φ = phase angle between voltage and current
The power factor defined by IEEE and IEC is the ratio between the applied active (true) power - and the apparent power , and can in general be expressed as:
PF = P / S (1)
where
PF = power factor
P = active (true or real) power (Watts)
S = apparent power (VA, volts amps)
A low power factor is the result of inductive loads such as transformers and electric motors. Unlike resistance loads creating heat by consuming kilowatts, inductive loads require a current flow to create magnetic fields to produce the desired work.
Power factor is an important measurement in electrical AC systems because
International standards such as IEC 61000-3-2 have been established to control current waveform distortion by introducing limits for the amplitude of current harmonics.
A industrial plant draws 200 A at 400 V and the supply transformer and backup UPS is rated 400 V x 200 A = 80 kVA .
If the power factor - PF - of the loads is 0.7 - only
80 kVA × 0.7
= 56 kW
of real power is consumed by the system. If the power factor is close to 1 (a purely resistive circuit) the supply system with transformers, cables, switch-gear and UPS could be made considerably smaller.
Required cross-section area of conductor with lower power factor:
Power Factor | 1 | 0.9 | 0.8 | 0.7 | 0.6 | 0.5 | 0.4 | 0.3 |
Cross-Section | 1 | 1.2 | 1.6 | 2.04 | 2.8 | 4.0 | 6.3 | 11.1 |
A low power factor is expensive and inefficient and some utility companies may charge additional fees when the power factor is less than 0.95 . A low power factor will reduce the electrical system's distribution capacity by increasing the current flow and causing voltage drops.
A Power Factor is usually stated as "leading" or "lagging" to show the sign of the phase angle.
Inductive and capacitive loads stores energy in magnetic or electric fields in the devices during parts of the AC cycles. The energy is returned back to the power source during the rest of the cycles.
In systems with mainly inductive loads - typically industrial plants with many electric motors - the lagging voltage are compensated with capacitor banks.
The total power required by an inductive device like a motor or similar consists of
The power factor for a three-phase electric motor can be expressed as:
PF = P / [(3) 1/2 U I] (2)
where
PF = power factor
P = power applied (W, watts)
U = voltage (V)
I = current (A, amps)
- or alternatively:
P = (3) 1/2 U I PF
= (3) 1/2 U I cos φ (2b)
U, l and cos φ are normally quoted on the motor nameplate.
Power (hp) | Speed (rpm) | Power Factor (cos φ ) | ||||
---|---|---|---|---|---|---|
Unloaded | 1/4 load | 1/2 load | 3/4 load | full load | ||
0 - 5 | 1800 | 0.15 - 0.20 | 0.5 - 0.6 | 0.72 | 0.82 | 0.84 |
5 - 20 | 1800 | 0.15 - 0.20 | 0.5 - 0.6 | 0.74 | 0.84 | 0.86 |
20 - 100 | 1800 | 0.15 - 0.20 | 0.5 - 0.6 | 0.79 | 0.86 | 0.89 |
100 - 300 | 1800 | 0.15 - 0.20 | 0.5 - 0.6 | 0.81 | 0.88 | 0.91 |
Typical un-improved power factors:
Industry | Power Factor |
---|---|
Brewery | 75 - 80 |
Cement | 75 - 80 |
Chemical | 65 - 75 |
Electro-chemical | 65 - 75 |
Foundry | 75 - 80 |
Forging | 70 - 80 |
Hospital | 75 - 80 |
Manufacturing, machines | 60 - 65 |
Manufacturing, paint | 65 - 70 |
Metalworking | 65 - 70 |
Mine, coal | 65 - 80 |
Office | 80 - 90 |
Oil pumping | 40 - 60 |
Plastic production | 75 - 80 |
Stamping | 60 - 70 |
Steel works | 65 - 80 |
Textiles | 35 - 60 |
Power factor before improvement (cosΦ) | Capacitor correction factor | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Power factor after improvement (cosΦ) | |||||||||||
1.0 | 0.99 | 0.98 | 0.97 | 0.96 | 0.95 | 0.94 | 0.93 | 0.92 | 0.91 | 0.90 | |
0.50 | 1.73 | 1.59 | 1.53 | 1.48 | 1.44 | 1.40 | 1.37 | 1.34 | 1.30 | 1.28 | 1.25 |
0.55 | 1.52 | 1.38 | 1.32 | 1.28 | 1.23 | 1.19 | 1.16 | 1.12 | 1.09 | 1.06 | 1.04 |
0.60 | 1.33 | 1.19 | 1.13 | 1.08 | 1.04 | 1.01 | 0.97 | 0.94 | 0.91 | 0.88 | 0.85 |
0.65 | 1.17 | 1.03 | 0.97 | 0.92 | 0.88 | 0.84 | 0.81 | 0.77 | 0.74 | 0.71 | 0.69 |
0.70 | 1.02 | 0.88 | 0.81 | 0.77 | 0.73 | 0.69 | 0.66 | 0.62 | 0.59 | 0.56 | 0.54 |
0.75 | 0.88 | 0.74 | 0.67 | 0.63 | 0.58 | 0.55 | 0.52 | 0.49 | 0.45 | 0.43 | 0.40 |
0.80 | 0.75 | 0.61 | 0.54 | 0.50 | 0.46 | 0.42 | 0.39 | 0.35 | 0.32 | 0.29 | 0.27 |
0.85 | 0.62 | 0.48 | 0.42 | 0.37 | 0.33 | 0.29 | 0.26 | 0.22 | 0.19 | 0.16 | 0.14 |
0.90 | 0.48 | 0.34 | 0.28 | 0.23 | 0.19 | 0.16 | 0.12 | 0.09 | 0.06 | 0.02 | |
0.91 | 0.45 | 0.31 | 0.25 | 0.21 | 0.16 | 0.13 | 0.09 | 0.06 | 0.02 | ||
0.92 | 0.43 | 0.28 | 0.22 | 0.18 | 0.13 | 0.10 | 0.06 | 0.03 | |||
0.93 | 0.40 | 0.25 | 0.19 | 0.15 | 0.10 | 0.07 | 0.03 | ||||
0.94 | 0.36 | 0.22 | 0.16 | 0.11 | 0.07 | 0.04 | |||||
0.95 | 0.33 | 0.18 | 0.12 | 0.08 | 0.04 | ||||||
0.96 | 0.29 | 0.15 | 0.09 | 0.04 | |||||||
0.97 | 0.25 | 0.11 | 0.05 | ||||||||
0.98 | 0.20 | 0.06 | |||||||||
0.99 | 0.14 |
An electrical motor with power 150 kW has power factor before improvement cosΦ = 0.75 .
