powerpower-engineeringtransmission line
Why power transmission lines voltage regulation is referenced to the receiving end voltage not the sending end voltage?
It's more logical to divide the difference between the sending and receiving end voltages by the sending voltage since it's held constant, right?
Reflections happen everywhere, not just in transmission lines. Transmission line is a model of the physical situation, which is easy to apply to a pair of conductors whose length is comparable to or larger than the wavelength of the signal, and which is regular in cross section.
What determines whether reflections matter is the frequencies in and the physical size of the circuit. If you have unmatched impedances then you do get reflected waves just as you describe, and either you have to deal with them or they are negligible for some reason. Here are two reasons:
For exclusively low-frequency circuits, the reflections reflect repeatedly and settle down on a timescale much faster than the signals change. That is, each double reflection is an extra signal which is merely out of phase with the original signal, but as they get more out of phase their amplitude drops quickly enough that they can be neglected. (Even RF circuits can be built this way, as can be seen from a lot of homebuilt HF amateur radio gear.)
As frequency increases, wavelength decreases, and the physical size of your components becomes relatively larger, and you start having to worry about avoiding impedance “bumps”. This is where you start using microstrip design techniques in printed circuits.
In digital circuits, sharp transitions may have high-frequency components that will reflect but you don't have to worry about this as long as your clock speed is much slower than the length of your traces/wires (there's a conversion via c to make that make sense, of course) because by the time the clock makes its next tick all the signals have settled down to a steady state.
(Note that there are no standing waves here because within the period of a single clock tick the driving signals are steps (high to low or low to high logic levels), not periodic signals.)
As clock speed increases, the settling time available decreases, requiring you to either minimize reflections or minimize signal travel time (so that the settling occurs faster).
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".)
Best Answer
The user at the receiving end of the line want to see a constant as possible voltage. So regulating in respect to the receiving end is the correct thing to do. That way the voltage at the receiving end becomes independent of the line load.
Compare this to a 4 wire power supply where the sense wires (almost no current and therefore no voltage loss) are connected to the end of the supply wires (voltage loss depends on the load). That way the voltage at the user or receiving end can be regulated by the power supply to be constant at the receiving end.