A comparative study of control techniques for PWM ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 18, NO. 6, NOVEMBER 2003

A Comparative Study of Control Techniques for PWM Rectifiers in AC Adjustable Speed Drives Mariusz Malinowski, Member, IEEE, Marian P. Kazmierkowski, Fellow, IEEE, and Andrzej M. Trzynadlowski, Fellow, IEEE

Abstract—Four control techniques for pulse-width modulation (PWM) rectifiers in ac adjustable speed drives are presented. In particular, the so-called virtual-flux oriented control (VFOC) and virtual-flux based direct power control (VF-DPC) schemes are described and compared with their voltage based counterparts. These are the voltage oriented control (VOC) and voltage-based direct power control (V-DPC) techniques. Theoretical background is provided, and results of computer simulations and laboratory experiments are given, documenting advantages and disadvantages of the individual control strategies. Index Terms—Direct power control, PWM rectifiers, vertical flux.

I. INTRODUCTION

T

HE RAPID growth of ac adjustable speed drives (ASDs) in industry exacerbates the problem of harmonic pollution of the power system caused by the commonly used line-side diode rectifiers. Apart from application of active and passive filters, use of PWM rectifiers constitutes the best solution. The rectifiers have an additional advantage of the bi-directional power flow. Therefore, issues of control of PWM rectifiers have recently been receiving significant attention of researchers. As illustrated in Fig. 1, control techniques for PWM rectifiers can generally be classified as voltage based and virtual-flux based. Overall, four types of these techniques can be distinguished: 1) voltage oriented control (VOC); 2) voltage-based direct power control (V-DPC); 3) virtual-flux oriented control (VFOC); 4) virtual-flux-based direct power control (VF-DPC). In this paper, theoretical background for each control technique is provided, and comparative analysis, based on computer simulations and laboratory experiments, is carried out. Operating characteristics, advantages, and disadvantages of individual techniques are described to serve as a guide for ASD design engineers.

Fig. 1. Four control techniques for PWM rectifiers discussed in the paper.

to maintain the output voltage (dc-link voltage), , at the required level, while currents drawn from the power system should, ideally, be sinusoidal and in phase with respective phase voltages to satisfy the unity-power-factor (UPF) condition. The classic solution, the voltage oriented control (VOC) scheme, is shown in Fig. 2. The UPF condition is met when the line current , is aligned with the phase voltage vector, vector, , of the power line supplying the rectifier. Therefore, a revolving reference frame aligned with is used, and , of the quadrature component of is set the reference value, to zero. Switching signals, , , and , for individual phases of the rectifier are generated by a classic space vector modulator [1], [2]. Another solution is based on the idea of direct power control (DPC) [3]. This control scheme, depicted in Fig. 3, will be referred to as voltage-based direct power control (V-DPC). The real and reactive powers, and , drawn from the power line are calculated using information about the dc-link voltage, rectifier state, and line currents, , , and . Specifically

(1)

II. CONTROL TECHNIQUES FOR PWM RECTIFIERS Most ASDs employ voltage-source inverters. Then, the PWM rectifier is of the current-source type, with the topology identical to that of the inverter. The goal of the control system is Manuscript received October 22, 2001; revised May 8, 2003. This work was supported by a Foundation for Polish Science (FNP) Scholarship and the U.S. National Science Foundation through a Grant to the University of Nevada, Reno. Recommended by Associate Editor G. K. Dubey. The authors are with the Department of Electrical Engineering, University of Nevada, Reno, NV 89557–0153 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TPEL.2003.818871

(2) where denotes inductance of the input reactor. The UPF condition requires the reactive power to be zero. Two bang-bang controllers, and an identifier of the vector-plane sector currently housing the line voltage vector, allow direct selection of the next state of the rectifier. Distinct similarities between the outlined control schemes and those for ac motor control can be detected. The VOC principle resembles the field orientation, and the use of bang-bang controllers for direct selection of the converter state in the

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MALINOWSKI et al.: COMPARATIVE STUDY OF CONTROL TECHNIQUES

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(a) (a)

(b) Fig. 2. Voltage oriented control (VOC): (a) block diagram and (b) vector diagram (stationary coordinates, rotating d q coordinates).

