The Power Triangle and its Components

From the previous discussions, AC impedance (Z) is defined as a complex quantity that made up of real resistance (R) and imaginary reactance (X). But for now, we will discuss about Apparent power (S) which is also a complex quantity that is made up of real active power (P) and imaginary reactive power (Q).

The object illustrated above is a power triangle, it consists a real power (P), apparent power (S), reactive power (Q) and phase angle (Ɵ). The relationship between these three can be expressed using vectors, Pythagorean Theorem, simple sohcahtoa and etc. For vectors, Real power is horizontal vector, Reactive power is vertical vector, and Apparent power is the hypotenuse of the right angled triangle. 

For the Pythagorean theorem:

S=√Q^2 + P^2

For the sohcahtoa:

sin Ɵ = Q/S

cos Ɵ = P/S

tan Ɵ = Q/P

To get the phase angle (Ɵ):

Ɵ = arccos* Power factor (P.F.)

Other formulas that 

include S, P, and Q are:

P = I^2*(R)

Q = I^2*(X)

S = I^2*(Z)

Formulas also discussed at ac power analysis can be used.


The Power Factor (P.F.)

- Power factor is defined as the ratio of the actual electrical power dissipated by an AC circuit to the product of the r.m.s. values of current and voltage. It is also the ratio of the real power flowing to the load, to the apparent power in the circuit: 

P.F. = P/S

This formula from phase 

angle could also be used:

P.F. = cos Ɵ