Australasian Universities Power Engineering Conference (AUPEC 2004)
26-29 September 2004, Brisbane, Australia
MATRIX CONVERTER FOR ISA 42 V POWERNET VEHICLE ELECTRICAL
SYSTEMS PART II: SIMULATED PHYSICAL IMPLEMENTATION
Keping You, M. F. Rahman
The School of Electrical Engineering and Telecommunication
The University of New South Wales, Australia
Abstract:
In this paper the feasibility of using matrix converters in (Integrated Starter/Alternator) ISA 42 V PowerNet vehicle
electrical system has been solidly proved by exploring the simulated physical implementation, where simple openloop control scheme and Venturini-PWM modulation for bidirectional operations were used to reveal the potential
advantages of the proposed three-phase ac dc bidirectional matrix converter. Results were presented to offer the
facility in assessment of the proposed converter in term of application-merit, and were sufficient to support the
proposed converter solution as a good candidate for ISA 42 V vehicle electrical system.
1
INTRODUCTION
The purpose of this article is to provide simulated
physical implementation result to verify the theoretical
feasibility worked out in Part I of this paper.
Vo1
Vi1
s11
Since this paper is focusing on the feasibilityverification of applying new converter to an emerging
application area, it is necessary and sufficient to design,
in an open-loop control scheme to achieve very basic
requirement as:
s21
s31
Vi 2
Vo 2
s12
s22
s32
Vi3
Vo3
s13
1) tight dc-voltage regulation in rectification with
fast transient response
s23
s33
2) high power factor
Figure 2-1 a three-phase ac dc bidirectional matrix converter
3) sinusoidal current and voltage in inversion
operation
[Vo (t )] = M (t )[Vi (t )]

T
[ I i (t )] = M (t )[ I o (t )]
1 = M (t )1

4) bidirectional operation
The behavior of torque and speed related to inversion
operation has not been taken into account because a)
whatever a pattern of torque and speed is needed, the
requirement for the converter to generate the sinusoidal
waveforms of voltage and current is always there, and
(b) as far as the converter is able to produce the
expected waveforms, the control of torque or speed can
be implemented by a separated controller.
2
(1)
where
 m11 (t ) m12 (t ) 1 − m11 (t ) − m12 (t ) 
M (t ) =  m21 (t ) m22 (t ) 1 − m21 (t ) − m22 (t ) 
 m31 (t ) m32 (t ) 1 − m31 (t ) − m32 (t ) 
PRINCIPLE OF OPERATION
(2)
The principle based on matrix converter theory [1] [3]
[4] was described in the part I. The mathematic model
of the three-phase ac dc bidirectional matrix converter
[2] is re-presented here for reference.
1
2 Vo 1
7
1
1
( cos(ωi t ) + cos(2ωit ) − cos(4ωi t )) +
36
36
3
3 Vi 2
2 Vo 1
2π
7
2π
1
2π
1
m12 (t ) =
( cos(ωit − ) + cos(2ωit + ) − cos(4ωit − )) +
3
36
3
36
3
3
3 Vi 2
Vi ,123 , I i ,123 ,
m11 (t ) =
ωi , φi ,θ i
T ,ω
Vdc , I dc
2 Vo
7
1
1
( zero + cos(2ωit ) − cos(4ωit )) +
36
36
3
3 Vi
2 Vo
7
2π
1
2π
1
m22 (t ) =
( zero + cos(2ωi t + ) − cos(4ωit − )) +
36
3
36
3
3
3 Vi
m21 (t ) =
2 Vo 1
7
1
1
(− cos(ωit ) + cos(2ωi t ) − cos(4ωit )) +
36
36
3
3 Vi 2
2 Vo 1
2π
7
2π
1
2π
1
(− cos(ωit − ) + cos(2ωit + ) − cos(4ωit − )) +
m32 (t ) =
3
36
3
36
3
3
3 Vi 2
m31 (t ) =
 3

V


Vo + o cos(3ωi t ) 

