ABSTRACT

A consumer takes a load of 50kVA at 0.7 p.f. lagging. Calculate (a) the active and reactive components of the load, (b) the leading kVAr taken from a capacitor to improve the p.f. to 0.9 lagging.

Active component (true power) k W k V A = p f https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315863122/b66584da-ae46-426e-a83c-08160dc244ad/content/inline-math1_29.tif"/>

Transpose to find kW

kW × 0.7 = 35 kW

Reactive component kW 2 = kVA 2 − kVAr 2 Or k V A r = k W 2 − k V A 2 = 50 2 − 35 2 = 35.7 kVAr https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315863122/b66584da-ae46-426e-a83c-08160dc244ad/content/math1_56.tif"/>

Leading kVAr required k W k V A = p f https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315863122/b66584da-ae46-426e-a83c-08160dc244ad/content/math1_57.tif"/>

Transpose for kVA k W 0.9 = 38.8 35 0.9 = 38.8 k V A r = 38.88 2 − 35 2 = 16.93 kVAr https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315863122/b66584da-ae46-426e-a83c-08160dc244ad/content/math1_58.tif"/>

76Lagging kVAr – leading kVAr = kVAr taken by capacitor

= 35.7 – 16.93 = 18.77 kVAr (see Figure 61). Power factor improvement https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315863122/b66584da-ae46-426e-a83c-08160dc244ad/content/fig1_61.tif"/>