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A New Space-Vector-Modulated Control for a Unidirectional Three-Phase Switch-Mode Rectifier Rong-Jie Tu and Chern-Lin Chen, Member, IEEE
Abstract— A unidirectional three-phase switch-mode rectifier that delivers sinusoidal input currents in phase with the corresponding input phase voltages is proposed and analyzed in this paper. In the proposed topology, three ac switches are placed before the bridge rectifier and, respectively, across two power lines. A simple control scheme combing space-vector modulation and hysteresis current control is presented. Sinusoidal input line currents are observed in experimental results. (a)
Index Terms— Hysteresis current control, space-vector modulation, switch-mode rectifier.
I. INTRODUCTION
O
FF-LINE switch-mode ac/dc and ac/dc/ac power converters have historically employed full-wave bridge rectifiers and simple capacitor filters to power the unregulated dc buses. Due to the side effects of these nonlinear and storage elements, the input line currents are narrow pulses with rich harmonics, resulting in a notoriously poor power factor. This dramatically increases the utility transmission power losses and causes harmonic pollution of power lines. Consequently, switch-mode rectifiers (SMR’s) have gained increasing research interest recently for improving the power factor deterioration. According to the number of input line phases, the SMR’s can be classified into two groups: single-phase SMR’s and three-phase SMR’s. Owing to its simple control design and excellent performance, the single-phase boost-type SMR has made its popularity in the applications where the power rating is small ( 2 kW) [1], [2]. However, in large power applications, the three-phase boost-type SMR is effective and dominant for its power handling capability. Conventionally, a three-phase boost-type SMR consists of six switches with anti-paralleled diodes as shown in Fig. 1(a). This system is ideally applicable to a dc-linked ac motor drive since it draws sinusoidal input currents and controls the dc bus voltage. However, since six switches must be controlled individually, it needs a more complicated control circuit and six corresponding driving circuits for the switches. This increases the total system cost dramatically.
Manuscript received September 24, 1996; revised April 18, 1997. This work was supported in part by the National Science Council, R.O.C. The authors are with the Power Electronics Laboratory, Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C. (e-mail:
[email protected]). Publisher Item Identifier S 0278-0046(98)00897-1.
(b) Fig. 1. Conventional three-phase boost-type switch-mode rectifiers.
Another three-phase SMR is presented by Kolar et al. [3]. This approach is basically a bridge rectifier with three Yconnected ac switches on the ac side of the bridge as shown in Fig. 1(b). Despite the limitation of unidirectional power flow, a lower system cost is possible due to its relatively simpler structure. A main drawback of the circuit is the relatively high conduction losses since the phase currents must follow through two series-connected ac switches when they turn on. Moreover, appropriate control strategy is not presented to make full use of the merits of the new topology. A space-vector modulation method for a three-phase SMR has been proposed recently [4]. The input phase voltages are divided into six 60 intervals where no sign change occurs. An excellent power factor is obtained by controlling only two currents in each interval, but this control scheme needs to process complicated computations with complex numbers. High-speed microprocessors or digital signal processors are required. Again, this will increase the complexity and total cost of the system. Another simple hysteresis current control scheme for the three-phase SMR is discussed in several papers [5], [6]. The input phase current is individually controlled to track the corresponding template current waveform. It is capable of delivering nearly sinusoidal current waveforms with unity power factor. However, the switching pattern is random. This increases the switching losses and deteriorates the system
0278–0046/98$10.00 1998 IEEE
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Fig. 2. The proposed three-phase boost-type switch-mode rectifier.
