The Essential Role and the Continuous Evolution of Modulation Techniques for Voltage-Source Inverters in the Past, Present, and Future Power Electronics

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS The Essential Role and the Continuous Evolution of Modulation Techniques for Voltage Source Inverters in Past, Present and Future Power Electronics J. I. Leon, Senior Member,IEEE, S. Kouro, Member,IEEE, L. G. Franquelo, Fellow Member,IEEE, J. Rodriguez, Fellow Member,IEEE and Bin Wu, Fellow Member,IEEE Abstract—The cost reduction of power electronic devices, the increase in their reliability, efficiency and power capability, lower development times, together with more demanding application requirements, have driven the development of several new inverter topologies recently introduced in industry, particularly mediumvoltage converters. New more complex inverter topologies and new application fields come along with additional control challenges, such as: voltage imbalances, power quality issues, higher efficiency needs and fault tolerant operation, which necessarily requires the parallel development of modulation schemes. Therefore, recently there have been significant advances in the field of modulation of dc/ac converters, which conceptually has been dominated during the last several decades almost exclusively by classic pulse width modulation methods. This paper aims to concentrate and discuss the latest developments on this exciting technology, to provide insight on where the state-of-the-art stands today, and analyze the trends and challenges driving its future. Index Terms—Multilevel systems, Modulation. I. INTRODUCTION POWER CONVERTERS have become over the last decades an enabling technology for a wide range of industrial applications mainly due to higher efficiency and performance. Converter topologies such as the ac/ac matrix converter, cycloconverters, current source inverters, loadcommutated inverters, dc/dc converters, dc/ac converters and diode or thyristor-based rectifiers cover a wide range of different nominal power applications [1]. In particular dc/ac converters, commonly known as voltage source inverters (VSI), Manuscript received August 24, 2015; revised November 17, 2015; accepted December 13, 2015. Copyright c 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. The authors gratefully acknowledge financial support provided by the Spanish Science and Innovation Ministry and the Andalusian Government under projects ENE2012-36897 and P11-TIC-7070 respectively, the Universidad Andres Bello, the Advanced Center for Electrical and Electronic Engineering (AC3E) center (CONICYT/FB0008), the Solar Energy Research Center SERC Chile (CONICYT/FONDAP/15110019), and the Chilean National Fund of Scientific and Technological Development (FONDECYT), under grants number 1150829 and 1151426. J. I. Leon and L. G. Franquelo are with the Electronic Engineering Department, Universidad de Sevilla, Sevilla, Spain (e-mail: [email protected]). S. Kouro is with the Electronics Engineering Department, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile (e-mail: samir[email protected]). J. Rodriguez is with Universidad Andres Bello, Santiago de Chile, Chile (email: [email protected]). Bin Wu is with the Department of Electrical and Computer Engineering, Ryerson University, Toronto, Canada (e-mail: [email protected]). b) c) v aN vdc t ton Ts vaN ^ vaN = Dvdc = vaN ^* D = ton/Ts vdc Sa N P + Sa _ vaN a Sb Sb _ vbN b Sc Sc _ vcN c DC AC Inverter Controller Modulator Digital Switching Signals Output Voltage 0 3.3 0 Measurements a) Drivers Isolated Switching Signals -8 15 (digital) Fig. 1. Introduction of the modulation concept. a) Typical structure of a control and modulation method of a voltage source inverter b) Three-phase two-level voltage source dc/ac converter c) Switched waveform and average value of the phase voltage vaN . are used to power a wide variety of applications in a non-stop energy demanding society with high efficiency, robustness and economical cost and possibility to reach high nominal power with reduced passive filters [2], [3]. The rich diversity of industrial applications require inverters that have very different power rating, output frequency, semiconductor devices, number of phases, operate at different voltage/current levels, and even have different types and number of dc input sources (current or voltage). Therefore, a wide range of different topologies have been developed over the years, particularly in the last decade for medium-voltage IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Gate Signals Generation Methods Closed-loop control methods with implicit modulator Hysteresis Current Control Direct Power Control Direct Torque Control One Cycle Control Finite Control Set Model Predictive Control Pulse Width Modulation (PWM) Pseudo-Modulation Square wave operation Nearest level operation (for multilevel) Nearest vector operation (for multilevel) Closed loop PWM Sigma-Delta Modulation Carrier based PWM Space Vector PWM Pre-programmed PWM Zero-sequence PWM Min-max sequence injection 3rd harmonic injection Selective Harmonic Mitigation (SHM) Selective Harmonic Elimination (SHE) Multilevel SVM Two-level SVM Multiphase SVM Open-End Winding SVM Phase-Shifted PWM (for CHB and FC) Level-Shifted PWM (for NPC) Multicarrier PWM (multilevel) Two-level PWM Trapezoidal PWM (for CSC) Sinusoidal PWM Random PWM 4-Wire Converters SVM (Three-dimensional SVM) Hybrid PWM (asymmetric multilevel VSI) Fig. 2. General classification of gate