Power Factor- Reactive (kVAr) power calculation

CALCULATION OF REACTIVE POWER

Consider: A 5-MVA transformer is loaded to 4.5 MVA at a power factor of 0.82 

lag. Calculate the leading kVAr necessary to correct the power factor to 0.95 lag. If the 

transformer has a rated conductor loss equal to 1% of the transformer rating, calculate 

the energy saved assuming 24-hour operation at the operating load.

Given Data:

•Transformer capacity (rated) = 5 MVA

•Transformer actual loading = 4.5 MVA

•Load power factor = 0.82 lagging

•Rated transformer loss = 1% of transformer rating

•Operating hours = 24

•CosØ1 = 0.82 lagging

•CosØ2 = 0.95 lagging

Task:

•Required leading kVAr to correct power factor at 0.95 lagging

Calculations:

𝐸𝑥𝑖𝑠𝑡𝑖𝑛𝑔 𝑝𝑜𝑤𝑒𝑟 𝑓𝑎𝑐𝑡𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 = ∅1 = cos−1 0.82 = 34.9°

𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑓𝑎𝑐𝑡𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 = ∅2 = cos−1 0.95 = 18.2°

𝑃 = 𝑆1 cos ∅1 = 4.5 × 0.82 = 3.69 𝑀𝑊

𝑄1 = 𝑆1 sin ∅1 = 4.5 × 0.572 = 2.574 𝑀𝑉𝐴𝑟

𝑄2 = 𝑃 tan ∅2 = 3.69 × tan 18.2 = 1.214 𝑀𝑉𝐴𝑟

The leading MVAr necessary to improve the power factor from 0.82 to 0.95 

 = Q1-Q2 = 1.362 MVAr

For a transformer load with improved power factor,

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