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2015

Alternative Measurement Approach UsingInverse Scattering Theory to ImproveModeling of Rotating Machines inUngrounded Shipboard Power SystemsPatrick Ryan Breslend

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FLORIDA STATE UNIVERSITY

COLLEGE OF ENGINEERING

ALTERNATIVE MEASUREMENT APPROACH USING

INVERSE SCATTERING THEORY TO IMPROVE MODELING OF

ROTATING MACHINES IN UNGROUNDED SHIPBOARD POWER SYSTEMS

By

PATRICK RYAN BRESLEND

A Thesis submitted to theDepartment of Electrical & Computer Engineering

in partial fulfillment of therequirements for the degree of

Master of Science

2015

Copyright c© 2015 Patrick Ryan Breslend. All Rights Reserved.

Patrick Ryan Breslend defended this thesis on August 3, 2015.The members of the supervisory committee were:

Chris S. Edrington

Professor Directing Thesis

Lukas Graber

Committee Member

Mischa Steurer

Committee Member

The Graduate School has verified and approved the above-named committee members, and certifiesthat the thesis has been approved in accordance with university requirements.

ii

I dedicate this dissertation to my loving fiance Alicia and my entire family. Without theirunderstanding, moral support, inspiration and most of all love, the completion of this dissertationwould not be possible. I must express the fact that I could not visit my family as much as I wouldhave liked to during the course of my masters and they wholeheartedly accepted it. I owe themquality time, which they missed during my studies.

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ACKNOWLEDGMENTS

I express my deep gratitude to my major professor Dr. Chris Edrington and advisor Dr. Mischa

Steurer for providing a significant opportunity to work on this project at the Center for Advanced

Power Systems funded under the Office of Naval Research. I thank them for their guidance,

encouragement, understanding, and patience throughout the duration of my graduate studies at

FSU. Without their research ideas, and financial support, this thesis would not be possible.

Special thanks to my friend and colleague Behshad Mohebali who worked with me on this

project. He provided generous help and time to help solve the problems I faced while working on

the research. His suggestions and ideas will always be cherished.

I would like to express my sincere thanks to my master’s thesis committee members Dr. Edring-

ton, Dr. Graber and Dr. Steurer for providing valuable suggestions as well as serving on the

committee and providing assistance where needed.

Thanks are due to all my friends and family who have helped me in various capacities in the

completion of this thesis. If it were not for them, I would have honestly struggled to finish.

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TABLE OF CONTENTS

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 High Frequency Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Organization of Master Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 State of the Art 102.1 High Frequency Electric Machine Modeling Approaches . . . . . . . . . . . . . . . . 11

2.1.1 Lumped Element Equivalent Circuit Models . . . . . . . . . . . . . . . . . . . 122.1.2 Distributed High Frequency Models . . . . . . . . . . . . . . . . . . . . . . . 142.1.3 Common-mode and Differential-mode Equivalent Circuit Models . . . . . . . 16

2.2 Scattering Methodology for Measuring Electric Machines . . . . . . . . . . . . . . . . 182.2.1 Linear Time-Invariant Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.2 Instrumentation for Characterizing Machine Coupling to Ground . . . . . . . 202.2.3 Port Determination and Measurement Process . . . . . . . . . . . . . . . . . 23

3 Problem Statement 29

4 Inverse Scattering Theory Applied to Three-Phase Electric Machine Modeling 314.1 Validity of Linear Time-Invariant Networks Applied to Rotating Machines . . . . . . 324.2 Parameter Extraction for Lumped Circuit Model . . . . . . . . . . . . . . . . . . . . 364.3 Virtual Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Results and Comparison to Conventional Techniques 435.1 Resonance and Anti-Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 Short Circuit Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.3 Virtual Measurement Comparison to Impedance Analyzer . . . . . . . . . . . . . . . 51

6 Conclusions and Future Considerations 576.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.2 Future Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.3 A Note to the Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Appendix

A Motor Models 62

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

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LIST OF FIGURES

1.1 All-electric ship proposed by the U.S. Navy [1] . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Equivalent circuit models for capacitors and inductors [2] . . . . . . . . . . . . . . . . 13

2.2 Equivalent lumped model plots for capacitors and inductors [2] . . . . . . . . . . . . . 13

2.3 Distributed high frequency circuit model with 17 turns per slot [3] . . . . . . . . . . . 15

2.4 Parasitic coupling of the ship MVDC power system and ship hull ground [4] . . . . . . 16

2.5 This is a visual representation of scattering parameters for a two–port network . . . . 22

2.6 Port representation for electric machine scattering measurements where T is for termi-nal and P is for port. T2P2 is terminal 2 and also port 2 of the measurement matrix.Each port of the matrix is measured by referencing it to a common ground. . . . . . . 24

2.7 Differential-mode and common-mode capacitive coupling [5] . . . . . . . . . . . . . . . 25

2.8 CM and DM impedance measurement connections [6] . . . . . . . . . . . . . . . . . . 27

2.9 Voltage waveforms corresponding to the 4-port PMSM network with Z0 = 50Ω forboth VNA cables and both single ended terminations . . . . . . . . . . . . . . . . . . 28

4.1 N-connector shield setup for scattering parameter measurements on electric machines(Left) using a vector network analyzer (Right) . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Variation of port 1 reflection (s11) of the brushless DC motor or synchronous machinewith cogged rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Variation of port 1 reflection (s11) of the induction or asynchronous machine withsmooth rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4 Per-phase representation of the induction motor including the high frequency modeland the dynamic dq model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5 Common-mode impedance of a lumped parameter model compared to impedanceanalyzer measurements and scattering parameter model representation . . . . . . . . . 38

4.6 Single–port scattering parameter measurement to obtain common–mode impedanceinformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.7 Single–port scattering parameter measurement to obtain differential–mode impedanceinformation like T1 + T2 to T3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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4.8 Single–port scattering parameter measurement to obtain phase–neutral impedanceinformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.9 Virtual measurements of impedance for phase-to-neutral, common-mode, and differential-mode are compared to measurements made on the physical machine . . . . . . . . . . 41

5.1 Induction motor impedances measured using IA and VNA measurements . . . . . . . 44

5.2 Common-mode impedance of a PMSM equivalent T-circuit . . . . . . . . . . . . . . . 47

5.3 PMSM fault current simulation using a measured fault to trigger a controlled voltagesource coupling terminal T1 to ground and phase T2 and T3 unloaded. . . . . . . . . 48

5.4 Measurement setup for a single phase to ground fault of a three-phase PMSM . . . . 49

5.5 Single phase to ground fault of a three-phase PMSM . . . . . . . . . . . . . . . . . . 50

5.6 T-circuit simulated fault current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.7 PMSM measured impedance compared to simulated T-circuit equivalent . . . . . . . . 51

5.8 Virtual measurement of common–mode impedance . . . . . . . . . . . . . . . . . . . . 52

5.9 Phase–neutral mode impedance data was measured virtually . . . . . . . . . . . . . . 53

5.10 Differential–mode impedance data was measured virtually . . . . . . . . . . . . . . . . 55

5.11 Impedance data was virtually measured and compared to known measured data withhigh accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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ABSTRACT

The Navy has proposed to use a shipboard power system operating at medium voltage direct cur-

rent to distribute power for their all-electric ship. The power is generated by electric machines as

alternating current and requires power electronic rectifiers to output direct current. Power elec-

tronics converters are needed to convert the direct current to alternating current for ship propulsion

and service loads. An increase in the use of fast switching power electronics is expected in future

ships. The increased voltage rise time on switches is known to produce unwanted high frequencies

with corresponding wavelengths of the same order of magnitude as the length of the ship hull.

These high frequency transients can cause the ship system to couple with the surrounding ship hull

causing adverse effects. The amount of high frequency content and the impact it has on the ship

system performance is difficult to calculate with current models. Increased voltage and performance

requirements for power electronics has led to advancements in switching frequencies into the 10s

to 100s of kilohertz and increased voltage edge rates. The faster switching corresponds to higher

frequency responses from the shipboard power system.

Research has shown that high frequency content in electrical power systems is responsible for

parasitic coupling and ultimately damage to the equipment. Electric machines, for instance, have

increased winding and iron losses, overvoltages at the terminals, and even bearing currents via

shaft voltages. The Navy is interested in simulating ship systems to test their electromagnetic

compatibility before implementing or committing to a specific design.

There are numerous techniques used to acquire machine parameters that have been proven to

be useful in modeling electric machine behavior. The approaches were considered by the amount of

proprietary information needed to acquire accurate results, the complexity of the modeling methods,

and the overall time it takes for implementation. A majority of system simulations gravitate towards

simple solutions for machine behavior which require assumptions to be made that deviate from

the actual machine behavior. Exact inner dimensions, winding layouts, end winding dimensions,

insulation thickness, and other information are proprietary and often not accurate representations

of the physical machine once built. It is time consuming to obtain an accurate working model when

assumptions are made or when detailed computer aided design models are needed to calculate

machine response quantities.

viii

The research modeling approach put forth in this paper is not aimed at capturing the steady-

state behavior of the machine. It is shown that a detailed understanding of the motor may not

be necessary to accurately model the high frequency effects. It is the transient behavior at non-

operating frequencies that need to be modeled correctly to develop new models of shipboard power

systems for grounding research. The frequency dependent information is most useful to determine

frequencies of interest that other modeling techniques are less likely to capture and point out.

Previously suggested measurement techniques have been considered useful in determining pa-

rameters of machines but are not always accurately implemented without in-depth knowledge of

the motor that may be proprietary. Lumped-parameter models are based on extracting informa-

tion at transitional frequencies or looking at the slope of a variable over a frequency range. These

models tend to be over simplified representations of the component by averaging the parameters

for given ranges. In reality a machine’s impedance varies with all frequencies. Lumped parameter

based models typically over simplify the grounding behavior of the machine by not varying the

impedance as a function of frequency.

The technique used in this research is based on scattering parameters, a way of determining

the terminal behavior of the machine without the knowledge of the actual inner workings of the

machine. The inverse scattering technique uses steady-state stimuli to calculate reflection and

transmission coefficients of system components allowing the device to be considered as a black box.

This can be understood as electrical snapshots of how the machine would respond when subjected

to a range of spectral content. The approach could have a significant impact on the modeling of

ground interactions with machines. The machine can now be measured and characterized with no

prior knowledge of the machine. The measurements are placed in simulation software in the typical

measurement configurations used in other approaches to extract parametric data. It was discovered

that these different configuration setups could now be measured in software without the need to

physically reconfigure the machine’s wiring for each measurement. This modeling approach was

coined ’virtual measurement modeling.’

To the best of the author’s knowledge there are not any known techniques for fast model

prototyping of electric machines which cover a broad range of frequencies with high accuracy. This

thesis will present a possible solution for consideration in future models developed for grounding

studies. This approach outlines a promising technique that can be easily implemented with high

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accuracy and reproducibility. The technique was derived from inverse scattering theory and was

implemented on electric machines for characterizing high frequency behaviors.

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CHAPTER 1

INTRODUCTION

The information disclosed in this manuscript will cover research on alternative measurement tech-

niques for characterizing high frequency electric machines and build grounding models. The re-

searcher has demonstrated in previous work how new measurement techniques can be applied to

modeling of various components in a shipboard power system for grounding studies. Although

research has been carried out on multiple devices, the focus in this manuscript will be limited to

the development of three-phase rotating electric machine techniques. The following chapter will

cover the motivation for the work, a brief description of high frequency transients, the significance

of the proposed approach with regards to modeling, and the outline of the remaining chapters of

the manuscript.

1.1 Motivation

The all-electric ship (AES) has been an ongoing research topic for the Office of Naval Research

(ONR) Electric Ship Research Development Consortium (ESRDC) [7, 8]. One of the main focus

of our group’s research is on the proposed shipboard electrical power system and the need for

full detailed models of electrical components as well as the environment in which the system will

operate. The all-electric ship proposed by the U.S. Navy can be seen in Figure 1.1. The classical

methods of system modeling cannot be assumed to directly apply to ship electrical power systems,

considering the physical differences between the domains of terrestrial and shipboard applications

[9]. The current approach is to operate the shipboard power system (SPS) ungrounded from the

ship hull. This will have an effect on the attenuation of high frequency content so it is pertinent that

research be conducted to understand these events and model their effect on the overall performance

of the entire ship system.

The SPS will mainly be comprised of power electronics, cabling, and machines. The SPS

will undoubtedly be subject to electromagnetic interference (EMI) and therefore electromagnetic

compatibility (EMC) will need to be explored further [10, 11, 12, 13]. Models which capture the

1

Figure 1.1: All-electric ship proposed by the U.S. Navy [1]

electromagnetic interaction between the SPS and ship hull are important for grounding considera-

tions such as fault location algorithms based on common mode (CM) and differential mode (DM)

noise [12, 14]. The use of SPS modeling could also mitigate issues prior to building the ship and

reduce equipment sizing through optimization and proper placement of components to lower the

destructive high frequency content in the system.