V cos(ωint )

2
2
3


Vi1 (t )   i1



2π
V
[Vo (t )] =  zero + o cos(3ωit )  , [Vi (t )] = Vi 2 (t )  = Vi 2 cos(ωint + )  ,


3
2
3


Vi 3 (t )  
4π 
 3

V
Vi 3 cos(ωint + ) 
 − Vo + o cos(3ωi t ) 

3 

2 3
 2

Vi ,123 , I i ,123 ,
ωi , φi , θi
 3

Io


cos(3ωi t + φ3ωi ) 
 Io +
 I in cos(ωint + φi )

2
2
3


 I i1 (t )  



2π
I
+ φi )  , [ I o (t )] =  zero + o cos(3ωi t + φ3ωi )  ,
[ I i (t )] =  I i 2 (t )  =  I in cos(ωint +


3
2 3


 I i3 (t )  

4π
 3

I
 I in cos(ωint +
+ φi ) 
−
I o + o cos(3ωi t + φ3ωi ) 


3
 2

2 3
,
The dc quantities relates to the amplitude of
corresponding phase quantities as
Vo =
1
Vdc
3
(3)
Io =
2
I dc
3
(4)
where
φi , φo
Vdc , I dc
(b)
Figure 2-2 Simplified Block diagram of (a) complete ISA 42 V
PowerNet electrical system, (b) simplified system for simulated
implementation of the three-phase ac dc bidirectional matrix
converter
3 POWER STAGE DESIGN AND SIMULATED
PHYSICAL IMPLEMENTATION
The design is illustrated on a proposed 42 V PowerNet
converter for the following specification:
Rated power: 6 kW (Max: 10 kW)
The voltage transfer ratio is limited as
Vo I i icos φi
3
=
≤
Vi I o icos φo
2
(a)
dc output voltage:
Vdc =42 V
ac rms line-to-line voltage: 3 × 50 V, (the 3 ×
415 V has also been used for reference only)
(5)
ac frequency range: 50 – 500 Hz (1:10)
are set to zero to achieve zero input
From these specifications, the amplitude of input phase
voltage is
current displacement.
A simplified block diagram of the proposed system is
shown in figure 2-2, where the figure 2-2(b), an openloop system, performance of which depends heavily on
the low frequency modulation matrix is in our
consideration. Without any particular controller the
inherent properties of a plant can be studied directly and
be revealed to an extent very close to the truth.
Vi =
50 × 2
= 40.8 V
3
(6)
The selection of 3 × 50 V is based on such a
consideration that the line-line terminal voltage can
comply with the general demand of safety standard (e.g.
50 V rms ac voltage, by IEE-60950 series), and
meanwhile, can satisfy the requirement by the matrix
theory – to bound the output phase voltage, i.e.
3 × Vi ≤ 2 × 50
Vo
3
≤
Vi
2
2
(7)
(8)
current orientation. The superscript * denotes the
desired value.
Substitute equation (3) into (8), and by the specification
of Vdc , the volts-value range of Vi in this consideration
is
28 ≤ Vi ≤ 40.8
m11
m12
m13
m31
m32
m33
ωi
(9)
In brief the limit of 40.8 V is selected only for the sake
of safety.
If proper insulation is assumed available and applicable
the amplitude of input phase voltage can be enlarged to
the extent allowed by the applicable lower limit of
modulation index. The 3 × 415 V is then selected as an
extra reference, can be seen in figure 5-3.
ωi*
ωi
3.1 Switching frequency
100 kHz is selected. The consideration is that (a) it is
allowed by existing commercialize microprocessor
system, (b) it enables the high power density design,
and (c) although it may need the aid of ZVS (Zero
Voltage Switched) technique [8] physically, a
simulation without ZVS does not lose the generality in
term of high frequency switching performance since
switching loss was kept unknown for this stage.
Figure 4-1 diagram of modulator and mode selector
4.2 Pulse generator design
To ease the illustration, a brief description about the
related principle based on Venturini-PWM [1] [4]
employed by matrix theory has to be presented before
giving out the design solution. Space Vector PWM
approach can also be presented but has to be ignored
here for the limit length of this paper.
3.2 Input/output filters
The single-stage low pass filter was placed at both input
