Direct Torque Control With Imposed Switching Frequency in an 11 ...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 4, AUGUST 2004

827

Direct Torque Control With Imposed Switching Frequency in an 11-Level Cascaded Inverter José Rodríguez, Senior Member, IEEE, Jorge Pontt, Member, IEEE, Samir Kouro, and Pablo Correa

Abstract—This paper presents the application of direct torque control in an induction motor, using a multilevel cascaded inverter with separated dc sources. The control strategy operates with imposed switching frequency, improving torque behavior. The paper studies the theoretical concepts related to this method, like vector selection, state variables estimation, and commutation time calculation. In addition, this paper presents results for a three- and 11-level inverter-fed drive, from which it can be appreciated that the increase of levels of the load voltage reduces the torque ripple. Index Terms—AC drives, direct torque control (DTC), multilevel inverters.

I. INTRODUCTION

M

ULTILEVEL inverters have shown an important development for high-power medium-voltage ac drives [1], [2]. Several topologies have found industrial acceptance: neutral point clamped, flying capacitors, and cascaded with separated dc sources [2]. For these inverters, several control and modulation strategies have been developed: multilevel sinusoidal pulsewidth-modulation (PWM), selective harmonic elimination, and space-vector modulation, among others [2]. One of the methods that has been used by one major manufacturer in three-level inverters is direct torque control (DTC), which is recognized today as a high-performance control strategy for ac drives [3], [4]. This method has been applied to five-level neutral-point-clamped inverters and other multilevel topologies, using multiple hysteresis comparators [5], [6]. However, several authors consider that the use of hysteresis comparators is an important drawback of DTC, because it operates with variable switching frequency. This has motivated the development of variations of DTC that work with constant switching frequency, as shown in [7] for a two-level inverter. In [8], a DTC strategy with switching frequency imposition has been developed for a four-level flying capacitor inverter. With the increase of levels, extra degrees of freedom can be used to improve torque behavior, however the complexity of the generation of the firing pulses for the power transistors increases significantly.

Manuscript received April 29, 2003; revised October 8, 2003. Abstract published on the Internet May 20, 2004. This work was supported by the Chilean Research Fund FONDECYT under Grant 1040183 and by the Research Department of the Universidad Técnica Federico Santa María, Chile, under Grant 230222. J. Rodríguez, J. Pontt, and S. Kouro are with the Departamento de Electrónica, Universidad Técnica Federico Santa María, Valparaíso, Chile. (e-mail: [email protected]; [email protected]; [email protected]) P. Correa is with the Institut für Leistungselektronik und Elektrische Antriebe, Universität Siegen, 57068 Siegen, Germany (e-mail: [email protected]). Digital Object Identifier 10.1109/TIE.2004.831733

Fig. 1.

Topology of the 11-level inverter.

This paper presents a DTC strategy combining both issues: imposed switching frequency and inverter topologies that generate load voltages with high number of levels. The proposed strategy originates an important reduction in the torque ripple. Section II presents the topology of the multilevel inverter and the voltages delivered to the drive. The basic concepts related to the DTC theory are studied in Section III. In Section IV the voltage vector selection is explained. Torque and flux observers are obtained in Section V. Section VI presents the most relevant theoretical aspects concerning the DTC strategy developed in this work. Finally, Section VII presents results obtained from the application of the strategy to a three- and 11–level inverter-fed drive. II. MULTILEVEL INVERTER TOPOLOGY The topology of the 11-level inverter considered in this work is illustrated in Fig. 1. Each phase has five power cells connected in series. The power cells are composed of a noncontrolled three phase rectifier, a dc-link capacitor, and a single-phase H-inverter. The power circuit of one power cell is shown in Fig. 2.

0278-0046/04$20.00 © 2004 IEEE

828

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 4, AUGUST 2004

TABLE I OUTPUT VOLTAGES PER CELL

Fig. 2. Power circuit of one power cell.

Clearly, from (2), it can be seen that this topology generates up to 11 levels of different voltages per phase. This can be related to the number of levels of the voltage between two phases of the load by the general expression (3) where is the number of levels between two phases of the load and the number of levels of one phase of the inverter. In this particular case and . The vector representation [9] of the voltages generated by the inverter ( ), denoted by , is defined as

(4) Fig. 3. Simplified circuits of one power cell. (a) With (P ; P ) = (0; 0). (b) With (P ; P ) = (0; 1). (c) With (P ; P ) = (1; 0). (d) With (P ; P ) = (1; 1).

