To obtain the solution to the problem, we first form an augmented cost function which factors the equality and inequality constraints as follows:

C = 50 *P1 + 300 * P1 ² + 50 *P2 + 250 * P2 ² -

l1 * (P1 - PL1 - V1 ²*cosf / Z + V1*V2*cos(f + d1-d2) /Z ) -

l2* (P2 - PL2 - V2 ²*cos f /Z + V1*V2 *cos(f + d2-d1) /Z ) +

p(P1-3.0)+p(P2-3.0)+p(V1-1.025)+p(V2-1.025)+p(0.975-V1)+p(0.975-V2)

where the penalty function has the form : , b being set to 100.

We then set all the partial derivatives to zero and solve the resulting equations to obtain the values of the variables which result in the minimum value of C. The equations to be solved are non-linear algebraic equations and can solved by a variant of Gauss Siedel method. (You may try the same using gradient descent method which was discussed in the previous lecture). A matlab program to do can be downloaded here: opf.m . This may be run by typing opf at the MATLAB prompt.