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2009

High Voltage DC Converter Systems Modeling, Simulation and High Voltage DC Converter Systems Modeling, Simulation and

Analysis Analysis

Manish A. Dalal Wright State University

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HIGH VOLTAGE DC CONVERTER SYSTEMS MODELING,

SIMULATION AND ANALYSIS

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science in Engineering BY

MANISH DALAL B.E., Gujarat University, India, 1992

2009 Wright State University

ii

WRIGHT STATE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

July 7, 2009

I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Manish A. Dalal ENTITLED High Voltage DC Converter Systems Modeling, Simulation and Analysis BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering.

___________________________ Dr. Marian K. Kazimierczuk Ph.D. Thesis Director ___________________________ Dr. Kefu Xue Ph.D. Department Chair

Committee on Final Examination ___________________________ Dr. Marian K. Kazimierczuk Ph.D. ____________________________ Dr. Kuldip S. Rattan Ph.D. ____________________________ Dr. Ray Siferd Ph.D. ____________________________ Dr. Joseph F. Thomas, Jr., Ph.D. Dean, School of Graduate Studies

iii

ABSTRACT

Dalal, Manish. M.S.E., Department of Electrical Engineering, Wright State University, 2009. High Voltage DC Converter Systems Modeling, Simulation and Analysis. The thesis provides insights into important modeling techniques to model the

converter system, machine design, control and power stages and integration of the

various sub systems to simulate the system level performance. This innovative

modeling and simulation project is very relevant to optimizing the system

performance, designing the sub circuits, components selection, predicting the system

stability and impulse responses. The thesis presents modeling and simulation of three

different 270VDC converter systems and comparing their performances against each

other. The 270VDC converter system accepts either Generator 3-phase AC voltages

or fixed three voltage source followed by single or dual converter stages depending

on different topologies. The models developed for the high voltage DC systems are

optimized to provide robust controls, close loop regulation and transient performance

without any algebraic loop by employing valuable modeling techniques. The detailed

modeling approach significantly minimizes the development cost by having the

model representation of the actual system before the prototype development to

ensure ‘first time right’ designs. The system model developed on industry common

software platforms establishes the ‘boiler plate’ to allow the new systems to be

modeled simply by delta changes on the base systems.

iv

Contents 1.0 Introduction ..................................................................................................................... 1

2.0 Thesis Problem Statement, Objectives and Approach ............................................ 3

2.1 Problem Statement ...........................................................................................................................3

2.2 Thesis Objectives ................................................................................................................................4

2.3 Thesis Approach .................................................................................................................................4

3.0 DC Converter System Topology Overview ................................................................. 6

4.0 AC Machine Vector control ........................................................................................... 8

5.0 Converter System Topologies..................................................................................... 18

5.1 Topology 1a - 270VDC High Voltage Converter System (115VAC, 3-Φ, 400 Hz

input – 270VDC output) .............................................................................................................18

5.2 Topology 1b - Inverter (270VDC input - 115VAC, 3Φ, 400 Hz output) ......................37

5.3 Topology 2a - 270VDC High Voltage Converter System (Diode Based)..................45

5.4 Topology 2b - 270VDC High Voltage Converter System (SCR Based)......................62

5.5 Topology 3 - 270VDC High Voltage Converter System (VFG input, 270VDC

output)...............................................................................................................................................71

6.0 MEA (More Electric Aircraft) ........................................................................................ 93

6.1 Power Converter Design Optimization ..................................................................................94

7.0 Conclusions.................................................................................................................... 97

7.1 Recommendation for Future Work .........................................................................................99

7.2 Thesis Contribution.........................................................................................................................99

References..........................................................................................................................101

v

List of Figures

Figure 4-1 Machine Stator - Rotor Relationship ...............................................................................8

Figure 4-2 Three phase AC Voltage Source Waveform..............................................................10

Figure 4-3 Phase A, B and C to α and β.............................................................................................10

Figure 4-4 Phase a, b, c to α and β to d and q Relationship.....................................................12

Figure 4-5 Phase a-b-c to α-β to d-q Model....................................................................................12

Figure 4-6 α-β to d-q relationship........................................................................................................13

Figure 4-7 Machine Stationary and Rotating Phase Relationship......................................... 14

Figure 4-8 Sine Wave Triangle Modulation......................................................................................15

Figure 4-9 Space Vector Modulation Switching States ..............................................................15

Figure 4-10 SVPWM Neutral and Phase Relationship.................................................................17

Figure 5-1 Topology 1a Simulink Model ............................................................................................18

Figure 5-2 Topology 1a Three Phase AC Source Waveform ....................................................19

Figure 5-3 Topology 1a AC-DC Converter Simulink Model........................................................20

Figure 5-4 Topology 1a AC-DC Converter Power Stage.............................................................21

Figure 5-5 Topology 1a AC-DC Converter Control Stage...........................................................24

Figure 5-6 Topology 1a Phase Voltages a-b-c, α-β, θ, d-q Waveforms..............................25

Figure 5-7 Topology 1a Phase Currents a-b-c, α-β Waveforms ............................................ 26

Figure 5-8 Topology 1a Vα-Vβ, θ, Iα-Iβ Waveforms.........................................................................27

Figure 5-9 Topology 1a Va-Vb-Vc, Ias-Ibs-Ics, Ia-Ib-Ic Waveforms................................................28

Figure 5-10 Topology 1a AC-DC Converter output Voltage & Current ................................29

Figure 5-11 Topology 1a DC-DC Converter Simulink Model.....................................................30

Figure 5-11 Topology 1a DC-DC Converter Power Stage..........................................................31

vi

Figure 5-12 Topology 1a DC Output Voltage Build Up & PWM Gate Pulses .....................32

Figure 5-13 Topology 1a Vref, Vo, Control Signal & Load on Waveform...............................33

Figure 5-14 Topology 1a Main Line Contactor Simulink Model ..............................................33

Figure 5-15 Topology 1a Vo & Io Waveform .......................................................................................34

Figure 5-16 Topology 1a Load Application Simulink Block.......................................................35

Figure 5-17 Topology 1a Vo Load Transients...................................................................................35

Figure 5-18 Topology 1a Vo Load Transients...................................................................................35

Figure 5-19 Topology 1a Two Converter Stages Cascade Technique.................................36

Figure 5-20 Topology 1b Inverter System Simulink Model........................................................37

Figure 5-21 Topology 1b Inverter System Simulink Model........................................................38

Figure 5-22 Topology 1b Inverter Power Stage Simulink Model ............................................39

Figure 5-23 Topology 1b Inverter Control Stage Simulink Model ..........................................40

Figure 5-24 Topology 1b Output Va-Vb-Vc, Ia-Ib-Ic Waveforms ................................................41

Figure 5-25 Topology 1b Output AC Load on Transient.............................................................42

Figure 5-26 Topology 1b Output AC Load off Transient ............................................................43

Figure 5-27 Topology 1b DC-Link Current........................................................................................43

Figure 5-28 Topology 1b FFT of Output AC Voltage.....................................................................44

Figure 5-29 Topology 2a AC-DC Converter System.....................................................................45

Figure 5-30 Topology 2a Converter System Simulink Model ...................................................46

Figure 5-31 Topology 2a Converter System Power Stage Simulink Model .......................47

Figure 5-32 Two Winding Transformer Model................................................................................48

Figure 5-33 Transformer Two-Winding Model ...............................................................................50

vii

Figure 5-34 Transformer Winding Voltage, Current and Winding Resistance

Model Per Phase................................................................................................................51

Figure 5-35 18 Pulse Transformer Model Primary and Secondary Phase A .....................52

Figure 5-36 18-Pulse Transformer Model 3-Phase Secondary Windings

Interconnections ...............................................................................................................53

Figure 5-37 PLECS Model for 18-Pulse Transformer...................................................................54

Figure 5-38 DC Converter Model Based on Three Phase 18-Pulse

Transformer Model...........................................................................................................56

Figure 5-39 Transformer Primary and Secondary Voltage Waveforms with

20º Phase Shifted Configuration................................................................................57

Figure 5-40 Transformer Primary and Secondary Voltage Waveforms with

20º Phase Shifted Configuration................................................................................58

Figure 5-41 Topology 2a Output Voltage Build up Waveform................................................59

Figure 5-42 Topology 2a Output Voltage 18-pulse ripple.........................................................60

Figure 5-43 Topology 2a IPT Leg & Output DC Current..............................................................61

Figure 5-45 Topology 2b Converter System Simulink Model ...................................................63

Figure 5-46 Topology 2b Converter System Power Stage Simulink Model .......................64

Figure 5-47 Topology 2b Converter Output Voltage-Current Buil-up..................................65

Figure 5-48 Topology 2b Output Voltage 18-pulse ripple.........................................................66

Figure 5-49 Topology 2b Output Voltage Load on & Load odd Transient .........................67

Figure 5-50 Topology 2b Input AC Voltage 18-pulse ripple......................................................68

Figure 5-51 Topology 2b IPT Leg & Output DC Current..............................................................69

Figure 5-52 Topology 2b SCR Bridge DC Output Voltages........................................................70

viii

Figure 5-53 Topology 3 VFG to AC-DC Converter System.........................................................71

Figure 5-54 Topology 3 VFG to AC-DC Converter System Simulink Model ........................72