Voltage is the output of one power cell, subindexes and represent the phase and the cell, is illustrated in Fig. 1. respectively; for example, Depending on the gating signals or firing pulses and , the output voltages of one cell can be deduced by the simplified switch diagrams of the H-inverter illustrated in Fig. 3, and summarized in Table I. Since the power cells are connected in series, the output voltages of the different phases of the multilevel inverter are determined by

(1)

is the voltage of phase with respect to the neutral where shown in Fig. 1. Considering the possible values of , the different results for (1) are

(2)

where . The coordinates decomposition of in a fixed – plane is determined by

(5)

Considering (5) and (2), there exist 331 different space vectors that can be generated by the 11-level inverter, which corresponds to all dots illustrated in Fig. 4. In general, the number of different space vectors generated by a -level inverter is equal . to The large amount of vectors that can be generated by the inverter provides more degrees of freedom for control purposes. The way to select the appropriate vector will be discussed later.

III. BASIC PRINCIPLE OF DIRECT TORQUE CONTROL The stator flux vector ( ) of an induction machine is related to the stator voltage vector ( ), referred in stator coordinates, by (6)

RODRÍGUEZ et al.: DTC WITH IMPOSED SWITCHING FREQUENCY IN 11-LEVEL CASCADED INVERTER

829

v ) generated by an 11-level inverter.

Fig. 4. Voltage vectors (

Maintaining constant over a sample time interval and neglecting the stator resistance , the integration of (6) yields (7) Equation (7) reveals that the stator flux vector is directly affected by variations on the stator voltage vector. On the contrary, the influence of over the rotor flux is filtered by the rotor and stator leakage inductances, and is, therefore, not relevant over a short time horizon. Since the stator flux can be changed quickly while the rotor flux rotates slower, the angle between both vectors ( ) can be controlled directly by . A graphical representation of the stator and rotor flux dynamic behavior is illustrated in Fig. 5. The exact relationship between stator and rotor fluxes is found in [10], and shows that keeping the amplitude of constant will produce constant rotor flux . Since the electromagnetic torque developed by an induction machine [9] can be expressed by (8) it follows that the change in the angle due to the action of allows for direct and fast change in the developed torque . DTC uses this principle to achieve the desired torque response of the induction machine, by applying the appropriate stator voltage vector to correct the flux trajectory [4].

Fig. 5.

Influence of

V

over  during a sample interval

1t .

IV. VOLTAGE VECTOR SELECTION Fig. 6 illustrates one of the 331 voltage vectors generated by , denoted by (central dot). The the inverter at instant next voltage vector to be applied to the load ( ), can be expressed by (9) where . Each vector corresponds to one corner of the elemental hexagon illustrated in gray in Fig. 4 and by the dashed line in Fig. 6. The task is to determine which will correct the torque and flux response, knowing the the torque and flux errors ( actual voltage vector

830

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 4, AUGUST 2004

TABLE II VOLTAGE VECTOR SELECTION LOOKUP TABLE

Fig. 6. Possible voltage changes

1v

that can be applied from a certain v .

V. TORQUE AND FLUX ESTIMATION Fig. 8 represents [omitting block (2)] a standard DTC configuration. The external loop controls the drive mechanical speed ( ). The internal loop controls the electromagnetic torque ( ) using DTC. To access the right voltage vector according to Table II [implemented in block (1)], an accurate estimation of the process variables is needed, in order to compute the torque and stator flux errors (and position). With the measurement of stator voltages and currents, and using the transformation from three-phase ( , , ) to two-phase ( , ) coordinates, the following observer is obtained for the interval): stator flux (from integration of (6) over a

Fig. 7. Illustration of voltage selection

1v

(10) in sector (2).

, ) and the stator flux vector position (sector determined by angle ). Note that the next voltage vector applied to the load will always be one of the six closest vectors to the previous , this will soften the actuation effort and reduce high dynamics in torque response due to possible large changes in the reference. Using (7) and (8), and analyzing, for example, sector (2) ilincreases the stator flux lustrated in Fig. 7, the application of witch implies a reduction of . amplitude but reduces angle reduces the magnitude of , while it inOn the contrary, and, thus, . If is applied to the load, both flux creases and torque increase, and it is clear that produces the conand are not considered for selectrary effect. Note that tion in sector (2), because both change their influence over , is located, they also depending in which part of the sector affect more than due to less action over angle . The same analysis can be carried out for the other sectors. Table II summarizes the vector selection according to this criterion for and the different sectors and comparators output (or desired corrections). Note that each sector uses only four of the six possible vectors; the other two vectors are not employed for the same reason as the particular case analyzed previously for sector (2).