performance. Moreover, this method cannot be directly applied to the unidirectional SMR. This paper presents a low-cost high-performance threephase unidirectional SMR system. The power circuit shown in Fig. 2 is investigated. It consists of a bridge rectifier with three delta-connected ac switches on the ac side of the bridge. Since the ac switches are placed on the ac side, the deadtime consideration to prevent two switches of the same bridge leg from conducting simultaneously is not necessary. Since the phase currents flow through only one ac switch at the storage phase of the boost inductors, it has relatively lower conduction losses than Fig. 1(b). The operation principle with simulation verification is described in the following sections. A simple control strategy combining space-vector modulation and hysteresis current control is proposed. Excellent power factor is observed in the experimental results. Moreover, the proposed control strategy has successfully reduced the switching losses by 33%. II. PROPOSED SMR TOPOLOGY Fig. 2 illustrates the unidirectional three-phase boost-type SMR discussed in this paper. In this approach, the conventionally used six switches are replaced by three delta-connected ac switches located between the boost inductors and bridge rectifier. Since the bridge rectifier is used, only unidirectional power flow is allowed. The proposed approach has its inherent limitation in the applications where bidirectional power flow is important, such as high power motor drive. However, many currently commercially available general-purpose inverters do not contain built-in SMR’s; instead they offer an optional choice to meet the corresponding power factor (PF) regulations. Thus they can keep costs minimal in the markets where PF regulations are not imposed yet and can meet the related PF requirements by offering an optional PF choice. The proposed approach offers an attractive choice in these applications, since it only adds three ac switches and boost inductors to the original circuit. The original circuit is not affected if the SMR option is not ordered. Since only three ac switches are to be controlled, it needs only three driving circuits for the corresponding ac switches. Moreover, since the delta-connected ac switches are placed on the ac side, the deadtime consideration to prevent two switches of the same bridge leg from conducting simultaneously is not necessary in this topology. It will simplify the control design greatly. An ac switch can be constituted by one or two power transistors [7]. It can conduct bidirectional currents when turned on and block ac voltages when turned off. Fig. 3
Fig. 3. Constitution methods of ac switches.
Fig. 4. The operational cycle is divided into six 60 intervals according to the phase voltage polarity.
illustrates some methods to constitute an ac switch. This paper adopts the first method since its driving is easier than the second one and its conduction loss is less than the third one. The operational cycle is divided into six 60 intervals according to the input phase voltage polarity. As shown in Fig. 4, no polarity change occurs in each interval. Each interval contains two positive and one negative phase voltages or one positive and two negative phase voltages. The ac switch connecting the two phases of same voltage sign is set normally open in every interval, since it will not effect the operation of the SMR (which will be explained later). Take interval , where and are positive and is negative, for example. Since the line currents are controlled to be in phase with the corresponding phase voltages, no current will flow through the diodes , , and . is set normally open, resulting in the subtopology in Fig. 5(a). According to the conducting states of and , there are four modes of operation in the example interval as shown in Fig. 5(b)–(e). Mode 1— ON, ON: As shown in Fig 5(b), , , and are short-circuited through the boost inductors. Currents flow from phases A and B, through the ac switches and the boost inductors, into phase C. All of the six diodes are reverse biased. At the same time, the buck capacitor discharges and supplies current to the load. By the basic circuit theory, we have (1) ON, OFF: Fig. 5(c) illustrates the resulMode 2— tant subcircuit of this mode. flows through the diodes and , supplies the load current, and flows back to phase C. The output capacitor must encounter the instantaneous unbalance between the input power and the output power. It
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(a)
(b)
(c)
(d)
(e) Fig. 5. Modes of operation in interval I where V a and Vb are positive and Vc is negative.
charges if is greater than the load current; it discharges and are forward biased. Phases A otherwise. Diodes and . By the and C are shorted through the inductors basic circuit theory, we have (2)
can safely set normally open without deteriorating the performance of the proposed SMR. Input currents in phase with the corresponding input voltages can be acquired by selecting proper operation modes in interval . That implies unity power factor. Since one of the three ac switches is set normally open in each interval, the switching loss is reduced by roughly 33%.
(3) Mode 3— OFF, ON: Fig. 5(d) illustrates the resultant subcircuit of this mode. Mode 3 is similar to Mode 2, and except that phases A and B are exchanged. Diodes are forward biased. It is clear that
III. SPACE-VECTOR MODULATION In this section, selection of appropriate operation modes by the space-vector concept is described. With the concept of the space vector, it is convenient to represent three-phase quantities (voltages and currents) as a space vector
(4) (8) (5) where Mode 4— OFF, OFF: As shown in Fig. 5(e), both phases A and B are connected to positive terminals of the output capacitor. and flow through the diodes, charge the output capacitor, and supply the load current. By the basic circuit theory, we have
Consequently, voltages before the rectifier bridge and can be represented as a voltage vector
,
,
(6)
(9)
(7)
Applying (9) into the four operation modes, four space voltage vectors are acquired in the interval as illustrated in Table I, where signifies normally open. Consequently, there are 24 voltage vectors in the whole operational cycle according to the conducting states of the switches. Some of them are identical. Fig. 5 shows the total resultant seven voltage vectors,
There are another four operation modes in the interval if turns on. Neglecting the conduction voltage drops of semiconductor devices, three of them are identical to Mode 1 and the fourth is identical to Mode 4. Therefore, we
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TABLE I VOLTAGE VECTORS ACCORDING TO THE OPERATION MODES IN THE INTERVAL I
where for for
(10)
Fig. 6. Voltage vectors corresponding to the voltages before bridge rectifier Va0 , Vb0 , and Vc0 .