Figure 5-55 Topology 3 Power Stage Simulink Model.................................................................73

Figure 5-56 Topology 3 Synchronous Machine Simulink Model............................................. 73

Figure 5-57 Synchronous Machine Detailed Simulink Model ..................................................74

Figure 5-58 Exciter Machine and Main Machine Model Parameters ...................................75

Figure 5-58 Topology 3 Load Application Simulink Model ........................................................76

Figure 5-59 Topology 3 High Speed, Output Voltage build-up ...............................................78

Figure 5-60 Topology 3 High Speed Output voltage Ripple .....................................................78

Figure 5-61 Topology 3 High Speed Load-on & Load-off Transient .....................................79

Figure 5-62 Topology 3 High Speed VFG AC Voltage Waveform...........................................80

Figure 5-63 Topology 3 High Speed VFG AC Current Waveform...........................................81

Figure 5-64 Topology 3 High Speed Exciter Field Current Waveform .................................82

Figure 5-65 Topology 3 High Speed V, I Waveforms ...................................................................83

Figure 5-66 Topology 3 Low Speed Output voltage Ripple ......................................................84

Figure 5-67 Topology 3 Low Speed Load-on & Load-off Transient ......................................85

Figure 5-68 Topology 3 High Speed Load-on & Load-off Transient VFG Side .................86

Figure 5-69 Topology 3 Low Speed Control Loop Signals.........................................................87

Figure 5-70 Topology 3 Output Load on Feed-Forward ............................................................88

Figure 5-71 Topology 3 Low Speed FFT of Output VDC .............................................................90

Figure 5-72 Topology 3 High Speed FFT of Output Voltage VDC........................................... 91

ix

List of Tables Table 3-1 Converter/Inverter topologies overview..........................................................................6

x

Acknowledgements I am greatly thankful and indebted to Dr. Kazimierczuk for being my advisor for the

thesis and for enriching me with valuable insights into power electronics, magnetic

design, and converter topologies.

I am quite amazed by Dr. Kazimierczuk boundless enthusiasm, passion to inspire

students, presentation skills and subject knowledge on each of these courses.

I am greatly thankful and appreciative to my organization GE Aviation for support

and encouragement to my research and development work.

I would like to express my heartfelt thanks to Dr. Abbas, Dr.Hao and Mr. Karipides for

their guidance in my research work.

Last but not the least; I would like to thank my wife, Shital Dalal for her consistent

love, support, encouragement and self-sacrifice for the life we experienced together,

both in my good time and not so good time.

xi

Dedicated to my Family Members and Teachers

1

1.0 Introduction

The thesis is divided into seven chapters. Chapter 1 discusses the abstract of the

thesis. Chapter 2 discusses the introduction, problem statement, thesis objectives and

thesis approach to achieve the objectives. Chapter 3 outlines the converter

topologies considered for the thesis and brief description of them. Chapter 4

discusses the vector control theory, abc-αβ-dq transformation, space vector and sine

wave modulation, modeling of the vector control to lay the strong theoretical

foundation before transitioning to modeling and simulation in following chapters.

Chapter 5 comprises of the main body of the thesis which outlines all different

converter topologies, modeling, simulation and analysis. Chapter 6 discusses the ever

increasing demand for the optimized converter system in MEA (More Electrical

Aircraft). Chapter 7 concludes the thesis with conclusions, recommendation of future

work and contribution of the thesis. The thesis cuts across various areas of the power

system modeling such as d-q transformation technique and modeling, machine

design and space vector PWM modeling, converter topology, design and modeling,

system simulation for a typical aircraft power system architecture while meeting the

power quality requirements for steady state operation, transient operation and

distortion requirements. In typical aircraft application, main generator output could

be CF (constant Frequency) 400Hz or VF (Variable Frequency) 380-760 Hz. The CF or

2

VF power is generated from main generator which is mounted on AMAD (Airframe

Mounted Accessory Drive) on the engine. In some applications, primary power

requirement is 270VDC. In such cases, VF or CF output is fed to converter to generate

270VDC or VF or CF with integrated rectifier modules on the flange can provide

270VDC. The thesis probes into various design considerations, modeling and

simulation 270VDC system. The primary focus would be on modeling of the power

system and predicting the performance. The thesis will cover various topologies,

trade study, machine design and optimization, converter architecture, design and

optimization and system level performance.

3

2.0 Thesis Problem Statement, Objectives and Approach

2.1 Problem Statement

State of art technological advances in area of high efficiency, high density power

generators and power converters has contributed significantly to fulfill the power

requirements on the aircraft. More and more integrated power solutions are

becoming reality to save the weight and volume on aircraft where the weight and

space is premium. The tools and techniques to design, model and simulate the power

system can play invaluable role in predicting and optimizing the power system

performance while meeting the stringent environmental requirements. Aircraft

environment is posing significant challenges on designer to optimize the

performance while meeting the environment and EMI (Electro Magnetic Immunity)

requirements. The typical challenging requirements in designing the power systems

are to meet the power quality of MIL-STD-704 specifications, EMI performance

requirements per MIL-STD-461E and other environment requirements such as

temperature, altitude, vibration, and shock per MIl-STD-810F. Many of the simulation

packages are difficult to use, often time consuming and inefficient for simulating

dynamics of the power switches. This thesis proposes a Simulink based modeling

approach for control stage and PLECS package used to simulate the power stage.

PLECS toolbox is integrated in Simulink package to integrate the system level

simulation.

4

Various simplified techniques for simulating the control and power stage is

demonstrated in the thesis which results into optimized modeling approach with

faster computation.

2.2 Thesis Objectives The primary objectives of the thesis are multipronged as outlined below.

• The complete converter system model developed on industry common

software platforms to provide the ‘boiler plate’ to allow the new systems to be

modeled simply by delta changes on the base systems.

• Demonstrate detailed system modeling and simulation approach for DC

Converter systems, Inverter Systems and AC synchronous machine.

• Demonstrate transitioning from converter model into inverter model

• Demonstrate detailed modeling and simulation of the d-q transformation for

motor control and how it relates to theory.

• Demonstrate the modeling and simulation of the complex 18-pulse

transformer using Matrix techniques.

• Electrical Power Quality Analysis such as output voltage regulation, output

voltage ripple, transient performance, FFT for the converter systems and

compare the performance.

2.3 Thesis Approach The thesis approach is outlined as below.

• Understanding theory of operation for vector control and PWM.

• Identify three different converter topologies for 270VDC converter system and

implement them using the system level modeling. The topologies were

5

selected based on my experience at work and selecting the converter power

switches as SCR, IGBT and Diodes to get the good understanding of the power

stage modeling.

• Use of Matlab/Simulink for system model design and PLECS for power stage

design integrated into Simulink model.

• Model simulation and detailed analysis for the performance of the various

converter systems

• Identify the key techniques to simulate more effectively such as transformer

modeling, linking the multi-stage of the converters, loads application/removal.

• Thesis conclusion

6

3.0 DC Converter System Topology Overview

For 270VDC high voltage system, three topologies explored in detailed are as

illustrated in Table 3-1.

Topology Input

Output (Steady State)

Converter Stage#1

Converter Stage#2

Switching Technology

1aThree phase voltage source 115, 400 Hz, 3-phase

270±5 VDC

AC-DC (PFC stage) DC-DC(Isolation) IGBT

1b 300±5 VDC

115VAC, 400 Hz, 3-phase

DC-AC (Inverter) IGBT

2aThree phase voltage source 115, 400 Hz, 3-phase

270±5 VDC

AC-DC (Isolation) - Diode

2bThree phase voltage source 115, 400 Hz, 3-phase

270±5 VDC

AC-DC (Isolation) - SCR

3Three phase Variable Frequency Generator

270±5 VDC AC-DC - Diode

Table 3-1 Converter/Inverter topologies overview

All three topologies provide 270VDC isolated output.

Per Topology 1, system receives three phase, 115VAC, and 400 Hz power from source

and converts it to 300VDC first using IGBT based PFC converter stage and then

converts it to 270VDC using IGBT based isolated DC-DC converter stage. This

topology can be modeled as a bidirectional converter where topology 1a is converter

and topology 1b is inverter.

7

Per Topology 2, system receives three phase, 115VAC, and 400 Hz power from source

and converts it to isolated 270VDC output using diode or SCR based converter stage.

Diode based converter will provide unregulated isolated output while SCR based

converter stage will provide regulated isolated output.

Per topology 3, system front end is 3-phase VFG (variable frequency generator) which

generates 3-phase variable AC voltages and variable frequencies. This VFG output is

rectified using diode bridge to generate 270VDC output.

8

4.0 AC Machine Vector control

Vector control principle can be implemented on AC machine if the feedback control of

the system is performed in the rotating frame. By working out the orthogonal rotating

reference frame, all the AC quantities are converted to DC values correspond to the

peak value of the AC waveform. The orthogonal relationship between the two

currents makes is practical to use two separate control loops to achieve desired

levels of d and q values.

