Output Power Increase at Idle Speed in
Alternators
by
Juan Rivas
B.S., Monterrey Institute of Tech.(1999)
Submitted to the Department of Electrical Engineering and Computer Science
in partial fulfillment of the requirements for the degree of
Master of Science
at the
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
June 2003
@
Massachusetts Institute of Technology, MMIII. All rights reserved.
Author
epartment of Electrical Engineering and Computer Science
une 1, 2003
Certified by_
David J. Perreault
Associate Professor of Electrical Engineering
Thesis Supervisor
Certified by_
Dr. Thomas A. Keim
Principal Research Scientist<,-L
oraqa'ty for Electromagiefl~i and Electronic Systems
hei~ervisor
Accepted by
Arthur C. Smith
Chairman, Department Committee on Graduate Students
MASSACHOSETTS lNSTTUf
OF TECHNOLOGY
0'-fioos
ww
JUL 0 7 2003
LIBRARIES
I
I
Output Power Increase at Idle Speed in Alternators
by
Juan Rivas
Submitted to the Department of Electrical Engineering and Computer Science
on June 1, 2003, in partial fulfillment of the
requirements for the degree of
Master of Science
Abstract
The use of a Switched Mode Rectifier (SMR) allows automotive alternators to operate at
a load-matched condition at all operating speeds, overcoming the limitation of optimum
performance at just one speed. While use of an SMR and load matching control enables
large improvements in output power at cruise speed, no extra power is obtained at idle.
This document proposes the implementation of a new SMR modulation strategy capable
of improving output power at idle speed without violating thermal or current limits of the
alternator. The output power improvements at idle (with no cost increase) makes the use of
an SMR a more attractive option for the industry, and will facilitate introduction of the new
42V electrical standard in the near future. The proposed research will investigate the design
and realization of a suitable modulation strategy and will experimentally demonstrate this
new approach.
Thesis Supervisor: David J. Perreault
Title: Associate Professor of Electrical Engineering
Thesis Supervisor: Dr. Thomas A. Keim
Title: Principal Research Scientist, Laboratory for Electromagnetic and Electronic Systems
Acknowledgements
I would like to thank Prof. David J. Perreault and Dr. Thomas Keim , my thesis supervisors,
for their patience, guidance, and support during the course of this journey. I have learned
a lot from them.
Thanks to Prof. John Kassakian for giving me the opportunity of conducting my research
at LEES - one of the greatest labs at MIT. I also thank Prof. Steve Leeb, Prof. George
Verghese, and Marylin Pierce, for their patience and support during my time at the Institute.
I'm also grateful for all the help provided by my colleagues and staff from LEES: Vivian
Mizuno, Wayne Ryan, Tim, Tushar, Rob 1, Rob 2 , Alejandro, Joshua, David, Frank, Ian,
Woosak, Kyomi, Karin, Gary. S. C. Tang, etc.
I would also like to thank the students that took 6.334 during the Spring semester of 2002
and 2003 for allowing me to learn from them.
I would also like to mention Dr. Javier Elguea (from Intelmex), Dr. Mayo Villagrain, Dr.
Sergio Horta, Dr. Jaime G6mez, and Dr. Carlos Reyes who motivated me to pursue my
dreams and professional goals. Worth mentioning are my Mexican friends at MIT: Antonio,
Chema, Ernesto, Gina, Jorge C., Marco E. Ulises, and Ray who supported me and never
stopped believing.
This work is also dedicated to my friends, Antonio Monterrubio, Arturo Castellanos, Edgar
Matamoros, Edgar Quintero, Eduardo G6mez, Jorge Andreu, Katty Ketlewell, M6nica
Carretero, Saul G6mez, Pilar Burguete, Steven Ketlewell, Tere Burguete, and Tofio Burguete for the life experiences we have shared. You all have played a great role in my life
and I could not ask for better friends.
To those that are not mentioned but contributed to this work.
To my uncle Enrique Rivas and my aunt Lilia Davila, two great relatives for whom I have
great admiration. They have always been a great source of advise and have pointed me in
the right direction.
I owe my deepest gratitude to my parents Carlos and Leticia, my siblings (also Carlos and
Leticia). Without their love and support I would not be where I am today.
-5-
Contents
1
2
Introduction
17
1.1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.2
Thesis Objectives and Contributions . . . . . . . . . . . . . . . . . . . . . .
20
1.3
Organization of this Thesis
21
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Background
23
2.1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.2
Power Generation in Automobiles . . . . . . . . . . . . . . . . . . . . . . . .
23
2.3
Switched Mode Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.4
Conventional Strategies for Increasing Output Power . . . . . . . . . . . . .
32
3 Increased Power at Idle
35
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.2
Modulation delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.2.1
Analytical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3.2.2
Pspice Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.3
Complete Modulation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.3.1
Analytical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.3.2
Pspice Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
4, Modulation Parameter Selection
47
4.1
Introduction . . . . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
4.2
Thermal limits at obtaining extra output Power < Pot > . . . . . . . . . .
47
4.3
Full Grid Search over J and <D . . . . . . . . . . . . . . . . . . . . . . . . . .
48
4.4
Simulation over Vov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
-7-
Contents
4.5
5
6
Simulation over
Vese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
55
Experimental Results
5.1
Introduction ........................
. . . .. . . .. . . .
55
5.2
Alternator Parameters ..............
. . . .. . . .. . . .
55
5.2.1
Back EMF at idle speed . . . . . . . . . . . . . . . . . . . . .
55
5.2.2
DC winding resistance . . . . . . . . . . . . . . . . . . . . . .
56
5.2.3
Winding Inductance . . . . . . . . . . . . . . . . . . . . . . .
58
5.3
Implementation of the gating signals for the new modulation scheme
59
5.4
Experimental Measurements . . . . . . . . . . . . . . . . . . . . . . .
61
67
Conclusions and Future Work
6.1
Introduction ........................
67
6.2
Objectives and Contributions ..........
67
6.3 Future Work
68
...................
A Mathematical Analysis of the new modulation scheme
69
A.1 Introduction ........................
69
A.2 Analytical Model for the 6 modulation .....
69
A.3 Analytical Model for the
6 and 4D modulation .
77
81
B MATLAB Files
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
. . . . . . . . . . . . . . . . . . . . .
81
B.3 MATLAB model for the complete simulation . . . . . . . . . . . . . . . . .
84
B.2 MATLAB model for the 6 simulation
C PSPICE Model
89
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
C.2 PSPICE Library models . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
C.3 PSPICE model for the SMR . . . . . . . . . . . . . . . . . . . . . . . . . .
98
-8-
Contents
D FPGA implementation
103
D.1 Introduction ....................................
103
D.2 Implementation schematics
103
...........................
Bibliography
109
-9-
List of Figures
1.1
Historical and anticipated average electrical load in high end automobiles,
showing a continuous increase in electric power consumption from 1970 to
2005 [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.2
Claw-pole alternator (Lundell machine) connected to a 3-phase diode bridge
19
1.3
Switched Mode Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
1.4
Calculated output power of an alternator plotted as a function of the effective
output voltage seen at the alternator machine, and parameterized in speed.
The dashed locus represents load-matched operation, in which output power
is maximized at all speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
Simple electrical model for the alternator-rectifier structure. The output
voltage is controlled by regulation of the field current flowing into the rotor.
24
Waveforms of alternator connected to a full diode bridge connected to a
constant output voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
Output Power vs. Output Voltage in a typical alternator for different rotational speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.4
Switched Mode Rectifier (SMR) . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.5
Switching Function and Voltage phase to ground for the SMR . . . . . . . .
30
2.6
Output Power vs. speed using a Diode Rectifier and an SMR . . . . . . . .
31
2.7
3-phase Full wave inverter structure. . . . . . . . . . . . . . . . . . . . . . .
32
3.1
Waveforms of alternator connected to SMR with an interval 5 introduced to
enhance output power at idle speed. . . . . . . . . . . . . . . . . . . . . . .
36
Calculated Output Power vs. 6 and IARMS vs. 6 at idle speed using the
modulation 6 (V, = 14V). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
Calculated Output Power increase vs. 6 and I1RMS increase vs. 6 at idle
speed using the modulation 6 (V, = 14V). . . . . . . . . . . . . . . . . . . .
39
Comparison between the MATLAB and PSPICE models for power and current
vs. the control parameter 6. . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
Waveforms for new modulation technique. . . . . . . . . . . . . . . . . . . .
41
2.1
2.2
2.3
3.2
3.3
3.4
3.5
- 11 -
List of Figures
3.6
Calculated Output Power vs.
4 and ILRMS vs. 4D at idle speed using the
new modulation. (f, = 180Hz, V,,8 = 14V, and, V0v = 20V)
3.7
3.8
4.1
4.2
4.3
4.4
. . . . . . .
44
Calculated Output Power increase vs. (D and IIRMS increase vs. 4 at idle
speed using the modulation. (f, = 180Hz, Vbae = 14V, and, V0V = 20V) .
45
Comparison between theMATLAB and PSPICE models vs. the control param.. ........ . . . . . . . . . . . . .. .. .
..
. . ......
eter ... .....
46
Measured power dissipation and temperature of a Lundell alternator running
at 1800 rpm and 3000 rpm. . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
Simulated output power (W) vs.
6 and di for Vav = 20V, Vase = 14V at idle
speed (1800rpm ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
Simulated RMS phase current (A) vs. 6 and 4 for Vv = 20V, Vbae = 14V
at idle speed (1800rpm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
Output power increase (%) vs. 5 and l for V
= 20V, Va,, = 14V. Also
shown the locus on which the RMS phase current are 15% higher than regular
operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
4.5
RMS phase current increase (%) vs. 6 and 4 for Vjv = 20V, V.,e = 14V. .
53
4.6
Output Power Increase (%) vs. 6 and P for V0, = 20V, V,ae = 14V when
4.7
4.8
phase current increase is limited to 15%. . . . . . . . . . . . . . . . . . . . .
53
Simulated Pot, Pat increase, IaRMS and IaRMS increase vs. Vov for 6 =
18*, = 60*, V,aee = 14V . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
increase, IaRMS and IaRMS increase vs. Vbae for 6 =
18 0, 4 = 60P, V0v = 20V . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
Simulated Pa,, Pt
5.1
Prototype Setup
5.2
Harmonic Content of a Lundell alternator running at idle speed (1800 rpm)
and full field current (if = 3.6A). . . . . . . . . . . . . . . . . . . . . . . . .
57
5.3
DC voltage vs. DC current through the alternator windings. . . . . . . . . .
58
5.4
Illustration of the modulation patterns of the SMR switches in relation to
the phase currents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
Measured va,, and vj,ene waveforms for the alternator with modulation parameters 6 = 00, 4 = 0*, Voy = OV, Vbase = 14V, f, = 180Hz. . . . . . . .
61
Measured vag, and Vjense waveforms for the alternator with modulation parameters 6 = 130, D = 00, Vov = OV, Vbwe = 14V, fs = 180Hz. . . . . . . .
62
Measured vag, and VIe&e waveforms for the alternator with modulation parameters 6 = 10.8, D = 540, Vov = 20V, Vbaae = 14V, f, = 180Hz. . . . .
63
5.5
5.6
5.7
-
12
-
List of Figures
5.8
Experimental and simulated phase current ia at idle speed and maximum
field current. 6 = 11.30, 1 = 00, V 0 V = OV, Vs8 e = 14V. . . . . . . . . . . .
64
Experimental and simulated phase current ia at idle speed and maximum
field current. 6 = 15*, D = 53.80, VoV = 18.7V, Vbase = 14V. . . . . . . . .
64
5.10 Measured increases in output power and RMS phase current at idle speed
and full field current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
A.1 Switched Mode Rectifier (SMR) . . . . . . . . . . . . . . . . . . . . . . . . .
70
5.9
A.2
Waveforms of alternator connected to SMR with an interval 6 introduced to
enhance output power at idle speed. . . . . . . . . . . . . . . . . . . . . . .
A.3 One phase model of the SMR for calculating the phase current ia.
71
. . . . .
72
A.4 Equivalent model for one phase of the SMR for calculating ia. . . . . . . . .
73
A.5 vag shifted by
x
angle in order to make the signal an even function. . . . . .
73
A.6 Equivalent circuit model for the fundamental component one phase of the
SM R for calculating ial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
A.7 Modulation 6 and d
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
Shifted version of the phase to ground voltage vag at the input of the SMR.
78
A.8
A.9 Equivalent circuit model for the fundamental component one phase of the
SM R for calculating ial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
C.1
90
PSPICE circuit model for the SMR power enhancement modulation . . . . .
D.1 Full FPGA implementation
. . . . . . . . . . . . . . . . . . . . . . . . . . .
104
D.2 Block that generates the gating signals for one of the MOSFET'S for the SMR105
D.3 Block that generates the 6 interval for the new modulation
D.4 Block that generates the
. . . . . . . . .
106
4 interval for the new modulation . . . . . . . . . 107
D.5 Block that generates the PWM structure
-
13
-
. . . . . . . . . . . . . . . . . . .
108
List of Tables
4.1
Harmonic content of the back EMF generated by the alternator and used in
sim ulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-
15
-
49
Chapter 1
Introduction
1.1
Introduction
In recent years, there has been a continuous increase in the electrical power requirements in
automobiles. This increase is partially driven by a continuous introduction of new luxury
and performance-enhancing features in cars and also in part by the replacement of vehicle
functions originally powered by the engine. Today, car manufactures are looking for ways
to make those features to be electrically driven thus reducing the number of sub-systems
mechanically connected to the engine belt. Focusing on increasing efficiency an performance,
car manufacturers are looking for strategies that may improve the overall efficiency in order
to reduce the net car weight. This reduction in weight brings a significant increase in fuel
economy. The increase in electrical power that has resulted from these factors is illustrated
in Fig. 1.1, and power requirements may be expected to continue rising in the near future
[2].
The increase in the electrical needs in the automotive industry over time is also discussed
in [3]. The continuous electrification has challenged the mere existence of the actual 14V
electrical system in that the new electric requirements drive the current system closer to
its limit. This situation has incited a wide range of research efforts focusing on ways to
deal with the large power needs and the implications for future vehicles. These efforts have
lead to a growing worldwide consensus that a new higher-voltage electrical system is needed
[3, 4]. A whole new electrical system standard incorporating a 42V power system is under
development which will enable more power to be handled and will overcome many of the
practical limitations of the current electrical system.
In present-day cars a Lundell machine, or Claw-Pole (alternator) connected to a 3-phase
diode bridge transforms mechanical energy from the engine into electrical energy. Part of
the generated energy is stored in a battery that keeps the system voltage constant, and
supplies energy to diverse car systems when the engine is not running. Figure 1.2 shows
a simplified diagram of an automotive alternator. The output voltage is controlled by
adjusting the current through the field winding, which resides in the rotor. A pair of slip
rings are used to drive the current from the stator structure into the field winding.
-
17
-
Introduction
Projected trends in automotive electri"at system
3aOO
... .
.....
2500
1000 . . . . .
. ... ... ...
...
... .
50
196
1970
1975
1960
199
196
199
200
200
2010
Year
Figure 1.1: Historical and anticipated average electrical load in high end automobiles, showing a continuous increase in electric power consumption from 1970 to 2005 [1]
The electromotive force (EMF) generated by the alternator depends on both the current
present in the field winding, and the speed at which the alternator shaft is rotating. The
power delivery of the alternator-bridge structure is analyzed in [5] where a 3-phase rectifier
connected to a constant voltage load is modelled, after some assumptions and simplifications,
as a simple set of resistors. Using the aforementioned approach, we can obtain the output
power characteristics of an alternator whose output voltage is unconstrained (i.e. allowed to
vary with operating condition, as shown in Fig. 1.4). Today's 14V alternators are designed
to operate optimally at idle speed (- 1800 rpm) thus maximizing output power at the
speed providing the least power. At higher speeds, the power capabilities of the machine
are under-utilized. If this same alternator were to be used at a higher output voltage
(e.g. 42V) higher output power would be available at higher speeds, but no power would
be obtained at lower speeds.
A slight and inexpensive modification to the alternator-rectifier structure is described in
[6, 7] in which the bottom diodes of the rectifier are replaced by controlled switches (power
MOSFET's), as illustrated in Fig. 1.3.
This Switched Mode Rectifier (SMR) allows matching of the effective voltage seen by the
alternator to that required for maximum power at any speed. This operation, properly
called "load matching", permits the alternator to operate along the dotted line shown in
Fig. 1.4 that allows maximum output power operation.
-
18
-
1.1
Introduction
Figure 1.2: Claw-pole alternator (Lundell machine) connected to a 3-phase diode bridge
Field Current
Regulator
I
Field
b
ib
YLS
____
Vsb%
-
V
y
IYY
vsc%
Figure 1.3: Switched Mode Rectifier
The practical implications of such a SMR with load matching control are clear: the average
output power capability of the alternator over normal driving cycles is increased. Furthermore, the SMR allows and alternator machines designed for 14V to be directly employed
at higher voltages.
One limitation of an alternator using an SMR is that even though the alternator works
optimally at any speed, it does not improve the power availability at idle. Some present
and future installed functions in cars will require higher electrical power at cruise speeds
(electromagnetic valves, water pumps, etc. ) making the SMR a good solution for dealing
with that demand. On the other hand, many other applications will benefit from power
improvements at all speeds, including idle. Thus, the described approach is still limited by
the already-optimized-at-idle alternator. Design and control approaches which can improve
output power at idle are therefore of particular value for future systems.
-
19
-
Introduction
Alternator output power vs. V
0
400
3500 -
..
- ---
---
00rp
-.
.
3000
5000 rpm
-
250
i-
0 ---
200 0-
- 4000
-
150
rp
3000 rpm
100
0
p
-
50
10
15
20
30
25
35
40
45
50
55
V (V)
Figure 1.4: Calculated output power of an alternator plotted as a function of the effective
output voltage seen at the alternator machine, and parameterized in speed. The dashed
locus represents load-matched operation, in which output power is maximized at all speeds.
