speed machine.
An induction machine, connected to a polyphase exciting source on its stator side, can be
made to generate (i.e., with the power flow reversed compared to that of a motor) if its rotor is
driven mechanically by an external means at above synchronous speed, so thatωm >ωsand
the slip becomes negative. If the machine is driven mechanically in the direction opposite to
its primary rotating mmf, then the slip is greater than unity and the machine acts as a brake. For
example, let the machine be operating normally as a loaded motor; if two of the three phase supply
lines to the stator are reversed, the direction of the stator rotating mmf will reverse. The rotor will