Question

An electric motor has the power P = 45 kW with terminal voltage Ueff = 380 V.
The power factor is cos (φ) = 0.85.
a) Explain the concept of the power factor! What is it?
b) Calculate the apparent power S, reactive power Q, and the currents Ieff, IW (active current) and IB (reactive current)!
c) What are the consequences for producers and consumers from the existence of reactive power or reactive current?

Answer 1

a)In electrical engineering, the power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor of less than one indicates the voltage and current are not in phase, reducing the average product of the two.

Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of RMS current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power. A negative power factor occurs when the device (which is normally the load) generates power, which then flows back towards the source.

b) P(real power)= 45 KW

Apparent power= S

We know,

cos= power factor= P/S

S=45 KW/ 0.85 =52.94 KW

Q= reactive power= P*tan(arccos(power factor))

Q= 45 KW* tan(31.78) = 27.889 KW

Ieff= P/Ueff= 118.42 amp