Modeling and Simulation of Matrix Converter Using Space Vector ...

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The simulation results of input current, output voltage and current waveforms are presented with their spectra. Keywords — Matrix converter, space vector control.
EUROCON 2005

Serbia & Montenegro, Belgrade, November 22-24, 2005

Modeling and Simulation of Matrix Converter Using Space Vector Control Algorithm Ebubekir Erdem, Yetkin Tatar, and Sedat Sünter

Abstract — In this work, Matlab/Simulink modeling and simulation of the three - phase matrix converter feeding a passive RL load have been performed using the space vector control algorithm. The model has been designed to support real time implementation with a simulation supported DSP control board. The algorithm uses a simpler method than the other control algorithms to control the input power factor. In addition, it has lower switching loses and easy implementation. Simulation has been implemented for various output frequencies at unity input power factor. The simulation results of input current, output voltage and current waveforms are presented with their spectra. Keywords — Matrix converter, space vector control algorithm

I. INTRODUCTION

T

HE matrix converters, fed by three - phase sinusoidal source with constant frequency and amplitude are an array of controlled nine bidirectional semi-conductor switches connected in the matrix form. Each output line is linked to each input line via a bidirectional switch. These switches provide to acquire voltages with variable amplitude and frequency at the output side by switching input voltage with various modulation algorithms [1], [2]. Fig.1 shows a typical three - phase input to three - phase output matrix converter, with nine bidirectional switches. Recently, the most popularly used switching algorithm is space vector modulation algorithm that allows the control of input current and output voltage vectors independently. Space vector modulation algorithm has many advantages with respect to the traditional modulation techniques such as, being able to obtain maximum voltage ratio ( 0 ≤ q ≤ 0.866 ) without adding third harmonics, being able to minimize the switching numbers that are required for commutation process, being more easily implemented due to facilitated control algorithm, easily being able to comprehend the commutation process and being easily operated under unbalanced conditions [3], [4]. In this study, Matlab simulation of three - phase to three - phase matrix converter feeding passive RL load has been performed. In the simulation, power circuit of matrix converter has been modeled using power electronics toolbox of Matlab Simulink. Although computation of the E. Erdem and Y. Tatar are with the School of Computer Engineering, University of Firat, 23119 Elazig, Turkey (e-mail: [email protected] and [email protected] ). S. Sunter is with the School of Electrical and Electronic Engineering, University of Firat, 23119 Elazig, Turkey (e-mail: [email protected] ).

Fig.1 Structure of 3x3 phases matrix converter switching duty cycle is complex, in space vector modulation algorithm, which is easy to implement, provides independent control of output voltage amplitude and frequency with minimum switching losses. This model has been designed to support real time implementation with a simulink supported DSP control board (for example, DS1103 control board). Furthermore, the current and voltage waveforms of input, output and harmonic spectra obtained by simulation for various output frequencies are investigated. II. MODULATION ALGORITHM The space vector algorithm is based on the representation of the three phase input current and three phase output line voltages on the space vector plane. In matrix converters, each output phase is connected to each input phase depending on the state of the switches. For safe switching in the matrix converter; • Input phases should never be short-circuited, • Owing to the presence of inductive load, the load currents should not be interrupted at any switching time. There are 27 different switching combinations for connecting output phases to input phases if the above two rules are provided. These switching combinations can be analyzed in three groups. Each output phase is directly connected to three input phases in turns with six switching combinations in the first group. In this case, the phase angle of output voltage vector depends on the phase angle of the input voltage vector. Similar condition is also valid for current vectors. For the space vector modulation technique, these switching states are not used in the matrix converter since the phase angle of both vectors cannot be controlled independently. There are 18 switching combinations in the second group in which the active voltage vector is formed at variable amplitude and frequency. Amplitude of the output voltages depend on the

β

maximum voltage transfer ratio between the input and output voltages of 86.6%. ( 0 ≤ q = vro ≤ 0.866 ). Sum of the r vi

+ 2, + 5, + 8

− 1, − 4 , − 7

v

II

III

Vi

αi

− 3, − 6 , − 9

v ii

IV αi −

VI

V

+ 3, + 6 , + 9

α

π

switching times in Eq. (1) must not exceed the switching period. Otherwise, the switches will turn on at overshoot mode. Sum of the switching times must ensure the condition given in Eq. (2).

6

TABLE 1.

+ 1, + 4, + 7

V0

− 2, − 5, − 8

(a)

SWITCHING CONBINATIONS IN SIX SECTORS İi

1. β

2. − 7 , − 8, − 9

III

+ 4 , + 5, + 6

3. + 1, + 2 , + 3

II

r

V o'

4.

r

vo

IV

αo

r

5.

