High-performance motor drives

1 High-Performance Motor Drives Marian P. Kazmierkowski, Leopoldo G. Franquelo, Jose Rodriguez, Marcelo Perez and Jose I. Leon Abstract-- Power electronic converter-fed high performance AC drives belong to high-tech industry and are one of main factors for energy saving and productivity growth. This paper reviews present state and trends in development of key parts of controlled induction motor drive systems: converter topologies, modulation methods, as well as control and estimation techniques. Following topologies are described: Twoand Multi-level Voltage Source Converters, Current Source Converters and Direct Converters. Among the modulation techniques are briefly presented: conventional bipolar and unipolar PWM, space vector modulation (SVM) with extension for multilevel converters, harmonic control techniques, variable frequency modulation (hysteresis, nearest level, and model predictive techniques). About the control strategies, the generic torque control methods are described in two groups: linear and nonlinear controllers. In linear group are presented field oriented control (FOC), direct torque control (DTC) with voltage SVM, and DTC with flux vector modulation (DTC-FVM). The group of nonlinear control include: classical switching table based hysteresis DTC, direct self control (DSC) and predictive DTC scheme. Also, selected simple flux vector observers/estimators are discussed. I. INTRODUCTION The main part of all the produced electric energy is used to feed electric motors and the conversion of electrical power into mechanical power involves motors ranging from below 1 W up to several dozen MW. The contemporary drive systems are expected to meet a variety of requirements among which are: • Maximum conversion efficiency, • Wide range steeples adjustment of angular speed, torque, acceleration, angular and linear position, • Fast error elimination when the control and/or disturbance signals are being changed, • Maximum utilization of motor power under reduced voltage, current, etc., • Reliable, user friendly operation. The present-day drive control engineering draws heavily on the theory of electric motors, control theory, and industrial electronics, however, it is the last of these disciplines what plays a decisive role in the development of automated electrical drive systems. The two basic divisions of industrial electronics: digital signal processing and power electronics, have opened the way to replace DC brush motors by AC motors in high performance drives. 2 The roots of power electronics go back to 1901 when P. C. Hewitt invented glass-bulb mercury-arc rectifier [1]. However, the present era of semiconductor power electronics started with the commercially introduced by General Electric (GE) silicon controlled rectifier (SCR), popularly called thyristor, in 1958. Next, the development continued in new semiconductor structures, materials, fabrication, etc. bringing on the market many new devices with higher power ratings and improved characteristics. Today among most common power electronic devices are: power metal oxide semiconductor field effect transistor (MOSFET) and insulated gate bipolar transistors (IGBT), and in very high power range the integrated gate-commutated thyristors (IGCT) ¡Error! No se encuentra el origen de la referencia.]. Also, integrated intelligent power modules (IPM) are available. Today very promising, opening new era of high voltage, high frequency, and high-temperature technology are semiconductor devices based on wide-band gap silicon carbide (SiC) material.[3]. The new power semiconductor devices have always triggered the development of new converter topologies. At the beginning it started with diode and thyristor line commutated converters and continued with modern forced commutated converters controlled via pulse width modulation (PWM) methods. The list of application of power electronics is too long to list them in all. Therefore, in Figure 1, a classification of the typical applications of power electronic converters from low to high power group is given. This paper presents an overview of power converter-fed high performance AC drives in three basic parts: power converter topologies, modulation techniques for power converters, control and estimation. Transportation Power Distribution Low power devices Low Power Medium Power High Power Power range Usual converter topologies Typical power semiconductors Technology trend Up to 2 kW AC/DC, DC/DC MOSFET High power density High efficiency 2 kW – 500 kW AC/DC, DC/DC, DC/AC MOSFET, IGBT Small volume and weight Low cost and high efficiency More than 500 kW AC/DC, DC/AC IGBT, IGCT, THYRISTOR High nominal power of the converter High power quality and stability Typical applications Renewable Energy IndustryRoof PVElectric VehiclesAppliances Figure 1. Classification of the power converter applications II. POWER CONVERTER TOPOLOGIES IV. 1. Voltage Source Converters 3 Voltage source converters are considered nowadays a mature technology and have become one of the most common power converter topologies in industry. The basic 2-level voltage source inverter (2L-VSI) is shown in 2a). It is composed by a DC capacitor or voltage source, which gives its name, and an arrangement of two power semiconductors per phase. The gating signals for both power switches are complementary, and the load is connected to the positive or the negative bar and generates only two possible output voltage levels. Using a modulation strategy to generate the gating pulses it is possible to synthesize output voltages with the desired fundamental component. Due to the high harmonic content in the output voltage that need to be filtered to produce nearly sinusoidal currents, these converters are usually applied to very inductive loads such as motors [2], but sometimes, depending on the application, an additional output filter could be required. The maximum output voltages when a maximum modulation index is used, is defined by the DC link voltage value. In order to efficiently drive high power loads, a large DC link voltage is required, but in practice, this voltage is limited by the blocking voltage of semiconductors and therefore its technology. For instance, some industrial drives use low voltage IGBT (LV-IGBT) to provide up to 690V output voltage. To avoid this voltage limitation, voltage source multilevel converters topologies have been developed during the last decades [3]–[9]. These converters are more complex than the two-level voltage source inverter (2L-VSI) in terms of topology, modulation and control, but the additional complexity can be considered as an opportunity to improve its power quality, reliability, power density, performance and efficiency. The three-level neutral point clamped (3L-NPC) is shown in Figure 2b) [10]. In this converter the DC link voltage is equally divided using two capacitors and, therefore, the phase output can be connected to the positive bar