0

0

(b) Fig. 4. Virtual-flux oriented control (VFOC): (a) block diagram (current sensorless version), (b) vector diagram (fixed coordinates, rotating d q coordinates).

0

0

it is the reference value, , of the direct component of the current vector that is set to zero. , in the reThe reference voltage vector, volving coordinates is calculated from the reference current sigand , and the vector, , of input nals, voltage to the rectifier, as (3) (4)

Fig. 3. Voltage based direct power control (V-DPC) scheme.

V-DPC is specific for the direct torque control method [4], [5]. An even closer analogy between the rectifier and induction motor controls is obtained using the so-called virtual flux , defined as a time integral of the phase vector, voltage vector, [6], [7]. It has been proposed to improve the rectifier control under nonideal supply voltage conditions, taking advantage of the integrator’s low-pass filter properties [8], [9]. A block diagram of the virtual-flux oriented control (VFOC) scheme with only voltage sensors is shown in Fig. 4. The vector of virtual flux lags the voltage vector by 90 . Therefore, for the UPF condition, in contrast with the VOC,

denotes resistance of the line reactor and is the where , and , to supply frequency. The phase input voltages, , the rectifier employed for calculation of , are computed from , and switching signals, , , and , as the output dc voltage,

(5)

Parameters and and the phase voltages, , , and , can be thought of as the stator resistance, leakage inductance, and EMF parameters of a virtual motor, respectively. As an alternative, if current sensors are used, a closed-loop current-control scheme analogous to that shown in Fig. 2 can be employed. The idea of virtual flux can also be used to enhance the direct power control [10]. The virtual-flux based DPC (VF-DPC)

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Fig. 5. Virtual-flux based direct power control (VF-DPC) scheme (voltage sensorless version). Fig. 6. Computational effort (number of instructions per sampling cycle).

TABLE I PARAMETERS OF THE POWER CIRCUIT

Fig. 7. Computation intensity (dSpace 1103).

scheme is shown in Fig. 5. The line voltage is estimated as a sum of the rectifier input voltage and voltage drop across the line reactors. The real and reactive powers are calculated as (6) (7) where subscripts and denote the direct and quadrature axes of a stationary reference frame in which vectors of the virtual flux and line current are expressed. III. COMPARATIVE INVESTIGATION For better assessment of the control techniques presented, a comparative investigation of these techniques was carried out. This issue is of great importance to designers and manufacturers of ac ASDs. PWM rectifiers have been increasingly employed as front-end converters in these drives, for instance by AllenBradley and Teco-Westinghouse. Results of the investigation are presented below. A. Conditions of Study All the four control schemes have been simulated using the SABER software package from Synopsys Systems. Values

of the sampling and switching frequency, respectively, were as follows: a) b) c) d)

VOC—5 kHz, 5 kHz; V-DPC—80 kHz, 5 kHz (average); VFOC—5 kHz, 5 kHz; VF-DPC—50 kHz, 4 kHz (average).

Other parameters of the power circuit are given in Table I. For fairness of the comparison, no outer-loop voltage controller was used in the dynamic investigation. The comparative study was conducted with respect to the complexity of control algorithms, operation with unbalanced and distorted line voltages, parameter sensitivity, and dynamic performance. B. Complexity of Control Algorithms To illustrate differences between the techniques with respect to the computational effort, the number of instructions per sampling cycle is shown in Fig. 6. Control strategies utilizing the virtual flux enjoy certain edge over their voltage-based counterparts. Computation intensity, that is, the processor load per sampling cycle, is illustrated in Fig. 7 for all methods under consideration. It can be seen that the direct power control strategies require distinctly faster processors than the VOC and VFOC techniques.


