THE POWER FACTOR IN SINUSOIDAL SYSTEMS (Electric Motor)

4.2
The line current drawn by induction motors, transformers, and other inductive devices consists of two components: the magnetizing current and the power-producing current.
The magnetizing current is that current required to produce the magnetic flux in the machine. This component of current creates a reactive power requirement that is measured in kilovolt-amperes reactive (kilovars, kvar). The power-producing current is the current that reacts with the magnetic flux to produce the output torque of the machine and to satisfy the equation
T = K<PI
where
T = output torque
0 = net flux in the air gap as a result of the magnetizing
current
1 = power-producing current
K = output coefficient for a particular machine
The power-producing current creates the load power requirement measured in kilowatts (kW). The magnetizing current and magnetic flux are relatively constant at constant voltage. However, the power-producing current is proportional to the load torque required.
The total line current drawn by an induction motor is the vector sum of the magnetizing current and the power-producing current. For three-phase motors, the apparent power, or kilovolt-ampere (kVA) input to the motor, is

where
IL = total line current VL = line-to-line voltage
The vector relationship between the line current IL and the reactive component Ix and load component Ip currents can be expressed by a vector diagram, as shown in Fig. 4.1, where the line current IL is the vector sum of two components. The power factor is then the cosine of the electrical angle 6 between the line current and phase voltage.
This vector relationship can also be expressed in terms of the components of the total kilovolt-ampere input, as shown in Fig. 4.2. Again, the power factor is the cosine of the angle 6 between the total kilovolt-ampere and kilowatt inputs to the motor. The kilovolt-ampere input to the motor consists of two components: load power, i.e., kilowatts, and reactive power, i.e., kilovars.
The system power factor can be determined by a power factor meter reading or by the input power (kW), line voltage, and line current readings. Thus,

FIGURE 4.1 Vector diagram of load current for one phase of the motor.

FIGURE 4.2 Vector diagram of power input without a power factor correction.

An inspection of the kilovolt-ampere input diagram shows that the larger the reactive kilovar, the lower the power factor and the larger the kilovolt-ampere for a given kilowatt input.