Figure 4-1 Machine Stator - Rotor Relationship

Three phase winding along with its stator lamination core is called an armature. Once

an armature is connected to a three symmetrical phase power source, it will flow

symmetrical currents in the three phases winding. These current will generate the

rotating mmf (magneto motive force) in the air gap.

a ax

is

b ax

is

c ax

is

X

Ø

X

XX

as

af

bs

bf

cs

cf

N

S

9

Current ia generates pulsating mmf and can not rotate. However, this mmf is a

combination of two rotating mmf rotating in opposite direction with the same

magnitude. Therefore three phase spatially symmetrical winding with timely

symmetrical three phase currents (same magnitude and 120° apart) generates a

rotating mmf. Similarly, a two phase spatially symmetrical winding with timely

symmetrical two phase currents (same magnitude and 90° apart) also generates a

rotating mmf. Therefore, we can use a two phase α, β winding to replace a three a, b,

c winding as long as both of them generate the same rotating mmf. This forms the

basis of Clarke Transformation.

Phases a, b and c are stationary vectors which are phase shifted by 120º from each

other. α and β are perpendicular stationary vectors representing the phases a, b and

c in stationary frame. As shown in Fig 4-3, at wt=0, a=0,b=-0.866, c=0.866 resulting

into α=0 and β=1. At wt=30º, α=0.5 and β=-0.866. The green vector rotates counter-

clockwise and completes one rotation of -п/2 to 3п/2 over one cycle of the phases a,

b and c. The projections of rotating green vector on α and β axis change continuously

over a period of one cycle of 360º.

10

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Phase a, b and c Unit based, 400 Hz

a b c

Vol

ts

Time (seconds)

Figure 4-2 Three phase AC Voltage Source Waveform

ß

a

ß

a

a=0ß=1

a=1ß=0

ß

a

a=0.5ß=-0.866

Figure 4-3 Phase A, B and C to α and β

11

As shown in Figure – 4-3, phase a, b and c can be represented in terms of stationary

vectors α and β. α is aligned with phase a. α is effectively phase a, b and c projected

on a-axis (same α axis). The β vector is perpendicular to α vector. The β can be

derived by reflecting phases a, b and c on β axis. As shown in Figure-Y, stationary

vectors α and β will take values from 0 to 1 over a complete cycle of 360º. The

conversion matrix of a-b-c to α-β can be represented as,

This will result into,

−

−−=

c

b

a

i

i

i

i

i

2

3

2

30

2

1

2

11

3

2

β

α

Now as ia + ib + ic =0, above matrix can be simplified as,

=

b

a

i

i

i

i

3

2

3

101

β

α

This is called Clarke transformation.

]240sin120sin0[3

2

]240cos120cos[3

2

cb

cba

iii

iiii

°+°+=

°+°+=

β

α

12

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

-1

-0.5

0

0.5

1

937 VFG/Rectifier - 26250 RPM - 75 kW transientPOR Voltage

a b c

Vol

ts

Time (seconds)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

-1

-0.5

0

0.5

1

α and β

α β

Am

pere

s

Time (seconds)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-4

-2

0

2

4Rotating Vector

Ang

le (

- π

to +π

)

Time (seconds)

Figure 4-4 Phase a, b, c to α and β to d and q Relationship

TrigonometricFunction 1

atan 2

To Workspace

simout

Sine Wave 2

Sine Wave 1

Sine Wave

Scope 7Gain

1

3ph ->SRF1

Figure 4-5 Phase a-b-c to α-β to d-q Model

13

The stationary frame α-β can be converted to the rotating frame d-q if the reference

angle θ is known. This is also called rotor position angle which is the angle between

α-axis and d-axis. Therefore, if the d-axis is aligned with α-axis then the reference

angle θ is zero. The d-q frame rotates depending on the values of α and β.

Figure 4-6 α-β to d-q relationship

id is a projection of α and β on d-axis. iq is a projection of α and β on q-axis.

This results into Park transformation,

−=

β

α

θθθθ

i

i

i

i

q

d

cossin

sincos.

Two separate control loops to achieve the desired values of d and q can be

optimized for the vector control of the AC machine. To implement the Vector

Control principles, we convert the stationary phases a, b, and c windings to

stationary frame α and β to rotating frame d and q windings that rotate at the

axisa

axisα

axisβ

axisd

axisq

θ

14

same speed as the rotor by Park transformation and control the d and q currents

in the new windings accordingly.

Figure 4-7 Machine Stationary and Rotating Phase Relationship

Triangular Sine Wave vs. Space Vector PWM control:

Over last few years, many different PWM (Pulse Width Modulation) techniques have

been developed and studied to gain following primary objectives: Wider linear

modulation range; improved switching performance with lower switching losses; less

THD Total harmonic Distortion); Simple implementation and less computation time.

Figure 4-8 shows the triangular sine wave modulation, where the carrier signal

frequency is usually at least 20X the modulation frequency. The PWM has two modes

of operation.

1) Linear Mode – In Linear mode, the modulation signal peak is less than or equal to

the carrier signal peak.

2) Nonlinear Mode – In Nonlinear mode, the modulation signal peak is above the

carrier signal peak which would cause THD of the output waveform to increase.

a axis

b axis

c axis

d axis

q axis

θ

axisα

β axis

ω

ω

ω

15

Figure 4-8 Sine Wave Triangle Modulation

In a linear modulation range, the line-to-neutral peak voltage would be

dcLN VV 5.0(max)=

Figure 4-9 shows the switching states of the space vector PWM.

Figure 4-9 Space Vector Modulation Switching States

The reference vector Vr rotates along inside the hexagon. The hexagon has six

sectors representing one sampling interval and eight switching states. Sector 1

represents the sine wave from п/2 to 5п/6; sector 2 represents the sine wave from

aI

cI

bI

nV

aV

bVcV

dcV

rVr

)100(1Vr

)110(2Vr

)010(3Vr

)011(4Vr

)001(5V )101(6V

zTVT /11

rzTVT /22

r

a,α

βb

c

)111(7Vr

)000(8Vr

16

5п/6 to 7п/6 and so on. The V1 through V6 are active vectors. The V0 and V7 are zero

vectors.

For linear modulation range, maximum line-to-neutral voltage peak would be,

30cos*3

2(max) dcLN VV =

dcLN VV 577.0(max)=

Therefore, space vector modulation provides 15% (0.577/0.5) better dc bus voltage

utilization compared to triangular sine wave modulation. Another important aspect of

the space vector modulation is that for sinusoidal waveforms, the reference vector Vr

must inscribe the circle. However for non-sinusoidal applications in some cases for

motor applications, where noise in ac waveforms is filtered by the motor inductances,

the reference vector is extended to the periphery of the hexagon.

Space Vector limitations:

The space vector modulation can not be used for inverter/converter applications

which have separate neutral. This is because space vector PWM generates zero

sequence voltage which is third harmonics. As shown in Figure A, the zero sequence

voltage exists for space vector modulation. However if the neutral is not used then

the effective inverter three phase voltages would be perfect sine wave signals

neglecting the higher order harmonics.

17

Figure 4-10 SVPWM Neutral and Phase Relationship

Vα, Vβ

Va, Vb and Vc with respect to DC-Link common

(Va+Vb+Vc )/3 Zero sequence (Third Harmonics)

(Va)- (Va+Vb+Vc )/3, (Vb)- (Va+Vb+Vc )/3, (Vc)- (Va+Vb+Vc )/3

18

5.0 Converter System Topologies

5.1 Topology 1a - 270VDC High Voltage Converter System (115VAC, 3-Φ, 400 Hz input – 270VDC output) This topology consists of two stages of the converters.

1. AC-DC PFC Converter

2. DC-DC Isolated Converter

The front end of the system is power factor corrected AC-DC converter which accepts

115Vac, 400 Hz, 3-phase voltages and convert it to 300 VDC. The second stage of this

system is DC-DC converter which accepts 300 VDC and converts it to regulated

270VDC output. This system provides isolated output from input.

System Modeling:

The system model is developed on Simulink platform. The power stage is developed

on PLECS platform and integrated into Simulink. The control stage is developed in

Simulink. The system model consists of the multi stage sub systems.

270

VDC Output

301.2

VDC Link

Scope2

Scope1

Phase C

Phase B

Phase A

Load

Load (Amps)

VDC Link S

I_Load

Vdc

Idc

IDC Link M

DC-DC Converter

VAC IN

IDC_Link S

VDC_Link M

IDC_Link M

AC-DC Converter

Figure 5-1 Topology 1a Simulink Model

19

AC Source

For this system, three phase fixed voltage source is used. The waveforms for the 3-

phase voltages are illustrated as below.

Figure 5-2 Topology 1a Three Phase AC Source Waveform

20

AC-DC power converter with PFC

2

IDC_Link M

1

VDC_Link M

atan2

TrigonometricFunction1

Vs_qd* StationarySS_abc

Space VectorSequencer

Scope2

Scope1

Scope

SRF->RRF2

AC_IN

DCLOAD

Gate_abc1

v_dc

iaigbt

i_dcbus

i_ain

Iabco2

VAC IN

Icap

VAC IN1

PLECSCircuit

Power Stage

In1Out1

Mod

In1Out1

Gate Drive

-K-

Gain

In2

In4

In1

In3

In5

Out1

Control Stage

3ph->SRF2

3ph->SRF1

2

IDC_Link S

1

VAC IN

InverterOutput Voltage

InverterOutputCurrent

InverterOutputCurrent

Figure 5-3 Topology 1a AC-DC Converter Simulink Model

21

Power Stage

Figure 5-4 Topology 1a AC-DC Converter Power Stage

The power stage of AC-DC converter is modeled on PLECS platform. The input 3-

phase voltages pass through the LC filter circuit and then applied to 3-phase IGBT

bridge. The gates of the IGBTs are controlled through SVPWM techniques to ensure

that the 3-phase AC source current is in phase with the 3-phase AC source voltages

by cancelling the leading AC current component caused by the LC filter in the front

end.