1.2
Thesis Objectives and Contributions
The primary goal of this thesis is to develop and experimentally demonstrate new control
laws for alternators with switched-mode rectification that provides increased performance
at idle speed. Analytical and numerical modelling methods are also introduced that allow
such control laws to be refined and optimized.
The existing load matching technique operates by modulating the SMR switches together
based on speed (and possibly other variables). This work takes the approach one step
further by allowing the three bottom switches to be modulated independently. Such a
scheme allows more power to be delivered at idle speed. Three important observations are
worth mentioning:
e The bottom MOSFETs of the SMR can only be effectively modulated while they carry
positive current; during other periods, their corresponding back-diodes conduct.
-
20
-
1.3
Organization of this Thesis
* Any viable scheme must keep the alternator within allowed thermal limits.
* For the modulation scheme to be practical given automotive cost constraints, it should
not require expensive sensors or controls.
There will be a focus on techniques that do not incur other costs (e.g. requiring position or
current sensors.)
It is expected that through the improved alternator performance that results from this work,
the use of an SMR will be a better, yet economical, option for high-power alternators. It
will also facilitate the introduction of the new 42V standard into the market by solving
some of the power challenges facing future vehicles.
1.3
Organization of this Thesis
Chapter 2 presents a background information on present technology automotive alternators,
and also presents some technologies developed to increase output power. A model which
describes operation with the SMR is also presented. Chapter 3 introduces a new modulation that makes use of the SMR to achieve an increase of the power available at idle speed.
Chapter 4 considers the practical implementation of the proposed modulation, starting with
proper PsPICE models that provide insight into the basic operation of this new technique.
Chapter 5 will analyze and compare the experimental results obtained with the setup with
both, the mathematical model and the PSPICE model. It also describes ways of characterizing and measuring the different parameters involved in a real alternator. The hardware
implementation and issues associated with the realization of the system are discussed. An
optimization on the output power under the constraints imposed by the conduction losses
will also be presented. Finally, chapter 6 summarizes the results of this thesis and suggests
directions for continued work in this area.
-
21
-
Chapter 2
Background
2.1
Introduction
This chapter provides some background information on power generation in automobiles
and also talks about different strategies being used in order to increase the output power
delivery at different speeds. In, addition the Switched Mode Rectifier (SMR) is introduced
and its advantages and shortcomings are discussed.
2.2
Power Generation in Automobiles
The Lundell alternator machine is a wound-field synchronous machine that has been widely
used in the automotive industry in order to provide electrical power to the different systems
involved in the operation of a modern car. In practice, the output voltage is regulated by
controlling the current flowing into the field winding which resides inside the rotor.
Figure 2.1 shows a simple electrical model for the Lundell alternator, which is modelled as
a Y-connected 3-phase Electromotive force (EMF) source followed by winding inductance.
These inductances, also called armature synchronous reactance, are relatively large and
dominate the dynamic performance of the electrical system. For simplicity the model does
not include any series resistance associated with the different windings, but they are also
a limiting factor in the amount of power that can be extracted from the alternator. These
resistances also impact the thermal performance of the machine and set the operational
limits for the maximum current that can be sustained. The alternator windings are then
connected to a bridge rectifier that provides a constant output voltage V which represents
the battery and the different loads connected to the electrical system.
Figure 2.2 shows the different waveforms for one of the phases at the input of the diode
bridge working at idle speed and connected to a constant voltage V(e.g. battery) at the
output. The waveforms are not drawn to scale and just provide an idealized representation
of the waveforms of interest.
-
23
-
Background
Fied Current
Regulatori
Figure 2.1: Simple electrical model for the alternator-rectifier structure. The output voltage
is controlled by regulation of the field current flowing into the rotor.
In particular, Fig. 2.2 shows the sinusoidal EMF voltages generated by the alternator with
a frequency w8 and a magnitude which is proportional to both the field current 'if and the
electrical rotational speed ws. In practice the current if is determined by applying a voltage
across the resistance of the field winding. The average field current is in turn determined by
-Ls
:s ib~)<
the average of a pulse width modulated voltage across this winding. The EMF generated
by the alternator is represented by the following expression:
VsV
Vsat)
=
VE MF sin(wst)
where,
VEMF
=
KMWSiJ
(2.1)
The same figure shows the phase current ia(t) that flows at the input of the rectifier structure. The voltage difference between the input of the diode bridge and ground is shown as
a square wave described by:
(V
0+
Vd
:
ia(t) >0(2)
which can also be mathematically described as:
vag(t)
[
+ VD]
Sfl (ia)
+ V
(2.3)
where V0 is a constant output voltage which represents the car battery and the electric loads
connected to it, and VD is the forward diode voltage drop. In the same equation sgn(x)
-
24
-
2.2
Power Generation in Automobiles
a
Vsa
Bottom diode 'off
Bottom diode 'on
/
Figure 2.2: Waveforms of alternator connected to a full diode bridge connected to a constant
output voltage.
represents the signum function.
It
is important to underline the fact that the fundamental component of the phase to ground
voltage
v,,g(t) shown in Fig. 2.2 is in phase with the phase current i,,(t).
Following the guidelines described in [5] it is convenient to represent the rectifier structure
connected to a constant output voltage in terms of the fundamental components of the
different waveforms involved in the operation of the system. Fundamental components
are the only ones that contribute to real output power (assuming sinusoidal back EMF
voltages). The aforementioned paper demonstrates that the fundamental component of one
of the phase currents (i.e. phase
a) has a magnitude Ialand phase a, relative to the back
EMF, described by the following expressions:
Ia, =
a
I"-
ae = tan- 11
where V,,g1
ag29
(2.4)
(2.5)
sa)
is the magnitude of the fundamental component Of vag(t). The magnitude of
this fundamental component is given by:
4
7r
Vag1 =
-
V
- +
2
25
-
Vd
( 2.6)
Background
Taking into consideration the rectified contribution of the 3 Y-connected EMF sources, it
is possible to find an appropriate expression for the average output power delivered to the
load. An expression for the average output power POUT is then:
POU.
1
= 3 VoVsa
ir wL,
2
(2.7)
sa
From equations 2.7 and 2.6 it can be appreciated that for any given alternator electrical
speed w,1, the output voltage can be selected in order to maximize the available output
power. By setting J, (POUT) = 0 and neglecting the forward drop at the diodes (e.g.
Vd = 0) we can find the output voltage V that maximizes the power delivered to the
output. The value of such output voltage V, is:
VO
=
maxPo
(2.8)
VaVaRMS
2
2 /zF
The condition in which the output voltage V is selected such that output power is maximum
at a given speed is properly called load matching.
Car manufacturers are presently constrained to one single output voltage, the bus voltage
(e.g. 14V in present day automobiles), thus the alternator design is optimized to work in
a load matched condition at a single speed. In particular car manufacturers design alternators that attain a peak operational performance at idle speed (~ 1800 RPM alternator
mechanical speed), because most of the actual electric loads will be running at all times.
Although it is true that there are electric loads that consume power which is proportional to
the car speed, many important loads require electric power to be provided by the alternator
at all operational speeds.
The angle a that exists between the EMF Va(t) source and the corresponding phase current
ia(t) in Fig. 2.2 can be related to the power factor. In particular, starting from equation
(2.5) we can express the tan 2 (a)as:
tan2 (a)=
Va
\Vagi
2
Now, using the trigonometric relation: tan
=
/
(2.9)
1
-
1 the power factor can be
'The electrical alternator speed and the mechanical alternator speed are related to each other by the
number of pole pairs in the alternator.
-
26
-
2.2
Power Generation in Automobiles
expressed with the following equation:
kpPF Cosa =Vagl
V aa
(2.10)
Figure 2.3 shows a plot of the available output power POUT vs. Output Voltage V, for
different speeds for a car alternator originally designed to operate at 14V output. The
same figure also shows lines along two operational output voltages, 14V and 42V, in order
to emphasize the difference in performance of the same alternator working at two different
operating conditions.
When operating at idle speed (~ 1800 RPM), the point at which the output power is
maximized occurs at an output voltage of around 14V. On the other hand, by holding the
output voltage at 14V and increasing the rotational speed, we can see that output power
also increases, but the alternator no longer works in a load matched condition. Now if the
same alternator were to be operated at a higher output voltage (e.g. 42V), the load matched
condition happens at a much higher rotational speed, specifically of around 4250 RPM for
this particular alternator. At this speed and output voltage, the alternator can provide
almost 2.5 times more power than using a lower voltage, but it is also evident that no
power would be delivered at lower speeds. This happens whenever the output voltage V is
higher than the maximum EMF voltage generated at any particular speed. This operational
characteristic is not acceptable for automobile applications because it is necessary to provide
enough electric power at all operational speeds.
If it is required to operate an alternator in a load matched condition, at idle speed, but
working at 42V output voltage, an alternative would be to rewind the alternator with three
times the number of stator winding turns, in order to stretch the horizontal axis of the
curve characteristics shown in Fig. 2.3, this would place the curve peak corresponding to
idle speed directly on the constant 42V voltage line. Because of the higher voltage, less
current would be required for the same output power than the lower voltage counterpart,
which implies that the 42V alternator requires three times the number of turns but wires
with just . of the copper area.
We can summarize the operation of a Lundell alternator connected to a constant output
voltage by making the following observations:
* Output Power is maximized at a single output voltage V, which if constrained to a
specific value (e.g 14V or 42V) implies that output power is optimized at a single speed.
" Unity power factor kp can't be achieved, because that would imply that V,. = Vag which
-
27
-
Background
Alternator output power vs. V
450
0
14V
42V
400 0-
6000 rpm
350
300 0
-
-
.6000 rpm
-
250
4000 rpm
0.CL
200
150 0.
3000 rpm
too
-.
..
. ...
.. ..
-
50
10
15
20
25
30
35
40
45
50
55
VX (V)
Figure 2.3: Output Power vs. Output Voltage in a typical alternator for different rotational
speeds.
when plugged into equation 2.7 results in zero total output power.
e For speeds w, different from the impedance-matched load condition, the alternator is
sub-utilized.
2.3
Switched Mode Rectifier
Realizing the fact that the alternator output power can just be optimized at a single speed,
a slight modification to the diode bridge structure was introduced in [61 in which the three
bottom diodes are replaced by active switches. Such structural change provide a new control
handle that allows to achieve a maximum output power in the alternator at all different
speeds. Figure 2.4 presents the aforementioned structure in which again the electrical model
does not explicitly show the series resistance associated with the copper windings.
In the Switched Mode Rectifier (SMR) the three bottom switches are modulated together at
a switching frequency that is many times larger than the electrical frequencies present in the
-
28
-
2.3
Switched Mode Rectifier
Fil Currnt
L
Feld
I .-
Ls
V
b___
Vsa
--
Vo
------------
Figure 2.4: Switched Mode Rectifier (SMR)
system (e.g. phase voltages and currents). This structure can be visualized as three boost
converters driven by the three-phase EMF sources, with a phase shift angle of 1200 generated
by the rotating alternator. With the synchronous reactance of each of the individual phases
of the Lundell machine taking the role of the inductors that store electrical energy in a
traditional boost converter.
The bottom switches are driven with a switching function that toggles between values one
and zero, with a duty cycle defined as d = t-, where T is the period of the switching signal.
Such switching function is shown in Fig. 2.5(a). With the described switching function it
is readily seen that for a positive current ia(t), when the switch is in the ON position, the
voltage Vag is zero (minus one diode voltage drop), and the upper diode remains reverse
biased. On the other hand, when the bottom switch is in the OFF position, the current
through the leakage reactance forces the upper diode to be ON, thus making the the voltage
Vag to be equal to the output voltage (plus one diode voltage drop). The voltage vag(t) at
the input of the switched mode rectifier is shown in Fig. 2.5(b) when ia(t) > 0. The local
average voltage (Vag) for ia(t) > 0 as a function of the duty cycle is:
(vag) = (1 - d) Vo
(2.11)
On the other hand, for ia(t) < 0 the current forces the the bottom diode to be in the ON
position, thus making the voltage Vag = 0 (minus one diode drop). So it is possible to
represent the voltage at the input of the SMR vag(t) as a square voltage in phase with the
current ia(t), having a high voltage equal to the local average for ia(t) > 0 of (1 - d)V and
zero when ia(t) <
0:
-
29
-
Background
q(t)
VAGMt
Vo-
-
- -- i
dT
T
dT
T
(a) Switching function q(t)
- -
VAM
T+dT
(b) Vg Voltage Phase to ground
Figure 2.5: Switching Function and Voltage phase to ground for the SMR
Vag (t)
=
(1
-
d)Vo + Vd
iai(t) > 0
Vd
:iai(t)
(2.12)
< 0
which is also represented as:
vag(t)
[(
O+
d)V +2 VD 1 sgn (iai)
-d)V
2
(2.13)
The duty ratio d can vary in range between 0 and 1. As implied by Eq. (2.11) this means,
that by controlling the value of d it is possibly to obtain any value of voltage (vag(t)) less
than the output voltage V. The magnitude of the fundamental component of vag(t) will
now a function of the duty cycle, and given by:
4 ((1 - d)Vo+V
d
Vagi = 2
7r
(2.14)
Plugging this new value of Vag, in equation (2.7), and again neglecting the forward diode
voltage drop, it is found that the output power for the SMR can be expressed as:
POUT-=-
3 VoVa
1
,r wL
-
(2(1 - d)V
7TrVsa
2
(215
The voltage V that maximize the output power delivery can be found to be represented by
the following equation:
-
30
-
2.3
Switched Mode Rectifier
Atternator Output Power vs. speed
SMR @ 50VX
4000
3500-
0
3000-
No extra power at idle
2000-
1500
I---
Diode @14V
-
- -
1000
15Mo
2000
2500
3000
3500
Alternator
4000
4500
5000
5500
6000
Speed (RPM)
Figure 2.6: Output Power vs. speed using a Diode Rectifier and an SMR
V
maxP
Vsa
ir
2/2(1d)
,rVsaRMS
(2.16)
2 (1-d)
Thus for a given V greater than the originals 14V the duty cycle d required to achieve a
load matched condition at any given speed is given by:
d
loadmatched
2r Vsa
= 1-
(2.17)
By operating the originally designed 14V alternator, with a SMR in a load matched condition, it is possible to obtain up to 2.5 times more power at higher speeds thus operating in
an optimal condition for all alternator speeds.
To demonstrate this potential, an automotive alternator was fitted with the proposed circuit,
and operated using the proposed control control law (Eq. 2.17) for a range of DC voltages.
The result, shown in Fig. 2.6, shows that at about 5800rpm and 50 volts, about 2.5 times
as much power is produced than with the same alternator at the same speed and at 14V
DC.
As indicated in Fig. 2.6, the use of a SMR does not improve the output power characteristics
of the alternator at low speed, specifically at idle. A significant advantage of implementing
the SMR is the fact that only minor changes have to be implemented to the conventional
-
31
-
Background
*F
=_t
lb
lo
*
+
V.
sytm ecuei
aciesice
r
rdrt
praei
eurd
Thos
d
ace
oa
s
Ice
condtio
ataO
sedsjs
he
ar1gon-eeecd"wihipsta
Figure 2.7: 3-phase Full wave inverter structure.
system, because in order to operate in a load matched condition at all speeds just three
active switches are required. Those switches are "ground referenced" which implies that
no complex drivers are needed in order to switch them between the "on" and "off" states.
Also, in order to control the SMR it is necessary to use information already available in the
car like output voltage and speed, so no expensive complicated sensors are required.
2.4
Conventional Strategies for Increasing Output Power
Other circuits and other control strategies have been used to increase the output power
of alternator systems. Among the most effective is the use of a 3-phase full wave inverter
structure (Fig. 2.7). With adequate DC-side voltage, this circuit can be used in a so-called
vector control mode to force the phase current waveform to be in phase with the back
EMF. For a given back EMF and phase current magnitude, such control maximizes the
delivered output power. This strategy has been proposed many times and implemented by
commercial companies like International Rectifier [8].
There are many drawbacks of this strategy as:
" The use of six active switches
" The high-side switches require isolated electronics, which tend to be expensive and complicated, in order to apply the correct gating signals
" The use of expensive current sensors and rotor position sensors is needed in order to
correctly implement the control pattern required by the active switches, although schemes
could potentially be designed that make use of simple sensors.
-
32
-
2.4
Conventional Strategies for Increasing Output Power
Another strategy proposed in order to increase the output power capabilities of a system
suitable to be used in automobiles is presented in [9], in which the same 6-switch active
bridge structure shown in Fig. 2.7 is used, but the number of current sensor is reduced by
the use of one simple position sensor which is utilized to detect a fixed point in the rotor.
With this information, the 6 switches are controlled at the same electrical frequency of the
system in order to artificially move the phase of the fundamental component of the current
to be closer to that of the generated EMF source. This approach results in an increase in the
available output power, but does not result in a load matched condition at any operational
speed but idle.
-
33
-
Chapter 3
Increased Power at Idle
3.1
Introduction
This chapter introduces two novel modulation techniques that effectively increase the output
power characteristics of an alternator considering the availability of a semi-bridge Switched
Mode Rectifier (SMR). The proposed schemes are simple and may be implemented without
the the addition of expensive sensors in a realistic implementation.
Based on the discussion presented in section 2.3 it was shown that even though an alternator
with a SMR and load-matching control provides almost 2.5 times more output power at
cruising speeds compared to an alternator with a simple diode bridge, no extra power is
obtained at idle speed.
To overcome the characteristic limitations of the load-matching technique, but keeping the
simplicity of the aforementioned SMR structure, a departure from the original control is
proposed. Instead of controlling the three active switches with the same duty cycle d, a
new degree of freedom is added to the scheme, by modulating the switches individually.
