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Power factor Calculations

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Power Factor Calculations.

Power factor is the ratio between the KW and the KVA drawn by an electrical load where the KW is the actual load power and the KVA is the apparent load power. It is a measure of how effectively the current is being converted into useful work output and more particularly is a good indicator of the effect of the load current on the efficiency of the supply system.

There are two types of power factor, displacement power factor and distortion power factor. Only displacement power factor can be corrected by the addition of capacitors.

Displacement Power factor.

The Line Current comprises two components of current, a real component indicating work current, and a reactive component which is 90 degrees out of phase. The reactive current indicates either inductive or capacitive current and does not do any work. The Real current, or in phase current, generates Power (KW) in the load and reactive current does not generate power in the load. The effect of the reactive curent is measured in KVARs. The composite line current is measured in KVA.
The vectors can be represented as two equivilant triangles, one triangle being the real current, the reactive current and the composite (line) current. The cosine of the angle between the line current phasor and the real current represents the power factor.
The second identical triangle is made up of the KW KVA and KVAR vectors.

For a given power factor and KVA (line current) the KVAR (reactive current) can be calculated as the KVA times the sine of the angle between the KVA and KW.

Power factor vector diagram and calculations showing KVA, KVAR and KW

Three phase calculations:

KVA = Line Current x Line Voltage x sqrt(3) / 1000
KVA = I x V x 1.732 / 1000
KW = True Power
pf = Power Factor = Cos(Ø)

KW = KVA x pf = V x I x sqrt(3) x pf
KVAR = KVA x Sine(Ø) = KVA x sqrt(1 -pf x pf)

Single phase calculations:

KVA = Line Current x phase Voltage /1000
KVA = I x V / 1000
KW = True Power
pf = Power Factor = Cos(Ø)

KW = KVA x pf = V x I x sqrt(3) x pf
KVAR = KVA x Sine(Ø) = KVA x sqrt(1 -pf x pf)

To calculate the correction to correct a load to unity, measure the KVA and the displacement power factor, calculate the KVAR as above and you have the required correcion.

To calculate the correction from a known pf to a target pf, first calculate the KVAR in the load at the known power factor, than calculate the KVAR in the load for the target power factor and the required correction is the difference between the two. i.e.

Measured Load Conditions:
KVA = 560
pf = 0.55

Target pf = 0.95

(1) KVAR = KVA x sqrt(1 - pf x pf) = 560 x sqrt(1 - 0.55 x 0.55)
             = 560 x 0.835
             = 467.7 KVAR

(2) KVAR = KVA x sqrt(1 - pf x pf) = 560 x sqrt(1 - 0.95 x 0.95)
             = 560 x 0.3122
             = 174.86 KVAR

(3) Correction required to correct from 0.55 to 0.95 is (1) - (2)
             = 292.8 KVAR (= 300 KVAR)

To calculate the reduction in line current or KVA by the addition of power factor correction for a known initial KVA and power factor and a target power factor, we first calculate the KW from the known KVA and power factor. From that KW and the target power factor, we can calculate the new KVA (or line current). i.e.

Initial KVA = 560
Initial pf = 0.55
Target pf = 0.95

(1) KW = KVA x pf = 560 x 0.55 = 308 KW
(2) KVA = KW / pf = 308 / 0.95 = 324 KVA
=> KVA reduction from 560 KVA to 324 KVA
=> Current reduction to 57% (43% reduction)

Last Updated ( Friday, 10 April 2009 10:08 )

Compound DC Motors

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Compound DC motors

DC compound motor is essentially a combination of Series DC motor and Shunt DC motor.


In a compound motor, we have both series winding and parallel winding. A winding is connected in series with the armature as in a Series DC motor. Another winding is connected in shunt with the armature as in a Shunt DC motor. This combination presents us the double advantage of having the torque characteristics of a series motor and the constant speed characteristic of a shunt motor in one compound wound motor.