The SPS preferred configuration will be a Direct current (DC) distribution network. An un-

grounded DC distribution network is said to be the most suitable option because it has the ability

to operate under certain fault conditions and it removes the need for redundant conversions found

in AC distribution [15]. The latest technology in power electronics need highly reliable intelli-

gent systems that can reconfigure quickly to maintain survivability. Power electronics continue

to increase in efficiency while being designed for higher voltages and currents that come with the

increased power density requirements for future ship design. The rectification and inversion of cur-

rent by means of power electronic switching is known to produce EMI due to steep rise times [16].

The study of EMC has produced substantial research describing transient behavior. Section 1.2

will discuss the effects of transients such as overvoltages, insulation break down, unwanted bearing

currents, and ultimately the coupling of the SPS with the surrounding ship hull through parasitic

2

paths. The frequency spectrum of the EMI in the system is related to the transient rise times and

can be accurately captured with wide-band frequency models [17, 18].

To properly study the effects of different grounding strategies [19], models must be developed

that capture the parasitic coupling effects of components and the ship hull. The current design

for the SPS is said to be likely an ungrounded system topology, also known as non-intentionally

grounded because it is impossible to have a power system completely isolated from ground due

to inherent parasitic elements [9, 14]. The parasitic coupling of the SPS and ship hull provides

a possible low impedance path back to the source. It is for this reason that studies need to be

done in order to capture high frequency responses of the SPS components. Our work focuses on

developing higher order grounding models of the SPS that properly characterize each component

at the frequencies determined to be of interest. The grounding schemes will have a large impact

on the system performance. Models which typically capture steady state time scales will need to

incorporate smaller time steps in order to properly describe the high frequency response.

High frequency models of power cables, power electronic devices, and electric machines were

designed in [20], [21], and [22] respectively. The common methods or techniques used to develop the

current high frequency models can be highly complex and specialized to each type of device in order

to capture wider frequency responses [16]. Techniques used to extract model parameters of various

components have been done primarily through on-line testing, lumped parameter approximations

from standstill frequency response , and finite element analysis [23], which are all further outlined

in Chapter 2 Section 2.1 where high frequency electric machine modeling approaches are discussed.

The main focus of this work is to introduce a new measurement method to this field of research

that provides information over a wide range of frequencies needed for modeling an electric machine.

The measurement of frequency response characteristics is already widely used by obtaining common-

mode (CM) and differential-mode (DM) impedances [24]. These impedance quantities can be used

for many different modeling approaches. In contrast using the inverse scattering theory to measure

a machine is a new approach, where input and output ratios for each port of the machine are

recorded. The scattering parameters can be transformed into familiar configurations such as CM

and DM impedances. Scattering parameters are most useful when considering the machine as a

black box were the internals of the machine are not necessarily known or readily available. Thus the

3

motivation for this research is to explain the significance of quality high frequency measurements

that can accurately be modeled with little to no knowledge about the machine.

1.2 High Frequency Transients

Transients in electrical systems can be defined as disturbances in voltage or current that re-

sult in a deviation from steady-state conditions for a short period of time. Transient responses

typically oscillate about a steady-state quantity. The oscillating behavior brought on by the tran-

sient will eventually attenuate and return to steady-state based on the circuit parameters and the

corresponding system configuration. The transients can operate at frequencies considered high for

electric ships due to the physical length of the ship and the corresponding cable lengths of the SPS.

Switching events in electrical power systems are known for producing high frequency transients.

The transient response of the various power system components can affect the behavior of the

system if not properly mitigated. A component’s parasitic elements produce varying electrical

responses at these higher frequencies. This behavior should be included in simulation models or

the system controls may misinterpret and calculate the incorrect response causing a cascade of

issues. The transient current radiates electromagnetic energy from the circuit that can couple with

neighboring conductors, causing unwanted interference [25]. This potentially unwanted coupling

between circuits and their connected ground paths can be highly complicated and difficult to predict

the full effect of the energy distribution if not modeled correctly [11]. The transient response of

the system can lower the impedance of unwanted paths through parasitic elements inherent to the

system’s construction and connected circuitry.

Research of transients and their high frequency effects on electric machines is largely due to the

damage it causes to insulation in windings and unwanted leakage currents to the frame through these

various parasitic paths [15]. The inductive coils in an electric machine try to impede the change

in current by producing a complementary voltage in the opposite direction known as electromotive

force (e.m.f.). High frequency transients are significant and can cause e.m.f. voltages to peak across

the windings. The e.m.f. can be much higher than the operating voltages due to the impedance

ratios of the windings. The higher the frequency the more irregularities in voltage distribution

across windings. Energy is thus stored in the magnetic field and its flux is proportional to the

rate of change in current flow. The magnetic field is a response produced to oppose the transient.

4

The collapse of the field in the magnetized coil can have faster fall times then the e.m.f. rise time

and produce even higher frequencies. These high frequency behaviors are what make transient

responses so destructive to electric machines [26].

A periodic switching transient can also produce constructive and destructive wave behaviors

in an electrical power system. When these waves constructively combine, the voltage can rise

more than twice the operating voltage in some cases [24, 27]. Each component has an inherent

impedance when seen from the source called its characteristic impedance. This impedance will

either be capacitive or inductive in nature with some real resistive behavior. Surges in energy from

the source traveling on a direct path through conductive material like cables and windings will be

met by the impedance of the machine called surge impedance.

The various impedance magnitudes will rise and fall at certain frequencies in the machine.

These specific frequencies are known as resonant and anti-resonant frequencies. Machine transient

responses can be mitigated by controlling or filtering the frequencies, which lower impedances

through unwanted parasitic paths [11, 25]. The impedance changes as a function of frequency and

it ultimately shapes the transient response of the system. To understand which frequencies will

have negative effects, the system’s characteristics and surge impedances are analyzed across the

frequency spectrum to determine frequencies of interest. Resonant frequencies with low impedance

can cause a ringing that decays slowly if there is nothing to attenuate the waveform. The transient

system behaviors need to be studied, not only at the operating frequency, but also at the frequencies

of the system’s response, which lower the impedance of parasitic paths.

High switching frequencies of inverters will have steep voltage edge rates between stator wind-

ings and motor frame, i.e. transients that cause electromagnetic interference in the motor. The

common–mode voltage (CMV) arises when the terminal voltage changes at a fast rate. Surge

propagation in stator windings can cause voltages to develop in the end winding, influence of in-

terturn voltage distribution, and voltage across the end winding. These voltages are not uniformly

distributed along windings due to smaller wavelengths corresponding to the higher frequencies

found in transients. The CMV on the motor windings produces a common-mode current that flows

through the distributed stray capacitance between the windings and motor frame. The frame of the

rotor is generally connected to the ground circuit giving CM current a low impedance path through

5

the cables capacitive coupling to ground. This has been well-documented in literature such as [20]

and explored through many different full spectrum models of electric machines.

Access to accurate models will help system performance by balancing line voltages and miti-

gating the negative sequence currents in the machine [25]. Reduction of the unwanted fields which

rotate in a direction counter to the normal field can decrease current losses due to heating and in-

creased torque, efficiency, and power. Typically models of power systems do not account for these

effects due to the complexity of the modeling methods needed to describe the high frequency be-

havior. Most of the models are simplified and designed to work well for terrestrial power systems.

Terrestrial systems are less concerned by these issues of ringing frequencies due to the attenua-

tion available with various circuit grounding configurations [15]. Designing an ungrounded circuit

that can attenuate the high frequency noise created from switching events requires larger model

bandwidth.

Our research involves the modeling of machines for use in all-electric ships, which will potentially

have an ungrounded power system with a lower attenuation characteristics. If there is nothing in

place to stop these frequencies or at least recognize their occurrences during certain electrical events

then the system will continue to oscillate and potentially cause degradation of the system. This

oscillation can be prevented by changing the capacitive or inductive characteristics of the impedance

at these specific frequencies causing issues. Reducing these effects can be achieved by changing the

switching frequencies to cause different responses that are less harmful or contain less energy at

the anti-resonant frequencies.

1.3 Significance

The significance of this work can be applied to many fields, but this research was conducted

for Naval applications. In terrestrial systems, higher frequencies are generally attenuated by the

earth ground. The hull of the ship provides a low impedance path for current to freely travel across

during parasitic coupling of the the ship power system and the ship hull. The large size of the

motors and generators used in electric ships are a large contributor to the capacitance present in

the system [28]. Understanding how the system will operate under various frequencies is of high

concern because of the adverse effects it could have on the rest of the system; especially unwanted

ground currents flowing in the ship hull [26, 8].

6

The research was first aimed at exploring state of the art literature on high frequency machine

modeling and to provide insight into new techniques that could simulate the ground coupling

and other high frequency effects. High frequency electric machine models presented in previous

literature were developed through many different techniques. Each model presented had a different

approach and results would vary in resolution. Whether computer aided design (CAD) or equation

based approaches were used, detailed information about the physical dimensions and design of the

machine were required in order to design an accurate model. Most of these models also required

short, open, and load based measurements to determine their parametric values. This can cause

damage to the motor if not done correctly. Much of the literature written on high frequency ship

power system models was focused on the inverter drive CM voltage and how to reduce this effect

using filters [15, 21, 29]. These system models were based on various approaches and normally used

simplified motor models such as π, RLC, or distributed ladder networks. Filtering can mitigate

these effects but models still need to accurately capture the frequencies of interest to build such

filters. Reducing the effects of high frequency through component design and physical location

considerations will also be a significant part of ship building. Accurate models will allow filters to

be designed specifically for the inherent response of the system. Also, the physical size of the filters

could be reduced and the placement of them in the ship system would be designed to lower the

impact of unwanted frequencies. After a thorough literature review on this topic, it was clear that

there were no universal methods capable of easy implementation for all types of electric machines.

The need for more accurate system models directed the research towards network based theories.

The field of communication and antenna theory relied heavily on a technique which standardized

their approach to obtaining measurements on various network components. This idea was proposed

to power system components and research in this area has been growing steadily [9, 30]. The

thought of using inverse scattering theory to determine or identify characteristics of power devices

has become a new field of exploratory research. This method has been applied to cables and even

three-phase EMI filters [30] which are typically considered non-linear devices. Early research in this

area first focused on simple geometries such as power cables [4, 31]. This provided a simple path

to determine viability for further implementation of other components such as electrical machines.

The standard approach to measuring devices based on the number of interface ports has proved

7

to be a powerful approach to simplifying the process needed to generate accurate and repeatable

models.

The originality of this research was to focus on applying inverse scattering theory measurements

to high frequency machine modeling. Until now, to our knowledge, no one has recorded or used

scattering parameters to model an electric machine. This required a large effort to be put forth

into understanding previous machine modeling approaches for inspiration. The measurements

were fairly easy to obtain in hindsight, but involved a substantial learning curve to understand

and prepare them for use in models. The combining of two separate fields of research (machine

modeling and scattering parameters) slowed the initial progress of model development due to the

lack of overlapping literature between the two topics. In the end, the work suggests to be a

significant addition to high frequency machine modeling approaches presented to date.

A simple methodology to develop highly accurate models could be used to better understand and

develop the ship system prior to installation [7, 4, 31, 32, 8]. The time saved and the knowledge

gained by the use of the proposed approach would translate into dollars saved in damages and

wasted time spent on other more intense modeling approaches. Previous modeling techniques

don’t offer the simplicity in model development and the ease of connection with other components

for full system modeling. The scattering parameters can also serve as a snapshot of the machine’s

parameters. These measurements can be used to monitor the current state of the machine’s health.

This could be used to study how aging and pollution on the windings of the machine can change

the machines characteristics.

1.4 Organization of Master Thesis

The manuscript begins with an introductory Section 1.1 where the motivation for high frequency

machine models which accurately address grounding for shipboard power systems was discussed.

In Section 1.2 an explanation of transient behaviors in shipboard power systems was covered. The

following Section 1.3 details the significance that the proposed work will have on machine modeling

techniques for future all-electric ship design. The main focus of this work is to fully characterize the

model of an electric machine using a scattering measurement technique previously used on other

components of the SPS with great success.

8

In Chapter 2 state-of-the-art research is discussed, which covers machine modeling approaches

to date and how scattering parameter methodology could be applied to model the entire SPS.

Section 2.1 can be further broken into the most common modeling approaches; lumped element

models in Subsection 2.1.1, distributed models in Subsection 2.1.2, and common–mode/differential–

mode equivalent models in Subsection 2.1.3. Section 2.2 will cover the scattering methodology

the linear time-invariant requirements for use in Subsection 2.2.1, the instrumentation needed

Subsection 2.2.2, and the different port determinations for setting up the measurement process

Subsection 2.2.3.

In Chapter 3 the scope of work was presented and the plan for conducting the necessary exper-

iments were organized. This chapter will also cover how the work will be accomplished, and how

it pertains to the motivation and significance of high frequency grounding models.

In Chapter 4 the proposed scattering parameter theory will be applied to three-phase electric

machines. This chapter is divided into three sections starting with linear time-invariant testing,

Section 4.1, then parameter extraction techniques Section 4.2, and finally virtual measurement

models Section 4.3.

In Chapter 5 the results from experiments are discussed and compared to conventional tech-

niques. This chapter will cover the importance of resonances and anti-resonances in Section 5.1,

short circuit high frequency response of an electric machine in Section 5.2, and Section 5.3 will

cover the results of virtual measurements and how they compare to impedance measurements.

