Pulse Density Modulation Control using Space Vector
Modulation for a Single-phase to Three-phase Indirect
Matrix Converter
Yuki Nakata

Jun-ichi Itoh

Energy and Environmental Science
Nagaoka University of Technology
Nagaoaka, Japan
nakata@stn.nagaokaut.ac.jp

Electrical Engineering
Nagaoka University of Technology
Nagaoaka, Japan
nakata@stn.nagaokaut.ac.jp

Abstract—This paper discusses pulse density modulation(PDM) control methods for a single-phase to three-phasematrix converter for high-frequency applications such as thegrid interface converter for a wireless power transfer systemand high-frequency transformer link system. The input
frequency for this converter is assumed as several hundred
kHz, and at the same time outputting a commercial gridfrequency, i.e. 50 Hz or 60 Hz. The proposed circuit achieves
high efficiency by implementing zero voltage switching from a
PDM control method. In this paper, the PDM that is based on
space vector modulation (SVM) is proposed in order toimprove the output waveform. Simulation and experimental
results are demonstrated and discussed. From the results, thetotal harmonic distortion (THD) of the output voltage, which iscontrolled by the PDM using delta-sigma conversion, and the
proposed PDM based on SVM are 5.96% and 2.15%,
respectively. Furthermore, the proposed circuit achieves
maximum efficiency up to 97.3% with the proposed PDM
based on SVM. From the results, the validity of the PDM
control based on SVM has been confirmed.

I.

INTRODUCTION

In recent year, wireless power transfer systems have been
actively researched [1-3]. There are two types of wirelesspower systems known as the electromagnetic induction andmagnetic resonant coupling. In the electromagnetic induction
type, the frequency of the coil for the transmission is low,
and it can transmit high-capacity power with relative ease.
However, when the coupling is reduced it will result thetransmitting efficiency decreases with increasing in thetransmission distance. As a result, a large coupling of thetransmission coils is necessary in order to improve thetransmitting efficiency. Likewise, the transmitting distanceneeds to become shorter. On the other hand, the efficiency ofthe electromagnetic resonant coupling type is over 90% at
the intermediate distance which is approximately 1 m [4].
In the wireless power transfer system, the frequency of
the generated voltage at the receiving coil is from tens of

kHz to several MHz, which is identical to the power source
frequency. Accordingly, in order to connect this system to aload, an interface converter which converts the received
power into a controlled output power is required. The
characteristic of this interface converter must has a highinput frequency from several hundred kHz and able todeliver a low output frequency (50 Hz or 60 Hz) suitable forcommercial power grid. That is, an AC-to-AC converter isgenerally clarified as the interface converter for this system.
Matrix converter (MC) has been attracted attentions as
the AC interface converter for the wireless system, because it
delivers advantages in terms of size reduction and energy
saving [5-7]. However, the implementation of MC in thehigh-frequency power source has not been reported.
In addition, the AC-to-AC converter for the highfrequency application is necessary in other case. For example,
the MC for high-frequency application can be applied totrans-linked converter, whose secondary side is connected tocommercial grid. In downsizing the converter, thetransformer for high-frequency link size is a majorbottleneck [8]. Therefore, the size of the transformer can besmall by higher frequency converter using high-speed
switching devices such as SiC and GaN.
This paper discusses the single-phase to three-phasematrix converter for high frequency operation. There are two
type topologies for the matrix converter, so called indirect
matrix converter (IMC) and conventional matrix converter(CMC). In this paper, the indirect matrix converter is used
due to the simple control. The authors have previously
proposed a Pulse density modulation (PDM) [9-11] control
method for the high-frequency power source [12-14]. The
proposed control method applies Zero Voltage Switching(ZVS) to reduce the switching loss. The PDM signals can beobtained from delta-sigma conversion. However, in thedelta-sigma conversion, the inverse voltage pulses and clamp
phenomena will occur in the output voltage waveform of theIMC. The clamp phenomenon will occur, when the phasebetween the output voltage and current becomes larger
instantaneously.
In this paper, the PDM control based on Space vector
modulation (SVM) is proposed in order to improve thequality of output waveform. The proposed method generates
switching patterns based on SVM in order to minimize thephase error between output voltage and current. Therefore,
there are no clamp phenomena will occur on the output
voltage waveform. This paper compares and investigates two
PDM control methods, which are based on the delta-sigma
conversion and SVM. Firstly, the configurations of the
proposed circuit are introduced. Secondly, the PDM control
strategy using the delta-sigma conversion and the improved
PDM method based on the SVM are discussed. Finally, thevalidity of the proposed method is confirmed in thesimulation and experimental results.
II.

