Space Vector Modulation Applied to Three-Phase Three ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 6, NOVEMBER 2007

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Space Vector Modulation Applied to Three-Phase Three-Switch Two-Level Unidirectional PWM Rectifier Flabio Alberto Bardemaker Batista and Ivo Barbi, Senior Member, IEEE

Abstract—This work presents a methodology to apply space vector modulation to a three-phase three-switch two-level Y-connected unidirectional pulsewidth modulation (PWM) rectifier. Converter switching stages are analyzed to determine switch control signals for space vector modulation. A switching sequence is proposed in order to minimize the number of switch commutations and to reduce the switching losses. Duty cycle functions are determined and the desired switching sequences are performed by a simple PWM modulator with no need of to determine the present sector of vector. For this propose is just necessary to impose the desired current sectors from input voltage references. The vector control structure used with the proposed modulation technique is also described. In order to validate the proposed modulation technique, experimental results are presented for a 20 kW prototype. Index Terms—Power factor correction (PFC), space-vector modulation, three-phase ac–dc converters, unidirectional rectifiers.

NOMENCLATURE A, B, and C M, P, and N ,

, and

and

Phase designation. Points of connection. Switches for phases A, B, and C. Switching period. Transformation matrices. Unit vector for axis

, ,

, and

,

Duty cycles for phases A, B, and C. Currents for direct axis and quadrature axis. Duty cycles for direct axis and quadrature axis. Space vectors.

,

, , ,

and for axis .

, and

Application interval of vectors. Duty cycles for axis and . Projection of the application interval of vectors in axis and .

Manuscript received April 20, 2006; revised September 25, 2006. Recommended for publication by Associate Editor M. Ferdowsi. F. A. B. Batista is with the Federal Center of Technological Education of Santa Catarina, CEFET/SC–Santa Catarina, Brazil (e-mail: [email protected]. br). I. Barbi is with the Federal University of Santa Catarina–CEFET/SC, Santa Catarina, Brazil. Digital Object Identifier 10.1109/TPEL.2007.909184

Desired vector. Source voltage. Fundamental component of rectifier voltage. Phase shift. I. INTRODUCTION HEN bidirectional power flux is not necessary, high power factor unidirectional rectifiers present some advantages as the decrease of the number of power switches, natural protection of short-through and smaller processing of energy for the active switches [1]–[3]. If output voltage is not so high, two-level topologies become attractive because they do not need to control midpoint voltage of the dc bus, reducing the number of sensors and controllers [4]. In this work, space vector modulation will be applied to a three-phase three-switch two-level Y-connected unidirectional pulsewidth modulation (PWM) rectifier [5] in order to minimize the number of switch commutations as well as reduce converter losses. This structure presents as main drawback a high number of semiconductors when compared with other topologies [1], [3]. Other characteristics of this topology are presented in [5]. The proposed application methodology of this modulation technique is based on sub-sectors definition, on rectifier operation stages analysis and on duty cycles determination. Therefore, it is not necessary to identify the present vector sector, just impose adequate current sector in phase with line voltages [6]. Section II presents the main characteristics of a two-level unidirectional PWM rectifier and in Section III the basic steps are described in order to apply space vector modulation to this converter. Vector control concepts used with the proposed modulation techniques are shown in Section IV. In Section V experimental results are presented and in Section VI conclusions and analysis results are discussed.

W

II. THREE-PHASE THREE-SWITCH TWO-LEVEL UNIDIRECTIONAL PWM RECTIFIER The three-phase three-switch two-level Y-connected unidirectional PWM rectifier, showed in Fig. 1, presents high power factor and output voltage regulation. Eight topological stages may be performed from switches states, according to Table I. This structure presents six symmetrical operation intervals [5], where six current sectors are defined in one line period: , , , , and , as shown in Fig. 2. Each sector has

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TABLE II AVAILABLE VECTORS

Fig. 1. Three-phase three-switch two-level unidirectional PWM rectifier.

