When trying to explain the need for high voltage in transmission lines, I came across a formula in one of my old courses: A transmission line is considered, and between the generator end and the load there is a resistor \$R_k\$ and inductor with an impedance \$ X_k\$ modelizing the transmission line. The voltage drop across it became this:

\$ \Delta U\;=\; U_1 \;-\;U_2 \; = \; \frac{1}{U_L}\big( PR_k+QX_k \big) \$

I'd like to know where this formula comes from, I might not have searched enough but I have not found it so far... Also, would it be correct to write the following:

\$ P=RI^2= \frac{U^2_1-U^2_2}{R}= \; \frac{1}{R\cdot U_L}\big( PR_k+QX_k \big)(U_1+U_2)\$
==> "To reduce transmission losses, current can be decreased, or the line voltage increased".

  • \$\begingroup\$ What is P, Q an U\$_L\$? Why isn't current factored in? \$\endgroup\$
    – Andy aka
    Commented Sep 1, 2015 at 9:38
  • \$\begingroup\$ P active power, Q reactive power \$U_L\$ line voltage... \$\endgroup\$
    – alexanzi
    Commented Sep 1, 2015 at 10:20
  • \$\begingroup\$ I have seen the "V_drop = PR + QX" calculation before in Serious Engineering Work. I think it is a simplified equation that is true under certain constraints on power factor etc. \$\endgroup\$ Commented Sep 1, 2015 at 10:53

1 Answer 1


The formula

$$ \Delta V \approx P R + Q X \textrm{ [per unit]}$$

appears to be based on an assumption that the voltage drop will be relatively small.

I have excerpted a few slides from a presentation by Kashem Muttaqi, originally found at http://egpreston.com/VoltageRegulation.pdf , below. The slides explain how we get to the approximate formula.

(This was found on the third page of a search for voltage drop pr qx - apparently pr qx is a fairly unique "phrase".)

enter image description here

enter image description here

enter image description here


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.