The manuscript closes with Chapter 6, which discusses conclusions to this work and future

considerations are given to help expand the research further.

9

CHAPTER 2

STATE OF THE ART

This chapter will discuss the literature review that was conducted. The researcher chose to focus his

search to literature on high frequency electric machine models and scattering parameter based mea-

surements. The majority of high frequency electric machine models found to be useful for grounding

research are discussed in Section 2.1. The approaches found most useful include lumped element,

distributed, and Common-/Differential–mode models. A majority of the models found required

detailed information on the exact design of the machine followed by a series of measurements and

calculations. Some of the most accurate models focused heavily on parameter extraction, in some

instances, one section of the motor or captured one high frequency phenomenon in great detail. In

other high frequency modeling approaches, the literature proposed different testing procedure for

isolating specific parameters, which would be used to make a full model. The search found very few

approaches that could be used as a standard modeling procedure across multiple machine types.

The models were also developed with great insight coming from the researcher’s experience with a

specific machine. This was determined to be an issue because it made these approaches difficult to

implement with ease on other machines with differing construction characteristics.

Research and previous experience with scattering parameter based models was influential in

determining alternate approaches to obtaining high frequency models of electric machines. The re-

search goal of our group was to create grounding models based solely on one measurement method-

ology that could be applied to all components in the ship’s power system. Essentially the group’s

research on scattering parameter network methodology was determined to be plausible and worth

exploring for devices such as the electric machine. In Section 2.2 the scattering methodology pro-

posed is applied to electric machines. The theory behind linear time-invariant networks is discussed

first. This is followed by instrumentation needed for measuring the terminals of large power equip-

ment. Lastly the ports of the machine were determined and the proposed measurement process is

outlined.

10

2.1 High Frequency Electric Machine Modeling Approaches

This section will explore the current state-of-the-art research involving high frequency charac-

terization of electric machines. In addition this chapter will cover a wide range of machine research

including models that only focus on the characterization of machine windings based on equivalent

circuits all the way to complete physics based models. The models vary in accuracy as well as

modeling capabilities and resulting resolutions. The state-of-the-art research explores numerous

machine models and the varied techniques used to obtain the modeling parameters as well as the

frequency ranges of interest. It is pertinent that all forms of machine modeling be explored before

proposing a new methodology. The coverage of such a wide field of science allows for some con-

clusions to be made about the current state-of-the-art, and points to why the statement of work,

discussed in Chapter 3, is desired.

The need for accurate high frequency machine models has been expressed in Chapter 1 and is

agreeable with the current research thrusts by the Navy. Developing high frequency machine models

has been approached many different ways through prior art seen in Appendix A. Not only are the

models different by design but the methods to determine each parameter differ across this field of

research. This may have happened due to each approach attempting to solve a different research

topic or developed from research groups with differing backgrounds. In the next few subsections an

overview of the most common approaches to modeling and parameter extraction will be covered.

High frequency electric machine models have been developed and tested in prior work. Cur-

rently there are many machine designs that incorporate parasitic and high frequency effects, but

these models have their limitations. In some cases, the modeling efforts were developed based

on previous models in order to closely approximate the electromagnetic effects. These models

were limited because they were unique to a specific machine or focused on one test condition and

were not considered to be useful models for the current SPS modeling requirements. The work

discussed in this section has been reduced to focus only on the high frequency electric machine

modeling approaches found in literature. High frequency characterization of machines has been

accomplished typically in either a lumped element circuits found in Subsection 2.1.1, distributed

circuits in Subsection 2.1.2, or mode type circuits for separating out CM and DM behavior found

in Subsection 2.1.3.

11

The author has chosen to not further study any finite element based models because they are

dependent on a physical understanding of the inner dimensions, connections, and full details on

material properties of the machine, which are typically proprietary and unavailable to the engineer.

These models are obviously useful for machine design because they include all the physics to simulate

but this is the most time consuming approach. Typically finite element methods (FEM) are one-off

solutions, which require heavy resources to solve even simple geometries. It’s highly unlikely that a

data sheet on a machine’s design will accurately match each machines actual parameter values let

alone be available to the end user. It was determined not to be feasible for rapid model generation.

The aim of this work was to investigate and suggest an approach that can be universally followed

for any machine. Also, most FEM approaches eventually extract parameters to be used in a more

simplified circuit representation to reduce the computational burden [33]. These simplified models

are not guaranteed or expected to provide the same level of accuracy seen with the FEM. Therefore,

this approach has been summarized and excluded from further discussion.

2.1.1 Lumped Element Equivalent Circuit Models

The process of extracting parameter values from frequency data for equivalent circuit modeling

is a common approach to high frequency modeling for overvoltage studies [34]. The equivalent

circuit model approach typically starts with three per phase circuits that are electromagnetically

coupled. Each circuit is equivalent, assuming symmetrical machine construction. The parameters

are normally found via analytical calculations [35, 36, 37], slopes and resonances in impedance data

[13, 34, 38], or CAD software [23, 39].

Previously suggested measurement techniques have been considered useful in determining pa-

rameters of machines but are not always accurately implemented without in-depth knowledge of

the motor. Looking at Figure 2.1a one can see the equivalent capacitance for a standard capacitor

with lead inductances and leakage current included. The general model for the inductor can be

seen in Figure 2.1b where the series resistance and skin resistance are included in the model [2].

Lumped-parameter models are based on extracting information at transitional frequencies or

looking at the slope of the impedance as a function of frequency. These models tend to be simplified

representations of the component by generalizing the parameters based on the specific impedance

found at a few frequency points. It is common for these parameters to be extracted in frequency

domain and converted to a single lumped circuit component in the time domain. In practice the

12

(a) Generic equivalent circuit for capacitor [2] (b) Generic equivalent circuit for inductor [2]

Figure 2.1: Equivalent circuit models for capacitors and inductors [2]

machine’s impedance varies over all frequencies as should the parameter values to most accurately

model the machine. In Figure 2.2 the impedance plot is shown for both an inductor and a capacitor.

The dotted line indicates the impedance of an ideal component. Any deviation from the dotted

line represents the real impedance due to the parasitic effects of the physical components.

(a) Actual versus ideal capacitor [2] (b) Actual versus ideal inductors [2]

Figure 2.2: Equivalent lumped model plots for capacitors and inductors [2]

Lumped parameter based models can over simplify the grounding behavior of the machine.

Models have been proposed that neglect the second resonance while others build more elaborate

circuits to account for these missing behaviors [24]. Capacitive currents are an issue in ungrounded

shipboard power system behavior and should not be neglected in the modeling approach. For this

reason it is not recommended to use single–phase equivalent circuit models to describe three–phase

circuits when capacitive currents are strong [26]. Any variations in the potential of each phase could

13

impose coupling and ultimately ground current. This effect could further increase high frequency

power loss due to the harmonics and imbalances in the electric machine phases.

Through extensive research on the topic, models were also discovered that included the bearing

capacitances and their high frequency contributions to CM currents [24, 40, 28, 41]. This was very

interesting to find because many papers mention the effects bearings have on the capacitance mea-

sured but choose to neglect these effects in the final model. It was first discovered when literature

was found were standstill frequency response (SSFR) techniques warned that measuring a machine

at rest would undoubtedly change the capacitance once the machine was moving. Furthermore it

was noted that the grease formed an insulation layer between ball and race [42, 43, 28] when in

rotation. This time-variant behavior was considered when researching new measurement methods

for machines.

There are numerous approaches to measuring a machine that lead to parameter estimation

and implementation into various high frequency models. Many authors started building tables to

organize the different models found on these topics of high frequency electric machine modes. An

example of these tables can be found in Appendix A on page 62. The extensive list of models are

all valid approaches to modeling but lack the ability to be applied to other machine types without

significant effort.

2.1.2 Distributed High Frequency Models

Some distributed HF parameter models of electric machines have been proposed by other au-

thors, and they are briefly introduced here. The concept of distributed high frequency (DHF)

models is typically based on ladder circuits to describe the machines stator windings and slot area

[3, 36, 44]. These models can be indexed continuously in the frequency domain to represent the

resistance, inductance, and capacitance for modeling the effects of incident waves on the motor

windings. Each winding circuit can be made up many latter circuits to model the distributed effect

of voltage across the windings during fast pulses. These models tend to have higher resolution when

compared to lumped element models which typically catch only the self-resonance frequency. The

tradeoff comes with a more complicated model that can have upwards of 500 elements per winding

and the need for numerical models to calculate the computationally heavy model. Examples of

distributed models are explained in literature such as [36, 45, 46, 47, 20, 3] or seen in Figure 2.3

found in [3].

14

Figure 2.3: Distributed high frequency circuit model with 17 turns per slot [3]

In [36] the values of the distributed winding model are calculated via a matrix of equations

representing the various positions of each winding and where it falls in the slot of the stator. It

was common to find contradicting information among these models. For instance in [3] the author

breaks their work into simplified high frequency (lumped equivalent circuit) and distributed high

frequency models. The first circuit was said to be used if measurements were available and the

second set of models was used for predicting high frequency effects. The contradiction is found

in [45] where the distributed equivalent circuit model is called a simplified high frequency model

similar to the lumped models name in [3]. The one thing that seems to hold true across all the

models is a notion that the values can be calculated as a per unit length value. Interesting work

was conducted in [46] where electromagnetic interference was studied with and without shielding

to show the ground plane interactions seen in Figure 2.4. This work used a distributed and lumped

model using the same parameters as input to the model reducing the complexity of simulating high

frequency behavior.

In [47] the machine was measured over a wide frequency range and was broken up into non

iterative stages. Each stage was made of linear RLC circuits bringing a new meaning to distributed

modeling. This model distributed the model over various frequencies while other models were

distributed based on per unit length positions within the machine. Interesting enough more work

into network theory has started to surface [47, 3] where the former utilizes line-impedance stabilizing

networks and the latter uses scattering parameters for higher frequency measurements.

15

Figure 2.4: Parasitic coupling of the ship MVDC power system and ship hull ground [4]

Among the DHF models mentioned, it was clear that these models took time to develop and

required special fitting techniques with measured data for better parameter estimations. The

results from these models were much closer to their measured values that seen in lumped element

approaches. An issue was observed where the effort needed for parameter extraction from measured

results in each DHF algorithm increased with complexity the higher the frequency range of interest.

2.1.3 Common-mode and Differential-mode Equivalent Circuit Models

When describing a machine using high frequency parametric data there are three types of circuits

that seem to be most prevalent. The first is the lumped equivalent model which approximates values

for equivalent circuit representations of three-phase machines. Equivalent circuit components are

added to the measurement circuit with their own tuned frequency response. In these circuits the

researcher begins with a basic equivalent circuit model and expands the circuit to capture effects

seen through measurement or calculation. The second is when direct quadrature zero (DQ0) theory

is used to describe the machine at low frequency and a complimentary coupling circuit is used to

adjust for high frequency content [38, 34]. The third is the most commonly found high frequency

modeling method which uses common-mode and differential-mode circuits to simplify the behavior

of the machine as a function of frequency. In these circuits the effects of high frequency on the

machine terminals would develop either a common or differential current to form in the circuit. This

circuit representation is quite useful for studies because each mode can isolate specific problems

such as parasitics with the ground, which is relevant for our own studies.

16

To clarify, common and differential measurements are one method of measuring which can be

used to determine all other model parameters. For example, a machine can be both measured

and modeled in common-mode and differential-mode circuits. All measurement techniques can

be converted to CM and DM modeling equivalents and all modeling parameters can be derived

from CM and DM measurements. The main methods for obtaining these measurements will be

discussed further in Section 2.2.3 on Page 23 or seen in Figure 2.8. As mentioned before, some

of the distributed models used CM and DM circuits to isolate certain high frequency behaviors.

Their contributing currents and values were measured in the frequency domain in order to build

the model found in [47].

In [40] the most basic CM and DM models are built using lumped circuit equivalent models.

The simulation to measured data was not as accurate as other methods but showed how simple it

was to get a general model built that was able to capture most of the key resonances and seemed to

fit for extracting slope values of the impedance as a function of frequency. This is accomplished by

updating the values of capacitance and inductance to match the measured data similar to [3, 13]

where the model was fit more closely to measured results.

Literature found discussing CM and DM circuits did not always identify high frequency behav-

iors in machines. For instance in [48] the modeling of the machine was accomplished with a simple

RL motor model. The point to be made is that not all CM and DM models are high frequency

models. This paper describes a design for removing CM currents without effecting DM currents

but does not mention the accuracy of the motor model just techniques on how to mitigate the

unwanted currents. There were papers in the scattering parameter field that also used the terms

common and differential to describe circuits being developed [49]. In the definitions of differential

and common mode signals apply to the port of the network and are used to redefine the scattering

matrix into separate matrices so the device model has common ports and differential ports. This

method is used to develop a mixed mode model based on scattering theory. This is worth further

investigation to determine its merits when applied to motor models.