As will be shown, adding a new dimension to the control of the SMR, it is possible to
advantageously manipulate the state variables of the system. In particular one can modify
the magnitude and phase of the different harmonic components of the phase currents that
determine the average output power.
3.2
Modulation delta
One modulation technique that we use to increase output power is illustrated in Fig. 3.1.
The main goal of this simple modulation technique is to store electrical energy in the
machine inductance (L,) of each phase, during one part of the electrical period, to release
it in another part of the period. In order to achieve this goal, a time interval 6 is introduced
for each phase starting whenever the current of a phase becomes positive. During this
-
35
-
Increased Power at Idle
I
V
/
Vsa
/
ag
-
/
/
/
Vx
/
/
/
/
Il
64\
4-
/
\
/
\
/
Figure 3.1: Waveforms of alternator connected to SMR with an interval J introduced to
enhance output power at idle speed.
delta interval, the switch for that phase is held on (d = 1), while the other switches are
modulated normally. This action results in the application of the full back EMF source
across the winding inductance, which in turn stores additional electrical energy in that
inductance; this energy will be released in another part of the conduction cycle.
The modulation was selected because of its simplicity of implementation: implementation
only requires sensing the direction of the current. Such information is readily available from
voltage measurements done directly at the SMR.
Figure 3.1 shows the waveforms of one of the phases of the SMR with an interval of length
6 introduced whenever the phase current ia turns positive. vsa is shown as a dotted line,
while the current i, is shown as a distorted sinusoid as a solid line. The voltage at the input
of the SMR vag is also shown. The amplitude of vag named V, represents the local average
of the pulse-width-modulated waveform seen at the input of the SMR. The same figure also
shows the phase angle between vsa and i, denoted as a.
-
36
-
3.2
3.2.1
Modulation delta
Analytical Model
A mathematical model for the delta modulation is derived in appendix A. There, it is
shown that a considerable amount of extra output power can be obtained by changing the
length of the interval 8 shown in Fig. 3.1. The same derivation demonstrates that such
increase in real power is followed by a significant increase in phase current ia. The increase
in losses due to dissipation will ultimately set the limit for which this modulation will be
able to provide extra power at idle speed.
As described in the analytical derivation, we can find an expression for the magnitude and
the phase angle of the fundamental component of the phase current ia, labelled ial. The
fundamental component is the only frequency component of the current that contributes to
real power (given sinusoidal back EMF's). In order to find a closed-form expression for the
phase current, a symmetric conduction condition is assumed. Under this approximation,
a positive current iai is assumed to circulate through the alternator's winding for exactly
half of the current period (i. e. for 0 < wat < 7r). The positive conduction angle of the
current with the 6 modulation is not exactly 180 degrees in practice. While the symmetric
conduction condition is not exact, it does provide a good insight into the benefits of the
proposed modulation method. By applying this conduction condition, it is found that the
magnitude ial and the phase angle a that exists between the back EMF and the phase
current, can be expressed as a function of the back EMF amplitude Va, the synchronous
impedance Z. = R, + jw
0 L, expressed in polar form Z, = IZ, ILz (representing the series
resistance and inductance of the windings), the local average at the input of the SMR V,
and the control handle 6. In particular, the phase angle a between the back EMF and the
phase current can be expressed as:
a = Oz - sin-
cos
sin
+ Oz)
(3.1)
Also, the magnitude of the fundamental component of the phase current
ia1 is found to be:
(§ + 0)]
(3.2)
IalI=
[[cos (a - Oz)] - 2V cos (§) [cos
Using equations 3.1 and 3.2 we can express the average output power delivered ((POUT)) to
the load by calculating the real power delivered by the back EMF source and subtracting
the conduction losses occurring in the windings. The contribution of the other two phases
that constitute the alternator have to be taken into account in the calculation for total
power delivered. The equation for (PouT) is then:
-
37
-
Increased Power at Idle
Output Power vs. 5
1 2 00 .. .. .
1 1 50 - - -.
0
. . .. . . .
-.
-.-.-.-.-.
-
..
-.
-.
.
-
-
...
5
-
-
..-..-..-..-..-...-..- -
900 - -..--...--.
0
-
-
- -
-
-..-.. --.. . . . .. -. .. .
-
- .-..-.-.-.-
--
--
---
- -
. .. - .95 0 - -- -.
-.
--
.-
- - - - ---
-
-
- ---
-.
..
--..
..
.. .
1 1 0 0 - - - -01050 -
-
- . . . .. . . - . ..
10
20
15
25
8 (degs)
30
35
40
45
50
IRMS vs.8
80 - . . . .
0
5
-.
- -. . ...-.
-..
- ..
I
I
10
15
I.
20
(POUT) = 3
.
25
5 (degs)
Figure 3.2: Calculated Output Power vs.
modulation 6 (V2
14V).
[Vaiai
..
. .. .
-.
..
-.-.-.
30
co~t]-
. . . .
. .
40
45
35
3 and I1RMS vs.
.-.-.
..
3
. .
50
at idle speed using the
3 [RJai](.3
- 3.3 we can plot, the output power (POUT) as a function of the
control handle 65 (simulation file presented in appendix B.2). Figure 3.2 shows the average
Making use of equations 3.1
output power (PouT) and the RMS value of the fundamental component of the phase
current (iai). The circuit parameters used in this simulation (representing the components
shown for the model shown in Fig. 1.3) are: VsaRMS =10.716V, RJ = 37mQ, L.
120p.H
180Hz; where VSaRMS represents the back EMF at idle speed (e. g. electrical
and f8
frequency f8 180Hz) and full field current (e. g. if = 3.6A), and the control parameter
S was varied from 0 to 500, V4 = 14V. Furthermore Fig. 3.3 shows the percent increase in
output power and the percent increase in RMS phase current ia1, again as a function of 3.
As mentioned before, the increase in output power is accompanied by a corresponding
increase in phase current, which in turn increases dissipation in the machine windings.
This, in turn limits the maximum power increase achievable within the thermal limits of
- 38
3.2
Modulation delta
Percent increase in output power vs. 8
20
--
15
(D
Cz
- -.-
-
-. ..
-. ..
-.
-.
t 10
-
-.
-.
-
-.-.-.--.-.....
.....
.
5
00
10
5
15
25
20
30
S (degs)
Percent increase in
11RMS
40
35
45
50
vs. 8
0
40
-
- -.
-~
S30
~
-
--
..-.
. . -.
-
-
-
- .-.
.. .-.
-
-
-
-
-
..-..
-
.
- .....
-- -----.-.-.-.
-......
--
-..
-..
20
--
10
U""
0
5
10
15
20
25
S (degs)
30
35
40
45
50
Figure 3.3: Calculated Output Power increase vs. 6 and IARMS increase vs. 6 at idle speed
using the modulation 6 (V = 14V).
the alternator. The main advantage of this modulation technique is its simplicity, because
in a practical implementation the direction of the phase current ia can be easily obtained
from measured voltages at the input of the SMR.
3.2.2
Pspice Verification
In order to corroborate the validity of the mathematical model described in section 3.2.1
and Appendix A, a PSPICE model was developed for the system. A detailed description of
the PSPICE model can be found in Appendix C.
Figure 3.4 shows a comparison between the results obtained using the Pspice model and the
results presented in section 3.2.1. In particular it shows the output power (POUT) and the
approximate RMS phase current vs. the control parameter 6. The alternator parameters
used for the simulation are: VsaRMS = 10.716V, R, = 37mQ, L, = 120pH, f, = 180Hz
and full field current (e. g. if = 3.6A). Again, Rs is the winding resistance and L, is
the machine inductance. The results shown in Fig. 3.4 corresponds to a modulation such
-
39
-
Increased Power at Idle
Pout
o increase vs. 5
vs.
1200
1100-
15
-:1000
-o
OWM
S10
a-0
onb
5
900
[-800
--
- -
0
10
20
30
40
-- Matlab
Fia-
I
Ppice
50
0
10
MSI RMS
Mvs
I IRMS
20
30
Pspice
40
50
increase vs. S
iRMS
80
(D
40
1R
30
0
S60
MRla
.......
.....-.
50
F
210
-1
Mattab
0
10
2
20
30
40
--
- [-
~
-L
-=Pspice
40'
P sp....
50
0
10
20
30
40
50
Figure 3.4: Comparison between the MATLAB and PSPICE models for power and current
vs. the control parameter 6.
that V = 14V. The 6 control parameter is varied from 0 to 50'. From the figure it
can be appreciated that there is good agreement between the two models. The principal
differences between the models are because the analytical model considered here only takes
into account dissipation due to the fundamental component of the phase current, while the
circuit simulation incorporates all dissipation components.
3.3
Complete Modulation
Based on the encouraging results obtained from the models presented in section 3.2, an
augmented modulation is proposed in which additional control handles are added to the
modulation scheme. Figure 3.5 shows the phase current and the instantaneous phaseto-ground rectifier voltage for one phase over an alternator electrical cycle for the full
modulation scheme explored here. The switching function for each of the legs of the SMR
structure is realized at a frequency many times higher than the line-current frequency and
the duty cycle is modulated in such a way as to obtain the "local-average" phase to ground
-
40
-
3.3
Vsa
Complete Modulation
'D
\a
/
/
9
/D
v
\vBASE
\
2)r /
Figure 3.5: Waveforms for new modulation technique.
voltage Vag shown in Fig. 3.5. Looking at this local average voltage waveform it is possible to
define the different intervals that describe the modulation scheme. The back EMF voltage
Vsa is shown with a dotted line, while the current ia is shown as a distorted sinusoid with
a solid line. The pattern is the same for the other phases, but delayed by 120 electrical
degrees of the fundamental.
The complete modulation technique consists then of the following subintervals:
*
5 : During this sub-interval, beginning when the phase current becomes positive, the
switch is kept on, forcing the phase-to-ground voltage to be near zero. During this J
portion, additional energy is stored in the winding inductance.
Operation at a nominal duty ratio and local average voltage Vase. This
voltage is close to that for the load matching condition, and will be a function of the
alternator speed.
* Mid-cycle:
*
b : From the beginning of this interval to the end of the positive portion of the line
current, the duty ratio is adjusted so as to obtain an average phase to ground voltage
that exceeds the nominal Vase by V,, volts.
- 41 -
Increased Power at Idle
The modulation strategy embodied in Fig. 3.5 enables additional output power to be
obtained from an alternator as compared to that achievable with diode rectification or
switched-mode-rectification with load matching control. At the same time, this modulation
is also simple enough to be implemented with inexpensive control hardware and without
the use of expensive current or position sensors. As already mentioned, the zero crossing of
the phase current waveform can be effectively detected by observing the phase-to-ground
voltage during the FET off state.
By means of adding these new degrees of freedom in the control of the SMR, it is possible to
manipulate the state variables of the system beneficially. In particular we adjust the magnitude and phase of the different harmonic components that constitute the phase currents
to enhance the average power delivered to the output.
3.3.1
Analytical Model
As mentioned, this modulation introduces two new subintervals to the normal operation of
the SMR. The conduction angle interval 6 is introduced beginning when the phase current
becomes positive, during which the bottom switch of the SMR is kept ON, the effect of which
was already discussed in section 3.2.1. In the second new subinterval, a conduction angle
interval 41 is introduced during which the duty cycle of the corresponding bottom switch is
adjusted such that the local average of the voltage at the input of the SMR vag is set to a
voltage V0v volts higher than in the main interval. The net result of these two subintervals
will produce a phase shift that reduces the total phase angle a between the back EMF
voltage va and the fundamental component of the phase current ia1 thus increasing the
amount of real power obtained at idle speed (1800 rpm). Furthermore, these intervals can
be used to increase the fundamental phase current, thereby increasing output power. The
modulation strategy embodied by Fig. 3.5 achieves this within the modulation constraints
of the semibridge SMR, and without requiring detailed position or current information.
A detailed derivation that analytically solves for the magnitude and the phase of the fundamental component of the phase current ia relative to the back EMF can be found in the
appendix A.3. There it is shown that the angle that exists between the back EMF v.a and
the fundamental component of the phase current ia1, a depends in the values of the different
control parameters, namely: Vov, 8, 4, and V.se. The expression obtained through the
derivation is reproduced here:
a = 0Z + sin-[ cl sin (x - 6 - Oz)
1Va
-
42
-
(3.4)
3.3
Complete Modulation
In this expression, ci = al + b2 and x = tan. Where al and b, are the fundamental
sine and cosine coefficients in the Fourier series that describes the local average of the phase
to ground voltage Va. The series inductance L, and resistance R, that model the phase
impedance can be represented by a total series impedance described by its magnitude IZLI
and its corresponding phase 0,. The magnitude of the fundamental component of the phase
current under the same modulation scheme is is also repeated here:
-l-Cos
ci
(X - 5 - OZ)
|ZL|
|Iail = [ VaCos (a - OZ)
IZLI
(3.5)
Using (3.5) and taking into account the contribution of the other two phases it is possible
to obtain the same simple expression for the average output power (POUT) as in Eq. 3.3:
-3
(POUT) = 3 Vsalai c
[R,-
(3.6)
The influence of 5 in the output power and the phase current was already presented in
Section 3.2, so now we will focus attention on the influence that the new control variable
4 has on those two quantities. Figure 3.6 shows the output power obtained when just
the control variable 4 is applied. Again the conditions of the simulations are: VaRMS =
10.716V, R, = 37mQ, L, = 120piH and f, = 180Hz and if = 3.6A. The modulation
parameters for the simulation shown in Fig. 3.4 corresponds to V , = 14V, and VOV =
20V. The value of 5 is set to zero and the parameter D is varied from 0 to 700.
From Fig. 3.7, it can be seen that for small values of - a small increase in phase current ia
is accompanied by significant increase in output power. With bigger values of the control
parameter 4, it is possible to obtain a moderate increase in the output power but with
an actual decrease in the magnitude of the phase current. This implies that is possible to
obtain an increase in output power with lower conduction loss.
3.3.2
Pspice Verification
Fig. 3.8 shows the increase in output power (POUT) and the corresponding increase in RMS
phase current versus the parameter D using both the PSPICE averaged model the analytical
results presented in section 3.3.1. The results are qualitatively similar, though differences
are significant for larger values of 4. The difference that exists between the simulation
and the numerical predictions arise because interval 1b is not small, thus the symmetric
-
43
-
Increased Power at Idle
Output Power vs. 0
1400
130 0 120 0 - 0.a 1
1 00 -
0 100 0
- .
90 0 -
---..--.
-.--
..
-..
--
- - -.-- -- . ..
-.
.
-..
---.-
10
- -.-
30
-.-.
.-.--.-- --.-.
-
40
- -
----
--
- - --
-
-- -
20
. - -.-. - -.-.-
-.-
.
- -.-- - -.-- -. ..
.- -. .
. . . . ..-..
--
0
--
-
- - -
-
- --
- ----
50
-60
70
4D (degs)
11RMS vs. 0
65 - -
55
J 45 - -
0
-
-.-.-
.. .-..
10
20
30
40
-
-.. .
-..
. -..
-.-.-.
-.-.-.-.
-.-
-.-... .
..
-..-
..
.. . .
w0 --
- -.-
-. -.
.
50
.
- .-..-
-.-.
---.-.
60
70
4) (degs)
Figure 3.6: Calculated Output Power vs. D and IIRMS vs. <D at idle speed using the new
modulation. (f, = 180Hz, Vaae = 14V, and, VoV = 20V)
conduction condition is not achieved. From this figure it is also clear that the PSPICE
model also predicts operating conditions in which additional output power is expected at
lower magnitude of the phase current.
It has been shown that the new modulation technique allows additional output power by
proper control over the parameters 6, <b, V0 v and Vbase, it can be observed that the increase
in alternator output power is - for many modulation conditions of interest - accompanied
by an increase in power dissipation. So a compromise between extra power and extra
dissipation has to be reached that will allow the maximum amount of power while not
exceding the dissipation limits of the machine. A systematic search over the different
paramenters involved in the new modulation will be explored in chapter 4.
-
44
-
3.3
Complete Modulation
Percent increase in output power vs. 1b
-- -
-.
........
-.
-.-.-.-. ........
.-.-.-.........
-.
.-.-.--.~ ~-- --. ~
~- - ~ - .
.. ..-- ~- -~ ~
~ ~ ~-.-- ~ ....
- -- - - - - - ca 25
(D
0
.......
-.
.............
-.
.......... ..... ...20 ....... -.
- -- - - - -- -.-.-.
- .-.-.
--.
15
-.
-. -. -.....
-. .....
-.
...... .........
- - -.....
..
10
-.
...
--.
----.
...
-. ..
-.-.-.-.-.- . .............
...
.5
35
30
u
0
10
20
30
40
50
60
70
(D (degs)
Percent Increase in
11RMS
vs. D
20 F
- - -....
-.
-..
10
Zn
.. -.
--.
...
-.
-.
-.
-.-.-.
0
-.--.-..
-.-....
-.
--.
-.
-.- .....
-.
-
-20
0
-
10
20
--
-.
........
- .......
- --
.-
30
40
50
.-..-
.-.-..-..
.....
-.
...
-.
... -.-.--.-.-.--.-.-.......
..-.....-. .. -.-- -.
-10
-
60
70
0 (degs)
Figure 3.7: Calculated Output Power increase vs. <b and lRMS increase vs. <D at idle speed
using the modulation. (f, = 180Hz, Vase = 14V, and, V0V = 20V)
-
45
-
Increased Power at Idle
P
out
increase vs. 0
Pout vs. 0
1-4VU
35-
k
Matlab
Pspice
1300
3025
1200
CO
20
- - p--
.0
15
.. . ..- -.
.t
-
/
-
- -
-
01000
.. . .. .
.. . . . .
5
900
0
20
40
0 (degs)
0
60
20
IPincrease vs. 0D
IM
1
iRMS
- - Matlab
Pspice
do
20
10
40
0 (degs)
60
IiRMS IAMS vs
..
6560-
S-Matlab
Pspice
[
.....
55-
0
0)
-. -
-
1100
. .....