CIRUIT CONFIGURATION

Fig. 1 shows circuit configuration of the proposed singlephase to three-phase IMC. This circuit is constructed from a
diode rectifier as an input interface and a three-phase inverter
for the rear side. Since this converter does not required
electrolytic capacitors in the DC link, the lifetime is longer
and the size is more compact than the conventional system,
which is constructed by a PWM rectifier, electrolytic
capacitors and a three-phase PWM inverter.
In addition, a low pass filter is connected to the input sidein order to smooth the input current and match the
impedance of the circuit and the source. The detail of inputfilter design method is explained in chapter IV.
Note that, in the experimental circuit, a snubber circuit isconnected to the DC link as a protection circuit. It isconstructed by a diode, a small capacitor and a resistor.
III.

Figure 1. Single-phase to three-phase indirect matrix converter.

CONTROL STRATEGY

A. PDM Control using Delta-sigma Conversion
A PDM control method is applied to the proposed system
in order to reduce the switching loss of the inverter side.
PDM controls the density and the plus/minus of the constantwidth pulse, and then these pulse signals are used as theoutput unit.
Fig. 2 shows the control block diagram of the proposed
circuit. The PDM signals used for the switching can beobtained by converting the delta-sigma command (vu*, vv*,vw*) value from each phase. In general, delta-sigma
conversion is used for analog-digital conversion. These PDM
signals are used to turn on/off the inverter arm of the
proposed circuit.
Additionally, the zero cross points exist with respects tothe frequency since the input voltage is a sinusoidal
waveform. The turn-on and off of the switching are
implemented at every zero cross points of the input voltage
in ZVS. The loss from the switching devices at the inverter
can reduce drastically because the switching loss can be

Figure 2. PDM control block diagram using delta-sigma conversion.

decreased nearly to zero by the implementation of the ZVS
operation.
However, there are problems in this method, due to theinverse voltage pulses and clamp phenomena that are
constant voltage areas will occur. Delta-sigma conversion
generates the inverse voltage pulses in order to cancel thequantization error. In the clamped parts, switching loss
increases because the ZVS cannot be achieved. The clamp
phenomenon occurs because when the phase between thevoltage and current becomes larger than 30 degrees, the DC
link current flows backward to the power source in the
inverter side. As a result, the DC link voltage is equaled tothe snubber capacitor voltage. In order to resolve thisproblem, the PDM based SVM is proposed to apply for thegeneration of PDM patterns. The detail of this method is
explained in the next section.
B. PDM Control based on Space Vector Modulation
In the proposed PDM based SVM, the phase error
between the voltage and current does not occur rapidly,
because the SVM controller can select the switching pattern,which results the phase change on the voltage becomes
smaller. Hence, the link current does not flow backward andthe snubber diode does not turn on. Therefore, the clamp
phenomenon does not occur. The switching loss of thedevice decreases applying this method, because the clamp
phenomenon does not occur.
Fig. 3 shows the PDM signal generation block based on
the SVM. The switching signals generated from the SVM isthe input to the D flip-flop (D-FF), and +/- detection signal
from the input voltage is used to detect the zero cross points
of input voltage, this signal is an input to the CLK. The
output of the D-FF, “Q” is synchronized at the edge of +/signal, which is the zero cross point of input voltage. As aresult, the switching signals generated by SVM are quantized

by the pulse where the width is half cycle of the input
voltage.
In addition, the switching frequency is proportional to thecarrier frequency of SVM. The ratio between the input
voltage and carrier frequency is very important factor related
to the control. Hence, decision of the carrier frequency of
SVM is significant in this method. This method is called“Space Vector Base Pulse Density Modulation” or “SVBPDM” for short.
Figure 3. PDM control block diagram based on SVM.

DESIGN OF THE INPUT FILTERIV.