In [50], and more recently expanded in [51], the use of CM and DM terminology differs from

other high frequency motor models available in literature. A new improved DM cable model in

conjunction with a simple lumped element motor model was proposed in [40]. The motor model

parameters are extracted from CM and DM impedance characteristics. The equations used in this

17

model for calculating parameters from CM plots was useful in defining our own circuit models for

comparison and are detailed further in Chapter 4.

2.2 Scattering Methodology for Measuring Electric Machines

The use of scattering parameters are well documented in any radio frequency (RF) or microwave

textbook but can be briefly defined as the amplitude of incident, transmitted, and reflected waves

for steady-state stimuli from matched sources of sinusoidal electrical signals of a certain frequency

[52]. The parameters are complex because they illustrate how the magnitude and phase of input

signals are changed by the device’s network. Ports, or electrical terminals, are typically identified

as the inputs or outputs of the machine, where voltage and current can be delivered or transmitted.

The machine contains a finite number of ports that are subject to incoming waves as well as

interactions internally from other ports transferring energy. The common device used to measure

scattering parameters and the preferred instrument used in this research is the Vector Network

Analyzer (VNA). The VNA connects to the various ports using measurement cables and special

high frequency termination equipment defined further in Section 2.2.2 on page 20.

Scattering parameters contain a given range of frequency data for each port-to-port combination.

The number of ports, N , are defined by N2 coefficients representing a possible input or output path.

There are N rows and N columns of scattering coefficients in the scattering matrix. The diagonal

parameters are the reflection coefficients referring to single port reflections e.g. s11, s22. The off

diagonal parameters are the transmission coefficients referring to the interactions between differing

ports e.g. s12, s21. A complete scattering matrix is essentially a tool used to determine voltage out

compared to voltage in for the various port combinations on a machine.

The following sections will cover linear time-invariant network theory, the instrumentation

needed for conducting scattering measurements, and the determination of port configurations for the

measurement process. Port selection for an electric machine will be discussed using two approaches;

single–port and multi–port scattering parameter measurements. Single–port measurements are

closely related to commonly used machine measurements done using CM and DM circuits. The

multi–port measurement is the most complete measurement matrix, which contains all reflection

and transmission coefficients defined between each port and the reference ground. The benefits and

shortcomings of each method will also be discussed further in this chapter.

18

2.2.1 Linear Time-Invariant Theory

Scattering parameters are only relevant when the network being measured is considered linear

and time-invariant for the frequency range considered. This can be defined by the Equation 2.1.

The output signal F (x) follows the rules of superposition where its inputs can be broken into smaller

pieces and applied separately to receive the same output.

F (ax1 + bx2) = aF (x1) + bF (x2) (2.1)

Linearity is also true if the network’s parametric values don’t change as a function of the voltage

and current inputs. This is accomplished when the network contains only resistors, inductors, and

capacitors and is not operating in saturation where hysteresis, and eddy current are present [53].

For the purposes of machine modeling we will consider electric machines to be linear for the range

of frequencies being applied. Each frequency is fired independently in the VNA allowing each signal

to be measured independent of the next measurement point.

The second stipulation is whether or not the machine can be considered time-invariant. Time-

invariance can be defined as any input signal producing a consistent response; regardless of a shift

in time (considering the machine is linear for small time steps and is not operating in saturation).

Similarly, in [54] the electric machine was considered as a discrete-time linear time-invariant system

because the measurements were taken at stand allowing these theories to hold true.

A test to determine the accuracy of these assumptions was designed to capture machine mea-

surements during specific rotor positioning. The time varying aspect of a machine comes from the

interactions between stator and rotor. The machine would, in theory, see the largest effects of the

stator to rotor interactions during the passing of the poles of the rotor against the poles of the

stator. This test is further described in Section 4.1 found on Page 32 where multiple positions of

the rotor where measured to observe the overall impact in measurements. Even though a machine

is not truly time-varying, it is possible to use for small time steps and therefore scattering param-

eter method is considered a viable measurement method for the discrete-time standstill frequency

response measurements conducted in this research.

19

2.2.2 Instrumentation for Characterizing Machine Coupling to Ground

There are many parameters that can be used to define an electric machine and most instrument

methods require an open or short circuit condition to properly characterize these parameters.

The vector network analyzer (VNA) uses a matched load instead of a short or open termination.

The matched load has a wider bandwidth allowing for higher frequency measurements without

energizing the machine. A VNA was used to extract scattering parameters because high frequency

measurements are of interest when characterizing the machine’s coupling to ground. Scattering

parameters for high frequency modeling were used in previous research of other power components

such as power cables [31] and three–phase EMI filters [30] with good results. The basic equipment

used to perform scattering measurements included a two–port VNA, two phase–stable leads, a

calibration test kit, and as many termination clamps as there are ports present on the equipment.

In the proposed approach a two–port VNA is used to measure scattering parameters of a

three–phase machine following the techniques used in [19]. A VNA manufactured with two signal

generators and two receivers is used to measure amplitude and phase properties of transmitted and

reflected power waves. The VNA uses an internal direct digital synthesizer to produce a variable

frequency continuous wave source signal. Each signal will pass through the device with a swept

frequency. The device will have a unique response corresponding to each test frequency. During

each measurement step a portion of the incident wave will return to the sending port as a reflected

wave while the remaining incident wave will transmit through to other ports. This scattering

measurement records how the traveling waves interact with the various structures and electrical

paths within the machine. The measured response to these changes in scattered energy throughout

the device, allows for full models to be developed that describe the machine across a wide range of

frequencies. Similar to the way light reflects at certain frequencies giving our surroundings color,

the inverse scattering reflects at certain frequencies that can be used to define the device in an

electrically visual representation.

When performing inverse scattering theory the measurement plane of reference is preferably as

close to the device as possible to ensure only the device is being measured. The VNA measurement

plane has to be calibrated to ensure the measurements are reflections and transmission due to the

electric machine and not the instrument or the measurement leads. Cables reaching from the VNA

to the electric machine are subject to calibration tests using a known calibration kit, purchased

20

separate from the VNA. The calibration kit consists of high frequency rated short, open, and load

terminations to be used in a series of calibration steps. Following the steps given in the VNA

calibration guide, the measurement plane can be properly set to the ends of the measurement

cables or the terminals of the electric machine. Calibration is recommended to be performed each

time the VNA is used and more importantly every time the measurement settings are changed such

as number of ports, frequency range, frequency points, power level, and bandwidth. Calibration is

not difficult to administer and is comparable in setup time to other measurement setups.

The electric machine is connected to the measurement cables at two of its defined ports (port

determination is covered in Section 2.2.3). The remaining ports are connected to the ground

plane through a high precision wide bandwidth load resistor equal to the VNA system impedance,

typically 50Ω. Using known terminations, measurements of each two–port combination were later

assembled into one complete scattering matrix. The complete scattering parameter measurement

matrix is stored in the industry standard Touchstone [55] or CITIfile format [56]. The scattering

parameters are each denoted by snm and form to make an n×m square matrix where the n is the

measurement port and m is the sending port.

Each of the two–port measurement combination creates four parameters which are s11, s12,

s21, and s22 seen in Figure 2.5 on page 22. Where a1 and a2 are the incident wave measurements

and b1 and b2 are reflected wave measurements. The off diagonal parameters are the transmission

coefficients and the diagonal parameters are the reflection coefficients. If the electric machine is

directional in nature then it can be described as having forward port and reverse port signals and

more importantly snm 6= smn. For modeling, the electric machine it is not necessary to classify

them as having directional ports. It was common to set snm = smn to simplify the calculations by

assuming symmetry between the phases. When transforming scattering data from the frequency

domain to the time domain it is better to have symmetry in the off-diagonal positions. Extra

confidence in measurements can be obtained by measuring all reverse measurements and averaging

the off-diagonal matrix parameters [19].

Measuring a machine with four–ports will produce 16 scattering parameter measurements for

each swept frequency. This is based on the 16 possible port-to-port interactions between each

machine terminal when neutral is accessible or 12 when neutral is inaccessible. Two machine ter-

minals, at a time, are measured by the two test ports of the vector network analyzer (VNA). While

21

Figure 2.5: This is a visual representation of scattering parameters for a two–port network

the other two ports of the electric machine are terminated with a 50Ω single-ended termination.

The matched termination load acts as an infinite transmission line and absorbs the wave without

reflection. The ports of the VNA are also matched similarly to allow the measurements to describe

the machine exactly without reflections from the VNA ports. This procedure is repeated by alter-

nating the measurement cable leads through all possible port combinations on the machine. The

magnitude and angle of each signal is stored under the respective test frequency being sent.

Scattering measurements will paint a frequency response picture of the entire machine. The two–

port measurement data are stored and assembled into multi-port representations, building the full

scattering matrix of the electric machine. In Section 4.3, this scattering matrix serves as a virtual

measurement model. The model can be connected to simulated probes allowing for measurements

to be taken as if the researcher were measuring the electric machine directly. The scattering

vector measurements contain magnitude and phase data that can later be used for complete time

domain characterization, device modeling, and vector-error correction. The resulting parameter

measurements are assembled and can be used to determine reflected voltages using the matrix

Equation 2.2

V −

1

V −

2

V −

3

V −

N

=

S11 S12 S13 S1N

S21 S22 S23 S2N

S31 S32 S33 S3N

SN1 SN2 SN3 SNN

V +

1

V +

2

V +

3

V +

N

(2.2)

22

where the positive voltage sign denotes an incident voltage and the negative sign represents

reflected voltages. Further explanation on the scattering parameter procedures can be found in

[19]. The act of measuring an N–port device using scattering measurements is well documented

[4, 31] for simple geometries, but to the author’s knowledge this is the first time it has been used

to measure machines for ground modeling.

When measuring at frequencies in the megahertz range and higher, the series resistance is much

smaller. In-turn the phase angle is more susceptible to large fluctuations and the overall impedance

of the machine will vary accordingly. Meaning, when obtaining measurements, the equipment must

be calibrated and the recommended procedures should be followed closely.

Special equipment was designed to interface between measurement cables and the machine due

to the physically large terminals of the machine. VNAs use high frequency coaxial connectors of

Type–N for interfacing with typically smaller devices. This is not the only connector available but

it was the connector of choice in this research for its simple construction and availability. The new

equipment was designed, built, and its frequency limitations were characterized by measurements.

Moving the measurement leads caused errors well above the desired maximum frequency of 10MHz.

The losses and distortion in data seen above 10MHz were discarded similarly to other motor models.

Effects above 10MHz are considered unnecessary for consideration because their effects are minimal

in SPS.

2.2.3 Port Determination and Measurement Process

There are many ways to measure and describe a machine depending on the variables of interest

and the level of detail that is desired. The most common way to determine the ports of a machine are

to look at how it interacts with its surroundings. The machines electrical connections to the power

system and any nearby capacitive interactions can be observed as ports. The ports are typically

three–phase connections and one neutral connection, seen in Figure 2.6. The measurements of all

the ports must reference a common ground to be valid for use in the scattering matrix.

Typically a three–phase electrical machine is measured with different configurations to help

isolate specific parameters. The same concept can be applied when measuring scattering param-

eters. There can be anywhere between 2-16 scattering measurements needed to characterize the

machine. Some useful machine models are constructed using single-port impedance data extracted

23

Figure 2.6: Port representation for electric machine scattering measurements where T is for terminaland P is for port. T2P2 is terminal 2 and also port 2 of the measurement matrix. Each port of thematrix is measured by referencing it to a common ground.

from scattering data when measured in a common-mode (CM), differential-mode (DM), and phase-

neutral configuration (phase-neutral is considered DM impedance with neutral terminal accessible

[6]). These single-port measurements will be covered in Section 2.2.3 where each measurement pro-

vides information that can be used for modeling and has been verified using alternative equipment

(impedance analyzer).

The machine can also be measured as a multi-port model arrangement. Where each electrical

terminations, on the machine is seen as a separate port and a full set of scattering measurements

are performed and assembled into one complete scattering matrix. The full port representation of

the machine is detailed in Section 2.2.3 where the machine can be modeled directly from scattering

parameters taken at each port.

Deciding whether a single–port or multi–port method is better for a specific application, was

not determined in this work because both are valid and are often useful in different modeling

approaches. For the purposes of laying the foundation for this research, both methods were used

to form a complete measurement set. The measurement matrices can then be used as needed to

help build the machine model that best represents the machine configuration and the frequencies

24

of interest. The measurement setup for the PMSM machine seen in Figure 2.9 details the possible

voltage waveforms to measure at each port of the four-port network.

Single-Port Scattering Measurements. There are two types of port configurations often

used to measure impedance spectrum of an electric machine for parametric modeling and can

be seen in Figure 2.8. The CM and DM configurations are quite useful for modeling because it

allows noise to be isolated from common and differential sources. In Figure 2.7 the source voltages

are applied to the corresponding differential-mode and common-mode circuit [5]. The capacitive

coupling between phase-to-phase and phase-to-ground sections allow for a return path to be created

and the current produced is measured as the disturbing CM or DM current. CM and DM noise

produce unwanted conduction paths for current to flow. Modeling the electric machine this way

makes it practical for technicians to locate problems and mitigate component fatigue. Also this

measurement configuration is widely accepted in high frequency modeling literature as a key step

for parameter extraction.

