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- Homework Statement
- A group of induction motors with a total power of 500kW and power factor 0.8 lagging are to be partially replaced with a synchronous motors of the same efficiency but leading power factor of 0.707. As the replacement proceeds the overall power factor improves. What percentage of the load will have been replaced when the overall power reaches 0.9 lagging?(Answer is 15.2%)

- Relevant Equations
- Power factor(pf) = cosθ

Average power(Pave) = VIcosθ

Apparent power(Pa) = VI

Reactive power(Pr) = VIsinθ

Induction motors:

pf = 0.8

triangle:

θ = arccos(0.8) = 36.86 degrees

Pa = 500/0.8 = 625 VA

Pr = sqrt(625^2-500^2) = 375 VAR

Synchronous motors:

pf = 0.707

triangle:

θ = arccos(0.707) = 45 degrees

Pa = 500/0.707 = 707 VA

Pr = sqrt(707^2-500^2) = 499.85 VAR

I am uncertain of how I can relate this information with the load percentage, any hints/tips will be much appreciated.

pf = 0.8

triangle:

θ = arccos(0.8) = 36.86 degrees

Pa = 500/0.8 = 625 VA

Pr = sqrt(625^2-500^2) = 375 VAR

Synchronous motors:

pf = 0.707

triangle:

θ = arccos(0.707) = 45 degrees

Pa = 500/0.707 = 707 VA

Pr = sqrt(707^2-500^2) = 499.85 VAR

I am uncertain of how I can relate this information with the load percentage, any hints/tips will be much appreciated.