Dear Dr Zimmerman, I am sorry I forgot to attach the image. Please find the 
attached image file. 

I am trying to understand the results that I got from a simple power flow , by 
verifying them through manual calculations - and the results do not add up. The 
very simple network that you see, has the 4 equations written.

1.  Is there any mistake that I cannot see, in my equations? Why aren't they 
verified by the results I got?
2.  In my results the DG at bus 5, sends power to bus 1 , and bus 1 sends 
reactive power to the grid. So 
     lines 1-2, 2-3, 3-5 have real powers going from right to left, and 
reactive powers going from left to right.
     Is this possible in reality to occur given that the current only travels 
one direction?  

<<attachment: SIMPLE.jpg>>

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