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Wright State University Wright State University
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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