# The Universal Torque-Slip Curve of an Induction Machine

## The Universal Torque-Slip Curve of an Induction Machine

As is the case with any electric machines, induction machines are reversible. This means that one and the same induction machine can operate as a motor, that is, convert electricity into mechanical energy (motoring action), or as a generator, that is, convert mechan­ical energy into electricity (generating action).

If we wish an induction machine to operate as a generator, we should apply an external mechanical force to its shaft and cause its rotor to revolve at a speed exceeding the synchronous one so that nn1 . Then the rotor will overtake the rotating magnetic field and its conductors will cut the magnetic lines of force in a direction opposite to that in which they cut the flux in motoring. As a conse­quence, the rotor emf and the rotor currents will be reversed in direction. As a result, the force produced by the interaction of the rotating magnetic field with the rotor currents is reversed and acts against the rotation of the rotor. So that the rotor can keep rotating, mechanical energy must be transferred to it from an external source. The magnetizing current remains unchanged, because the condi­tions for a rotating magnetic field to be excited are the same in an induction motor and an induction generator. In the generating mode, however, the power developed by the machine is negative which means that it delivers energy to, rather than draws energy from, the supply line. Now the slip is

s = (nl - n)/nl < 0

The negative slip is an indication of generating action. As the slip increases in magnitude, the inductive reactance of the rotor winding increases, and so does the phase shift between the rotor emf and current. On the other hand, the rotor emf which is proportiona1 to the slip increases and, since the opposing torque of an induction generator is defined in the same way as the driving torque developed by an induction motor, Eq. (14.27),

T = const X ΦrI2 cos φ2

it follows that this torque will be a maximum when the slip, Eq. (14.31), is

scr = -rw2/( ’’leak,l + leak,2)

Any further increase in the negative slip brings about a decrease in the torque. To sum up, the torque-slip curve of an induction gener­ator resembles, in general, that of an induction motor and is actually its extension in the third quadrant of the Carte­sian coordinate system (Fig 30).

An induction generator draws an inductive reactive (magnetizing) current in much the same way as an induction motor does, and so it needs a source of reactive power. In other words, an induction ge­nerator cannot operate on its own. When connected to the generator impairs the overall power supply line, an induction factor of the system.

The situation is different and an induction generator can operate on its own if the required reactive current is supplied by capacitors connected in parallel with the generator. Now at starting the induc­tion generator is self-excited due to the effect of the residual magnet­ization in its magnetic circuit.

An advantage of induction generators is that they are simple in design and to operate .

If an external mechanical force is applied to spin the rotor of an induction machine in a direction opposite to that of its rotating magnetic field, the speed n in the slip equation, Eq. (14.8), will take a "-" sign, so that

s = (nl + n)/nl > 1

The direction of current flow in the rotor winding will remain un­changed, and the rotor will develop a torque opposing the load torque applied to the shaft. Now the machine will he using the mechanic­al energy applied to the shaft and the electric energy drawn from the supply line. This will he braking action. The plot of torque as a func­tion of slip at s > 1 is a direct continuation of the motor characteristThe braking mode is used to bring the machine to a rapid stop or when it is advisable to use an induction machine to brake a driven machine, such as cranes or. hoists when the load is lowered.

An induction motor can be switched into the braking mode by what is called plugging (reverse-current braking). For this purpose one interchanges any two phases of the stator (see Fig 7 a), and this causes the magnetic field to rotate in the opposite direction to the rotor. Now the slip is

s = (nl + n)/nl > 1

and the rotor moves against the field under the action of an extern­al mechanical force (such as the weight of the load being lowered) or by inertia. When the rotor comes to a stop, it is essential to dis­connect the machine from the supply line, or else it will go motoring.