switching on the two upper switches, to the mid-point using the two central switches or to the negative bar using the two lower switches [11][12]. Each semiconductor needs to block only the half of the total DC link voltage allowing increasing the power rating using the same semiconductor technology than the conventional 2L-VSI. The semiconductors normally used in these converters are the high voltage IGBT (HV-IGBT) [13] and the IGCT [14]. A well documented problem presented in this converter is the unbalance of the capacitors produced by asymmetries in the converter hardware and mainly the operational conditions [15]. Several strategies to deal with this problem have been proposed, mainly focused to modify the modulation strategy [16][17]. Another issue of this converter is the unequal distribution of losses, which causes that the outer switches switching losses differ from the central ones, depending on the operation condition. This problem cannot be easily addressed using the conventional scheme and modified topologies like active neutral point clamped (ANPC) have been proposed [16]. In this converter, the clamping diodes are 4 replaced by controlled switches, then selecting the appropriate combination of switches it is possible to reduce and equally distribute the losses. The NPC converter can be scaled up to achieve more than three levels simply dividing the DC-link in more than two values using several capacitors [18]. Each one of these partial DC-link voltages can be connected to the load using an expanded arrangement of switches and clamping diodes. Along with the increased power rating, the advantages of several output voltage levels are a better power quality, smaller dv/dt and associated EMI [19]. However, when the NPC converter has more than three levels additional problems arise. From the point of view of the power topology, the clamping diodes require to block higher voltage than the main switches, therefore it is necessary to use different technology or use several clamping diodes connected in series. In addition, the unequal use of the power devices of the topology (also present in the 3L-NPC for the inner power semiconductors), becomes critical. Finally, the reliability is also reduced due to the increment of the components count [20]. The mentioned drawbacks limit the use of NPC with more than 3 levels in industrial applications [21]. 5 Figure 2. Topologies and phase voltages of the conventional two-level and multilevel voltage source inverters Converters based on modular power cells as such as the cascaded Hbridge (CHB) and the flying capacitor (FC) converter have been proposed so far to provide higher number of output voltage levels than the 3L-NPC. The CHB converter topology, shown in Figure 2c), is a highly modular converter based on several single phase inverters, usually called power cells, connected in series to form an phase [22][23]. Each power cell is implemented based on 6 standard low voltage components, which provides an easy and cheap replacement in case of failure [24]. The main advantage of this converter is that using only low voltage components it is possible to drive medium voltage high power loads. Although the switching frequency in each cell is low, the equivalent switching frequency applied to the load is high, which reduces the switching losses, produces low dv/dt and helps to avoid resonances [25]. Additionally, several fault tolerant strategies can be implemented increasing their reliability and overall availability [26]. In the CHB converter, each power cell requires an isolated DC power source which can be obtained for example from photovoltaic (PV) panels or using a multi-pulse transformer with several secondaries diode rectifiers and a DC-link capacitor. The first option provides high scalability and allows the PV energy to be directly connected to the medium voltage grid. The second option has become the standard for drive applications, providing galvanic isolation and high quality input current, cancelling out the low order harmonics produced by the diode rectifiers. The cancellation of current harmonics is produced by a phase shift between the transformer secondaries which leads to a more complex transformer, especially when a high number of cells is used. This input transformer however reduces the scalability of the converter. The DC-link is designed to have a very large capacitance which, on one hand, allows having a good ride-trough capability but on the other hand increasing the size of each cell where at least half of its size are only capacitors and requires additional circuits to safely charge and discharge the DC-link. As mentioned above, the standard solution to provide the isolated DC sources is using a diode rectifier, which does not provide regenerative operation and cannot be used in applications such as downhill conveyors, or GNL turbines where the load is always regenerating or, at least, great part of its operating time. In these cases a regenerative converter, where the diode based rectifiers are replace by controlled rectifiers, has been proposed [27]. This alternative can control bidirectional active power, which additionally gives precise control of the DC-link voltage, the input reactive power and provides sinusoidal input currents which help to simplify the input transformer configuration. The drawbacks of the regenerative topology are the requirement of inductive input filters and its associated cooling system, the increased losses by the forced commutation of the controlled rectifier and the reduction in the reliability [28][29]. Several topologies based on the cascaded approach have been proposed in the literature. In particular, the asymmetrical CHB converter, built using different values of the dc voltage for each power cell, allows to increase the number of output voltage levels using only a reduced number of power cells [30]. It can produce up to 27 output voltage levels using only three power cells (only nine levels conventional symmetrical CHB converter), but it requires the 7 use of different devices in each power cell and a control system to avoid regeneration in the low voltage cells [31][32]. The FC converter topology is shown in Figure 2d). The output voltage is generated connecting directly the phase output to the positive or negative bars or through the floating capacitors. The number of output voltage levels depends on the number of floating capacitors and the relation among their different DC voltages. For example, the topology shown in Figure 2d) generates 5 output voltage levels. This converter, as in the CHB case, also presents a modular topology, where each cell is composed by a DC capacitor and two complementary switches. However, on the contrary of the CHB case, the addition of extra power cells in the FC converter does not increase the nominal power of the converter but only reduces the dv/dts improving the harmonic content of the output waveforms. As the CHB converter, the