# The Power Balance of an Induction Motor

## The Power Balance of an Induction Motor

The total (apparent) power of an induction motor is

S = P1 + jQl = 3V1I1 cos φ1 + j3V1I1 sin φ1

where P1 is its active power and Q1 is it reactive power.

The active power P1 defines the average power associated with the irrever­sible conversion of the electric energy drawn by the motor from the supply line into mechanical, thermal and other forms of energy.

The reactive power Q1 defines the maximum time rate of energy exchange between the supply source and the mag­netic field of the motor, Eq. (2.52).

The active power and efficiency of an induction motor. The way in which elec­tric power is converted in an induction motor is illustrated in Fig. 20. In this diagram, P1 = 3V1I1 cos φ1 is the power drawn by the motor from a three phase supply line . Pw1 is the power lost as heat in the stator conductors. The remaining power, Prf is converted to the power of a rotating magnetic field. Pc is the core loss which includes hysteresis and eddy-current losses in the stator core. The rotor core loss is of no practical importance because at the rotor frequency f2 (1-3 Hz) hysteresis and eddy-current losses in the rotor core are negligible.

The remainder of the rotating magnetic field power is the elec­tromagnetic power of the rotor

Pem = Prf - Pc

On substracting the power lost as heat in the rotor conductors, Pw2 from Pem we obtain the mechanical power developed by the rotor, Pm . Hence

Pm = P1 - PW1 - Pc - PW2

However, the useful mechanical power available at the motor shaft, P2 is less than the developed mechanical power Pm by the pow­er lost through windage and friction, Pwf , so

P2 = Pm - Pwf

The ratio of the available mechanical power P2 to the active pow­er drawn from the supply line, P1 gives the efficiency of an induc­tion motor

η = P2/P1

Under rated operating conditions the efficiency of present-day induction motors is 80%-95%.

The reactive power and power factor of an induction motor. The reactive power Ql is associated with the reversible exchange of ener­gy between the magnetic field of the motor and the supply line. The existence of a magnetic field is essential to the operation of an induc­tion motor, so reactive power is inevitable.

In the design and operation of induction motors, it is important to know the relation between active and reactive power. This rela­tion is defined in terms of the power factor

cos φ1 = P1/ √(P21+ Q21)                                      (14.21)

As follows from an analysis of Eq. (14.11b), when the stator-phase terminal voltage Vl is constant and IlIl,rtd the magnetic flux Φr associated with the rotating magnetic field of the machine is like­wise constant and independent of load. This implies that the ener­gy stored in the magnetic field of an induction motor and the reac­tive power are constant, too, and independent of load. However, as the load is increased, the active power of an induction motor goes up. Therefore, it follows from Eq. (14.21) that an increase in load causes the power factor of the machine to increase too. If, at no load the power factor of an induction motor is 0.1-0.15, it usually goes up to 0,8-0,9 at rated load.