Power Flow Calculation for 3 Bus System w/ Equal Impedance

[Sara Samuel]

Homework Statement

If a 3 bus power system with buses A and B as generator buses and bus C as load bus.
Power injection at bus A is 30 MW, at bus B is 60 MW and at bus C 90 MW withdrawal. Impedances in the 3 transmission corridors B-A, A-C and B-C are equal, i.e. X1 = X2 = X3. What is the power flow in each of the 3 transmission corridors?
Note: power flow direction in transmission corridors is indicated as B-A, A-C and B-C.

Homework Equations

The Attempt at a Solution

I assumed that equal impedances makes the power injection at bus B be equally divided bet. the 2 transmission corridors B-A and B-C, i.e. Power in B-A is 30 MW and in B-C is 30 MW and in A-C is 30 + 30 = 60 MW.
Is my assumption correct?

 

[KataKoniK]

I would approach this problem by first looking at the power flow equations for a 3 bus system. These equations take into account the power injections at each bus, the impedance of each transmission corridor, and the voltage at each bus.

Based on the given information, it seems that the power flow in each transmission corridor would be equal, as the impedances are equal and the power injections at bus A and B are also equal. However, I would want to confirm this by using the power flow equations and solving for the power flow in each corridor.

Additionally, I would also consider the voltage at each bus and how it may affect the power flow. If the voltage at bus A and B is higher than bus C, then the power flow in the B-A and B-C corridors may be slightly higher due to the higher voltage causing a higher current flow.

In conclusion, while your assumption may be correct, I would want to confirm this by using the appropriate equations and considering all factors that may affect the power flow in each transmission corridor.