Control Stage

In power converter applications, it is important to maintain the power factor of the

source AC voltages close to unity. For this, close loop control with d-q transformation

approach becomes integral to the feedback control system. The feedback control

system is performed in rotating reference frame that is synchronized to an angle of

22

the incoming 3-phase voltages. Three phase AC voltages Va, Vb and Vc are converted

to Vα and Vβ. The reference phase angle θ is measured by estimating arctangent of

(Vb/ Va). The objective of achieving the close to unit power factor can be realized by

ensuring that three phase source currents Ia, Ib and Ic are in phase with Va, Vb and Vc.

The reference phase angle θ is the common parameter to tie voltage and current

phase relationship. Therefore, the three phase measured currents Ia, Ib and Ic is

converted to Iα and Iβ. In order to achieve unity power factor, Vα should be in phase

with Iα. In order to achieve this, measured stationary Iα and Iβ are converted to

rotating frame Id and Iq using the reference phase angle of θ. Therefore all AC

quantities of Iα and Iβ are converted to DC quantities Id and Iq. This DC levels are

corresponding to the peak values of AC waveform of AC currents. The reference

angle θ is at zero position when reference vector is lined up with α-axis. At θ=0, both

α-axis and d-axis are in phase. Therefore, id is the component of the current which is

in phase with source AC voltage and iq is the component of the current which is 90º

out of phase with the source AC voltage. The orthogonal relationship between id and

iq makes it practical to use two separate PI control loops to adjust the output voltage

of the inverter to force id and iq to follow a desired command. So, id represents the

current which is phase with source voltage. This is the parameter which controls real

power transferred between the AC and DC buses. The commanded value of id

depends on the third PI control loop that adjusts the current set point id based on the

difference between DC output voltage measured across the output filter capacitor

and the desired DC output voltage. The voltage feedback loop will force the in-phase

current (id) to be at the proper level to keep the DC bus of the inverter at a constant

23

output voltage under the influence of varying DC load currents. Importantly, the

command value of iq can be set to a constant value in order to inject a lagging

reactive current in the line which cancels the leading line currents being generated by

the input LC EMI filter.

24

Id PI Loop

Iq PI Loop

Stationary to RotatingTransformation

Rotating to StationaryTransformation

DC Bus PI Loop

Id=(2/3)(Vo*Io/Vd)i_inductor

i_switch

id*

iq*

1

Out1

Scope3

Scope1

Scope

SRF->RRF2

RRF->SRF

8.2

Iq SetpointTo Cancel Capacitive

Input Filter

1s

Integrator2

1/s

Integrator1

1/s

Integrator

2/3Gain9

3

Gain8

-1

Gain7

-K-

Gain6

Kp

Gain5

Ki

Gain4

Kp

Gain3

-1

Gain2

1

Gain10

Ki

Gain1

Divide1Divide

300

DC Bus Regulation Setpoint

5

In5

4

In3

3

In1

2

In4

1

In2

Figure 5-5 Topology 1a AC-DC Converter Control Stage

25

The outer control loop is voltage control loop. The DC voltage reference is set to 300

VDC and the feedback is measured from the DC bus. The error between the reference

and feedback is fed through the error amplifier to set the inductor current set point iL.

The current through the inductor is same as id* - id. So id*=id+iL. The inner loop is the

current loop which sets the duty cycle to control the gates of the IGBT to close the

loop.

0.005 0.01 0.015 0.02-200

-100

0

100

200

Va Vb Vc

Vol

ts

Time (seconds)

0.005 0.01 0.015 0.02-200

-100

0

100

200

α β

Vol

ts

Time (seconds)

0.005 0.01 0.015 0.02-4

-2

0

2

4

θ

Pha

se (

- π

to +π

)

Time (seconds)

0.005 0.01 0.015 0.02-50

0

50

100

150

200

Vd

Vq

Vd,

Vq

Time (seconds)

Figure 5-6 Topology 1a Phase Voltages a-b-c, α-β, θ, d-q Waveforms

26

0.005 0.01 0.015 0.02-200

-150

-100

-50

0

50

100

150

200

Va Vb VcIn

vert

er C

irren

t

Time (seconds)

0.005 0.01 0.015 0.02-200

-150

-100

-50

0

50

100

150

200

Iα Iβ

I α,I β

Time (seconds)

Figure 5-7 Topology 1a Phase Currents a-b-c, α-β Waveforms

27

0.005 0.01 0.015 0.02-200

-100

0

100

200

Vα VβIn

vert

er C

irren

t

Time (seconds)

0.005 0.01 0.015 0.02-4

-2

0

2

4

θ

θ (-π

to π

)

Time (seconds)

X: 0.005002Y: -1.566

0.005 0.01 0.015 0.02-200

-100

0

100

200

Iα Iβ

Inve

rter

Cirr

ent

Time (seconds)

Figure 5-8 Topology 1a Vα-Vβ, θ, Iα-Iβ Waveforms

28

0.005 0.01 0.015 0.02-200

-100

0

100

200

Va Vb VcV

olts

Time (seconds)

0.005 0.01 0.015 0.02-200

-100

0

100

200

Ia Ib Ic

Inve

rter

Cur

rent

Time (seconds)

0.005 0.01 0.015 0.02-200

-100

0

100

200

Ia Ib Ic

Inpu

t C

urre

nt

Time (seconds)

Figure 5-9 Topology 1a Va-Vb-Vc, Ias-Ibs-Ics, Ia-Ib-Ic Waveforms

29

Output Voltage and Current

Figure 5-10 Topology 1a AC-DC Converter output Voltage & Current

VDC = 300VDC

IDC at 40kW Load

30

DC-DC Isolated Converter

feed forward control

Vo

VL

D= (VO+VL)/VDCL

Iload

Iload_before_cap

3

IDC Link M

2

Idc

1

Vdc

1

scale

Zero-OrderHold7

Zero-OrderHold6

Zero-OrderHold5

Zero-OrderHold3

Zero-OrderHold1

Zero-OrderHold

Vref 270VDC

Scope3

Scope2

Scope1

Scope

Saturation

RepeatingSequence

Gate_abc1

In1

ILoad

Vo

Io

Idcl

Iload

PLECSCircuit

Power Stage

In1Out1

PI Loop 2In1Out1

PI Loop 1

I_Load

V_POR_Sense

I_Load_SP

Main Line Contactor Logic

1

Gain6

-1

Gain

> 0

CompareTo Constant

2

I_Load

1

VDC Link S

Figure 5-11 Topology 1a DC-DC Converter Simulink Model

31

Power Stage

Figure 5-11 Topology 1a DC-DC Converter Power Stage

The power stage receives input DC link voltage from first AC-DC converter output. The

power stage consists of front end H bridge IGBT converter. The gates of these IGBTs

are controlled by the control stage sine wave triangle PI controller. The output of the

H bridge converter is fed to the high frequency isolation transformer. The parameters

of the transformer are as follows.

L1=10mH, L2=10mH, M=9.9999mH. Therefore the co-efficient of coupling

K=2*1 LL

M=0.99999 and leakage inductance = Lleakage=L1 *(1-

2k ) = 0.2uH. The

transformer secondary is connected to full wave rectifier bridge to converter to DC

output. The output filter stage consists of the LC filter. The filter inductor is 56uH and

filter capacitor is 100uF which gives a filter cut off frequency of ~2125 Hz.

Control Stage

The control stage consists of the outer voltage loop which receives 270VDC reference

compares to the output voltage feedback to generate the error signal. The error

signal passes through PI error amplifier and creates the DC load current set point. The

32

feed forward control is used by using the summing circuit to add the difference

between the measured load current and load current before the filter capacitor to

provide the phase boost. The summing circuit output passes through another error

amplifier and generates the inductor voltage set point VL. The simplified form of the

relationship between the duty cycle and VL is given by

VDCLink* D = Vo + VL which results into

D = VDCLink

VL Vo +. In order to match the sine wave triangle PWM logic the duty cycle

reference is adjusted by subtracting it from 1.

The next stage compares the triangle waveform to the control signal and generates

the gate pulses to drive the IGBTs.

Figure 5-12 Topology 1a DC Output Voltage Build Up & PWM Gate Pulses

DC Output Voltage Build up

PWM Gate Pulses

33

Figure 5-13 Topology 1a Vref, Vo, Control Signal & Load on Waveform

MLC (Main Line Contactor) Logic

1

I_Load_SPSwitch1

S

R

Q

!Q

S-RFlip-Flop

10

Pre Load

MLC Delay

boolean

Data Type Conversion

> 265

CompareTo Constant1

2 V_POR_Sense

1

I_Load

Figure 5-14 Topology 1a Main Line Contactor Simulink Model

Vref = 0 to 270VDC

Vout = 0 to 270VDC

Vcontrol

Iload (10 amp to 150 amps)

34

Main line contactor is located between the three phase AC voltage source and

converter input. The control logic measures the output DC voltage and ensures that

the contactor closes when output voltage exceeds 265 VDC. When MLC closes the

loads on the bus gets applied to the converter.

