Numerically Robust Load Flow Techniques in Power System Planning

Abstract

Since deregulation of the electric power industry, investment in the sector has not kept up with demand. State grids were interconnected to form vast power networks, which increased the overall system’s complexity. Conventional generation sources have, in some cases, closed under financial stress caused by the growing penetration of renewable sources and unfavourable government measures. The power system must adapt to a more demanding environment to that for which it was conceived. This thesis investigates the robustness of planning and simulation study tools for the determination of bus-voltages and voltage stability limits. It also provides an approach to obtain greater certainty in the determination of voltages where conventional methods fail to be deterministic. Two complementary methods for determining the collapse voltage are developed in this thesis. The first method applies Robust Padé approximations to the holomorphic embedding load flow method; while the second method uses the Newton-Raphson numerical calculation method to obtain both high and low voltage solution branches, and voltage stability limits of power system load buses. The proposed methods have been implemented using MATLAB and been demonstrated through a number of IEEE power system test cases. The robust Padé approximation algorithm improves the reliability of solutions of load flow problems when bus-voltages are presented in Taylor series form by converting the series into optimised rational functions. Differences between the classic Padé approximation algorithm and the new robust version, which is based on singular value decomposition (SVD), are described. The new robust approximation method can determine an optimal rational function approximation using the coefficients of a Taylor series expansion. Consequently, the voltage collapse points, as well as the steady-state voltage stability margin, can be calculated with high reliability. Voltage collapse points (i.e. branching points) are identified by using the locations of poles/zeros of a rational function approximation. Numerical examples are devised to illustrate potential use of the proposed method in practical applications. Use of the Newton-Raphson method, combined with the discrete Fourier transform and robust Padé approximation, enables the calculation of the voltage stability limits and both the high and low voltage solution branches for the load buses of a power system. This can work to a great advantage of existing N-R based software users, as problems of initial guess, multiple solutions and Jacobian matrix conditioning when operating close to the voltage collapse point are avoided. The findings are assessed by comparisons with conventional Newton-Raphson, the holomorphic embedding load flow method, and continuation power flow method. This thesis contains a combination of conventional and publication formats, where some introductory materials are included to ensure that the thesis delivers a consistent narrative. For this reason, the first two chapters provide the required background information, research gap identification and contributions, whilst other chapters are written to provide more detailed work that has not yet been published or to summarise the research outcomes and future research directions. Furthermore, publications are listed in their publication formats, complete with statements of the authors’ contributions.