modularity reduces the cost of component replacement and maintenance, and also allows to implement fault tolerant strategies. Finally, the FC converter has also its asymmetrical version, and for instance if the floating DC voltage relations of the topology shown in Figure 2d) are changed to 3Vdc/7 and Vdc/7 it is possible to generate 8 different symmetrical output voltage levels [33][34]. As in the asymmetrical CHB case, the increase of levels is achieved at the expense of losing the converter modularity. The FC converter requires only one DC source to feed all the cells and phases. Therefore the input transformer can be avoided and the number of cells can be arbitrary increased depending on the required output power. Similarly to NPC, this converter requires a control strategy to regulate the voltages in the capacitors. Along with the classical structures there are several mixed structures, using for example single phase 3L-NPC as one power cell of the CHB [35], or combining and Active NPC with a FC [36]. Recently, the modular multilevel converter (MMC) has been proposed as a completely modular topology [37][38]. This converter can operate with DC or single-phase AC sources. The cells are based on DC-DC boost converter for the DC cell and a half bridge inverter for the AC cell, both cases with a floating DC capacitor. This converter does not require isolated DC sources because each cell has a floating DC capacitor. The number of cell in series in this converter is very large compared to CHB which generating very low dv/dt and a high equivalent switching frequency. This converter always requires a DC voltage control scheme because the floating DC voltages must be kept at the reference value. There are independent controllers implemented to handle the input and output currents and an additional controller to minimize the circulating current which is a current that flows only inside the converter. This circulating current is a particular characteristic of this converter [39]. 8 IV. 2. Current Source Converters The standard topology of a current source inverter (CSI) is shown in Figure 3a). These converters always require a controlled rectifier in order to provide a constant current flowing through the DC link. In the basic topology a thyristor-based rectifier is usually chosen. A split inductor is used in the DC-link in order to reduce the common mode voltage in the load [40]. The inverter is an arrangement of power semiconductors similar to the VSI, but composed by gate turn-off thyristors (GTO) or IGCT. The output current has a PWM waveform and can not be applied directly to an inductive load such as the motor. An output capacitive filter which eliminates the di/dt and applies a very smooth voltage to the load is mandatory [41]. This converter can achieve medium voltage operation and, moreover, is intrinsically regenerative [42][43]. A back-to-back configuration as shown in Figure 3b) can be used when high quality input current is required. In this case, the input side also requires a second order LC to filter due to the PWM currents presented at the input terminals of the rectifier [44]. Figure 3. Topologies and output waveforms of the conventional current source inverters IV. 3. Direct Converters A third category of converters which do not require energy storage elements is presented in this section. The direct converter transmits the energy directly from the input side to the output side. The main advantage of these converters is the reduction in size but it comes with a complexity in the control scheme. The cycloconverter, shown in Figure 4a), has been widely used in high power applications such as grinding mills and belongs to this category [45]. This converter is composed by a thyristor-based dual converter per phase, which can produce a variable DC voltage controlled in order to follow a sinusoidal 9 waveform reference [46]. The input of each converter is fed by a phase shifted transformer where low order harmonics of the input current are cancelled out. The output voltage results in a combination of segments of the input voltages which fundamental component follows a sinusoidal reference as can be seen in Figure 4b). Due to its operation principle, this converter is well suited to drive high-power low-frequency loads [47][48]. The matrix converter, in its direct and indirect versions, also belongs to the direct converters category. The direct matrix converter (DMC) is shown in Figure 4c). The basic operation principle behind this converter is the connection of the phase output to any of the input voltages [49][50]. The converter is composed by nine bidirectional switches which can connect any input phase to any output phase allowing the current flow in both directions. A second order LC input filter is required to improve the input current [51]. The output is directly connected to the inductive load. Not all the possible combinations of switches are allowed, they are restricted to only 27 valid switching states. As mentioned earlier the main advantage of matrix converter is the reduction in size being specially suited for automotive and aircraft applications [52][53]. Several variations on the DMC have been proposed in the literature, the most important is the indirect matrix converter (IMC) which is composed by a bidirectional three-phase rectifier, a virtual DC link and a three phase inverter [54] as shown in Figure 4e). The number of power semiconductors is the same as the DMC, if the bidirectional switch is considered as two unidirectional switches, but the number of possible switching states is different and its analysis is simpler. Using the same configuration of the IMC it is possible to simplify its topology and reduce the components count restricting its operation to positive voltages in the virtual DC-link [55]. This reduced topology is called sparse matrix converter (SMC) and it is shown in Figure 4f). 16 table for a range of modulation indexes and interpolated to generate the switching pattern. As the SHE technique is based on the Fourier transform calculation of a period of the voltage waveform, it is difficult to apply this modulation in fast dynamic close loop applications. Several approaches to calculate online the switching angles have been proposed in the literature [64],[65]. III.4.b. Selective Harmonic Mitigation Technique The grid requirements, imposed by the governments and the electrical providers, usually define maximum limits of the harmonic distortion for each harmonic order up to 50 th and a maximum value of the total harmonic distortion (THD). In this way, the elimination of low order harmonic components by the SHE technique does not ensure to comply with harmonic restrictions imposed by the current grid codes. The non eliminated harmonics present when the SHE technique is applied can take any value and mostly are above the limits imposed by the grid codes. This fact leads to design highly cost, bulky and heavy filters in