Stochastic Optimal Load Flow Using Newton-Raphson Iterative Technique

ABSTRACT

In this paper we consider the problem of stochastic optimal power flow for an all thermal electric power system. The formulation includes the effects of variables uncertainty modeled as stochastic and normally distributed. The system performance is represented by the load flow equations in polar form, reformulated to include the uncertainty aspect. Inequality constraints are handled using Powell's penalty function method. We employ a variational approach to derive the optimality conditions resulting in a set of nonlinear equations. Newton's method is employed, to actually implement the optimum strategy by solving the nonlinear set of optimality conditions iteratively. An application example involving the IEEE standard 14 bus system is presented and the stochastic solution is compared with a deterministic solution for the same system in order to demonstrate the applicability of the proposed method.