A New Family of Matrix Converters
R. W. Erickson and O. A. Al-Naseem
Colorado Power Electronics Center
University of Colorado
Boulder, CO 80309-0425, USA
rwe@colorado.edu
Abstract—A new family of matrix converters is introduced, that employs relatively simple
voltage-clamped buses and can generate multilevel voltage waveforms of arbitrary
magnitude and frequency. The basic configuration includes a nine-cell matrix that uses fourquadrant switch cells. Each four-quadrant switch cell resembles a full-bridge inverter and
can assume three voltage levels during conduction. Semiconductor devices in a switch cell
are clamped to a known constant dc voltage of a capacitor.
Control of the input and output voltage waveforms of the proposed converter can be
achieved through space vector modulation. Simulation results show how the converter can
operate with any input and output voltages, currents, frequencies, and power factors while
maintaining constant dc voltages across all switch cell capacitors.
1
Comparison of conventional matrix converter
with proposed new family of converters
Conventional
matrix converter
Proposed new
matrix converters
Voltage conversion
ratio Vout/Vin
Buck only:
Vout ≤ 0.866Vin
Buck–boost:
0 ≤ Vout < ∞
Switch commutation
Coordination of
4-quadrant switches
Simple transistor +
freewheeling diode
Bus bar structure
Complex
Modular
and simple
Multilevel operation
No
Possible
Utility-side
filter elements
AC capacitors
Inductive
Machine-side
filter elements
Inductive
Inductive
2
II. Converter Derivation and Operation
Basic Configuration of New Matrix Converter
Basic converter
Modular switch cell
Symbol
n
b
Three-phase
ac system 1
Realization
ic
Three-phase
ac system 2
c
A
iA
+
–
a
ib
–
+
B
iB
+
–
ia
–
+
A
iC
D1
a
Q3
D3
D2
A
D4
Q2
Q4
• Converter contains a matrix of switch cells
N
C
Q1
• Switch cells include dc capacitors
+
–
–
+
a
• Input and output ports include inductive
elements
3
Operation of Switch Cell
• DC capacitor voltage = V
• When semiconductor devices conduct,
switch cell can produce instantaneous
voltages vaA of +V, 0, or –V
• Switch cell can block voltages of
magnitude less than or equal to V
Q1
D1
a
Q3
D3
D2
A
D4
Q2
Q4
• Diodes clamp maximum transistor
voltage to V
• Break-before-make operation: it is
allowed to turn off all transistors in the
converter; diodes are able to provide a
conducting path for inductor currents
4
• Modular switch cells lead
to modular bus structure:
simple H-bridges
Branch connections
n
ia
• 81 valid combinations of
conducting branches
a
• At rated voltage: two-level
operation
• At low voltage: three-level
operation is possible
–
+
ib
b
–
+
Three-phase
ac system 1
ic
Three-phase
ac system 2
c
A
iA
+
–
–
+
B
iB
+
–
• To avoid interrupting the
input and output inductor
currents, five of the nine
branches of the matrix must
conduct at any instant
C
5
iC
+
–
N
Example
• Three valid choices of
switching combinations, for
V = 240 V and all for the
same choice of conducting
branches
UTILITY SIDE
(a)
MACHINE SIDE
Branch Aa
-240V+
Phase A
VAB = 0V
V+
240 +
VCA = 0V Phase B
a
ch B
0V
Bran
-24
a
+
C
VBC = 0V
0V
ch
ran ch Cb -24
B Bran
Phase C
• In each case, the four
nonconducting branches
block voltages less than or
equal to 240 V
(b)
Phase A
VAB = 0V
VCA = 0V
Phase B
VBC = 0V
• When a line-to-line voltage
of 2V = 480 V is produced at
one side of the switch
matrix, then the voltages at
the other side must be zero
Phase C
(c)
Phase A
VAB = 0V
VCA = 0V Phase B
VBC = 0V
• Number of valid switching
combinations: 19683
Phase C
6
Branch Cc
Phase a
Vab = 0V
Phase b
Vbc = 0V
-240V+
Phase c
-240V+
Phase a
+
0V
-24
+
0V
-24
+
0V
-24
Vab = 0V
0V
Vca = 0V
Phase b
Vca = -240V
Vbc = 240V
Phase c
-240V+
Phase a
+
0V
4
2
+
0V
-24
+
0V
-24
+240V-
Vab = 0V
Phase b
Vbc = 480V
Phase c
Vca = -480V
Increasing the number of levels
n
Series connection of
switch cells
–
+
–
+
ia
ib
–
+
Three-phase
ac system 1
ic
For this example—
At low voltage: five-level
operation is possible
