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.

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)

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)

As a large proportion of the inductive or lagging current on the supply is due to the magnetizing current of induction motors, it is easy to correct each individual motor by connecting the correction capacitors to the motor starters. With static correction, it is important that the capacitive current is less than the inductive magnetizing current of the induction motor. In many installations employing static power factor correction, the correction capacitors are connected directly in parallel with the motor windings. When the motor is Off Line, the capacitors are also Off Line. When the motor is connected to the supply, the capacitors are also connected providing correction at all times that the motor is connected to the supply. This removes the requirement for any expensive power factor monitoring and control equipment. In this situation, the capacitors remain connected to the motor terminals as the motor slows down. An induction motor, while connected to the supply, is driven by a rotating magnetic field in the stator which induces current into the rotor. When the motor is disconnected from the supply, there is for a period of time, a magnetic field associated with the rotor. As the motor decelerates, it generates voltage out its terminals at a frequency which is related to it's speed. The capacitors connected across the motor terminals, form a resonant circuit with the motor inductance. If the motor is critically corrected, (corrected to a power factor of 1.0) the inductive reactance equals the capacitive reactance at the line frequency and therefore the resonant frequency is equal to the line frequency. If the motor is over corrected, the resonant frequency will be below the line frequency. If the frequency of the voltage generated by the decelerating motor passes through the resonant frequency of the corrected motor, there will be high currents and voltages around the motor/capacitor circuit. This can result in severe damage to the capacitors and motor. It is imperative that motors are never over corrected or critically corrected when static correction is employed.

Static power factor correction should provide capacitive current equal to 80% of the **magnetizing current**, which is essentially the open shaft current of the motor.

The magnetizing current for induction motors can vary considerably. Typically, magnetizing currents for large two pole machines can be as low as 20% of the rated current of the motor while smaller low speed motors can have a magnetizing current as high as 60% of the rated full load current of the motor. It is not practical to use a "Standard table" for the correction of induction motors giving optimum correction on all motors. Tables result in under correction on most motors but can result in over correction in some cases. Where the open shaft current can not be measured, and the magnetizing current is not quoted, an approximate level for the maximum correction that can be applied can be calculated from the half load characteristics of the motor. It is dangerous to base correction on the full load characteristics of the motor as in some cases, motors can exhibit a high leakage reactance and correction to 0.95 at full load will result in over correction under no load, or disconnected conditions.

Static correction is commonly applied by using on e contactor to control both the motor and the capacitors. It is better practice to use two contactors, one for the motor and one for the capacitors. Where one contactor is employed, it should be up sized for the capacitive load. The use of a second contactor eliminates the problems of resonance between the motor and the capacitors.

Static Power factor correction __ must not be__ used when the motor is controlled by a variable speed drive or inverter. The connection of capacitors to the output of an inverter can cause serious damage to the inverter and the capacitors due to the high frequency switched voltage on the output of the inverters.

The current drawn from the inverter has a poor power factor, particularly at low load, but the motor current is isolated from the supply by the inverter. The phase angle of the current drawn by the inverter from the supply is close to zero resulting in very low inductive current irrespective of what the motor is doing. The inverter does not however, operate with a good power factor. Many inverter manufacturers quote a cos Ø of better than 0.95 and this is generally true, however the current is non sinusoidal and the resultant harmonics cause a power factor (KW/KVA) of closer to 0.7 depending on the input design of the inverter. Inverters with input reactors and DC bus reactors will exhibit a higher true power factor than those without.

The connection of capacitors close to the input of the inverter can also result in damage to the inverter. The capacitors tend to cause transients to be amplified, resulting in higher voltage impulses applied to the input circuits of the inverter, and the energy behind the impulses is much greater due to the energy storage of the capacitors. It is recommended that capacitors should be at least 75 Meters away from inverter inputs to elevate the impedance between the inverter and capacitors and reduce the potential damage caused.

Switching capacitors, Automatic bank correction etc, will cause voltage transients and these transients can damage the input circuits of inverters. The energy is proportional to the amount of capacitance being switched. It is better to switch lots of small amounts of capacitance than few large amounts.

Static Power Factor correction capacitors __ must not__ be connected to the output of a solid state soft starter. When a solid state soft starter is used, the capacitors must be controlled by a separate contactor. The capacitor contactor is only switched on when the soft starter output voltage has reached line voltage. Many soft starters provide a

If the soft starter is used without an isolation contactor, the connection of capacitors close to the input of the soft starter can also cause damage if they are switched while the softstarter is not drawing current. The capacitors tend to cause transients to be amplified, resulting in higher voltage impulses applied to the SCR’s of the soft starter, and due to the energy storage of capacitors, the energy behind the impulses is much greater. In such installations, it is recommended that the capacitors be mounted at least 50 meters from the soft starter. The elevated the impedance between the soft starter and the capacitors reduces the potential for damage to the SCR’s.