signals generation methods for voltage source dc/ac power converters. applications, to cater the needs and fulfil the specifications of each niche. Apart from well-known multilevel converter topologies such as neutral-point-clamped (NPC), flying-capacitor (FC) and cascaded H-bridge (CHB), in the last years a great deal of new inverter topologies have been introduced in industry, particularly in medium voltage multilevel converters like: modular multilevel converter (MMC), five-level active NPC (5L- ANPC), transistor clamped converter (TCC), stacked multicell, to name a few [4], [5]. In addition, multiphase applications have been gaining more and more attention due to a series of advantages like higher power density, lower torque ripples and fault tolerant operation [6]. As another example, openend-winding fed drives also have different voltage space vector distribution and extension of classic modulation methods is not straight forward. All these new power converters come along with modulation challenges, which include additional voltage space vectors and different switching harmonics [7]–[12]. A modulation technique generates the power semiconductors gate signals of a power converter obtaining a switched output waveform in such a way that the fundamental component can be adjusted with an arbitrary magnitude, frequency and phase, which are essential for the proper control of the process fed by the inverter. Taking into account this fact, the modulation concept that has been the mainstream solution for two-level power converters in general, including inverters, from the early beginnings of power electronics is Pulse Width Modulation (PWM) [13], [14] which is a simple and effective way to produce a pulse or switched voltage (or current) waveform whose time average is equal to a desired reference as shown in Fig. 1. However, each new converter topology comes with new modulation and control challenges like dc voltage balancing, circulating currents, more available switching redundancies, and other issues that can be dealt with in the modulation stage. The aim of this paper is to summarize the state-of-the-art and analyze the more recent advances in modulation concepts and technology for voltage drivers drivers drivers Controller Modulator Load dc-ac converter Load measurements Controller Load Load measurements b) c) Converter measurements Converter measurements Controller Modulator Load dc-ac converter a) dc-ac converter S S S Fig. 3. Block diagrams to operate a dc/ac power converter. a) Open-loop operation b) Closed-loop operation using a controller and a modulator c) Closed-loop operation using a controller with implicit modulator. source dc/ac converters, discussing the present challenges and possible future scenarios and trends. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS II. TYPES OF VOLTAGE SOURCE DC/AC POWER CONVERTER CONTROL SCHEMES VSI can operate using an open-loop or a closed-loop control method to generate the voltage references which determines the switching signals (S) for the gate drivers as shown in Fig. 3. The open-loop operation of an inverter consists in generating a fixed reference that does not depend on any measurement. Usually, this reference is determined externally (operator, outer control loop, etc.) for a certain operation point. It is mainly used for applications such as fans, pumps and fixed speed motor drives where the dynamic response is not a critical issue. This type of operation has become very successful due to its extreme simplicity at the expense of using a fixed operation point usually leading to performance losses. The drawbacks introduced by the open-loop operation of an inverter can be reduced if a closed-loop control method is designed and implemented [15]. In this case, the controller has to follow one reference (or more) defined by the user; references such as currents, torque and flux, active and reactive power, etcetera. The output of the controller (desired value of u,u∗) is the input of the modulator and it is usually the voltage reference that the modulator has to generate during the next sampling time. This approach has become a mainstream solution for adjustable speed drives and a wide number of other applications where adjustable amplitude, frequency and phase are necessary for a higher performance of the drive or process. As examples, two vastly used closed-loop controllers are the proportional-integral regulator in current controls based on synchronous reference frame and the proportional-resonant regulators used in current controls based on stationary reference frames or in harmonic active filter applications. On the other hand, in the last decades several closedloop control methods have been introduced with an implicit modulator implemented inside the control law. This kind of techniques are known as direct controllers and are conceptually simple and have easy digital implementation generating the switching signals of the inverter as a direct consequence of the control output avoiding the use of a modulator. This control scheme has been proved as a successful industrial solution during the last decades. Direct controllers such as hysteresis current controller or direct torque control in their conventional formulation are examples of closed-loop controllers with implicit modulators. III. MODULATION PRINCIPLE FOR VOLTAGE SOURCE DC/AC POWER CONVERTERS Before addressing the commonly used modulation methods for dc/ac converters, the modulation concept introduced in Fig. 1 should be clearly