TABLE I SWITCHING STAGES

Fig. 3. Space vector coordinates.

null vector represents the situation where the three points are connected. In this notation, used for unidirectional converters, the available vectors representation does not agree with the switching states because the potentials of points A, B and C depend on the input currents direction. By the application of Clark transformation (1) space vector representation is made with a regular hexagon divided in six vectors sectors, where vector coordinates are determined as shown in Fig. 3 (1) Fig. 2. Current sectors.

an interval of 60 and it is defined by the current that has the greater value and its respective signal. Specific sector analysis, described below for sector , can be extended for each other sectors considering the adaptation of the direction of input currents. In sector (where phase A current is positive with higher value) five equivalent topological stages are verified in stages 4, 5, 6, 7 and 8 of Table I. When current is flowing from one phase to another, without circulate in the load, two switches must be turned on and in order to obtain null line voltages all three switches should be turned on. III. SPACE VECTOR MODULATION From the analysis of structure showed in Fig. 1, seven available vectors are defined as shown in Table II. Nonnull vectors are represented by the potential of points A, B, and C, and the

[Fig. 4], nonnull In order to implement a desired vector vectors are averaged in the switching period. Sector 1 has the following relationship: (2) The application intervals of vectors are calculated using the projection of desired vector in the axis and in the axis as represented in Fig. 4, resulting in

(3)

(4)

BATISTA AND BARBI: SPACE VECTOR MODULATION

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Fig. 6. Sub-sectors definition.

Fig. 4. Space vector representation.

Fig. 5. Relationship between input voltages and rectifier fundamental voltage component.

Null vector application interval is calculated as

(5) For unidirectional rectifiers, the definition of the sectors is a little different from the traditional way [7], [8]. In this case, available vectors implementation considers phase currents direction. Supposing that the currents are in phase with the respective voltages, each phase presents an equivalent circuit with the relationship between input voltages and rectifier fundamental voltage component showed in Fig. 5. Sub-sectors are defined from the intersection of vector sectors and current sectors, as shown in Fig. 6. Therefore, space vector representation is made in one diagram divided in these sub-sectors as shown in Fig. 7, where each current sector is divided in two sub-sectors and presents four available vectors. For the sector , the sub-sector SS1A and the sub-sector SS1C are considered. In sub-sector SS1A, the higher current is in phase A and this current is positive and vectors , and are used. For these current signals, space vector is performed in the operation stage of Fig. 8(a) and space vector is performed in the operation stage of Fig. 8(b). However, in sub-sector SS1C, the higher current is in phase C and this current is negative and used vectors are the same as the previous case: , and . Therefore, space vector

Fig. 7. Space vector representation with sub-sectors definition.

is performed in the operation stage of Fig. 9(a) and space vector is performed in the operation stage of Fig. 9(b). In both sectors, in order to implement the null vector, it is necessary that the three switches be turned on. The logic for determine the command signals considers that the switch in the arm which processes the higher current be turned on in the respective current sector interval, so the proposed control signals for implementing these vectors are shown in Table III. The general rule for the representation of vectors is: to get the one value in the desired vector, the switch in the correspondent phase is turned on when the current with greater value is positive (sectors , and ) and the switch is turned off when this current is negative (sectors , and ). To get the zero value in the vector, this logic is inverted. These rules may not be applied to null vector. The main objective of the logic of distribution of the command signals is the minimization of the number of commutations of the switches and reduction of the switching losses of the

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Fig. 8. Operation stages in sub-sector SS1A: (a) vector


0! V

and (b) vector

0! V .

converter. However, the selected switching pattern was chosen so that, in three phases, the level of the control signal is the same (on) at the beginning and at the end of the switching period. For sub-sector SS1A, the proposed vectors sequence is , resulting in the drive signals in Fig. 10. Therefore, the intervals for the commands of switches are

Fig. 9. Operation stages in sub-sector SS1C: (a) vector

0! V . V , (b) vector 0!

TABLE III CONTROL SIGNALS FOR SUB-SECTORS SS1A AND SS1C

(6) Using the projections of the vectors in the axes and for the respective sectors, the three-phase duty cycles are determined in function of and duty cycles (9)

(7) For sub-sector SS1C, the proposed vector sequence is , resulting in the drive signals for Fig. 11. In this case, the intervals for the commands of switches and the three-phase duty cycles are

(8)

Using the same methodology for all sub-sectors, one can determine the duty cycles as in Table IV. Applying the inverse of Park transformation (10), and duty cycles are calculated as (10)

(11) Extending this analysis to the other sectors, the duty cycle functions for each switch are defined as shown in Fig. 12. In this picture, the duty cycle for switch is presented for and .


