STUDY OF A SINGLE STAGE BUCK-BOOST THREE-PHASE RECTIFIER WITH HIGH POWER FACTOR OPERATING IN DISCONTINUOUS CONDUCTION MODE (DCM)

Transcription

1 STUDY OF A SINGLE STAGE BUCK-BOOST THREE-PHASE RECTIFIER WITH HIGH POWER FACTOR OPERATING IN DISCONTINUOUS CONDUCTION MODE (DCM) Altamir Ronsani Borges and Ivo Barbi* *Power Electronic Institute (INEP): Federal University of Santa Catarina (UFSC) Florianópolis SC Brazil ivobarbi@inep.ufsc.br Department of Electrical and Telecommunications Engineering: University of Blumenau (FURB) Blumenau SC - Brazil arb@furb.br Abstract This paper presents a three-phase Buck- Boost rectifier operating in discontinuous current mode (DCM). The main advantage of the proposed circuit is to provide, with a single stage, output voltages lower or higher than input voltage peaks. The command is very simple, with all switches simultaneously powered by the same pulse. The control of the structure is achieved by a voltage loop only. This can be accomplished because in DCM operation the input current shape is determined by the input voltage. Practical results of a 90 V input voltage project are presented. Sinusoidal currents with lower distortion and high power factor on Buck and Boost modes were obtained. Principle of operation, theoretical analysis and practical result are presented. Keywords - Three-phase rectifiers, power quality, power factor correction, Buck-Boost converter. I. INTRODUCTION The use of equipments that require the most electric power and the most energy quality is increasing in industry. Power electronic arises as an attractive option in order to attend this requirement. The semiconductor development and the constant research efforts enabled the increasing of electric power that can be electronically processed. The AC/DC three-phase converters have an important position in this evolution. The three-phase AC/DC converters are preferred in high power applications because they have lower output voltage ripple, lower switch stresses, better power distribution among phases, and other benefits presented in [1] and []. Therefore, the three-phase AC/DC converter research field had its development related with a constant search in order to attend the strict power quality standards. The power factor correction is one of the most important research topics on three-phase AC/DC converters. Initially the power factor correction was done by using only passive elements. This technique has several drawbacks like bulkiness and weight of the filter elements []. To follow, the single-phase and three-phase active power factor correction techniques had been developed. These techniques have been presenting innovative solutions until today. A brief review of the most important techniques of the three-phase active power factor correction and its most important features is presented in this paper. Afterwards, a single stage three phase Buck-Boost rectifier topology that operates in wide range input voltages is presented. II. BRIEF REVIEW OF SOME THREE-PHASE ACTIVE POWER FACTOR CORRECTION (PFC) THECHNIQUES Initially the three-phase rectifiers were associated to converters DC/DC. Later they were incorporated to form a single stage of rectification and power factor correction. Some of the techniques of greater prominence are presented in [1], [] and [3]. The simplest technique uses (in each one of the phases) a single-phase rectifier followed by a DC/DC converter. This technique has the advantage of allowing the direct application of already known techniques of the single-phase power factor correction. As a negative characteristic we can cite the greater difficulty of structure control due to the interferences among the phases [1]. Another technique is the use of a three-phase rectifier associated to a DC/DC converter operating in the discontinuous conduction mode (DCM) using only one switch. The most popular topology of this technique is the Boost single switch rectifier presented in [1] and []. Although simple, this technique has power limitations due to the high stress that the switch is submitted to []. The incorporation of DC/DC converter to the three-phase rectifier is verified in the Buck and Boost three-phase rectifiers presented in [1,, 3]. The Boost rectifier operating in CCM is most frequently used, presenting as main characteristics high efficiency and low EMI emission [1]. As negative aspect it can be detached that the output voltage must be higher than the peak of the input voltage [5], which represents a limitation in its use. The Buck rectifier presents as main characteristic its inherent protection against short circuits, easiness of inrush control and low output voltage. As main negative characteristics can be cited the discontinuity of the input currents and the amount of semiconductors in series, which results in bigger conduction losses []. The union of the characteristics Boost and Buck in an single circuit is a very interesting alternative in applications where the operation inside of a wide range of input voltages is important [4, 5]. In [5] is presented a topology formed for three singlephase modules of power factor correction. Each module has /09/$ IEEE 870