Sharing of voltage stress:
semiconductor blocking
voltages are reduced by
factor of two
7
c
A
iA
B
iB
C
iC
+
–
b
+
–
a
Three-phase
ac system 2
+
–
At rated voltage: three-level
operation
N
III. Control
Space vectors of basic converter
q
• Derived space-vector control
algorithm for proposed new
converters
(0, 2 3 Vcap)
(1.5Vcap, 1.5 3 Vcap)
• Showed that dc capacitor voltages
can be controlled
(0, 3 Vcap)
(3Vcap, 3 Vcap)
(1.5Vcap, 0.5 3 Vcap)
• Developed extensive computer
program to verify operation of
control algorithms
(3Vcap, 0)
8
d
Space Vector Control
VREF = d 1V1 + d 2V2 + d 0V0
q-axis
V1
(0,√ 3Vcap)
F
60°
(0,0)
V
d0V0 0
V2
(1.5Vcap, 0.5√ 3Vcap)
RE
V
d1V1
φ
3 = V
REF sin (φ)
2
VREF
2
sin (φ) = M sin (φ)
d1 =
3 V1
d 2 V2 3 = VREF sin (60° – φ)
2
VREF
2
sin (60° – φ) = M sin (60° – φ)
d2 =
3 V2
d 1 V1
d2V2
d-axis
d0 = 1 – d1 – d2
VREF
VREF
2
2
M=
=
3 V1
3 V2
Space vector control can be
applied to the proposed new
converters
9
Simulated Waveforms:
Basic converter in a wind power application
Space vector control algorithm
Operating point #1
Utility side:
60 Hz, 240 V, p.f. = 1
Generator side:
25 Hz, 240 V, p.f. = 1
Smooth waveforms: line
currents
PWM waveforms: lineline voltages
10
Simulated Waveforms
Regulation of capacitor voltages within switch cells
—Dashed lines show nominal voltages ± 12%
Operating point #1
11
Simulated Waveforms
Switching states of
each cell
Operating point #1
12
Spectrum, utility-side voltage
Operating point #1
Low switching
frequency of
1 kHz
Utility frequency
= 60 Hz
Harmonics are
sidebands of
switching
frequency
Harmonic order
13
Spectrum, utility-side voltage
Operating point #1
Switching frequency
increased to 20 kHz
Utility frequency =
60 Hz
Harmonic order
14
Simulated Waveforms
Change of operating point
Operating point #2
Utility side:
60 Hz, 240 V, p.f. = 0.5
Generator side:
6.25 Hz, 60 V, p.f. = 1
Smooth waveforms: line
currents
PWM waveforms: lineline voltages
15
Simulated Waveforms
Operating point #2
Regulation of capacitor voltages is maintained at nonunity power factor
16
IV. Conclusions
•
Introduction of a new family of matrix converters, that are fundamentally
different from the traditional matrix converter
•
New converters can both increase and decrease the voltage amplitude
and can operate with arbitrary power factors
•
Extension to multilevel switching can be attained with device voltages
locally clamped to dc capacitor voltages
•
Demonstration of space vector modulation to control the input and
output voltage waveforms
•
It is also demonstrated that the controller can stabilize the dc voltages
of the capacitors
•
Operation of the basic version of the new family of matrix converters
has been confirmed.
17
References
[1] A. Nabae, I. Takahashi, and H. Akagi, “A New Neutral-Point Clamped PWM Inverter,”
IEEE Trans. Industry Applications, vol. IA-17, No. 5, Sept./Oct. 1981, pp. 518-523.
[2] P. Bhagwat and V. Stefanovic, “Generalized Structure of a Multilevel PWM Inverter,” IEEE
Transactions on Industry Applications, vol. IA-19, no. 6, Nov./Dec. 1983, pp. 1057-1069.
[3] F. Z. Peng and J. S. Lai, “A Multilevel Voltage-Source Inverter with Separate DC Sources,”
Proceedings IEEE Industry Applications Society Annual Meeting, 1995, pp. 2541-2548.
[4] O. A. Al-Naseem, “Modeling and Space Vector Control of a Novel Multilevel Matrix
Converter for Variable-Speed Wind Power Generators,” Ph.D. thesis, University of
Colorado, April 2001.
[5] A. Alesina and M. Venturini, “Analysis and Design of Optimum Amplitude Nine-Switch
Direct AC-AC Converters,” IEEE Transactions on Power Electronics, vol. 4, no. 1, January
1989.
[6] L. Huber and D. Borojevic, “Space Vector Modulated Three-Phase to Three-Phase Matrix
Converter with Input Power Factor Correction,” IEEE Transactions on Industry Applications,
vol. 31, no. 6, Nov./Dec. 1995.
[7] S. Bernet and R. Teichmann, “The Auxiliary Resonant Commutated Pole Matrix Converter
for DC Applications,” IEEE Power Electronics Specialists Conference, 1997.
18