System performance

Steady State Performance

Figure 5-15 Topology 1a Vo & Io Waveform

Transient performance

Load application and removal is implemented by model developed as below.

1

Load

Switch1Selector

Repeating

Sequence4

Repeating

Sequence3

150

Constant4

10

Constant3

Voutput

Ioutput

35

Figure 5-16 Topology 1a Load Application Simulink Block

Figure 5-17 Topology 1a Vo Load Transients

Figure 5-18 Topology 1a Vo Load Transients

Load on Load off

Output Load 10 amps to 150 amps

Load on Load off

Output Load 10 amps to 150 amps

36

Power Quality

Both transient and steady state performance meets the MIl-STD-704F power quality.

The loads on transient results into output voltage dip from 270VDC to 256 VDC which

is above minimum required MIl-STD-704F acceptable limit of 200VDC. The loads off

transient results into output voltage overshoot from 270VDC to 284 VDC which is

below maximum required MIl-STD-704F acceptable limit of 330VDC. The steady state

voltage regulation for 270VDC system per MIl-STD-704F specifications is < 6 Vrms.

The steady state ripple voltage observed for this system is <0.25 Vrms.

Modeling Technique to link multiple converter stages in sequence

Scope2

Scope1

Phase C

Phase B

Phase A

Load

Load (Amps)

VDC Link S

I_Load

Vdc

Idc

IDC Link M

DC-DC Converter

VAC IN

IDC_Link S

VDC_Link M

IDC_Link M

AC-DC Converter

Figure 5-19 Topology 1a Two Converter Stages Cascade Technique

As seen in the model AC-DC Converter model is linked to DC-DC converter through

two ports.

37

Voltage Ports: VDC_Link_M is measured DC voltage from converter 1 linked as

voltage source VDC Link S for converter two.

Current Ports:

IDC Link M is measured current of converter two is linked as applied load IDC_Link S

for converter one.

5.2 Topology 1b - Inverter (270VDC input - 115VAC, 3Φ, 400 Hz output)

The inverter system receives 300VDC input voltage and converts it to regulated 3-

phase AC voltage 115VAC, 3-phase, 400 Hz.

System Modeling:

The system model is developed on Simulink platform. The power stage is developed

on PLECS platform and integrated into Simulink. The control stage is developed in

Simulink. The system model consists of the multi stage sub systems. The system

model is obtained from converter model just by making minor changes in model such

as changing the direction of current, PI loop references and feedback.

300VDC

Scope

RepeatingSequence

1

Load (kW)

DC Bus

Power(kW)

Vabc

Iabc

INVERTER

Figure 5-20 Topology 1b Inverter System Simulink Model

38

2

Iabc

1

Vabc

1000

s+1000

Transfer Fcn

Vabc

Pnom

I_Load_S

Subsystem

Vs_qd* StationarySS_abc

Space Vector

Sequencer

Scope1

SRF->RRF3

SRF->RRF2

SRF->RRF1

DC Bus

Gate_abc1

Iload

v_dc

iaigbt

i_dcbus

i_ain

Iabco2

Icap

VAC Out

POWERSTAGE

Power Stage

In1 Out1

Mod

In1Out1

Gate Drive

Phase

Idq_sw

Vdq

Idq_op

Out1

Control

Clock1

In1Out1

Angle

3ph->SRF3

3ph->SRF2

3ph->SRF1

2

Power(kW)

1

DC Bus

InverterOutput Voltage

Figure 5-21 Topology 1b Inverter System Simulink Model

39

Power Stage The power stage of DC-AC inverter is modeled on PLECS platform.

Figure 5-22 Topology 1b Inverter Power Stage Simulink Model

The input DC voltage is applied to 3-phase IGBT bridge. The gates of the IGBTs are

controlled through SVPWM techniques to ensure that the 3-phase AC output current

is in phase with the 3-phase AC source voltages by cancelling the leading AC current

component caused by the LC filter in the front end.

40

Control Stage

Id PI Loop

Vd

Vq

Id

Id PI Loop

Iq

1

Out1

RepeatingSequence

RRF->SRF

0

Iq Setpoint

1/s

Integrator5

1/s

Integrator4

1/s

Integrator3

1/s

Integrator1

Kp

Gain3

-1

Gain2

Kp

Gain16

Ki

Gain15

2

Gain14

2

Gain13

200

Gain12

200

Gain10Ki

Gain1

4

Idq_op

3

Vdq

2

Idq_sw

1

Phase

Figure 5-23 Topology 1b Inverter Control Stage Simulink Model

Close loop control with d-q transformation approach becomes integral to the

feedback control system. The feedback control system is performed in rotating

reference frame that is synchronized to a reference angle of the output 3-phase

voltages. Measured three phase AC voltages Va, Vb and Vc are converted to Vα and Vβ.

The reference phase angle θ is set for -∏ to +∏. Vd and Vq are generated using the

reference angle θ and Vα and Vβ. Vd reference voltage of 162 (115*1.4142) and Vq

reference voltage of 0 is set for close loop control. The outer voltage PI control loop

receives Vd and Vq references and feedback and provides Id and Iq references for the

inner PI control loop. The reference phase angle θ is the common parameter to tie

voltage and current phase relationship. Therefore, the three phase measured

currents Ia, Ib and Ic is converted to Iα and Iβ which are again converted into rotating

frame Id and Iq using the reference phase angle of θ. The inner PI current loop uses

the feed-forward control for improving the transient response. Close to unity power

41

factor can be realized by ensuring that three phase currents Ia, Ib and Ic are in phase

with Va, Vb and Vc.

Figure 5-24 Topology 1b Output Va-Vb-Vc, Ia-Ib-Ic Waveforms

AC 3-Phase Voltage

AC 3-Phase Current

42

Figure 5-25 Topology 1b Output AC Load on Transient

AC 3-Phase Voltage

AC 3-Phase Current

Load On 1kW-40kW

AC 3-Phase Voltage

AC 3-Phase Current

Load Off 40kW-1kW

43

Figure 5-26 Topology 1b Output AC Load off Transient

Figure 5-27 Topology 1b DC-Link Current

DC Link Input Voltage

DC Input Current

Output Load On 1kW-40kW

44

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

20

40

60

80

100

120

140

160

180

Frequency (Hz)

Mag

nitu

de (

V)

Figure 5-28 Topology 1b FFT of Output AC Voltage

Vabc FFT Fundamental 400 Hz, 162 Vpeak (115Vrms) at 40kW load

45

5.3 Topology 2a - 270VDC High Voltage Converter System (Diode Based)

This topology consists of single stage of the converter.

The front end of the system is three phase voltage source which is applied to input

inductor which simulates the machine leakage inductance if machine is used instead

of fixed voltage source. This is followed by 18-pulse isolation transformer which is

followed by the Diode or SCR based converter. The output of the SCR converter is fed

through the IPT (Inter phase Transformer) circuit to generate 270VDC. This output

passes through the output LC filter circuit to provide filtered 270VDC output. This

system provides isolated output from input.

Figure 5-29 Topology 2a AC-DC Converter System

Interphase Transformer

+VDC

Return

Primary

Secondary

46

System Model

Leg A Voltages

Leg B Voltages

Leg c Voltages

Leg A Currents

Leg B Currents

Leg c Currents

Vrms v abc

VSCF Control

Scope6

Scope5

Scope4

Scope3

Scope2

Scope1

Ia'

Ib'

Ic'

Vabc

Va

Vb

Vc

Vout

Out2

Out3

Out4

Out5

ic1

ic2

ic3

Iout

POWERCircuit

Power Circuit

MatrixMultiply

Matrix Multiply3

MatrixMultiply

Matrix Multiply1

MatrixMultiply

Matrix Multiply

L1 M12 M13 M14 M15 M16 M17M12 L2 M23 M24 M25 M26 M27M13 M23 L3 M34 M35 M36 M37M14 M24 M34 L4 M45 M46 M47M15 M25 M35 M45 L5 M56 M57M16 M26 M36 M46 M56 L6 M67M17 M27 M37 M47 M57 M67 L7

Leg A Matrix

1s

Integrator2

1s

Integrator1

1s

Integrator

44.55

Display2

270.6

Display

105.5

Constant

GeneralInverse

(LU)

LU Inverse

Figure 5-30 Topology 2a Converter System Simulink Model

47

Power Circuit

Figure 5-31 Topology 2a Converter System Power Stage Simulink Model

48

Transformer Model

Transformer Two-Winding Matrix Model

The two-winding transformer circuit can be shown as Figure 10, where

Lp = Primary leakage inductance

Lm = Primary magnetizing inductance

Ls = Secondary leakage inductance

M12 = Mutual Inductance between primary and secondary

Lsi2

Ideal Transformer v2

Lp

Lm

i1

v1

Np : Ns

M12

Figure 5-32 Two Winding Transformer Model

This model can be represented in matrix form as follows.

