power-flow equations, DC power-flow solution(Newton,fast decoupled). Using MATLAB.

Consider the following power system.

Use j0.1 as the transmission line impedance for the three lines between Buses 1 and 4, 2 and 4, and 3 and 5 respectively.

Suppose the following are specified:

PG2 = 0.6, V2 = 1.05, PG3 = 1.0, V3 = 1.06

PL2 = 0.2, PL3 = 0.3, PL4 = 0.8, PL5 = 0.8

QL2 = 0.1, QL3 = 0.1, QL4 = 0.2, QL5 = 0.2

a) Classify the bus types and write out the power-flow equations.

b) Find the power-flow solution using “fsolve” in Matlab.

c) Compute the DC power-flow solution.

d) Starting from the DC power-flow solution, implement the Newton-Algorithm till all the power mismatch errors are smaller than 0.001 pu. How many iterations does it take to reach convergence?

e) Starting from the DC power-flow solution, implement the fast decoupled power-flow algorithm until all the power mismatches are smaller than 0.001 pu. How many iterations does it take to reach the convergence?

f) Repeat parts c, d and e, when each of the loads specified, PL2 through PL5, and QL2 through QL5, become twice the values stated above. Comment on your results.

g) Repeat parts c, d and e, when each of the loads specified, PL2 through PL5, and QL2 through QL5, become half of the values stated above. Comment on your results.