3-Phase System

The illustration below is an example of a 3-phase system. It is a common method of AC power generation, transmission, and distribution. Its component values involve Van, Vbn, and Vcn, which are the phase voltages, Vl which is the line voltage, Zl which is the line impedance, Z which is the load impedance, and Ia, Ib, and Ic which is the phase currents. The 3 phases carry voltages and currents which are 120 degrees out of phase with each other. This illustration represents Y-Y connection, other samples are delta-Y, Y-delta, and delta-delta.

From a 3-phase system, we could create a single phase system. But a 3-phase system is more economical than a single-phase or two-phase system because it uses less conductor material (wire) to transmit electric power, at the same voltage. Written below are the common formulas for obtaining the unknown value in a 3-phase system, you could also use the other formulas introduced on the previous posts:

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