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TABLE IV DUTY CYCLES FOR ALL SUB-SECTORS

Fig. 10. Drive signals for sub-sector SS1A.

Fig. 11. Drive signals for sub-sector SS1C.

In the analysis of duty cycle equations of Table IV, one can verify that the expressions for neighboring sub-sectors are equal in the same current sector. Therefore, it is not necessary to identify the sectors of vectors; only to impose desired current sectors from input voltages. The switches control signals to implement the desired vectors are performed by a simple PWM modulator, through the comparison of duty cycle functions with a triangular waveform. IV. VECTOR CONTROL Vector control structure is shown in Fig. 13. In the control system, input currents are sampled, Clark and Park transfor-

Fig. 12. Duty cycle for switch S .

mations are applied to these variables and dq0 currents are obtained. For a system with high power factor, the q axis current must be zero. Therefore, the reference for the controller of this current is also zero and the reference for d axis current comes from the voltage controller. The outputs of current controllers are the duty cycles for d axis and for q-axis. These duty cycles are decoupled [9] and in-

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TABLE V SPECIFICATIONS USED IN EXPERIMENTATION

Fig. 14. Laboratory setup.

Fig. 13. Vector control structure.

verse Park transformation is applied to these variables. The duty cycles for axis and for axis are the result of this transformation, and these signals are used in space vector modulation. In digital control of the PWM rectifier, the TMS320LF2407A DSP is used. For current loops, the sample rate is the switching frequency and for voltage loop, the sample rate is the line frequency. V. EXPERIMENTAL RESULTS Power parameters used in experimental verification are shown in Table V. An example of design procedure is presented in [5]. The laboratory setup for a 20 kW PWM rectifier is presented in Fig. 14. The selected components of the converter are as follows. 1) Switches , and : SKM50GAL120. 2) Diodes , and : SKM50GAL120. 3) Diodes , and : HFA30PB120. 4) Output Capacitor : . 5) Input Inductors , and : 2.4 mH/40 A. Drive signals for sub-sector SS1A are in Fig. 15 and drive signals for sub-sector SS1C are in Fig. 16. These signals are according to proposed signals shown in Fig. 10 and Fig. 11.

Fig. 15. Drive signals for sub-sector SS1A (2 V/div).

Duty cycles for three switches, with format similar to theoretical duty cycles are presented in Fig. 17. The input currents in the unidirectional PWM rectifier are presented in Fig. 18, where it should be observed that they present a low current distortion . The input current in phase A and the voltage reference for phase A are presented simultaneously in Fig. 19. In this case, the system presents a high power factor (0.998). Fig. 20 shows the THD for rectifier input currents as function of output power. The rectifier power factor as function of the output power is shown in Fig. 21. In this case, the measured total harmonic distortion of the input voltage is 2.83%.


Fig. 16. Drive signals for sub-sector SS1C (2 V/div).

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Fig. 19. Input voltage reference and current in phase A.

Fig. 20. THD for input currents as function of output power ( experimental measurements). Fig. 17. Duty cycles for switches A, B and C (5 V/div).

Fig. 21. Power factor as function of output power ( measurements).

Fig. 18. Input line currents (20 A/div).

experimental

The rectifier efficiency as function of output power is presented in Fig. 22. The rectifier efficiency is greater than 95% when it is operating above one half of nominal load.

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Fig. 22. Rectifier efficiency as function of output power ( measurements).

experimental

VI. CONCLUSION A methodology to apply space vector modulation technique was proposed to three-phase three-switch two-level unidirectional PWM rectifier. This methodology is summarized as follows. — Identification of current sectors and vector sectors and definition of sub-sectors. — Analysis of topological stages of converter and verification of available vectors in each sub-sector. — Definition of more adequate logic for disposing the command signals and vectors sequence. — Determination of intervals for application of vectors and calculus of duty cycles functions in sub-sectors. — Implementation of command signals from PWM modulator. With this methodology, it is not necessary to determine the sectors of vectors, only to impose desired current sectors from input voltage references and the proposed methodology could be applied to other two-level unidirectional PWM rectifiers [10], [11]. The proposed modulation technique reduces the number of commutations of switches and the switching losses are minimized. The vector control structure was described for an implementation with DSP controller and experimental results validate the implemented modulation technique and the applied control strategy. Unidirectional two-level PWM rectifier presents regulated output voltage, high efficiency, high power factor, and low input current THD. REFERENCES [1] J. W. Kolar and H. Ertl, “Status of the techniques of three-phase rectifier systems with low effects on the mains,” in Proc. 21st Int. Telecommun. Energy Conference, INTELEC ’99, Jun. 6–9, 1999.

