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Typical motor power factor

The power factor (PF) in an alternating current system is the ratio between active power, which performs useful work, and the apparent power supplied. For induction electric motors, the power factor is always inductive and less than one, since part of the energy is used for magnetizing the magnetic field, without generating mechanical work.

Power Factor Formula

Section titled “Power Factor Formula”

The general expression for power factor is the quotient between active and apparent power, which coincides with the cosine of the phase angle between voltage and current.

PF = cos(φ) PF = P / S

For a three‑phase motor, the formula relates directly to line voltage and current:

PF = P / (√3 × U × I)

Variable Meaning Unit
PF Power factor dimensionless
φ Phase angle between voltage and current radians / degrees
P Active or real power W (watt)
S Apparent power VA (volt‑ampere)
U Line voltage V (volt)
I Line current A (ampere)

Typical Power Factor Values in Electric Motors

Section titled “Typical Power Factor Values in Electric Motors”

Induction motors exhibit a very low power factor at no load and improve substantially as full load is approached. The following table shows indicative values for three‑phase 1800 rpm motors.

Power range Speed PF no load PF at 1/4 load PF at 1/2 load PF at 3/4 load PF at full load
0 – 5 hp (0 – 3.73 kW) 1800 rpm 0.15 – 0.20 0.5 – 0.6 0.72 0.82 0.84
5 – 20 hp (3.73 – 14.9 kW) 1800 rpm 0.15 – 0.20 0.5 – 0.6 0.74 0.84 0.86
20 – 100 hp (14.9 – 74.6 kW) 1800 rpm 0.15 – 0.20 0.5 – 0.6 0.79 0.86 0.89
100 – 300 hp (74.6 – 223.7 kW) 1800 rpm 0.15 – 0.20 0.5 – 0.6 0.81 0.88 0.91

Power Factor by Industry

Section titled “Power Factor by Industry”

Before applying correction, different industrial sectors operate with characteristic power factors due to the type and number of motors installed.

Industrial sector Uncorrected power factor (%)
Brewery 75 – 80
Cement 75 – 80
Chemical 65 – 75
Electrochemical 65 – 75
Foundry 75 – 80
Forging 70 – 80
Hospitals 75 – 80
Manufacturing (machinery) 60 – 65
Paint 65 – 70
Metallurgy 65 – 70
Coal mining 65 – 80
Offices 80 – 90
Oil pumping 40 – 60
Plastics 75 – 80
Stamping 60 – 70
Steel mills 65 – 80
Textiles 35 – 60

Frequently Asked Questions (FAQ)

Section titled “Frequently Asked Questions (FAQ)”

What is the typical power factor of a 10 hp motor at full load?

Section titled “What is the typical power factor of a 10 hp motor at full load?”
A 10 hp (7.46 kW) motor at full load has a power factor close to 0.86, according to the table for the 5 to 20 hp range.

How does a power factor of 0.7 affect conductor size?

Section titled “How does a power factor of 0.7 affect conductor size?”
With a power factor of 0.7, the conductor cross‑section must be multiplied by 2.04 relative to that required with unity PF, increasing copper weight and Joule losses.

At what power factor value do electric utilities typically apply penalties?

Section titled “At what power factor value do electric utilities typically apply penalties?”
Many supply companies penalize when the power factor is below 0.95, requiring the installation of compensation systems.

What minimum value does the power factor of a motor reach when operating at no load?

Section titled “What minimum value does the power factor of a motor reach when operating at no load?”
A three‑phase induction motor at no load can drop to 0.15 – 0.20, practically consuming only magnetizing current without delivering mechanical power.

What percentage of an 80 kVA transformer capacity is utilized if the load power factor is 0.7?

Section titled “What percentage of an 80 kVA transformer capacity is utilized if the load power factor is 0.7?”
With a power factor of 0.7, the useful active power is only 56 kW, i.e., 70 % of the transformer’s apparent capacity, wasting 30 % in reactive power.

In which industrial sectors are the lowest power factors recorded?

Section titled “In which industrial sectors are the lowest power factors recorded?”
The textile and oil pumping sectors show the lowest values, with ranges of 35 – 60 % and 40 – 60 % respectively, due to the high presence of small induction motors and fluctuating load regimes.

References

Section titled “References”