=

2

1

212

121

2

1

i

i

LM

MLs

V

V

Transformer Multi-Winding Matrix Model

For multi-winding transformer, the coupling between the primary-secondary and

secondary-secondary results into complex matrix. The mutual inductance between

49

all the windings needs to be incorporated in the matrix. This would result in matrix as

below.

•

•

••

•••••

•••••

••

••

=

•

•

nnnn

n

n

n i

i

i

LMM

MLM

MML

s

V

V

V

2

1

21

2221

1121

2

1

Where

Ln = Self inductance of nth winding

Mnm = Mutual inductance between nth winding and mth winding

Vn = voltage across nth winding

in = current through nth winding

The above matrix is symmetric and the all the parameters of this matrix can be

calculated or measured. In order to implement this model in simulation, the derivative

must be removed and replaced with the integral. This can be achieved by inverting

the matrix as below. So that the model becomes the transconductance devices such

that the currents are controlled through the integral of a linear combination of the

voltages.

•

•

••

•••••

•••••

••

••

=

•

•

−

nnnn

n

n

n V

V

V

LMM

MLM

MML

s

i

i

i

2

1

1

21

2221

1121

2

1

1

50

Model Implementation

The two winding model can be implemented as shown in Figure 11. It shows that the

inductance matrix is multiplied to the voltage and then integrated to provide the

current control. This model can be extended to any number of windings.

i1

v1

+

-

Mux

InductanceMatrix

MatrixInverse

MatrixMultiply 1/s

i2

v2

+

-

DeMux

v1 v2

i1 i2

R1 R2

Figure 5-33 Transformer Two-Winding Model

The transformer design is based on 7-winding configuration where w1 is primary, w2,

w3 and w4 are identical three separate main secondary windings, w5, w6 and w7 are

zigzag secondary windings to achieve 18-pulse configuration.

51

Figure 5-34 Transformer Winding Voltage, Current and Winding Resistance Model

Per Phase

The Figure 14 circuits are integrated into sub circuit per Figure 15.

52

Figure 5-35 18 Pulse Transformer Model Primary and Secondary Phase A

Figure 16 shows the three phases of the transformer and 7 windings per phase. The

primary windings w1 are connected in delta configuration as shown. Secondary

windings w2 through w6 are connected to achieve transformer configuration per

Figure 13. The 9-phases are generated from this configuration which is similar to 20º

phase shifted configuration similar to Figure 4. The winding voltages are multiplexed

and the winding currents are de-multiplexed as shown. Figure 16 circuits are

integrated into sub circuit per Figure 17 which shows the power stage of the DC

converter. The transformer power stage as shown in Figure 17 is integrated into DC

Converter system model Figure 18.

53

Figure 5-36 18-Pulse Transformer Model 3-Phase Secondary Windings

Interconnections

54

Circuit 1

Ia'

Ib'

Ic'

Vabc

Iipt

Va

Vb

Vc

Vo

Vi2

Vi3

Out4

Vi1

ic1

ic2

ic3

Out6

Vipt

TRANSFORMERCircuit

Figure 5-37 PLECS Model for 18-Pulse Transformer

Figure 19 shows the complete system model with the inductance matrix. This is an

extension of Figure 11 for 3-phase multi winding transformer model. The inductance

matrix is based on calculating the self and mutual inductances as explained earlier.

The winding resistances are calculated as explained earlier and the values are

55

incorporated in the model. The identical inductance matrix is used for all three

phases due to symmetry. Figure 20 and 21 depicts the verification the transformer

model.

56

Transformer Model Verification

Leg A Voltages

Leg B Voltages

Leg c Voltages

Leg A Currents

Leg B Currents

Leg c Currents

Matrix Multiply 2

MatrixMultiply

Matrix Multiply 1

MatrixMultiply

Matrix Multiply

MatrixMultiply

Leg A B and C Matrix

L1 M12 M13 M14 M15 M16 M17M12 L2 M23 M24 M25 M26 M27M13 M23 L3 M34 M35 M36 M37M14 M24 M34 L4 M45 M46 M47M15 M25 M35 M45 L5 M56 M57M16 M26 M36 M46 M56 L6 M67M17 M27 M37 M47 M57 M67 L7

Integrator 2

1s

Integrator 1

1s

Integrator

1s

Display 1

Constant

115

Circuit 1

Ia '

Ib '

Ic '

Vabc

Iipt

Va

Vb

Vc

Vo

Vi2

Vi3

Out4

Vi1

ic1

ic2

ic3

Out6

Vipt

TRANSFORMERCircuit

AC Control

Vrms vabc

LU Inverse

GeneralInverse

(LU)

Figure 5-38 DC Converter Model Based on Three Phase 18-Pulse Transformer Model

57

Figure 5-39 Transformer Primary and Secondary Voltage Waveforms with 20º Phase Shifted Configuration

58

-300

-200

-100

0

100

200

300

0.017 0.0195 0.022

Phase 4 Phase 1 Phase 7 Phase 2

Phase 5 Phase 8 Phase 3 Phase 6

Phase 9 Primary AB

Figure 5-40 Transformer Primary and Secondary Voltage Waveforms with 20º Phase Shifted Configuration

59

System Performance

Output Voltage Build-up

Figure 5-41 Topology 2a Output Voltage Build up Waveform

Output Voltage Build Up

60

Output Voltage and Current Ripple

Figure 5-42 Topology 2a Output Voltage 18-pulse ripple

Steady State Output Voltage

Steady State Output Current

18-pulse ripple (over 2.5ms)

61

Output DC Current and IPT Currents

Figure 5-43 Topology 2a IPT Leg & Output DC Current

Steady State Output Current

IPT Leg A, B and C Currents

62

5.4 Topology 2b - 270VDC High Voltage Converter System (SCR Based)

Topology 2b is similar to 2a except the Diodes are replaced with SCR switches and

control circuits for the SCR to regulate the output voltages to 270VDC.

Interphase Transformer

+VDC

Return

Primary

Secondary

Control Stage

Figure 5-44 Topology 2b AC-DC Converter System

63

Simulation Model:

Leg A Voltages

Leg B Voltages

Leg c Voltages

Leg A Currents

Leg B Currents

Leg c Currents

a b bb a bb b a

ipt Matrix

VtermVcontrol

Vrms v abc

VSCF Control

1000

s+1000

Transfer Fcn

MOD ON

TRU Control

Switch

Scope9

Scope8

Scope7

Scope6

Scope5

Scope4

Scope3

Scope2

Scope1

MatrixMultiply

Matrix Multiply4

MatrixMultiply

Matrix Multiply3

MatrixMultiply

Matrix Multiply1

MatrixMultiply

Matrix Multiply

12

Load in kW

v o

LoadLoad Current

L1 M12 M13 M14 M15 M16 M17M12 L2 M23 M24 M25 M26 M27M13 M23 L3 M34 M35 M36 M37M14 M24 M34 L4 M45 M46 M47M15 M25 M35 M45 L5 M56 M57M16 M26 M36 M46 M56 L6 M67M17 M27 M37 M47 M57 M67 L7

Leg A Matrix

1s

Integrator3

1s

Integrator2

1s

Integrator1

1s

Integrator

1/(N^2)

Gain

MOD_ON

Vabc

Vc

MOD_A

MOD_B

MOD_C

Fire/Blank and MOD1

42.84

Display2

0

Display1

270.2

Display115

Constant1

115

Constant

Ia'

Ib'

Ic'

Vabc

Iipt

Gates_A

Gates_B

Gates_C

Load

Va

Vb

Vc

Vo

Vi2

Vi3

Out4

Vi1

ic1

ic2

ic3

Out6

Vipt

Ia

Ib

Ic

POWERCircuit

Circuit1

GeneralInverse

(LU)

LU Inverse1

GeneralInverse

(LU)

LU Inverse

Figure 5-45 Topology 2b Converter System Simulink Model

64

Power Stage:

Figure 5-46 Topology 2b Converter System Power Stage Simulink Model

65

System Performance:

Voltage Build Up

Figure 5-47 Topology 2b Converter Output Voltage-Current Buil-up

Output Voltage Build Up

Output Current Build Up

66

Steady state voltage and current

Figure 5-48 Topology 2b Output Voltage 18-pulse ripple

Steady state Output voltage ripple

Steady state Output Current

18-pulse output voltage ripple (over 2.5ms)

67

Load on and Load off transients

Figure 5-49 Topology 2b Output Voltage Load on & Load odd Transient

Load Off - Output Voltage Overshoot Load On - Output Voltage Dip

Load Off Load On

68

Input AC Current 18-pulse 3-phase

Figure 5-50 Topology 2b Input AC Voltage 18-pulse ripple

69

Output DC Current and IPT Currents

Figure 5-51 Topology 2b IPT Leg & Output DC Current

Steady State Output Current

IPT Leg A, B and C Currents

70

SCR Bridge 1, 2 and 3 Voltages

Figure 5-52 Topology 2b SCR Bridge DC Output Voltages

SCR Bridge#1 DC Output

SCR Bridge#2 DC Output (20º Lead)

SCR Bridge#3 DC Output (20º Lag)

71

5.5 Topology 3 - 270VDC High Voltage Converter System (VFG input, 270VDC output)

This topology consists of 3-phase VFG (Variable Frequency Generator) as a source

followed by 6-pulse full wave rectifier-bridge to generate 270VDC output. The rectifier

bridge and output filter circuit can be integrated on the flange of the generator to

provide space saving integrated package design. Alternatively the rectifier bridge and

output filter circuit can be a split box located in environmentally controlled area away

from the VFG. This topology provides 6-pulse output from the rectifier bridge which is

filtered through output filter capacitor to provide clean 270VDC. The close loop

control is provided by controlling the field exciter voltage of the machine to regulate

the stator three phase AC voltages and thereby regulating the 270VDC output. This

system provides isolated output from input.

