abstract: For a (N+1)-bus power system, possibly 2N solutions exists. One of these solutions is known as the high-voltage (HV) solution or operable solution. The rest of the solutions are the low-voltage (LV), or large-angle, solutions. In this report, a recently developed non-iterative algorithm for solving the power- flow (PF) problem using the holomorphic embedding (HE) method is shown as being capable of finding the HV solution, while avoiding converging to LV solutions nearby which is a drawback to all other iterative solutions. The HE method provides a novel non-iterative procedure to solve the PF problems by eliminating the non-convergence and initial-estimate dependency issues appeared in the traditional iterative methods. The detailed implementation of the HE method is discussed in the report. While published work focuses mainly on finding the HV PF solution, modified holomorphically embedded formulations are proposed in this report to find the LV/large-angle solutions of the PF problem. It is theoretically proven that the proposed method is guaranteed to find a total number of 2N solutions to the PF problem and if no solution exists, the algorithm is guaranteed to indicate such by the oscillations in the maximal analytic continuation of the coefficients of the voltage power series obtained. After presenting the derivation of the LV/large-angle formulations for both PQ and PV buses, numerical tests on the five-, seven- and 14-bus systems are conducted to find all the solutions of the system of nonlinear PF equations for those systems using the proposed HE method. After completing the derivation to find all the PF solutions using the HE method, it is shown that the proposed HE method can be used to find only the of interest PF solutions (i.e. type-1 PF solutions with one positive real-part eigenvalue in the Jacobian matrix), with a proper algorithm developed. The closet unstable equilibrium point (UEP), one of the type-1 UEP’s, can be obtained by the proposed HE method with limited dynamic models included. The numerical performance as well as the robustness of the proposed HE method is investigated and presented by implementing the algorithm on the problematic cases and large-scale power system. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015