2 as base a single-phase Buck+Boost converter in discontinuous conduction mode (DCM) applied in the correction of the factor of power presented in [4], but operating in continuous conduction mode (CCM). Each module operates as Buck or Boost in due to the value of the input voltage. In [7] is presented a topology that associates a three-phase Buck rectifier to a DC/DC Boost converter. In [8] is presented a topology that associates a three-phase Boost rectifier to a DC/DC Buck converter. In the same way as in [5], the circuit operates as Buck or Boost due to the input voltage value. The structures described in [4], [5], [7] and [8] have at least two common points: The buck or boost operation modes is defined by the input voltage; The buck or boost modes have topological differences, with different switches acting in each mode. In [9] is proposed a circuit with buck and boost operation and one stage. The circuit is based in the buck-boost converter and operates in DCM. III. THE PROPOSED CIRCUIT The presented topology incorporates the Buck and Boost operation modes in a single rectifier circuit, being that the definition of the operation in Buck or Boost mode is simply done by the variation of the duty cycle applied to the switches. The circuit is based on DCM Buck-Boost single-phase PFC converter presented in [4]. The basic configuration is shown in Fig. 1 (the input filter was omitted for greater simplicity): Fig.. Final circuit of single-phase Buck-boost PFC converter. IV. PRINCIPLE OF OPERATION For the DCM operation, the command pulses are applied simultaneously to all the switches, resulting in the same stages of operation of the single-phase circuit. The description of the stages will be made for the interval between 60º and 90º of phase A. In this interval, phase A is positive and the other phases are negative and V AN > V BN > V CN. D1A DA L1A D3A D4A S1A D7A D5A D6A S A D1B DB L1B D7B D3B D4B S1B D5B D6B S B D1C DC L1C D7C D3C D4C S1C D5C D6C S C LA LB LC Fig. 1. DCM Buck-Boost single phase PFC. D8A D8B D8C In the DCM operation the command pulses are applied to the two switches simultaneously, resulting in three stages of operation: Energy Storage Stage: switches closed; Energy Transference Stage: switches opened; Discontinuous Stage. For the attainment of the three-phase version of the circuit some alterations were carried out in the single-phase version. As shown in Fig., switch S 1 is incorporated to the rectifier circuit together with diodes D 1 and D ; inductor L is divided into two equal inductors (L 1 and L ) and is added to the D 8 diode. The voltage source V O represents the association of the output capacitor with the resistive load presented in Fig. 1. The three-phase rectifier circuit is gotten using a single-phase module for each phase, connected in wye, as presented in Fig. 3: VAN VBN VCN Fig. 3. Three phase Buck-Boost rectifier proposed. A. Energy Storage Stage This stage begins when the switches enter in conduction. The complete circuit showing the semiconductors in conduction and the direction of phase current circulation is presented in Fig. 4. B. Energy Transference Stage This stage begins when the switches are blocked. As in the instant of the blockade the inductors lead different currents, the transference happens at distinct stages: All the inductors transfer energy (soon after the blockade); The inductors of phase C unload completely, blocking diodes D 7C and D 8C ;. The inductors of phase B unload completely, blocking diodes D 7B and D 8B ; /09/$ IEEE 871