Figure 2.7: Differential-mode and common-mode capacitive coupling [5]

The CM configuration is setup by connecting the three phases of the machine in parallel to

make a single measurement node. This node is then measured with respect to the machine case

or grounding point seen in Figure 2.8a. This measurement setup provides a frequency response

25

representation of the parasitic coupling between the machines windings and the case ground. If the

neutral terminal is available then another CM configuration can be seen in Figure 2.8b.

DM is similar to a single-port CM measurement but the terminal setup consists of two parallel

phases connected in series with the remaining phase. This setup will provide information about

the interaction between phases.

Phase–neutral measurement is achieved only if the neutral point of the machine is accessible.

The three phases of the machine are connected in parallel, like the CM setup, to create one node

and then measured with respect to the neutral point. This measurement is not necessarily needed

for parameterizing lumped models because it is a redundant DM measurement but it could be

useful in increasing accuracy of calculated parameters found using multiple CM and DM methods

[34].

Describing the machine in the three proposed single–port representations is considered a com-

mon approach to high frequency motor modeling [22, 34]. This approach allows for standstill

measurements to be made that help determine lumped parameter quantities of common machine

circuit representations. Using a VNA for this approach offers the same results found when using an

impedance analyzer but with higher resolution due to the ease of frequency sweeps with no delay

between measurements. In most cases the measurement process is less involved when using scatter-

ing parameter methods because it is standardized. This work presents an alternative measurement

approach that has the potential to be applied universally to other components in the system such

as the cables and power electronic devices. Having a similar measurement process and data post

processing method for all devices shows promise for future research.

Multi-Port Scattering Measurements. Subsection 2.2.3 discussed how to use widely ac-

cepted machine measurement protocols using a VNA instead of an impedance analyzer. In this

section the machine is measured as having at least three main nodes corresponding to the three–

phase connections and an optional fourth node for the neutral point. This would be the standard

approach to following the scattering methodology, where the device under test is viewed by the

ports in which energy in the system is transferred through to the device. The problem with this

approach is that it has not been verified for three–phase machines and no power systems modeling

software packages are using S-parameters for motor modeling are known.

26

(a) CM neutral inaccessible (b) CM neutral accessible

(c) DM neutral inaccessible (d) DM neutral accessible

Figure 2.8: CM and DM impedance measurement connections [6]

Scattering parameter software has recently been used in new ways to describe other power

equipment [31, 32]. It would be safe to assume that a release of new software packages in the

future will meet the demand for more complex networks like electric machines. This would allow

for full measurement sets to be used directly as the machine model. The model would be capable

of connecting with other components using the same measurement approach. In the single port

approach the machine was only looked at for the CM and DM operating modes. The single port

approach also lost accuracy when applied to a lumped model approximate circuit discussed in

Chapter 4 Section 4.2.

The multi–port measurement approach will need further research to determine its accuracy

as a complete model. However, it was found that this technique could be used to develop a

standalone model for simulating the single–port measurements termed ‘Virtual Measurements’.

This is described further in the Section 5.3 and Section 4.3. This method allowed for the full matrix

model to be probed as though it was being physically measured in all the possible configurations.

Measured scattering data converted to the time-domain from the frequency-domain using Fourier

transforms were not extensively considered because the measurements were still being analyzed for

their accuracy to capture the machine at frequencies above the operating point. In this research

27

it was found that transforms must operate on uniformly sampled data that extends across the

entire frequency range; 5 Hz to 10 MHz. Scattering parameter data can be captured using either

a linear or logarithmic frequency sweep. Sampling is valid only if the amplitude and phase charac-

teristics are adequately sampled to capture all salient frequencies. Logarithmically swept data can

sometimes be used, but linearly swept data is always preferred.

Figure 2.9: Voltage waveforms corresponding to the 4-port PMSM network with Z0 = 50Ω forboth VNA cables and both single ended terminations

The proposed scattering parameter measurement approach can be found in the companion paper

[32] explaining how measurements are to be conducted on shipboard power system components.

The network parameters defining reflection and transmission coefficients for measured frequency

vectors of n-port devices is defined in [57]. The measurement setup for the PMSM machine seen

in Figure 2.9 which details the voltage waveforms measured at each port of the four-port network.

There are four reflected signals, one for each port depicted in Figure 2.9. The other 12 signals needed

to assemble the scattering matrix describe the four-port internal network interactions between each

port. It is not certain if any of the measurements can be discarded by assuming the matrix to be

symmetrical because each machine type is constructed differently. If the machine is symmetrically

designed then it is possible to average redundant measurements to make the matrix symmetrical

and take advantage of mathematical transforms.

28

CHAPTER 3

PROBLEM STATEMENT

The current process to design models using current available methods are time consuming and

require special circuit representations and detailed information about the equipment, which is typ-

ically considered proprietary. The models are commonly found to be unique to one problem or can

only give insight into a specific phenomenon while neglecting others or deeming them insignificant.

Characterization of different type electric machines usually requires multiple test measurements to

isolate each parameter and are not always applicable with other machines. The process to develop

such models can exhaust research hours and provide no standard approach that can be easily im-

plemented on all machines. The models to be developed are not guaranteed to be accurate due to

assumptions made with each step of the available modeling approaches. Even the more accurate

models that describe the physics and material properties of the system are not ideal because they

are difficult to solve with current software. Also, in most cases the motor information is proprietary

or the information given lacks enough detail to fully depict the machine’s construction geometry.

These models are also prone to solver issues, and can be more computationally demanding versus

a scattering type model.

One of the main objectives in the scope of work is to research the prior art which is outlined

in Chapter 2 Page 10. The goal of this work is in determining the validity of proposing a new

measurement approach to capture the high frequency behavior of an electric machine. A secondary

objective is to use techniques found in scattering research and apply them to electric machines

found in our facility. This will require the machines to be validated under the network theory

principles which govern scattering theory i.e. linear and time-invariant, which will be discussed in

4.1.

Another objective is to compare the results from scattering measurements to other known

measurement techniques. This requires managing the data, converting, and comparing it to known

characterization approaches seen in 4.2. The measurements are expressed in impedance parameters

29

instead of the native scattering parameters to utilize prior art techniques of extraction and allow

for more definitive comparison between the various measurement approaches.

The concept and process of conducting virtual measurements will be formulated. The virtual

measurement model is created from a physical electric machine measurement using inverse scatter-

ing methods. The data is assembled into an equivalent multi-port scattering matrix, which defines

the electric machine as having ports for each terminal with respect to a common ground. Each port

in the simulated model becomes a measurement point or load to be used for various experiments.

Scattering parameters can be converted to many different network parameters with impedance

being the most useful to this body of research. This unique approach to measuring machines is

further discussed in Section 4.3. The proposed statement of work is captured in Chapters 2 and 4

and results from select experiments are discussed in Chapter 5.

30

CHAPTER 4

INVERSE SCATTERING THEORY APPLIED TO

THREE-PHASE ELECTRIC MACHINE MODELING

Primarily due to the complex geometry, non-linearity, and time variance of machines; state of

the art research has yet to explore inverse scattering theory (IST) for machine characterization.

The work summarized in this chapter will serve as the initial foundation for researchers to follow

when modeling electric machines using IST to capture the frequency response. The extent of this

research was confined by available equipment, time, and current state of the full SPS model. Typical

approaches to measuring machines are based on voltage and current measurements, which are not

suitable at high frequency. The scattering methodology applied in previous research of power cables

can be utilized to set a foundation for this work [31].

Scattering parameter methodology is desired because the universal measurement process for

developing models is well documented in [19] and provides the researcher with a structured approach

to modeling all the components in the system. Currently, there is a disconnect between what

researchers can perform in a lab and what can be performed in the field. Equipment specifications

are typically limited to what is found on the nameplate. This limits the options for high frequency

modeling approaches. IST can be used to capture information about the internal interactions of the

machine. If the machine is repaired or replaced on a ship the typical control models in place would

no longer accurately model the new changes. Using the scattering parameter approach allows for

any device to be quickly described as an N–port device and can be connected to other devices.

This modeling method is simple enough that a technician could generate a model directly from

measurement. The measurements are transferable in the Touchstone format to any simulation

software package. Once the model is set to accept scattering parameter measurements, it can be

maintained by updating the measurement data when the system configurations change. To grasp

this concept, imagine each component described by an electrical image that captures multiple

snapshots of the frequency responses of the machine. Each machine model is based on a frequency

sweep of snapshots that can be retaken at any time to maintain the most accurate models. Also

31

the model can be used in other forms such as CM, DM, or even full three–phase configurations for

virtual measurements.

This chapter will cover how scattering parameters could be adopted and how this approach

compares to other measurement techniques when it comes to developing accurate high frequency

electric machine models. The Instrumentation and measurement setup is critical to receiving valid

data and was discussed in detail in Section 2.2. An experiment was conducted to validate the

assumptions that a motor can be considered to be a linear and time-invariant (LTI) network, a

prerequisite for applying LTI network theory. The stator to rotor interaction, which tests LTI

compliance, is further detailed in Section 4.1. Parameter extraction for a lumped circuit model is

discussed in Section 4.2. It was also found that measurements could be used to build a full model

of the machine. The simulated model, detailed in Section 4.3, can be virtually measured as though

the machine were physically present.

4.1 Validity of Linear Time-Invariant Networks Applied to

Rotating Machines

Scattering parameters by definition apply to linear time-invariant (LTI) networks covered in

Section 2.2.1. Early research was set out to verify scattering theory as a valid approach to measure

electric machine’s high frequency behavior. An electric machine is typically described as having a

time varying field due to the interactions between the stator and rotor. An electric machine is also

considered non-linear due to the hysteresis found in the back iron [53].

Electric machines are technically not considered LTI, but the inside of the machine is made

up of easily measurable impedances such as resistors, inductors, and capacitors. Literature has

shown that non-linear devices have been modeled using scattering measurements in [39]. Also the

LTI network theory was proven to be capable of accurately measuring the impulse response of an

induction motor at standstill for [54].

Time variance was expected to be caused by the interactions between stator and rotor. An

experiment was setup with two similarly rated power machines, one with a smooth rotor and one

with a cogged rotor. Differences were noted in the physical resistance to rotating the synchronous

cogged motor shaft when compared to the asynchronous machine’s smooth rotation and lack of

cogging. It was hypothesized that measuring the two machines would generate a non significant

32

error between cogging positions. If any error would be seen it would likely come from the cogged

rotor and not from the motor with no cogging resistance. The complexity of mapping the scattered

incident wave as it reflects and transmits through the machine made the mathematical approach

unreasonably difficult. It was determined that the time-variant conditions could be tested by

analyzing the scattering measurements as a function of rotor position. The measurement setup

can be seen in Figure 4.1 where the VNA is using N–type connectors and measurement leads to

interface with the machine.

Figure 4.1: N-connector shield setup for scattering parameter measurements on electric machines(Left) using a vector network analyzer (Right)

In [16] it was concluded that impedance response measurements had substantial error due to

rotor position effects below the first resonance frequency. The test was setup so a comparison

could be made when varying the rotor position during stator measurements. Three rotor positions

were chosen, 0, 270, and 345, corresponding to three different cogging positions of the machine.

Scattering parameters were measured at each cogging position on a 250W brushless DC motor,

which has a similar design as a permanent magnet synchronous machine. Figure 4.2 is the resulting

deviation in scattering results due to rotor position. The maximum had only a 0.4 dB difference

found in the lower frequency ranges given by Equation 4.1. The measurements from initial testing

were scrutinized for errors and determined to be accurate representations of the machine with the

deviations less than 3 dB, thus the scattering measurements are considered valid measurements.

max(S110, S11270

, S11345)−min(S110

, S11270, S11345

) ≤ 0.4dB (4.1)

Measurements were also carried out on an asynchronous machine and the deviations were also

found to be insignificant with a maximum value less than 0.025 dB seen in Figure 4.3. Therefor, the

33

rotor position does not have a significant effect on the measured results. However, measurements

made with the absence of the rotor did affect the frequency response below the first resonance of

the common–mode impedance plot Zm and it had less of an effect on the phase–neutral impedance

plot Z0n confirmed in [24].

Figure 4.2: Variation of port 1 reflection (s11) of the brushless DC motor or synchronous machinewith cogged rotor

When calibrating the measurement equipment, it is impossible to make a perfect short circuit

required, as there will always be some inductance measured in the short. It is also impossible

to make a perfect open circuit, as there will always be some fringing capacitance. Most error

in these forms can be neglected to some degree if the majority of the impacted frequencies are

further removed through proper calibration prior to making measurements. The model number

of the calibration kit is entered into the VNA to ensure proper settings when using that specific

calibration set. The calibration was not able to remove signal noise from the power mains found

at 60Hz. Suggestions for error reduction are given in Chapter 6 conclusions. In comparing our

34

Figure 4.3: Variation of port 1 reflection (s11) of the induction or asynchronous machine withsmooth rotor

results to other published work we found that our data was erroneous at points well below the

first resonance. Depending on the port configuration being measured, the machine was considered

to be either heavily dominated by the parallel capacitance to ground or dominated by the series

inductance of the machine windings . This is where lumped circuit models of machines approximate

the lower frequencies to a specific reactance value. The reactance can be found using the slope of

the impedance in the frequency domain and solving for the corresponding capacitance or inductance

in Equation 4.2.

