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Total Reactive Power drawn from a three-phase balanced load where line voltage = V P , Line current = V L , Phase voltage = V P and Phase current = I P is given by:
The total reactive power (Q) of a three-phase balanced system is defined as the sum of reactive powers in each phase. It is calculated using the line voltage (VLтАЛ), line current (ILтАЛ), and the phase angle (phi) between the phase voltage and phase current as Q=3тАЛVLтАЛILтАЛsin╧Х.
The total reactive power (Q) of a three-phase balanced system is defined as the sum of reactive powers in each phase. It is calculated using the line voltage (VLтАЛ), line current (ILтАЛ), and the phase angle (phi) between the phase voltage and phase current as Q=3тАЛVLтАЛILтАЛsin╧Х.
Q=3VPтАЛIPтАЛsin╧Х
Q=3тАЛVLтАЛILтАЛsin╧Х
In a balanced three-phase circuit, the total power is the sum of the powers in the three individual phases. While real power is P=3VPтАЛIPтАЛcos╧Х=3тАЛVLтАЛILтАЛcos╧Х, the reactive power, which represents the oscillatory energy exchange between the source and the load's reactive components, is given by Q=3VPтАЛIPтАЛsin╧Х. Substituting the line-to-line relationships (VLтАЛ=3тАЛVPтАЛ for star connections or ILтАЛ=3тАЛIPтАЛ for delta connections) into the expression results in the standard line-value representation.
Reactive power is measured in Volt-Ampere Reactive (VAR).
In a balanced system, the power factor angle ╧Х is the same for all three phases.
Reactive power does not perform useful work but is essential for maintaining electromagnetic fields in inductive loads.
Standardized calculation for balanced systems
Allows for power factor correction analysis
Applicable only to balanced loads
Does not account for harmonic distortion
Electrical power system design
Industrial motor drive efficiency analysis
The option selected reflects the standard expression in terms of line values.
Option 1 (3VPтАЛIPтАЛcos╧Х) represents total active power.
Option 2 (3тАЛVLтАЛILтАЛcos╧Х) also represents total active power in line values.
Option 4 (3тАЛVPтАЛIPтАЛsin╧Х) is dimensionally incorrect for total power in a 3-phase system.
C is correct тАФ The total reactive power in a three-phase balanced load expressed in terms of line values is 3тАЛVLтАЛILтАЛsin╧Х.
Remember that Active Power always uses cos╧Х and Reactive Power always uses sin╧Х. For 3-phase systems, if using line values, a 3тАЛ factor is required for both active and reactive power.
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