defined. Usually, in a power converter control scheme, a controller is designed to track several targets (typically active and reactive power, dc-link voltage, phase currents, etcetera) and its output u∗is the voltage that the VSI has to generate in order to achieve them. For example, the conventional three-phase two-level VSI shown in Fig. 1b can only generate voltages 0and +vdc in the phase voltages vaN ,vbN and vcN . Focusing on phase a, if a desired phase voltage v∗ aN has to be obtained, the modulator generates a switched waveform which, in average over the sampling period Ts, is equal to the desired value as shown in Fig. 1c. So, the modulator has to calculate a switching sequence to properly switch the power semiconductor devices normally using the well-known duty cycle D(defined as the ratio ton/Tsof the switching signal). The final obtained switched waveform presents a harmonic spectrum where undesired harmonic distortion appears due to the switching. This undesired distortion has to be below certain limits and it could lead to use expensive and bulky passive filters. So, there is a trade-off between the maximum switching frequency of the modulator (directly proportional the switching losses of the power converter and therefore its cooling system) and the filter size. It is important to notice that the final switching is slightly modified due to the required inclusion of the dead-time (waiting time to avoid the shoot-through of inverter arms due to the dynamics of switching on/off of the power devices). The required dead-times increments the low-order voltage/current harmonics, non-negligible phenomenon if high-power devices are used as in the multi-megawatt power converters. Multiple methods have been proposed in the last decades in order to compensate the dead-time effects [16], [17]. IV. CLASSIFICATION OF MODULATION METHODS FOR VOLTAGE SOURCE DC/AC POWER CONVERTERS A global classification of the gate signals generation methods for dc/ac power converters, which have had, recently or in last decades, industrial and/or academic impact to a lesser or greater degree is introduced in Fig. 2. These methods can be classified in three vast groups, addressed in the following sections. V. TRADITIONAL PULSE WIDTH MODULATION TECHNIQUES FOR TWO-LEVEL VSI Mainly, the required voltages to be generated by the VSI are sinusoidal and, in first approximation, a conventional twolevel three-phase VSI could generate a square waveform in the phase voltages as shown in Table I for each phase. This leads to a maximum utilization of the dc voltage generating a waveform with maximum modulation index m(ratio between the output voltage peak and the dc voltage value) at the expense of high distortion in low-order harmonics of the obtained waveforms. A. Carrier-based Pulse Width Modulation Techniques The objective of a modulation technique is to generate a desired reference waveform with minimum distortion in the low-order harmonics moving the unavoidable distortion to the high-order harmonics making easier the filtering process. A dominant modulation concept from the early days of power electronics in the 60 s is PWM [18], [19]. PWM is a simple and effective way to produce a switched voltage waveform whose time average is equal to a desired reference. This basic concept is the foundation that all other variations of classic PWM have in common. The comprehensive and indepth analysis performed by Prof. Holtz in [13], [14] has been IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS TABLE I CLASSIC MODULATION SCHEMES FOR THREE-PHASE TWO-LEVEL VOLTAGE SOURCE INVERTERS Item description Square-wave Modulation Pulse-Width Modulation Space-Vector Modulation Selective Harmonic Elimination Operating principle Sector 1 Block diagram + – + – + – + – + – + – Duty cycle calc. Sector Angle lookup table Angle/time conv. m Voltage waveform Spectrum 0.1 0.2 0.3 0.4 0.5 0.6 1 5711 13 17 19 23 25 29 31 [pu] 0.1 0.2 0.3 0.4 0.5 Harmonic number [pu] 0 1 0.6 0.1 0.2 0.3 0.4 0.5 Harmonic number (ignoring triplen) [pu] 0 1 0.6 0.1 0.2 0.3 21 0.4 0.5 3 11 9 1 15 13 19 23 25 29 27 [pu] 0 0.6 17 Pros Simple implementation Switching harmonics in mf Industrially accepted Switching sequence control Better usage of dc-link voltage Low switching frequency No low order harmonics Cons f1not controlled, high THD Low order harmonics Rigid switching sequence Complex implementation Suitable only for 3-phase VSI Off-line pre-programmed method Poor dynamic performance References [20] [18] - [24] [25] - [27] [30] - [32] for the last two decades, the main reference on PWM found in literature. In PWM, the phase voltage is generated by comparing the reference voltage with a higher frequency carrier (usually triangular) as shown in Table I. The fundamental-frequency component in the output voltage can be adjusted by changing the amplitude of the modulation index m. The frequency modulation index mfis defined as the ratio between the frequencies of the carrier fcr and modulating waves fm[20]. If mfis an integer, the carrier wave is synchronized with the modulating waveform and the modulation scheme is known as synchronous PWM; otherwise, it is called asynchronous PWM, in which fcr is usually fixed and is independent of fm. However, when mfis a small number (i.e. less than 21) its output spectrum contains low frequency harmonics (sub-harmonics) causing high currents in transformers and inductors. Note that in case of mfbeing a large number, the amplitudes of the sub-harmonics are very reduced and do not pose critical