The impedance matching is important on the circuit for
the high-frequency application. In this system, the input filter
is connected to the input side as an impedance matchingcircuit, which can match the impedance of the source and thecircuit. The general high-frequency power sources have 50 Ωof matching impedance. The design method, which matches
the impedance to 50 Ω is explained in this chapter.
Fig. 4 shows the configuration of input filter. It isconstructed from a reactor Lf and a capacitor Cf. The
impedance of the load connected to the filter is expressed byresister Rload as shown in Fig. 4. The value of Lf and Cf aredecided in order that the real part of the synthetic impedance
equals to 50 Ω and the imaginary part is equal to 0 Ω toachieve the 50 Ω of matching impedance. Lf and Cf arecalculated by (1) and (2), where, ω=2πf is the input voltage
angular frequency. Lf and Cf are 80 μH and 16 nF
respectively, when the frequency of f is 100 kHz, and Rload is
100 Ω. These values are used in the experiment.

Lf =

Cf =

C f Rload2

1 + (ωC f Rload ) 2
1

ωRload

V.

Rload
−1
50

(1)

Figure 4. Design of the input filter.

500
0
-500

Input voltage vin [V]Input current iin [A]1

SIMILATION RESULTS

The following is the simulation results using indirect typecircuit as shown in Fig. 2. The simulation conditions arefollows, a 100-kHz and, 400-V sinusoidal voltage is used as
the input, then the output voltage is 50 Hz, 200 V, and theload is a 300-W inductive load.
A. Simulation Results of PDM using Delta-sigma
Conversion
Fig. 5(a) that, the output waveforms are 50-Hz sinusoidal
waveforms. The PDM control operation which uses the halfcycle of the input sinusoidal waveform as a pulse can beverified and confirmed at the simulation results. However,some voltage pulses are inversed in this method. These
pulses result the distortion occurs on the output voltage
waveforms.
Fig. 5(b) shows the extended view of the interval “A” in
Fig. 5(a). From the result, the output line-line voltage vuv

-500

0

0

-1

-1

500
0
-500

Input voltage vin [V]Input current iin [A]1

Output voltage vuv [V]Output current iu [A]

1

(2)

500
0

500
0
-500
1

0

0

-1

-1

ms/div
A(a) Input and output operation
waveforms.

Output voltage vuv [V]Output current iu [A]s/div(b) Extended each operation
waveform.

Figure 5. Operation waveforms of the proposed circuit in the simulation
with PDM using delta-sigma conversion.

confirms that the switching of the inverter occurs at
approximately each zero cross point of the 100-kHz
sinusoidal input waveform. However, there are some areas,
constant voltage is remained. In these areas, switching loss
increases because ZVS cannot be achieved.
Fig. 6(a) shows the harmonics analysis on the output
voltage from the simulation result with PDM using deltasigma conversion. From (a), it can be confirmed that the loworder harmonic components in the output voltage are low
and the output voltage THD is 2.2%.
Fig. 6(b) shows the harmonics analysis on the input
current from the simulation result with PDM using deltasigma conversion. From (b), the input current includes of theintegral-multiple harmonic nearly closed to 100 kHz andtherefore the input current THD is 42.9%.

B. Simulation Results of SVB-PDM
Fig. 7(a) shows that the output waveforms are 50-Hz
sinusoidal waveforms. The PDM control operation can beverified and confirmed at this simulation results. It is notedthat the problem of the inverse voltage pulses is resolved inthis case. The inverse voltage pulses do not exist around thezero cross point unlike the previous method using deltasigma conversion.
Fig. 7(b) shows extended view of the interval “B” in Fig.
7(a). As a result, the output line-line voltage vuv confirms that
the ZVS can achieve. In this case, areas that contain theconstant voltage have been resolved. Therefore, switchingloss is relatively small compared to Fig. 5.
Fig. 8 is the harmonics analysis result for the output
voltage and input current. From Fig. 8(a), the output voltage
does not consist of low-order harmonic components and theoutput voltage THD is 1.8%. In this case, output voltage
includes of the integral-multiple harmonic nearly to 5 kHz,
which is the carrier frequency of SVM used in thissimulation.

Figure 6. Harmonics analysis of output voltage and input current in thesimulation with PDM using delta-sigma conversion.

Fig. 8(b) shows the harmonics analysis on the input
current. The input current includes of the integral-multiple
harmonic nearly to 100 kHz and therefore the input current
THD is 42.8%.
VI.