3 Fig. 6. Equivalent circuit of energy storage stage. Fig. 4. Energy Storage Stage. The inductors of phase A unload completely, blocking diodes D 7A and D 8A, finishing the stage of energy transference. The complete circuit showing the semiconductors in conduction and the direction of circulation of the phase currents at the beginning of the stage is presented in Fig. 5. The equivalent circuits of the energy transference stage are presented in Fig. 7. The Fig. 7(a) shows the stage in which all inductors are transferring energy to the load. In Fig. 7(b) the inductor from lower amplitude phase (L C ) had transferred all its energy, while in Fig. 7(c), only the inductor from greater amplitude phase (L A ) is still transferring energy to the load. It must be observed that although diodes D 7,8A, D 7,8B and D 7,8C are in conduction, they appear in the circuit equivalent for representing the existing isolation among the inductors of each one of the phases. For simplification of the analysis of each stage, it will be considered that inside of a switching period, the amplitude of the input voltages do not present significant variation. Fig. 7. Equivalent circuits of the energy transference stage. C. Discontinuous Stage Fig. 5. Energy transference stage. In this stage all the semiconductors are blocked and the output capacitor feeds the load. This stage lasts until the beginning of the next switched period. V. EQUIVALENT CIRCUITS AND QUANTITATIVE ANALISYS The equivalent circuit of the energy storage stage is presented in Fig. 6, where: LA = LA1 + LA LB = LB1+ LB (1) LC = LC1+ LC A. Inductor currents during the energy storage stage This current begins with the application of the command pulse to the switches. The period of duration of the pulse is defined as t 1. The relation between t 1 and the switching period (T S ) defined as duty cycle (D) according to expression (): t1 D = () T chav In the circuit of Fig. 6, considering a balanced system, we know that the voltage on the inductors is equal to the voltage of the respective phase. Then we have: ΔIL ΔI k k VkN = Lk = Lk (3) t1 t1 where k represents the phases A, B and C. In the DCM, the variation of the inductor current is equal to the value of peak of the input current. Then: 1 1 VkN D Ikp = VkN t1 = (4) L L f k chav /09/$ IEEE 87

4 The peak of the inductors current is determined by the value of the voltage phase and by the duration of the command pulse of the switches (t 1 ). Considering that the maximum value of current happens when the phase voltage passes its maximum value V PP (phase voltage peak), the peak of the current in the inductors can be written as (5): 1 VkP D IkP = (5) L f B. Inductor currents during the energy transference stage Due to the amplitude differences among phase voltages, in the blockade of the switches, the inductor currents can present different values. Fig. 8 presents an amplitude configuration that occurs during the analyzed interval: Fig. 8. Inductor currents and output current wave forms during the transference energy stage. where I L_Xp represents the value of the phase currents at the beginning of the energy transference stage. It can be observed that I A > I B > I C and therefore the inductor of phase C will be unloaded first, followed by the inductor of phase B and finally of phase A. C. Total energy storage in the inductors The energy stored in inductors is determined by the expression (6): 1 E = L IMAX (6) At the end of the first stage, the energy stored in the inductors is determined by the addition of the energies stored in each one of them, according to expression (7): 1 ETotal = L ( IL_Ap + IL_Bp + IL_Cp ) (7) s Substituting (5) in (7) and generalizing for the all input period we obtain: 1 D ETotal = ( VAN + VBN + VCN ) (8) L fs From expression (8) is possible to verify that the total stored energy in the inductors is, at any instant, constant and defined by the expression (9): 3 D VPP ETotal = (9) 4 Lf D. Static Gain The energy delivered for the load within a switching period, whereas the output voltage is constant is defined by (10): ELOAD = PO Ts = Ts (10) R LOAD In the MCD, all the stored energy in the inductors is transferred to the load. Thus, equaling (9) and (10), the expression of the static gain is obtained: 3 RLOAD GS = = D (11) VPP L fs Replacing R LOAD by (1): R LOAD = (1) IO where I O is the output current of the circuit. The expression (11) can be rewritten according to (13): D G = S V = PP I (13) Op where I Op (parameterized output current) is defined by expression (14): 4 L fs IO IOp = IO = (14) 3 VPP 3 VPP 4 L fs From expression (14) one gets the abacuses of Fig. 9, that represent the behavior of the static gain due to the parameterized output current. E. Maximum duty cycle (D) The maximum duty cycle that guarantees the DCM operation is defined considering the maximum energy stored in the inductors and the necessary time to transfer this energy to the load. Fig. 10 illustrates the behavior of the current and voltage in an inductor at the limit of the DCM operation. From the circuit equivalent of Fig. 6 we know that during the energy storage stage, the voltage a applied to the inductors is equal to the voltage of the respective phases. From the Fig. 7 we know that during the energy transference stage, the voltage applied on each one the inductors is equal the output voltage. Thus the peak current can be express according (15): VPP I = P t1 t L = L (15) s /09/$ IEEE 873

