power factor definition for a three

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Power Factor definition for a three-phase electrical motor

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The power factor of an AC electric power system is defined as the ratio of the active (true or real) power to the apparent power

where

y 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.y Apparent Power is measured in volt-amperes (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.

y Reactive Power is measured in volt-amperes reactive (VAR). Reactive Power is power stored in and discharged by inductive motors, transformers andsolenoids

Reactive power is required for the magnetization of a motor but doesn't perform any action. The reactive power required by inductive loads increases the amountsof apparent power - measured in kilovolt amps (kVA) - in the distribution system. Increasing of the reactive and apparent power will cause the power factor - PF -to decrease.

Power Factor

It is common to define the Power Factor - PF - as the cosine of the phase angle between voltage and current - or the "cos".



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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 resistive loads creating heat by consuming kilowatts, inductiveloads require a current flow to create magnetic fields to produce the desired work.

Power factor is an important measurement in electrical AC systems because

y an overall power factor less than 1 indicates that the electricity supplier need to provide more generating capacity than actually requiredy the current waveform distortion that contributes to reduced power factor is caused by voltage waveform distortion and overheating in the neutral cables of

three-phase systems



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International standards such as IEC 61000-3-2 have been established to control current waveform distortion by introducing limits for the amplitude of currentharmonics.

Example - Power Factor

A industrial plant draws 200 A at 400 V and the supply transformer and backup UPS is rated 200 A × 400 V = 80 kVA.

If the power factor - PF - of the loads is only 0.7 - only

80 kVA × 0.7

= 56 kVA

of real power is consumed by the system. If the power factor is close to 1 (purely resistive circuit) the supply system with transformers, cables, switchgear andUPS 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.

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

Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle.

y With a purely resistive load current and voltage changes polarity in step and the power factor will be 1. Electrical energy flows in a single direction acrossthe network in each cycle.

y Inductive loads - transformers, motors and wound coils - consumes reactive power with current waveform lagging the voltage.y 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.



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Power Factor for a Three-Phase Motor

The total power required by an inductive device as a motor or similar consists of

y Active (true or real) power (measured in kilowatts, kW)y Reactive power - the nonworking power caused by the magnetizing current, required to operate the device (measured in kilovars, kVAR)

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)

Typical Motor Power Factors

Power (hp) Speed (rpm) Power Factor

1/2 load 3/4 load full load

0 - 5 1800 0.72 0.82 0.84



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5 - 20 1800 0.74 0.84 0.86

20 - 100 1800 0.79 0.86 0.89

100 - 300 1800 0.81 0.88 0.91

y 1 hp = 745.7 W

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Calculating power factor

As was mentioned before, the angle of this ³power triangle´ graphically indicates the ratio between the amount of dissipated (or consumed) powerand the amount

of absorbed/returned power. It also happens to be the same angle as that of the circuit's impedance in polar form. When expressed as a fraction, this ratio

between true power and apparent power is called thepower factor for this circuit. Because true power and apparent power form the adjacent and hypotenuse

sides of a right triangle, respectively, thepower factor ratio is also equal to the cosine of that phase angle. Using values from the last example circuit:



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It should be noted that power factor, like all ratio measurements, is aunitless quantity.

For the purely resistive circuit, the power factor is 1 (perfect), because the reactive power equals zero. Here, the power triangle would look like a horizontal line,

because the opposite (reactive power) side would have zero length.

For the purely inductive circuit, the power factor is zero, because truepower equals zero. Here, the power triangle would look like a vertical line, because the

adjacent (true power) side would have zero length.

The same could be said for a purely capacitive circuit. If there are no dissipative (resistive) components in the circuit, then the true power must be equal to zero,

making any power in the circuit purely reactive. The powertriangle for a purely capacitive circuit would again be a vertical line (pointing down instead of up as it

was for the purely inductive circuit).

Power factor can be an important aspect to consider in an AC circuit, because 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. If our last example circuithad been purely resistive, we would have been able to deliver a full 169.256 watts to the load with the same 1.410 amps of current, rather than the mere 119.365

watts that it is presently dissipating with that same current quantity. The poor power factor makes for an inefficient power delivery system.

Poor power factor can be corrected, paradoxically, by adding another load to the circuit drawing an equal and opposite amount of reactive power, to cancel out

the effects of the load's inductive reactance. Inductive reactance can only be canceled by capacitive reactance, so we have to add a capacitor in parallel to our

example circuit as the additional load. The effect of these two opposing reactances in parallel is to bring the circuit's total impedance equal to its total resistance

(to make the impedance phase angle equal, or at least closer, to zero).