Switching capacitors, Automatic bank correction etc, will cause voltage transients and these transients can damage the SCRs of Soft Starters if they are in the Off state without an input contactor. The energy is proportional to the amount of capacitance being switched. It is better to switch lots of small amounts of capacitance than few large amounts.

Power Factor Introduction

Displacement Power Factor

Power Factor Correction

Bulk Correction

Static Correction

Power Factor Calculations

Distortion Power Factor

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The Power factor of the total current supplied to the distribution board is monitored by a power factor controller which then switches capacitor banks in a fashion to maintain a power factor better than a preset limit. (Typically 0.95) Ideally, the power factor should be as close to unity as possible. There is no problem with bulk correction operating at unity, however correction should not be applied to an unloaded or lightly loaded transformer. If correction is applied to an unloaded transformer, you create a high Q resonant circuit between the leakage reactance of the transformer and the capacitors and high voltages can result. Bulk compensation systems are usually incorporated with the switchgear supplying all or part of the plant.

More information : Power factor Calculations : Power Factor Controllers

Power Factor Introduction

Displacement Power Factor

Power Factor Correction

Bulk Correction

Static Correction

Power Factor Calculations

Distortion Power Factor

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Distortion power factor is caused by the presense of harmonics in the current waveform. The harmonics are caused by a non linear load which is commonly a solid state rectifier of SCR based controller.

The major sources of harmonics in industry are the input rectifiers of AC and DC drive systems and switchmode power supply systems.

Distortion power factor can only be corrected by reducing the harmonic currents, This can be achieved by the use of passive harmonic filters, active filters or active rectifier circuits.

Like displacement power factor, distortion power factor indicates the potential losses in the supply that can be reduced by the appropriate correction. Additionally, a poor distortion power factor can have a serious affect on other equipment connected to the supply. Hence, a poor distortion power factor is far more damaging and less desirable than a poor displacement power factor.

Power Factor Introduction

Displacement Power Factor

Power Factor Correction

Bulk Correction

Static Correction

Power Factor Calculations

Distortion Power Factor

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**Displacement Power Factor Definition : Displacement Power factor is the Cosine of the angle between the ****supply voltage and the ****current flowing in the load.**

A poor power factor due to an inductive load can be improved by the addition of power factor correction capacitors to the load or to the supply.

Reactive current flowing in the supply is refered to as reactive power and is usually expressed in VARs or KVARs. A VAR is the product of the reactive current and the applied voltage. A KVAR is equal to 1000 VARs.

Common loads causing a poor displacement power factor are induction motors, transformers, reactive ballasts used for lighting and voltage control, welding systems (non inverter based).

An induction motor draws current from the supply, that is made up of resistive components and inductive components. The resistive components are: 1) Load current.

2) Loss current.

and the inductive components are:

3) Leakage reactance.

4) Magnetizing current.

**Power Factor Definition : 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.**

All current will cause losses in the supply and distribution system. A load with a power factor of 1.0 results in the most efficient loading of the supply and a load with a PF of 0.5 will result in much higher losses in the supply system.

A poor power factor can be the result of either a significant phase difference between the voltage and current at the load terminals, or it can be due to a high harmonic content or distorted/discontinuous current waveform.

Poor load current phase angle is generally the result of an inductive load such as an induction motor, power transformer, lighting ballasts, welder or induction furnace.

A distorted current waveform can be the result of a rectifier, variable speed drive, switched mode power supply, discharge lighting or other electronic load.

**Capacitive Power Factor correction (Power Factor Compensation) is applied to circuits which include induction motors as a means of reducing the inductive component of the current and thereby reduce the losses in the supply. There should be no effect on the operation of the motor itself.**

In the interest of reducing the losses in the distribution system, power factor correction is added to neutralize a portion of the magnetizing current of the motor. Typically, the corrected power factor will be 0.92 - 0.95 Some power retailers offer incentives for operating with a power factor of better than 0.9, while others penalize consumers with a poor power factor. There are many ways that this is metered, but the net result is that in order to reduce wasted energy in the distribution system, the consumer will be encouraged to apply power factor correction.

Power factor correction is achieved by the addition of capacitors in parallel with the connected motor circuits and can be applied at the starter, or applied at the switchboard or distribution panel. The resulting capacitive current is leading current and is used to cancel the lagging inductive current flowing from the supply.

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