order to smooth the output waveforms keeping the harmonic distortion below the limits and therefore fulfilling the grid code requirements. To overcome this problem, a modified modulation method, based on the SHE modulation concept, has been proposed where the switching angles are calculated not to eliminate a given number of low order harmonic components but to reduce the distortion below the limits imposed by the grid codes. This modulation technique is called Selective Harmonic Mitigation (SHM) [66]. The SHM method can be used in all the applications where the SHE technique operates obtaining better results in terms of the resulting necessary filter to be used in the power system. The SHM technique is based on the offline calculation of the switching angles defining and cost function to be minimized by a search algorithm. This cost function includes terms for the harmonic distortion components, the THD and the minimum time between consecutive switching angles. If the harmonic distortion components or the THD value are below the limit imposed by the applied grid code, its contribution to the cost function is zero. III.5.Variable frequency modulation techniques The fixed switching frequency modulation methods are superior to the variable frequency ones in terms of better harmonic distortion distribution. The fixed frequency methods present a harmonic spectrum where the switching distortion is located around the switching frequency and its multiples. This does not happen when a variable frequency modulation method is used because a spread harmonic spectrum is generated. However, in some specific conditions, 17 variable frequency modulation methods, which are very simple mathematically and conceptually, can be also applied achieving good results. It has to be noticed that the variable frequency modulation techniques are not indeed modulation methods because they do not synthesize a reference voltage as an average of the discrete switching states of the power converter. In this way, the concept of switching sequence is not used in these techniques and the switching of the power devices only occurs when some control conditions are fulfilled. This is why the switching frequency of the output waveforms is not constant. III.5a. Hysteresis control Also called bang-bang or on-off control, it consists on the determination of the power devices switching depending on a comparison between the measured control variable x m (usually a current) with a reference waveform x ref with a hysteresis band ±∆x. The aim of the controller is keep the control variable inside the hysteresis band leading to a non-periodic switching of the power devices of the converter topology. The control variable ripple is directly defined by the hysteresis band until the hysteresis band is smaller than the dynamic response of the load. In order to design a hysteresis controller, the effect of the switching of the converter on the control variable has to be known. In this way, the controller design is very simple at the expense of generating a spread harmonic spectrum [67]. III.5b. Nearest level control The nearest level control determines the switching of the power converter comparing the phase voltage reference with the possible voltages that can be generated by the converter topology. Finally, the switching associated to the nearest voltage level is applied and, in this way, as only one switching state is used during each sampling period, the switching losses are reduced compared with conventional PWM or SVM techniques [68]. This is achieved at the expense of a more distorted output voltage because the reference voltage is not generated in average over a sampling period. The nearest level control can only be applied achieving high performance in power converters where the difference between consecutive voltage levels is not large, which means that is specially well designed to be applied to multilevel converters with a high number of levels (for instance for a cascaded h-bridge converter with more than four power cells per phase). III.5c. Space vector control As has been explained above, the nearest level control is a PWM method where only the closest switching state of the switching sequence is finally applied to the converter. The space vector control applies the same concept to the SVM technique. In this way, instead of using a switching sequence formed 18 by the state vectors closest to the reference vector, only the closest one is applied to the power converter [69]. As in the nearest level case, the space vector control reduces the switching losses at the expense of a higher distortion and a spread harmonic spectrum of the output voltages and currents. In the same way, this technique has to be used in power converter topologies where the geometrical distance between the reference vector and the closest vectors is not large. Therefore, as in the nearest level control, it is suitable to be used in multilevel converter with a high number of levels. III.5.d. Model predictive control Model predictive control is performed in discrete time, where in each sample time the output current is predicted for each one of the valid switching states using a model of the load and the converter. All the predicted values are evaluated in a cost function and the switching state that minimizes this function is selected to be applied at the next sample time [70]. Similarly to hysteresis, this control has a time-based operation, producing a variable switching frequency and consequently a spread harmonic spectrum. One of the main advantages of this algorithm is its flexibility, because the cost function can be easily modified including simultaneously several primary and secondary control objectives such as a frequency-related term to improve its frequency behavior, the dc voltage balance in a NPC converter, switching frequency and commonmode voltage reduction among others. At the present state of the art, the coefficients (usually called weighting factors) of the different terms which form the cost function are determined by empirical procedure. There is no analytical or numerical solution proposed yet to obtain an optimal solution to the problem for FSC-MPC. In [71], some guidelines are presented to help the weighting factor design process. IV. CONTROL AND ESTIMATION IV.a. Introduction The general block scheme of high performance speed controlled AC motor drives is shown in Figure 6. The core of the scheme are internal flux and torque control loops with the estimator block which can be implemented in different ways, whereas the outer speed control loop is rather unified and generates command values for torque M c and flux Ψ c (via Flux program block) controllers. The speed feedback signal can be measured by a mechanical motion (speed/position) sensor Ω m or delivered from the estimator Ω m creating possibility of the speed sensorless operation. 