**Significance of Power Factor in A.C Systems**

Power factor is an important parameter in designing of electrical equipment's, fixing of tariff, power factor correction, improving the regulation and efficiency of transmission lines, load forecasting, etc.. in electrical engineering.

Power factor can be defined in three ways :

a) Basic (standard) definition of power factor: It is the cosine angle between the voltage and current i.e. cosф, where ф is the phase angle between the voltage and the current. It is illustrated by fig 1.

b) By using impedance triangle: power factor can be defined as it is the ratio of resistance to the impedance i.e. Cosф=R/IZI. It is illustrated by fig 2.

c) By using power triangle: power factor can be defined as it is the ratio of active (real) power (P) to apparent power(S) i.e. cosф=P/S. It is illustrated by fig 3.

**Range of power factor:**The range of the power factor can be decided as follows

**Minimum value of power factor:**for pure capacitor I leads V by 900 &for pure inductor I lags V by 900 , cosine value is minimum for 900, cosфmin=cos900=0.Therefore power factor is minimum (cosфmin=0).

**Maximum value of power factor:**In case of resistor (pure) I in phase with V i.e. phase angle is 00. cosфmax=cos00=1 cosine value is max for 00 .

therefore power factor is unity (cosфmax=1).other than the above cases (combination of resistance and inductor or combination of resistance and capacitance) phase angle between the V&I is less than 900 and greater than 00 .Therefore power factor is >0 and <1.Therefore the range of power factor is 0 to 1.

**The power factor is more significant in A.C than D.C:**Consideration of power factor is an important aspect in ac systems than dc systems. In D.C systems, the phase angle between the voltage and current is 00 at any instant of the time. Therefore the power factor is always unity in dc systems. Whereas in A.C systems Power factor value varies from 0 to 1 because phase angle between V&I varies from 900 to 00 according to the type of the load applied on the system.

The power factor should be maintained high for the better performance (good regulation, better efficiency, less losses) of electrical systems. But the power factor is low for the starting of the induction motors, induction heating, electrical welding, etc. In such cases the current drawn by the equipment, machines will be high as fixed power and constant voltage P1ф α VLIL cosф Where P1ф &VL are constant =====> IL α 1/ cosф.i.e. if the power factor cosф is low, load current will be high. If the load current is high, the I2R losses high so that efficiency will be low. Similarly voltage drop IR is high; hence the regulation will be poor. Therefore the efficiency and regulation of transmission line, transformer and other electrical equipment's/devices will be decreased due to the low power factor.The low power factor also making the equipment /machinery expensive & increasing size of the same. For example 100MVA Transformer is operating with unity p.f, if the power factor of the load is decreased to 0.8, then what will be rating of the transformer? We know that cosф =P/S => P=S cosф S1cosф1= S2cosф2 ==>100X1= S2 X0.8 ==> S2=100/0.8=125MVA.

Therefore the rating of the transformer is increased to 125MVA with reduced power factor of 0.8.this is also indicating that size of the transformer is increased ,thus cost of the transformer also increases.

Hence the transformer becomes expensive with reduced power factor. Hence the Power factor is very useful to determine the capacity of the equipment/machines like transformer, alternator & circuit breakers.

It is also helps to know the KVAR rating of the capacitor for the improvement of the power factor.

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Ambhoji. Venkateswarlu

H.O.D, EEE Departement

LAQSHYA Institute of Technology & Sciences

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