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TABLE II ADVANTAGES AND DISADVANTAGES OF CONTROL TECHNIQUES FOR PWM RECTIFIERS

Fig. 9. THD of the line current as a function of the magnitude of fifth harmonic of the line voltage.

Fig. 8. THD of the line current as a function of voltage imbalance.

C. Effect of Unbalanced and Distorted Line Voltages Figs. 8 and 9 illustrate the effect of nonideal line voltage on the current drawn by a rectifier under various control options. Distorted line voltages are given by

where varies from zero to 0.25 for a 0–25% distortion coeffiand denote peak values of the positive-secient, and quence and negative-sequence components, respectively. The unbalanced line voltages are

(9) (8)

Specifically, the total harmonic distortion (THD) of the current is shown as a function of the coefficient of imbalance

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Fig. 10.


Current THD versus error in estimation of the line inductance.

Fig. 12. Response of the VFOC rectifier to a step change in the active power (no outer-loop voltage controller).

value are minimized when input voltage is sensed directly, but such solution raises the cost of control system. As expected, the VOC and VFOC techniques are insensitive to these variations because the line inductance affects only the estimated angular position of the line voltage or virtual flux vectors. Therefore, it influences the input power factor but not the THD of the current. To the contrary, in the DPC schemes, the line inductance directly affects the estimated active and reactive power values, which in the closed control loop define switching instants and, as a result, the current THD. However, the impact of inaccurate line inductance estimation on the performance of a VF-DPC rectifier is considerably lower than that of a V-DPC rectifier. It is so because in the former rectifier no line current differentiation is performed [see (1) and (2)] and the integrator used in the flux calculation displays a low-pass filter behavior. Fig. 11. Response of the VF-DPC rectifier to a step change in the active power (no outer-loop voltage controller).

(Fig. 8) and magnitude of the fifth harmonic related to that of the fundamental (Fig. 9). Again, the VFOC and VF-DPC strategies display distinct superiority over the VOC and V-DPC schemes. D. Parameter Sensitivity Fig. 10 shows the dependence of the line current THD on variations of the line inductance. Effects of an incorrect inductance

E. Dynamic Performance A simulated response to a step change in the active power in the virtual-flux based control systems under consideration is shown in Figs. 11 and 12. As seen in Fig. 11, to reduce the control error, the VF-DPC scheme selects directly an appropriate voltage vector, providing very fast power control. Contrastingly, the dynamic response of a VFOC rectifier, illustrated in Fig. 12, is determined by the performance of current controllers. With PI controllers, the rectifier’s reaction is slower than that with hysteresis controllers.


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operation of the rectifier is illustrated in Fig. 13 and a transient condition (load increase) in Fig. 14. In spite of nonideal voltages, the current waveforms are almost purely sinusoidal [11]. IV. CONCLUSION

Fig. 13. Oscillograms of the line voltage (200 V/div), current (5 A/div), real power (2 kW/div), and reactive power (2 kVAr/div) in the steady state.

Fig. 14. Transient of the step change of the load in the improved VF-DPC (start-up of the rectifier). From the top: line voltage (200 V/div), line current (5 A/div), instantaneous active power (2 kW/div), and instantaneous reactive power (2 kVAr/div).

F. Comparison and Experimental Results Advantages and disadvantages of the control schemes compared are listed in Table II. Taking into account all operational features, the VF-DPC technique seems to be the most advantageous of all. A laboratory setup used for experimental investigation of the VF-DPC rectifier consisted of two commercial inverters (Danfoss VLT 5000, 5.2 kVA), one working as the rectifier, and a 3-kW, 220-V induction motor driving a dynamometer. The inverters were controlled from a dSpace DS1103 board installed in a PC. The mixed RISC/DSP digital control system, based on a 333-MHz PC604e microprocessor, a TMS320F240 DSP controller, and four 12-b, 0.8-s A/D converters, provided very fast signal processing. Figs. 13, and 14 depict waveforms of the line voltage, line current, and real and reactive power. Steady-state