10
0
OF
- . . . -.-.
0-
- -..... -..
- - -- - - - 4-
0
-- --
-10
- -
-
0-
-
. .. . .. ... . .
-
-
---
40
- -
-
35
-20
-
- - -- - -
-
-.-
.
-
30
0
20
40
0 (degs)
0
60
20
40
0 (degs)
60
Figure 3.8: Comparison between theMATLAB and PSPICE models vs. the control parameter
4.
- 46 -
Chapter4
Modulation Parameter Selection
4.1
Introduction
This chapter addresses the selection of control parameters for the proposed modulation
technique. Practical constrains in selection of modulation parameters are described. Grid
searches over the modulation parameters(3, 4, VoV and Ve) based on averaged circuit
simulations are used to identify good parameter values.
4.2
Thermal limits at obtaining extra output Power < Pt
>
Based on the mathematical and circuit models presented in section 3.3, it can be observed
that the increase in alternator output power is - for many modulation conditions of interest
- accompanied by an increase in power dissipation. In particular, it was shown in section 3.3
that for increasing values of the parameter 6 (with others at nominal values) the dissipation
in the alternator windings will increase significantly. On the other hand, it was shown that
for changes in parameter 1 additional power can be accompanied by either an increase or
a decrease in winding currents and dissipation.
The alternator winding temperature increases with the square of the RMS phase current.
We can then infer that the amount of extra power that can be obtained through the proposed
modulation strategy is ultimately limited by the thermal capabilities of the electric machine.
Thus, it is necessary to properly adjust the modulation parameters in order to maximize
output power, while staying within the temperature limits of the alternator machine.
The power dissipation and the temperature profiles of an alternator are both a function
of the rotational speed. In particular Fig. 4.1 shows some experimental measurements of
the power dissipation and the stator winding temperature of an alternator working at full
output power and running at 1800 rpm and near 3000 rpm. In [10, 11], it is shown that a
typical alternator reaches a maximum temperature when running at 3000 rpm.
-
47
-
Modulation Parameter Selection
180-
3000
-2500
150;
W 2000
12001
-1500
90
0 1000
60
500
.
0
C.
0
E
30
C
1800
30Q
Speed (rpm)
0
.
Figure 4.1: Measured power dissipation and temperature of a Lundell alternator running
at 1800 rpm and 3000 rpm.
It can be seen in Fig. 4.1 that it is possible to increase the power dissipation at idle speed
(by using the proposed modulation for example) while not exceeding the normal operating
temperature of the alternator when the alternator is running at 3000 rpm. This suggests
that some degree of increased power dissipation at idle speed is permissible. In particular,
based on the thermal model described in [10, 11], at least a 15% increase in RMS stator current at idle speed is allowable from a thermal standpoint in a typical automotive
alternator.
Dissipation occurring in the alternator windings is proportional to iaRMS, which implies
that an increase in the RMS phase current of 15% corresponds to an increase in power
dissipation of 32%. Such an increase is permissible at idle speed because the resulting
temperature rise is still below that which occurs for operating conditions at higher speeds.
4.3
Full Grid Search over 6 and 1D
Given a limitation on RMS phase current, we can explore how the output power depends on
the different control parameters, and identify control parameters that provide the greatest
improvement in output power consistent with the thermal limits of the alternator.
We begin by exploring the response of the new modulation to parameters 6 and 4. The
-
48
-
4.3
Harmonic Component n
n = 1 fundamental
ni= 2
Full Grid Search over 6 and b
RMS Amplitude
10.716V
23.071mV
Phase
00
153.710
n=3
0.45689V
-16.0730
n= 4
n= 5
19.978mV
0.40452V
121.560
-166.8*
Table 4.1: Harmonic content of the back EMF generated by the alternator and used in
simulation
averaged PSPICE model (Appendix C) is a convenient way of exploring the performance of
the new technique for the different parameters involved. The simulation uses the following
parameters, based on measurements of an alternator: R, = 37mQ for the alternator stator
phase resistance, and L, = 120pH for the inductance (Fig. 1.3). The rotational speed of
the alternator was set to run at 1800 rpm (idle speed) which corresponds to an electrical
frequency of 180Hz. In real alternators, the back EMF voltage generated is not strictly
sinusoidal, but actually contains significant harmonic components. The harmonic content
of the back EMF of the alternator V.aRMS is characterized by the magnitude and the phase
at the different harmonic frequencies. The back EMF components used for the simulation
are shown in table 4.1 for idle speed conditions. The angle 6 was varied between 0* and
550, the angle D was swept between 00 and 900.
= 14V
Figure 4.2 shows the output power < Pot > obtained at idle speed when Ve
and VOv = 20V using the PSPICE simulation. It can be appreciated from the figure that
a significant increase in power can be obtained for different combination of 5 and 4. Not
all combinations of J and d shown in Figure 4.2 are possible, however, because of the large
increase in phase current which is incurred. Figure. 4.3 presents the RMS magnitude of
the phase current vs. operating condition. From the figure, it can be observed that the
magnitude of the current will either increase or decrease depending upon the value of the
parameters 6 and l selected.
The percent output power increase and the percent phase current increase predicted over
those obtained using load-matched control, are presented in Figs. 4.4, and 4.5. As mentioned
in section 4.2, the amount of additional output power allowed by using the new technique
presented here is bounded by the maximum permitted increase in conduction losses in the
alternator windings. Figure 4.4 also highlights the locus of operation conditions for which
the increase in RMS phase current is 15%. The limit in the increase in current was selected
in order to keep the alternator within acceptable thermal limits as explained in section 4.2.
As previously discussed, just the set of values of 5 and 4 for which the current increase is 15%
is of practical interest for the moment. In order to better appreciate the performance of the
-
49
-
Modulation Parameter Selection
Output Power increase at Idle speed:- Vbase=1 4 , V0,=20V
1400
---
-.
1300
1200
-
1100
1000
0
700
600r--
-
--
50.
-
-
--
40
so90
0
-0
20.
(5 (degs)
t
2030
0 0
10
Figure 4.2: Simulated output power (W) vs.
speed (1800rpm).
6 and
0
a)(degs)
<D for V,,, = 20V, Vase = 14V at idle
modulation technique under that dissipation constraint, Figure 4.6 shows the projections
of the locus described in Fig. 4.4 onto the three planes bounding the figure. This illustrates
the output power increase that can be obtained by adjusting the parameters as indicated
in the projection on the floor of the graph. The simulations predicts that a 22% increase in
output power can be obtained at idle while keeping the alternator within thermal limits.
The simulation results presented so far suggest that by setting 6 = 18', and <D = 600 in
the modulation described in section 3.3, with Vase = 14V and V0v = 20V, it is possible
to obtain a significant amount of additional output power at idle speed, as compared to
load-matched control alone. The performance of the power enhancement technique as a
function of the other control parameters will be now discussed.
4.4
Simulation over Voy
The voltage Vov by which the local average of vag exceeds Vbase during the <D interval
will have a significant impact on the duration of the positive conduction period of the
phase current. In particular, the higher the value Vov, the faster the energy stored in the
phase inductance is delivered to the output, thus shortening the effective duration of the <}
50
-
4.5
Simulation over Vase
Phase Current at Idle speed Y/ase=14V Vov=20V
70
60
Figure 4.3: Simulated RMS phase current (A) vs. 3 and <b for V0 n
idle speed (1800rpm).
=
20V, Vbase =14V at
interval. This process can be thought of a negative feedback interaction in that increasing
Vo decreases the effective duration of <b, resulting in smaller changes in output power than
might be otherwise expected.
Figure. 4.7 shows the simulated variables (Output power and RMS current) when the variable Vo is varied with the other control variables held at 3 = 180 and <b
60g. It can
be appreciated that for Vo varying from 10 to 30 Volts, the output power remains steady,
and the phase current changes only a small amount. In this region of operation, system
performance is relatively insensitive to the selected value of Voy.
4.5
Simulation over Vbase
The parameter Vaa8 e greatly influences the performance of the modulation. It is this control
parameter Vbase which realizes the load matched condition in conventional load-matching
control. Figure 4.8 shows the output power, the output power increase, the RMS phase
current and the RMS phase current increase when Vbs is varied over an interval at which
the other parameters are: 3 = 18 , <b = 60w, Voy
20V.
-
51
-
Modulation ParameterSelection
Output Power increase at Idle speed: V
e
4
,
V =20V
40
Cn
20 - ....
0
S-200.
-40
40
Pout6 0
=
914.2W
80
40
(5(degs) 20
20
0
60
(D(degs)
C~es
0
Figure 4.4: Output power increase (%) vs. 6 and <D for V,, = 20V, Vbae = 14V. Also
shown the locus on which the RMS phase current are 15% higher than regular operating
conditions.
The results presented so far does not provide an exhaustive search over the parameter
space involved in the new modulation scheme. However, they do provide useful guidelines
for selecting parameters combinations that result in a significant increase in output power
at an acceptable increase in dissipation.
-
52
-
4.5
Phase Current Increase at Idle speed: Vbase
4
Simulation over Vbase
V Vo=20V
0
Excessive dissipation!
00ft
00
C
ler operation
-0
)'48.46A
Ia('0;1D
40
6
20
40
5(degs)
20
0 0
so
g
60
*D(degs)
Figure 4.5: RMS phase current increase (%) vs. 3 and <D for V, = 20V, Vase = 14V.
Output Power Increase at Idle speed,
Phase current increase @ 15%
40'
20
22% increase in output power
@ 15% increase phase current
0
-0
1~
*1
40
80
40
20
5(degs)
0
0
20
60
8
*(degs)
Figure 4.6: Output Power Increase (%) vs. &and <D for Vv = 20V, Vase = 14V when phase
current increase is limited to 15%.
- 53 -
Modulation ParameterSelection
Increase in Output Power vs. VOV
-.
......
-. ...
- -....- .....-- 1200
-.
......
---.
.. -.--.
-.
-1150
-.
. - --.. ..... .-.
-..-- .
1100
-.
.- ...-.-----.-.
51050
- . -. -..
.. . .. .. . ....-.
. -..
24
*22
220
18
L 16
-7--- -.
...-........--- ..-.......
14
12
0
10
20
O1000
-
950
30
....
-..... ....-.
.
-..
-.
---.
.
-.
-30
10
20
0
V0 v (V)
V0 v, (V)
Phase Current Increase vs. VOV
-
- ....
-- - - ..-.-- ...-.-. -----.
.--
19
Output Power vs. VOV
Phase
vs.....O
- -. -Current .-
... -
58
..
-- ....- .---... .... -.
.. ..
....
---- ..-... --- ....
-.
.....
-. -..
.
18
17
16
-- ..
-...
15
---
.
57.5
57
56.5
Cn
56
55.5
.-
55
14
10
0
20
Vo (V)
Figure 4.7: Simulated Po,
180,,b = 600, Vb,,e = 14V
Pt
30
0
increase,
Increase in Output
Power
vs.
820
- ..- -.
...
.
1200
.. -.0
-.
a1000
c
---....
-.-.--.-.----.
0S
-5
0
-30
800
12
14
16
(V)
V.
10
18
65
--.--. . - .- ---.--..-.-.---.--.
--
Z60
55-
10
-.-
050
CD
--.- -
0
12
Figure 4.8: Simulated Pt,
14
V
16
(V)
18
- .....
-. ........--.
...
- - - -. -.
. ....
-.
--. -.
..
.
--.--....
-.-...
..-..-..-
a: 45
40-
1
12
Phase Current vs. Vbs
70
. -..
--..
....
.~...
40
U) -10
a: -20
.....
- -.. -.
900
Phase Current Increase vs. Vbase
0
--.- .-.-
- -.
- -.
...
-. ....
- ..
-.-.......
0 5
20
for 5 =
- - -.-.--.-.-
1100
----.
...
....
.. -.. ..
-..
...
30
Output Power vs. Vbase
Vb..e
15
Z5 10
20
V0 v (V)
and IaRMS increase vs. Vo
LaRMS
. -.-.-.
- -..
.... .-.
--
25
10
14
Vba.
16
18
10
(V)
Post increase, aRMS and
(D = 60', Vov = 20V
-
54
-
- ... ...
.............12
14
V.
16
(V)
18
LaRMS increase vs. Vbse for J = 180,
Chapter 5
Experimental Results
5.1
Introduction
A prototype system (Fig. 5.1) has been developed to demonstrate the proposed modulation
technique. The setup consists of an alternator that is driven with an 3-phase motor, a
switched-mode rectifier of the type illustrated in Fig. 1.3, and a controller. An electronic
load (not shown) simulates the battery connected to the SMR system. This chapter first
describes the parameters that characterize the alternator. Then, the implementation of the
modulation controller is addressed and a comparison between experimental and averaged
simulation waveforms is presented. The chapter concludes with experimental confirmation of the effectiveness of the new modulation technique for improving idle speed power
capability.
5.2
Alternator Parameters
As described in chapter 2 the output power characteristics of an alternator are determined
by the back EMF generated and the large inductance of the windings. Furthermore the
temperature at which the alternator operates depend directly on the series resistance of the
alternator windings. Accurate measurement of these parameters is thus important. In this
section, means for accurately determining the alternator parameters are described.
5.2.1
Back EMF at idle speed
The back EMF waveform is determined by measuring the phase-to-neutral open circuit
voltage of the alternator at idle speed full field current (if = 3.6A). In the experimental
alternator, the RMS of the back EMF voltage generated is Vg = 10.71V at f, = 180Hz.
From Eq. (2.1) it is determined that KMWS = 2.97TVhs Furthermore, the back EMF
voltage of the alternator is not purely sinusoidal, but actually presents harmonic components
-
55
-
Experimental Results
Figure 5.1: Prototype Setup
that can be directly measured using a harmonic analyzer. Fig. 5.2 shows the measured
back EMF voltage running at idle speed (f, = 180Hz) and at full field current (if = 3.6A).
The same figure shows the RMS voltage of the harmonic content of the waveform, and
the phase relative to the fundamental of the different components. The harmonic content
expressed as percentage of the fundamental is also shown.
For the analysis and simulation used in the grid search described in chapter 4, the amplitude
and phase of the fundamental and harmonics up to the fifth harmonic were used, as can be
seen in Table 4.1.
5.2.2
DC winding resistance
The DC resistance for each of the phases of the alternator can be easily calculated by
applying a DC current through each of the stator windings and measuring the resulting
voltage drop. Figure 5.3 shows the voltage drop measured phase to neutral when a DC
current is passed through each of the phase windings at ambient temperature (~ 25 0C).
The DC resistance increase due to temperature rise was taken into account by measuring
the DC voltage after running the alternator at full output power, and after the alternator
-
56
-
5.2
Alternator Parameters
Harmonic content of the back EMF. FrEund= 180Hz
back EMF Voltage
0.5 . . .
. . .. .. . . .
15
w
-
0-)
5
L-
-.
0.4 - - -.-.
10
-
.
.. .
0.3
0
0
C,,
20.2
-5
-10
. -..
..
-..-..
.. -..
.
-
-
--
0 .1
-15
0
0.01
0.02
0.03
0.04
4
time
Harmonic content of the back EMF percent of the fundamental
14
Harmonic content of the back EMF (Phase Angle)
-.
150
4
6
8
10
12
Harmonic number
- .-- -
100
3
0
2
-50 -..-100
----.-
-150
4
6
8
10
12
Harmonic number
14
-.
4
8
10
6
12
Harmonic number
.- . 14
Figure 5.2: Harmonic Content of a Lundell alternator running at idle speed (1800 rpm) and
full field current (if = 3.6A).
reached thermal steady state. From this data it was established that the DC winding
resistance of the alternator is 37mg at operating temperature.
The aforementioned procedure provides a good estimate of the DC winding resistance.
Nevertheless if a more accurate calculation is required, the A C resistance should be used.
This can differ from the DC resistance due to proximity, skin effect and due to core loss
effects [12, 13, 14]. Core loss effects, in particular can be amplitude dependent. The averaged
models described throughout this thesis do not consider the change in resistance as more
phase current is circulated through the windings due to thermal or other reasons; thus a
difference between predicted and measured results should be expected.
-
57
-
Experimental Results
DC Voltage vs. Current in ahtemation windings
-
-
p hA--31.7nt2
phB=31.9m3
phC=33.0mQ
0.2
- ----
--
--
0.15F-
- --- -- - -- -
0
--
-
--
-
-
- -
0.1
0.05
0.5
1
1.5
2
2.5
3
3.5
DC current (A)
4
4.5
5
5.5
6
Figure 5.3: DC voltage vs. DC current through the alternator windings.
5.2.3
Winding Inductance
Measuring the inductance of each of the alternator windings is based on the analytical circuit
model described in [5]. For this calculations it is considered that the DC winding resistance
is the same for the three phases and has a value of R, = 37mQ as described in section 5.2.2.
The inductance can be easily calculated by measuring the output power delivered to a
constant-voltage output, and by measuring the RMS voltage of the fundamental component
of Vag. For an alternator connected to a 3-phase diode bridge we know that Vag can be
express using Eq.(2.3), repeated here as Eq. (5.1).
Vag (t>
[
+-
Vd
s9
(ia) +
o
(5.1)
From this we can obtain the amplitude of the fundamental component, which is:
Vagi =
[+
7rJ
Vd
(5.2)
By measuring the harmonic content of the phase current ia, we can obtain the magnitude
of its fundamental component labelled Ial. The following expression found in [5] can be
used to find the effective machine inductance of the winding in terms of the fundamental
component of the back EMF and the fundamental component of the phase current:
-
58
-
5.3
Implementation of the gating signals for the new modulation scheme
L, =
SV
-*V2
(27rf,)2 (Vi - 1)
_ y2
[(_2 Ial
2
-( VoiRs
(RVa)2
(5.3)
For the alternator used in the experimental setup it was found that at idle speed (electrical
frequency f, = 180Hz): VIRMS = 6.9509V, 1I1 = 45.3A, and Rs = 37m. Thus by using
equation (5.3) it is determined that the value of the phase inductance is L, t 120/H.