C =1

ωImZ ; L =ImZ

ωwithω = 2πf (4.2)

Even though the VNA available for research was capable of capturing frequencies as low as

5Hz it was found that the measurements were corrupted by the noise floor on the VNA below a

few 100Hz. Later it was determined that this problem originates in low signal power and could

have been avoided if known. It was good to stumble into this problem because we researched

ways to correct the missing data and learned how the simulation software handled noisy data.

Our data was considered corrupted in the frequency ranges where our measurements were effected.

35

Two techniques are typically used in the proposed method for extrapolating to the DC point or

0Hz. Constant extrapolation uses the closest known point to determine the next point or linear

extrapolation which uses two points as a reference for calculation.

It was concluded that for our purposes, the lower frequency measurements were not critical to

our models performance. Since the research was focused on modeling the interactions between the

machine and ground, our lower frequency limit was moved to 1 kHz and our upper bounds were set

at 10MHz. These frequency ranges were considered acceptable for developing the grounding models

of three–phase electric machines [50, 13, 40, 58]. For frequencies well above the power frequency,

the motor can be considered linear and the time variance at lower frequencies was mitigated by

raising the lower frequency limit to an acceptable frequency where the effects were negligible [59].

Using the slope of the impedance at 1 kHz allowed for extrapolation to approximate the DC point.

The measurement range chosen will capture the leakage currents [60] or CM currents [58] found

oscillating between 100 kHz and 10MHz.

4.2 Parameter Extraction for Lumped Circuit Model

The proposed approach to measure a three phase machine will produce either single-port or

multi-port measurements across a given frequency range. The multi-port measurement is the

preferred method because it contains all the data necessary for multi-port modeling capabilities like

virtual measurements discussed in Section 4.3. The process of extracting parameter values from

frequency data for equivalent circuit modeling is common approach to high frequency modeling

for overvoltage studies [34, 35], etc. The equivalent circuit model approach typically starts with

three per-phase circuits that are electromagnetically coupled. Each per-phase circuit is equivalent

assuming a symmetrical machine construction (Figure 4.4). The parameters are normally found via

analytical calculations, slopes and resonances in impedance data, or FEA software. In some cases

the winding and slot geometry were used separately to calculate more accurate representations of

the windings [35].

The process to determine each parameter and the overall accuracy of the model is highly de-

pendent on the circuit chosen to represent the device. This approach insist that there is knowledge

about the internals of the machine and specific details not typically released by the manufactures

of the machine. In research it is common to see work done based on an abundance of information

36

Figure 4.4: Per-phase representation of the induction motor including the high frequency modeland the dynamic dq model

about the machine construction [44]. One can argue that a high frequency model could be general-

ized based on a much simpler machine type, which would loosely fit measured data like the phase

model in [38]. The problem with this thought is that small errors in the frequency domain can

result in large errors in the time domain.

Using scattering parameter data is preferred by the author because it is based specifically on

the device being measured. In the IST approach the researcher develops a circuit model based

on the data extracted instead of measuring the device to fill in parameters of a general machine

model. It is safe to assume that a machine’s construction and parameters are unique to the

designer. The modeling approach should accommodate this uniqueness by first measuring the

device, and second determining circuit representation that best fits the data. This approach is the

least favorable because one must use transforms to breakdown the frequency data into separate

pieces with equivalent capacitance, inductance or resistance. This approach was found to be fairly

accurate but still considered a tedious approach.

The equivalent per-phase circuit in [34] and seen in Figure 4.4 was designed. Special equations

were made to help with parameter extraction. These equations are unique to this model and are

not universal to other machine types. The extraction Equations 5.15-4.9 will complete the high

frequency portion of the model, while the low frequency is controlled via the commonly used dq

model.

37

Figure 4.5: Common-mode impedance of a lumped parameter model compared to impedance ana-lyzer measurements and scattering parameter model representation

Cg ≈ 1

2

(

1

3

)

1

(2πflow)‖Zpg‖flow(4.3)

Rg ≈ 3xReZpgfhigh (4.4)

Ld ≈ 2

Cg

(

1

2πfpole−Zpn

)2

(4.5)

Re ≈ 3x‖Zpn‖fpole−Zpn(4.6)

Ct ≈Cg

10(4.7)

Lt ≈1

Ct

(

1

2πfzero−Zpn

)2

(4.8)

Rt ≈ 3xReZpnfzero−Zpn(4.9)

The equivalent model common-mode impedance was plotted excluding the dynamic dq branch

and compared to impedance measurements and scattering parameter model results. The equivalent

model clearly misses the higher order behavior, while the scattering parameter model has high

fidelity and tracks the actual measurements with little error (Figure 5.11). The most detailed

modeling approach found [44] covers just the inductive portion of the machine from 20 kHz to

20MHz.

38

4.3 Virtual Measurement Model

Electric machine models based on multi-port scattering data are capable of virtual measure-

ments. Scattering measurements from the machine were assembled into one complete measurement

matrix and brought into the Agilent’s Design Software (ADS). The scattering data was constructed

in a four-port model matrix and placed in the software for simulation. The probes from the simula-

tion software were placed on the terminals (now referred to as ports) of the electric machine model

to mimic typical measurements made on physical machines. The probes can act as an impedance

analyzer and return impedance information drawn from the measurement model or the model can

be wired to match specific designs and measured for the resulting characteristics. Previously dis-

cussed measurements of phase-neutral, common-mode, and differential-mode are virtually measured

and the model connections can be seen in Figures 4.6-4.8.

Figure 4.6: Single–port scattering parameter measurement to obtain common–mode impedanceinformation

Figure 4.7: Single–port scattering parameter measurement to obtain differential–mode impedanceinformation like T1 + T2 to T3

The results were found to be identical with the actual impedance analyzer measurements taken

on the machine. The impedance plots in Figure 4.9 capture more resonances and anti-resonances

than found by using any equivalent circuit, finite element analysis (FEA), frequency response

39

Figure 4.8: Single–port scattering parameter measurement to obtain phase–neutral impedanceinformation

function (FRF), or stand still frequency response (SSFR) techniques given in previous literature

[50, 23, 39, 42]. This is a significant step in the direction to develop accurate models for future

all-electric ships, considering the accuracy and the effort needed to develop such models. The

computation method to combine scattering measurements into one matrix model, discussed further

in [19], can be left in the default state and only need to be considered if any of the reference

impedances entered are complex. Complications with making accurate scattering measurements

for building models of ship power system components are discussed in [61] and used in conjunction

with the work in [62].

Virtual measurements of CM and DM impedances were significant parts of my research The

important concept realized is how much information was captured by scattering measurements and

how it can be extracted by different modeling techniques. This approach has significant advantages

considering that all devices in a shipboard power system can be connected to a VNA and measured

in the same protocol with differences only in the amount of ports per device. The component

connections can be configured in different combinations and probed for measurement information.

One application relevant to our work is determining the grounding of the shipboard power system

to the ship hull. The simulations could be configured in the various grounding arrangements of

interest. Then each simulation would be scrutinized and ultimately suggestions would be passed

to the final design.

Another application that is significant but most likely overlooked is the sharing of component

models. The physical machine does not need to be present in the lab for researchers to administer

measurements and configuration testing. A machine could be measured by the manufacturer in

40

(a) 2.5MW Squirrel-cage induction machine with neutral accessible

(b) 17kW Permanent magnet synchronous machine with neutral accessible

Figure 4.9: Virtual measurements of impedance for phase-to-neutral, common-mode, anddifferential-mode are compared to measurements made on the physical machine

41

standard scattering format and distributed out to various researchers, all working on different

simulation tests. The machine’s performance can be tested without ever leaving the manufacturers

factory. Ship power system components are large and shipping cost can be unreasonable when

shipped to labs individually. The model can be distributed and used as a simulated device in

hardware-in-the-loop testing.

When a specific impedance profile is needed, the scattering parameters could be chosen first

and the motor could be designed to fit the desired parameters. These design requirements can be

passed back to the manufacturer where the machine could be reconfigured to fit approved scattering

profiles. This concept can be seen in commercial lighting for plants, where a specific frequency is

desired for stronger yields. The researchers would determine the appropriate wavelengths of interest

and the manufacturer would design accordingly.

42

CHAPTER 5

RESULTS AND COMPARISON TO

CONVENTIONAL TECHNIQUES

The results discussed within this chapter will be added to the foundational prior work towards

alternative grounding models using IST. There were three main research experiments that were

conducted to explore this work further and they will be discussed in the next three sections.

The first important discovery was knowing that the VNA measurements were giving valid IST

measurements. The VNA captured the unique behavior of multiple electric machine types using a

universal measurement procedure. The resonant and anti-resonant behaviors were captured with

high fidelity and are further discussed in Section 5.1. The next insight came while measuring

the permanent magnet synchronous machine (PMSM) in the lab and devising a measurable event

to capture the electric machine’s high frequency response to transients. A short circuit test was

designed and prepared for testing the response of the motor when a terminal voltage collapses

to zero due to a short circuit. The short circuit test was used to capture a measurable event to

compare simulation approaches. The results from the short circuit model and measurement model

are discussed in Section 5.2. In Section 5.3, a proposed modeling approach opens up the possibility

for virtual measurements. Virtual measurement models are capable of being expressed in terms

of scattering data. The virtual measurements are useful in capturing parameter information when

setting up simulations. The benefits and results from these models are discussed towards the end

of Section 5.3.

5.1 Resonance and Anti-Resonance

It was convenient to convert scattering parameters to impedance parameters in order to compare

measurements conducted by other approaches. Typically these impedance plots are inspected

manually to determine inductance and capacitance. The calculated magnitude of common-mode

impedance can produce estimated values for inductance and capacitance by measuring the slope

before and after the anti-resonance point. This can be visually spotted because the plot follows

43

a ‘V’ shape where the local minimum marks the anti-resonance frequency. This shape holds true

for most models found in prior art. The more accurate and detailed the model is made the better

chance the model will capture all the effects seen by resonances and anti-resonances. It was found

that the lowest order models can still capture the global minimum impedance, which is at the

lowest frequency point in the plot where the impedance slope caused by the capacitance found in

the lower frequencies and the slope in impedance from the inductance in higher frequencies cross,

causing resonant behaviors of interest.

Figure 5.1: Induction motor impedances measured using IA and VNA measurements

Looking at Figure 5.1 the magnitude of CM data is noisy in the lower frequencies. As the fre-

quency increases, the measurement fidelity was much more accurate between the two anti-resonant

points at 35 kHz and 1.0MHz and alternated between capacitive and inductive behaviors.

The machine is mainly capacitive in nature at frequencies below the first resonance. The first

resonance point can be used to calculate the CM inductance of the machine. The coil is much higher

44

and reduces the effect of parallel capacitances found closer to the neutral point of the machine.The

CM impedance also contains a global minimum considered the anti-resonance point, where the

lowest impedance is found. The anti-resonance also is a frequency at which the resistance can be

calculated. This frequency point is to be noted when developing shipboard power system layouts,

because CM noise passing through the machine at this frequency has a low impedance path to

ground.

The common-mode impedance is usually modeled by two capacitances and in some cases only

one. It is clear though from Figure 5.1 that a second order model is not accurate enough to

capture all the parasitic effects. The impedance generally starts between 1-10 kΩ and decreases

with frequency until the first resonance based on the capacitance to ground. The inductance due

to skin effect will increase the impedance until the second resonance and then continues decreasing

as a function of the combined ground and turn-to-turn capacitances. This is a generalization of the

impedance plots for typical machines. The actual number of resonances and anti-resonances can

vary based on the machine type. Having a universal measurement protocol and model development

procedure would allow for fast model building and tends to have higher accuracy based on this

work.

The anti-resonance point will generally happen in the higher frequencies where the machine is

more strongly coupled to the ground. This coupling adds an inductive path between the phases

and ground at an anti-resonance point, where the lowest local impedance path is present. If a

frequency in this range were to perturb the machine it would have the least impedance path and

could ultimately cause damage. Setting boundaries with minimum impedances for each machine

or avoiding specific frequencies should be considered when designing the SPS. If we remove all low

impedance paths to ground then we can avoid or maintain the ground coupling issues. Adding

resistance can also raise the bottom line on impedance but this can produce unwanted losses. A

low impedance path can cause partial discharge or degradation of the insulation material. In severe

cases this can manifest into a short circuit path. Looking at the graphical representation of these

measurements will help designers to choose specific operating frequencies and reduce the risk of

problematic resonances with voltage escalations.

A unique finding was brought to our attention in the results around 1.0MHz. It seems as

though all three measurement types have a minimum impedance near this frequency. This needs

45

to be explored further to determine the cause and whether this can be used to build better models.

The DM measurements approach their resonant impedances at frequencies lying to the left and

right of the CM’s anti-resonant frequency.

