# Power Factor

ByAPSEEE

### Power Factor

The electrical energy is almost exclusively generated, transmitted and distributed in the form of alternating current. Most of loads are inductive in nature and have low lagging power factor. The low power factor is highly undesirable as it causes additional losses of active power in all the elements of power system from power station generator down to the utilization devices.

Current taken by any circuit consists of two components. One is the current transformed into the useful work is called working component Iw and the other is magnetizing current Iμ which often termed as wattless component because it does no useful work. Component Iw being in phase with the voltage and the component Iμ being in quadrature with the voltage represents no work and is mainly responsible for the creation of magnetism.I2 = I2w+ I2μ

(KVA)2 = (KW)2 + (KVAR)2

Definition

The cosine of the angle between voltage and current is called is power factor.

or

It is the ratio of resistance to the impedance.

or

It is the ratio of true power to the apparent power.

Cause of Low Power Factor

1. Most of the a.c. motors are of induction type which has low lagging power factor. These motors work at a power factor which is extremely small on light load and rises to 0.8 or 0.9 at full load.
2. Arc lamps, electric discharge lamps and inductrial heating furnances operate at low lagging power factor.
3. The load on the power system is varying ; being high during morning and evening and low at other times. During low load period, supply voltage is increased which increases the magnetization current. This results in the decreased in P.F.

The magnitude of line current supplying a given balanced three phase load P at voltage V and P.F.  cosΦ is given as :

Low P.F. for a given load and supply voltage means more current. This has the following effects.

Large KVA rating of equipment

The electrical machinery (e.g. alternators, transformers, etc) always rated in KVA.

It is clear that KVA rating of an electrical machine is inversely proportional to power factor. The smaller the power factor, larger the KVA rating.  Therefore, at low P.F., the KVA rating of an electrical machine has to be made more, making an electrical machine larger and expensive.

Greater conductor size

For a given cross sectional area of line conductors, line losses are proportional to 1/cos2Φ. Poor power factor means more line losses and low transmission efficiency. Alternatively, if efficiency of transmission is to be kept same, poor P.F. will require cross-section of the line conductors which will be inversely proportional to 1/cosΦ. This will therefore increase capital investment in the transmission lines.

Larger copper losses

The large current at low P.F. causes more I2R losses in all the elements of the supply system. This result in poor efficiency.

Poor voltage regulation

Greater the value of phase angle difference or lower the value of P.F., greater will be the  value of voltage regulation. Extra voltage regulation equipment will be required to keep the voltage drop prescribed limits. Futher the armature reaction due to the lagging currents in an alternator being demagnetizing, it requires higher excitation to maintain given value of generated voltage, as P.F. of the load becomes poor. This will increase the rating of exciter too. This will again increase the cost.

Reduced handling capacity of system

The lagging P.F. reduces the handling capacity of all the elements of the system. It is because the reactive component of current prevents the full utilization of installed capacity.