Power Triangle

What is Power Triangle?

The relationship between real power, reactive power and apparent power. Which can be expressed by representing the quantities as vectors. Real power is represented as a horizontal vector and reactive power is represented as a vertical vector. The apparent power vector is the hypotenuse of a right triangle formed by connecting the real and reactive power vectors. This representation is often called the power triangle. Using the Pythagorean Theorem, the relationship among real, reactive and apparent power is: 

(apparent power)^2 = (real power)^2 + (reactive power)^2 

Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both sinusoids with a known phase angle between them.

Below is the figure of a Power triangle.

The power triangle graphically shows the relationship between real (P), reactive (Q) and apparent power (S).

The power triangle also shows that we can find real (P) and reactive (Q) power, given S and the impedance angle θ.

Sample Problem :

Calculate the complex power for the circuit and correct the power factor to
unity by connecting a parallel reactance to the load.

Solution
Known Quantities: Source voltage; load impedance.
Find:

1. S = Pav + jQ for the complex load.

2. Value of parallel reactance required for power factor correction resulting in pf = 1.

Schematics, Diagrams, Circuits, and Given Data: 

VS = 117∠0 V; RL = 50 ohms ; jXL = j86.7 ohms .

Assumptions: Use rms values for all phasor quantities in the problem.

Analysis:

First, we compute the load impedance:

ZL = R + jXL = 50 + j86.7 = 100∠1.047

Next, we compute the load current:

and the complex power, as defined in equation
S = VI = 117∠0 × 1.17∠1.047 = 137∠1.047 = 68.4 + j118.5 W


Therefore
Pav = 68.4 W Q = 118.5 VAR

To compute the reactance needed for the power factor correction, we observe that we need
to contribute a negative reactive power equal to −118.5 VAR. This requires a negative
reactance and therefore a capacitor with QC = −118.5 VAR. The reactance of such a

capacitor is given by

In this lesson, I've learned that this topic is really essential and "MUST LEARN" topic because you cannot proceed to other topics for a reason that this topic is the base line of them all. You cannot find the values of the apparent power, real power and complex power if you don't know how to draw the power triangle and how it is used. In this particular topic, We students must know also the different formula to be use so that we can compute for the different power.