[2] J. W. Kolar and F. C. Zach, “A novel three-phase utility interface minimizing line current harmonics of high-power telecommunications rectifier modules,” IEEE Trans. Ind. Electron., vol. 44, pp. 456–467, Aug. 1997. [3] B. Singh et al., “A review of three-phase improved power quality AC-DC converters,” IEEE Trans. Ind. Electron., vol. 51, no. 3, pp. 641–660, Jun. 2004. [4] J. W. Kolar, U. Drofenik, and F. C. Zach, “Space vector based analysis of the variation and control of the neutral point potential of hysteresis current controlled three-phase/switch/level PWM rectifier systems,” in Proc. Int. Conf. Power Electron. Drive Syst., Feb. 21–24, 1995, vol. 1, pp. 22–33. [5] D. Borgonovo, Y. R. Novaes, and I. Barbi, “A three-phase three-switch two-level PWM rectifier,” in Proc. 34th Annu. IEEE Power Electron. Specialists Conf., 2003, pp. 1075–1079. [6] T. Viitanen and H. Tuusa, “Experimental results of vector controlled and vector modulated VIENNA I rectifier,” in Rec. 35th IEEE Power Electron. Specialists Conf., Jun. 25–26, 2004, vol. 6, pp. 4637–4643. [7] J. W. Kolar and J. W. Droferuk, “A new switching loss reduced discontinuous PWM scheme for a unidirectional three-phase/switch/level boost-type PWM (VIENNA) rectifier,” in Proc. 21st Int. Telecommun. Energy Conference, INTELEC ’99, Jun. 6–9, 1999. [8] H. W. Van Der Broeck, H. Skudelny, and G. V. Stanke, “Analysis and realization of a pulsewidth modulator based on voltage space vectors,” IEEE Trans. Ind. Applicat., vol. 24, pp. 142–150, 1988. [9] M. Cichowlas and M. P. Kamierkowski, “Comparison of current control techniques for PWM rectifiers,” in Proc. 2002 IEEE Int. Symp. Ind. Electron., L’Aquila, Italy, Jul. 8–11, 2002, vol. 4, pp. 1259–1263. [10] R.-J. Tu and C.-L. Chen, “A new space-vector-modulated control for a unidirectional three-phase switch-mode rectifier,” IEEE Trans. Ind. Electron., vol. 45, no. 2, pp. 256–262, Apr. 1998. [11] W. Koczara and P. Bialoskorki, “Unity power factor three-phase rectifiers,” in Proc. 24th Annu. IEEE Power Electron. Specialists Conf., Jun. 20–24, 1993, pp. 669–674.

Flabio Alberto Bardemaker Batista was born in Alegrete, Rio Grande do Sul, Brazil, in 1971. He received the B.S. degree in electrical engineering from the Federal University of Santa Maria, Santa Maria, Brazil, in 1995 and the M.S. and the Ph.D. degrees in electrical engineering from Federal University of Santa Catarina, Florianopolis, Brazil, in 1996 and 2006, respectively. Currently, he is Professor of the Federal Center of Technological Education of Santa Catarina. His research interests include power factor correction and digital control.

Ivo Barbi (M’76–SM’90) was born in Gaspar, Santa Catarina, Brazil, in 1949. He received the B.S. and M.S. degrees in electrical engineering from Federal University of Santa Catarina, Florianópolis, Brazil, in 1973 and 1976, respectively, and the Ph.D. degree from the Institut National Polytechnique de Toulouse, France, in 1979. He founded the Brazilian Power Electronics Society and the Power Electronics Institute of the Federal University of Santa Catarina. Currently he is Professor of the Power Electronics Institute of the Federal University of Santa Catarina.