Calculation of voltage drop in power systems - The value that matters is not obtained directly by Ohm's law formula. Most Commonly Used Approximate Formula where neither “er” nor “es” is known is dV=[R.cos(phi)+X.sin(phi)] x I per phase.

1. EBH - Calculation of voltage drop in power systems:
Attention! The value that matters is not obtained directly by Ohm's law formula.
Most Commonly Used Approximate Formula where neither “er” nor “es” is known:
ConsiderV1(=esinthe fig) andV2 (=er inthe fig) the complex values(magnitude andangle)
and abs (V) = magnitude of V,then:
a) Ohm'slaw:V1-V2 = Z.I => abs (V1-V2) = abs(Z.I) = sqrt (R ^ 2 + X ^ 2) .I per phase.
b) dV that usuallymattersinpowersystems:dV =abs (V1) -abs(V2) = K. [R.cos(phi) + X.sin
(phi)].I.(approximate equation);where K= 1 per phase;K = sqrt (3) forthree-phase system
and K = 2 for single-phasesystems (2conductors).Thisequationcanbe deducedbyfollowing
the considerationsinthe figure (phasordiagram).
and:
[cos(phi)] ^ 2+ [sin(phi)] ^2 = 1 => sin(phi) =sqrt {1- [cos(phi)] ^ 2}
or sin(phi) = sin{arccos [cos (phi)]}
Note that:
1. abs (V1) - abs(V2) ≠ abs (V1-V2),sothe dV that usuallymattersinpowersystemsis
not a value obtaineddirectlyfromOhm'slaw.
2. If you knowV1 or V2 you can calculate the exactdV,withoutthisformula,thisformula
isuseful whenyoudonotknow both.