problems with the currents by inductors and transformers [20]. From the harmonic spectra represented in Table I, it can be observed that using the PWM method, the distortion has moved to harmonic orders around mfand no low-order harmonics appear. This fact is extremely important in power conversion applications because the necessary output filters can be minimized or even avoided at the expense of increasing the switching losses if fcr is too large [20]. A direct method to increase the maximum amplitude of the output fundamental voltage is to raise mto be greater than unity, entering the nonlinear over-modulation region. The over-modulation generates low-order harmonics and thus is rarely used in practice. Therefore, to increase dc voltage utilization, modified modulation schemes based on injecting zero-sequence signals into the modulating waveforms can be employed provided that the neutral of the load is floating. Among all the possible injection methods for three-phase VSI, the third-order harmonic injection, min-max sequence injection and discontinuous PWM schemes have been proved to deliver the best results in terms of obtainable linear range and/or harmonic distortion [21]–[24]. B. Space-Vector Modulation Techniques Space vector modulation (SVM) is basically a PWM method introduced originally for three-phase converters but using a vectorial representation of the VSI switching states in the well-known α-βframe as shown in Table I [13], [14], [21], [25]–[27]. SVM technique is also applicable to multiphase converters in general extending the concept. SVM technique determines the switching signals for the VSI gate drivers calculating a sequence of switching states to be applied during the sampling period. So, SVM technique deals with the modulation as a geometric mathematical problem obtaining the sequence of switching states and the corresponding duty cycles: IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS v∗ s=1 Ts (t1v1+t2v1+t0v0), t1+t2+t0=Ts.(1) In SVM, VSI (regardless of number of phases) is considered as a whole to determine the gating signals, while carrierbased PWM approach considers each VSI phase separately. However, it has been demonstrated that SVM and carrierbased PWM are equivalent (zero-sequence injection explicitly present in carrier-based PWM and implicitly in SVM) leading to the same dc-link utilization and harmonic performance [28], [29]. C. Pre-programmed PWM Modulation Techniques Pre-calculated PWM methods are not a conventional timebased modulation strategy like classic PWM or SVM but they are focused on the output harmonic spectrum of the VSI. Among these methods, the most well-known strategy is the selective harmonic elimination (SHE) technique. In the classical SHE, the times where the gating signals of the power converter are changed (usually named switching angles) are determined to work with an specific modulation index meliminating some non-triple harmonics. The switching angles are determined by solving off-line a nonlinear equations system as shown in Table I [30]–[32] and are stored afterward in a look-up table. In order to facilitate the calculations, it is normally imposed a quarter period symmetry with 4k commutations per period. The number of commutations k determines the number of harmonics to be eliminated (k-1). Normally, kis small leading to keep the switching losses below reasonable limits to facilitate the cooling systems design for high power applications. In addition, the effort of the SHE method is focused on the elimination of low-order harmonics which is the most convenient solution to reduce as much as possible the necessary output filter in terms of weight, volume and economical cost. Although SHE achieves good results, it can be only applied to low dynamic power systems because of the low bandwidth of the closed-loop controller in order to follow the SHE patterns tightly (hence eliminating the harmonics adequately) rather than having a faster dynamic performance [33]. VI. PSEUDO-MODULATION METHODS The family of pseudo-modulation methods shown in Fig. 2 directly imposes the VSI output voltage by a simple comparison of the desired reference voltage and imposing the switching state that leads to reduced errors. The simplest pseudo-modulation technique is the square-wave modulation (or staircase waveform) where the reference voltage is compared to zero as shown in Table I [20]. On the other hand, the nearest level control is a pseudo-modulation technique where the closest voltage level to the desired voltage is applied. The space-vector control is just an extension of the nearest level control but applied to three-phase systems and working with space vectors (see Table II) [34]. As a general rule, the pseudomodulation schemes achieve good results when applied to VSI with large number of levels reducing the switching losses at the expense of slightly increased total harmonic distortion (THD) and non-fixed switching frequency (leading to spread harmonic spectra). VII. CONTROL TECHNIQUES WITH IMPLICIT MODULATOR The classification shown in Fig. 2 also includes closed-loop control methods that directly generate the gate signals for the inverter. In this case, these gate signals are not necessarily related in principle with the fundamental component’s amplitude, phase and frequency of a reference voltage, and therefore can not be considered modulation schemes. In this case, the switching of the inverter (S) is not related to follow a reference voltage but is determined to directly reduce the error