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Since we know that the (uncorrected) reactive power is 119.998 VAR (inductive), we need to calculate the correct capacitor size to produce the same quantity of

(capacitive) reactive power. Since this capacitor will be directly in parallel with the source (of known voltage), we'll use the powerformula which starts from voltage

and reactance:

Let's use a rounded capacitor value of 22 µF and see what happens to our circuit: (Figure below)



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Parallel capacitor corrects lagging power factor of inductive load. V2 and node numbers: 0, 1, 2, and 3 are SPICE related, and may be ignored for the moment.

The power factor for the circuit, overall, has been substantially improved. The main current has been decreased from 1.41 amps to 994.7 milliamps, while

the power dissipated at the load resistor remains unchanged at 119.365

watts. The power factor is much closer to being 1:



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Since the impedance angle is still a positive number, we know that the circuit, overall, is still more inductive than it is capacitive. If our powerfactor correction

efforts had been perfectly on-target, we would have arrived at an impedance angle of exactly zero, or purely resistive. If we had added too large of a capacitor in

parallel, we would have ended up with an impedance angle that was negative, indicating that the circuit was more capacitive than inductive.

A SPICE simulation of the circuit of (Figure above) shows total voltage and total current are nearly in phase. The SPICE circuit file has a zero volt voltage-source

(V2) in series with the capacitor so that the capacitor current may be measured. The start time of 200 msec ( instead of 0) in the transient analysis statement

allows the DC conditions to stabilize before collecting data. See SPICE listing ³pf.cir power factor´.

pf.cir power factor

V1 1 0 sin(0 170 60)

C1 1 3 22uF

v2 3 0 0

L1 1 2 160mH

R1 2 0 60

# resolution stop start

.tran 1m 200m 160m



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.end

The Nutmeg plot of the various currents with respect to the applied voltage Vtotal is shown in (Figure below). The reference is Vtotal, to which all other

measurements are compared. This is because the applied voltage, Vtotal, appears across the parallel branches of the circuit. There is no single current common to

all components.We can compare those currents to V total.

Zero phase angle due to in-phase Vtotal and Itotal . The lagging IL with respect to Vtotal is corrected by a leading IC .

Note that the total current (Itotal) is in phase with the applied voltage (Vtotal), indicating a phase angle of near zero. This is no coincidence. Note that the laggingcurrent, IL of the inductor would have caused the total current to have a lagging phase somewhere between (Itotal) and IL. However, the leading capacitor current,

IC, compensates for the lagging inductor current. The result is a total current phase-angle somewhere between the inductor and capacitor currents. Moreover, that

total current (Itotal) was forced to be in-phase with the total applied voltage (Vtotal), by the calculation of an appropriate capacitor value.

Since the total voltage and current are in phase, the product of these two waveforms, power, will always be positive throughout a 60 Hz cycle, realpower as in

Figure above. Had the phase-angle not been corrected to zero (PF=1), the product would have been negative where positive portions of one waveform



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overlapped negative portions of the other as in Figure above. Negative power is fed back to the generator. It cannont be sold; though, it does waste power in the

resistance of electric lines between load and generator. The parallel capacitor corrects this problem.

Note that reduction of line losses applies to the lines from the generator to the point where the power factor correction capacitor is applied. In other words, there is

still circulating current between the capacitor and the inductive load. This is not normally a problem because the power factorcorrection is applied close to the

offending load, like an induction motor.

It should be noted that too much capacitance in an AC circuit will result in a low power factor just as well as too much inductance. You must be careful not to over-

correct when adding capacitance to an AC circuit. You must also be very careful to use the proper capacitors for the job (rated adequately for power system

voltages and the occasional voltage spike from lightning strikes, for continuous AC service, and capable of handling the expected levels of current).

If a circuit is predominantly inductive, we say that its power factor is lagging(because the current wave for the circuit lags behind the applied voltage wave).

Conversely, if a circuit is predominantly capacitive, we say that itspower factor is leading. Thus, our example circuit started out with a powerfactor of 0.705

lagging, and was corrected to a power factor of 0.999 lagging.

y REVIEW:

y Poor power factor in an AC circuit may be ³corrected´, or re-established at a value close to 1, by adding a parallel reactance opposite the effect of the

load's reactance. If the load's reactance is inductive in nature (which is almost always will be), parallelcapacitance is what is needed to correctpoor power factor.

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power factor definition for a three

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