5 Fig. 11. Limit between the DCM and the CCM operation. Fig. 9. Abacuses that presents the static gain (G S ) versus parameterized output current (I Op ). Fig. 10. Limit of DCM operation. As all the energy of the inductor will be transferred inside a switching period we have: DMAX (16) VPP + The expression (16) defines the limit of the DCM operation for the circuit. The abacus presented in Fig. 11 was traced from this expression where the region above the curve corresponds to the operation in the MCD and the region below the curve indicates the entrance in the CCM region. F. Inductor Calculation Considering a system without losses, the input three-phase power and the output power can be related by the expression (17): VPP I PP PO = 3 PPHASE = 3 (17) with I PP corresponding to the filtered input phase current peak. From (17) it can be determinate the expression for I PP : PO IPP = (18) 3 VPP Considering that the switching frequency is much superior to the frequency of the input voltage and that the power factor is unitary, the peak value of the filtered current can be approached to the instantaneous average value of the current in a switching period, calculated in the instant that the input voltage passes by the peak value. In such a way, from the Fig. 10 we have: 1 IPP t1 IPP = (19) Ts Substituting () and (18) in (19) and equaling to (5): 3 VPP D L = (0) 4 f s P O From (0) the parameterized output power is defined (P Op ): 4 Lf s POp = P O (1) 3 VPP Then it can be written according to (): PSp = D () Fig. 1 presents the parameterized output power versus duty cycle (D) /09/$ IEEE 874

6 Fig. 1. Parameterized output power versus duty cycle (D). G. Input Filter The input filter is of LC type easily found in literature. The project of the elements was made on the basis of [10]. Fig. 13 presents the structure of the filter. Fig. 13. Input filter struture. VI. OPERATION LIMIT The topology proposal presents a restriction related to the minimum output voltage value that guarantees the principle of operation, the presented characteristics and the mathematical analysis. This restriction can be easily understood from Fig. 14, that represents the equivalent circuit of energy storage stage with V AN > V BN > V CN. The diodes and the output voltage weren t presented in Fig. 6 because this figure refers to the normal operation. through a voltage divider where V LP is the peak of line voltage. Considering that the inductors have the same value and that the three-phase system is balanced, the voltage V XY can be determined with a voltage divisor where V LP is the peak line voltage. VLP VYX = (3) For an output voltage smaller than V XY, the diodes enter in conduction placing the output voltage in contact with the inductors during the energy storage stage. This modifies the principle of operation of the circuit. In such a way, the smaller value of output voltage so that the circuit operates the way it was presented is defined by (4): 3 VPP (4) VII. PRACTICAL RESULTS A rectifier with the following parameters was implemented: Input phase voltage: 90 V RMS ; Load resistor: 50 Ω; Switching frequency: 40 khz; Inductors: 5 μh; Input filter inductor: mh; Input filter capacitor: μf; IGBT s: IRGP50B60PD; Diodes: BYT 30P 1000; Adjusted duty cycle (D): 0.4 and 0.4. A. Operation with V O < V PP (D = 0.4) With D = 0.4 the circuit presents output voltage lower than input phase voltage peak. In Fig. 15 is shown the output voltage (11 V) and the input phase voltage (90.4 V RMS ): Fig. 15. Output voltage (Ch 1) and phase C voltage (Ch 3) waveforms with D = 0.4. Fig. 14. Equivalent circuit of energy storage stage operating below minimum output voltage. Knowing that the inductors are equal and that the threephase system is balanced, the tension V YX can be determined Fig. 16 presents a phase voltage and current. It is observed that these wave forms are in phase, which shows the structure high power factor. Fig. 17 presents a detail of inductor current and the command pulse waveforms. It can be noticed hat the duty cycle is approximately 0.4 and the circuit is operating in discontinuous conduction mode (DCM) /09/$ IEEE 875