N

ROTORPMG

S

GVR and POWER Supply Assembly

PMG STATOR

PMG STAGE

EXCITER STATOR

EXCITER ROTOR

ROTORMAIN

EXCITER

MAIN STATOR

MAIN MACHINE

3-Ø

RECTIFIER ASSEMBLY

VFG (VariableFrequencyGenerator)

Figure 5-53 Topology 3 VFG to AC-DC Converter System

72

System Model

Zero-OrderHold7

Zero-OrderHold2

Zero-OrderHold1

Vref 270VDC

Wm

Vex

Iload

Iabc

Vabc

m_m

m_e

m2

Iex

Vo

ILoad_M

IL_M

POWER STAGECircuit

VFG & RectifierPLECS MODEL

26250

Speed (rpm)Scope6

Scope5

Scope2

Scope1

In1Out1

PI Loop 2

In1Out1

PI Loop 1

pi/30

10.27

Display2

270.2

Display

DC Load

Amps

Figure 5-54 Topology 3 VFG to AC-DC Converter System Simulink Model

The system model consists of the power stage and the control circuit integrated to

regulate 270VDC output. The VFG can be run at any speed in the range of 14000 rpm

to 26000 rpm.

73

Power Circuit:

Figure 5-55 Topology 3 Power Stage Simulink Model

The power stage consists of the VFG synchronous machine whose 3-phase output is

fed to rectifier-bridge to convert to DC. The output filter consists of LC circuit for

which filter capacitor is selected at 300uF and filter inductor selection depends on the

leakage inductance provided by the Main VFG. If the VFG leakage inductance is

sufficient then external filter inductance L is not required.

VFG:

Figure 5-56 Topology 3 Synchronous Machine Simulink Model

74

The VFG model receives two inputs.

• Speed Wm (rad/s)

• Excitation voltage Vex (VDC)

The VFG is a synchronous generator which consists of two machines inside.

• Exciter Synchronous Machine

• Main Synchronous Machine

The exciter machine receives DC excitation voltage on exciter stator. This generates

three phase AC voltages on exciter rotor which is rectified using rotating rectifier

bridge in exciter rotor. This rectified DC voltage from exciter rotor is fed to the main

machine rotor. This results into three phase AC voltages generated on main machine

stator. These AC 3-phase voltages are shown as A, B, C on the VFG. The VFG machine

detailed diagram is shown as below.

Figure 5-57 Synchronous Machine Detailed Simulink Model

The two synchronous machine models have parameters for stator and rotor

inductances and resistances, number of pole pairs etc. are selected as below.

75

Figure 5-58 Exciter Machine and Main Machine Model Parameters

76

Control Circuit

The control circuit consists of the outer control loop which receives the 270VDc

reference and 270VDC feedback and compares them to generate the error signal.

The error signal passes through PI controller to generate the current reference signal.

The inner control loop consists of the feed forward control which receives the load

current reference signal (I_Load_Ref) and adds it to the actual load current

(I_Load_Measured) measured at the output. The load current measured ahead of the

filter capacitor (I_Load_Rectifer) is subtracted form this value to generate the error

signal. So under steady state condition, both I_Load_Measured and I_Load_Rectifier

are identical as capacitor does not draw any current. But during the transient

conditions, I_Load_Measured responds faster than I_Load_Rectifier to improve the

close loop control.

Load Application Circuit:

1

DC Load

Switch1Selector

RepeatingSequence4

RepeatingSequence3

150

Constant4

10

Constant3

Figure 5-58 Topology 3 Load Application Simulink Model

77

Load application circuit shows that either 150 amps can e applied as a load all the

time or by flipping the selector switch in lower position, load transients can be applied

to study the response of the system.

78

Output Voltage Build up- High Speed

Figure 5-59 Topology 3 High Speed, Output Voltage build-up

Output Voltage Ripple - High Speed

Figure 5-60 Topology 3 High Speed Output voltage Ripple

Output Voltage Build Up

High Speed - Output Steady State Voltage Ripple – 15.6 kHz

79

Load On and Load off Transients - High Speed

Figure 5-61 Topology 3 High Speed Load-on & Load-off Transient

Load On Voltage Dip Load Off Voltage Overshoot

Load Change 10A to 150A

Load Change 150A to 10A

80

VFG AC Voltage – 40kW DC on – High Speed

Figure 5-62 Topology 3 High Speed VFG AC Voltage Waveform

81

VFG AC Current – 40kW DC on – High Speed

Figure 5-63 Topology 3 High Speed VFG AC Current Waveform

82

Exciter Field Stator Current – High Speed

Figure 5-64 Topology 3 High Speed Exciter Field Current Waveform

Load On

Load Off

Initial Output Build Up

83

VFG Machine V and I Measurements – High Speed

Figure 5-65 Topology 3 High Speed V, I Waveforms

Field Rotor Rectified V

Field Rotor I

Main Rotor I

Field Rotor L-L V

Field Stator I

Field Stator V

84

Output Voltage Ripple - Low Speed

Figure 5-66 Topology 3 Low Speed Output voltage Ripple

Low Speed - Output Steady State Voltage Ripple – 8.4 kHz

85

Load On and Load Off Transients - Low Speed

Figure 5-67 Topology 3 Low Speed Load-on & Load-off Transient

Load On Voltage Dip Load Off Voltage Overshoot

Load Change 10A to 150A

Load Change 150A to 10A

86

VFG 3-Phase AC Voltage Build Up, Load on Transient and Load off Transient

Figure 5-68 Topology 3 High Speed Load-on & Load-off Transient VFG Side

VFG 3-Phase AC Voltage Build Up

VFG Load On

VFG Load Off

VFG 3-Phase Steady State Voltage

87

Control loop Signal during Load Application–Low Speed

Figure 5-69 Topology 3 Low Speed Control Loop Signals

PID Loop#1 Error Signal

PID Loop#2 Current Reference

Load Current Feedback

Bridge Current Feedback

PID Loop#2 Error Signal

Exciter Voltage Control Signal Feed Forward Effect

Output Load Feed Forward

88

Figure 5-70 Topology 3 Output Load on Feed-Forward

Output Voltage Dip- Load Application

Output Load Application 10A to 150A – Feed-Forward Control

89

Observations:

Output Voltage AC Ripple

The VFG with rectifier bridge topology provides 6-pulse regulated 270VDC output.

Both main and Exciter machines have 6 pole pair, therefore the commutation

frequency at low speed and high speed are estimated as below.

HzpolepairPPrpmSpeed

Hzf 140060

6*14000

60

)(*)()(14000 === and

HzpolepairPPrpmSpeed

Hzf 260060

6*26000

60

)(*)()(26000 ===

Therefore, low speed output voltage AC ripple has 8.4 kHz (1400 Hz * 6) frequency

component in 1.2V peak-to-peak. High speed output voltage AC ripple has 15.6 kHz

(2600 * 6) frequency component in 0.4V peak-to-peak.

Output DC Voltage Transients

At low speed, during the load application from 10A to 150A, the output DC voltage

dips to ~225VDC and during the load removal from 150A to 10A, the output voltage

overshoots to ~315VDC. At high speed, the output voltage dips to ~215VDC during

the load application and overshoots to ~328VDC during the load removal. The higher

voltage dip and overshoot at high speed compared to low speed is due to the higher

voltage drop in the machine inductance at high frequency.

Steady state voltage ripple and load transients are well within MIL-STD-704

specifications for power quality.

90

Distortion Spectrum

Low Speed:

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

50

100

150

200

250

300

Frequency (Hz)

Mag

nitu

de (

V)

7600 7800 8000 8200 8400 86000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (Hz)

Mag

nitu

de (

V)

Model Output VDC

269.4

269.6

269.8

270

270.2

270.4

270.6

270.8

271

271.2

0.0526 0.0527 0.0528 0.0529 0.053 0.0531 0.0532

Time (ms)

Out

put V

DC

Output VDC

Figure 5-71 Topology 3 Low Speed FFT of Output VDC

The model output voltage ripple matches very close to FFT analysis.

FFT of Output VDC at 150 amp load

270VDC

8400 Hz component = 0.715 Vpeak = 0.50Vrms

8400 Hz component = 1.5Vpeak-to-peak = 0.53Vrms

91

High Speed:

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

50

100

150

200

250

300

Frequency (Hz)

Mag

nitu

de (

V)

1.4385 1.439 1.4395 1.44

x 104

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)M

agni

tude

(V

)

Model Output VDC

270.3

270.4

270.5

270.6

270.7

270.8

270.9

271

271.1

0.055 0.0551 0.0552 0.0553 0.0554 0.0555 0.0556

Time (ms)

Out

put V

DC

Output VDC

Figure 5-72 Topology 3 High Speed FFT of Output Voltage VDC

FFT of Output VDC at 150 amp load

270VDC

14400 Hz component = 0.2 Vpeak = 0.14Vrms

8400 Hz component = 0.4Vpeak-to-peak = 0.14Vrms

92

The model output voltage ripple matches very close to FFT analysis.

