Research And Insight

# Power factor

The motor power factor is the phase angle between voltage and current (cosφ). cos phi (φ) is used, among other purposes, to calculate the power consumption of a motor.

Power consumption is of high importance for pumps. For pumps with standard AC motors, the power input is found by measuring the input voltage and input current and by reading the value cosφ at full load on the motor name plate. Cosφ is the phase angle between voltage and current. Cosφ is also referred to as power factor (PF). The power consumption P1 can be calculated by the formulas shown below depending on whether the motor is a single-phase or a three-phase motor.

AC single-phase motor, e.g. 1 x 230 V

P1 = U × I × cosφ

AC three-phase motor, e.g. 3 x 400 V

P1 = × U × I ×cosφ

The power curve shows the power consumption of the pump at a given flow.

P (power) can be calculated if η is known by using the following equation:

__ρ x g x H x Q __

P = η

P = power [W]

ρ = density [kg/m^{3}]

g = acceleration due to gravity [m/s^{2}], ‘9.81’ is normally used as the value for g.

H = head [m]

Q = flow [m^{3}/s]

η = efficiency (has no unit)

The following equation is used to get a quick but not accurate calculation of the power:

__Q x H x 2.73 __

P = η

P = power [W]

H = head [m]

Q = flow [m^{3}/h]

η = efficiency (has no unit)

ρ and g are a part of the ‘2.73’ factor, where ρ = 1000 [kg/m^{3}] (water at 4 °C) and g = 9.81[m/s^{2}]. Q is in [m^{3}/h] instead of [m^{3}/s] and is also a part of the ‘2.73’ factor.

Get the motor power factor from a calculation of the power consumption shown on a power curve using the information on the Grundfos pump nameplate.