**POWER FACTOR - 2**

**POWER AND POWER FACTOR IN AN AC CIRCUIT:**

Power consumed by a resistor is dissipated in heat and not returned to the source. This is true power. True power is the rate at which energy is used. Current in an AC circuit rises to peak values and diminishes to zero many times a second. The energy stored in the magnetic field of an inductor, or plates of a capacitor, is returned to the source when current changes direction. Power in an AC circuit is the vector sum of true power and reactive power. This is called apparent power.True power is equal to apparent power in a purely resistive circuit because voltage and current are in phase. Voltage and current are also in phase in a circuit containing equal values of inductive reactance and capacitive reactance. If voltage and current are 90 degrees out of phase, as would be in a purely capacitive or purely inductive circuit, the average value of true power is equal to zero. There are high positive and negative peak values of power, but when added together the result is zero.

The formula for apparent power is:

P = EI

Apparent power is measured in volt-amps (VA).True power is calculated from another trigonometric function,the cosine of the phase angle (cos q). The formula for truepower is:

P = EI cos q

True power is measured in watts.

In a purely resistive circuit, current and voltage are in phase.There is a zero degree angle displacement between current and voltage. The cosine of zero is one. Multiplying a value by one does not change the value. In a purely resistive circuit the cosine of the angle is ignored.In a purely reactive circuit, either inductive or capacitive,current and voltage are 90 degrees out of phase. The cosine of 90 is zero. Multiplying a value times zero results in a zero product. No power is consumed in a purely reactive circuit.

CALCULATING APPARENT POWER IN A SIMPLE R-L-C CIRCUIT:

In the following 120 volt circuit, It is equal to 84.9 milliamps.Inductive reactance is 100 W and capacitive reactance is1100 W. The phase angle is -45 degrees. By referring to atrigonometric table, the cosine of -45 degrees is foundto be .7071.

The apparent power consumed by the cirucuit is

P = EI

P = 10.2 VA

The true power consumed by the ciruit is

P= EI COS (phi) = 120 x 0.0849 x 0.7071 = 7.2 watts

another formula for true power is

P = 0.0849 X 0.0849 X 1000 = 7.2 watts

**POWER FACTOR:**

Power factor is the ratio of true power to apparent power in an AC circuit. Power factor is expressed in the following formula:

PF = PT/PA

Power factor can also be expressed using the formulas for true power and apparent power. The value of EI cancels out because it is the same in the numerator and denominator.Power factor is the cosine of the angle.

In a purely resistive circuit, where current and voltage are inphase, there is no angle of displacement between current and voltage. The cosine of a zero degree angle is one. The powerfactor is one. This means that all energy delivered by the source is consumed by the circuit and dissipated in the form of heat.In a purely reactive circuit, voltage and current are 90 degrees apart. The cosine of a 90 degree angle is zero. The powerfactor is zero. This means the circuit returns all energy it receives from the source to the source.In a circuit where reactance and resistance are equal, voltage and current are displaced by 45 degrees. The cosine of a 45degree angle is .7071. The power factor is .7071. This means the circuit has used approximately 70% of the energy supplied by the source and returned approximately 30%.

**LEADING AND LAGGING POWER FACTOR:**

Since current leads voltage in a capacitive circuit, power factor is considered leading if there is more capacitive reactance than inductive reactance. Power factor is considered lagging if there is more inductive reactance than capacitive reactance since current lags voltage in an inductive circuit. Power factor is unity when there is no reactive power or when inductive reactance and capacitive reactance are equal, effectively cancelling eachother.

It is usually more economical to correct poor power factor than to pay large utility bills. In most industrial applications motors account for approximately 60% or more of electric power consumption, resulting in a lagging power factor (more inductive than capacitive). Power factor correction capacitors can be added to improve the power factor.

**POWER FACTOR PROBLEMS:**

It can be seen that an increase in reactive power causes a corresponding decrease in power factor. This means the power distribution system is operating less efficiently because not all current is performing work. For example, a 50 kW load with a power factor of 1 (reactive power = 0) could be supplied by a transformer rated for 50 kVA. However, if power factor is 0.7(70%) the transformer must also supply additional power for the reactive load. In this example a larger transformer capable ofsupplying 71.43 kVA (50 ÷ 70%) would be required. In addition,the size of the conductors would have to be increased, adding significant equipment cost.

**Power Factor.**

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 causes 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 power factor 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 balasts, 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.

A poor power factor due to an inductive load can be improved by the addition of power factor correction, but, a poor power factor due to a distorted current waveform requires an change in equipment design or expensive harmonic filters to gain an appreciable improvement. Many inverters are quoted as having a power factor of better than 0.95 when in reality, the true power factor is between 0.5 and 0.75. The figure of 0.95 is based on the Cosine of the angle between the voltage and current but does not take into account that the current waveform is discontinuous and therefore contributes to increased losses on the supply.

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