Four techniques for control of PWM rectifiers have been described and compared. In the voltage oriented control scheme, the unity power factor is obtained by aligning the direct component of the line voltage vector with the current vector. An analogous approach in the virtual-flux oriented control method is based on the desired orthogonality of the virtual flux and current vectors. In the direct power control schemes associated with the voltage and virtual-flux oriented control techniques, bang-bang controllers of the real and reactive power are employed for selection of the next state of the rectifier. Strong similarities between the voltage and virtual-flux oriented control methods and the field orientation principle in ac motor drives can be observed. Also, the direct power control schemes are similar to the direct torque control of ac motors. These similarities allow extending some of the expertise gained in the area of adjustable-speed ac drives on the field of PWM rectifier control. Based on the comparative investigation, the virtual-flux based direct power control appears to be superior to the other three control techniques for PWM rectifiers. Simple algorithm with low sensitivity to nonideal supply voltage, and lack of the pulse width modulator, are the most prominent advantages of that method. On the other hand, the variable switching frequency and fast sampling required for digital implementation of hysteresis controllers are disadvantageous. These drawbacks can be eliminated by replacing hysteresis comparators with a switching table and employing PI current controllers providing a reference voltage vector to a space vector modulator. This leads to another DPC-SVM control scheme, which is the subject of another study [12]. REFERENCES [1] M. P. Kazmierkowski, R. Krishnan, and F. Blaabjerg, Control in Power Electronics. London, U.K.: Academic, 2002. [2] J. Holz, “Pulsewidth modulation—a survey,” IEEE Trans Ind. Electron., vol. 39, pp. 410–420, Oct. 1992. [3] T. Noguchi, H. Tomiki, S. Kondo, and I. Takahashi, “Direct power control of PWM converter without power-source voltage sensors,” IEEE Trans. Ind. Applicat., vol. 34, pp. 473–479, May/June 1998. [4] I. Takahashi and Y. Ohmori, “High performance direct torque control of an induction motor,” IEEE Trans. Ind. Applicat., vol. 25, pp. 257–264, Mar./Apr. 1989. [5] D. Telford, M. W. Dunnigan, and B. W. Williams, “A comparison of vector control and direct torque control of induction machine,” in Proc. APEC’00 Conf., 2000, pp. 421–426. [6] S. Bhattacharya, A. Veltman, D. M. Divan, and R. D. Lorenz, “Fluxbased active filter controller,” IEEE Trans. Ind. Applicat., vol. 32, pp. 491–502, May/June 1996. [7] M. Weinhold, “A new control scheme for optimal operation of a threephase voltage dc link PWM converter,” in Proc. PCIM Conf., 1991, pp. 371–3833. [8] P. J. M. Smidt and J. L. Duarte, “A unity power factor converter without current measurements,” in Proc. EPE’95 Conf., vol. 3, 1995, pp. 275–280. [9] J. L. Duarte, A. van Zwam, C. Wijnands, and A. Vandenput, “Reference frames fit for controlling PWM rectifiers,” IEEE Trans. Ind. Electron., vol. 46, pp. 628–630, June 1999.

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[10] M. Malinowski, M. P. Kazmierkowski, S. Hansen, F. Blaabjerg, and G. Marques, “Virtual flux based direct power control of three-phase PWM rectifiers,” IEEE Trans. Ind. Applicat., vol. 37, pp. 1019–1027, July/Aug. 2001. [11] F. Blaabjerg, S. Hansen, and M. Liserre, “Design and control of an LCLfilter based three-phase active rectifier,” in Proc. Conf. IEEE-IAS Ann. Conf., vol. 1, 2001, pp. 299–307. [12] M. Malinowski and M. P. Kazmierkowski, “DSP implementation of direct power control with constant switching frequency for three-phase PWM rectifiers,” in Proc. Proc. IECON’02, Barcelona, Spain, 2002.