19 Figure 6. Block diagram of the speed controlled AC motor drive with internal flux and torque loops IV.2. Control Methods Several Torque Control (TC) methods have been developed in the last 40 years. Not all of them have found wide industrial applications. Therefore, we present only the most popular strategies used commercially and some of future trends. Existing TC methods can be classified in different ways [72][73]. In this paper, the TC methods are presented in two main groups: linear and nonlinear controllers. The discussed generic TC methods are presented for the induction motor drives; however, they can be easily expanded for control of permanent magnet synchronous motors (PMSM) with sinusoidal electromotor force (EMF) and currents. IV.3. Linear Torque Control The linear torque controllers operate in association of voltage pulse width modulators (PWM). The controllers calculate the required stator voltage vector, averaged over a sampling period. The voltage vector is finally synthesized by a PWM technique which in most cases is the SVM. So, differently from the nonlinear TC schemes where signals are processed on instantaneous values, in a linear TC scheme, the linear (PI) controllers operate on values averaged over the sampling period. Therefore, the sampling frequency can be reduced from about 40 kHz in nonlinear TC, to 2-5 kHz in linear TC schemes. In the linear group, the following TCs are described: Field Oriented Control (FOC), Direct Torque Control with voltage Space Vector Modulation (DTC-SVM) and Direct Torque Control with Flux Space Vector Modulation (DTC-FVM). 1) Field Oriented Control M αβS U αβS I ˆ e Ψ ˆ Ω ˆ m Ω m γ m Ω mc d dt 20 The Field Oriented Control, proposed in 1970-ties by Hasse [74] and Blaschke [75], is based on an analogy to the mechanically commutated DC brush motor. In this motor, owing to separate exciting and armature winding, flux is controlled by exciting current and torque is controlled independently by adjusting the armature current. So, the flux and torque currents are electrically and magnetically separated. Contrarily, the cage-rotor IM has only a threephase winding in the stator, and the stator current vector, I s , is used for both flux and torque control. So, exciting and armature current are coupled (not separated) in the stator current vector and cannot be controlled separately. The decoupling can be achieved by the decomposition of the instantaneous stator current vector, I s , into two components: flux current, I sd , and torque-producing current, I sq , in the rotor-flux-oriented coordinates (R-FOC) dq (see vector diagram in Figure 7). In this way, the control of the IM becomes identical with a separately excited DC brush motor and can be implemented using a current controlled PWM inverter with linear PI controllers and voltage SVM (see block scheme in Figure 7). The core of the FOC scheme are coordinate transformation blocks which allow calculation of field oriented current components I sd , I sq by using αβ/dq transformation, and reference voltage vector components V sαc , V sβc by using inverse dq/αβ transformation. So, in the FOC torque and flux is controlled indirectly by field oriented current vector components. Figure 7. Vector diagram and block diagram of rotor FOC. Torque is controlled indirectly via torque current I sq control loop 2) Direct Torque Control with Voltage SVM αβ α s V V α s I I s β αβ s β V c II ˆ γ r ˆ ˆ 21 A block scheme of DTC-SVM with closed-loop torque and flux control operating in Cartesian stator flux coordinates [76][77] is presented in Figure 8. The output of the PI flux and torque controllers is interpreted as the reference stator voltage components, V Ψ c and V Mc , in S-FOC (dq). These DC voltage commands are then transformed into stationary coordinates (αβ), and the commanded values, V sαc and V sβc , are delivered to the SVM block. Note that this scheme can be seen as a simplified stator flux oriented control (S-FOC) without current control loops [78] or as a classical ST-DTC scheme (see Figure 10 ) in which switching table is replaced by a modulator (SVM) and a hysteresis torque and flux controllers are replaced by linear PI [76][77][79]. So, in the DTC-SVM scheme torque and flux are controlled directly in closed loops, and therefore an accurate estimation of motor flux and torque is necessary. Contrarily to classical hysteresis based DTC, the DTC-SVM operates at constant switching frequency. This improves considerably the drive performance in terms of reduced torque and flux pulsations, reliable start-up and low speed operation. Figure 8. Vector diagram and block scheme of DTC-SVM. Torque is controlled directly via voltage vector component V M 3) Direct Torque Control with Flux SVM Further simplification can be achieved in a block scheme of DTC with flux vector modulation - FVM as shown in Figure 9. For torque regulation, a PI αβ α s V V α s I I s β s β V c ˆ γ s ˆ ˆ ˆ ˆ ˆ 22 controller is applied and its output produces an increment in the torque angle, ∆δ Ψ (see vector diagram in Figure 9) [80][81]. Assuming that the rotor and flux magnitudes are approximately equal, the torque is controlled only by changing the torque angle, δ Ψ , which corresponds to the increment of the stator flux vector ∆Ψ ΨΨ Ψ s . The commanded stator flux vector is calculated by addition of the estimated flux position γ s and change of the torque angle ∆δ Ψ . Its value is compared with the estimated flux and the stator flux error ∆Ψ ΨΨ Ψ s is used directly for calculation of VSI switching states in the FVM block [82][83]. Thanks to internal stator flux loop used for calculation of ∆Ψ ΨΨ Ψ s in flux pulse width modulator, the flux PI controller of Figure 8 is eliminated. Figure 9. Vector diagram and block scheme of DTC-FVM. Torque is controlled directly via stator flux vector increment ∆Ψ ΨΨ Ψ s with Flux Vector Modulation (FVM) IV.4. Nonlinear Torque Control The presented nonlinear TC group departs from the idea of coordinate transformation and the analogy with DC motor control, which is basis for the FOC. It proposes to replace the decoupling control with the bang-bang control, which meets very well with on-off operation of the inverter semiconductor power devices. Compared to the conventional FOC (Figure 7), the DTC schemes have the following features: • Simple structure, • There is no current control loops and current is not regulated directly, • Coordinate transformation is not required, • There is no separate voltage pulse width modulator, • Speed sensor is not required, • Accurate stator flux vector and torque estimation is required. αβ α s V V α s I I s β s β c ˆ γ s ˆ ˆ σ c β ˆ α s ˆ ˆ 23 This section includes the Switching Table based Direct Torque Control (STDTC), Direct Self Control (DSC) and on-line optimized Model Predictive DTC. Also, neural networks (NN’s) and fuzzy logic controllers (FLC’s) belong to the class of nonlinear control. 