For a required power factor after improvement cosΦ = 0.96 - the capacitor correction factor is 0.58 .
The required KVAR capacity can be calculated as
C = (150 kW) 0.58
= 87 KVAR
Recommended sizes of KVAR units needed for correction of induction motors to approximately 95% power factor.
Induction Motor Rating (HP) | Nominal Motor Speed (rpm) | |||||
---|---|---|---|---|---|---|
3600 | 1800 | 1200 | ||||
Capacitor Rating (KVAR) | Reduction of Line Current (%) | Capacitor Rating (KVAR) | Reduction of Line Current (%) | Capacitor Rating (KVAR) | Reduction of Line Current (%) | |
3 | 1.5 | 14 | 1.5 | 23 | 2.5 | 28 |
5 | 2 | 14 | 2.5 | 22 | 3 | 26 |
7.5 | 2.5 | 14 | 3 | 20 | 4 | 21 |
10 | 4 | 14 | 4 | 18 | 5 | 21 |
15 | 5 | 12 | 5 | 18 | 6 | 20 |
20 | 6 | 12 | 6 | 17 | 7.5 | 19 |
25 | 7.5 | 12 | 7.5 | 17 | 8 | 19 |
30 | 8 | 11 | 8 | 16 | 10 | 19 |
40 | 12 | 12 | 13 | 15 | 16 | 19 |
50 | 15 | 12 | 18 | 15 | 20 | 19 |
60 | 18 | 12 | 21 | 14 | 22.5 | 17 |
75 | 20 | 12 | 23 | 14 | 25 | 15 |
100 | 22.5 | 11 | 30 | 14 | 30 | 12 |
125 | 25 | 10 | 36 | 12 | 35 | 12 |
150 | 30 | 10 | 42 | 12 | 40 | 12 |
200 | 35 | 10 | 50 | 11 | 50 | 10 |
250 | 40 | 11 | 60 | 10 | 62.5 | 10 |
300 | 45 | 11 | 68 | 10 | 75 | 12 |
350 | 50 | 12 | 75 | 8 | 90 | 12 |
400 | 75 | 10 | 80 | 8 | 100 | 12 |
450 | 80 | 8 | 90 | 8 | 120 | 10 |
500 | 100 | 8 | 120 | 9 | 150 | 12 |
Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors.
Real, imaginary and apparent power in AC circuits.
The alternating current In an AC circuit is generated by a sinusoidal voltage source.
Characteristics of all-aluminum conductors (AAC).
Typical electrical motor data like nominal current, fuse, start ampere, size of contactor and circuit breaker - for asynchronous induction motors.
Calculate amps, hp and kVA for electrical motors.
480V electrical motor wiring data - NEMA amps, starter size, HMCP size for motors ranging 1/2 to 500 hp.
Slip is the difference between an electrical induction motor's synchronous and asynchronous speed.
Electrical motors NEMA frame dimensions.
Heat loss from an electrical motor to the surroundings.
Electrical motors NEMA temperature and insulation classes.
NEMA locked rotor indicating code letters for electrical motors.
Service factor - SF - is a measure of periodically overload capacity at which a motor can operate without beeing damaged.
Speed of an operating electrical motor with load is lower than the synchronous speed (no load) of the motor.
The speed of electrical motors with 2, 4, 6 or 8 poles at 50 Hz and 60 Hz.
Direct-on-line starters, star-delta starters, frequency drives and soft starters.
Abbreviations according the International Electrotechnical Commission (IEC).
Amount of heat transferred from electrical motor to ambient room vs. locations of fan and motor.
The eight - S1 - S8 - IEC duty cycles of operating electrical motors.
Synchronous and full load speed of amplitude current (AC) induction motors.
One side of a triangle when the opposite angle and two sides are known.
Increased voltage imbalance and decreased efficiency.
Power is the rate at which work is done or energy converted.
Power equations for single phased electrical systems.
Full load amps, wire and conduit sizes for three phase electrical motors.
Electrical 3-phase equations.
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