LOSS ANALYSISThe following is the loss analysis results using indirect
circuit as shown in Fig. 1. The simulation condition is assame as the parameters discussed in chapter IV. The device
parameters are from datasheets MOSFET： IRFP460 (500 V,
20 A) and diode: S20L60 (600 V, 20 A), which are similar in
the prototype circuit[15-16].
A. Loss Analysis of PDM using Delta-sigma Conversion
Fig. 9 shows result of loss analysis with PDM using
delta-sigma conversion. The figure compares the converter
loss and the time delay in switching. Rectifier loss, snubber
loss and conduction loss of the inverter are maintained
virtually constant about 7 W. Switching loss of the inverterchanges accordingly to the time delay.

Figure 7. Operation waveforms of the proposed circuit in the simulation
with SVB-PDM.

The frequency of the voltage which is applied to theswitch is twice input frequency of 100 kHz. On the other
hand, the frequency of the current which flows through theswitch is the output frequency of 50 Hz. Hence, the current
can be assumed constant during switching period.
Additionally, the voltage becomes the peak value when thetime delay of switching equals to one-fourth of input cycle.
Therefore, the switching loss becomes maximum value then.
Even, the time delay of switching Tdelay is 0 μs, there isswitching loss of 1.4 W occurs due to the phase error
waveforms.
B. Loss Analysis of SVB-PDM
Fig. 10 shows result of loss analysis with SVB-PDM.
The characteristics of this result are same to the delta-sigma
conversion. The difference in this case is when the time

Figure 8. Harmonics analysis of output voltage and input current in thesimulation with SVB-PDM.

delay of switching is 0 μs, there is no switching loss because
phase error waveform does not exist. Comparing to the result

from Fig. 9, the loss is reduced by approximately 18%.
Therefore, the size of snuber circuit can be smaller than thatwith the PDM using delta-sigma conversion.
VII. EXPERIMENTAL RESULTS
In order to demonstrate the validity of the proposed
circuit, a prototype circuit has been built and tested. The
single-phase to three-phase IMC was tested in theexperiment with the two proposed PDM control methods. A
high-frequency power source, where the matching
impedance is 50 Ω is used as the input circuit initially toconfirm the basic principle of the two proposed control
methods. Table 1 shows the experimental conditions.
A. Experimental Results of PDM using Delta-sigma
Conversion
Fig. 11(a) shows the operation waveforms of the
proposed circuit with delta-sigma conversion. From theresult, the output voltage and current are 50-Hz sinusoidal
waveforms. The PDM control operation using delta-sigma
conversion can be verified and confirmed at the experimental
results. Similarly to the simulation results, certain voltage
pulses are inversed due to the failure on the patternconversion.
Fig. 11(b) shows the extended view of the interval “C” inFig. 11(a). The results confirm that the ZVS is performed at
the zero cross point of the input voltage waveform. However,the switching has a 1 μs delay due to the following reasons;(i) detection of the zero cross points is slow and (ii) the deadtime of the inverter. The delay of the zero cross point
detection is approximately 0.5 μs, and dead time of theinverter is set to 0.5 μs. The delay can be improved bymodifying the zero cross point at the detection circuit. Thus,
the dead time period can be improved by studying andevaluating the device parameters. Additionally, although theswitching has a short delay, the surge voltage is lower thanthat of the hard switching method. However, due to theclamp phenomena, as covered in the section III-A, switchingloss increases because ZVS cannot be achieved. Therefore,
the circuit has low efficiency in this experiment.

18
16

switching

14
12

conduction

10
8
Snubber loss
6
4
Rectifier loss

2
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Figure 9. Converter losses vs delay time of switching with PDM using
delta-sigma conversion.
18
18
16
16

switching
Switchingloss ofinverter

14
14
12
12

conduction
Conduction

10
10

loss ofinverter88

Snubber
Snubberlossloss

66
44

Rectifier loss
Rectifier
loss

22
00

0
0.5 1.01
1.5 2.02
2.5 3.03
3.5 4.04
4.5 5.0
5
0.0
0.5
1.5
2.5
3.5
4.5

Time delay of switching Tdelay [ s]Figure 10. Converter losses vs delay time of switching with SVB-PDM.
TABLE I.

EXPERIMENTAL PARAMETERS.

