Help with power transfer between two power source

[lukicama]

I am strugling with this for hours so any help would be aprecitated.



The voltage source on the left side and on the right side have same voltage level. The main question is; if the angle of the first one is 30degrees what angle do we need on second power source for maximum power transfer from left to right. I tried to simulate something in one program and I picked many angles and found one and with that angle right watmetar shows largest power. Not sure if it's correct. I must know the way to do that on paper, not guesing. It is strange to me that the left side is giving 3,19W and the right can take a lot more... I can't figure the 3,58A. It should be I=U/Z*sin(fi) and from it, it couldn't be grater then 2A (U=10/Z=5)......

 

[kak111]

With ideal power sources ( Z = 0+j0 ) and equal frequencies
power has max. value , when phase difference is 180 degr. ( Pi rad. )

 

[lukicama]

That was my first idea but got confused cause a program showing larger value on right power meter.
It makes sense cause when the difference between them is 180, current flow is highest, power meter shows same power on both sides wich means that power produced on the left side is full acepted on the right. Still confused cause a programs right power meter shows larger value. If I put the difference between them 180 degr. same voltage, freq., I have 4A and power meter 12W and -12W. If power meter shows negative value that means that power source accepting power. I don't see how in first case it can take so much cause on the left is only 3,19W giving. If the 180degr.difference is the answer how much power do I transfer in this case? 12W?

 

[FvM]

If power meter shows negative value that means that power source accepting power.

That's not true for the right power meter, because it's connected to measure power flow from left to right. You may want to correct it.

With the present phase settings, both sources are sourcing real power.

If I put the difference between them 180 degr. same voltage, freq., I have 4A and power meter 12W and -12W.

This can hardly happen with a partly resistive impedance connecting both sources. At least part of the transferred power will be necessarily absorbed.