Types of Compound Motors

Depending on the relative polarity of the series and shunt windings, we have different types of compound motors. There are 3 major classifications of DC compound motors:
1. Cumulative Compound Motors
2. Differential Compound Motors
3. Compound Interpole Motors

Cumulative Compound Motors

In cumulative compound motors, the polarity of the shunt winding is such that it adds to the series fields. This shunt winding can be either short shunt where the shunt is parallel with only the armature or long shunt where the shunt is in parallel with both armature and the series field. Since the shunt windings are done in such a way as to assist both armature and series field producing a cumulative effect, the motor is termed cumulative compound motors.

Cumulative wound motors give high starting torque like a series motor and reasonable good speed regulation at high speeds like a shunt dc motor. It can start with even huge loads and run smoothly (if the load varies only slightly) after that. As this type of motor offers the best of both series and shunt motor, it is practically suitable for most common applications, and so is widely used.

Differential Compound Motors

In differential compound motors, polarities of the armature and the shunt field are such that they oppose each other. In this type of motor, negative terminal of the shunt field is connected to the positive terminal of the armature.

In differential compound motors, magnetic fields of the shunt winding oppose the armature magnetic fields and the series fields. This kind of differential winding provides different torque and speed characteristics. Here as the shunt field is producing an opposite effect, it is unlike a shunt motor. So when the load is reduced, differential compound motor behaves more like a series motor and tends to over speed. When the load is increased, its speed is reduced drastically.

Compound Interpole Motors

Compound Interpole motors are different from both cumulative and differential motors. This motor has additional interpoles in series with the armature. The interpoles are connected in series in between the series winding and the armature. Physically, it is placed besides the series coils in the stator. The polarity of the interpoles and the series fields are same and they assist each other. Interpoles are of same gauge (thickness) as series windings. But we can have as many turns of interpoles as required to have strong magnetic field.

Interpoles help preventing armature and brushes from arcing. So brushes will last longer and it is not necessary to cut down the armature often. Overall, interpoles help to improve smooth functioning of the motor and prolong its life.

Compound DC Motor Speed Control

The speed of a DC compound motor can be easily controlled. It is enough if we change just the voltage supplied to it.

AC motors are well known for constant speeds and DC motors are popular for variable speeds. This was the situation before three decades. But, the advent of solid-state components and microprocessor-based controls has revolutionized the way we control motor speeds. Today, a solid-state AC variable-frequency motor drive can be used to vary the speed of an AC motor as easily as that of DC motors.


Cumulative compound wound motors are virtually suitable for almost all applications like business machines, machine tools, agitators and mixers etc. Compound motors are used to drive loads such as shears, presses and reciprocating machines.

Last Updated ( Sunday, 13 July 2008 17:13 )

Shunt DC Motors

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Shunt DC Motors

Shunt DC motor works on direct current (DC). In electrical terminology, a parallel connection is termed shunt. In a Shunt DC motor, the armature and field windings are connected in parallel. This type of winding is called shunt winding and the motor Shunt DC motor.

Parts and Principle of operation of a Shunt DC Motor

Construction and principle of operation of a Shunt DC motor is same as any other DC motor. It also has all the fundamental components-rotor (armature), stator (field windings) and commutator - required for the operation of a motor. In a Shunt DC motor, a rotational torque is produced as a result of the interaction between the magnetic field produced around the current carrying armature and the magnetic field established around the stator windings. Current is supplied from the stationary housing to the rotating armature through commutator & brushes arrangement. As the stator is stationary, power is applied directly to it.

In Shunt DC motor, the field windings of the stator are connected in parallel with the armature. The field windings of a Shunt DC motor are made of fine coil of wire with large number of turns. As small gauge wire cannot handle heavy currents, shunt windings of a shunt motor require large number of turns to produce strong magnetic field.

As a Shunt DC Motor cannot carry high currents, it is unsuitable for applications requiring a high starting torque. So, it requires its shaft load to be small to start functioning.