1) Classical ST-DTC Scheme The block diagram of the classical ST-DTC scheme is shown in Figure 10 [84]. The stator flux magnitude sc Ψ and the motor torque c M are the command signals which are compared with the estimated s Ψ ˆ and e M ˆ values, respectively. The digitized flux and torque errors generated by the hysteresis controllers Ψ d , M d and the position sector )( s N γ of the stator flux vector obtained from the angular position )/( αβ γ sss arctg Ψ Ψ = selects the appropriate voltage vector from the switching selection table. Thus, pulses S A , S B , S C for control the inverter power switches are generated from the vector selection table. The characteristic features of the ST-DTC scheme of Figure 10 include: • Sinusoidal stator flux and current waveforms with harmonic content determined by the flux and torque controller hysteresis tolerance bands, • Excellent torque dynamics (depending on voltage reserve), • Flux and torque hysteresis bands determine the inverter switching frequency, which varies with the synchronous speed and load changes. Many modifications of the classical ST-DTC scheme aimed at improving starting, overload conditions, very low speed operation, torque ripple reduction, variable switching frequency functioning, and noise level attenuation have been proposed during the last decade [7]. ˆ γ s ˆ ˆ αβ α s V V α s I I s β s β ˆ ˆ 24 Figure 10. Vector diagram and block scheme of switching table based DTC. Torque is controlled directly via stator flux vector movement by selection of appropriate forward/backward active voltage vector (V 1 or V 6 ) and stops by selection zero voltage vector V 0 . Stator flux vector moves on circular path 2) Direct Self Control (DSC) Scheme The block diagram of the DSC method is shown in Figure 11 [85]. Based on the command stator flux sc Ψ and the actual phase components sA Ψ ,sB Ψ ,sC Ψ , the flux comparators generate digital variables A d , B d , C d , which corresponds to active voltage states (V 1 –V 6 ). The hysteresis torque controller generates signal M d , which determines zero states. So, the Stator flux controller imposes the time duration of the active voltage states, which move the stator flux along the commanded trajectory, and torque controller determinates the time duration of the zero voltage states, which keep the motor torque in the defined-by-hysteresis tolerance band. The characteristic features of the DSC scheme of Figure 11 are: • Non-sinusoidal stator flux and current waveforms that, with the exception of the harmonics, are identical for both PWM and six-step operation, • The stator flux vector moves along a hexagon path also under PWM operation, 25 • No voltage supply reserve is necessary and the inverter capability is fully utilized, • The inverter switching frequency is lower than in the ST-DTC scheme of • • • Figure 10 , • Excellent torque dynamics in constant and weakening field regions. Figure 11. Vector diagram and block scheme of DSC. Torque is controlled directly in similar way as in the ST-DTC scheme, however, stator flux vector moves on hexagonal path because of different sector definition Note, that the behavior of a DSC scheme can be reproduced by a ST-DTC scheme from Figure 10 for flux hysteresis of 14% wide. 3) Predictive DTC Scheme The current and future trend in control of AC motors is to incorporate more advanced techniques like the model predictive control - MPC [86][87]. This trend is supported by the DSP producers which not only increase the operation speed and computation capacity, but also expand their offer by specialized circuits (for example Texas Instruments C2000 family). Predictive control is a very wide class of controllers which uses the model of the system (called predictive model) for the prediction of the future behavior of the controlled variables. This information is used for the controller to calculate the optimal actuation which minimizes a predefined cost function. The simplified block diagram of the predictive DTC scheme is shown in Figure 12. This type of the MPC is classified as MPC with finite control set FCS ˆ αβ α s V V α s I I s β s β ˆ ˆ ˆ ˆ ˆ 32 conveyors,” IEEE Transactions on Industry Applications, vol. 38, no. 1, pp. 203 –210, Jan./Feb. 2002. [13] M. Rahimo and S. Klaka, “High voltage semiconductor technologies,” in 13th European Conference on Power Electronics and Applications, EPE’09, pp. 1 –10, Sept. 2009. [14] Y. Suh and P. Steimer, “Application of igct in high-power rectifiers,” IEEE Trans. on Ind. Appl., vol. 45, no. 5, pp. 1628 –1636, Sept.-Oct. 2009. [15] K. K. Tan, F. Gao, P. C. Loh, and F. Blaabjerg, “Enhanced buck-boost neutral-point-clamped inverters with simple capacitive-voltage balancing,” IEEE Transactions on Industry Applications, vol. 46, no. 3, pp. 1021 –1033, May-June 2010. [16] S. R. Pulikanti, M. S. A. Dahidah, and V. G. Agelidis, “Voltage balancing control of three-level active npc converter using she-pwm,” IEEE Transactions on Power Delivery, vol. 26, no. 1, pp. 258 –267, Jan. 2011. [17] C. Wang and Y. Li, “Analysis and calculation of zero-sequence voltage considering neutral-point potential balancing in three-level npc converters,” IEEE Transactions on Industrial Electronics, vol. 57, no. 7, pp. 2262 –2271, July 2010. [18] J. Pou, R. Pindado, and D. Boroyevich, “Voltage-balance limits in fourlevel diode-clamped converters with passive front ends,” IEEE Trans. on Industrial Electronics, vol. 52, no. 1, pp. 190 – 196, Feb. 2005. [19] T. Chaudhuri, A. Rufer, and P. Steimer, “The common cross-connected stage for the 5l anpc medium voltage multilevel inverter,” IEEE Trans. on Industrial Electronics, vol. 57, no. 7, pp. 2279 –2286, July 2010. [20] J. Fang, C. Mao, J. Lu, D. Wang, and Q. Zhang, “The research on protection of over-voltage about npc three-level medium voltage motor drives,” in International Conference on Electrical Machines and Systems, ICEMS 2008, pp. 1595 –1599, Oct. 2008. [21] N. Hatti, Y. Kondo, and H. Akagi, “Five-level diode-clamped pwm converters connected back-to-back for motor drives,” IEEE Transactions on Industry Applications, vol. 44, no. 4, pp. 1268 –1276, July-Aug. 2008. [22] M. Malinowski, K. Gopakumar, J. Rodriguez, and M. Perez, “A survey on cascaded multilevel inverters,” IEEE Transactions on Industrial Electronics, vol. 57, no. 7, pp. 2197–2206, July 2010. [23] M. Marchesoni, M. Mazzucchelli, and S. Tenconi, “A nonconventional power converter for plasma stabilization,” IEEE Transactions on Power Electronics, vol. 5, no. 2, pp. 212–219, Apr. 1990. [24] P. Hammond, “A new approach to enhance power quality for medium voltage ac drives,” IEEE Transactions on Industry Applications, vol. 33, no. 1, pp. 202–208, Jan./Feb. 1997. [25] S. Lu and K. Corzine, “Advanced control and analysis of cascaded multilevel converters based on p-q compensation,” IEEE Transactions on Power Electronics, vol. 22, no. 4, pp. 1242–1252, July 2007. [26] P. Lezana, J. Pou, T. Meynard, J. Rodriguez, S. Ceballos, and F. Richardeau, “Survey on fault operation on multilevel inverters,” IEEE Trans. on Industrial Electronics, vol. 57, no. 7, pp. 2207–2218, July 2010. [27] J. Rodriguez, J. Pontt, E. Silva, J. Espinoza, and M. Perez, “Topologies for regenerative cascaded multilevel inverters,” in IEEE 34th Annual Power Electronics Specialist Conference, PESC ’03, vol. 2, pp. 519 – 524, June 2003. 