α

I

V o' ' − 1, − 2, − 3

6. VI

V

− 4, − 5, − 6

+ 7 , + 8, + 9

(b)

Fig.2 Space vector representation a) Input currents b) Output line voltages selected input line voltages. In this case, the phase angle of the output voltage space vector does not depend on the phase angle of the input voltage space vector. Similar condition is also valid for current vectors. The last group with 3 switching combinations consists of zero vectors. In this case, all of the output phases are connected to the same input phase [5], [6]. Output line voltage and input current space vectors are used in the application of the space vector control technique to the matrix converter. Fig.2 shows the representation of the input current and output line voltage r r vi and vo represent space vectors. Where, instantaneous input and output voltage vectors respectively, α i and α 0 represent the phase angels of input and output voltages respectively. In order to determine the switches that will conduct, it should be decided that α i and α 0 are in which sectors of input current and output line voltages shown in Fig.2. There are 36 sectors based on the position of α i and α 0 . Table 1 shows the combination of the switches which will be turned-on for each sector. The switching combinations for turning on are determined according to the specified vector. Duty period of each switch is determined by considering the common switching combinations of both vectors. Duty period of the switches for each switching combinations should be calculated to obtain the desired voltage amplitude and frequency at the output of matrix converter. Equation (1) gives the switching times for being both α i and α 0 in sector 1. Solution interval for Equation (1) is; 0 ≤ α i ≤

π 3

, −

π 6

≤ α0 ≤

π 6

. This algorithm gives a

δ1+ =

2

δ 3− =

2

δ 4− =

2

δ 6+ =

2

3

1.

2.

3.

4.

5.

6.

+1 − 3 +2 − 3 −1 + 2 −1 + 3 −2 + 3 +1 − 2 −4+6 −5+6 + 4−5 +4−6 −7 + 9 −8 + 9 +7 − 8 +7 − 9 +1− 3 + 2−3 −1+ 2 −1+ 3 +4 − 6 −8 + 9 −4 + 5 −4 + 6 − 7 + 9 + 5− 6 + 7 −8 +7−9 +4 − 6 +5 − 6 −4 + 5 +1 − 3 −1+ 3 − 2 + 3 +1− 2 −4+6 −1 + 3 −2 + 3 +1 − 2 +1 − 3 + 7 − 9 + 8− 9 − 7 + 8 −7+9 +7 − 9 +8 − 9 −7 + 8 +4 − 6 −4+6 −5+ 6 + 4− 5 −7+9

+5−6 − 4+ 5 +8 − 9 −7 + 8 − 2 + 3 +1− 2 −5 + 6 +4 − 5 +8−9 −7+8 +2 − 3 +4 − 5 − 5 + 6 −1+ 2 +2 − 3 −1 + 2 −8+9 + 7−8 +5 − 6 +7 − 8 −8+9 − 4+5

π  π  Ts q sin  α o +  sin  − α i  6  3 

(1)

π  Ts q sin  α o +  sin α i 6 3 

3

3

π  π  Ts q sin  − α o  sin  − α i  3  6  π  Ts q sin  − α o  sin α i 6 

δ1+ + δ 3− + δ 4− + δ 6+ ≤ Ts

(2)

where Ts is the switching period. Switching order in the space vector control algorithm can be obtained by considering the rules given below. [6] • 1. and 4. switching order must have two same letters in same position. • 2. and 3. switching order must only change one letter according to 1. and 4. switching order, respectively. • The last zero voltage configuration (5. switching order) has only one letter changed according to 1. and 4. switching order. While turn on order of the switches is randomly given in the first column of Table 2, these orders are given according to the rules given above in the fourth column. Here, A, B, C, and a, b, c represent the output phases and input phases, respectively. TABLE 2. TURN ON ORDER OF THE SWITCHES Config +1 -3 -4 +6 0 0 0

ABC abb acc aba aca aaa bbb bbb

1. 2. 3. 4. 5. 1. …

Config -4 +1 -3 +6 0 -4 …

ABC aba abb acc aca aaa aba …

III. SYSTEM MODELING

IV. SIMULATION RESULTS

Matlab/Simulink package program has been used for modeling the matrix converter. Fig.3 shows simulink model of three-phase matrix converter applying the space vector control algorithm. Power circuit of the matrix converter has been modeled using Power Electronic Toolbox in Matlab/Simulink, as shown Fig.3.a. The model consists of four main parts. First part is LC filter, second part is input voltage source, third part corresponds to the duty cycle generator in which the turn - on time of the switches for each output phase is calculated and then the control signals are generated, and last part represents the ideal bidirectional switch blocks with snubber circuits. In the model, the switches that will be turned on should be determined in one switching period to obtain the output phases. Therefore, α i and α 0 are calculated in duty cycle

