I know that the mathematical equation for the calculation of Line - Line voltage with same frequency, same Phase angle, same Voltage of 3 lines from the same generator.

now, i want to know having different properties of Line - Line Voltage.

what are the mathematical techniques use for this example problem.


L1 — 100V, 50Hz, 30 degree phase angle,

L2 — 230v, 60Hz , 120 degree phase angle,

<code>enter image description here</code>

 (I think it is not practically workout, just assume those are individual generators connected to same neutral )


what is the line to line voltage of L1 & L2 ?

  • \$\begingroup\$ If the frequencies were not different, you would calculate the voltage using phasors or complex numbers. With two different frequencies, you have a non-sinusoidal periodic waveform. \$\endgroup\$ Oct 25 '18 at 17:04
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    \$\begingroup\$ I'm voting to close this question as off-topic because hit is a homework or study question with no effort to solve shown. \$\endgroup\$ Oct 25 '18 at 17:05
  • \$\begingroup\$ i am asking just what are the techniques for that kind of problem, not for exactly solution. i given problem is for just understanding the concept. \$\endgroup\$ Oct 25 '18 at 17:11
  • \$\begingroup\$ trigonometry is the skill-set needed. \$\endgroup\$ Oct 25 '18 at 17:15
  • \$\begingroup\$ The circle marked V? is assumed to be a load, but it could be just a meter to get the voltage across it, you subtract the lower voltage from the higher one. Use complex numbers or phasors. If you don't understand the use of those, you need to lear that first. \$\endgroup\$ Oct 25 '18 at 17:19

Superposition is the only way to do this mathematically.

All the sources but one get shut down. Voltage sources go short. Current sources go open. Calculate everything with one source at a time. Then finally add up all the answers over the appropriate node.

  • \$\begingroup\$ Yes there will be a beat modulated sine wave with a peak voltage equal to the sum of the two sources. \$\endgroup\$
    – KalleMP
    Oct 25 '18 at 21:34

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