and output terminals. The filter resonant frequency is
selected at 5.6 kHz which is very lower than the preset
bandwidth at 25 kHz according to the existence theorem
[4]. The capacitance is C =22 µ F , and inductance
sij represents each switch connecting different input
line denoted by subscript j to one and only one output
line denoted by subscript i , mij represents the
Let
36.715 µ H . The determination of the exact values is
performed in several iteration, and may be further
adjustable (should keep the capacitor value at a nominal
one) in experimental design.
corresponding switching duty ratio, i.e. the element of
the low frequency modulation matrix, T is the
switching period, mijT thus the width of corresponding
pulse of corresponding switching cycle.
3.3 Power switches
n
Ideal switches with 4.5 mΩ ON resistance were used
to simulate a commercially available MOSFET with 75
V, 209 A, and 4.5 mΩ ON resistance. This is
reasonable since ZVS and switching loss were not in
consideration for verification of the feasibility.
T =constant,
∑m
j =1
= 1 is the basic constraint for the
ij
behavior of the switching action.
The event occurs under an ideal condition during a
whole cycle period can be sequentially depicted as that
in the lower part of figure 4-2
4 CONTROL AND MODULATOR DESIGN
AND
SIMULATED
PHYSICAL
IMPLEMENTATION
where
tstart , sij , k : calculation
{tstart , sij ,k , mij ,k , T }
n
tstart , sij , k = k iT − T i∑ mih ,k
An open-loop control scheme for both rectification and
inversion operation was implemented in a less complex
way that was proved necessary and sufficient for the
verification of the theoretical feasibility.
n
mij : calculation
h= j
k : counter
T : cnt
tstart , sij = T − T i∑ mih
h= j
k iT
mi 2 iT
mi1 iT
mi 3 iT
4.1 Modulator and mode selector
(k − 1)iT
The modulator was based on the instantaneous model
shown in (2), where one trigonometric function, four
adders, and one multiplier are used.
k −1
The sign of dc current (CS) was used by the mode
selector to switch the modulation between voltage and
3
k
k +1
t
Figure 4-2 diagram of the principle of Venturini-PWM pulse
generator
Synchronously rotating reference frame transformation
K se [6] was used to offer the modulator the amplitude
Any rectangle pulse has four elements including
amplitude (Height), pulse-width, frequency, and phase
(starting position/time). To generate the right switching
driving signal is exactly the process of controlling the
four elements according the requirement of switching
operation. In most cases of PWM modulation the
amplitude and frequency for a specific modulation is
always keep unchanged. The pulse-width and phase
consist of the two-freedom space for a PWM pulse.
of ac phase quantities.
So for the implementation of Venturini-PWM it is
necessary to incorporate pulse-phase control technique,
as shown in the upper part of figure 4-3, into the pulse
generator.
5 RESULTS OF SIMULATED
IMPLEMENTATION
Vi
ωi
g i1
mi 2
gi 2
mi 3
gi 3
θi
Figure 4-4 synchronization and synchronous transformation
PHYSICAL
Results and necessary description are given in this
section.
A pulse generator based on above principle then can be
easily achieved by asynchronous sequential digital
circuit diagram of which shown in figure4-3.
mi1
K
e
s
5.1 Effectiveness of input/output filters
The effectiveness of LC input/output filter is verified by
input ac current.
40
30
mi ( n −1)
g i ( n −1)
min
g in
Current before filtering(A)
20
Figure 4-3 diagram of switching pulse generator
In Figure 4-3 the pulse generator can converter a dutyratio to a fixed-height pulse with the input duty-ratio at
a desired fixed frequency. The trigger is used to
