The Power Triangle

 

What is power?

In the electrical domain, the electric power is the amount of energy transferred to some other form per unit of time like light, heat, etc. Mathematically, it can be defined as the product of voltage and current. Thus, since DC circuits performs as a resistive circuit, the voltage and current are in the similar phase and the power can be derived as follows:

P = V*I

What is power triangle?

 

Source: electricalbaba.com

 

Power Triangle is a right-angled triangle who sides viz., Base/adjacent, Perpendicular/vertical/opposite and Hypotenuse represent Active, Reactive and Apparent power respectively. The triangle is the graphical representation of real or active power, reactive power, and apparent power in a right-angled triangle.

In a power triangle, active power P, reactive power Q, and apparent power S form a right-angled triangle.

Therefore, hypotenuse (square) = base (square) + perpendicular (square)

S (square) = P (square) + Q (square)

Here, apparent power (S) is measured in Volt-Ampere (VA)

Active power (P) is measured in Watt (W); and Reactive power (R) is measured in Volt-Ampere Reactive (VAR)

 

Key Takeaways

·      Active power or true power refers to the entire amount of power dissipated in an electrical circuit. It is measured in Watt (W) or KiloWatt (KW) and presented with P.

·      Reactive power or imaginary power is the power that does not do any real work and causes zero power dissipation. ‘T’ is also known as watt-less power. The is the power derived from reactive elements like the inductive load and the capacitive load. The reactive power is denoted by Q and is calculated in KiloVolt Amp Reactive (VAR).

·      The total power in the circuit, both absorbed and dissipated, is known as apparent power and is computed by multiplying the Root Mean Square (r.m.s) voltage with r.m.s current without any phase angle quantity.

·      Ohm’s Law always works with DC circuits, but in the case of AC, it only works when the circuit is purely resistive, i.e., the circuit does not have any inductive or capactive load. But most of the AC circuits consist of a series or parallel combination of RLC (Resistance, Inductance, Capacitance). Due to this, voltage and current become out of phase, and a complex quantity is introduced.

·      The power of the three-phase system is = root of 3 * power factor * voltage * current.

·      When an active power component of current is multiplied by the circuit voltage V, it results in active power. It is this power that produces torque in the motor, heat in the heater, etc. This power is measured by the wattmeter.

·      When the reactive component of the current is multiplied by the circuit voltage it gives reactive power. This power determines the power factor, and it flows back and forth in the circuit.

·      Thus, the factor may be determined by taking the ratio of true power to the apparent power i.e.,

Power factor Cos (theta) = Active power / Apparent power = KW / KVA

 

As we know, power means the product of voltage and current but in AC circuit except for pure resistive circuit there is usually a phase difference between voltage and current and thus, VI does not give real or true power in the circuit.

 

Going through the Pythagoras theorem, we could derive the following (SOHCAHTOA)

 

Sin Φ = Q/P (1)

Cos Φ = P/S (2)

Tan Φ = Q/S (3)

 

And for this explanation we take, only (2) i.e., Cos Φ is the power factor

Therefore, power factor = P/S where P = active power; and S = Apparent power

Then we derive,

            Power factor (pf) = Active Power/Apparent power = MW / MVA

 

When the voltage and current waveforms of a purely resistive circuit are in-phase with each other, the active power by the circuit is the same as the apparent power and the phase difference will be 0. It is referred to as the unity power factor

            i.e., power factor = Cos 0 degree = 1

In another case, when the voltage and the current waveforms of a purely resistive circuit out-phase with each other by an angle of 90 degrees, then the phase difference will be 90 degrees.

            i.e., Power factor = cos 90 degree = 0

 

Thus, when the power factor lies between the value of -1 and +1. This is because the power factor depends on the degree between the real power and the apparent power. The values could be derived from different variant of Cos Φ (as given in the following table)

 

 

Also, it is to be noted that the capacitive loads are leading (current leads voltage) and indicative loads are lagging (current lags voltage).