33 [28] M. Perez, J. Espinoza, J. Rodriguez, and P. Lezana, “Regenerative medium-voltage ac drive based on a multicell arrangement with reduced energy storage requirements,” IEEE Transactions on Industrial Electronics, vol. 52, no. 1, pp. 171–180, Feb. 2005. [29] J. Rodriguez, J. Pontt, M. Perez, P. Lezana, and P. Hammond, “High power synchronous machine fed by a cascaded regenerative inverter,” in IEEE Industry Applications Society Annual Meeting, IAS ’08, pp. 1–7, Oct. 2008. [30] J. Dixon, J. Pereda, C. Castillo, and S. Bosch, “Asymmetrical multilevel inverter for traction drives using only one dc supply,” IEEE Transactions on Vehicular Technology, vol. 59, no. 8, pp. 3736 –3743, Oct. 2010. [31] M. Perez, P. Cortes, and J. Rodriguez, “Predictive control algorithm technique for multilevel asymmetric cascaded h-bridge inverters,” IEEE Trans. on Ind. Electronics, vol. 55, no. 12, pp. 4354 –4361, Dec. 2008. [32] J. Dixon, A. Breton, F. Rios, J. Rodriguez, J. Pontt, and M. Perez, “Highpower machine drive, using nonredundant 27-level inverters and active front end rectifiers,” IEEE Transactions on Power Electronics, vol. 22, no. 6, pp. 2527–2533, Nov. 2007. [33] T. Meynard, M. Fadel, and N. Aouda, “Modeling of multilevel converters,” IEEE Trans. on Ind. Electronics, vol. 44, no. 3, pp. 356–364, June 1997. [34] L. Xu and V. Agelidis, “Flying capacitor multilevel pwm converter based upfc,” IEE Proceedings-Electric Power Applications, vol. 149, no. 4, pp. 304 – 310, July 2002. [35] J. Holtz and N. Oikonomou, “Optimal control of a dual three-level inverter system for medium-voltage drives,” IEEE Transactions on Industry Applications, vol. 46, no. 3, pp. 1034–1041, May-June 2010. [36] F. Kieferndorf, M. Basler, L. Serpa, J.-H. Fabian, A. Coccia, and G. Scheuer, “A new medium voltage drive system based on anpc-5l technology,” in IEEE International Conference on Industrial Technology (ICIT’10), pp. 643 –649, Mar. 2010. [37] M. Hagiwara, K. Nishimura, and H. Akagi, “A modular multilevel pwm inverter for medium-voltage motor drives,” in IEEE Energy Conversion Congress and Exposition, ECCE 2009, pp. 2557–2564, Sept. 2009. [38] A. Lesnicar and R. Marquardt, “An innovative modular multilevel converter topology suitable for a wide power range,” in IEEE Power Tech Conference Proceedings, Bologna, vol. 3, pp. 1-6, June 2003. [39] M. Hagiwara, K. Nishimura, and H. Akagi, “A medium-voltage motor drive with a modular multilevel pwm inverter,” IEEE Transactions on Power Electronics, vol. 25, no. 7, pp. 1786–1799, July 2010. [40] J. Dai, D. (David) Xu, B. Wu, and N. R. Zargari, “Unified dc-link current control for low-voltage ride-through in currentsourceconverter-based wind energy conversion systems,” IEEE Transactions on Power Electronics, vol. 26, no. 1, pp. 288–297, Jan. 2011. [41] M. Naguib and L. Lopes, “Harmonics reduction in current source converters using fuzzy logic,” IEEE Transactions on Power Electronics, vol. 25, no. 1, pp. 158–167, Jan. 2010. [42] H. Bilgin and M. Ermis, “Design and implementation of a current-source converter for use in industry applications of d-statcom,” IEEE Trans. on Power Electronics, vol. 25, no. 8, pp. 1943–1957, Aug. 2010. 34 [43] Y. W. Li, M. Pande, N. Zargari, and B. Wu, “An input power factor control strategy for high-power current-source induction motor drive with active front-end,” IEEE Trans. on Power Electronics, vol. 25, no. 2, pp. 352 – 359, Feb. 2010. [44] F. Gao, P. C. Loh, F. Blaabjerg, and D. M. Vilathgamuwa, “Five-level current-source inverters with buck-boost and inductive-current balancing capabilities,” IEEE Trans. on Industrial Electronics, vol. 57, no. 8, pp. 2613–2622, Aug. 2010. [45] B. Wu, J. Pontt, J. Rodriguez, S. Bernet, and S. Kouro, “Current-source converter and cycloconverter topologies for industrial medium-voltage drives,” IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2786–2797, July 2008. [46] J. Vobecky, “Future trends in high power devices,” in 27th International Conf. on Microelectronics Proceedings (MIEL), pp. 67–72, May 2010. [47] M.-K. Nguyen, Y.-G. Jung, H.-Y. Yang, and Y.-C. Lim, “Single-phase zsource cycloconverter with safe-commutation strategy,” IET Power Electronics, vol. 3, no. 2, pp. 232 –242, March 2010. [48] J. Pontt, J. Rodriguez, J. Rebolledo, K. Tischler, and N. Becker, “Operation of high-power cycloconverter-fed gearless drives under abnormal conditions,” IEEE Transactions on Industry Applications, vol. 43, no. 3, pp. 814–820, May-June 2007. [49] C. Ortega, A. Arias, C. Caruana, J. Balcells, and G. Asher, “Improved waveform quality in the direct torque control of matrix-converter-fed pmsm drives,” IEEE Transactions on Industrial Electronics, vol. 57, no. 6, pp. 2101–2110, June 2010. [50] R. K. Gupta, K. K. Mohapatra, A. Somani, and N. Mohan, “Direct-matrixconverter-based drive for a three-phase open endwinding ac machine with advanced features,” IEEE Transactions on Industrial Electronics, vol. 57, no. 12, pp. 4032–4042, Dec. 2010. [51] J. Monteiro, J. F. Silva, S. F. Pinto, and J. Palma, “Matrix converterbased unified power-flow controllers: Advanced direct power control method,” IEEE Trans. on Power Delivery, vol. 26, no. 1, pp. 420-430, Jan. 2011. [52] S. Kwak, “Fault-tolerant structure and modulation strategies with fault detection method for matrix converters,” IEEE Transactions on Power Electronics, vol. 25, no. 5, pp. 1201–1210, May 2010. [53] S. Bernet, S. Ponnaluri, and R. Teichmann, “Design and loss comparison of matrix converters, and voltage-source converters for modern ac drives,” IEEE Transactions on Industrial Electronics, vol. 49, no. 2, pp. 304–314, Apr. 2002. [54] R. Pena, R. Cardenas, E. Reyes, J. Clare, and P. Wheeler, “A topology for multiple generation system with doubly fed induction machines and indirect matrix converter,” IEEE Transactions on Industrial Electronics, vol. 56, no. 10, pp. 4181–4193, Oct. 2009. [55] P. Correa, J. Rodriguez, M. Rivera, J. Espinoza, and J. Kolar, “Predictive control of an indirect matrix converter,” IEEE Transactions on Industrial Electronics, vol. 56, no. 6, pp. 1847–1853, June 2009. REFERENCES MODULATION SECTION 35 [56] J. Holtz, "Pulsewidth modulation-a survey," IEEE Transactions on Industrial Electronics, vol.39, no.5, pp. 410-420, Oct 1992. [57] G.Buja and G.Indri, "Improvement of pulsewidth modulation techniques", Archiv für Elektrotechnik, n. 57, pp. 281-289, 1975. [58] B. P. McGrath and D. G. Holmes, "Multicarrier PWM strategies for multilevel inverters," IEEE Transactions on Industrial Electronics, vol.49, no.4, pp. 858-867, Aug. 2002. [59] L. R. Limongi, R. Bojoi, G. Griva, A. Tenconi, „Digital Current-Control Schemes“ IEEE Industrial Electronics Magazine, vol. 3, No. 1, pp. 