A two-bus power system is interconnected by one transmission line. Bus 1 is a generator bus with specified terminal voltage magnitude of |V1| pu. We desire to solve the power flow problem for this system. a. Identify the variables in the solution vector assuming Bus 2 is a load bus with specified demand as PD pu and QD pu.
b. Identify the variables in the solution vector assuming Bus 2 is a PV bus.

a) | v2 | ,  β2   ( load, bus voltage at bus 2 )

  p1 ,  q1 ( slack, bus power at bus 1 )

b) q2 , β2  

  p1 and q1 ( slack, bus power at bus 1 )

Explanation:

Attached below is a schematic representation of the solution

a) Identify the variables in the solution vector assume Bus 2 is a load bus

The specified parameters are ; P2 and q2

while | v2 | and β2 are not specified

given that bus 2 is a load bus, bus 1 is a slack bus with ; | v1 |  and β1 been specified while p1 and q1 are not specified

Hence the variables in the solution

= | v2 | ,  β2   ( load, bus voltage at bus 2 )

  p1 ,  q1 ( slack, bus power at bus 1 )

b) Identify the variables in the solution vector ( assume Bus 2 is a PV bus )

specified at Bus 2 are ; | p2 | , | v2 |

unspecified : q2 , β2

Bus 1 ( still a slack bus )

specified parameter : | v1 |  and β1

unspecified : p1 and q1

Hence the variables in the solution

= q2 , β2  

  p1 and q1 ( slack, bus power at bus 1 )