93

6.0 MEA (More Electric Aircraft)

The ever increasing demand of reducing the operating and maintenance costs of the

aircraft while having more and more power to be extracted from the engine

demands a paradigm shift in a way how the traditional power available on the

aircraft in terms of hydraulic, pneumatic and electric. The need to get more power

extraction with lower cost is pushing the boundary to go towards more electric

aircraft. The particular area of power generation and power conversion with the

potential of achieving the excellence in fuel economy, higher power density is

• ESG (Engine Starter Generator) – ESG replaces conventional pneumatic starter

and AC generator with integrated starter generator which can do both

functions.

• High Voltage DC Generating Systems – 270VDC high voltage DC systems are

replacing conventional 115VAC systems to achieve significant feeder weight

savings.

• No Break power Transfer (NBPT) and Paralleling Operation with VFG systems.

• Integrated Power generating System with high DC output.

94

6.1 Power Converter Design Optimization

High power density converter designs can be achieved by employing intelligent

packaging concepts, modular power switches and state of art cooling designs. The

PWB design using Thermal Clad material (Berquist Thermal) can replace the discrete

and modular power switches. Thermal Clad is a cost effective solution which can

eliminate components, allow more simplified designs, smaller devices and overall less

complicated production processes. Additional benefits of Thermal Clad include lower

operating temperatures, longer life and more durability. Power conversion

applications can enhance their performance by replacing FR-4 with Thermal Clad

dielectrics in multi-layer assemblies. Typical Thermal clad material has base layer of

aluminum of copper, dielectric layer on top which has very low thermal resistance.

The top of the dielectric layer is the circuit layer.

Circuit LayerThis is the printed circuit foil with thickness of 1oz to 10oz (35-350µm) in standard Thermal Clad.

Dielectric Layer

This offers electrical isolation with minimum thermal resistance. The multiple-layer dielectric is the key element of Thermal Clad, and bonds the base metal and circuit metal together. The dielectric has UL recognition, simplifying agency acceptance of final assemblies

Base Layer

This is often aluminum, but other metals such as copper may also be used. The most widely used base material thickness is 0.062" (1.6mm) in aluminum, although many thicknesses are available. In some applications, the base layer of metal may not be needed

95

Silicon carbide power devices have become more attractive alternate to silicon

switches for certain applications demanding

• Higher operating temperatures – up to 300ºC

• Lower On resistance for SiC based switches compared to Si switches.

• Lower thermal resistance resulting into higher power density

• Lower switching losses

• Higher switching frequencies

SiC diodes are becoming more and more available but SiC MOSFETs are still few years

away before it becomes economical resulting from process stabilization to achieve

higher yield.

In general, the switches for power converters can be broadly categorized as SCR,

MOSFET and IGBTs. The switching frequency capability of the switches is listed below.

• SCR – 10 kHz

• IGBT – 60 to 70 kHz

• MOSFET - Up to 500kHz

The converter packaging design fundamentally is driven by the cooling mechanism

either it is liquid cooled (such as PAO), self air cooled (fan), forced air cooled (external

cooling duct or tubing) or convection/conduction cooled. The thermal modeling using

the co-efficient of heat transfer and actual packaging of the components with their

losses in watts at the worst case condition will help to identify if the design is capable

96

of handling the worst case environment (high temperature, sea level (ambient) or low

temperature, high altitude (ambient) or high temperature, high altitude (controlled

environment). This study becomes integral part of the risk mitigation to identify that

all the switches selected can survive with sufficient thermal margin under worst case

operating environment and worst case operating loads.

97

7.0 Conclusions

1. The complete system level modeling including the power stage and control

stage provides sufficient insights into the system level performance to ensure

that the power quality requirements are met. This upfront modeling approach

helps to create single iteration optimized designs.

2. The three topologies for the 270VDC converter system are modeled to

compare the system performance and it is concluded that the two stage

converter system with PFC front end followed by DC-DC converter provides

the best power quality performance for the steady state regulation, ac ripple

and load transients. This topology also provides the benefit of improving the

power factor and reducing the distortion by using the d-q transformation for

three phase voltages and currents. The d-q transformation helps to

individually control the resistive and reactive power by employing

independent control loops.

3. The system performance is better with using three phase fixed AC voltage

source instead of the AC generator. This is because AC generator has internal

voltage drop across the impedance which is caused by the winding

resistance and reactance (n*f*LC), where,

98

a. n=Number of pulses(n=6 for 6-pulse system)

b. f=Frequency of the generator

c. LC = Leakage inductance of the machine windings

At high generator speed (high generator frequency), the internal impedance of

the generator is high resulting into more voltage drop inside the machine.

Therefore, at high speed, generator requires higher machine voltages for the

same load compared to low speed.

4. The d-q control technique can not be employed in topology with the generator

and 6-pulse rectifier-bridge. This is because the degree of freedom is limited to

regulate the output voltages just by controlling the field current in absence of

active switches such as MOSFETs or IGBTs.

5. The multi-pulse isolation transformer model in topology 2 with voltage and

current sources approximates the actual transformer function by closely

sharing the output DC current through each of the three phase secondary

winding groups.

6. The converter topology 1 is a bidirectional converter so it can act as an

inverter also. Therefore modeling it as a converter provides flexibility to make

delta changes to simulate the model as an inverter. This topology can be

really very helpful for engine starter generator applications where the

bidirectional converter is in inverter mode to start the engine through

machine. Once engine picks up speed it lights off and power flows from

engine to machine to converter where converter converts 3-phase AC power

to DC output to power the aircraft.

99

7.1 Recommendation for Future Work

Following work is considered in order to extend the full benefits of the thesis.

• Develop fully integrated power generation and conversion model with AC

synchronous machine, AC-DC converter followed by DC-DC converter. This will

pose a challenge to optimize the model due to added complexity of the

machine model with the active power switches may slow down the simulation

time.

• Develop the bidirectional converter model using the AC-DC converter model

and DC-AC inverter model to extend the thesis work for engine starter

generator applications where the transition form the starter mode to

generator mode will require bidirectional converter system.

• Extend the system simulation approach to develop the thermal model and

identify the optimized weight vs. performance approach.

7.2 Thesis Contribution

• The thesis provides valuable insights into various topologies for DC converter

systems for aerospace applications.

• The modeling and simulation of the DC converter systems provide the

baseline for the future designs by establishing the boiler plate.

• The detailed theoretical explanation together with modeling for vector control

and space vector modulation establishes strong foundation for understanding

the modeling approach.

100

• The thesis provides the understanding of how to analyze the power quality of

the output and identify the optimum approach for the design.

101

References

[1] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converters,

Applications, and Design, 3rd Ed., New York: John Wiley & Sons, 2004.

[2] M. K. Kazimierczuk, Class notes, EE 741-Power Electronics I, Wright State

University, Fall 2005.

[3] G. Massobrio and P. Antogetti, Semiconductor Device Modeling with SPICE, 2nd

Ed. New York: McGraw-Hill, 1993.

[4] Ivan Jardic, Dusan Borojevic, Richard Zhang, Control of Synchronous Generator

in Generator-Sets with Inverter Output, IEEE Trans. Power Electronics, pp. 139-

145, 1998.

[5] M.Osama, T. Lipo, Modeling and Analysis of Wide Speed range Induction Motor

Drive based on Electronic Pole Switching, IEEE Transactions on Industrial

Applications, VOL 33, No. 5, Sep/Oct 1997

[6] J. G. Kassakian, M. F. Schlecht and G. C. Verghese, Principles of Power

Electronics, Addison-Wesley Publishing Company, 1991.

[7] W. J. Bonwick, “Voltage waveform distortion in synchronous generators with

rectifier loading,” IEEE Proceedings, Vol. 127, Pt. B, No. 1, January 1980, pp. 13-

19.

[8] B. H. Cho, “Modeling and Analysis of Spacecraft Power Systems, ” Ph.D.

Dissertation, Virginia Polytechnic Institute and State University, Blacksburg,

Virginia, October 1985.

102

[9] W. J. Bonwick and V. H. Jones, “Performance of a synchronous generator with a

bridge rectifier, ” Proceedings IEE, Vol. 119, No. 9, September 1972, pp. 1338-

1342.

[10] W. J. Bonwick, “Voltage waveform distortion in synchronous generators with

rectifier loading,” IEEE Proceedings, Vol. 127, Pt. B, No. 1, January 1980, pp. 13-

19.

[11] R.Zhang, F.C.Lee, D. Borojevic and H.Mao, “New high Power, High Performance

Power Converter Systems,” in IEEE Power Electronics Specialists Conference

(PESC), 1998.

[12] R. D. Middlebrook and S. Cuk, Advances in Switched-Mode Power Conversion,

vols. I, II, and III. Pasadena, CA: TESLAco, 1981.

[13] H. W. van der Broeck, H.ch. Skudenly, “ Analysis and Realization of Pulse Width

Modulator Based on Voltage Space Vectors”, Institute of power Electronics and

Electrical Drives , Aachen, University of Technology, West Germany