of the controller goal. These techniques achieve good results usually at the expense of having a non-constant switching frequency leading to widespread harmonic spectra. A. Hysteresis current control In the hysteresis current control, Sis generated to keep the phase currents inside hysteresis bands which surround the reference currents as shown in Table II. This control technique is the simplest implementation of a closed-loop control and has been extensively used in industrial products [20]. B. Direct torque control / Direct power control Direct torque control (DTC) is a well-established (in academia and industry) direct control method for motor drives applications where the torque and flux references are tracked using hysteresis controllers and using look-up tables (LUT) to choose the best switching state to achieve both objectives (see Table II for more details) [35]. On the other hand, direct power control (DPC) is the dual method for grid connected applications where active and reactive power are the controller objectives instead torque and flux [36]. C. Finite-states Model Predictive Control Finite-states model predictive control (FS-MPC) predicts the behavior of the VSI for all the possible switching states (n) and determines the final switching of the VSI by a minimization of an objective-defined cost function evaluated for all nswitching states as shown in Table II: gi(tk+1) = |x∗(tk+1)−xpi(tk+1)|, i = 1, . . . , n S=min{gi(tk+1)}(2) Multiple objective variables can be included in the cost function to be part of the control targets such as phase currents, dc voltages, switching losses and common-mode voltages [37], [38]. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS TABLE II PSEUDO-MODULATION AND CLOSED-LOOP METHODS WITH IMPLICIT MODULATOR Item description Hysteresis Control Nearest Level/Vector Control DTC / DPC Model Predictive Control Operating principle Nearest Level Control Nearest Vector Control Block diagram + – + – + – – – – Nearest Level Control Nearest Vector Control + – + – Pros Simple implementation Simple implementation Fast dynamic control Simple design, Look-Up Table based Conceptually simple High dynamic performance Flexible (can include constraints) Variable switching frequency Variable switching frequency Variable switching frequency Dispersed harmonic spectrum Cons Dispersed harmonic spectrum For converters with high # levels Only for two-level converters High computational burden Only for two-level converters ↑THD when modulation index ↓Empirical weighting factor design References [20] [34] [35], [36] [37], [38] VIII. ADVANCES ON CARRIER-BASED PWM TECHNIQUES Conventional carrier-based PWM technique has been extended using of multiple carriers being extensively studied in the last decades since the new family of multilevel converters appeared [39]. Among the multi-carrier PWM techniques, the phase-shifted PWM (PS-PWM) and the level-shifted PWM (LS-PWM) methods are the most common. The use of PS-PWM for CHB converters has been demonstrated very convenient (unipolar PWM with carriers phase shifting between consecutive H-bridges equal to π/k(where kis the number of power cells of the CHB) as shown in Table III) achieving equal power distribution and equalization of the power losses among the H-bridges, multiplicative effective of the output voltage switching frequency (2kmf) and reduced distortion in the input currents (when the dc voltages of the CHB inverter are fed by multiple diode bridges). [40]. In addition, PS-PWM method has been also applied to the flyingcapacitor converter (bipolar PWM with phase shifting between consecutive carriers equal to 2πdivided by the number of flying-capacitor cells) achieving multiplicative effect of the output voltage switching frequency and natural balance (but with low dynamic behavior) of the floating dc voltages of the converter [41]. The concept of use multiple phase-shifted carriers can be also applied to any modular converter with series connection of different power cells. For instance, for the MMC, it is possible to apply a bipolar carrier-based PWM method for each power cell with phase shifting between consecutive carriers equal to 2πdivided by the number of power cells of each branch, upper or lower. In this case, the dc voltage balancing issue can be solved by slightly changing the voltage reference of each power cell [42]–[44]. On the other hand, LS-PWM technique is very suitable to be used in the NPC topology with direct generation of the switching signals by simply comparing with multiple voltageshifted carriers as shown in Table III [21], [39]. Comparing both multi-carriers PWM techniques (LS-PWM and PS-PWM) with the same final effective switching frequency of the phase voltage, LS-PWM has been demonstrated superior by placing harmonic energy into a carrier component in each phase voltage and relying upon the cancellation of this component when the line-to-line voltages are formed [45]. In this way, several authors have been focused on developing LS-PWM methods for the flying-capacitor and the CHB converters [46]–[48]. Usually, these modified LS-PWM methods implement a conventional voltage level disposition of the triangular carriers but carry out an interleaving between them associating the gate signals sequentially to the carriers. These methods have the harmonic advantages of the LS-PWM technique and the even power distribution of the PS-PWM method but also the floating voltage balancing for the flyingcapacitor converter and the reduced harmonic distortion of the