I am new to per unit quantities, and have tried various combinations of search terms on Google over the span of a week and a half but I'm finding myself still stuck.

In the SI edition of Power Systems Analysis by Grainger/Stevenson/Chang, the authors present a list of formulas (p42) that relate various base quantities for single-phase systems. All of them make sense to me except the ones encircled in red.

kW = kVA holds true only when power factor is zero right? Surely this equality does not hold in general for single-phase systems? Why is this formula in this list at all?

Equations 2.48 & 2.49 on p42 of Grainger/Steven/Chang


1 Answer 1


You are correct that KW only equals KVA when power factor is 1. They are not suggesting otherwise.

The text is just telling you that the base for \$KW_{pu}\$ and \$KVA_{pu}\$ is the same numerical value. Just like the impedance base is the same numerical value for resistance, \$R_{pu}\$, as it is for reactance, \$X_{pu}\$.

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    \$\begingroup\$ My original comment didn't go through -- thank you for understanding my question and helping me out here relayman \$\endgroup\$ Commented Mar 16, 2022 at 2:15
  • \$\begingroup\$ You are very welcome. \$\endgroup\$ Commented Mar 16, 2022 at 2:29

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