ThreePhase Electrtical Motors  Power Factor vs. Inductive Load
Inductive loads and power factors with electrical threephase motors.
The power factor of an AC electric power system is defined as the ratio active (true or real) power to apparent power , where
 Active (Real or True) Power is measured in watts ( W ) and is the power drawn by the electrical resistance of a system doing useful work
 Apparent Power is measured in voltamperes (VA) and is the voltage on an AC system multiplied by all the current that flows in it. It is the vector sum of the active and the reactive power
 Reactive Power is measured in voltamperes reactive ( VAR ). Reactive Power is power stored in and discharged by inductive motors, transformers and solenoids
Reactive power is required for the magnetization of an electric motor but does not perform any work. Reactive power required by inductive loads increases the amounts of apparent power  and the required supply to the grid from the power supplier to the distribution system.
Increased reactive and apparent power will decrease the power factor  PF .
Power Factor
It is common to define the Power Factor  PF  as the cosine of the phase angle between voltage and current  or the " cosφ ":
PF = cos φ
where
PF = power factor
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
 an overall power factor less than 1 indicates that the electricity supplier need to provide more generating capacity than actually required
 the current waveform distortion that contributes to reduced power factor is caused by voltage waveform distortion and overheating in the neutral cables of threephase systems
International standards such as IEC 6100032 have been established to control current waveform distortion by introducing limits for the amplitude of current harmonics.
Example  Power Factor
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, switchgear and UPS could be made considerably smaller.
 Any power factor less than 1 means that the circuit's wiring has to carry more current than what would be necessary with zero reactance in the circuit to deliver the same amount of (true) power to the resistive load.
Conductor CrossSection vs. Power Factor
Required crosssection area of conductor with lower power factor:
Power Factor  1  0.9  0.8  0.7  0.6  0.5  0.4  0.3 
CrossSection  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.
"Leading" or "Lagging" Power Factors
A Power Factor is usually stated as "leading" or "lagging" to show the sign of the phase angle.
 With a purely resistive load the current and voltage changes polarity in step and the power factor will be 1 . Electrical energy flows in a single direction across the network in each cycle.
 Inductive loads  transformers, motors and wound coils  consumes reactive power with current waveform lagging the voltage.
 Capacitive loads  capacitor banks or buried cables  generates reactive power with current phase leading the voltage.
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.
Power Factor for a ThreePhase Motor
The total power required by an inductive device like a motor or similar consists of
 Active (true or real) power (measured in kilowatts, kW)
 Reactive power  the nonworking power caused by the magnetizing current, required to operate the device (measured in kilovars, kVAR)
The power factor for a threephase 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.
Typical Motor Power Factors
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 
 1 hp = 745.7 W
Power Factor by Industry
Typical unimproved power factors:
Industry  Power Factor 

Brewery  75  80 
Cement  75  80 
Chemical  65  75 
Electrochemical  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 
Benefits of Power Factor Corrections
 reduced power bills  avoiding low power factor penalty from the utility power company
 increased system capacity  additional loads can be added without overloading the system
 improved system operating characteristics by reduced line loss  due to less current
 improved system operating characteristics by gaining voltage  excessive voltage drops are avoided
Power Factor Correction with Capacitor
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 
Example  Improving power factor with capacitor
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
Suggested Capacitor Ratings for TFrame NEMA Class B Motors
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 
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