7 Fig. 18 presents a detail of output current and the command pulse waveforms. It can be observed that the practical output current waveform is very similar to the theoretical one presented in Fig. 8. Fig. 19. Output voltage (Ch 1) and phase C voltage (Ch 3) waveforms with D = 0.4. Fig. 16. Voltage (Ch 1) and phase C current (Ch - 1 A/V) waveforms with D = 0.4. Fig. 0. Phase C voltage (Ch 1) and current (Ch 1 A/V) waveforms with D =0.4. Fig. 17. Detail of the phase C inductor current (Ch 1A/V) and the command pulse (Ch 1) waveforms with D = 0.4. Fig. 1 presents a detail of inductor current and the command pulse waveforms. It can be observed that the duty cycle is approximately 0.4 and that the circuit remains operating in discontinuous conduction mode (DCM). Fig. 18. Wave form detail of the Output current (Ch - 1A/V) and command pulse (Ch 1) with D = 0.4. B. Operation with V O > V PP (D = 0.4) With D = 0.4 the circuit presents output voltage higher than input phase voltage peak. In Fig. 19 is shown the output voltage (19 V) and the input phase voltage (90. V RMS ). Fig. 0 presents a phase voltage and current. It is observed that with D = 0.4 the wave forms remains in phase, which shows the structure high power factor. Fig. 1. Detail of the phase C inductor current (Ch 1A/V) and the command pulse (Ch 1) wave form with D = 0.4 VIII. CONCLUSION The proposed converter presents an important characteristic that becomes conceptually different from the majority of topologies found in literature: it is not composed for an association of converters but instead as a single threephase structure that operates in the modes Buck or Boost /09/$ IEEE 876

8 Another important factor is that the operation as Buck or Boost is defined only by the duty cycle applied to the switches. Moreover, operating inside a wide range of input voltages and with great load variation, the structure presents input currents with low distortion and in phase with its respective phase voltage, guaranteeing the high power factor power of the structure throughout all the operation range. Another interesting characteristic is the command simplicity: all the switches are commanded simultaneously by the same signal. As negative aspects it can be mentioned that operating in the DCM, the high peaks of input currents imply a power limitation. Moreover, the number of semiconductors in series may cause significant conduction losses, reducing the efficiency. [10] C. M. Seixas, Analysis and Project of a Power Factor Correction System Using a Multiphase Boost Converter Operating at Discontinuous Conduction Mode and Constant Frequency, Master Tesis, INEP/EEL/UFSC, Florianópolis SC Brazil, pp. 19-1, 1993 (in Portuguese). [11] I. Barbi, Eletrônica de Potência: Projetos de Fontes Chaveadas, Author Edition, Florianópolis, Brazil, 001. REFERENCES [1] H. Mao, F. C. Y. Lee, D. Boroyevich, S. Hiti, Review of High-Performance Three-Phase Power-Factor Corrections Circuits, IEEE Transactions on Industrial Electronics, vol. 44, no. 4, pp , August 1997 [] J. Shah and G. Moschopoulos, Three-Phase Rectifiers with Power Factor Correction, IEEE CCCE/CCGEI, pp , May 005. [3] B. Singh, B. N. Singh, A. Chandra, K. Al-Hadad, A. Pandey and D. P. Kothari, A Review of Three-Phase Improved Power Quality AC-DC Converters, IEEE Transactions on Industrial Electronics, Vol. 51, no. 3, June 004. [4] E. G. Schmindtner, P. W. Busch, Off-line Power Supply with Sinusoidal Input Current and an Active Limit to the Inrush Current, Power Conversion (PCIM) Conference Proceedings, Nurnberg, Germany, June 5 7, [5] R. Ridley, S. Kern and B. Fuld, Analysis of a Wide Input Range Power Factor Correction circuit for Threephase Applications, Proceedings of IEEE Applied Power Electronics Conference, pp , [6] B. Fuld, S. Kern and R. Ridley, A Combined Buck and Boost Power Factor Controller for Three-Phase Input, Proceedings of the 5th European Conference on Power Electronics Applications, Brigthon, UK, Vol. 7, pp , September (13-16) [7] M. Baumann, U. Drofenik and J. W. Kolar, New Wide Input Voltage Range Three-Phase Unity Power Factor Rectifier Formed by Integration of a Three-Switch Buck- Derived Front-End and a DC/DC Boost Converter Output Stage, nd IEEE Int. Telecommunications Energy Conference, Phoenix, Arizona, USA, pp , September, 000. [8] T. Takauchi, S. Fukuda and A. Moki, Control of a Three-Phase Voltage Source Rectifier with Buck-Boost Operation, Proceedings of the Power Converter Conference, Osaka, Japan, pp , 00. [9] C. Liu, J. Chai, X. Sun, S. Wei, Single Switch Step/Down Three-Phase Rectifier with Sinusoidal \input Current, Proceedings of IEEE Industry Applications Society, pp , /09/$ IEEE 877