5.2 Short Circuit Test

In a MVDC ship board power system it is more likely that a fault will happen on the DC

network and not the AC due to the percentage of the system that is DC versus AC. In the actual

testing of the effects of faults, the short circuit path should be faulting the DC side of the inverter

not the phase winding of the AC motor or generator. The purpose of the test described herein

was to capture the parasitic characteristics of the motor itself without the added coupling of the

inverter and cables. In this test the motor is isolated from all other effects and can be modeled

as such. This would create a better representation of the motor’s true response to high frequency

effects. The focus is not on system modeling but rather machine modeling for this test.

The electric machine model should characterize a wide frequency spectrum in order to pre-

dict accurately how the machine will act in the shipboard power system. The model is initially

developed using the conventional method of an equivalent circuit (EC), based on parameterized

lumped elements, to help benchmark the accuracy of the test [25]. The equivalent T-circuit has

three phases consisting of two resistive-inductive (RL) components split by a capacitance to ground

on each phase and a wye connected neutral. The RL values are to represent the resistance and

inductance of the machine windings while the capacitor represents the equivalent parasitic capac-

itance to ground. The common mode impedance is measured from the equivalent T-circuit where

the terminals are connected in parallel and measured with respect to ground (Figure 5.2).

The electric machine model was subjected to a test designed to characterize the high frequency

response without connecting an inverter or long cables which could misrepresent the actual response

of the modeled PMSM. The simulation was set up such that the neutral was ungrounded and

the machine was left unloaded with one phase equipped to fault to ground through a switch.

The unloaded generator will produce alternating phase voltages that are functions of the rotor

revolutions and the number of pole pairs. The parasitic capacitance between the windings and

frame will provide a low impedance path to ground at higher frequencies. If a phase is shorted

to ground then the reflected voltage wave back into the machine will contain a wide spectrum of

46

Figure 5.2: Common-mode impedance of a PMSM equivalent T-circuit

frequencies corresponding to the fall time of the short. The phase voltage short to ground will

produce frequencies that correspond to the inverse of the fall time tshort (Equation 5.1). At these

higher frequencies the low impedance path will cause a transient current into the ground path.

fshort = 1/tshort (5.1)

For simulation the capacitors and inductors are given an initial voltage and current correspond-

ing to the phase voltages and currents of an unloaded system prior to fault time tfault. The short

is characterized to match the experimental fault waveform by using a controlled voltage source.

Sending the experimental waveform into the simulation will better match the switch fall time and

provide a more accurate response from the model seen in Figure 5.3.

The model parameters for the T-circuit approximation are given in Equations 5.2-5.15. The

capacitance was calculated at 1 kHz from the phase to ground impedance measurement. The induc-

tance and resistance was calculated at 10MHz from the phase to neutral impedance measurement.

Each phase is modeled by a T-circuit with the phase inductance and resistance split by a capaci-

tance to ground. The neutral is wye connected without any source voltage because the capacitors

are initially charged.

Vrms = 480V (5.2)

47

Figure 5.3: PMSM fault current simulation using a measured fault to trigger a controlled voltagesource coupling terminal T1 to ground and phase T2 and T3 unloaded.

Vpk = Vrms ×√2√3= 391.92V (5.3)

Vc1 = Vpk = 391.92V (5.4)

Vc2 = Vc3 = Vpk ×−1

2= −195.96V (5.5)

tfault = 2× 10−9 s (5.6)

tsim = 1× 10−6 s (5.7)

∆ttol = 1× 10−9 s (5.8)

tstep,max = 1× 10−8 s (5.9)

C =−1

2× π × f × ‖Zpg‖= 1.16× 10−8 F (5.10)

L =‖Zpg‖

2× π × f= 1.95× 10−6H (5.11)

R = ReZpn = 24.66Ω (5.12)

Rs =3

2×R = 36.99Ω (5.13)

Ls =3

2× L = 2.93× 10−6H (5.14)

Cg =C

3= 3.86× 10−9 F (5.15)

48

The physical experiment involved an unloaded 8 pole PMSM rotating at nominal speed and

setup for a terminal fault to ground via solid state relay (SSR). A virtual push button in the Real

Time Digital Power System (RTDS) controls the initiation of fault logic when pressed and stays

on for greater than one full cycle i.e. 1/60Hz = 16.67 s. The terminal voltages are measured with

a differential probe that has CM rejection capability for an isolated measurement. The voltage

of terminal T1 is relayed through to the RTDS program called RSCAD. A push button in RTDS

controls the initiation of the fault logic. Fault logic checks for next positive edge zero crossing,

calculates a 90 phase shift, and sets the terminal fault signal initiation process at the peak voltage

Vpk of terminal T1. RSCAD then initiates the fault signal to output an analog 10VDC signal to

activate the SSR and trigger an oscilloscope to capture the transient response. The full setup of

the physical test performed can be seen in Figure 5.4.

Figure 5.4: Measurement setup for a single phase to ground fault of a three-phase PMSM

The results can be seen in Figure 5.5, where the top plot is the fault current and the bottom

plot shows terminal voltages T1, T2, and T3. The transient fault current peaked at 1.4A for 1 s.

Terminals T2 and T3 rise to 3 times their voltage before the fault and settle out at twice their

voltage 80 s after the fault.

49

Figure 5.5: Single phase to ground fault of a three-phase PMSM

Figure 5.6: T-circuit simulated fault current

50

The modeled fault was found to be inaccurate and displayed a peak current more then 5.5A

and lasted less than 0.2 s, seen in Figure 5.6. The impedance plots in Figure 5.7 shows where the

equivalent circuit does not capture the higher frequencies that the VNA captures.

Figure 5.7: PMSM measured impedance compared to simulated T-circuit equivalent

5.3 Virtual Measurement Comparison to Impedance Analyzer

The virtual measurement model was not a goal for this research but it was found to be a

useful tool for delivering model data in a form that allowed quick model information. This concept

was found when data was converted from scattering data to impedance data. The data captured

across all frequency measurements was found to be highly accurate to the true impedance at those

corresponding frequencies. This meant a motor could be measured using data in the scattering

form. An interesting thing was observed when the terminals were tied together in the CM and

DM configurations leading to a new measurement set later used for virtual measurement models.

These models are capable of extracting the impedances with high accuracy. In ADS the model was

considered a four–port network. The results can be seen in Figures 5.8, 5.9, and 5.10 where the 3

port configurations were discussed in Subsection 4.3.

51

Figure 5.8: Virtual measurement of common–mode impedance

52

The common-mode impedance Z0g was measured from a full four-port scattering matrix. The

results were analyzed at the lower frequencies and found to match the capacitance measured by

the impedance analyzer. There are distinct frequencies in the data where three points of interest

stand out, one at 100kHz, and the other two at 3 MHz and 7 MHz. These frequencies of interest

are useful for modeling and should be measured in detail. This was difficult to accomplish with the

impedance analyzer (IA) which manually stepped each frequency. This is why there are less data

points seen in Figure 5.11. The scattering results were at much higher resolutions due to the ease

in linearly sweeping the test frequencies for more than ten thousand data points. When compared

to the IA measurements which were difficult to transition and manually record each point. It was

found that 10 - 20 IA measurements per logarithmically spaced frequency sections were enough

to infer that both were valid approaches. It was clear after running multiple experiments that

scattering parameters were obtained faster with higher resolutions and less effort.

Figure 5.9: Phase–neutral mode impedance data was measured virtually

53

In Figure 5.9 the typical inductive behavior is captured before the first resonance which is

found at approximately 200 kHz. The typical phase pattern was also captured in this figure, where

early impedances are not effected by the added inductance. Skin effect takes place and brings

the phase towards the highest inductive behavior before transitioning to capacitive behavior due

to the capacitance between turns in the windings of each phase. In the megahertz and higher

regions, the machine transitions multiple times from capacitive to inductive. Capturing all these

transitional frequencies in detail allow for accurate models when using scattering measurements.

This measurement is considered another form of DM impedance measurements and is comparable to

the more accepted form found in Figure 5.10. The interesting effect is seen when you compare both

of these DM methods. In the Zm plot the same phase characteristics were found at lower frequencies

starting inductive and then drop to a lower inductance when the series resistance was introduced.

The plots have similar visual features such as the shape of the resonances and anti-resonances.

The difference is that they occur at different frequencies due to the terminal connections used to

measure signals passing from one terminal phase to the opposing parallel phase combination.

Taking a further look at the results in Figure 5.11 it is clear that the VNA was more dominant

and covered more frequency points with higher accuracy than the IA. This does not mean that

IA measurements are incorrect but it was found to take much longer to measure each individual

frequency. Newer models of IA may have corrected this but the current model that was used lacked

a quick measurement operation.

54

Figure 5.10: Differential–mode impedance data was measured virtually

55

Figure 5.11: Impedance data was virtually measured and compared to known measured data withhigh accuracy

56

CHAPTER 6

CONCLUSIONS AND FUTURE CONSIDERATIONS

6.1 Conclusions

Similar to the way light reflects at certain frequencies giving our surroundings color, the incident

wave reflects at certain frequencies that can be used to characterize the device in an electrical

representation. Scattering is when a known incident wave is sent into a device/network and the

reflections and transmission ratios of input voltage to output voltage of each port are recorded.

A full scattering parameter matrix is very useful for modeling the higher order behaviors inherent

to electric machines. The matrix can be used as a stand alone model, in conjunction with other

scattering models, or for extraction of other parameters for use in existing models. Use of the inverse

scattering theory (IST) method has been explored and analyzed for accuracy. In conclusion, it is

recommended that the IST methodology be considered for use in future shipboard power system

analysis when concerned with ground interactions with ship-hull ground. These ground interactions

are typically best understood as common-mode coupling. The causes of common-mode currents

or stator ground currents have been covered extensively in [58, 60, 63, 64]. Different methods to

suppress these currents have been proposed. However, little has been done to model the parasitic

effects, electromagnetic interference (EMI), or circulating bearing currents that are part of common–

mode (CM) currents in the detail found when using scattering data.

According to [13] it was found that plotting various motors for size and power ratings did not

produce any trends that were consistent. Some parameters would follow a trend while others would

not track well. It is too difficult to derive any trends of parameters based on power ratings and size

with the given scope of this research. The inductances for example are strongly related to turns

and slot characteristics. Each machine is different due to how it was physically built. The same

machine sizes were measured and produced varying results. Low frequency circuits will not see

these differences. However, current high frequency models are needed and each machine can have

its own scattering parameter fingerprint essentially.

57

Understanding what causes high frequency phenomenon in shipboard power systems (SPS) and

using proper machine models capable of capturing these effects are critical to future ship building.

Using techniques such as changing the switching frequencies or reconfiguring cable lengths are

possible solutions to minimize unwanted effects. Research proposed in [65] also suggested criteria

to follow when designing a CM filter. These types of studies are all realizable with the data obtained

using IST.

Describing the machine in the three proposed single–port representations is considered a com-

mon approach to HF motor modeling [16, 22, 34]. This approach allows for standstill measurements

to be made that help determine lumped parameter quantities of common machine circuit represen-

tations. Using a vector network analyzer (VNA) for this approach does not offer differing results

from results found when using an impedance analyzer. In most cases, the measurement process was

simplified to a set of standardized measurement sets, when using scattering parameter methods.

This work presents an alternative measurement approach that has the potential to be applied uni-

versally to other components in the system such as the cables and power electronic devices. Having

a similar measurement process and data post processing method for all devices makes this method

promising for future research.

Preliminary high frequency models were proposed and analyzed for their merits. It was found

that IST methods for measurement were valid in accurately measuring ground interactions between

the motor and the surrounding system. A systematic approach was followed to extract high fre-

quency characteristics from machines using universally accepted scattering methods for devices not

typically considered linear and time–invariant (LTI). Passive models for motor applications were

completed and the introduction of virtual measurements was discussed.

6.2 Future Considerations

Leading the efforts in machine modeling using IST methods has opened up many possibilities

that should be considered for future work. The work covered within was nearly scratching the

surface with possible scenarios and improvements that can be made. Further work into the relative

error is an obvious thrust that must be considered if these measurements are to standardize mod-

eling efforts. There was literature found that could help reduce error in measurements and clean

parametric data [66, 67, 57]. Even the use of other types of network analyzers is an area that could

58

be explored further. The use of microwave transition analyzers (MTA) or large signal network

analyzers (LSNA), which measure both amplitude and phase of the fundamental and harmonics.

It was barely touched on in this work but equipment health snapshots could be a critical tool to

monitor the behavior of devices after certain events and can be used to predict possible failure when

series of data are taken and trends are established. On a Navy ship, large amounts of energy are

being transfered back and forth throughout the ship sources and loads. These events can degrade

the equipment and snapshots may help with preventative maintenance and serve as a living model

that is always held current. Measurements used to time stamp the current state of the machines

health considering aging and pollution of windings in machines is based on an existing method but

this particular approach is new and needs further work to define all the procedures.

Finite element analysis (FEA) could be used to extract scattering parameters for design and

implementation without building the machine. Aging can be predicted and modeling can be done to

see the effect of aging on the machine. Adding this known progression to update models over time

of use can be a simple approach to predict current state of equipment or predicting the lifetime of

equipment. This can allow the Navy to be proactive in maintenance schedules and new snapshots

can be taken to track the change in system parameters. Models can be easily updated to properly

represent current state of the ship.

