The interior point methods have been proven successful for solving power system optimal power flow problem. Many engineering problems, including the operation of power systems, are concerned with the efficient use of limited resources to meet specified objective. Two methods commonly used are linear and quadratic programming. The former solves those problems where both the objective and constraints are linear in the decision variables. The quadratic optimization method assumes a quadratic objective and linear constraints. The well-known simplex method has been used to solve linear programming problems. In general, it requires burdensome calculations, which hamper the speed of convergence. Affine-scaling methods have no known polynomial time complexity, and can require an exponential number of iterations if they are started close to the boundary of the feasible region. Path-following methods generally require O iterations in the worst case, work by using Newton's method to follow the central path of optimal solutions obtained by family of problems defined by logarithmic barrier function.