Simulation of the matrix converter has been performed with a passive RL load. The simulink model given in Fig.3 is used with ideal bidirectional switches. A snubber circuit

generator block as shown in Fig.3.a and then, the sector is determined by considering the input current and output line voltage vectors as shown in Fig.2. This block also contains sub blocks where the order of switches which will be turned on and duty cycle calculation for each switch for 36 sectors are determined. One of the sub blocks is shown in Fig.3.b. The block shown in Fig 3.b. determines the order of the switches which will be turned on and calculates the duty period of switches for being both α i and α 0 in

of Rs=46.13ohm, Cs= 15e −9 F is placed across each bidirectional switch. The load parameters in the model are taken as 10ohm and 0.12H. The switches in the model are controlled by using space vector control algorithm where the voltage ratio, q is taken as 0.8. The converter is fed by a three- phase supply which has line voltage and frequency of 220V and 50Hz, respectively. Simulation results for various output frequencies are given in Figs.4-5. The switching frequency was taken as 5kHz. Fig.4.a shows the input current and voltage waveforms of the converter for 50 Hz output frequency without using input filter. Similar results are given in Fig.4.c except for the input filter. Fig.4.b illustrates harmonic spectrum of the input current given in Fig.4.a. As can be seen in Fig.4.b, the peak value of the first harmonic is 1.53A with a zero input displacement factor. Similar results are obtained for various output frequencies and voltage ratios. Fig.5.a, Fig.5.b and Fig.5.c shows the output current and output line voltage waveforms and corresponding harmonic spectra for output frequency of 100Hz, 50Hz and 25 Hz, respectively.

sector 1. The switches for one output phase connect the related input phases to the output phase in turn for a calculated time. The signal obtained from the output of this switch forms the portion of output phase corresponding to the related input phase. Hence, sum of the portions related to all input phases gives the target output waveform.

(a)

(a)

(b)

(c) (b)

Fig.3 3x3 Phase matrix converter using space vector control algorithm a) Simulik model b) Block diagram of the drive signals

Fig.4 Simulation waveforms of three - phase matrix converter a) Input voltage and unfiltered phase current b) Harmonic spectrum c) Input voltage and filtered phase current (fs=5khz, f0=50Hz)

(a)

(c)

(b)

Fig.5 Simulation waveforms of output line voltage, harmonic spectrum, and output currents of three phase matrix converter. (fs=5khz) a) f0=100Hz b) f0=50Hz c) f0=25Hz [5]

V. CONCLUSIONS In this study, modeling and simulation of the threephase matrix converter with RL load employing space vector control algorithm have been realized in Simulink /Matlab package program. The input and output waveforms of the converter for various output frequencies and voltage ratios have been investigated. Simulation results have demonstrated that the output waveforms do not have major harmonics except for those around switching frequency. It has been seen from the harmonic analysis that the first harmonic of the unfiltered input current is in phase with the input voltage. In this work, the model is realized in such way that it can be used and implemented in real time using DSP control board. REFERENCES [1]

[2]

[3]

[4]

Venturini M., “A new sine wave in sine wave out, conversion technique which eliminates reactive elements”, in Proc. POWERCON 7, 1980 Venturini M. and Alesina A., “The generalized transformer: A new bidirectional sinusoidal waveform frequency converter with continuously adjustable input power factor”, in Proc. IEEE PESC’80, 1980, pp. 242–252 Casadei D., Serra G., Tani A., Nielsen P., “Performance of swm controlled matrix converter with input and output unbalanced conditions ”, EPE '95, Sevilla, Spain, 1995 Sunter S., “A vector controlled matrix converter induction motor drive “, PhD Thesis, University of Nottingham, U.K., 1995

[6]

[7]

Çoşkun İ., Saygın A., Gençer Ç., “Bulanık mantık denetleyicili matris converter ile asenkron motor hız kontrolü”, International 12. Turkish Symposium on Artificial Intelligence and Neural Networks, TAINN, 2003 (in Turkish) Casadei, D., Grandi, G., Serra, G., and Tani, A., “Space vector control of matrix converters with unity input power factor and sinusoidal input/output waveforms”, Power Electronics and Applications, Fifth European Conference, 1993, pp. 170-175. Math Works, MATLAB for Microsoft Windows. Math. Works. Mass., 1999