implement pulse-phase control. gij denotes a pulse
10
0
-10
-20
-30
-40
0
0.01
Time (s)
0.02
0.01
Time (s)
0.02
output.
4.3 Synchronization
transformation
and
40
synchronous
30
Synchronization is compulsorily needed in an openloop control scheme involving three-phase ac
quantities. It is because two implications are inherently
with the matrix converter theory, and they are necessary
and sufficient for converting a given set of signals to a
desired set of signals. They are
ƒ
Current after filtering (A)
ƒ
20
Low frequency modulation matrix must
synchronize the first input phase voltage in
positive phase sequence.
10
0
-10
-20
-30
The sequence of rows/columns of low
frequency modulation matrix/its transpose
must restrictively be corresponding to the
sequence of input signals.
-40
0
Figure 5-1 ac phase current before/after filtering (rectification
operation with
Phase-locked loop (PLL) was used to implement the
synchronization.
4
f i = 100
Hz)
5.2 Tight dc-voltage regulation in rectification
operation with fast transient response
current. (b) Input ac phase-current
ii ,a
FFT analysis, (c) FFT
analysis of output dc voltage
The figure 5-2 (a-c) shows a rectification operation with
phase-voltage arbitrarily selected at 120 V. Besides the
good performance of output voltage regulation, low
frequency harmonics were effectively suppressed.
Vdc
340
300
In figure 5-3 the operation under the step-changed
phase voltage from 40 V to 340 V is depicted.
ac voltage phase a
Voltage ( V ) Current ( A )
190
130
dc output current
100
output dc current
100
output dc voltage
42
0
-100
Voltage (V) Current ( A )
-190
dc output voltage
42
-300
-340
0
0.01
0.02
0.03
0.04
0.045
0.05
Figure 5-3 Rectification operation under condition of
step change in amplitude of phase voltage, within 15
ms, from 40 V to 190 V and to 340 V.
ac input current phase a
-50
-100
5.3 Fast regulation and, fast transient response to
sudden load dump
ac input voltage phase a
-130
0
0.002 0.004 0.006 0.008 0.01 0.012 0/014 0.016 0.018 0.02
Time (s)
(a)
Magnitude based on "Base Peak" - Parameter
0.015
Time (s)
0
The performance of dc output voltage when load dump
happens is one of the important aspects highly
concerned by the 42 V PowerNet electrical systems
An extreme worse case, a sudden load dump at 50 A
(from 105 A to 55 A) occurred during the very first
cycle of ac inputs, was simulated, and the result was
shown in figure 5-4. The transient was very short and
the overshoot of voltage was still less than 70 V, which
is still the safety dc voltage, comparing with such a big
load dump. In practice this voltage spike can be
clamped by means of low cost transient voltage
suppressor (TVS).
25
20
15
10
5
0
0
1
2
3
4
6
8
10
12
Order of Harmonic
14
16
18
(b)
100
80
Io, output dc current
60
40
Voltage (V) Current ( A )
Magnitude based on "Base Peak" - Parameter
0
-0.05
Vdc, output dc current
20
0
Ii, input ac current, phase a
-20
-40
-0.1
-60
Vi, input ac voltage, phase a
-80
-0.15
-100
-120
-0.2
0
2
4
6
8
10
12
Order of Harmonic
14
16
18
0.005
0.01
Time (s)
0.015
0.02
Figure 5-4 Very fast response and tight voltage regulation in an
extreme worse case of load dump at a magnitude of 50 A
20
(c)
A relatively light sudden load dump at 10 A is much
more similar to the case in real world. Figure 5-5 shows
the transient response of dc output voltage to a sudden
load dump of 10 A. By the figure 5-5 (b), a much closer
view of the transient period, the short spike of dc
voltage is less than 46 V, marginally complying with
Figure5-2 Rectification operation (a) the waveforms of ac phase
voltage and current and corresponding output dc voltage and
5
the specification defined in the draft standard of 42 V