Also, the input phase voltages and currents can be represented as space vectors (11) (12) If the phase quantities are balanced three-phase sine waves, the corresponding vector trajectories form a circuit on the complex plane. The derivative of the current vector can be written as (13) where
Equation (13) states that the current derivative vector is and (i.e., the opera function of the voltage vectors ation modes). The proper voltage vector can be decided according to the desired current derivative vectors and the given voltage vector . Then the appropriate conducting states of the switches can be decided. However, this needs complicated computations with complex numbers. A highspeed microprocessor or digital signal processor must be used to handle these computations. To design a simple control strategy, (13) must be further simplified. Due to three-phase balanced input, the input current vector in the example interval can be rewritten as (14) Therefore, the current error vector can be defined as (15) where is the current command vector. The trajectories of form a circle synchronous with the input voltage vector . If the phase current errors and can be limited within a preset band , the current error vector is limited in the rhombus as shown in Fig 6. There are four voltage vectors in interval to limit the current error vector within the desired area. To select the proper voltage vector, the current and are fed into the hysteresis comparators. errors If the input current is greater than the preset hysteresis band , the binary signals and are “0.” If the input current is smaller than the preset hysteresis band , binary signals and are “1.” When the current error vector meets the hysteresis bond, the voltage vector is selected according to Table II to draw the current error vector toward the origin
Fig. 7. The proposed control strategy. TABLE II VECTOR SELECTION IN INTERVAL
point. It can be mathematically proven that the current error can be limited in the rhombus area if and only if the voltage vector is selected according to Table II under the condition where is the peak value of the input line that voltage. Digital simulation with ideal elements is made to verify the deduced control strategy (see Fig. 7). The hysteresis band is set to one-tenth of the peak value of the input currents. Fig. 8(a) shows that the input currents are controlled within the hysteresis band. Since three phases are balanced, the third phase current is the negative sum of and . However, the is two times . Fig. 8(b) shows maximum current error of that the current error vector is limited within the predicted rhombus area. One necessary condition of this control strategy is that the output voltage must be greater than 1.5 times of the peak line-to-line voltage, which will be too high for some applications. However, the proposed control strategy still can work, even without satisfying the wanted condition, with some sacrifice of performance. Fig. 8(c) illustrates the result current . It is seen that the error vector trajectory with current vector outsteps the predicted rhombus area. However, since the current derivative vector is smaller, the number of
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(a)
(b)
(c) Fig. 8. The simulation results.
total switching is smaller than that in Fig. 8(b). To get the same current harmonics, the hysteresis band can be set to a smaller value than that of Fig. 8(b). IV. EXPERIMENTAL SYSTEM
AND
RESULTS
A three-phase boost-type SMR with the proposed control strategy is implemented and tested in the laboratory. The laboratory model is constrained by a limited university research budget to low power ratings of 500-W output. The experimental load is a pure resistance load. However, the results reported here are applicable to other types of load and have universal applications by resorting to the usual scaling law. Fig. 9 shows the block diagram of the proposed control is obtained by multiplying the scheme. Current command input phase voltage and the error voltage , which is obtained from the voltage compensation loop. The frequency response of the voltage compensation is far lower than 120 Hz. As the line frequency is concerned, can be treated as a dc value. Therefore, if the input current is controlled to follow the current command, it follows the input voltage in its waveform and follows the error voltage in its magnitude. The input currents are controlled to follow the current command by selecting the appropriate voltage vector . The desired voltage vectors are selected by the EPROM switching table outputs. The inputs of the EPROM consist of two groups
Fig. 9. Block diagram of the proposed control strategy.
of binary signals: signs of the input voltages , , and , and the signals , , and . The signs of the input voltages , , and divide the input voltage into six 60 intervals are according to Fig. 5. The binary signals , , and into the hysteresis obtained by feeding the current errors comparators. If the input current is greater than the current command, the digital signal is “0.” Otherwise, it is “1.” The outputs of the hysteresis comparators determine the desired
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(a)
(b)
(c) Fig. 10.
The experimental results.
