FACTA UNIVERSITATIS (NI Š)
S ER .: E LEC . E NERG . vol. 22, no. 2, August 2009, 245-252
Investigation of Three-Phase to Single-Phase Matrix
Converter
Mihail Antchev and Georgi Kunov
Abstract: A three-phase to single-phase matrix converter is investigated in the present
paper. Based on the state matrix vector, a mathematical analysis of the converter is
performed giving the relation between the sinusoidal line voltage (current) and the
output voltage (current). The results of the investigation are confirmed using computer
simulation of the converter by the program product Cadence PSpice
Keywords: Power Electronics, matrix converter, PSpice simulation.
1 Introduction
development of new methods and circuits for electrical energy conversion
with improved characteristics is a basic way for increasing of the energy efficiency of power electronic converters with respect to mains network. The matrix converters realize a direct conversion of alternating current to alternating current [1,2]. Investigations exist for the electrical motor control, where the frequency
of the output voltage is lower than the frequency of the mains network voltage [3,4].
The single-phase matrix converter is investigated in [5]. The aim of the present paper is the investigation of the three-phase to single-phase matrix converter. The
frequency of the single-phase output voltage is higher than the frequency of the
three-phase line input voltage. Based on the state matrix vector, a mathematical
analysis of the converter is performed giving the relation between the sinusoidal
line voltage (current) and the output voltage (current). The results of the investigation are confirmed using computer simulation of the converter by the program
product Cadence PSpice.
T
HE
Manuscript received on June 14, 2009
The authors are with Technical University of Sofia, Department of Power Electronics, 1156 Sofia,
Bulgaria (e-mail: [antchev, gkunov]@tu-sofia.bg).
245
M. Antchev and G. Kunov:
246
2
Mathematical Description
The circuit for mathematical analysis is presented in Fig. 1a. Bidirectional switches
are used, realized as shown in Fig. 1b and controlled by a corresponding algorithm.
R
SW4
SW1
SW6
SW3
SW2
SW5
S
T
Vout
V D1
V-
V T2
SW
V+
V T1
V D2
N
0
(a)
(b)
Fig. 1. Circuit for investigation. (a) Equivalent circuit. (b) Bidirectional power switch.
The converter is supplied directly by the mains network. The three-phase line
input voltages are described by the following equations:
vR (t) = Vm sin ω t
(1)
2π
)
3
2π
vT (t) = Vm sin(ω t + )
3
vS (t) = Vm sin(ω t −
(2)
(3)
The state of the bidirectional switches - open or closed, can be described in
matrix form in the following way:
[SW ] =
SW 1 SW 3 SW 5
SW 4 SW 6 SW 2
The following dependencies are valid for the elements in (4):
(4)
Investigation of Three-Phase to Single-Phase Matrix Converter
247
SW 1 = SW 4
SW 3 = SW 6
(5)
SW 5 = SW 2
The state of the power devices can be described in matrix form in the following
way:


vR (t)
v+ (t)
SW 1 SW 3 SW 5 
=
vS (t) 
v− (t)
SW 4 SW 6 SW 2
vT (t)
(6)
The single-phase output voltage vout (t) = v+ (t) − v− (t) has the form:
vout (t) = (SW 1 − SW 4)vR (t) + (SW 3 − SW 6)vS (t) + (SW 5 − SW 2)vT (t)
(7)
where:
SW 1 − SW 4 = A1 sin(ωS t) +
∞
∑
An sin(nωS t)
(8)
n=3,5...
SW 3 − SW 6 = A1 sin(ωS t −
∞
2π
2π
) + ∑ An sin(nωS t − )
3
3
n=3,5...
(9)
SW 5 − SW 2 = A1 sin(ωS t +
∞
2π
2π
) + ∑ An sin(nωS t + )
3
3
n=3,5...
(10)
The parameter ωS in (8), (9) and (10) is the commutation frequency of the
bidirectional switches. The coefficient A1 is the magnitude of the commutation
function. The first harmonic of the Fourier expansion of A1 is of the value π4 . The
higher harmonics An have significantly lower magnitudes and can be neglected.
