Which expression correctly defines reactive power Q in a balanced three-phase system?

Which expression correctly defines reactive power Q in a balanced three-phase system?

• A. 3 V_LL I sinφ
• B. √3 V_LL I cosφ
• C. V_LL I sinφ
• D. √3 V_LL I sinφ

Answer: (D)

Reactive power in a balanced three-phase system scales with the sine of the angle between voltage and current, just like in a single phase, but the three-phase geometry adds the √3 factor. Each phase has voltage V_phase = V_LL/√3 and current I, so the reactive power per phase is V_phase I sinφ. Adding the three phases gives Q = 3 V_phase I sinφ = 3*(V_LL/√3)*I*sinφ = √3 V_LL I sinφ. This is why the correct expression is √3 V_LL I sinφ. The other forms either miss the √3, use cosφ (which gives real power), or omit the sinφ factor, which would not describe reactive power.

Reactive power in a balanced three-phase system scales with the sine of the angle between voltage and current, just like in a single phase, but the three-phase geometry adds the √3 factor. Each phase has voltage V_phase = V_LL/√3 and current I, so the reactive power per phase is V_phase I sinφ. Adding the three phases gives Q = 3 V_phase I sinφ = 3*(V_LL/√3)Isinφ = √3 V_LL I sinφ. This is why the correct expression is √3 V_LL I sinφ. The other forms either miss the √3, use cosφ (which gives real power), or omit the sinφ factor, which would not describe reactive power.