what is the farmulae for finding capacitor value to inprove the power factor from lagging to leading?

Answer 1

Power Factor Correction:
If an inductive load with an active power demand P has an uncorrected power factor of cosf1 lagging, and is required to have a corrected power factor of cosf2 lagging, the uncorrected and corrected reactive power demands, Q1 and Q2, are:
Q1 = P tanf1
Q2 = P tanf2
where tanfn = (1 / cos2fn - 1)½

The leading (capacitive) reactive power demand QC which must be connected across the load is:
QC = Q1 - Q2 = P (tanf1 - tanf2)


The uncorrected and corrected apparent power demands, S1 and S2, are related by:
S1cosf1 = P = S2cosf2
Comparing corrected and uncorrected load currents and apparent power demands:
I2 / I1 = S2 / S1 = cosf1 / cosf2

If the load is required to have a corrected power factor of unity, Q2 is zero and:
QC = Q1 = P tanf1
I2 / I1 = S2 / S1 = cosf1 = P / S1



Modern capacitor values:
In around 1970, a standardized set of capacitor base numbers was devised so that the value of any modern electrolytic capacitor could be derived from multiplying one of the modern conventional base numbers 1.0, 2.2, 3.3, or 4.7, by a power of ten. Therefore, it is common to find capacitors with values of 10, 22, 33, 47, 100, 220, and so on. Using this method, values ranging from 0.1 to 4700 are common in most applications. Values are generally in microfarads (µF).

How standardized values help:

Most electrolytic capacitors have a tolerance range of 20 %, meaning that the manufacturer guarantees that the actual value of the capacitor lies within 20 % of its labeled value.

A 10 µF capacitor, for example, may in actuality be as low as 8 µF whereas a capacitor marked 8 µF may in fact be as high as 9.6 µF. This causes an overlap of 1.6 µF. The standardized base values help this by alleviating overlaps due to tolerance, illustrated by the following table:

The left numbers are the base values.
The center numbers are the differences based on ± 20 % tolerance.
The numbers on the right illustrate the range of actual values by applying the tolerance.
In an effort to cut costs in the manufacturing process, the number of possible values was limited, because having overlapping values would be viewed as unneeded and redundant, since for most practical applications, having a 20 % (or even higher) tolerance did not adversely affect the functionality of the device. The reduction of variations in the product allowed companies to produce greater quantities of existing samples. This in turn, allowed for lower cost components.

(Retrieved from "http://en.wikipedia.org/wiki/Electrolytic_capacitor_value"
http://en.wikipedia.org/wiki/Power_factor_correction_unit)

WHY CAN CAPACITORS "CORRECT" power factor on circuits involving motors? We know that in inductive apparatus, such as an a-c motor, current lags voltage. Capacitors draw current that leads the voltage-therefore, they offset the lag.

But why does current lead voltage in a capacitor? Back when we were learning basic electricity, a common explanation went like this: When the circuit is first closed, current must flow into the capacitor to build up a charge on the plates before voltage can build up on those plates. Hence, current must lead voltage.

That explanation leaves much to be desired. More often, "fundamentals" training begins with lead-lag relationships as "givens," and only the consequences of those relationships are explained in detail.

What, then, is the real reason we say that, in a "perfect" capacitor, the current not only leads the voltage in time phase, but leads by exactly 90 degrees? Why does current lead, and why not some other angle?

FORE MORE PL. VISIT:
http://www.bowest.com.au/library/electric.html

Answer 2

Why do you want to change the PF from lag to lead? Do you realize that you maybe on a dangerous path?
For you to ask what the formular is, it appears you don't have the necessary experience to carry out the task.
By changing lagging to leading PF, you will increase the voltage which can cause flash overs in motors/transformers and also cause ferro resonance in the transformer feeding the circuit.
Be very careful and consult a professional electrical engineer before you embark on a path which may lead to the destruction of your equipment/cables/transformer/switchgear etc.

Source: Electrical engineer (ret.) with 45+ yrs experience

Answer 3

Go to a library and request a Electrical Engineering Hand book.

They have it in reference section only, but if the demand is not there they will let you check it out but only over night, this is true only if they know you well(good record with the library). and they have this policy.

Look under AC theory or AC formula