Replacing (8), (9) and (10) in (7), the following dependence is obtained for vout (t):
4
2π
2π
4
vout (t) = Vm sin ω t sin ωS t + Vm sin(ω t − ) sin(ωS t − )
π
π
3
3
2π
4
2π
+ Vm sin(ω t + ) sin(ωS t + )
π
3
3
(11)
The program product CadencePSpice is used for the investigation of the matrix
converter. The voltages on the bidirectional switches are shown in Fig. 2. The
single-phase output voltage vout (t) is presented in Fig. 3.
M. Antchev and G. Kunov:
248
Fig. 2. The voltages on the bidirectional switches.
Fig. 3. The single-phase output voltage vout (t).
3
3.1
PSPICE Simulation of the Electrical Circuit of the Three-Phase to
Single-Phase Matrix Converter
Basic electrical circuit
The electrical circuit of the matrix converter is shown in Fig. 4. The principle
of operation is illustrated using equivalent circuits, corresponding to the respective
intervals, in which the bidirectional switches act.
Investigation of Three-Phase to Single-Phase Matrix Converter
Eg1n E
GAIN = 3
+
-
G1
Eg3n E
GAIN = 3
Q1N
+
-
Rg1n 5
0
+
-
G5
Rg3n 5
0
Q5N
+
-
Rg5n 5
0
Q1P
V
V-B
FREQ = 50Hz
VAMPL = 100V
VOFF = 0V
PHASE = -120
Eg5n E
GAIN = 3
Q3N
+
-
Q3P
Q5P
V
V-A
FREQ = 50Hz
VAMPL = 100V
VOFF = 0V
PHASE = 0
+
-
G3
249
Rout
FREQ = 50Hz
VAMPL = 100V
VOFF = 0V
PHASE = 120
20
V
V-C
V+
V-
Eg4n E
GAIN = 3
0
+
-
G4
Eg6n E
GAIN = 3
Q4N
+
-
+
-
G6
Rg4n 5
0
Eg2n E
GAIN = 3
Q6N
+
-
+
-
G2
Rg6n 5
0
Q2N
+
-
Rg2n 5
0
Q4P
Q6P
Q2P
Fig. 4. Electrical circuit of the matrix converter.
In the interval, in which the most positive is the phase A, the switches SW1 and
SW 4 (SW 4 = SW 1) are active. The duration of this interval corresponds to 1200.
From 0◦ to 60◦ the switches SW6 and SW3 (SW 3 = SW 6) , connected to the most
negative phase B, are active. The switches SW5 and SW2 are non-active. This
allows to simplify the electrical circuit as shown in Fig. 5.
Eg1n E
GAIN = 3
+
-
G1
Eg3n E
GAIN = 3
Q1N
+
-
Rg1n 5
+
-
G3
0
Eg1n E
GAIN = 3
Q3N
+
-
Rg3n 5
0
V-A
+
-
G1
Eg5n E
GAIN = 3
Q1N
+
-
Rg1n 5
0
Q1P
Q3P
+
-
G5
Rg5n 5
0
V-A
Q1P
[+](V-A)max
Q5P
[+](V-A)max
V-B
Rout
V-C
Rout
(V-B)max[-]
Eg4n E
GAIN = 3
+
-
G4
Eg6n E
GAIN = 3
Q4N
+
-
Rg4n 5
0
+
-
G6
(V-C)max[-]
Eg4n E
GAIN = 3
Q6N
+
-
Rg6n 5
0
Q4P
Q5N
+
-
+
-
G4
Rg4n 5
0
Q6P
(0-60)grad
Fig. 5. Equivalent cicuit from 0◦ to 60◦ .
Eg2n E
GAIN = 3
Q4N
+
-
+
-
G2
Q2N
+
-
Rg2n 5
0
Q4P
Q2P
(60-120)grad
Fig. 6. Equivalent cicuit from 60◦ to 120◦ .