vehicle
electrical
system.[9][10]
80
Phase Voltage ( V ) Phase Current ( A )
60
120
105
Io, output dc current
95
Voltage ( V ) Current ( A )
84
Vdc, output dc current
46
42
35
0
Ii, input ac current, phase a
-50
Vi, input ac voltage, phase a
20
0
-20
-40
-60
-80
-100
-120
40
0
0.002
0.004
0.006
0.008
0.01
Time (s)
0
0.005
0.01
Time ( s )
0.015
0.02
(a)
(a)
1
THD, Fundamental Frequency = 500 Hz ( 0.002 s)
105
Io, output dc current
95
Voltage ( V ) Current ( A )
84
Vdc, output dc current
46
42
35
Ii, input ac current, phase a
0
Vi, input ac voltage, phase a
0.01
0.0104
Time ( s )
(b)
(a) overview, and (b) an extended view within 0.4 ms (400
1 + THD 2
0.6
0.5
0.4
0.3
0.2
0.1
0
0.002
0.004
0.006
0.008
Time of Calculation (s)
Invalid result in the first cycle (0 - 0.002 s)
0.010
Figure 5-6 Observation of power factor in rectification with 500
Hz three ac input by (a) input current displacement, and (b)
online calculated THD
From the figure 5-6 (a) the input phase waveforms
V1 (t ), I1 (t ) is displayed. The phase current
displacement from the phase voltage was observed
around zero, then the IDF (Input Displacement Factor)
was believed to be almost 1; and the on-line calculated
THD (Total Harmonic Distortion) result in figure 5-6
(b) shows the THD is zero after the instant at 0.002 s,
before which the rms value of the fundamental
waveform was not available.
1
0.7
(b)
µs )
5.4 High power factor
pf = IDF ×
0.8
0
Figure 5-5 Performance of open-loop tight output voltage
regulation during a 10 A load dump
By
0.9
5.5 Inversion operation with satisfied Sinusoidal
waveforms of current and voltage
In this case a three-phase Y connected reactive load
with normal phase-phase voltage at 84 Vrms, active
power at 10 kW, and inductive reactive power at 1 W
was used, and a dc current source was used.
A normal inversion operation with a stiff current source
shown in Figure 5-7 (a), in which the input ac current
was bounded by dc output current, agreeing with the
matrix converter theory.
, the unit power factor
While in real life, the batteries are not able to be ideal
current sources, the magnitude of charging/discharging
current is changed by the internal electro-chemical
processing with respect to real time. It is possible to
approximate the current-shrinking behavior during the
high-current discharging period by a down-ramp
was believed achieved.
6
the dc terminal voltage a lot. This, again, confirmed the
tight regulation capability of the matrix converter.
changing of the magnitude of current, as shown in the
following figure 5-7 (b). The result was still satisfied.
The overshot voltage during the initial transient period
can be overcome by TVS’s available in market.
150
109
dc current
200
78
dc voltage
84
42
ac current phase a
Voltage (V) Current (A)
Voltage (V) Current ( A )
150
dc voltage
42
0
-31
-44
-50
ac voltage phase a
ac current
-84
-120
ac voltage
dc current
-100
-200
0
0.01
Time (s)
150
ac current phase a
6
dc voltage
50
0.002
0.003
0.004
0.005
Time (s)
0.006
0.007
0.008
0.009
0.01
CONCLUSION
1) Bidirectional operation
ac voltage phase a
-120
0.001
The objective converter proposed in this paper offers
the following distinct features:
0
-84
0
Figure 5-8 Bidirectional operation. A dc battery and resistive
load at dc side, and a three-phase resistive-inductive in
symmetric series connection with a Y connected three phase ac
voltage-source at ac side.
200
84
-150
0.02
(a)
Voltage ( V ) Current ( A )
0
-10
dc current
2) Tight output dc voltage regulation with fast
transient response
-200
0.01
Time (s)
3) Unity three-phase ac input power factor
0.02
4) No low-frequency harmonics on either input or
output; and
(b)