In conclusion, the value of the inductance used in the PSPICE models and the numerical
models throughout this work are: R, = 37mQ and L, = 120piH.
5.3
Implementation of the gating signals for the new modulation scheme
Accurate timing of the modulation with respect to the alternator phase currents is of
great importance in realizing the modulation scheme described in section 3.3. This can
be achieved using sensors to acquire information about the line currents from which the
different subintervals are determined. The proposed modulation scheme only relies in vary
basic information about the sign of the phase currents. In the prototype system this information is obtained through the use of Hall-effect current sensors and an incremental
position encoder, though these would not be necessary in practice. Separately, we have experimentally demonstrated that the desired timing information can be obtained with only
phase-to-ground voltage sensors [15]. In our current prototype the different parts of the
modulation switching control signals are generated using a small Field-Programmable Gate
Array (FPGA) XS40005XL. Details of the implementation using the FPGA are described
in Appendix D. It may be expected that the proposed modulation scheme will result in
little incremental cost over a system with an SMR and load-matching control. Figure 5.4
qualitatively illustrates the duty-cycle variations of the MOSFET gating signals in relation
to the corresponding phase currents. In the actual system, the switches are modulated at
100kHz much higher than the alternator electrical frequency (~ 180Hz).
Figure 5.5 shows some representative signals for one of the phases of the SMR. The waveforms shown in the figure corresponds to an alternator at idle speed operation. The duty
cycle of the gating signal was selected in order to achieve a load-matched condition at this
speed (no new modulation applied). The switching frequency for the active switches is
100kHz. The SMR is connected to an output load of 42V, which results in the va, waveforms shown in the top figure. The duty cycle applied to the active switch is such that
-
59
-
Experimental Results
00
t
iDlI
l
I UMEL
t
Figure 5.4: Illustration of the modulation patterns of the SMR switches in relation to the
phase currents.
the local average Vag = 14V. The middle figure shows the output of a Hall-effect current
sensor that monitors the phase current. To get a better insight on the switching pattern
implemented, the bottom figure shows a close-up view of the Vag voltage when the phase
current is turning positive. For a negative phase current, the current circulates through
the back diode connected to the corresponding MOSFET, thus producing the zero output
voltage shown in the bottom figure. As soon as the current is positive, the voltage Vag can
be effectively modulated with the desired duty cycle d.
Figure. 5.6 shows the SMR operating when just the interval 6 of the new modulation scheme
is applied. From the top waveform of the figure, the interval during which the voltage Vag
is tied to ground by the ON state of the MOSFET can be observed; this corresponds to a 5
interval applied over a conduction angle of 130 just when the phase current turns positive.
The waveform at the center of the figure shows the output of one of the current sensors
that monitor the phase currents. The bottom waveform shows a closer view of the interval
when the phase current is going positive. The presence of some modulation pulses before
the introduction of the J interval arise because of the lack of resolution of the incremental
encoder used in the prototype implementation. At an electrical frequency of 180Hz the
-
60
5.4
Experimental Measurements
Vin for the SMR with delta =0, Phi=0, Vov=0
40
30
-
-
-
10
-1
-10
-8
-8
-4
-2
2
4
0
Current Sensor Output Time (s)
.
-2 -.
-8
-10
40
-6
-4
6
8
-3
.. . . . . .
-2
0
Detai Pos. zero
2
4
crossing Time
6
(s)
8
-3
-
j20
0 ,- *--6
...
-
-
- - -----
. .--.
?1 0 -. ..- .- --. --
-- -.--5slO
-
---
--- - -
-5.5
0.
.-
-
-5
-4Z5
T
.
-n()
4
-3.5
Figure 5.5: Measured Vag, and Vlsense waveforms for the alternator with modulation parameters 6 = 0', 4D = 00, Vov = OV, Viase = 14V, f3 = 180Hz.
resolution of the position encoder used corresponds to 2.160. Note the increase in the
amplitude of the phase current in this case, as compared to the one shown in Fig. 5.5.
Figure 5.7 shows measured waveforms when the modulation parameters are:
6 = 10.80,
<D = 540, Vov = 20V, and Vase = 14V. The waveform at the top of the figure shows the
voltage Vag over time. The detailed switching pattern cannot be observed because of the
high frequency of the switching (100kHz) compared to the electrical line frequency (180Hz).
It can be appreciated from the middle waveform how the phase current is distorted as a
result of the length of the different intervals added. The bottom waveform of the figure
shows a detailed view of Vag when the <b interval starts; the change in the duty cycle d as
can be clearly appreciated.
5.4
Experimental Measurements
This section presents some experimental results obtained using the prototype system described in section 5.1. We first validate the PSPICE averaged models used to search for
preferred operating points. Figure 5.8 shows the measured phase current ia for the operating condition 6 = 11.3' and <( = 00 with if = 3.6A, Vbase = 14V, VoV = OV and
f, = 180Hz. The same figure also shows the current waveform simulated using PSPICE for
the same conditions. Close agreement between the averaged model and the experimental
-
61
-
Experimental Results
Vin for the SMR with 8 =13. I=0, V v
0
- -
40
--
-
--
--
30
- . ..---.-
-..
-...
20
0
Current
0
0
-10
Sensor Output
Timne (s)
.......-
0
-8
-6
-4
-2
-18
-6
-4
-2
0
2
Detail Pos. zero crossing
-
-
2
xC104
4
6
8
6
8
-2-
401- -
0
13 - - -
20 - - -
0
-
-
-....-
i
- -----.-
-- -----.-
--.-
-
4
Tine (s)
x 10-3
-
-
- --.-.-
--.-.-.-.-.-
--
1
2
3
4
time (s)
Figure 5.6: Measured Vag, and vlsense waveforms for the alternator with modulation parameters J = 13', <D = 00, Vov = OV, Vase = 14V, f, = 180Hz.
measurement is observed.
Figure. 5.9 shows another operating condition ( 6 = 15', 4D = 53.8', Vov = 18.7V, if =
3.6A, Vase = 14V, and fs = 180Hz at idle speed). Again, excellent agreement between
simulation and experiment is observed. Note that the phase current for this condition: there
is an interval in which no current circulates through that particular phase. As a result of
this, the output current will have increased in current ripple. However, this increase is not
overly important because the output current is composed of the rectified contributions of
the three phases. Furthermore the battery will buffer most of the variations.
Figure 5.10 shows experimentally measured increases in output power and the corresponding
increases in phase current for a variety of operating conditions. These results show that
for appropriate variations in D, significant increases in power delivery to the load can be
achieved in combination with a reduction in the RMS phase currents and associated losses.
Furthermore, it is clear from these results that significant increase in output power (- 15%
or more) are achievable with limited (and acceptable) increases in RMS phase currents and
losses. Figure 5.10 also confirms the expected operation of the modulation condition in
which increased output power is obtained along with a decrease in RMS phase current. In
particular it can be seen that almost 10% increase in power is accompanied by a decrease
of 5% in the phase current for the appropriate modulation settings.
-
62
-
5.4
VinfortheSMRwithB=10.8', 4V=54
-
40
--
V, =20V, V
=14V
-...-
-..
E
5 30 -
e,
Experimental Measurements
-
20 10 0L_
-2
0
2
2
-
4
8
a
10
Current Sensor Output
12
Time (2
14
18
X 10-3
-
-
-2
0
0
40
4
.
-- - -..
-
-
0 1.76
-1.78
-
. .. A
- -
- -
-
-
12
lime(s)
14
18
X 10-3
--
- -
-
.
-
6
8
10
Detail Pos. zero crossing
-
-.-. .
--
40
53
2-
-
--
-
--......--.....
- -
--.
-
1.8
1.82
1.84
1.86
lime (s)
1.88
1.9
Figure 5.7: Measured Vag, and Vlsense waveforms for the alternator with modulation parameters 6 = 10.80, <D = 540, Voy = 20V, Vba,, = 14V, f, = 180Hz.
The measured increase of 14% in output power at idle speed is valuable for dealing with
the electrical demand in modern automobiles. Furthermore, the fact that such an increase
in power results from a simple control scheme, provides an incentive for exploiting the
characteristics of the Switched-Mode-Rectifier.
-
63
-
Experimental Results
Phase Current la(t):
S 11.3*, (D =0*,Vo =OV, f =180Hz
S=
100---------------
0
C
.
~-50
- --
10
0
20
15
Time [ms]
Figure 5.8: Experimental and simulated phase current ia at idle speed and maximum field
current. S = 11.3', <) = 00, VOV = OV, Vbase = 14V.
Phase Current
ia(t) :
o0=15), D =53.8*,Voy =18.7V, f =180Hz
-
Meastd
Siulte
C
. ----- - -. --.-..-.-.
. -..
...
...
0 ..
.
10
10
15
20
Time [ms]
Figure 5.9: Experimental and simulated phase current ia at idle speed and maximum field
current. J = 15', <D = 53.8', Vov = 18.7V, Vbae = 14V.
-
64
-
5.4
'-1 5
Experimental Measurements
Output Power Increase at Idle speed VBASE=l 4 V V 0 ,=2OV
0
0
0.
U
6=0
0
0 i=0 [D
261
g=0
y=0
=46
=0
D=55
RMS Current Increase at Idle speed
63
12
8=9
=55
VBASE=l
4
V
(D=62
VV=20V
S20
0)
L2 0
(I)
W 10
0
D=0
=0
=:0 6 0
S-0
(D=26 (D=46 (D55 4=63
9
55
712
o
(J 62
0
Figure 5.10: Measured increases in output power and RMS phase current at idle speed and
full field current.
-
65
-
Chapter 6
Conclusions and Future Work
6.1
Introduction
In this chapter, the thesis is concluded with an evaluation of thesis contributions in relation
to the original thesis objectives and a discussion of future work that can be pursued in the
area of asymmetric modulations.
6.2
Objectives and Contributions
As noted in the introductory chapter of this thesis report, the objectives of this thesis
were: first to develop and experimentally demonstrate new control laws for alternators with
switched-mode rectification that provide increased performance at idle speed.Second, to
develop analytical and numerical modelling methods that provide insight into the capabilities of the techniques proposed. A modulation technique was developed that focused
on ways of obtaining additional power without the use of expensive sensors. Furthermore,
averaged circuit simulations were developed that permitted a simple and systematic search
of the different parameters of the modulation. Based on these simulations, the parameters
that achieve an increase performance in output power while keeping the alternator within
thermal constraints were identified
The primary objectives have been fulfilled. A new modulation technique has been proposed
that only requires very basic information about the direction of the phase currents. This
modulation provides enough degrees of freedom as to improve the power transfer from the
alternator. Using an experimental setup it was demonstrated that a 14% increase in output
power is possible while keeping the phase current within allowable operating boundaries.
In addition to the contributions mentioned above, this thesis report will also contribute to
a broader set of applications of the SMR, in an area that pushes in the direction of better
utilization of the generated electric power in automotive applications.
It is hoped that this report will be useful to those working on applications of the SMR in
-
67
-
Conclusions and Future Work
the future, and that it will help to bring the SMR closer to practical implementation in the
automotive industry. Also it is hoped that through the improved alternator performance
that results from this work, the use of an SMR will be a better, yet economical, option for
high-power alternators and that It will facilitate the introduction of the new 42V standard
into the market.
6.3
Future Work
The development of new applications and enhanced performance of the SMR is a task in
progress. Furthermore there are several significant challenges to be faced before this new
modulation can be implemented in a real automotive environment. The future work on
this project can be summarized in terms of plans in the short term and goals for the longer
term.
There are many directions in which the work presented here can be expanded. These including experiments with perhaps more complex modulations; such methods may obtain
additional performance improvements while maintaining the inherent simplicity of the approach. It would also be fruitful to consider schemes operating across many speeds which
consider the thermal limitation and the current handling capabilities of the electrical machine. A practical under-the-hood implementation of the simple modulations described in
chapter 3 is feasible, but nevertheless will require a significant amount of engineering. Furthermore, the implementation of concepts such as synchronous rectification can be easily
applied to the structure reducing conduction losses in the bottom devices, improving overall
efficiency of the system. Also further work can be pursued in integrating the techniques
described in this report along with other applications developed for the SMR, like operation
in dual-output systems. [16].
In the long term, many challenges have to be faced concerning the packaging of the SMR
structure into a real alternator. The thermal limitations of the power semiconductors requires careful considerations on the thermal model of alternator using the controlled rectifier
structure [10, 11]. Also in the long term, improvements in the design of the alternator itself, knowing the availability of this new techniques can lead to further improvements in
the efficiency and performance the techniques described here.
-
68
-
Appendix A
Mathematical Analysis of the new
modulation scheme
A.1
Introduction
This appendix presents a mathematical analysis of the proposed modulation scheme for obtaining additional output power at idle speed. a simplified modulation scheme is considered
first, followed by an analysis of the complete modulation strategy.
A.2
Analytical Model for the J modulation
This section presents a mathematical description for the 6 modulation described in section
3.2.1.
Looking at the circuit SMR structure shown in Fig. A.1, we begin by defining the time
domain characteristic of the different back EMF voltage sources generated by the alternator:
Vsa = VEMF sin (wat)
Vab =VEMF sin
V.c= VEMF sin
wat
-
(A.1)
(27r
(wst + T
Where the back EMF magnitude VEMF is given by VEMF = KMWSif.
By applying Kirchoff's Voltage Law, KVL around the SMR structure for each of the phases
-
69
-
Mathematical Analysis of the new modulation scheme
Field Current
Regulator
I
Fied
I
LS
Lai
b
IVSO%
Vo
VVcb
- --- --- --
- -
Figure A.1: Switched Mode Rectifier (SMR)
we can calculate the neutral to ground voltage Vng which can be expressed as:
Vng = -Vsa
+ ZRLia + Vag
-Vsb
+ ZRLib + Vbg
Vng
Vng = -Vsc
+
ZRLic
±
Vcg
Adding the three equations that describe the the neutral to ground voltage
the following expression:
3
Vng
(A.2)
Vng,
(Vsa + Vsb + vsc) +ZRL (ia + ib + ic) + (vag + Vbg + vcg)
we obtain
(A.3)
=0
=0
As clearly shown in equation (A.3), the term (vsa + Vsb + vsc) is equal to zero, because the
three back EMF voltage sources vsa(t), Vb(t) and v,,(t) are a balanced three-phase set, as
presented in equation (A.1).
Figure A.2 shows the waveforms of one of the phases of the SMR with an interval of length
J introduced when the phase current ia turns positive. The rectifier MOSFET for that phase
is held on during the J interval, resulting in a zero phase to ground voltage. Vsa is shown
as a dotted line, while the current ia (distorted sinusoid)is shown as a solid line. The local
average I voltage at the input of the SMR Vag is also shown. The local average of Vag has an
amplitude of V., and represents the local average of the pulse-width-modulated seen at the
input of the SMR. The same figure also shows the phase angle between Vsa and la denoted
as a.
'We follow the definition of [121 for local averages of PWM waveforms. That is for a PWM period T, we
ft T x(-r)dr.
define the local average t(t) of waveform x(t) to be x(t) =
-
70
-
Analytical Model for the J modulation
A.2
V
vsa
/
\
Vx
\
/
\
/
Figure A.2: Waveforms of alternator connected to SMR with an interval 5
enhance output power at idle speed.
introduced to
As Fig. A.2 shows and by applying the superposition principle, it can be seen that the
3I
local
average voltages at the three inputs of the SMR, ;Vag (t),Vbg (t) and Ocg(t) can be decomposed
into their dc and
ac components:
1/
3/
+ 6ag
Vag
(ag)
Vbg
(Vbg) + 'jbg
;Vcg
cVrg)
(A.4)
+ 'jA
Again, the ac voltages presented in Eq.(A.4) are equal in magnitude, but phase shifted
by 21 radians. This implies that the dc components for the three signals are the same:
(Vag ) = (Vbg ) = (Vg ).
By plugging equation (A.4) into equation (A.3) and solving for the neutral to ground voltage
Vng we Obtain:
Vng
[6'ag + 'g
-
71
+ ' cg|+ (Vag)
-
(A. 5)
Mathematical Analysis of the new modulation scheme
Rs
Ls
VsV
Vng
7
Figure A.3: One phase model of the SMR for calculating the phase current ia.
Now, in order to simplify the calculations, it is possible to analyze just one of the phases of
the SMR. By applying KVL around the loop in which the current ia circulates, it is possible
to develop a simplified model which can be helpful in order to obtain the magnitude and
corresponding phase of the current i,. Figure A.3 shows such a circuit.
By looking at Fig. A.3 and the expressions given by equations (A.4) and (A.5), the equivalent
circuit can be simplified even more, by placing in the circuit an equivalent source vev=
Vag - Vng, the following expression results:
2Veqv = Vag - Vng =
Vag -
1
1
-Vbg -
-V~g
(A.6)
The simplified circuit shown in Fig. A.4 allows an intuitive and simple calculation of the
current ia. From that result, the output power delivered to the output voltage V and
dissipation losses Pis, can be easily calculated by taking into consideration the contribution
of the two other phase currents 2
In order to obtain an equation for the phase current ia from the circuit presented in Fig. A.4,
it is necessary to obtain the AC components of the voltages at the input of the SMR, iag,
v'j g,and 6,g so, that an analytical description of the equivalent voltage source Veq, can be
obtained.
We can describe the voltage Vag in terms of its Fourier series description.
2
Currents ia, ib, ic are equal in shape and magnitude but phase-shifted by 13 radians from each other
- 72 -
A.2
Analytical Model for the 3 modulation
Rs
vsa
Ls
reqv
Figure A.4: Equivalent model for one phase of the SMR for calculating ia.
V
2
2
2
2
Figure A.5: Vag shifted by X angle in order to make the signal an even function.
