# Incentive/Penalty for Power factor why and How?

# Power factor Incentive

Electric power power is measured and billed as kWh, short form of kilo Watt Hour.

In case of Direct current :

Energy = Voltage x Current x No of Hours

In case of Alternating current

Electric Energy = Voltage x Current X power factor X No of Hours

Let’s do with example:

Voltage = 230 Volts

Current = 10 A

If this is a direct current,

Power = Voltage x Current

= 230 V X 10 A

= 2300 Watts

= 2.3 kW (to convert Watts to kilo Watts value is divided by 1000)

In case of alternating current, the entire current is not converted to power

The product Voltage x Current is termed as apparent power and is not the active power

Active Power = Voltage x Current x Power factor

If the value of power factor is 0.8 to take as an example

Active Power = 230 V x 10 AX 0.8

= 1840 W

= 1.84 kW

The product Voltage x Current termed as Apparent power is

Apparent power = Voltage x Current

= 230 V x 10 A

= 2300 VA

= 2.3 kVA

Please notice that for the same current in DC and AC power is different.

Now to calculating Energy consumption for say 10 Hours for using the same load,

Electric Energy = Power x Time (If power is given in kW and time in Hours Unit of energy is kilo Watt Hour of kWh, though this unit is used very rarely for energy other than electricity)

For No of hours = 10

Energy = 1.84 kW x 10 Hours

= 18.4 kWh or 18.4 Units of electrical energy

The product of 2.3 kVA x 10 Hours = 23 kVAh

Power factor is calculated by the distribution companies as

Power factor = Total kWh / Total kVAh

= 18.4/23

= 0.8 ( we have actually started with this power factor hence the answer here is evident)

**Why the distribution companies can’t bill for the kVAh?** and Where is the difference between kVAh and kWh going? These may be questions on who are not familiar with property of electric power.

Theoretically the energy produced and consumed is only the active power measured in kWh. The complementary part of active power (kW) to apparent power(kVA) which is called as reactive power (kVAR) is neither produced nor consumed and constitutes to be an imaginary component not contributing to energy. It is important to notice that Active power and reactive power can’t be added as values but only as a vector sum. This we will discuss elsewhere.

Only real element in practice is the increased current in the circuit. This, though is not converted to energy in the load which has inductive / capacitive nature associated, causes transmission losses in the distribution system. This is a loss to the power production and distribution companies for which they are adding as penalty to the consumer.

It is thus important for the consumer to use only the current that converts to energy by maintaining power factor to unity.

How to maintain Power factor to Unity?

Most of the loads connected are of inductive nature as they all has coils those cause inductive reactance on the circuit. Capacitive reactance can be added to the circuit which is equal in magnitude dynamically calculating the exact value of inductive reactance of the load. This is done with Automatic Power Factor Correction panels equipped with Capacitor banks.