input currents in the CHB converter. The idea of using the interleaved carriers have been also recently applied to conventional two-level converters to reduce the common-mode voltage obtaining superior performance [49]. In recent years, the number of new multilevel converter topologies has increased and several of them can be already found as industrial products such as the 5L-ANPC [5]. All of them can generate the gate signals using some multi-carrier PWM method. Many of the new converter topologies are based on the series connection of different power cells and therefore the PS-PWM method or a hybrid modulation are suitable to be used for symmetrical and asymmetrical converter topologies respectively. For instance, the 5L-ANPC can use a hybrid IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS modulation implemented by a square-wave modulation for the high-voltage power devices and a modified PS-PWM method for the medium-voltage devices which achieves natural balance of the dc voltages of the floating capacitors (see Table IV) [50]. One of the most important concerns about multilevel converters is the dc voltage control of the capacitors (dc-link voltage imbalance of the NPC topology, floating voltages of the flying capacitors in the FC and, in general, dc voltage control) when multilevel converters are working as active rectifiers or static synchronous compensators (STATCOM). The control of these voltages can be assumed completely by the controller using a raw modulator but other solution is to design modified modulation techniques to deal with this issue [51]–[53]. A high-performance control of the voltage imbalance of the three-level NPC can be achieved using a LS-PWM technique but adding a zero-sequence signal to the reference waveforms [54], [55]. A similar idea has been also applied to five-level NPC converters using the offset voltage to regulate the average currents flowing into and out of the inner junction without affecting output line-to-line voltage [56]. This can be considered solved for three-level NPC but it presents stability problems with NPC converters with higher number of levels where usually an external hardware is used to achieve the proper operation [57]. It has to be noticed that PWM methods can be also implemented in microprocessors using mathematical algorithms which digitally describe the conventional concept of the comparison of the reference waveform with the triangular carriers [58]. In this way, the mathematical implementation of the multi-carrier PWM methods can obtain exactly the same gate signals. Researchers have designed modified mathematically described multi-carrier PWM methods in order to achieve extra control targets such as minimization of the switching losses and dc voltage control [59]–[61]. IX. ADVANCES ON PRE-CALCULATED PWM TECHNIQUES As it has been commented previously, the SHE technique is usually a quarter-wave symmetry method simplifying the mathematical calculations to determine the switching angles. However, recently several studies have been done presenting solutions with half-wave symmetry [62] and non-symmetrical waveforms [63]. In both cases, the modification of the conventional SHE technique leads to find new solutions to eliminate the low-order harmonics because new degrees of freedom appear at the expense of increasing the computational cost of the heuristic mathematical search of the solutions. However, this can not be considered as an important drawback of these methods because all the calculations are carried out offline. About this issue, the mathematical calculations to determine the switching angles of a SHE method are not simple and usually some mathematical search algorithm such as the Newton-Raphson method is applied. A great effort of the researchers has been focused on the simplification and the improvement of the accuracy of the mathematical determination of the switching angles [64]–[66]. Using these advanced mathematical search algorithms, local solutions are avoided and global solutions are obtained with high accuracy. However, the computational cost of these algorithms is usually high and all the calculations have to be done offline previous to the operation of the power converter. This fact leads to the drawback of poor dynamic performance of power systems using pre-calculated PWM techniques. In order to reduce this problem, the researchers have developed real-time algorithms to calculate the switching angles. In this way, the angles are not pre-calculated but they are determined online. The method to calculate the switching angles varies from artificial neural network to eliminate some loworder harmonics [67] to real-time Newton-Raphson algorithms to minimize the total harmonic distortion value [68]. On the other hand, the synchronous optimal PWM technique is another offline pre-calculated PWM method with the objective to generate a sinusoidal waveform with an specific modulation index and minimum total harmonic distortion which is an important target in motor drive applications [69]– [71] (see Table IV). The conventional method is used in openloop low-performance drives such as industrial fans or pumps. The method has been improved in the last years to be used in closed-loop control systems to work in high-dynamic drives by extracting the fundamental component of the stator flux linkage vector from its distorted trajectory and modifying the conventional pulse pattern of the synchronous optimal PWM method [72]. The pre-programmed PWM methods, and specifically the SHE