Overmodulation Region Research Articles

An Improved Type of Synchronized Space Vector PWM Based on Switching Angles for High‐Power AC Drive Application

Synchronized space vector pulse width modulation (SSVPWM) is widely employed in high‐power AC drive systems. The existing methods are carrier‐based, in which the carrier ratio, position of samples, and switching sequences used to generate every sample for a given SSVPWM are settled, which causes two problems: (i) the control delay changes, and a voltage phase modulation error appears suddenly during transition between different SSVPWMs with different carrier ratios, which causes motor current spikes; (ii) due to the particular switching sequences, some kinds of SSVPWM cannot get into six‐step operation by overmodulation. This paper proposes an improved type of SSVPWM based on switching angles, in which the carrier ratio of a given SSVPWM can change flexibly, and the problems mentioned above can be solved. Theories including switching angle calculation, overmodulation strategy, carrier ratio setting principle, and transition rules between different SSVPWM modes are given in this paper. Meanwhile, the switching angles change linearly with modulation index which makes it easy to implement, and the modulation error in the overmodulation region is effectively limited so that the proposed scheme is suitable in the whole modulation index range. A case study of a 5.5‐kW experimental platform is presented to validate the proposed method. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Dynamic overmodulation strategy based on torque and flux optimal tracking for DTC‐SVM of surface‐mounted PMSM drives

AbstractDirect torque control with space vector modulation has been increasingly attracting emphasis for permanent‐magnet synchronous machine control, benefiting from a high dynamic response and low torque ripple. However, the rapid tracking performance of torque and stator flux linkage is gradually deteriorating as the machine enters the overmodulation region because of the output‐voltage limitation of the inverter. Therefore, to enhance the system tracking performance in the overmodulation region, an innovative overmodulation method based on torque and flux optimal tracking is proposed. In contrast to the conventional overmodulation method where only one of the torque and stator flux linkage tracking is considered, the proposed strategy first constructs the weightless cost function to achieve a trade‐off control between the torque and stator flux linkage. Then, by using an equivalent geometric path to intuitively express the weightless cost function, the minimum cost function can be easily solved and the optimal output voltage vector can be determined correspondingly, to achieve the fast‐tracking of both the torque and stator flux linkage. Additionally, the voltage utilization of different overmodulation schemes is also analysed. Finally, the experimental results demonstrate the efficiency and practicality of the proposed strategy.

A Comprehensive Review on Comparison and Performance of Five-Phase Space Vector Pulse Width Modulation Overmodulation Strategies

High-performance overmodulation strategies for voltage source inverters (VSIs) can further broaden the operation range of machines. Among them, Space Vector Pulse Width Modulation (SVPWM) is worth researching as it performs well in digital implementation. This paper presents a detailed comparison of various SVPWM overmodulation strategies and analysis of their performance. It firstly briefly elaborates fundamental laws of two subspaces of five-phase VSIs. Then, it focuses on several overmodulation strategies. Their corresponding basic principles and main characteristics are researched, and conclusions are given. In addition, differences and relationships between them are proved and summarized. Lastly, comparative simulations and experiments were carried out and verify that in the overmodulation region, the output voltage distortion degree increases with the increase in modulation ratio, and strategies with more control degrees of freedom (CDFs) are capable of better controlling the third harmonic subspace, which means that higher-quality output voltage waveforms would be obtained.

A Variable Speed Induction Motor Drive With 24-Stepped Voltage Waveform Throughout Modulation Range

Multi-level inverters produce low order harmonics in over-modulation region, which can be eliminated by generating polygonal space vector structure. A variable speed induction motor drive to generate 24-stepped voltage waveform throughout modulation range is proposed in this article. An open-end winding configuration induction motor (OEIM) is fed with primary and secondary inverter from both the ends of OEIM and generates a 24-stepped phase voltage. The proposed scheme also produces 96-stepped phase voltage waveform at extreme modulation index with highly suppressed higher order harmonics and excellent quality phase voltage. The motor terminal sees a 24-stepped waveform at all speeds, devoid of low order harmonics up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$19^{th}$</tex-math></inline-formula> order. The scheme does not require vector timing calculation due to availability of highly dense 24-sided polygonal structure. Primary and secondary inverters are derived by cascading flying capacitor and CHB cells. Experimental verifications are performed on in-house developed laboratory prototype. Motor phase voltage and phase current waveforms during steady state and transient conditions justifies performance of the proposed scheme. Dynamic performance and floating capacitors voltage balancing method are verified by experimental results.