Speaking of validation it is pertinent these models be further scrutinized at higher frequencies

using faster switches. Validation methods using a fast switching MOSFET in [31] helped to set a

standard for IST measurements on power equipment. The MOSFET used has a steep rise time in

the nanoseconds range which corresponds to higher frequencies, subsequently found with available

measurement leads used in this research. Measurement responses of the incident pulse were captured

using S-parameter models with reasonable accuracy and should be considered to advance the upper

frequency bounds set in this work.

For future modeling considerations, it is important to develop active models. The models

developed in this research were all passive loads acting as variable impedances based on the input

frequencies into the model. These models are well suited as motors but do not contain internal

sources needed when discussing electric machines as power generators. Work will need to be done

to incorporate dependent voltage sources that respond based on scattering data provided in typical

IST measurement protocols.

59

It was also found that the termination resistance was not highly accurate in the higher fre-

quencies which caused deviations in similar measurements. There was also slight variations in

repeatability when the resistance was lower then the complex impedance. It was determined to

be most likely caused by improper terminations into non-ideal 50Ω impedances. Another issue

with accuracy was found when machines did not have an accessible neutral terminal. In [57] a new

method for working around this problem seems possible. The use of CM and DM circuits with the

neutral terminal inaccessible was previously discussed but should be brought up again and explored

in further detail.

Engineers have continued to have difficulty modeling machine bearing contact impedances be-

tween stator and rotor when measuring at standstill i.e. SSFR. Future work could determine the

frequency that this interaction will effect and remove this from the scattering matrix to better rep-

resent its response quantities when the motor is rotating and the bearings are no longer in direct

contact. SSFR research could be further looked at with scattering theory in mind in order to help

further the usability of scattering measurements.

Model validation on other machine types and sizes must be considered in the future. Also, full

system models with various grounding schemes have not been explored and would likely bring up

new information on the usability of scattering parameters on all components of the power system.

The first use suggested from this work would be to identify certain frequencies of interest that may

cause low impedance to ground paths. This would require further developments on test conditions

that can be reproduced in the lab for validation and verification of scattering models. The last

and probably more crucial step for future work would be the implementation of scattering models

into various simulation platforms. Researchers all have their own ”go to” software packages for

simulation. Using Touchstone format, models data could be easily shared via email and then

dropped into the modeling software of the researchers choice.

6.3 A Note to the Reader

Throughout this manuscript and body of work, extensive research of the state of the art was

conducted. The references that did not get mention in this document were all inspiration to the work

in some capacity but were not drawn on specifically when writing. Each reference has been left in

folders for others to draw from when extending this work further. Discussed in this document were

60

high frequency transients and frequency dependent measurement methods which capture transient

effects.

61

APPENDIX A

MOTOR MODELS

Summary

of m

odels

Litera

ture

Zhongand

Lipo(1995)

Consoliet

al.

(1996)

Grandiet

al.

(1997b,a,

2004

)

Ranet

al.

(1998a,b)

Bogliettiet

al.(1999,

2001

,20

07)

Moreira

etal.(2002)

Llaquet

etal.

(2002)

Gubıa-

Villabona

etal.(2002)

Web

eret

al.

(2004)

Maki-Ontto

andLuomi

(2005)

Proposed

model

Mach

inety

pe

Induction

motor

Induction

motor

Induction

motor

Induction

motor

Induction

motor

dual-vo

ltage

acinduction

motor

Induction

motor

acmotor

Induction

motor

Induction

motor

wound-rotor

Modelty

pe

Distributed

Lumped

Lumped

Distributed

Lumped

Lumped

Distributed

Lumped

Lumped

Distributed

Lumped

Use

ofmodel

EMI

EMI

EMI

EMI

EMI

EMI

EMI

EMI

EMI

Bearing

current

Dynamic

simulation

Fre

quency

range(H

z)

1K–500K

10K–2M

10K–1M

1K–3M

1K–1M

1K–2M

10K–1M

N/A

1K–100M

10K–10M

0.01–51.2K

Typeofdata

DM

CM/DM

CM/DM

CM/DM

CM/DM

CM/DM

CM

CM

CM/DM

CM,machine

dim

ensions

Admittance

matrix

Fitting

meth

od

N/A

Analytical

Analytical

Analytical

Least

squares

Analytical

Analytical

Analytical

Analytical

Analytical

GA

Variables

abc

qd0

abc

abc

abc

abc

abc

abc

abc

abc

abc/qd

DC

resistance

YN

NN

YN

NY

NY

Y

Eddycurrent

loss

YY

YY

YY

YY

YN

Y

Sta

torleakage

inducta

nce

YY

YY

YY

YY

YY

Y

Phase-to-

phase

inductive

coupling

YN

YN

NN

NN

YY

Y

Phase-to-

phase

capacitive

coupling

YN

NN

NN

YN

YN

N

Turn

-to-turn

capacitance

YY

YN

YY

YY

YN

N

Phase-to-

gro

und

capacitance

YY

YY

YY

YY

YY

Y

Iron

resistance

YN

YY

YY

YN

YY

Y

Main-fl

ux

satu

ration

NN

NN

NN

NN

NN

Y

Low-fre

quency

behavior

NN

NY

YY

NN

NN

Y

Roto

r

components

NN

NN

NN

NN

NN

Y

62

Summary

of m

odels (C

ont.)

Litera

ture

Schinkel

etal.(2006)

Mirafzal

etal.(2007,

2009)

Henze

etal.

(2008)

Idir

etal.

(2009)

Magdunand

Binder

(2012)

Wanget

al.

(2010)

Deganoet

al.

(2010)

Deganoet

al.

(2012)

Boucenna

etal.(2012)

Proposed

model

Mach

inety

pe

Induction

motor

Induction

motor

Induction

motor

Induction

motor

squirrel-cage

squirrel-cage

induction

motor

Induction

motor

Induction

motor

wound-rotor

Modelty

pe

Lumped

Lumped

Distributed

Lumped

Lumped

Lumped

Lumped

Lumped

Distributed

Lumped

Use

ofmodel

EMI

EMIand

bearing

current

EMI

EMI

EMI

EMI

EMI

EMI

Bearing

current

Dynamic

simulation

Fre

quency

range(H

z)

10K–30M

10–10M

100K–10M

100K–40M

1K–100M

100–10M

10K–30M

10K–30M

10K–200K

0.01–51.2K

Typeofdata

CM/DM

CM/DM,

machine

dim

ensions

Machine

dim

ensions

CM/DM

CM/DM,

machine

dim

ensions

CM/DM

CM/DM

CM/DM,

machine

dim

ensions

Machine

dim

ensions

Admittance

matrix

Fittingmeth

od

Analytical

Analytical

FEM

Analytical

Analytical

Analytical

GA

GA

FEM

GA

Variables

abc

abc

N/A

N/A

abc

abc

abc

abc

N/A

abc/qd

DC

resistance

YY

YN/A

NN

NN

N/A

Y

Eddycurrent

loss

YY

YN/A

YY

YY

N/A

Y

Sta

torleakage

inducta

nce

YY

YN/A

YY

YY

N/A

Y

Phase-to-p

hase

inductive

coupling

YY

NN/A

NY

YY

N/A

Y

Phase-to-p

hase

capacitive

coupling

NN

NN/A

NN

NN

N/A

N

Turn

-to-turn

capacitance

NY

YN/A

NY

YY

N/A

N

Phase-to-

gro

und

capacitance

YY

YN/A

YY

YY

N/A

Y

Iron

resistance

YY

NN/A

YY

YY

N/A

Y

Main-fl

ux

satu

ration

NN

NN

NN

NN

NY

Low-fre

quency

behavior

YY

NN

NN

NN

NY

Roto

r

components

NY

NN

NN

NN

NY

63

Results for 3-phase Induction motor (AsynM)

103

104

105

106

107

108

109

-8

-6

-4

-2

0

S-Parameter Magnitude S11

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-600

-400

-200

0

200

S-Parameter Angle S11

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-50

-40

-30

-20

-10

0

S-Parameter Magnitude S12

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-600

-400

-200

0

200

S-Parameter Angle S12

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

64

103

104

105

106

107

108

109

-40

-30

-20

-10

0

S-Parameter Magnitude S13

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-200

-100

0

100

S-Parameter Angle S13

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-60

-40

-20

0

S-Parameter Magnitude S21

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-600

-400

-200

0

200

S-Parameter Angle S21

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

65

103

104

105

106

107

108

109

-8

-6

-4

-2

0

S-Parameter Magnitude S22

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-600

-400

-200

0

200

S-Parameter Angle S22

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-40

-30

-20

-10

0

S-Parameter Magnitude S23

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1000

-500

0

S-Parameter Angle S23

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

66

103

104

105

106

107

108

109

-40

-30

-20

-10

0

S-Parameter Magnitude S31

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-200

-100

0

100

S-Parameter Angle S31

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-40

-30

-20

-10

0

S-Parameter Magnitude S32

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1000

-800

-600

-400

-200

0

S-Parameter Angle S32

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

67

103

104

105

106

107

108

109

-8

-6

-4

-2

0

S-Parameter Magnitude S33

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-600

-400

-200

0

200

S-Parameter Angle S33

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

68

Results for 3-phase brushless DC motor (SM)

103

104

105

106

107

108

109

-10

-5

0

S-Parameter Magnitude S11

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-600

-400

-200

0

200

S-Parameter Angle S11

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-60

-40

-20

0

S-Parameter Magnitude S12

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1500

-1000

-500

0

S-Parameter Angle S12

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

69

103

104

105

106

107

108

109

-60

-40

-20

0

S-Parameter Magnitude S13

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1000

-500

0

S-Parameter Angle S13

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-60

-40

-20

0

S-Parameter Magnitude S21

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1500

-1000

-500

0

S-Parameter Angle S21

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

70

103

104

105

106

107

108

109

-15

-10

-5

0

S-Parameter Magnitude S22

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-500

0

500

S-Parameter Angle S22

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-100

-50

0

S-Parameter Magnitude S23

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1000

-500

0

S-Parameter Angle S23

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

71

103

104

105

106

107

108

109

-60

-40

-20

0

S-Parameter Magnitude S31

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1000

-500

0

S-Parameter Angle S31

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

103

104

105

106

107

108

109

-100

-50

0

S-Parameter Magnitude S32

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-1000

-500

0

S-Parameter Angle S32

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

72

103

104

105

106

107

108

109

-10

-5

0

S-Parameter Magnitude S33

Frequency [Hz]

Magnitude [

dB

]

103

104

105

106

107

108

109

-500

0

500

S-Parameter Angle S33

Frequency [Hz]

Angle

[]

Rotor Position 0° Rotor Position 270° Rotor Position 345°Rotor Position 0° Rotor Position 270° Rotor Position 345°

73

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BIOGRAPHICAL SKETCH

Patrick R. Breslend was a research Assistant at the Center for Advanced Power Systems, Florida State Uni-

versity in Tallahassee, Florida from the years 2012–2015. In this position, he was responsible for

the development of research models for use in the Electric Ship Research Development Consor-

tium (ESRDC). His work has led to the development of rapid model generation tutorials for use on

MathWorks website. Currently working on M.S. in Electrical Engineering at Florida State Univer-

sity, where he has focused his efforts in the areas of electrical machine grounding techniques. His

approach to modeling the electric machine incorporates scattering parameters in order to analyze

ground currents due to higher switching frequencies present in future electric ships.

Prior to these positions, he was cofounder and President of Sustainable Engineered Solu-

tions (SES) a student organization at Florida State University from 2011-2012. Through his direct

leadership the group completed multiple projects in the area of sustainability. The successes of

SES lead to a conference trip to Association of Energy Engineers World Energy Engineering Con-

ference. The trip was fully funded due to the hard work of Patrick and his supporting staff. He

also contributed to the group by acquiring the management responsibilities for the FAMU/FSU

Solar Car in the hope that the group could spread awareness and support for sustainability in our

community.

Also, in his masters program he found time to Co-found and hold the position of Vice-President

for the Society of Engineering Entrepreneurs (SEE). His business ideas and breadth of experience

was instrumental in the growth of this organization during its infancy. He has lead future planning

and put together the first entrepreneur group specifically aimed at young engineers looking to start

businesses.

Mr. Breslend has held various jobs since the age of eleven where he started his own lawn

mowing company Leprechaun Lawn Service. It was at this job where the seed for his first patent

was planted. It was years later in college, working for FedEx , he decided to patent his idea

for use in the shipping industry. He is currently in the process of starting up his own business

Optimal Bagging and its first product the Quick-Pack. He looks forward to turning his patent into

a commercial product seen in industries such as shipping, hotels, restaurants, etc. He plans to soon

file for a new patent and start the next business with his entrepreneurial spirit in hand.

81

If starting a business was not enough, Mr. Breslend has now begun new research into high

voltage pulsed power plasma reaction engineering for production of various chemical species needed

in the growth of plants. His research is currently funded by the Chemical & Biomedical Engineering

department at Florida State University under the direction of Dr. Bruce Locke. His experience in

entrepreneurship and background in high voltage and high frequency applications has moved this

research in great strides towards commercialization.

82