what is pf. how to calculate capacitor bank value to
maintain unity pf.
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Answer Posted / ezzuddin
The correct answer and below is the proof of the formula:
KVAR= KW X [√(1–(COSФ)^2)]/COSФ
The proof:
Pythagoras Theorem states that in a right-angled triangle
the square of the hypotenuse is equal to the sum of the
squares of the other two sides.
so that:
Q is the hypotenuse.
S is the opposite.
P is the adjacent.
TanФ= opposite/adjacent = S/P -----> S=P x(TanФ)
Pf=COSФ= adjacent/hypotenuse = P/Q ---->Q=P/COSФ
Pythagoras said that:
Q^2= P^2 + S^2
P^2/(COSФ)^2= P^2 + (P^2 x (TanФ)^2)
by divide P^2:
1/(COSФ)^2 = 1 + (TanФ)^2
by changing the both sides:
(TanФ)^2 = (1/(COSФ)^2) - 1
(TanФ)^2 = (1/(COSФ)^2) - ((COSФ)^2/(COSФ)^2)
by Taking the (1/(COSФ)^2) Common factor:
(TanФ)^2 = {1/(COSФ)^2)} x ( 1 - (COSФ)^2)
by taking the square root:
TanФ = [√(1–(COSФ)^2)]/COSФ
so that:
KVAR = KW x [√(1–(COSФ)^2)]/COSФ
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