Engineering Power Flows and Losses in a line between two buses

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The discussion focuses on verifying calculations related to power flows and losses between two buses in a power system. The original poster acknowledges initial confusion but concludes that the calculations are simpler than expected due to pre-calculated voltages and powers. They identify an error in calculating losses, stating that the correct method involves using the voltage difference multiplied by the current, rather than the conjugate current. The reactive power produced is calculated based on the current and capacitive reactance. Ultimately, the poster admits to being incorrect and acknowledges the accuracy of the other participant's calculations.
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Homework Statement
Attached below.
Relevant Equations
Attached below.
Question:
question.png

Equations:
eq.png

My solution:
attempt.png


Could someone verify my answer?
 
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I apologize for the delay. At first glance it seemed complicated especially because Ybus = 0. in reality it is much easier because the voltages and powers are already calculated.
The calculation seems correct to me except for the losses between 2 and 3 which must be the product of V2-V3 voltage with the current and not V2 with the current conjugated as for the flow. There are not actual losses since no resistance is there but only a capacitor of 0.1 ohm reactance. That means the reactive power produced in there it is I^2*Xcap
If I23=0.038-0.053i and Iabs=0.0652 the Qloss=0.0652^2*0.1=0.0004253 [Var] p.u.
The product (V2-V3)*I23=-0.0004253 [Var] p.u. also.
 
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Sorry. Following the publication of Mr. Hadi Saadat

Power System Analysis chapter 6 Power Flow Analysis Example 6.7

it turns out that I was wrong and you are right.

I am still very busy and I have no time to check this.
 

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