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For a balanced sinusoidal load, the phase-angle sine gives three-phase reactive power.
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Formula
Q in var; ULL in V RMS; IL in A RMS
| Symbol | Meaning | Unit |
|---|---|---|
| Total reactive power | var | |
| RMS line-to-line voltage | V | |
| RMS line current | A | |
| Phase angle between phase voltage and phase current | rad |
Q=\sqrt{3}U_{LL}I_L\sin\varphiThis belongs to the balanced sinusoidal model where S2=P2+Q2 and P=√3ULLILcosφ. State the sign convention for inductive versus capacitive power. With harmonics, a single phase angle does not fully describe power decomposition.
This belongs to the balanced sinusoidal model where S2=P2+Q2 and P=√3ULLILcosφ. State the sign convention for inductive versus capacitive power. With harmonics, a single phase angle does not fully describe power decomposition.
For a balanced sinusoidal load, the phase-angle sine gives three-phase reactive power.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Reactive power in a balanced three-phase system” and check its unit and magnitude.
At ULL=400 V, IL=10 A and sinφ=0.6, Q≈4.16 kvar.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Q in var; ULL in V RMS; IL in A RMS.
Formula cluster
For a balanced sinusoidal load, the phase-angle sine gives three-phase reactive power.
At ULL=400 V, IL=10 A and sinφ=0.6, Q≈4.16 kvar.
Assess reactive-power flow and power factor for balanced loads.
Here is how to work through a typical Reactive power in a balanced three-phase system (Q = √3 ULL IL sinφ) task step by step:
Task
Work through the numerical example for “Reactive power in a balanced three-phase system” and check its unit and magnitude.
Solution path
At ULL=400 V, IL=10 A and sinφ=0.6, Q≈4.16 kvar.
P is average power that performs work. Q describes periodic exchange of stored electric or magnetic energy between source and field. For sinusoidal quantities, cosφ and sinφ represent orthogonal power components. The sine relation assumes balanced sinusoidal phases and an explicitly chosen inductive/capacitive sign convention. Application: Assess reactive-power flow and power factor for balanced loads. The numerical example At ULL=400 V, IL=10 A and sinφ=0.6, Q≈4.16 kvar anchors the idea in a concrete measurement case. The corresponding units are Q in var; ULL in V RMS; IL in A RMS. At ULL=400 V, IL=10 A and sinφ=0.6, Q≈4.16 kvar. This checks that the reference quantities are compatible.
Under passive sign convention, inductive reactive power is often positive and capacitive negative, but meters and grid conventions can differ. State current direction and load/generator reference arrows before interpreting signs. The sine relation assumes balanced sinusoidal phases and an explicitly chosen inductive/capacitive sign convention. The corresponding units are Q in var; ULL in V RMS; IL in A RMS. At ULL=400 V, IL=10 A and sinφ=0.6, Q≈4.16 kvar. This checks that the reference quantities are compatible. Scope: This belongs to the balanced sinusoidal model where S2=P2+Q2 and P=√3ULLILcosφ. State the sign convention for inductive versus capacitive power. With harmonics, a single phase angle does not fully describe power decomposition. A practical application is Assess reactive-power flow and power factor for balanced loads.
Near-unity power factor means a small phase angle and relatively small reactive magnitude for fixed apparent power. Capacitive/inductive equipment, harmonics and voltage control may still matter; one power-factor value is not a full network assessment. The sine relation assumes balanced sinusoidal phases and an explicitly chosen inductive/capacitive sign convention. Scope: This belongs to the balanced sinusoidal model where S2=P2+Q2 and P=√3ULLILcosφ. State the sign convention for inductive versus capacitive power. With harmonics, a single phase angle does not fully describe power decomposition. A practical application is Assess reactive-power flow and power factor for balanced loads.
Write the quantity and unit from the variable list next to every value: Q in var; ULL in V RMS; IL in A RMS. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example At ULL=400 V, IL=10 A and sinφ=0.6, Q≈4.16 kvar. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. The sine relation assumes balanced sinusoidal phases and an explicitly chosen inductive/capacitive sign convention.
The background states this starting condition: This belongs to the balanced sinusoidal model where S2=P2+Q2 and P=√3ULLILcosφ. State the sign convention for inductive versus. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. The sine relation assumes balanced sinusoidal phases and an explicitly chosen inductive/capacitive sign convention.
Quanta exam set
Curated exam set for "Reactive power in a balanced three-phase system":
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Which formula describes Reactive power in a balanced three-phase system?
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How do you rearrange Reactive power in a balanced three-phase system for Base equation for the target quantity?
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Which common mistake happens with Reactive power in a balanced three-phase system?
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Create a curated FSRS exam set for Q = √3 ULL IL sinφ: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
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