# How to choose the receiving end voltage for a transmission line using a short line approximation

I am confused as to how to choose the receiving end voltage for a short line approximation

For example if i have a 220kV transmission line at 50Hz at 60Km. At the end of teh line theirs a load of 50MW and the lines impedance is Z=5+6j. The question asks find the sending end voltage using Vs=VR+ZIR. I can do the calculations all fine etc. The problem i have is what would i select my Recieving end voltage to be?

Do i do 220kV or do i do something less than 220kV, does it matter at all if i choose less than 220kV since as the transmission line is 220kV does this mean the line wants to see 220kV along it (like example 220kV is seen in the middle of the line and the sending end is higher and recieving end lower?)

Hence i am confused as to what to choose for VR as its not given, all that is stated is the line voltage being 220kV for the transmission line. What does the transmission line voltage mean?

When i state i have a 220KV transmission line does that mean the end voltage of the line is 220kV

Note i know to get Vr its line to neutral voltage but to just get the concept what line to line voltage would be used

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• This question i state is made up by myself for understanding purposes

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I find that the concept of sending/receiving end voltage is somewhat meaningless in most cases. Actual transmission lines are connected in complex networks with distributed impedance (the line itself) and point impedance (loads tapped off) all over the network. There is no set beginning or end.

In the real world you have to keep all points on the line within the stated tolerance of the nominal voltage. Typically that's +/-10%. At lower, distribution level voltages where the source impedance is higher, they will often times use voltage regulators or on-load tap changers to maintain the bus voltage dynamically.

But for your text book question I think that they want the receiving end voltage to be the nominal 220kV and the sending end voltage would be chosen to allow for drop.

• Thanks!! Sorry the question was made up for a better understanding. I have to actually design a short line for a nominal voltage of 220 kV ( i calculated using empirical formula). Hence my recieving end voltage could be 200Kv up to 220KV actually as thats 10% of the nominal. Also you wouldnt possibly have a reference to this tolerance would you? So for example i couyld choose 220kV as my receiving end voltage, then if i had a loss of 5kV, the sending end voltage would be 225kV and as this is less than 10% this is all fine? Apr 10, 2018 at 13:35
• Also is there a reason in any circumstance where you would have to use a lower receiving end voltage when compared to teh nominal voltage or is that only when the tolerance is to high (eg i chose 220kV as recieving end and the loss was 30kV (higher than 10%), then i would have to choose a lower recieving end voltage for all points to be less than 10%? Apr 10, 2018 at 13:36

You say: -

The question asks find the sending end voltage

If you are given a voltage and a line length and a line impedance then clearly the voltage you have been given (220 kV) is the voltage at the end of the line feeding the 50 MW load.

There can be no other reasonable options. Make your assumptions and answer the question. In stating your assumptions and working through the problem you will demonstrate that you know how to answer this question.

• Sorry the question is made up just for a better understanding, i understand if it was a textbook question it would be that but the actual task i have been set is to design a short line transmission line. I used the empirical formula to get the transmission line voltage i needed and hence got confused as i was unsure that this line voltage eg 220kV i calculated would be the receiveing endd voltage for the load or not or it wouldnt matter whether the receiving end is 10% less than the 220kV Apr 10, 2018 at 13:24
• I'm unsure how you want me to respond. Apr 10, 2018 at 13:53
• The answer above your states that the nominal voltage has to be within 10% of the voltage across the line. Hence aslong as the received end voltage is less than 10% (i.e. could be eg for 220kV could be anywhere from 220kV to 200kV) and then aslong as the sending end voltage is less than 10% it is fine? Apr 10, 2018 at 14:01
• Ditto my previous comment. We seem to be confusing each other. Get to your point please. Apr 10, 2018 at 14:07
• Essentially can the receiving end voltage be within 10% of the nominal voltage as long as the sending end voltage is also within 10% of the nominal voltage. Anyways thanks for the help Apr 10, 2018 at 14:12