Parameter
Input voltage
Input voltage
Output line-to-line voltage
Output frequency
Rload
Load
Lload

Value
200 [V]
100 [kHz]
100 [V]50 [Hz]
100 [Ω]10 [mH]In addition, Fig. 12 shows the harmonics analysis on the
output voltage and input current. From (a), output voltage
does not include low-order harmonic components, and theintegral-multiple harmonic nearly closed to 200 kHz. The
frequency is DC link voltage fluctuating frequency is
included in the high-order harmonic components. The output
voltage THD of 5.96% is obtained. It is larger than thesimulation result, because of the surge voltage in the output.
Moreover, (b) shows that the input current has the integralmultiple harmonic nearly closed to 100 kHz, and therefore
input current THD is 79.7%.
B. Experimental Results of SVB-PDM
Fig. 13(a) shows the operation waveforms of the
proposed circuit in the experiment with SVB-PDM. The
result confirms that 50 Hz sinusoidal waveforms are
obtained on the output voltage and current. The PDM control
operation based on SVM can be verified and confirmed at

Figure 11. Operation waveforms of the proposed circuit in the experimentwith PDM using delta-sigma conversion.

the experimental results. Notice there are no inverse voltage
pulses in this case.
Fig. 13(b) shows the extended view of the interval “D” in
Fig. 13(a). As a result, the output line-line voltage vuv
confirms that the switching of the inverter is happened at
approximately each zero cross point of the 100 kHz
sinusoidal input waveform. However, the switching has a 1
μs delay due to the same reasons as mentioned in the
explanation of Fig. 11.
Fig. 14 shows the harmonics analysis on the output
voltage from experimental result with SVB-PDM. From theresult, the low-order harmonic components closely to 50 Hz
are not included in the output voltage, and the output voltage
THD of 2.15% can be obtained. Therefore, the improvementof the output voltage waveform is confirmed. In this case,
output voltage includes of the integral-multiple harmonicnearly to the carrier frequency of 5 kHz, which is theswitching frequency. Additionally, the integral-multiple
harmonic nearly to the 200 kHz is included in the output
voltage because of the same reason as case of Fig. 12.
Furthermore, input current includes the integral-multiple
harmonic nearly closed to 100 kHz and input current THD is
55.5%.

Figure 12. Harmonics analysis of output voltage and input current with
PDM control using delta-sigma conversion.

VIII. MESUREMENT OF THE EFFICIENCY

IX.

CONCLUSIONSIn this paper, the implementation of PDM control
methods in a single-phase to three-phase IMC is discussed
and evaluated by the simulations and the experiments. In the
PDM control using delta-sigma conversion, the output
waveform has inverse voltage pulse and clamp phenomenaon the output voltage waveform. Hence, an improvement
method of the output waveform based on SVM is proposed.
In SVM, the phase error between the voltage and current aredramatically reduced.
A prototype circuit has been built and tested. From theresults, ZVS operation and clear sinusoidal output waveform

Output voltage vuv[p.u.]

In addition, the maximum efficiency with PDM control
using delta-sigma conversion and with PDM control basedon SVM are 93.4% and 97.3% respectively.

Figure 13. Operation waveforms of the proposed circuit in the experimentbased on SVM.

Input current iin[p.u.]

Fig. 15 shows the efficiency characteristics of the
proposed circuit with PDM control using delta-sigma
conversion and PDM control based on SVM. The input andoutput voltage conditions are same as shown in table 1, andthe output power is controlled by changing the load value.
From the result, the efficiency of the circuit is improved as
output power increases in both the PDM control methods.
Furthermore, the efficiency for the PDM control based on
SVM is higher than that for the PDM control using deltasigma conversion at all measurement regions. This isbecause the switching loss decreases due to resolution of theclamp phenomenon and reduction of the switching frequency
applying the PDM control based on SVM. As a result,validity of PDM control based on SVM is confirmed about
efficiency improvement.

Figure 14. Harmonics analysis of output voltage and input current with
PDM control based on SVM.

have been confirmed. On the other hand, it is confirmed that
the PDM control based on SVM can resolve the problems
with clamp phenomenon. As a result, the THD of the output
voltage with delta-sigma conversion and PDM pattern
method based on SVM are 5.96% and 2.15% respectively.
Furthermore, the maximum efficiency has been improved
from 93.4% to 97.3% by applying the proposed PDM
method. From the results, a validity of PDM control basedon SVM has been confirmed.

100
98
96
94
92
90
88
86

In future work, the zero cross point detection circuit will
be improved to reduce the switching loss.

40

ACKNOWLEDGMENT
A part of this study was supported by Industrial
Technology Grant Program in 2009 from New Energy andIndustrial Technology Development Organization (NEDO)
of Japan.
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