How can we determine the phase voltage of a balanced triangle three-phase source when impedances are present in that source and knowing the line voltage?

When we only have voltage sources, the line voltage gives us the value immediately:

line voltage = (triangle) phase voltage

When we include impedances within the source, this relationship isn't true anymore. How do we find the values of the (triangle) sources (e1,e2 and e3) in that case?

Here's an image of a circuit to better visualize the problem (consider R1 = R2 = R3).

Delta with resistances

Thank you!

  • \$\begingroup\$ We will help you, but we don't do homework for you. What is the relationship between phase voltage and line voltage if there was no resistance in the phase? Edit your question stating what you know and where you are stuck. \$\endgroup\$ – StainlessSteelRat Aug 13 at 22:26
  • \$\begingroup\$ I stated (maybe not explicitly) in my question what I knew; when we have no resistances, the line voltage is directly equal to the (triangle) phase voltage. When we include resistances, we don't have that direct relationship anymore, and I don't know the steps involved in finding the values of (triangle) e1,e2,e3 in that case :-) \$\endgroup\$ – FredV Aug 13 at 22:45
  • \$\begingroup\$ So what does KVL tell you? \$\endgroup\$ – StainlessSteelRat Aug 13 at 23:23
  • \$\begingroup\$ if v1, v2 and v3 are the voltages across each resistor, then we have v1 + v2 + v3 + e1 + e2 + e3 = 0 \$\endgroup\$ – FredV Aug 13 at 23:54
  • \$\begingroup\$ We have to do that as vectors. And would v1 add to the voltage generated by e1? Do the loop for vRS. \$\endgroup\$ – StainlessSteelRat Aug 13 at 23:59

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