The matrix converter is reduced to a single-phase full bridge inverter. The
positive half-wave of the voltage on the load resistor Rout is obtained when SW 1
250
M. Antchev and G. Kunov:
and SW 6 are switched on, and the negative half-wave - when SW 4 and SW 3 are
switched on. From 60◦ to 120◦ the most negative is phase C. In this subinterval the
active switches are SW 1, SW 4, SW 5 and SW 2 (SW 5 = SW 2). The switches SW3
and SW6 are non-active. The equivalent circuit is shown in Fig. 6. The positive
half-wave of the voltage on the load resistor Rout is obtained when SW1 and SW2
are switched on, and the negative half-wave - when SW 4 and SW5 are switched on.
Similar considerations are valid for the next intervals when the most positive are
phase B or phase C.
The basic waveforms, illustrating the principle of operation of the matrix converters are shown in Fig. 7. They are obtained using the CadencePSpice simulator.
The sequence of intervals can be seen, in which two couples of switches act simultaneously (connected to the most positive and to the most negative phase for each
interval).
Fig. 7. The basic waveforms, illustrating the principe of operation of the matrix converter.
The obtained rectangular alternating voltage on the load resistor Rout can be
used for example to supply a resonant converter for induction heating [5, 6].
Investigation of Three-Phase to Single-Phase Matrix Converter
251
3.2 Basic control circuit
An example circuit of the system producing the basic control signal for the bidirectional switches, is shown in Fig. 8. The full bridge diode rectifier D1-D6 together
with the optocoupler OC1-OC6, produce logical impulses Q1-Q6. They define the
intervals, in which the phases A, B and C are the most positive or the most negative.
The commutation impulses for the couples of switches SW 1 − SW 4, SW 3 − SW 6
and SW 5 − SW 2, are produced by three equal logical circuits. The logical circuit
for the switches SW 1 − SW 4 is presented in Fig. 8. Q1=1 and Q4=0 when the
phase A is the most positive. In this case (SW 4 = SW 1) , i.e. G1 advances in phase
G4. The logical values Q1=0 and Q4=1 when the phase A is the most negative. In
this case (SW 1 = SW 4), i.e. G4 advances in phase G1. It can be seen from the
waveforms presented in Fig.7.
OC1
Vcc
OC3
Vcc
OC5
Q1
Rb1
R1
Vcc
Vp
Q3
Rb3
R3
Q5
Rb5
R5
Qp
V1 = 0V
V2 = 5V
TD = 0
TR = 0.1us
TF = 0.1us
PW = 416.665us
PER = 833.333us
Vn
V1 = 0V
V2 = 5V
TD = 416.666us
TR = 0.1us
TF = 0.1us
PW = 416.665us
PER = 833.333us
Qn
0
FREQ = 50Hz
VAMPL = 30V
VOFF = 0V
PHASE = 0
FREQ = 50Hz
VAMPL = 30V
VOFF = 0V
PHASE = -120
FREQ = 50Hz
VAMPL = 30V
VOFF = 0V
PHASE = 120
Va_S
D1
D3
0
D5
0
0
0
1
Vb_S
U7A
2 74ACT08
Rdc
2k
3
1
Q1
Vc_S
2
U19A
74ACT32
3
G1
1
U8A
2 74ACT08
D4
0
D6
V
3
D2
Vcc
OC4
Vcc
OC6
Vcc
1
OC2
U9A
2 74ACT08
3
1
Q4
2
1
Q4
Rb4
R4
0
Q6
Rb6
R6
0
U10A
2 74ACT08
Q2
Rb2
3
U20A
74ACT32
3
G4
V
R2
0
Qp Qn
Fig. 8. Basic control circuit.
4 Conclusions
A three-phase to single-phase matrix converter has been investigated. Based on the
state matrix vector, a mathematical analysis of the converter is performed giving
the relation between the sinusoidal line voltage (current) and the output voltage
(current). Based on corresponding equivalent circuits, the principle of operation is
considered and the control circuit is constructed. The matrix converter is simulated
using the Cadence PSpice and the waveforms illustrating the principle of operation,
are obtained.
252
M. Antchev and G. Kunov:
Acknowledgement
The study carried out in this work made is in a connection with Contract VU-TN116/2005, between the TU-Sofia and the Ministry of Education and Science of
Bulgaria.
References
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[2] T. Scvarenina, The Power Electronics Handbook. CRC Press, 2002.
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