The resistance of the shunt windings in a Shunt DC motor is very high. As a result, when electric voltage is supplied to the Shunt DC motor, very low amount of current flows through the shunt coil. Armature draws enough current to produce a strong magnetic field. Due to the interaction of magnetic field around armature and the field produced around the shunt field, the motor starts to rotate. When the armature starts turning, it produces a back EMF. The theory behind the generation of back EMF is the simple electromagnetic principle, which states that when a conductor (armature in this case) rotates in a magnetic field, electricity is induced in it. The polarity of this generated back EMF is such that it opposes the armature current. So, as the motor turns, armature current is controlled by the back EMF and is kept low.

Last Updated ( Friday, 26 September 2008 23:16 ) Read more...

Series DC Motors

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Series DC Motor

Like any other motor, series motors convert electrical energy to mechanical energy. Its operation is based on simple electromagnetic principle by which when the magnetic field created around a current carrying conductor interacts with an external magnetic field, a rotational motion is generated.

Parts and Principles of operation of a Series DC Motor

A DC series motor has all the 6 fundamental components-axle, rotor (armature), stator, commutator, field magnet(s) and brushes-that are present in a generic DC motor. The motor casing where two or more electromagnet pole pieces are housed forms the stationary part of the motor, the stator. The armature, windings on a core, electrically connected to the commutator comprise the rotor. Rotor has a central axle about which the rotor rotates in relation to the stator. Power is supplied to the armature windings through the stationary brushes touching the rotating commutator.


A typical DC motor layout is given in the following diagram:

Series Motor - Electrical Diagram

In series motors stator windings and field windings are connected in series with each other. As a result the field current and armature current are equal. Heavy currents flow directly from the supply to the field windings. To carry this huge load, field windings are very thick and have few turns. Usually copper bars form stator windings. These thick copper bars dissipate heat generated by the heavy flow of current very effectively.


Note that the stator field windings S1-S2 are in series with the rotating armature A1-A2.

In a series motor electric power is supplied between one end of the series field windings and one end of the armature. When voltage is applied, current flows from power supply terminals through the series winding and armature winding. The large conductors present in the armature and field windings provide the only resistance to the flow of this current. Since these conductors are so large, their resistance is very low. This causes the motor to draw a large amount of current from the power supply. When the large current begins to flow through the field and armature windings, the coils reach saturation that results in the production of strongest magnetic field possible.

The strength of these magnetic fields provides the armature shafts with the greatest amount of torque possible. The large torque causes the armature to begin to spin with the maximum amount of power and the armature starts to rotate.

Last Updated ( Friday, 10 April 2009 10:52 ) Read more...

Brushless DC Motors

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Brushless DC Motors (BLDC)

Brushless DC motor is a rotating electric machine that converts electrical energy into mechanical power. It works on direct-current electricity. Similar to a generic DC motor, a brushless DC motor has both a rotor and a stator. In a standard DC motor the armature conductors will rotate and the magnetic field comprising the stator remains physically static. But in a brushless DC motor, the roles of the conductor and the magnetic field are reversed. Here the conductors remain stationary and the magnetic field rotates. Due to this feature a brushless DC motor is equivalent to a reversed DC commutator motor. In this armature remains static and the magnets rotate.

Construction Characteristics

Unlike DC motors with brushes, brushless DC motors have electronically controlled commutation system. They have powerful switching transistors to supply electric power to the motor.

Principle of Operation

In a DC motor, a rotating torque is produced when the polarity of the magnetic field in which the conductors are placed gets reversed. In a general DC motor, the polarity reversal of the magnetic field is achieved by the commutator and the brushes arrangement. In the brushless DC motor, there are no brushes to achieve polarity reversal. Power transistors switching in synchronization with the rotor position perform it.

In a brushless DC motor, sensors are used to detect the position of the rotor at any instant. Rectangular voltage pulses that fluctuate in accordance with the rotor position drive a brushless DC motor.

The rotor magnet generates the rotor flux that on interaction with the stator flux produces the rotating torque. Brushless DC motors have three-phase stator. Fluctuating voltage strokes are appropriately applied to this three phase winding system of the stator in such a way that the phase angle between the rotor flux and the stator flux is nearly 90 degrees. This 90 degrees phase difference between the rotor flux and the stator flux ensures generation of maximum torque.

Last Updated ( Friday, 26 September 2008 23:15 ) Read more...
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