00
Vag = ao + E
00
an cos (nwt) + E
n=1
bn sin (nwt)
(A.7)
n=1
To simplify the analysis, we make the assumption that the phase current ia remains positive
for exactly half a period. This is an approximation, because the addition of an interval 3 in
this modulation results in asymmetries in the length of the conduction period of the phase
current. Under this assumption we can shift the signal Vag shown in Fig. A.2 to left by an
angle x to make the signal an even function. The shifted waveform ivag shift is shown in
Fig. A.5. The angle X required to make fagIshift an even function is:
6
7r
x= 2 + a + 2
(A.8)
Because the shifted version of Vag is an even function, we find that all the coefficients bn
in the Fourier series representation are equal to 0. The Fourier series representation of the
the shifted Vag is then:
-
73
-
Mathematical Analysis of the new modulation scheme
00
=aO+
Vag
W hift
(vtg)
(A.9)
an
coS (nWt)
n=
ag
Where the coefficients ao and an are given by:
vx
' x (-7r -)
27r
ao
an = -
sin (nf
(A.10)
-")
It is now possible to find an expression for the shifted equivalent voltage source veqv in the
model consisting of one phase of the system by plugging Eq. (A.9) into Eq. (A.6). Recall
that vag, vbg and vc, are just the same signal but shifted by 2 radians from each other.
The shifted Veqv that results can be expressed as:
=
Ishift
n=1
an cos (nwt) - 3Ean COS nt
n=1
-
n
E an cos (nwst
n=1
(A.11)
or equivalently:
2an cos (nwot) 1 - cos
=
,hift
I27r n)
23
3 n.
(A.12)
n=1
To get a further insight into the equation equation (A.12) can also be written as:
Veqv
shift=
.
for n=1,2,4,5,7,...
=1 ancos (nt))
for n = 3,6,9,...
0
(A.13)
From equation (A.13) we can see that all 3n harmonics axe zero, an observation which is
consistent with the triphasic nature of the alternator system.
By shifting back the equation obtained in equation (A.13) by an angle -x (Eq. A.8), we
obtain an analytical expression for the equivalent voltage source Veq, of the equivalent onephase model shown in Fig. A.4. The resultant Vegq is given by:
-
74
-
A.2
Analytical Model for the 6 modulation
Rs
Ls
V.. sin(wyt+a)
to t-+j5
a sin
Figure A.6: Equivalent circuit model for the fundamental component one phase of the SMR
for calculating
ial-
Veqv
=
for
for
E=1
n ancos(nwst - nX))
= 1,2,4,5,7,...(
n
n=3,6,9...
For sinusoidal back EMF, the fundamental component of
ia
(A.14)
is the only component that
contributes to real output power, so we choose to analyze the circuit model presented in
Fig. A.4 in terms of just its fundamental components.
The n=1 term in Eq. (A.10) gives the coefficient corresponding to the magnitude of the
fundamental component of the equivalent voltage source veqv:
a1 = -
2Vx.
IT
J
7r
sin - --(2
2)
2Vx
cos
6
-
/7
(A.15)
After phase shifting the signals properly to simplify the analysis, we obtain the equivalent
circuit shown in Fig. A.6, which may be used to solve for the fundamental component of
the phase current i.
The series inductance L, and resistance R, that model the phase impedance can be represented by a total series impedance described by its magnitude and its corresponding phase
ZL = IZL IZOz expressed as a function of the electrical frequency w8 , where:
Gz= tan- 1
IZLI = VR2 + W2L2
(A.16)
By using phasor analysis techniques, it can be found that the fundamental component of
the phase current i, in a polar representation can be described as:
VIail I
=
"Z
|ZLI
_V)
-,
-75-
- ai
IZLI
+ 0z
2
(A.17)
Mathematical Analysis of the new modulation scheme
By expressing equation (A.17) in rectangular form we find ial =
Refiai} = Ial =-
-os (a - 0z) _
lZe{iai} +j2m{ial}
where:
J +0
Cos
(A.18)
Im{iai} = 0 =
+6z
sin
sin (a - Oz) -
From the Im{iai} = 0 we can solve for the phase angle a and obtain the following analytical
expression:
a=
- sin~
(')
czCos
sin
+ Oz
(A.19)
By plugging the result found in equation (A.19) into lZe{iai} given in equation (A.18) we
find that the magnitude of the fundamental component of the phase current al is given by:
Iail =V' [COS (a - Oz)] - Ig VCOS
(A) [COS (A +0z)]
(A.20)
Using this equation, it is possible now to find the output power delivered by the alternator
under this modulation scheme.
In particular, the output power per phase can by calculated by calculating the power delivered by the back EMF source Va and subtracting the conduction losses of the winding
resistance R,. Thus the total output power delivered to the output by the alternator connected to a SMR with the 6 modulation is:
(POUT) = 3
saIa cos(a)
-3
[R,
]
(A.21)
The MATLAB program presented in B.2 evaluates the expressions obtained by equations
(A.19), (A.20) and (A.21). The same program plots the additional output power as a function of the angle 6 as well as the RMS magnitude increase of the fundamental component
of the phase current ial.
-
76
-
Analytical Model for the 6 and 1 modulation
A.3
V
VO
a7
/
I
\
+
/\
Figure A.7: Modulation
A.3
6 and D
Analytical Model for the J and <D modulation
This appendix presents a mathematical description for the complete modulation described
in section 3.3.1.
Figure A.7 shows the waveforms of one of the phases of the SMR with an interval of length
6 introduced when the phase current i, turns positive. Another interval labelled 4 is
introduced at the end of the interval during which the phase current is positive. The back
EMF voltage vsa is shown as a dotted line, while the phase current ia is depicted as a
distorted sinusoid with a solid line. The local average voltage at the input of the SMR Vag
is also pictured. The amplitude of vag is Vase from the end of the interval 6 through the
beginning of interval 4. During the interval i the duty cycle of the corresponding switch
is modified so as to obtain a local average with an amplitude VOV Volts over the normal
Vbase. The phase angle that exists between the back EMF voltage and the fundamental
component of the phase current iai is called a. The mathematical derivation for this new
modulation closely follows that of the 6 modulation presented in section A.2.
In particular, we again obtain a model for just one phase of the SMR structure under the
new modulation of the form presented in Fig. A.4, where again the equivalent voltage source
Veqv is given by Equation (A.6). In order to find a simple expression for i'3g we shift the Vag
waveform to the left by wt = + a rad, which results in the signal presented in Fig. A.8.
It is clear that this resultant waveform is not an even nor an odd function.
-
77
-
Mathematical Analysis of the new modulation scheme
Vag
VOV
-0-4
I~-
f
-
,r-(5-cF
Yr -(5
Figure A.8: Shifted version of the phase to ground voltage Vag at the input of the SMR.
By expressing the shifted waveform in terms of its Fourier components:
00
00
an cos (nwt) + E bn sin (nwot)
ao +E
Vag
shift
(A.22)
n=1
n=1
We can obtain the different frequency components ao, an, and bn that form the Fourier
series expansion. The formula for the frequency components are:
ao =
Vase+VOV
an = Vbse+
n7r
bn = Vbase _Vbase
n*r
J] Vbase +
[
sin (n7r - n) -
+VOV cos (n7r - n) +
n7r
gr 2
o
-sin
[4]
7r _
Vov
2
(n7r - nJ - n(b)
n7
(A.23)
cos (n7r - n6 - nb)
n7r
From this we can find an equation for just the fundamental component, as determined by
the coefficients a1 and b, of the Fourier series expansion.
Vbase +VOV .
sin (J) 7r
al = Vae+O
___
-o sin (6
7
+
<D)
(A.24)
Vbase
bi=
+
Vbase + V 0 v
cos (6) -
VoV
cos (6±+
<)
Using simple trigonometric identities, we can find that the fundamental component of shifted
Veqv can be written as
Veqvl
=
ci sin(W't +
-
78
shift
-
x)
(A.25)
A.3
Analytical Model for the 5 and <) modulation
Rs
Ls
V, sina(wt+ a)
Ccnsin(a t+Z-6)
Figure A.9: Equivalent circuit model for the fundamental component one phase of the SMR
for calculating ial.
Where ci and
x
are given by
x = tan- 1
a 1=+ b
(A.26)
Using the above results and after shifting all the signals by wt = a + 6 rad to the right,
we can find an equivalent circuit suitable to analyze one phase of the SMR. With such a
circuit we can obtain an equation for the fundamental component of the phase current ialThe equivalent circuit is shown in Fig. A.9.
The series inductance L, and resistance R, that model the phase impedance can be represented by a impedance ZL
ZL IZOZ expressed as a function of the electrical frequency w,
where:
IZLI = VR2 + w2L2
OZ = tan-1(''f )
(A.27)
By using phasor analysis techniques, it can be found that the fundamental component of
the phase current ia in a polar representation can be described as:
(A.28)
Val1I ZO = Vsa ( - 0,, - ci Z(X - 6 - Oz)
|ZI|
|ZL|
By expressing equation (A.28) in rectangular form we find ial = Re{iai} +jIm{ia1} where:
Re{ia} = Ial= [iKV cos (a - Oz) - ci cos (x - 6 - Oz)
|Z I|
.|ZL|
(A.29)
Im{ial} = 0 =
|IZL|
sin (a - Oz) -
-
79
-
ci sin (x - 6 IZ I|I
Oz)
Mathematical Analysis of the new modulation scheme
Setting the Im{ial} = 0 we can solve for the phase angle a and obtain the following
analytical description:
a = Gz + sin~ -E.'sin (X - 6 - Oz)
Va
(A.30)
By plugging the result found in equation (A.30) into Re{ial} given in equation (A.29) we
find that the magnitude of the fundamental component of the phase current ial is given by:
|al =
V1a cos (a - Oz) -i
cos (X - J - Oz)
(A.31)
where ci,X and a are as previously defined.
The output power per phase, can by calculated by calculating the power delivered by the
back EMF source Va minus the conduction losses of the winding resistance R,. Thus the
total power delivered to the output by the alternator under this new modulation scheme
(which has the new control parameters 5, VOv, and <)) is:
(POUT) = 3 VaIai cos(a)] - 3
[R
(A.32)
The appendix B.3 contains the MATLAB program that evaluates the expressions obtained
by equations (A.30-A.32).
-
80
-
Appendix B
MATLAB Files
B.1
Introduction
This appendix presents the MATLAB files that can be used for simulating the different
modulations schemes presented in chapter 3. In particular, section B.2 contains the model
for the simpler modulation introduced in section 3.2 in which just an interval 6 is introduced.
Section B.3 contains the model for the complete modulation scheme described in section 3.3.
B.2
MATLAB model for the 6 simulation
X/.Program for plotting the input power drawn from the alternator using%%%
XXthe modulation delta scheme in which the lower switches of the
%%%
MX/alternator are turn on after the positive zero crossing of the
X
XX.phase current.
%%%
XY.Written by: Juan Rivas, Cambridge MA
XX.Massachusetts Institute of Technology
%%%
%%%
XThe goal in this modulation scheme is to increase the output power at
%iddle speed by means of storing energy on the inductor for
%cycle.
part of the
XThe parameters required in order are:
Y.Vsa-rms = Vrms of the fundamental of the back emf Voltage
XVx = The Output Voltage (add to diode drops if required)
Xr-s = Series Resistance of the alternator's stator in ohms
%1-s = Series Inductance of the stator
%del = delta interval
%freq = Electrical frequency of the alternator back emf in Hertz
%The plots obtained are:
-
81
-
MATLAB
Files
%-Output Power vs. Delta
%-Normalized Output Power vs. Delta
%-inductor current magnitude vs. Delta
%-normalized inductor current vs. Delta
function [del,powoutl-p,powoutl,ial-rms-p,ial.rms]=mod-delta()
%parameters:
Vsa-rms=10.716;
Vx=14;
rs=37e-3;
1.s=120e-6;
freq=180;
cdc;
del=[0:0.01:50J; Urray of delta in electrical degrees to be ploted
%Get the EMF magnitude from its rms value.
Vsa=Vsa-rms*sqrt(2);
ZL=complex(r-s,(2*pi*freq*l-s)); %Get the complex R+jwL
%Get the magn. of complex impedance
magZL=abs(ZL);
%Get the phase of complex impedance
ang-ZL=angle(ZL);
del-r=del*pi/180;
%Transforms delta from degs to rads
%Get the phase angle of the current Ial from the analytical model:
varl=(2/pi)*(Vx/Vsa).*cos(del-r./2); %Intermediate variable 1
Intermediate variable 2
var2=sin((del-r./2)+ang-ZL);
angle of Ial
%Phase
ial-phr=angZL-asin(varl.*var2);
ia1_phd=ia1_phr.*180./pi;
%Transform phase angle from radians to degs
7Get the magnitude of the current Ial from the analytical model:
varl=(Vsa/mag-ZL).*cos(ia1phr-angZL); %Intermediate varaiable I
var2=(2/pi).*(Vx/mag-ZL).*cos(del-r./2).*cos((del-r./2)+ang-ZL);
ial.mag=varl-var2; %Magnitude of Ial
ia1_rms=ia1lmag./sqrt(2); %RMS value of the phase current ial
%Get pow-in at input of alternator as Vmax*Imax*Cos(phase-between)/2
pow.outl=3*((Vsa.*ia.mag.*cos(iaphr)./2)-(r.s.*(ialmag.^2)/2));
%Get the Xinc of values of the output power and phase current
ial-rmsp=((ial.rms./ial-rms(1))-1)*100;
powoutl.p=((powoutl./pow.outi(l))-1)*100;
-
82
-
B.2
Make the
plots
MATLAB model for the 6 simulation
%
figure;
subplot(2,1,1)
a=plot(del,pow-outi, 'r');
title('Output Power vs. \delta');
grid ON;
xlabel('\delta (degs)');
ylabel('Output Power (W)');
set(a,'linewidth',3);
axis([min(del) max(del) min(pow-outl)-100 max(pow-outl)+100);
%figure;
subplot(2,1,2)
b=plot(del,iarms,'g');
title('I_{1RMS} vs. \delta ');
grid ON;
xlabel('\delta (degs)');
ylabel('I_{1RMS} A');
set(b,'linewidth',3);
axis([min(del) max(del) min(ia.rms)-10 max(ialrms)+10]);
XPlot of the phase angle of i.al vs delta (not plotted)
Zfigure;
%subplot(2,2,3)
%c=plot(del,iaI.phd,'g');
%title('phase angle i{1} vs. \delta');
%grid ON;
%xlabel('\delta (degs)');
%ylabel('phase angle i{1} (degs)');
Xset(c,'linewidth',3);
%axis([min(del) max(del) min(ial-phd)-5 max(ia-phd)+5J);
figure;
subplot(2,1,1);
d=plot(del,powoutI-p,'r');
title('Percent increase in output power vs. \delta');
grid on;
xlabel('\delta (degs)');
ylabel('1 increase');
-
83
-
MATLAB
Files
set(d, 'linewidth',3);
axis(Emin(del) max(del) min(pow-out-p) max(pow-outl-p)+4]);
%figure;
subplot(2,1,2);
e=plot(del,iarmsp, 'g');
title('Percent increase in I_1RMS} vs. \delta');
grid on;
xlabel('\delta (degs)');
ylabel('X increase');
set(e, 'linewidth',3);
axis([min(del) max(del) min(iai-rms-p) max(ia1_rmsp)+10]);
B.3
MATLAB model for the complete simulation
%.Program for plotting the input power drawn from the alternator using%=X
XXMthe modulation delta-phi scheme in which the lower switches of the UM%
%%%
7X/.alternator are turn on after the positive zero crossing of the
%%%
%%phase current. Then the duty cycle is modefied at the end of the
X
XXpositive current portion of the cycle to get a local average that
X
UXexceeds the voltage Vbase by Vov volts
WXXWritten by: Juan Rivas, Cambridge MA
%%/Massachusetts Institute of Technology
%%%
%%%
%The goal in this modulation scheme is to increase the output power at
%idle speed by means of storing energy on the inductor for part of the
%cycle and by changing the phase angle between the back EMF and the phase
%current
%The parameters required in order are:
%Vsa-rms = Vrms of the fundamental of the back emf Voltage
Vbase = The Output Voltage (add to diode drops if required)
%r-s = Series Resistance of the alternator's stator in ohms
%1-s = Series Inductance of the stator
del = delta interval (in electrical degrees)
Xphi = phi interval length (in electrical degrees)
%Vov = Voltage added to Vbase during the phi interval
-
84
-
B.3
model for the complete simulation
MATLAB
%freq = Electrical frequency of the alternator back emf in Hertz
7,The plots obtained are:
X-Output Power vs. Delta
%-Normalized Output Power vs. Delta
%-inductor current magnitude vs. Delta
%-normalized inductor current vs. Delta
function moddelphi()
7.parameters:
Vsa-rms=10 .716;
Vbase=14;
rs=37e-3;
l-s=120e-6;
Vov=20;
freq=180;
Vsa=Vsa-rms*sqrt(2);
ZL=complex(r-s,(2*pi*freq*l.s));
mag-ZL=abs (ZL);
angZL=angle(ZL);
%Get
%Get
%Get
%Get
the
the
the
the
amplitude Vsa
complex R+jwL
mag. of the complex imp.
phase of the complex imp.