technique, are especially well suited for high-power systems because the number of commutations (related to the number of switching angles) is limited. This fact makes that a great amount of SHE techniques have been applied to different multilevel converter topologies which have been designed for medium-voltage high-power applications (as shown in Table III) by just defining the pre-calculated waveform and following the same rules introduced for conventional two-level VSIs. The study of generalized SHE methods for multilevel converters, and specially for CHB converters, has been the focus of the researchers in the last decade [73]. Another important research topic for SHE-based multilevel converters is related to the voltage balancing of the dc voltages of the power converter with topologies such as the cascaded rectifier [74], the active neutral-point-clamped (ANPC) [75], the 5L- ANPC [76] and the modular multilevel converter (MMC) [77]. Another recent advance of the pre-calculated PWM methods has been the consideration of grid codes in the determination of the switching angles. In this way, some authors have been focused on the implementation of a SHE technique but including the minimization of the non-eliminated harmonics [78]. Other publications have taken into consideration the maximum limit imposed by the grid codes and have included them into the heuristic search looking for solutions with distortion below the maximum limits. This method has been called selective harmonic mitigation (SHM) and obtains better results compared with the conventional SHE in terms of the weight, volume and cost of the necessary output filter of the power converter [79], [80] (see Table IV). The mathematical calculations of the SHM method are not simple because they IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS TABLE III CONVENTIONAL MODULATION SCHEMES FOR MULTILEVEL VOLTAGE SOURCE INVERTERS Item description LS-PWM (3L-NPC example) PS-PWM (5L-CHB example) Multilevel SVM (3L example) Multilevel SHE (3L example) Operating principle vcr1va * vcr2 vcr2 vcr1 va * vcr4 vcr3 va * θ=90º 100 110 200 210 220 120 221 211 000 111 α β Block diagram – + – – + – vcr1 vcri 1 i . . . – + – – + – vcr1 vcr2 1 2 unipolar PWM for each cell Sector Nearest vectors calc. Duty cycle calc. Angle lookup table Angle/time conv. m Voltage waveform va{f1} vaN vdc t vdc va{f1} vaN vdc t vdc α1 α1 ≤ ... ≤ αi ≤ π/2 α2 α3α5 α4 Spectrum 0.1 0.2 0.3 0.4 0.5 Harmonic number [pu] 0 1 0.6 0.1 0.2 0.3 0.4 0.5 Harmonic number [pu] 0 1 0.6 4 8 0.1 0.2 0.3 0.4 0.5 Harmonic number (ignoring triplen) [pu] 0 1 0.6 0.1 0.2 0.3 21 0.4 0.5 3 9 1 15 19 23 25 29 27 [pu] 0 0.6 17 Pros Simple implementation Multiplicative frequency effect Switching sequence control Low switching frequency Superior harmonic performance Power and losses equalization Coding independent of # levels No low order harmonics Suitable for NPC, TCC DC voltage balance in FC High switching redundancy Look-Up Table based method Cons Harmonic distortion in mfPhase-shifting synchronization Complex implementation Off-line method Cons Not well-suited for CHB or FC High THD with small mSuitable only for 3-phase VSI Poor dynamic performance Unequal losses distribution Sidebands harmonic distortion High non-eliminated harmonics References [39] - [58] [39] - [58] [83] - [89] [62] - [78] include a system of inequations imposing the limits of the grid code considered for the switching angles determination. However, it has to be noticed that these inequations are solved offline as in the conventional SHE case. The SHM concept can consider any grid code and can be applied to a dc/ac converter with any number of levels. In particular, it has been successfully applied to several multilevel converter topologies [79]–[82]. X. ADVANCES ON VECTOR-BASED METHODS The introduction of more and more complex converter topologies (i.e. multilevel converters) has led to a high number of degrees of freedom which can be used by the SVM algorithm to improve the converter performance. In this way, in the last years the contributions related to SVM methods for multilevel converters have been mainly focused on the simplification of the computational cost of the modulation algorithm (calculation of the three nearest switching vectors and the corresponding duty cycles) and the use of the redundant state vectors (switching vectors located in the same position of the α-βframe) to control some power converter features as shown in Table III [83]–[85]. The equivalence between carrierbased PWM and SVM still is valid for multilevel converters as was analytically described in [60] where a simple singlephase modulator (which is a mathematical implementation of a multicarrier LS-PWM method and is addressed in Table IV as the unidimensional modulator) is demonstrated to achieve the same switching sequence and the same duty cycles compared with the classical SVM technique introduced in [83]. Taking into account the equivalence between PWM and SVM, there are two ways to face auxiliary control objectives such as the common-mode voltage minimization or the dc voltage control among others. If a PWM method is used, the usual way to face the problem is to include additional control loops in the controller design generating reference voltages u∗ which considers the control objective. On the other hand, using a SVM method the problem can be directly solved choosing carefully the best redundant switching state once the sequence of voltage states is determined [86]– [88]. In this way, for instance, the