Once by

is estimated, the electromagnetic torque is obtained

(11)

VI. DTC WITH IMPOSED SWITCHING FREQUENCY A. General Description Fig. 8 [including block (2)] represents a simplified block diagram of the DTC configuration used in this work. The main difference with the classic DTC [4] is the incorporation of an imposed switching frequency algorithm and a torque ripple minimization principle, achieved by the appropriate use of the state ), and the extra degrees of freedom variables estimation ( provided by the multilevel inverter. Block (1) in Fig. 8 selects the appropriate voltage vector ( ) necessary to correct the behavior of torque and flux, according to the comparators output, flux vector position ( ). Block (2) in Fig. 8 performs the switching frequency imposition, by calculating at instant the commutation time that . will ensure zero torque error at the next sampling period

RODRÍGUEZ et al.: DTC WITH IMPOSED SWITCHING FREQUENCY IN 11-LEVEL CASCADED INVERTER

Fig. 8.

831

DTC with imposed switching frequency simplified block diagram.

number of levels of the inverter will reduce the difference beand , minimizing in this way the torque tween voltages ripple. VII. RESULTS

Fig. 9.

Imposed switching frequency principle.

At time the new voltage vector will be applied to the load, imposing one commutation per sampling interval. B. Switching Frequency Imposition The strategy is illustrated in Fig. 9, in which an example of the behavior of reference torque and real torque is illustrated. Considering the different torque slopes and their duration in time, the relation to estimate the commutation time can be deduced, obtaining

(12)

is the torque reference, and the torque and where its derivative at instant , both estimated in block (3) of Fig. 8 is the according to the drive measured variables. Finally, selected previtorque variation predicted for voltage vector ously [8]. Note that torque is assumed linear due to small sampling time . Torque ripple reduction is achieved by selecting voltage veclocated closely to the previous vector as seen in tors Section II, due to lower actuation effort. An increase in the

is shown in Steady-state line-to-line load voltage Fig. 10; the high number of levels [21 according to (3)] generated by the 11-level inverter can be clearly appreciated in the voltage waveform. Fig. 11(a) presents the transient behavior of torque and speed for an induction motor driven by a three-level inverter, using of 0.15 the proposed DTC strategy. For a sampling period ms, the imposed switching frequency resulted almost constant, especially in steady state. Variations of the switching frequency where small in a range around 6.7 kHz. From Fig. 9 it can be deduced that one period of the torque ripple is approximately (when the reference torque variations are small), resulting in a frequency of 3.3 kHz; this can be observed in the frequency spectrum of the torque shown in Fig. 11(b). Fig. 12(a) presents the same transient response for torque and speed, using an 11-level inverter. The torque has significantly smaller ripple, conserving the same imposed switching frequency, which can be clearly appreciated in Fig. 12(b). The torque spectrums shown in Figs. 11(b) and 12(b) are scaled to appreciate in a better way the torque ripple present in the signal, therefore, the continuous component is not plotted completely, it appears saturated on 0.3 N m, while in fact it is approximately 23.75 N m. VIII. CONCLUSION This paper has demonstrated the possibility of applying DTC with imposed switching frequency in medium-voltage cascaded inverters with a high number of cells. Results presented for three- and 11-level inverters show that an increase in the number of levels improves the torque quality reducing ripple amplitude. The use of a frequency imposition algorithm helps to minimize the variations of the switching frequency typical in standard DTC applications due to hysteresis comparators. This improvement produces a narrow torque spectrum, even for high-frequency harmonics.

832

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 4, AUGUST 2004

Fig. 10. Line-to-line load voltage v (t), generated by the 11-level cascaded inverter.

Fig. 11.

DTC using a three-level inverter and imposed switching frequency strategy. (a) Torque T (t) and speed ! (t) transient response. (b) Torque T spectrum.

Fig. 12.

DTC using an 11-level inverter and imposed switching frequency strategy. (a) Torque T (t) and speed ! (t) transient response. (b) Torque T spectrum.