Mariusz Malinowski (S’99–M’03) received the M.S. and Ph.D. degrees in electrical engineering (with honors) from the Institute of Control and Industrial Electronics, Warsaw University of Technology (WUT), Warsaw, Poland, in 1997 and 2001, respectively. He was a Visiting Scholar at Aalborg University, Denmark, and at the University of Nevada, Reno. He is an author of two patents and 40 technical papers, and a coauthor of two book chapters in Control in Power Electronics New York: Academic, 2002). His current research activities include control of PWM rectifiers, modulation techniques, and DSP applications. Dr. Malinowski received the Siemens Prize for his Ph.D. dissertation, a WUTPresident Prize, and a Best Paper Award at the IECON’2000 Conference. He is a Scholar of the Foundation for Polish Science and an active member of Polish Section IEEE.

Marian P. Kazmierkowski (M’89–SM’91–F’98) received the M.S., Ph.D., and Dr.Sci. degrees in electrical engineering from the Institute of Control and Industrial Electronics (ICIE), Warsaw University of Technology, Warsaw, Poland, in 1968, 1972, and 1981, respectively. From 1967 to 1969, he was with the Institute of Electrical Engineering, Warsaw, Poland, and from 1969 to 1980 he was an Assistant Professor at ICIE. From 1980 to 1983, he was with RWTH Aachen, West Germany, as an Alexander von Humboldt Fellow. From 1986 to 1987, he was a Visiting Professor at NTH Trondheim, Norway. Since 1987, he has been a Professor and Director of ICIE. He was a Visiting Professor at the University of Minnesota, Minneapolis, in 1990, at the Aalborg University, Denmark, in 1990 and 1995, and at the University of Padova, Italy, in 1993. He was a Coordinating Professor of the International Danfoss Professor Program from 1997 to 2000 at the Aalborg University. Since 1996, he has served as an elected member of the State Committee for Scientific Research in Poland. He is engaged in experimental research and theoretical work on electric drives and industrial electronics. He is the author or coauthor of over 200 technical papers and reports, as well as 13 books and textbooks. He co-authored Automatic Control of Converter-Fed Drives (New York: Elsevier, 1994). Recently, he co-edited and co-authored the compendium Control in Power Electronics (New York: Academic, 2002). Dr. Kazmierkowski was Chairman of the 1996 IEEE International Symposium on Industrial Electronics held in Warsaw (Poland). He has held several functions in the IEEE Industrial Electronics Society, and he is an Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. He is Chairman of Polish section of IEEE.

Andrzej M. Trzynadlowski (M’83–SM’86–F’99) received the M.S. degree in electrical engineering, the M.S. degree in electronics, and the Ph.D. degree in electrical engineering from the Technical University of Wroclaw (TUW), Poland, in 1964, 1969, and 1974, respectively. From 1966 to 1979, he was on the faculty of TUW. Later, he worked at the University of Salahuddin, Iraq, University of Texas, Arlington, and the University of Wyoming, Laramie. Since 1987, he has been with the University of Nevada, Reno, where he is now Professor of electrical engineering. In 1997, he spent seven months at the Aalborg University, Denmark, as the Danfoss Visiting Professor. In 1998, he was a Summer Faculty Research Fellow at the Naval Surface Warfare Center, Annapolis, MD. He has authored or coauthored more than 140 publications on power electronics and electric drive systems, and he has been granted 12 patents. He is the author of The Field Orientation Principle in Control of Induction Motors (Boston, MA: Kluwer, 1994), Introduction to Modern Power Electronics (New York: Wiley, 1998), and Control of Induction Motors (New York: Academic, 2001). He wrote a chapter on power electronic converters for the recently published book Control in Power Electronics (New York: Academic, 2002). Dr. Trzynadlowski received the 1992 IAS Myron Zucker Grant and is listed in Who’s Who in the World, Who’s Who in America, Who’s Who Among American Teachers, and Who’s Who in Polish America. He is an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS and the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, and a member of the Industrial Drives and Industrial Power Converters Committees, IEEE Industry Applications Society (IAS).