Overmodulation Strategies for an Open-End Winding Induction Motor Drive With a Floating Capacitor Bridge

This paper considers a 3-phase induction motor with open-end windings fed by a primary bridge connected to the main power source and a floating bridge. The floating bridge supplies the motor with the required reactive power, while the primary inverter only exchanges active power with the main power source. This greatly extends the speed range over which the drive can operate at rated power. To further utilize the input power source, the primary inverter can work in the overmodulation region, and the floating bridge, acting as a harmonic compensator, improves the quality of the current flowing through the motor phases. Also, the paper includes some considerations on the sizing of the floating capacitor. Three different overmodulation techniques are evaluated and compared in terms of peak torque/power and efficiency. The highest performance is obtained when the main inverter generates a six-step voltage waveform, which increases motor power by almost 20% and ensures a broader speed range at maximum efficiency.

Level vector pulse width modulation for multilevel inverters

SummaryIn this paper, a novel method named as level vector pulse width modulation (LVPWM) is proposed for multilevel inverters. Similar to the conventional space vector pulse width modulation (SVPWM), the proposed method is a vector‐based method in the α–β frame. Unlike the SVPWM, the variables of each of the α and β axes are considered separately. Instead of space vectors, level vectors are considered for the synthesis of the reference vectors. There is no need to consider multiple switching states, vectors, and large lookup tables in the algorithm. The appropriate switching states for the synthesis of the reference vectors are determined using simple computations at each sampling time. Generality for different inverter topologies, online implementation, simplicity of the algorithm and computations, independency of the algorithm complexity from the number of switching states, and easy extension to overmodulation region are the advantages of the proposed method. Implementation of the LVPWM in different inverter topologies is studied. The validation of the proposed modulation strategy is carried out by simulation and experimental results.

Modulated Model-Predictive Integral Control Applied to a Synchronous Reluctance Motor Drive

This paper investigates an innovative modulation technique for a predictive control applied to a synchronous reluctance motor drive. The new formulation of the duty cycles, in both linear and overmodulation regions, relies on the identified flux-versus-current characteristics. Furthermore, integral terms have been introduced in the predictive control to achieve satisfactory reference tracking performance with zero steady-state error, even under model parameters mismatches. Low current ripple with smooth and fast dynamic responses are achievable at fixed switching frequency over the whole current operating range. Simulations and experimental evidence show the effectiveness of the proposed controller against standard controllers such as field-oriented current control and deadbeat current control, guaranteeing low current ripple, robustness against parameters variations, and fast dynamic performance.

Flux Weakening Controller Design for Series-Winding Three-Phase PMSM Drive Systems

Series-winding three-phase PMSMs have a higher bus voltage utilization than the conventional three-phase PMSMs with star connection. This topology is suitable for applications with a limited bus voltage. However, the zero-sequence current controller will reduce the bus voltage utilization of the series-winding PMSMs, which causes problems in the flux-weakening controller design. The conventional flux-weakening control algorithms will cause the series-winding PMSMs to enter the overmodulation region early and degrade the performance of the zero-sequence current suppression algorithm. In this paper, a new flux-weakening controller with a dynamic fundamental voltage limit (FW-DFVL) is designed for the series-winding three-phase PMSM traction system. Firstly, the space vector modulation method combines the proposed virtual zero-sequence vectors to realize both the fundamental current generation and the zero-sequence current suppression. The accurate bus voltage utilization in the fundamental current subspace can be derived from the proposed modulation method. Secondly, the gradient descent method generates the flux-weakening d-axis reference current with the dynamic fundamental voltage, which will converge faster than the conventional PI-based flux-weakening control scheme. Thirdly, the flux-weakening controller in the overmodulation region is also designed where the zero-sequence current will no longer be suppressed. The bus voltage utilization is Vdc in this operation mode. Finally, both the simulation and experimental results are utilized to verify the effectiveness of the proposed FW-DFVL, where faster dynamic performance and higher bus utilization are observed.