RODRÍGUEZ et al.: DTC WITH IMPOSED SWITCHING FREQUENCY IN 11-LEVEL CASCADED INVERTER

REFERENCES [1] R. Teodorescu, F. Blaabjerg, J. Pedersen, E. Cengelci, S. Sulistijo, B. Woo, and P. Enjeti, “Multilevel converters–A survey,” in Proc. European Power Electronics Conf., EPE 99, Lausanne, Switzerland, 1999, CD-ROM. [2] J. Rodríguez, J.-S. Lai, and F.-Z. Peng, “Multilevel inverters: A survey of topologies, controls and applications,” IEEE Trans. Ind. Electron., vol. 49, pp. 724–738, Aug. 2002. [3] P. Lataire, “White paper on the new ABB medium voltage drive system using IGCT power semiconductors and direct torque control,” EPE J., vol. 7, no. 3, pp. 40–45, Dec. 1998. [4] N. Mohan, Advanced Electric Drives: Analysis, Control and Modeling using Simulink. Minneapolis, MN: MNPERE, 2001, ch. 8. [5] T. Ishida, K. Matsuse, T. Miyamoto, K. Sasagawa, and L. Huang, “Fundamental characteristics of five-level double converters with adjustable DC voltages for induction motor drives,” IEEE Trans. Ind. Electron., vol. 49, pp. 775–782, Aug. 2002. [6] D. Casadei, G. Serra, and A. Tani, “Improvement of direct torque control performance by using a discrete SVM technique,” in Proc. IEEE PESC’98, 1998, CD-ROM. [7] J.-K. Kang and S.-K. Sul, “New direct torque control of induction motor for minimum torque ripple and constant switching frequency,” IEEE Trans. Ind. Applicat., vol. 35, pp. 1076–1082, Sept./Oct. 1999. [8] C. Martins, X. Roboam, T. Meynard, and A. Carvalho, “Switching frequency imposition and ripple reduction in DTC drives by using a multilevel converter,” IEEE Trans. Power Electron., vol. 17, pp. 286–297, Mar. 2002. [9] D. W. Novotny and T. A. Lipo, Vector Control and Dynamics of AC Drives. New York: Oxford Univ. Press, 1996. [10] M. Kazmierkowski, R. Krishnan, and F. Blaabjerg, Control in Power Electronics. New York: Academic, 2002.

José Rodríguez (M’81–SM’94) received the Engineer degree from the Universidad Técnica Federico Santa María, Valparaiso, Chile, in 1977 and the Dr.-Ing. degree from the University of Erlangen, Erlangen, Germany, in 1985, both in electrical engineering. Since 1977, he has been with the University Técnica Federico Santa María, where he is currently Vice Rector of Academic Affairs and a Professor in the Electronics Engineering Department. During his sabbatical leave in 1996, he was responsible for the Mining Division of Siemens Corporation in Chile. He has extensive consulting experience in the mining industry, especially in the application of large drives like cycloconverter-fed synchronous motors for SAG mills, high-power conveyors, controlled drives for shovels, and power quality issues. His research interests are mainly in the areas of power electronics and electrical drives. Recently, his main research interests have been multilevel inverters and new converter topologies. He has authored or coauthored more than 130 refereed journal and conference papers and contributed to one chapter in the Power Electronics Handbook (New York: Academic, 2001).

833

Jorge Pontt (M’00) received the Engineer and Master degrees in electrical engineering from the Universidad Técnica Federico Santa María (UTFSM), Valparaíso, Chile, in 1977. Since 1977, he has been a Professor in the Department of Electrical Engineering and Department of Electronic Engineering, UTFSM. He is the coauthor of the software Harmonix used in harmonic studies in electrical systems. He has authored more than 60 international refereed journal and conference papers. He is a Consultant to the mining industry, in particular, in the design and application of power electronics, drives, instrumentation systems, and power quality issues, with management of more than 80 consulting and R&D projects. He has had scientific stays at the Technische Hochschule Darmstadt (1979–1980), University of Wuppertal (1990), and University of Karlsruhe (2000–2001), all in Germany. He is currently Director of the Center for Semiautogenous Grinding and Electrical Drives at the UTFSM.

Samir Kouro (S’04) was born in Valdivia, Chile, in 1978. He received the Engineering and M.Sc. degrees in electronics engineering from the Universidad Técnica Federico Santa María, Valparaíso, Chile, in 2004. He is currently a Research Assistant in the Electronics Engineering Department, Universidad Técnica Federico Santa María. His main research interests are automatic control and power electronics.

Pablo Correa was born in Santiago, Chile, in 1976. He received the Ingeniero Civil Electronico degree and the M.Sc. degree in electrical engineering from the Universidad Técnica Federico Santa María, Valparaíso, Chile, in 2001. He is currently working toward the Doktor-Ingenieur degree at Siegen University, Siegen, Germany. His research interests include modern microprocessor applications and power electronics.