TABLE III STATES OF SWITCHES Sbc, Sca, AND Sab ACCORDING TO THE SIGNS OF INPUT PHASE VOLTAGES AND THE OUTPUTS OF HYSTERESIS
input current follows the corresponding current command by the hysteresis control. Fig. 10(c) shows one of the gate driving signals. It is seen that the ac switch is set normally open in onethird of the operation cycle. Therefore, the switching losses are reduced by 33%. V. CONCLUSIONS
voltage vectors (i.e., operation modes) in the corresponding interval. However, for the simplicity of hardware design, the mapping between the voltage vectors and states of the ac switches is incorporated directly in the switching table as shown in Table III. For example, if , , then is i.e., in interval , and selected. That is, and are triggered. From the above discussion, and will grow up to follow the current commands until another voltage vector is selected. A sinusoidal input current in phase with the corresponding input phase voltage is obtained as shown in Fig. 10(a). Excellent power factor is observed. Fig. 10(b) shows that the
This paper presents a space-vector-modulated control strategy for an unidirectional three-phase boost-type SMR. Remarkable advantages are obtained. 1) Employing only three delta-connected ac switches, the presented approach makes the operational principle clear and gives the possibility of simple control design. Since the ac switches are placed on the ac side, the deadtime consideration to prevent two switches of the same bridge leg from conducting simultaneously is not necessary. 2) Since the phase currents flow through only one ac switch at the storage phase of the boost inductors, the presented approach has relatively lower conduction losses than Fig. 1(b). 3) The proposed control scheme combines the space vector modulation and hysteresis current control. To control the input currents, a simple EPROM switching table instead of microprocessors or digital signal processors (DSP’s) is used. This makes the hardware design simple and inexpensive. 4) Only two of the three ac switches are controlled in each interval. The overall switching power losses are reduced by 33%.
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5) The proposed approach offers an attractive choice as an external optional SMR. It only adds three ac switches and boost inductors to the original circuit. The original circuit is not affected if the option is not ordered. Nevertheless, the proposed approach has some potential disadvantages. The first is that the diodes used in the rectifier bridge must be fast-recovery type. The second is that only unidirectional power flow is allowed. The proposed approach is not suitable in the applications where bidirectional power flow is important, such as motor drives. However, owing to its remarkable simplicity, excellent performance, and lower cost, the proposed approach offers an attractive choice of SMR for medium and large power applications such as power supplies (UPS’s).
[6] J. W. Dixon, A. B. Kulkarni, M. Nishimoto, and B. T. Ooi, “Characteristics of a controlled current PWM rectifier link,” in IEEE IAS Conf. Proc., 1986, pp. 685–691. [7] J. S. Lin, C. L. Chen, and C. Y. Lai, “A high-bandwidth PWM servo amplifier the direct-drive-valve actuation system,” in IEEE APEC’93 Conf. Proc., 1993, pp. 328–332.
Rong-Jie Tu was born in Miao-Li, Taiwan, R.O.C., in 1968. He received the B.S. degree in electrical engineering from the National Sun Yat-Sen University in 1991. Presently, he is working toward the Ph.D. degree in electrical engineering at the National Taiwan University, Taipei, Taiwan, R.O.C. His current research interests are in the areas of switch-mode rectifiers and induction motor drives.
REFERENCES [1] P. N. Enjeti and R. Martinez, “A high performance single phase ac to dc rectifier with input power factor correction,” in IEEE APEC’93 Conf. Proc., 1993, pp. 190–195. [2] S. Manias, “Novel full bridge semicontrolled switch mode rectifier,” Proc. Inst. Elect. Eng., vol. 138, pt. B, no. 5, pp. 252–256, 1991. [3] J. W. Kolar, H. Ertl, and F. C. Zach, “Realization considerations for unidirectional three-phase PWM rectifier system with low effects on the mains,” presented at the Int. Conf. on Power Electronics and Motion Control, 1990. [4] R. Wu, S. B. Dewan, and G. R. Slemon, “A PWM ac-to-dc converter with fixed switching frequency,” IEEE Trans. Ind. Applicat., vol. 26, pp. 880–885, Mar./Apr. 1990. [5] B. T. Ooi, J. C. Salmon, J. W. Dixon, and A. B. Kulkarni, “A 3-phase controlled current converter with leading power factor,” IEEE Trans. Ind. Applicat., vol. 23, pp. 78–84, Jan./Feb. 1987.
Chern-Lin Chen (S’86–M’90) was born in Taipei, Taiwan, R.O.C., in 1962. He received the B.S. and Ph.D. degrees in electrical engineering from the National Taiwan University, Taipei, Taiwan, R.O.C., in 1984 and 1987, respectively. He has been with the Department of Electrical Engineering at the National Taiwan University since 1987, where he is currently a Professor. His current research interests are in the analysis, design, and application of power electronics converters, and in motor drives.
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