%del=[0:0.01:50J; /Array of delta in electrical degrees to be ploted
del=O;
del-r=del*pi/180;
XTransforms delta from degs to rads
phi=[0:0.01:70J;
Xphi=O;
phi-r=phi*pi/180;
V2=Vbase+Vov;
XGet the max voltage of Vag
%Coefficient Values for the fundamental components
%of the signals al and bi
7XExpression for al
al=(V2.*sin(del-r) ./pi)-(Vov.*sin(del-r+phi-r)./pi);
7.Expression for bi
bl=(Vbase./pi)+(V2.*cos(del-r)./pi)-(Vov.*cos(del.r+phir)./pi);
%So now I can get the the "all-sine" fundamental
%component in the form cl*sin(wt+xi-angle)
cl=sqrt ((al.-2)+(bl.^2));
-
85
-
MATLAB
Files
if bI~=0
chi-r=atan(al./bl);
else
chi-r=pi/2;
end;
%angle between the corrent and the back-emf voltage in rads
ialphr=angZL+asin(cl.*sin(chi-r-del-r-angZL) ./Vsa);
iaIphd=ia.phr.*180./pi; %Get the angle in electrical degrees
%Get the magnitude of the line current
varl=(cl.*cos(chir-del.r-angJZL)./mag-ZL)
ial-mag=(Vsa.*cos(ial.phr-angZL)./magZL)-varn;
ia1_rms=ia1_mag./sqrt(2); %RMS value of the phase current ial
%Get pow-in at input of alternator as Vmax*Imax*Cos(phase-between)/2
pow-out1=3*((Vsa.*ialmag.*cos(ial-phr) ./2)-(r-s.*(ialmag.^2)/2));
ialrmsp=((ial1rms ./ial.rms(1))-1)*100;
powoutlp=((pow.outi./pow.outl(1))-1)*100;
XMake the plots
%
figure;
subplot(2,1,1)
a=plot(phi,powouti, 'r');
title('Output Power vs. \Phi');
grid ON;
xlabel('\Phi (degs)');
ylabel('Output Power (W)');
set(a, 'linewidth',3);
axis([min(phi) max(phi) min(pow-outl)-100 max(pow.outl)+100]);
YXfigure;
subplot(2,1,2)
b=plot(phi,iarms, 'g');
title('I_{1RMS} vs. \Phi ');
grid ON;
xlabel('\Phi (degs)');
ylabel('I.{1RMS} A');
set(b, 'linewidth',3);
-
86
-
B.3
MATLAB
model for the complete
axis([min(phi) max(phi) min(ial-rms)-10 max(ialrms)+10));
figure;
subplot(2,1,1);
d=plot(phi,pow.out1.p, 'r');
title('Percent increase in output power vs.
grid on;
xlabel('\Phi (degs)');
ylabel(') increase');
set(d,'linewidth',3);
\Phi');
axis([min(phi) max(phi) min(pow-outl-p) max(pow-outip)+4]);
%figure;
subplot(2,1,2);
e=plot(phi,ia1_rms-p,'g');
title('Percent Increase in I_{1RMS} vs. \Phi');
grid on;
xlabel('\Phi (degs)');
ylabel('% increase');
set(e,'linewidth',3);
axis([min(phi) max(phi) min(ialrms-p) max(ia-rms.p)+10]);
-
87
-
imtlation
Appendix C
PSPICE Model
C.1
Introduction
An Averaged PSPICE model was developed to validate the analytical model and to explore the parameter space (to optimize performance of the SMR). In order to reduce the
time of the calculations required, the simulation makes use of averaged models instead of
high frequency switching models. Figure C.1 shows the structure of the PsPIcE averaged
model. In particular it shows the alternator parameters V,, (the back EMF voltage of the
x phase), R. and L, (the alternator's winding resistance and inductance). The modulation
technique presented in this paper was implemented using dependent voltage sources connected to each phase of the alternator. In particular vag, vbg, and Vg each generate the
corresponding neutral-to-ground voltage as determined by the new modulation shown in
Fig. 3.5. The output power POUT and the IRMS phase current were obtained by an analog
circuit implemented in the simulation to ensure a fast acquisition of the results .
The different parameters of the simulation 6, <, VOy and Vaae can be independently controlled and varied thus making this a flexible simulation tool for this new power enhancing
technique.
C.2
PSPICE Library models
This section presents the library models of all the subcomponents needed to simulate the
new modulation technique proposed in this document.
***
Library of PSpice Personalized models for
***
Pspice Simulations
by Juan Rivas
*** Cambridge,MA, 2002
*** Version: 12/23/02
***
***
-
89
-
PSPICE Model
Vsa
Vsb
Rs
Ls
Rs
Ls
Rs
Ls
Vt Vsc
V1:)
Cg(t
b9t
Vbg(t)
-
V(ag~t
+
N
Figure C.1: PSPICE circuit model for the SMR power enhancement modulation.
***
MODEL: DELTAGEN
signal corresponding to ***
the delta interval required in the modulation ***
that obtains extra power at idle speed
*** Application: + Generates the gating
*** Limitations: None
* Parameters:
Nodes:
*
* INCS
*
*
: Input coming from the current sensor that detects
the zero crossing of the line current in the modulation
FREQF: Input coming from a voltage source that determines the
fundamental frequency of the EMF generated by the alternator
DELTA-D: Input coming form a voltage suource that determines the
length of the delta interval (in degrees) of the modu-
*
*
*
*
*
*
*
lation
* DELTA_G: Output which contains the gating signal for the bottom
*
*
*
switches of the SMR that corresponds to the delta interval
in the modulation
-
90
-
*
*
*
*
*
*
*
*
*
C.2
PSPICE Library models
*CIRCUIT DESCRIPTION:
.SUBCKT DELTA-GEN IN-CS FREQF DELTA-D DELTAG
.PARAM: RMEG
-
iMEG
*
El 101 0 VALUE={SGN(-V(INCS))}
R1 101 0 {RMEG}
Si 102 0 101 0
SMOD
.MODEL SMOD VSWITCH (ROFF=lMEG RON=lE-3 VOFF=0.2
G1 0
102
VALUE={V(FREQF)*E-3/V(DELTA-D)}
C1 102 0 {lE-3/360} IC=0
R2 102 0 {RMEG}
E2
R3
VON=0.7)
DELTAG 0 VALUE={STP(-(V(101)+V(102)))}
DELTAG 0 {RMEG}
.ENDS DELTA-GEN
* MODEL: DELPHI-GEN
*
* Application: + Generates the gating signal corresponding to
*
*
the delta and phi interval required in the modulation *
*
that obtains extra power at idle speed
*
*
*
* Limitations: PHID has to be less than 180, because at
*
PHI.D=180 degrees the controlled current source
*
G2 blows up.
*
*
*
* Parameters:
* Nodes:
* INCS :
*
*
*
*
*
Input coming from the current sensor that detects
the zero crossing of the line current in the modulation
Input coming from a voltage source that determines the
fundamental frequency of the EMF generated by the alter-
*
nator
*
*
*
*
FREQF:
DELTA-D: Input coming form a voltage suource that determines the
length of the delta interval (in degrees) of the modulation
*
*
*
*
PHID:
Input coming from a voltage source that determines the
length of the phi interval (in degrees) of the modulation
*
-
91
-
*
*
*
*
*
*
*
PSPICE
Model
Input coming form a voltage source that determines the
overvoltage applied to the nominal DC output voltage at
*
*
*
the output of the SMR
*
*
*
*
*
*
*
*
VOV3V:
DELTAG: Output which contains the gating signal for the bottom
switches of the SMR that corresponds to the delta interval
in the modulation
PHIVOV: Output which contains the overvoltage applied during the
phi interval which will be applied over the output of the
*
*
*
*
*
*
*
SMR
*CIRCUIT DESCRIPTION:
.SUBCKT DELPHI-GEN INCS FREQ.F DELTAD PHID VOV3V DELTAG PHIVOV
.PARAM: RMEG = iMEG
*Generation of the delta Inteval length
El 101 0 VALUE={SGN(-V(INCS)-2m)} ;checa esto
R1 101 0 {RMEG}
SMOD
Si 102 0 101 0
.MODEL SMOD VSWITCH (ROFF=lMEG RON=lE-3 VOFF=0.2 VON=0.7)
VALUE={V(FREQF)*iE-3/V(DELTAD)}
102
G1 0
C1 102 0 {IE-3/360} IC=0
R2 102 0 {RMEG}
E2 DELTAG 0 VALUE={STP(-(V(101)+V(102)))}
R3 DELTA-G 0 {RMEG}
*Generation of the phi interval length and overvoltage
SMOD
S2 202 0 101 0
*.MODEL SMOD VSWITCH (ROFF=IMEG RON=lE-3 VOFF=0.2 VON=0.7)
VALUE={V(FREQF)*1E-3/(180-V(PHI-D))}
202
G2 0
C2 202 0 {1E-3/360} IC=0
R4 202 0 {RMEG}
E3 PHIVOV 0 VALUE={v(VOVV)*STP(V(202)-1)}
R5 PHI3VOV 0 {RMEG}
.ENDS DELPHI-GEN
* MODEL: EMFALT
*
* Application: Emulates the EMF voltage generated by a lundell machine *
(Alternator) in which up to 5 harmonics and their phases*
*
*
are included. The fundamental frequency is set by a
*
*
DC voltage source.
*
-
92
-
C.2
PSPICE Library models
*
*
*
Limitations: NONE
*
*
Parameters:
VRMSF : Vrms of the fundamental component of the generated EMF.
VRMS_2 : vrms of the second harmonic of the generated EMF.
PH2
: Phase .of the second harmonic in electrical degrees
VRMS-3 : vrms of the third harmonic of the generated EMF.
PH-3
: Phase of the third harmonic in electrical degrees
VRMS-4 : vrms of the fourth harmonic of the generated EMF.
PH_4
: Phase of the fourth harmonic in electrical degrees
VRMS_5 : vrms of the fifth harmonic of the generated EMF.
PH_5
: Phase of the fifth harmonic in electrical degrees
*
*
*
*
*
*
*
*
*
*
*
EMF-A :
EMF-B :
EMF.C :
NEUT :
FREQF:
*
*
nator
*
*
*
*CIRCUIT DESCRIPTION:
.SUBCKT EMFALT EMF_A EMFB EMF.C NEUT FREQ(F
+
+
+
+
+
+
+
+
+
+
*
*
*
*
*
*
*
*
Output Phase A of the EMF that includes 5 harmonics
Output Phase B of the EMF -120 deg
Output Phase C of the EMF +120 deg
Neutral point of the lundell machine
Input coming from a voltage source that determines the
fundamental frequency of the EMF generated by the alter-
*
*
*
* Nodes:
*
*
PARAMS:
VRMSF =
VRMS-2 =
PH.2
=
VRMS.3 =
PH_3
=
VRMS_4 =
PH4
=
VRMS_5 =
PH_5
=
10.716
23.071M
153.71
0.45689
-16.073
19.972M
121.56
0.40452
-166.8
.PARAM PI=3.14159265
RI
ElA
E2_A
NEUT 0 10MEG
; JUST A HUGE RESISTOR BETWEEN NEUTRAL AND GROUND
1A NEUT
VALUE={SQRT(2)*VRMSF*SIN(2*PI*(1*V(FREQ-F)*TIME))}
2A 1A
VALUE={SQRT(2)*VRMS_2*SIN(2*PI*(2*V(FREQF)*TIME+
+ (PH_2/360)))}
E3A
3A 2A
VALUE={SQRT(2)*VRMS_3*SIN(2*PI*(3*V(FREQ-F)*TIME+
-
93
-
*
*
*
*
*
*
*
PSPICE
Model
+ (PH-3/360)))}
E4_A 4A 3A
+ (PH.4/360)))}
VALUE={SQRT(2) *VRMS_4*SIN(2*PI*(4*V(FREQF) *TIME+
E5_A EMFA 4A
VALUE={SQRT(2)*VRMS_5*SIN(2*PI*(5*V(FREQ-F) *TIME+
+ (PH.5/360)))}
E1_B
1B NEUT
VALUE={SQRT(2)*VRMSF*SIN(2*PI*(l*V(FREQF)*TIME-
+ (1/3)))}
VALUE=SQRT(2)*VRMS.2*SIN(2*PI*(2*V(FREQ-F)*TIME+
E2_B 2B 1B
+ (PH.2/360)-(2/3)))}
VALUE={SQRT(2)*VRMS-3*SIN(2*PI*(3*V(FREQF)*TIME+
E3B 3B 2B
+ (PH.3/360)))}
VALUE={SQRT(2)*VRMS-4*SIN(2*PI*(4*V(FREQF)*TIME+
E4-B 4B 3B
+ (PH_4/360)-(1/3)))}
E5-B
EMFB 4B
VALUE={SQRT(2)*VRMS-5*SIN(2*PI*(5*V(FREQ-F)*TIME+
+ (PH-5/360)-(2/3)))}
EIlC 1C NEUT
+ (1/3)))}
E2-C
2C
1C
VALUE={SQRT(2)*VRMSF*SIN(2*PI*(l*V(FREQF)*TIME+
VALUE={SQRT(2)*VRMS-2*SIN(2*PI*(2*V(FREQF) *TIME+
+ (PH.2/360)+(2/3)))}
E3C
3C 2C
VALUE={SQRT(2)*VRMS-3*SIN(2*PI*(3*V(FREQF) *TIME+
+ (PH_3/360)))}
VALUE={SQRT(2) *VRMS_4*SIN(2*PI* (4*V(FREQ.F) *TIME+
E4_C 4C 3C
+ (PH4/360)+(1/3)))}
VALUE={SQRT(2) *VRMS_5*SIN(2*PI* (5*V(FREQF) *TIME+
E5C EMFC 4C
+ (PH.5/360)+(2/3)))}
.ENDS EMFALT
*
MODEL: LRW3PH
*
*
* Application: Model the winding series inductance and
and series resistance, of a three phase system
values of those
* who parameters
* LIMITATIONS: NONE
*
*
* being possible to adjust the
* Parameters: L-s=Series Inductance in uH
*
*
*
*
*
(120uH default)
R.s=Series Resisance in Ohms (37mOhms default)
Nodes:
1: Input terminal Phase A
*
*
*
*
*
-
94
-
C.2
* 2:
* 3:
* 4:
* 5:
* 6:
PSPICE Library models
Output terminal Phase A
Input terminal Phase B
Output terminal Phase B
Input terminal Phase C
Output terminal Phase C
*
*
*
*
*
*
.subckt LRW3PH INA OUTA IN.B OUT-B INC OUTC
+params: L-s=120u R-s=37m
RA
LA
RB
LB
RC
LC
INA
x
INB
y
IN-C
z
x
OUTA
y
OUTB
z
OUT-C
{Rs} ;Series Resistance of phase A
{Ls} ;Series Inductance of phase A
{R-s} ;Series Resistance of phase A
{L-s} ;Series Inductance of phase A
{Rs} ;Series Resistance of phase A
{L-s} ;Series Inductance of phase A
.ends LRW3PH
*
MODEL: IDMOS
*
Application: Ideal Mosfet, which consist of a ideal switch
*
and an antiparallel diode
*
this model also includes the driver so any voltage
referenced to ground can be used to drive it on
*
Parameters: Ron = On resistance of the switch (3m Ohms)
*
*
*
*
*
*
*
* Nodes:
*
*
Default
*
*
*
*
*
Gate: Gate of the ideal mosfet
Drain: Drain of the ideal mosfet
Source: Source of the ideal mosfet
.subckt IDMOS Gate Drain Source
+params: Ron=3m
Sw
Dsw
Da
Rbig
Drain
x
X
Source
Source Drain
Gate
0
Gate
Dideal
Dideal
100E3
0
Swideal
-95-
*
*
*
PSPICE Model
Csn
Drain
Source
10p
.MODEL Dideal D (N=0.001)
.MODEL Swideal VSWITCH (RON={Ron} ROFF=lE+7 VON=0.9 VOFF=0.1)
.ends IDMOS
* MODEL: SMR1PH
* Application: 1 Leg of the SMR which is composed of an upper
diode a bottom mosfet and the output voltage source
*
which introduces the corresponding over voltage during
*
the phi interval
*
* Limitations: None
*
*
* Parameters:
*
* NODES:
*
*
*
Input of the SMR leg
Gate of the bottom mosfet of the SMR leg
* IN-GATE:
* IN-VOVPH: Input of the over voltage during the phi interval
Input of the nominal output voltage that the leg of
* VDCOUT:
the SMR sees during the nominal duty cycle
*
* IN-PH:
*
*
*
*
*
*
*
*
*
*
.subckt SMR1PH IN-PH INGATE INVOVPH VDCOUT
XMOS
Dl
IN-GATE IN-PH 0
1 Dideal
IN-PH
IDMOS
.MODEL Dideal D (N=0.001)
0 VALUE={V(VDCOUT)+V(IN3VOVPH)}
1
El
.ENDS SMR1PH
*
*
* Application: + Generates the gating signal corresponding to
the delta and phi interval required in the modulation*
*
that obtains extra power at idle speed for the three *
*
* MODEL: DELPHIGEN-3PH
*
*
phasaes of the alternator
*
*
* Limitations: PHILD has to be less than 180, because at
*
PHID=180 degrees the controlled current source
-96
-
*
*
C.2
PSPICE Library models
G2 blows up.