20-31, March 2009. [60] N. Celanovic and D. Boroyevich, "A fast space-vector modulation algorithm for multilevel three-phase converters," IEEE Transactions on Industry Applications, vol.37, no.2, pp. 637-641, Mar/Apr 2001 [61] M. M. Prats, L. G. Franquelo, J. I. Leon, R. Portillo, E. Galvan and J. M. Carrasco, "A SVM-3D generalized algorithm for multilevel converters," The 29th Annual Conference of the IEEE Industrial Electronics Society (IECON '03), vol.1, pp. 24-29, 2-6 Nov. 2003. [62] J. I. Leon, S. Vazquez, J. A. Sanchez, R. Portillo, L. G. Franquelo, J. M. Carrasco and E. Dominguez, "Conventional Space-Vector Modulation Techniques Versus the Single-Phase Modulator for Multilevel Converters," IEEE Transactions on Industrial Electronics, vol.57, no.7, pp. 2473-2482, July 2010. [63] H. S. Patel and R. G. Hoft, “Generalized techniques of harmonic elimination and voltage control in thyristor inverters: Part 1—Harmonic elimination,” IEEE Transactions on Industry Applications, vol. IA-9, no. 3, pp. 310–317, May/Jun. 1973. [64] R. Ray, D. Chatterjee, and S. Goswami, “Harmonics elimination in a multilevel inverter using the particle swarm optimisation technique,” IET Power Electronics, vol. 2, no. 6, pp. 646 –652, Nov. 2009. [65] A. I. Maswood and S. Wei, “Genetic-algorithm-based solution in pwm converter switching,” IEE Proceedings - Electric Power Applications, vol. 152, no. 3, pp. 473 – 478, May 2005. [66] L. G. Franquelo, J. Napoles, R. Portillo, J. I. Leon, and M. A. Aguirre, “A flexible selective harmonic mitigation technique to meet grid codes in three-level PWM converters,” IEEE Transactions on Industrial Electronics, vol. 54, no. 6, pp. 3022–3029, Dec. 2007. [67] M. Mohseni and S. Islam, “A new vector-based hysteresis current control scheme for three-phase pwm voltage-source inverters,” IEEE Trans. on Power Electronics, vol. 25, no. 9, pp. 2299–2309, Sept. 2010. [68] S. Kouro, R. Bernal, H. Miranda, C. A. Silva and J. Rodriguez, "HighPerformance Torque and Flux Control for Multilevel Inverter Fed Induction Motors," IEEE Transactions on Power Electronics, vol.22, no.6, pp. 2116-2123, Nov. 2007. [69] J. Rodríguez, L. Morán, P. Correa, and C. Silva, “A vector control technique for medium-voltage multilevel inverters,” IEEE Transactions on Industrial Electronics, vol. 49, no. 4, pp. 882–888, Aug. 2002. [70] S. Kouro, P. Cortes, R. Vargas, U. Ammann and J. Rodriguez, "Model Predictive Control—A Simple and Powerful Method to Control Power Converters," IEEE Transactions on Industrial Electronics, vol.56, no.6, pp.1826-1838, June 2009. 36 [71] P. Cortes, S. Kouro, B. La Rocca, R. Vargas, J. Rodriguez, J. I. Leon, S. Vazquez, and L. G. Franquelo, “Guidelines for weighting factors design in model predictive control of power converters and drives,” in IEEE International Conference on Industrial Technology (ICIT’09), Gippsland (Australia), pp. 1-6, Feb. 10–13, 2009. REFERENCES CONTROL AND ESTIMATION SECTION [72] M. P. Kazmierkowski, R. Krishnan and F. Blaabjerg, Control in Power Electronics, Academic Press, 2002. [73] R. Krishnan, Electric Motor Drives, Prentice Hall, New Jersey, 2001. [74] K. Hasse: "Drehzahlgelverfahren fur schnelle Umkehrantriebe mit stromrichtergespeisten Asynchron-Kurzchlusslaufermotoren",Reglungstechnik, 20: pp. 60-66, 1972. [75] F. Blaschke, “The principle of field-orientation as applied to the Transvector closed-loop control system for rotating-field machines”, Siemens Review 34, pp. 217-220, 1972. [76] I. Boldea, S.A. Nasar, Electric Drives, CRC Press, Boca Raton-Ann Arbor-London-Tokyo, Second Edition 2006. [77] G. S. Buja, M. P. Kazmierkowski, „Direct Torque Control of PWM Inverter-Fed AC Motors – A Survey”, IEEE Trans. on Industrial Electronics, vol. 51, no. 4, pp. 744-757, Aug.2004. [78] L. Xu and M. Fu, “A sensorless direct torque control technique for permanent magnet synchronous motors,” in Proceedings IEEE Ind. Appl. Conference, vol. 1, pp. 159–164, 1999. [79] D. Casadei, F. Profumo, G. Serra and A. Tani, “FOC and DTC: Two Viable Schemes for Induction Motors Torque Control”, IEEE Transactions on Power Electronics, vol. 17, no. 5, pp. 779-787, 2002. [80] T. Ohtani, N. Takada, K. Tanaka, “Vector Control of Induction Motor Without Shaft Encoder”, IEEE Transactions on Industry Applications, Vol. 28, no. 1, pp. 157-165, 1992. [81] A. Tripathi, A. M. Khambadkone, and S. K. Panda, “Stator flux based space vector modulation and closed loop control of the stator flux vector in overmodulation into six-step mode,” IEEE Trans. on Power Electronics, vol. 19, no. 3, pp. 775–782, May 2004. [82] A. Steimel, “Direct Self-Control and Synchronous Pulse Techniques for High-Power Traction Inverters in Comparison”, IEEE Transactions on Power Electronics, vol. 51, No. 4, pp. 810-820, 2004. [83] I. Takahashi, I. Takahashi and T. Noguchi, “A new quick response and high-efficiency control strategy of an induction motor.,” IEEE Trans. on Industry Applications, vol. IA-22, no. 5, pp. 820–827, Sep./Oct. 1986. [84] L. M. Grzesiak and M. P. Kazmierkowski, „Improving Flux and Speed Estimators for Sensorless AC Drives”, IEEE Industrial Electronics Magazine, vol. 1, No. 3, Fall 2007, pg 8-19, [85] M. Depenbrock, "Direct Self Control of Inverter-Fed Induction Machines", IEEE Transactions on Power Electronics, vol. PE-3, no.4, pp.420-429, Oct. 1988. [86] M. P. Kazmierkowski, R. M. Kennel and J. Rodriguez: “Special Section on Predictive Control in Power Electronics and Drives – Part I”, IEEE 37 Trans. on Ind. Electronics, Part I, vol. 55, no. 12, pp. 4309-4429, Dec.2008. [87] M. P. Kazmierkowski, R. M. Kennel and J. Rodriguez: “Special Section on Predictive Control in Power Electronics and Drives – Part II”, IEEE Trans. on Ind. Electronics, vol. 56, no. 6, pp. 1823-1963, June 2009. [88] J. Holtz, “Sensorless control of induction machines—With or without signal injection?” IEEE Trans. on Industrial Electronics, vol. 53, no. 1, pp. 7–30, Febr. 2006. [89] B. K. Bose, Modern Power Electronics and AC Drives, Englewood Cliffs, Prentice-Hall, 2001. [90] M. P. Kazmierkowski and H. Tunia, Automatic Control of Converter Fed Drives, ELSEVIER, 1994. [91] R. Krishnan, Electric Motor Drives, Prentice Hall, New Jersey, 2001. [92] R. Nilsen, M. P. Kazmierkowski, “Reduced order observer with parameter adaption for fast rotor flux estimation in induction machines,” IEE Proceedings Part D, Vol. 136, No. 1, pp. 35-43, 1989. [93] C. Lascu, I. Boldea, F. Blaabjerg, „Variable-Structure Direct Torque Control – A Class of Fast and Robust Controllers for Induction Motor Drives”, IEEE Trans. on Ind. Electronics, vol. 51, no. 4, 2004, pp. 785792. [94] T. Ohtani, N. Takada, K. Tanaka, “Vector Control of Induction Motor Without Shaft Encoder”, IEEE Trans. on Industry Applications, Vol. 28, no. 1, pp. 157-165, 1992. [95] A. Steimel, “Direct Self-Control and Synchronous Pulse Techniques for High-Power Traction Inverters in Comparison”, IEEE Trans. on Power Electronics, vol. 51, No. 4, pp. 810-820, 2004.