Write the equations of the power flow problem and plug in the value of the parameters. Articulate what variables need to be solved and by what equations.

Engineering by Geoffrey

4-bus power system has the following model data:

BaseMVA = 100.

Transmission line data:

Line from_bus to-bus r (p.u.) x (p.u.) b (p.u.)
1 1 2 0.00 0.1 2
2 1 4 0.00 0.2 2
3 2 4 0.00 0.2 2
  • ‘from_bus/to_bus’: the buses connected to the transmission line
  • ‘r (p.u.)’: series resistance in p.u. of transmission line
  • ‘x (p.u.)’: series reactance in p.u. of transmission line
  • ‘b (p.u.)’: total shunt susceptance of transmission line

Transformer data:

Transformer from_bus to-bus x (p.u.) t angle (deg)
1 3 1 0.1 1.01 0
  • ‘from_bus’: the bus connected to the primary winding of transformer
  • ‘to_bus’: the bus connected to the secondary winding of transformer
  • ‘x (p.u.)’: leakage reactance in p.u. of transformer at nominal tap
  • ‘t’: tap ratio by the transformer
  • ‘angle(deg)’: phase shift in degree by transformer

Bus data:

Bus Type Pd (MW) Qd  (MVAR) gs (p.u.) bs (p.u.)
1 1 200 100 0 1
2 3 0 0 0 0
3 2 0 0 0 0
4 2 400 200 0 0
  • ‘Type’: type of bus. ‘1’: PQ bus; ‘2’: PV bus; ‘3’: Vθ bus
  • ‘Pd’: real power of load to bus
  • ‘Qd’: reactive power of load to bus
  • ‘gs/bs (p.u.)’: conductance/susceptance in p.u. of shunt device at bus

Generator data:

Generator Bus Pg (MW) Vm (p.u.)
1 2 * 1.00
2 3 100 1.00
3 4 100 1.00
  • ‘Bus’: the bus to which generator is connected
  • ‘Pg’: real power generation.
  • ‘Vm (p.u.)’: output voltage magnitude in p.u. of generator

Questions: 1) list the knowns and unknowns of the power flow problem

2) write the equations of the power flow problem and plug in the value of the parameters. Articulate what variables need to be solved and by what equations.

3) (required for 5332 students only) Find the expression of the Jacobian matrix

4) (required for 5332 students only) follow the example code and implement the Newton-Raphson algorithm to solve the power flow with a cold start.

5) (required for 5332 students only) find the values for the unknown listed in Part 1).

Note: Bus 1 has a shunt capacitance