*
*
* Parameters:
*
*
Nodes:
*
INCSA,B,c:
Input coming from the current sensor that detects
*
the zero crossing of the line current in the modulation
* FREQHZ:
Input coming from a voltage source that determines the
*
fundamental frequency of the EMF generated by the alter*
nator
* DELTADEG:Input coming form a voltage suource that determines the
*
length of the delta interval (in degrees) of the modu*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
lation
PHIDEG:
Input coming from a voltage source that determines the
*
length of the phi interval (in degrees) of the modu*
lation
VOVVOLT: Input coming form a voltage source that determines the
*
overvoltage applied to the nominal DC output voltage at
*
the output of the SMR
*
DELTAGA,B,C: Output which contains the gating signal forthe bottom*
switches of the SMR that corresponds to the delta interval*
in the modulation
*
PHIVOVA,B,C: Output which contains the overvoltage applied during *
the phi interval which will be applied over the output of *
the SMR
*
*CIRCUIT DESCRIPTION:
.SUBCKT DELPHIGEN-3PH IN-CS-A INCSB IN.CS-C DELTAGA DELTAGB
+ DELTAGC PHI3VOVA PHIVOVB PHI3VOVC FREQ-HZ DELTA-DEG
+ PHI-DEG vOV_VOLT
XDPGA
IN-CSA FREQHZ DELTADEG PHI-DEG VOV_VOLT DELTAGA PHI3OVA
+ DELPHIGEN
XDPGB
INCSB FREQ-HZ DELTA-DEG PHIDEG VOVVOLT DELTA.G.B PHI3VOVB
+ DELPHI.GEN
XDPGC
INCSC FREQ-HZ DELTADEG PHI-DEG VOVVOLT DELTAG.C PHI3VOVC
+ DELPHIGEN
.ENDS DELPHIGEN-3PH
* MODEL: SMR3PH
* Application: 3 Legs of the SMR which is composed of an upper
-
97
-
*
*
PSPICE Model
diode a bottom mosfet and the output voltage source
which introduces the corresponding over voltage during
the phi interval
*
* Limitations: None
*
*
*
*
*
*
* Parameters:
*
* NODES:
*
*
Input of the SMR leg
Gate of the bottom mosfet of the SMR leg
* IN-GATE:
* INVOVPH: Input of the over voltage during the phi interval
Input of the nominal output voltage that the leg of
* VDC-OUT:
the SMR sees during the nominal duty cycle
*
* IN-PH:
*
*
*
*
*
*
*
.SUBCKT SMR3PH IN.PH.A INPHB IN-PH.C INGATE-A INGATE-B IN-GATEC
+ IN3VOVPHA IN3VOV.PHB INVOVPHC VDC.OUTBAT
XSMRA INPH-A INGATEA IN-VOVPH.A VDCOUTBAT SMRIPH
XSMR.B INPHB IN-GATE-B IN-VOV-PHB VDCOUTBAT SMR1PH
XSMR.C IN-PH-C INGATEC IN.VOVYPH.C VDCOUT.BAT SMRIPH
.ENDS SMR3PH
C.3
PSPICE model for the SMR
This section presents the simulation file required to simulate the new modulation using
PSPICE
***
Circutit file that simulates de Switched Mode Rectifier (SMR)
***
*** using modulation that obtains extra Output Power at Idle speed. ***
***
Only average quatities are simulated to save simulation time
***
Made by Juan Rivas
*** Cambridge,MA
** ** ****
12/23/02
*** * *** ******
***
** ****
*
-
98
-
***
C.3
*** LIST OF LIBRARIES USED
.LIB "SMR-IDLE.lib"
.LIB "nom.lib"
****
PSPICE model for the SMR
***
;Library of models of this simulation
;Default Pspice library
Options required to avoid convergence problems
***
.OPTIONS ABSTOL=InA
GMIN=10p
ITL1=5000
ITL2=2000
ITL4=400
RELTOL=0.005
+
+
+
+
+
+
VNTOL=O.lmV
.OPTION STEPGMIN
****
options to keep the output file small
.OPTIONS
+ NOPAGE
+
NOBIAS
+
NOECHO
+ NOMOD
+
NUMDGT=8
.WIDTH OUT=132
*** CIRCUIT GLOBAL PARAMETERS
****** ** ******************
****
***
***
*.PARAM:
******* * ** *** **********
***CIRCUIT DESCRIPTION
***
***
XALT3 EMFA EMFB EMFC NEUT FREQ EMF.ALT
+ PARAMS:
+ VRMSF = 10.716
+ VRMS-2 = 23.071M
+ PH-2
;3-Phase Generated EMF
= 153.71
-99
-
PsPIcE Model
+
VRMS.3 = 0.45689
= -16.073
+ PH.3
+
VRMS_4 = 19.972M
= 121.56
+ VRMS_5 = 0.40452
= -166.8
+ PH-5
+ PH-4
XLRW3 EMFA RLWA EMFB RLWB EMFC RLWC
LRW3PH ;Winding Resis and Induc
+params: L-s=120u R-s=37m
;Dummy Voltage to measure line current
RLWA IN-SMRA 0
RLWB INSMRB 0
VXA
VXB
VXC
RLWC IN-SMR-C 0
HA
HB
IN-CS.A 0 VXA le-2
INCSB 0 VXB le-2
;Current sensor
;Current sensor
HC
INCS.C 0 VXC le-2
;Current sensor
*CONTROL
*
XCONTROL INCS.A INCS.B IN.CSC GATEA GATEB GATEC PHIVOVA
+
PHIVOVB PHIVOVC
+ FREQ DELDEG PHIDEG
*
SMR
VOVVOLT DELPHIGEN_3PH
*
XSMRO3PH INSMRA INSMR.B INSMRC GATEA GATEB GATE.C
+ PHIVOVA PHIVOVB PHIVOV.C BATT SMR3PH
** ****
* **** * *****
** ****
*Modulation Settings
*
0 179.882 ;Sets the operating electrical freq
;Length of the "delta" interval degrees
0 0.01
;Length of the "phi" interval degrees
0 0
VFREQ
VDELDEG
VPHIDEG
FREQ
DELDEG
PHIDEG
VVOVVOLT
VOVVOLT 0 20
VBATT
BATT
0 14
;Overvoltage applied during "phi"
;Nominal Output to the SMR
** ***** *** ***** ****** *** ***************
*RMS phase current calculation 2nd
order
-100
*
-
C.3
E2RMS_1
L2RMS-1
R2RMS_1
C2RMS-1
E2RMS-2
R2RMS-2
RMS_21
RMS-21
RMS-22
RMS_22
RMS-23
RMS-23
0
RMS-22
0
0
0
0
** ******
** ******
*** ********
0
for the SMR
vALUE={PWR(I(VXA),2)}
0.01 IC=0
0.15
IOM IC=0
VALUE={SQRT(V(RMS-22))}
1K
*** * *** *
*Average Output Power 2nd order
E20POW-1 POW21
PSPICE model
*
VALUE={(I(VXA)*V(INSMRA))+(I(VXB)*V(IN-SMRB))
+ +(I(VXC)*V(INSMRC))}
L20POW.1
R20POW_1
C20POW_1
E20POW2
R20POW-2
POW21
POW22
POW22
POW23
POW23
**************
POW22 0.01 IC=O
0
0.15
0
10m IC=0
0 VALUE={V(POW22)}
0
1K
** ******
***
*** Analysis Description
***
.TRAN 10m 3200m 0
10u UIC
.PRINT TRAN V(R2RMS_2) V(R20POW_2) V(VDELDEG) V(VPHIDEG) V(VVOVVOLT)
+ V(VBATT)
.PROBE V(R20POW-2) V(R2RMS2) I(VXA)
.END
-
101
-
Appendix D
FPGA implementation
D.1
Introduction
This appendix contains the schematic files that describe the implementation of the modulation controls presented in this thesis report. A Field-Programmable Gate Array (FPGA)
was programmed to established the gating signals for the switches used in the SMR structure.
The reason for using a (FPGA) is the simplicity for replicating the multiple control processing units of different parts of the implementation. In particular the gating control for
the MOSFET of one of the SMR phases is easily replicated for the other two phases of the
structure.
D.2
Implementation schematics
The Field-Programmable Gate Array (FPGA) used for the experimental setup is from
XILINX model XS40005XL. A test board made by XESS corp was used; this provided the
stand for the chip as well as the required interface electronics for the easy programming of
the logic device [17, 18].
-
103
-
FPGA
INPUTS.
RELQJ
O E WHEEL
FORCED
Irn
ELOJ: CdpTAl
j
1 -1
AFGE
RESET
IC DLT)U'-
..
NPORMALLOAD:
DECLAV:
F=d
A.mr
LOADA
DECPT
:
i,.
mdTA
SM
t
Wnh of
s
fth
W Ad "NgPh
deka by -I,
by -
CycE
A
posAn
ZO -
t
mCC
f
dCr
.h
pha-
d
-VI C rT
CATd III pr-s,
CURRENTSENSCRfi: Z=rD
CURRENTSENSORC: Z.r.CCing
w
A
Position
Ud
9s
ho intea
of t pNcrmswin
Setaftrft iWlthepostwoZer
of pnsiin
t wunm slwt
DrmPA
CURRENT-SENSORA:
COUNTER
-C
AC OfA AtDCCa pCACT
CCd
OW ATht
ImA.
TGnCAr AT
dT
CTy cyC of t P W1aD wTh ft
ATh
SON th.
PHL.NITWAPOS:
DWACQT [0
t
a 25ME
"
CDELTA:
L4
CAVALUE.165
for
wmaTTD
Oft d
CODE AEEL
FOCEDTRESET:
a
PN
poAn
by -nI
T
A
C 1w
C
B
pAC
pA.
INC
DELTA
PL OeK
RAM OENAB
VC
C VLE
IPC
T
T
AL
A ATTETALOAD
P
25MZ4_CLCK
A'
...
$07
DFG
rA39
MIAT
zESET
iT7:1
T-
PHO UF
-ETDELTAA
FAST
FAST
ETPH1tNTERVA7%T
TYAOVERSHOOTT7D
_ _
7ERO emOS
UIRRENT
.PMOS~l
FW
0
25WZ
F
FAST
-CLCK
WHIEELI4_OR_1
-_RESET
;E
.-
UTTS
PWM
,$11
OUTPUT
3ETP -iINTERVA1.71
........
--.
)tUTYOVERSHDOT1710..
M+O1cAA
a
FFAST
PWM
TC+WO
CUTrPULT =
i F
FAS T
FAST
25%iZ_CLCK
_ESET
IT:
PWM
FAST
=TP" _INTEVAL[701
%l
RRENT
l"YOVE RSH)OT[7;101
3|RMNT
SEN';OR C
PWM
_7FRQCRMi
MODUA
OUTPUT C
OUTPUT
FS
C LEE-
TRVOFAST
FAST
OUTPUTS:
PTWM_OUTPUT._A:
AiCA
PWCUTPUT_ALED: VIuA
GAwTg
f th.
PWMOUTPUTLB: Gadrvngr
WpA for
PW sgnAl
fwia
VsuA EnckaC 1w t
PWMOUTPUTC: CArg sIa for phT-,
PWM._OUTPUTCEC: VAA IndICAr
PW_OUTPUTBLED:
PW
C
ft
pTC
of
01r 8hs
sgA
A
p.
A
A
pha
C
PWM Wg"D
of
LEE
C
PAs.
S.
.kia
77 Massadcue-
Rias
MI
T
we 10-015
Dapiflwm?
m
Figure D.1: Full FPGA implementation
Preeci
Dt:40
ALPHDVO
WMco
LYTPHOVI
DUTY MAWU
L17
25MHZ_--j
I CONSTANT C1JMDT
-1
WHEE1-OD-.
C
WMDT
rK
PWM
-CYCLqpCMMEQ0
.
-M710
?WM,0UT .39
PUT DOWN
~AK
PWM IBMX=KGEN
CUrRarEN..ZEF*-AWL1
DUS
s15
H12
SET
SET_.PHI NTERVAt47.01
CURRENT-AEA01CP1SS
HIINTERVAL[7:0]
U
OR2
WEELIOR_1
PWM
FIIEOMARK
PHI-GEN
0
~11
H1i
SETDEL
SETDELTAINTERVAL17..
TAINTERVA4l7:01,
ERR-T,-PWM
DELTA,(J
FREG, MASK
DILT
Based on the
fr one phaseof ti
INPUTS:
inpu
this ock
signals.
Sll
25azCLCK Colk signal
e
WHEELR OR
signai
generates the PWM gaing OUTPUTS:
PWMOUT: Gaing signal for
DUYOVERSHOOT:sethdtyydeofth Ph inEM
of posiln
SET_PHLNTERVA Set the numter
DUTYMAX:MaxnMu-
one of the
uvIN
phases
of
tie
WTr
new madkodlan
at25MHz
of the ecrmenial posionencoder
:Oneof
mossing of the phase
the zero
aEts
CURRENTZEROCROSS: Signat
SETDUTY_CYCLE: Set heditycyeofVbase
SETDELTAINTERVAL Set ie
F RESET: Fored ReSetignal
GENOU
numer
i
of
y
nS%
&"
tIat Trm
Sts for
posion
se
delta
PH
culen
AM Fevas
77 T
j7ssuslawe
Project: ALTERI
Mamo MmOULATORVO_
10015
D(s:
11/J101
Figure D.2: Block that generates the gating signals for one of the MOSFET'S for the SMR
Is
1-
CID
$143
DELTA-OUT
AND2
$121
SETDELTAINTERVAL[7:0]
COMPMB
IA(71
GT
L11
lb
LT
c-I.
0
$|11
ASYNC CTRL
$13
PWVM..
0-
--
_ZEE*
CURFN
FR
q.MW
a-
D
Q
__
,C
D
$8
FD
Q
INV
C
AD
OLOCK
owq
C.1
WEEELA
Genemtes
InpLes
--
$117
FD
Deta Intev after Zero-Current Ccndikion
Zero Crossing Ddecor
Sgr at PWM freq ir tre Pwt blok Generator
+WHEEL-ROR!: One othf two sias prodied by he poution Sensor
+CurrenLzero _aoss:
PWMFreqMark:
Set
deantevag:
t
Nrber of pobon
ls ftat w onform le dea rt
Juan Rivas
LEES, MFT
77 Massauseetis ave 10015
Date Last Modified: 619/02
Prmject ALTER1
Macro: DELTAGEN
Date: 11/30/01
Figure D.3: Block that generates the 6 interval for the new modulation
'HII NTERVAL[7:0]
GT
$111
$110
A
L3
qOiO
qNV
OR2
$15
-
CUIRREWZERO-R
.
D
D
PHI0M
$19
ASYNCCTRL
6
FD
LT
B(7O
.--
j3
9
AND2
a
INV
rLOCK
,CUNT_ ER
WHEELFL
0-
Grumales
Phknftd afer Zemo-CU Cndon
+Cu lnterma oss: Zaro Cossrg De(eIr
PWM_Freq_Mark Sigial al PWMA b94 fmom to Perntbodc Ownealor
+WHEE-_FOR_1:
Cne
at to twm slis pmduc
d by to poition Swwr
SeLdltaJnterapostion sits at vhdie ph iw start
Q
Juan Rivas
LEES, MrT
77 Massadiuseas ave 10015
Date Last Modfied: 12/3/01
Pftject ALTER1
Macr- PHLGEN
Date: 11/3W01
Figure D.4: Block that generates the <D interval for the new modulation
Ql
PWM Ceakr
"~p Signav
(25Miz for 10OKz O *A freqency)
+WYMAXUMIT: 238 out of 250 lor 95% nf nun Dy Cyde
as arrpmd
wkh Wvld to
PMWMUTYCYCLE 8 bk rurlbv
+ C
cowi
DigWa PWM Outpo
DgiM
PWM
#W go-s Lp -s PWM
VWa gows dam as PWM-d
Sinaat
PWM
freq.
+PWVMOUTUJP
+PWMOUT_ DOWN
+PWM_freqMadt
(-Min
edge
cLyqd
_ycyde
an )
L6
wM
g-s Lip
go-
Lp
$14 COMPM8
7:20j-
SULW701
:0
A[7:0]
.
O
GT
LT
s15
7:0]
$12COMPM8
A[T.0
L8
SUM[7 0,L
C7
0-O~fB77
AND2
$13
IN
-1
CO
GT
LT
00
-
DUTY_-MAXUIMITr7k~
FD8CE
DU TYCYCLE[7:0]
Drr0q
Aj7q
ANC2
LT_
q7
-
E-1
CE
>C LR
S$18
_ r7
Juan Rivas
LEES, MFT
77 Massachuseds ave 10-015
Date Last Modified: 1/7/02
Figure D.5: Block that generates the PWM structure
ProjeCt ALTER1
Maco: PWMBLOCK-GEN
Date: 11/30/01
Bibliography
[1] J.M. Miller. "Multiple voltage electrical power distribution system for automotive applications". Washington, DC, August 1996. Intersociety Energy Conversion Conference
(IECEC).
[2] J. M. Miller and P. R. Nicastri. "The next generation automotive electrical power system architecture: Issues and challenges". pages 115/1 - 115/8 vol.2. AIAA/IEEE/SAE,
31 Oct- 7 Nov 1998.
[3] J.M. Miller, D. Goel, D. Kaminski, H.P. Sh6ner, and T.M. Jahns. "Making the case for
a next generation automotive electrical system". IEEE/SAE InternationalConference
on TransportationElectronics (Convergence), (SAE paper 98C-0006), 1998.
[4] J.G. Kassakian. "Automotive electrical systems- the power electronics market of the
future". In Proceedings of IEEE Applied Power Electroics Conference and Exposition
(APEC 2000), volume 1, pages 3-9, New Orleans, February 2000. IEEE.
[5] V. Caliskan, D.J. Perreault, T.M. Jahns, and J.G. Kassakian. "Analysis of three-phase
rectifiers with constant-voltage loads". In Power Electronics Specialists Conference.,
volume 2, pages 715-720. PESC 99, 1999.
[6] D.J.Perreault and V. Caliskan. "Automotive power generation and control". Technical
Report TR-00-003, LEES Technical Report, Massachusetts Institute of Technology,
Cambridge MA, May 24 2000.
[7] D.J. Perreault and V. Caliskan. "A new design for automotive alternators". IEEE/SAE
International Congress on Transportation Electronics (Convergence), (SAE paper
2000-01-C084), 2000.
[8] Peter Sommerfeld. "active integrated rectifier regulator". MIT Consortium ProjectReports, MIT/Industry Consortium on Advanced Automotive Electrical/ElectronicComponents and Systems, March 2003.
[9] Atsushi Umeda. US005726557A. United States Patent Office, 1998.
[10]
S. C. Tang, T.A. Keim, and D. J. Perreault. "Thermal modeling of Lundell alternators".
IEEE Transactions on Energy Conversion, Submitted.
[11] S. C. Tang, T. A. Keim, and D. J. Perreault. "Thermal analysis of lundell alternator".
MIT Consortium ProjectReports, MIT/Industry Consortium on Advanced Automotive
Electrical/ElectronicComponents and Systems, Summer 2002.
-
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