In a three-phase AC power system, power can be calculated using the power triangle or the power formula. The power triangle is a graphical representation that helps visualize the relationship between active (real) power (P), reactive power (Q), apparent power (S), and the power factor (PF). The power formula relates these parameters as follows:
Apparent Power (S): Apparent power is the vector sum of active and reactive power. It represents the total power consumed by the system, taking into account both the real and reactive components. It is measured in volt-amperes (VA).
S = P + jQ
Where j is the imaginary unit (j = √(-1)).
Active Power (P): Active power is the actual power that performs useful work in the circuit. It is measured in watts (W).
Reactive Power (Q): Reactive power represents the power that oscillates between source and load due to reactive elements (inductors and capacitors). It doesn't perform any useful work but is necessary for the operation of reactive components. It is measured in volt-amperes reactive (VAR).
Power Factor (PF): Power factor is the cosine of the angle between the active power and the apparent power vectors in the power triangle. It is a dimensionless value between 0 and 1, representing the efficiency of power usage in a system.
The power triangle is a graphical representation of these relationships. It is a right triangle where the hypotenuse represents the apparent power (S), the horizontal leg represents the active power (P), and the vertical leg represents the reactive power (Q). The angle between the hypotenuse and the horizontal leg is the angle of the power factor (θ).
To calculate power using the power triangle, follow these steps:
Measure the apparent power (S) and power factor (PF) from the system.
Calculate the active power (P) using the formula: P = S * PF
Calculate the reactive power (Q) using the formula: Q = S * sin(θ)
Alternatively, you can directly calculate apparent power from active power and reactive power using the Pythagorean theorem:
S = √(P^2 + Q^2)
Remember that in practical applications, power factor correction might be needed to improve the efficiency of power usage and reduce reactive power.