control of the dc-link voltage imbalance in the NPC topology can be carried out by a SVM technique taking into account the redundant states present in the multilevel converter (see for instance the nearest virtual vector SVM method introduced in Table IV [89], [90]). Both ways to face the problem (using PWM or SVM) are valid and achieve very similar results, even identical. So, the decision about how to face the problem finally depends on the researcher know-how. The advantage of considering a SVM technique is the direct analysis of the effect of the redundant states in the power converter performance at the expense of a higher computational cost compared with using a PWM method where all the control objectives are tracked by the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS TABLE IV SOME RECENT CONTROL AND MODULATION TECHNIQUES FOR VOLTAGE SOURCE INVERTERS Modulation Technique Operating Principle / Block Diagram Advantages / Drawbacks Synchronous Optimal PWM [68]-[71] Pattern Selector Modulator DC /AC Converter M 3~ LUT Optimal Patterns f 1 + − Controller Control Target 3Well suited for low-performance ac drives 3Optimal pre-programmed PWM patterns optimized for targets such as: - Minimum total harmonic distortion - Minimum peak values of the phase currents 7Originally poor dynamic performance (improved recently with modified patterns) 7Complex off-line calculations obtaining optimal switching patterns Selective Harmonic Mitigation [79]-[82] 1 2 3 4 5 1 25 [%] 0 6 37 31 35 3941 45 43 33 49 47 Grid Code 9 5 7 11 13 17 15 23 29 27 2119 3 3Fulfillment of grid codes dealing with individual harmonic distortion and THD 3Flexible tool for harmonic shaping reducing the filtering weight, size and cost 3Better results compared with SHE even with low number of switching angles 7Poor dynamic performance inherent to pre-programmed PWM methods 7Complex off-line solutions searching of a non-linear inequations system Hybrid PWM (Example 5L-ANPC) [50] va * 1 0 1 S sign( v a * ) + Σ + v dc v cr1 + _ + 1 0 1 0 2 S Σ Σ 3 S v cr2 _ 0 +_ Σ + _ 3High simplicity only including comparators and standard PWM 3Well suited for asymmetrical multilevel converters (asymmetric CHB, 5L-ANPC) 3Can obtain the advantages of using both LS-PWM/PS-PWM in the PWM stage 7Particular solution for each power converter topology 7Leads to unequal distribution of features (active power or switching losses) Unidimensional and Multidimensional PWM [59]-[61] v1 v2 v3 v m 3 vm 1 vm 2 van * Plane P 2 X X X X X XX X X 10 00 01 02 11 12 20 21 22 v 1 v v an * dc1 v dc2 v dc1 -v dc2 -v m1 v m2 v 3Generalized and comprehensive PWM method 3Natural common-mode voltage elimination if applied to multiphase converters 3Multi-objective modulation technique added as extra features 3Specially well suited for multilevel cascaded converters (CHB, MMC) 7Not applicable to other topologies such as NPC, T-type or Flying-capacitor 7Requires extra calculations to achieve secondary control targets Nearest Three Virtual Vectors SVM [89], [90] Sector 1 1 4 5 3 2 Virtual vectors with zero average current through the neutral point of the dc-link 3Accurate DC voltage balance control with zero average neutral point current 3Possible extension for NPC with any number of levels using the same concept 3Optimized to achieve lower harmonic distortion for linear-and-balanced ac loads 7Slight increase of switching losses due to using switching redundancy 7Only suited for NPC or T-Type converters, not suitable for other topologies DTC-SVM [97] S A S B S C IM 3~ v dc ABC d-q αβ c c v dc SVM Voltage Calculation Flux Torque Speed Estimator αβ αs V V αs I I s β s β V V cα V V sβ ˆ γ r Mc Ψsc PI PI Ψ M Me ˆ Ψs ˆ Ωm ˆ Ωm ˆ Ψ ˆ s c s 3Fixed switching frequency leading to non-spread harmonic spectra 3Good performance at starting and low-speed operation 3Possible closed-loop control of both torque and flux of the machine 3Relatively low sampling frequency compared with hysteresis-based DTC 7More complexity in the overall control and modulation scheme 7High computational cost compared with simple hysteresis-based DTC controller. On the other hand, multiphase inverters are becoming attractive in the last decades for a wide range of applications. From the initial mathematical extension done in [91], SVM techniques have been generalized to be applied to multiphase power converters usually at the expense of making complex the representation of the space vectors since it is not possible to further use the conventional α-βframe with more than three phases. So, a conventional way to develop a SVM method for multiphase converters is to use multiple coupled d-qframes [92]. In this way, the SVM concept remains but the computational complexity usually increases with the number of phases. Generalized SVM strategies independent of the number of phases of the VSI have been presented (even for multilevel multiphase converters). One interesting but conceptually complex generalized SVM method has been digitally implemented using matrices and carries out all the calculations by products and sorting processes making the modulation stage computationally efficient [93]. To simplify the calculations and mainly to make the modulation stage conceptually simple, in [60] it is demonstrated that the same results can be obtained by applying digital PWM to each phase of the converter. Other recent interesting implementation of the SVM method has been related to the control of open-end winding machines operated with dual converters (connected to each side of the