Date of Award

Spring 1-1-2021

Degree Type


Degree Name

Master’s In Electrical Engineering Degree


Electrical Engineering And Computer Science

First Advisor

Ye, Hongxing

Second Advisor

Dr Hongkai Yu

Third Advisor

Dr Zhiqiang Gao


With increasing load and aging grid infrastructure, an accurate study of power flow is very important for operation and planning studies. The study involves a numerical calculation of unknown parameters, such as voltage magnitude, angle, net complex power injection at buses and power flow on branches. The performance of traditional iterative power flow methods, such as Newton-Raphson, depends on initial starting point, does not guarantee solution for heavily loaded, and poor convergence for unbalanced radial power system. Holomorphic load embedding is a non-iterative and deterministic method for finding steady-state solutions of any power system network. The method involves converting voltage parameter at every bus into an embedded parameter (a) where analytic continuation is applied using Pade' approximants. The embedded parameter (a) acts as a well-defined reference for the complex analysis and solution obtained when setting a simple value a is known as Germ Solution, by some texts. Using the values of coefficient of Maclaurin Series, the Holomorphic method can find solutions in the whole complex plane using analytic continuation as it extends the nature offunction beyond the radius of convergence. The holomorphic embedding method has been applied in the past to solve power flow problems in balanced power system models. There are several advantages ofthe iv said method over traditional iterative techniques, such as guaranteed convergence, the existence of solution, and faster calculation for certain cases. The method dives into complex analysis, algebraic curves, Taylor series expansion, Pade' approximants, and solving a linear set of equations. . For simplicity purpose, the networks are often assumed to be balanced with constant power loads. Power flow analysis and its derivatives are performed on a single-phase equivalent of the same system. For bulk systems, the assumption is acceptable as load aggregation balances the loads in each phase to an acceptable level. However, in low-voltage distribution systems, ignoring such parameter could lead to an incorrect solution. In this work, a class of Holomorphic load-flow method is proposed to solve the power flow problem in three-phase distribution systems with unbalanced wye-connected loads.