To calculate the total power in a three-phase circuit, you need to consider both the active (real) power and the reactive power. The total power in a three-phase circuit is the sum of these two components, known as apparent power.
Here are the steps to calculate the total power in a three-phase circuit:
Measure the line-to-line voltage (VLL): Measure the voltage between any two phases. The line-to-line voltage is typically denoted as VLL.
Measure the line current (IL): Measure the current flowing in one of the phases. This current is the line current.
Determine the power factor (PF): The power factor is the ratio of active power to apparent power and is represented as a decimal or percentage. It is the cosine of the phase angle between the voltage and current waveforms in the circuit.
Calculate the active power (P): The active power, also known as real power, is the portion of power that does useful work and is measured in watts (W). It is given by the formula:
P = √3 × VLL × IL × PF
Calculate the reactive power (Q): The reactive power is the portion of power that doesn't perform useful work but is necessary to maintain the magnetic fields in inductive loads. It is measured in volt-amperes reactive (VAR). The reactive power is given by the formula:
Q = √3 × VLL × IL × sin(θ)
Where θ is the angle between the voltage and current phasors (power factor angle).
Calculate the apparent power (S): The apparent power is the total power consumed in the circuit, combining both active and reactive power. It is measured in volt-amperes (VA). The apparent power is given by the formula:
S = √(P^2 + Q^2)
So, the total power in a three-phase circuit (apparent power S) is the square root of the sum of the squares of the active power (P) and the reactive power (Q):
S = √(P^2 + Q^2)
Keep in mind that the actual power factor angle (θ) may vary depending on the type of load (resistive, inductive, capacitive) in the circuit. For purely resistive loads, the power factor is 1 (cosine of 0 degrees), and there is no reactive power. For purely inductive or capacitive loads, the power factor is 0 (cosine of 90 degrees), and there is no active power. For practical loads, the power factor can be anywhere between 0 and 1.