Solução do problema de fluxo de potência no plano complexo via métodos de gradientes conjugados

Abstract

The technical literature in numerical analysis offers several alternatives of iterative methods for the solution of nonlinear optimization problems applied to the energy industry. However, when it comes to iterative methods applied to nonlinear power flow, the Newton-Raphson iterative method and its variations are practically unanimity. The work proposal of this master’s thesis aims to investigate the performance of nonlinear Complex Bi-Conjugate Gradient Methods (CBiCG) in their application to power flow problems, in comparison with the classical formulation, using the Newton- Raphson in polar coordinates in the domain of real numbers. These methods, however, were implemented in the complex domain through the use of the Generalized Wirtinger calculus and the extension of Taylor series to the complex domain. The main motivations for this approach are that the conjugate gradient methods are first order and do not require factoring the Jacobian matrix as is done in the traditional Newton-Raphson method, thus reducing the computational effort required to obtain the solution. In addition, in view of the current computational complexity, there has been a tendency for processor architecture to incorporate SIMD (Single Instruction, Multiple Data), which refers to a set of operations for efficiently handling a large amount of data in parallel, using a vector or matrix processor, suitable for the algebra of complex numbers.