Assessment and Exploitation of the Minimum Current Harmonic Distortion Under Overmodulation in Five-Phase Induction Motor Drives

This paper compares the most prominent overmodulation (OVM) techniques for five-phase induction motor drives with respect to the minimum current distortion (MCD) achievable. To attain a benchmark of the latter, two MCD OVM approaches are devised. Contrarily to previous strategies aimed at voltage distortion reduction/minimization, these MCD methods are focused on minimizing the harmonic stator copper loss (HSCL), thus minimizing the current total harmonic distortion (THD). One of these MCD strategies minimizes the HSCL while injecting only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$y$</tex-math></inline-formula> harmonics. The other MCD method exploits <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> harmonic injection to further decrease the HSCL and to cover the whole OVM region. Moreover, the dual-mode OVM, which is one of the three-phase methods with the lowest distortion, is extended here for five-phase drives. The findings provide insight into how close the OVM methods are to the benchmark imposed by the MCD strategies. Notably, these MCD techniques yield a significant reduction of current THD, HSCL and peak current, especially for machines with negligible third-order space harmonic. The average switching losses are also decreased. Indications for real-time implementation of the MCD solutions are also given.

A Novel SVPWM for Open Winding Permanent Magnet Synchronous Machine With Extended Operation Range

In this article, a novel space vector pulsewidth modulation (SVPWM) with the zero sequence current (ZSC) control strategy is proposed to extend the operation range for an open winding (OW) permanent magnet synchronous machine (PMSM). The proposed SVPWM can achieve the ZSC control and extend the operation range by considering voltages in the zero sequence axis and voltage vectors in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \beta $ </tex-math></inline-formula> -plane, both of which are mapped by switching combinations in an OW drive. The effect of switching combinations with non-null zero sequence voltage (ZSV) on the modulation region of a common-dc bus OW-PMSM is investigated for the first time. The proposed SVPWM has optimal selection of switching combinations on the large hexagon rather than on the small hexagon in the conventional SVPWM for ZSC control and still maintains the controllability of ZSC in the overmodulation region. Compared with the conventional SVPWM strategy, the operation range of OW-PMSM can be extended over 10% with the proposed SVPWM strategy. The performance of both the conventional and proposed SVPWMs is compared experimentally.

An Overmodulation Strategy Based on Voltage Vector Space Division for High-Speed Surface-Mounted PMSM Drives

The overmodulation strategy plays an important role in the field weakening control for high-speed permanent magnet synchronous motor (PMSM) drives. However, the voltage jumps between the output voltage vectors (OVVs) in high overmodulation regions result in the deterioration of both current performance and loading capability. In order to solve this problem, a novel overmodulation strategy based on the voltage vector space division is proposed. The overmodulation regions are divided by the amplitude and the phase of reference voltage vectors to guarantee the continuity of OVVs. When the overmodulation region changes, the voltage jump can be efficiently suppressed, which contributes to eliminating current ripples. In addition, the proposed parallel projection replaces the traditional center projection to increase the modulation index, which can also improve the fundamental voltage amplitude, and make a reduction of the field weakening current and its current overshoot. By improving the utilization of the dc bus voltage, the higher capability of the output torque can be achieved in the field weakening region. Finally, the effectiveness of the proposed strategy is verified on a high-speed surface-mounted PMSM platform by the experimental results.

Investigative uses of overmodulation techniques in modular multilevel cascaded converter

Sinusoidal pulse width modulation (SPWM) is a method to generate the switching gate pulse of the converter. Overmodulation is a method where the modulation index exceeds the unity value and the system goes into the nonlinear region. To maintain the system in a linear region when operating in the overmodulation region, some techniques are developed. These techniques helped to operate the system in the linear range. Medium and high-power energy conversion systems mostly use a modular multilevel cascaded converter (MMCC), which has been an issue improving significantly in recent years. In this article, MMCC-based overmodulation techniques are compared with conventional PWM and analyzed on DC bus utilization (DBU), and total harmonic distortion (THD). MATLAB/Simulink digital platform used demonstrate overmodulation technique.

