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For a balanced three-phase system, apparent power is √3 times line voltage and line current.
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Formula
S in VA; ULL in V RMS; IL in A RMS
| Symbol | Meaning | Unit |
|---|---|---|
| Total apparent power | VA | |
| RMS line-to-line voltage | V | |
| RMS line current | A |
S=\sqrt{3}U_{LL}I_LAssumes balanced sinusoidal phases and uses line-to-line voltage and line current. S is not real power; for sinusoidal loads P=S cosφ. For imbalance, calculate phase complex powers and sum them.
Assumes balanced sinusoidal phases and uses line-to-line voltage and line current. S is not real power; for sinusoidal loads P=S cosφ. For imbalance, calculate phase complex powers and sum them.
For a balanced three-phase system, apparent power is √3 times line voltage and line current.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Apparent power in a balanced three-phase system” and check its unit and magnitude.
At ULL=400 V and IL=10 A, S≈6.93 kVA.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: S in VA; ULL in V RMS; IL in A RMS.
Formula cluster
For a balanced three-phase system, apparent power is √3 times line voltage and line current.
At ULL=400 V and IL=10 A, S≈6.93 kVA.
State electrical loading of a balanced three-phase system.
Here is how to work through a typical Apparent power in a balanced three-phase system (S = √3 ULL IL) task step by step:
Task
Work through the numerical example for “Apparent power in a balanced three-phase system” and check its unit and magnitude.
Solution path
At ULL=400 V and IL=10 A, S≈6.93 kVA.
S=UI describes voltage-current loading regardless of the fraction converted to real power. Volt-amperes distinguish it from watts and vars. For sinusoidal loads P=S cosφ. Use RMS line quantities and a balanced sinusoidal system. Application: State electrical loading of a balanced three-phase system. The numerical example At ULL=400 V and IL=10 A, S≈6.93 kVA anchors the idea in a concrete measurement case. The corresponding units are S in VA; ULL in V RMS; IL in A RMS. At ULL=400 V and IL=10 A, S≈6.93 kVA. This checks that the reference quantities are compatible.
For three balanced phases, total apparent power is three times Uph Iph. Using ULL=√3 Uph and the corresponding line current gives S=√3 ULL IL; it also holds for balanced delta loads using line quantities. Use RMS line quantities and a balanced sinusoidal system. The corresponding units are S in VA; ULL in V RMS; IL in A RMS. At ULL=400 V and IL=10 A, S≈6.93 kVA. This checks that the reference quantities are compatible. Scope: Assumes balanced sinusoidal phases and uses line-to-line voltage and line current. S is not real power; for sinusoidal loads P=S cosφ. For imbalance, calculate phase complex powers and sum them. A practical application is State electrical loading of a balanced three-phase system.
Many power meters calculate S from RMS voltage and current. Distorted or unbalanced signals make definition and summation more involved. Check whether the instrument shows total, per-phase or a particular power definition. Use RMS line quantities and a balanced sinusoidal system. Scope: Assumes balanced sinusoidal phases and uses line-to-line voltage and line current. S is not real power; for sinusoidal loads P=S cosφ. For imbalance, calculate phase complex powers and sum them. A practical application is State electrical loading of a balanced three-phase system.
Write the quantity and unit from the variable list next to every value: S in VA; 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 and IL=10 A, S≈6.93 kVA. 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. Use RMS line quantities and a balanced sinusoidal system.
The background states this starting condition: Assumes balanced sinusoidal phases and uses line-to-line voltage and line current. S is not real power; for sinusoidal. 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. Use RMS line quantities and a balanced sinusoidal system.
Quanta exam set
Curated exam set for "Apparent power in a balanced three-phase system":
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Which formula describes Apparent power in a balanced three-phase system?
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How do you rearrange Apparent power in a balanced three-phase system for Base equation for the target quantity?
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Which common mistake happens with Apparent power in a balanced three-phase system?
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