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For balanced sinusoidal three-phase power, total real power is √3 times line voltage, line current and power factor.
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Formula
P in W; ULL in V; IL in A; cosφ dimensionless
| Symbol | Meaning | Unit |
|---|---|---|
| Total real power across all three phases | W | |
| RMS line-to-line voltage | V | |
| RMS line current | A | |
| Phase power-factor angle | rad |
P=\sqrt{3}U_{LL}I_L\cos\varphiThe formula assumes a balanced three-phase system with sinusoidal quantities and RMS values. ULL is line-to-line voltage; power factor refers to phase quantities. For unbalanced or distorted loads, sum phase powers or use an appropriate power measurement.
The formula assumes a balanced three-phase system with sinusoidal quantities and RMS values. ULL is line-to-line voltage; power factor refers to phase quantities. For unbalanced or distorted loads, sum phase powers or use an appropriate power measurement.
For balanced sinusoidal three-phase power, total real power is √3 times line voltage, line current and power factor.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Real power in a balanced three-phase system” and check its unit and magnitude.
At ULL=400 V, IL=10 A and cosφ=0.8, P≈5.54 kW.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: P in W; ULL in V; IL in A; cosφ dimensionless.
Formula cluster
For balanced sinusoidal three-phase power, total real power is √3 times line voltage, line current and power factor.
At ULL=400 V, IL=10 A and cosφ=0.8, P≈5.54 kW.
Calculate total real power of a balanced three-phase load.
Here is how to work through a typical Real power in a balanced three-phase system (P = √3 ULL IL cosφ) task step by step:
Task
Work through the numerical example for “Real power in a balanced three-phase system” and check its unit and magnitude.
Solution path
At ULL=400 V, IL=10 A and cosφ=0.8, P≈5.54 kW.
In a balanced three-phase system, phase and line-to-line voltage differ by √3. Total power is three times one phase’s real power. Using ULL=√3 Uph gives P=√3 ULL IL cosφ. The factor depends on using line voltage. Use RMS line-to-line voltage and line current; the √3 form assumes a balanced sinusoidal load. Application: Calculate total real power of a balanced three-phase load. The numerical example At ULL=400 V, IL=10 A and cosφ=0.8, P≈5.54 kW anchors the idea in a concrete measurement case.
Yes: for three identical phases, P=3 Uph Iph cosφ. Do not mix phase and line quantities; their relations depend on star or delta connection. The stated formula uses line-to-line voltage and line current. Use RMS line-to-line voltage and line current; the √3 form assumes a balanced sinusoidal load. The corresponding units are P in W; ULL in V; IL in A; cosφ dimensionless. At ULL=400 V, IL=10 A and cosφ=0.8, P≈5.54 kW. This checks that the reference quantities are compatible.
Not in this compact form. Under imbalance, phase currents and possibly phase voltages differ. Calculate real power per phase and sum, or use suitable instrumentation for the specific system. Harmonics also require a more careful power definition. Use RMS line-to-line voltage and line current; the √3 form assumes a balanced sinusoidal load. Scope: The formula assumes a balanced three-phase system with sinusoidal quantities and RMS values. ULL is line-to-line voltage; power factor refers to phase quantities. For unbalanced or distorted loads, sum phase powers or use an appropriate power measurement. A practical application is Calculate total real power of a balanced three-phase load.
Write the quantity and unit from the variable list next to every value: P in W; ULL in V; IL in A; cosφ dimensionless. 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 cosφ=0.8, P≈5.54 kW. 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-to-line voltage and line current; the √3 form assumes a balanced sinusoidal load.
The background states this starting condition: The formula assumes a balanced three-phase system with sinusoidal quantities and RMS values. ULL is line-to-line voltage; power. 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-to-line voltage and line current; the √3 form assumes a balanced sinusoidal load.
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Which formula describes Real power in a balanced three-phase system?
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