Nonlinear optimal power flow by interior and noninterior point methods

Optimization of power systems is one of the areas where interior-point (IP) methods are being applied extensively; due to the size and special features of these problems, IP methods have computationally proven to be a viable alternative for their solution. In this thesis, we propose and investigate a number of IP methods for solving large nonlinear programming (NLP) problems. The IP method that we study belongs to the class of infeasible primal-dual path-following methods. Four higher-order variants of this IP method are considered as well: (i) the predictor-corrector method, (ii) the perturbed composite Newton method, (iii) the multiple predictor-corrector method, and (iv) the multiple centrality corrections method. The proposed IP algorithms are then applied to specialized optimal power flow (OPF) problems that use voltages either in polar or in rectangular coordinates. When formulated in rectangular coordinates, some OPF variants have quadratic objective and quadratic constraints. Such quadratic features allow for ease of matrix setup and inexpensive incorporation of second-order information in higher-order variants of the IP method.; A non-interior-point (NIP) method for solving nonlinear OPF problems is also proposed in this thesis. Unlike IP methods, the NIP method handles the complementarity conditions for optimality in such a way that the strict positivity conditions are not required to be satisfied at every iterate. This approach derives from reformulations of complementarity problems as nonlinear systems of equations, and allows for a Newton-type method to be used. To reformulate the OPF problem as a nonlinear system of equations, we handle the complementarity conditions by means of an NCP-function, which is a function ψ_μ: $R2\to R$ that satisfies the property: $yma,b=0\iff a>0,b>0$ and $ab=m$, for any μ > 0. Since the non-negativity of any limit point is automatically assured by NCP-functions, without imposing additional conditions, the initial point and the iterates do not necessarily have to stay in the positive orthant.; In this thesis, we have derived the proposed IP and NIP algorithms based on an NLP problem form that is suitable to express most OPF problems. Many important issues for the efficient implementation of these algorithms, as related to nonlinear OPF solution, are discussed in detail. Numerical results illustrate the viability of the proposed algorithms as applied to several power networks that range in size from 14 to 2098 buses.