Figure 5-7 (a) normal inversion operation with a stiff current
source (b) inversion operation with a ramp-shrink current
source
5) Single-stage power conversion without
intermediate energy storage
5.6 Bidirectional operation
Implementing the four-quadrant switch by MOSFE the
three-phase ac dc bidirectional matrix converter is a
good candidate for medium-power, high voltage
application. In high power application the IGBT can be
used.
Figure 5-8 described an example of bidirectional
operation beginning from inversion ending with
rectification, the pattern of which is corresponding to
the process of starting-generating operation in a vehicle.
Its property of high-voltage application enables the
design-base of the ISA machine in a high-voltage/lowcurrent pattern, therefore, will definitely, in short term,
expand the range of options for system
commercialization, and in the future, will benefit the
sustainability of system efficiency as the power
capacity increasing.
During the inversion only a normal dc voltage source,
36 V, was used for simplified procedure, and this
treatment is sufficient for observing the bidirectional
operation.
Current sign was successfully used as the mode selector
to switch the modulation matrix between voltage-source
and current-source orientation.
So this solution of three-phase ac dc bidirectional
matrix converter can meet the philosophy of reducing
fuel consumption by introducing ISA 42 V vehicle
electrical system in a sustainable way [7].
The dc side transferred power to ac side before the
instant of 0.003 s, at which the three-phase voltage
source began to plug-in, then the current sign changed,
the dc output voltage consequently started to be
regulated at the desired magnitude. At 0.006 s, the
amplitude of three-phase voltage step up to around 109
V, causing a surge current at dc bus but unable to affect
REFERENCE:
[1] M. Venturini, "A new sine wave in, sine wave out,
conversion technique eliminates reactive elements,"
7
in Proc. Powercon 7, pp.E3-1-E-15(San Diego,
CA), 1980
[6] Krause, Wasynczuk, Sudhoff, “Analysis of Electric
Machinery” IEEE press, 1995, New York
[2] Holmes, D.G.;"A unified modulation algorithm for
voltage and current source inverters based on ACAC matrix converter theory", Industry Applications,
IEEE Transactions on , Volume: 28 Issue: 1 , Jan.Feb. 1992, Page(s): 31 -40
[7] Kassakian, J. G., H. C. Wolf, J. M. Miller and
C.J.Hurton, 1996, “ Automotive Electrical
Systems circa 2005,” IEEE Spectrum, Aug. 1996,
pp. 22-27
[8] V. Vlatkovic, D. Borojevic, and F. C. Lee, "A zerovoltage-switched, three-phase isolated PWM buck
rectifier," IEEE Trans. Power Electron., vol. 10, pp.
148-157, Mar. 1995
[3] Alesina, A.; Venturini, M.; “Intrinsic amplitude
limits and optimum design of 9-switches direct
PWM
AC-AC
converters”,
Power Electronics Specialists Conference, 1988.
PESC '88 Record., 19th Annual IEEE , 11-14 April
1988,Pages:1284 - 1291 vol.2
[9] 42 V WORKING DRAFT Work Group,
“Conditions for Electrical and Electronics
Equipment for a 42 V PowerNet- Condition 2:
Electrical Loads”, 2000.
[4] Alesina, A.; Venturini, M.; “Solid-state power
conversion: A Fourier analysis approach to
generalized transformer synthesis”Circuits and
Systems, IEEE Transactions on , Volume: 28 ,
Issue: 4 , Apr 1981,Pages:319 - 330
[10] Hans-Dieter Hartmann, "The 5th Report FAKRA
AA-I 3/AK14 (May 27.02) Standardization of
42V,"
http://www.bordnetzforum42v.de/bordnetz/normung_e.html, May 27.02
[5] Holmes, D.G.; Lipo, T.A.; “Implementation of a
controlled rectifier using AC-AC matrix converter
theory”; Power Electronics, IEEE Transactions on ,
Volume: 7 , Issue: 1 , Jan. 1992;Pages:240 - 250
8