#### Title

Mixed mesh/nodal magnetic equivalent circuit modeling of a six-phase claw-pole automotive alternator

#### Date of Award

4-2016

#### Degree Type

Thesis

#### Degree Name

Master of Science in Electrical and Computer Engineering (MSECE)

#### Department

Electrical and Computer Engineering

#### First Advisor

Steven D. Pekarek

#### Committee Chair

Steven D. Pekarek

#### Committee Member 1

Gregory M. Shaver

#### Committee Member 2

Scott D. Sudhoff

#### Abstract

Magnetic equivalent circuits (MECs) have been employed by many researchers to model the relationship between magnetic flux and current in electromagnetic systems such as electric machines, transformers and inductors [1] ,[2]. Magnetic circuits are analogous to electric circuits where voltage, current, resistance and conductance are the respective counterparts of magneto-motive force (MMF), magnetic flux, reluctance and permeance. The solution of MECs can be accomplished with the plethora of techniques developed for electrical circuit analysis. Specifically, mesh analysis, based on Kirchoff’s Voltage Law (KVL), and nodal analysis, based on Kirchoffs Current Law (KCL), are two very common solution techniques. Once an MEC is established, the question is often of which circuit analysis technique should be applied in order to minimize computational effort.

For linear circuits, there is little advantage to using mesh over nodal analysis. Using one method may yield a system with fewer equations, but for most problems the difference in unknowns is insignificant. When analyzing nonlinear magnetic systems, researchers have noted a significant difference in mesh versus nodal analysis. Derbas et al have noted that for nonlinear MECs a mesh analysis reduces the number of iterations required to solve the nonlinear system using a Newton-Raphson method [3]. It was further shown that for strong nonlinearities caused by magnetic saturation, a nodal-based solution will often fail to converge whereas a mesh-based solution will converge.

It is relatively easy to apply MEC analysis to stationary magnetic systems. However, modeling electric machinery with MECs can be challenging since the circuit structure can depend on the position of the rotor. Specifically, in the case in which mesh-based solution techniques are applied, the circuit components representing the airgap will tend to infinite values as stator/rotor structures (i.e. teeth) come into and out of alignment. As a result, one must eliminate these elements and establish new KVL loops with the remaining non-infinite components. Researchers have developed algorithms to automate the loop construction process [4]. However, the algorithms require one to categorize all potential overlap positions, which is a challenge for claw-pole machines. One does not experience this issue in nodal-based solution techniques. However, since machines tend to operate in saturation, issues of convergence are often encountered.

In this research, an alternative solution technique is provided in which mesh analysis is used in all magnetically nonlinear flux tubes while nodal analysis is used to solve for quantities in the airgap. This has the potential to use the advantage of each solution technique. This research builds upon that presented in [5], in which permeance expressions for all flux tubes were developed for a nodal MEC model of a three-phase claw-pole alternator with a delta-connected stator. In addition to the mixed mesh/nodal system a second focus is to explore new model configurations including six-phase machines with wye-connected stator and permanent magnets on the rotor. Validation of the models that are proposed is performed using both FEA models and experimental data from commercially-available alternators.

#### Recommended Citation

Horvath, Daniel C., "Mixed mesh/nodal magnetic equivalent circuit modeling of a six-phase claw-pole automotive alternator" (2016). *Open Access Theses*. 775.

https://docs.lib.purdue.edu/open_access_theses/775