This paper presents a MATLAB/Simulink simulation of direct and indirect space vector modulation for matrix converter. Different switching patterns for both direct and indirect methods are simulated and compared. Three criteria are chosen to compare the performance of switching patterns: (1) total harmonic distortion (THD); (2) harmonic spectrum analysis of output voltages; and (3) number of switching in each switching period. Switching strategies are completely implemented using the power library in MATLAB/Simulink environment.
Three-phase matrix converter is an AC-to-AC converter with nine bidirectional switches. These switches are organized in a
Space vector switching methods for matrix converter are classified into two different strategies: (1) indirect space vector modulation which takes the advantage of a virtual dc link [
In this paper first the two methods of indirect and direct space vector modulation of matrix converter are reviewed. Then different switching patterns are introduced, and each switching pattern will be simulated in MATLAB/Simulink software. Simulations and comparison are done under the same conditions of the input power supply and the output load. In order to compare the performances of switching patterns three criteria are considered: total harmonic distortion, harmonic analysis of output voltage, and number of switching. The rest of the paper is as follows: Section
The
Direct matrix converter.
The restriction is expressed as
The output voltages and input currents of the matrix converter can be represented by the switching function
A space vector is obtained from three phase quantities through the following transformation:
Many engineers are familiar with the space vector modulation (SVM) for voltage source inverters (VSIs) [
Indirect matrix converter.
This is done by dividing the switching function
So the space vector for the two voltage source converters shown in Figure
The rectifier part of the equivalent circuit can be assumed as a current source rectifier (CSR) with the averaged value of
The nine rectifier switches have nine permitted combinations to avoid an open circuit at the dc link. These combinations include three zero and six nonzero input currents given in Table
Current vectors for rectifier stage.
Type | Vector |
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Active |
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1 | 0 | 0 | 1 | 0 | 0 |
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1 | 0 | 0 | 0 | 0 | 1 | |
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0 | 0 | 1 | 0 | 0 | 1 | |
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0 | 1 | 1 | 0 | 0 | 0 | |
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0 | 1 | 0 | 0 | 1 | 0 | |
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0 | 0 | 0 | 1 | 1 | 0 | |
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Zero |
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0 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | |||
0 | 0 | 0 | 0 | 1 | 1 |
The reference input current vector is synthesized by impressing the adjoining switching vectors (
Input current space vector in complex plane.
The duty cycle of the active vectors are calculated by
The inverter can be assumed as a separate VSI. The switching method is exactly similar to conventional VSI [
The output voltage space vector,
The inverter switches have eight permitted combinations to avoid a short circuit. These combinations include three zero and six nonzero input currents (see Table
Voltage vectors for inverter stage.
Type | Vector |
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Active |
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1 | 0 | 0 | 1 | 0 | 1 |
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1 | 0 | 1 | 0 | 0 | 1 | |
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0 | 1 | 1 | 0 | 0 | 1 | |
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0 | 1 | 1 | 0 | 1 | 0 | |
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0 | 1 | 0 | 1 | 1 | 0 | |
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1 | 0 | 0 | 1 | 1 | 0 | |
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Zero |
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0 | 1 | 0 | 1 | 0 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 1 |
The reference output voltage vector is synthesized by impressing the adjoining active vectors
Output voltage space vector in complex plane.
The duty cycles of the active vectors can be written as:
In direct space vector modulation the actual matrix converter circuit is considered without any assumption of an equivalent circuit. For operation of the matrix converter one and only one switch in each output phase must be conducting. This leads to twenty-seven possible switching combinations for the matrix converter. Modulation is more complicated because these vectors vary continuously and depend on instantaneous magnitude of sources. The output voltage states are usually classified in three groups: 18 combinations with fixed directions, 3 zero vectors, 6 rotating vectors.
The 6 combinations of rotating vectors in group 3 are not used. Similar to indirect space vector modulation the reference output voltage vector is synthesized by impressing the adjoining active vectors. The reference input current vector is also synthesized by impressing the adjoining switching current vectors. Figure
Switching configurations.
Switches on |
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1, 5, 6 |
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4, 2, 3 |
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4, 8, 9 |
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7, 5, 6 |
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7, 2, 3 |
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1, 8, 9 |
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4, 2, 6 |
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1, 5, 3 |
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4, 5, 9 |
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4, 8, 6 |
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1, 8, 3 |
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7, 2, 9 |
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4, 5, 3 |
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1, 2, 6 |
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7, 8, 6 |
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4, 5, 9 |
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1, 2, 9 |
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7, 8, 3 |
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1, 2, 3 | 0 | 0 |
4, 5, 6 | 0 | 0 |
7, 8, 9 | 0 | 0 |
The output voltage and input current reference space vectors.
If
In these equations
The order in which the vectors are placed along one period is called switching pattern.
A proper choice of the switching pattern should be applied to the switches of the matrix converter in order to achieve the desired output. There are different combinations for ordering the time segments corresponding to duty ratios. In this paper two switching patterns are considered for indirect space vector modulation. A single and a double distributions of time periods during a switching period are selected. These patterns are shown in Figure
Switching patterns for indirect modulation: (a) single sided; (b) double sided.
Four switching patterns are simulated and analyzed for direct space vector modulation: (1) asymmetrical single sided, which uses only one of the three zero vectors; (2) asymmetrical double sided switching pattern; (3) symmetrical single sided, which utilizes all the three zero vectors and (4) symmetrical double-sided pattern. Figure
Switching patterns for direct modualation: (a) asymmetrical single sided; (b) asymmetrical double sided; (c) symmetrical single sided; (d) symmetrical double sided.
In order to compare the performances of the direct and indirect space vector modulation techniques, these methods are applied to an AC/AC matrix converter. This system consists of a simple source voltage that is connected to a resistive load through a matrix converter. The simulations were performed with Matlab/Simulink software as shown in Figure
Test case system parameters.
Parameter | Value |
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Source voltage (peak) | 100 V |
System frequency | 60 Hz |
Load resistance | 5 Ω |
Switching frequency | 6 kHz |
Modulation index | 0.8 |
Sampling time | 2 |
Simulation results.
Pattern | THD% | Number of Switching for |
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Single side indirect | 69.59 | 88 |
Double side indirect | 68.15 | 159 |
Asymmetrical single side direct | 70.84 | 62 |
Asymmetrical double side direct | 66.92 | 163 |
Symmetrical single side direct | 67.21 | 130 |
Symmetrical double side direct | 65.32 | 192 |
Test case schematic in Matlab/Simulink.
Harmonic spectrum of output voltage: (a) single side indirect; (b) double side indirect; (c) asymmetrical single side direct; (d) asymmetrical double side direct; (e) symmetrical single side direct; (f) symmetrical double side direct.
Based on these simulation results, the double-sided patterns show the following characteristics over the single-sided pattern: lower harmonic distortion, greater number of switching.
In addition, the analysis for symmetrical and asymmetrical patterns shows that the symmetrical pattern is more appropriate choice for a lower harmonic distortion in spite of greater switching losses.
This paper compares different switching patterns of direct and indirect space vector modulations for three-phase matrix converter. Two methods of indirect and direct space vector modulation of matrix converter were completely described. Double-sided and single-sided patterns as well as symmetrical and asymmetrical patterns were analyzed in Simulink. Comparison results were evaluated based on three criteria: (1) total harmonic distortion (THD); (2) harmonic spectrum analysis of output voltages; and (3) number of switching in each switching period. As expected the double-sided as well as symmetrical patterns produces lower harmonic distortions. However, the number of switching increases when using double-sided and symmetrical patterns.