Overmodulation Strategy for Torque Balance of Dual-Motor Systems Considering Angle Offset

An overmodulation method is proposed for an in-wheel system where two motors are coupled to a sum gear. In the dual-motor dual-inverter single shaft systems, the output voltage magnitudes of two inverters are not the same in the overmodulation range due to the angle offset between two motors. In this article, to maintain torque balance in the overmodulation region, holding vectors are defined between adjacent vertices of two voltage hexagons. Around these vectors, the holding region is also defined by the holding angle. If a reference voltage vector is in the holding region, it is modulated to the holding vector; otherwise, it is modulated to the vector on the arc of inscribed circle. For a given the modulation index (MI), the holding angle is obtained based on the Fourier series expansion. The proposed method keeps the output voltages of two inverters the same even if two motors have the angle offset. Further, it has the characteristic of maintaining the linearity between the reference and output MI to the maximum MI. The proposed overmodulation method is demonstrated by simulation and experimental results.

A Harmonic Suppression SVPWM Strategy for the Asymmetric Six-Phase Motor Fed by Two-Level Six-Phase VSI Operating in the Overmodulation Region

For the asymmetric six-phase motor fed by a two-level six-phase voltage source inverter (VSI), when the modulation index is less than 0.5774, the motor operates in the linear region, and the harmonics in the Z1 − Z2 subspace can be suppressed to zero. When the modulation index is beyond 0.5774 and less than 0.6221, the motor operates in overmodulation regions, and the harmonics in the Z1 − Z2 subspace cannot be suppressed to zero. To minimize the harmonics in the Z1 − Z2 subspace for these regions, a harmonic suppression strategy, namely, harmonic suppression overmodulation strategy (HSOS), is proposed in this paper. The lower-order harmonics of the Z1 − Z2 subspace, namely, the 5th, 7th, 17th and 19th, are considered. Compared with the traditional four-vector overmodulation strategy (TFOS), the content of the 5th harmonic is reduced by about 20%, and the total harmonic distortion (THDZ1Z2) of these four kinds of harmonics is reduced by about 21% in the proposed HSOS. Finally, the simulation and experiment are carried out to verify the effectiveness of the proposed strategy.

A novel adaptive state-of-charge balancing control scheme for cascaded H-bridge multilevel converter based battery storage systems

Variations in state-of-charges (SOCs) of batteries in a cascaded H-bridge multilevel converter (CHB-MLC) based battery storage system (BSS) could lead to undesired efficiency and performance drops, even failure of the whole system. Hence, SOC balancing is crucial for BSSs. Avoiding over-modulation region, ensuring zero common-mode voltage and reaching balanced SOC condition as quickly as possible are the key points to consider while performing SOC balancing. In this paper, a gain-scheduling based adaptive SOC balancing method is proposed for single-phase CHB-MLC based BSSs. In the proposed method, gains of the proportional controllers are updated at each sampling time based on the mathematical relationship between instantaneous SOCs and voltage reference of the CHB-MLC. Performance of the proposed method is validated through a Monte Carlo simulation based numerical analysis and experimental studies on a single-phase three-module CHB-MLC based BSS. Results reveal that the proposed method achieves SOC balancing at least two times faster than the traditional constant gain methods while avoiding over-modulation region and having zero common-mode voltage.

A Simple Virtual-Vector-Based PWM Formulation for Multilevel Three-Phase Neutral-Point-Clamped DC–AC Converters including the Overmodulation Region

Neutral-point-clamped (NPC) power conversion topologies are among the most popular multilevel topologies in current industrial products and in industrial and academic research. The proper operation of multilevel three-phase NPC DC–AC converters requires the use of specific pulse-width modulation (PWM) strategies that maintain the DC-link capacitor voltage balance and concurrently optimize various performance factors such as efficiency and harmonic distortion. Although several such PWM strategies have been proposed in the literature, their formulation is often complex and/or covers only particular cases and operating conditions. This manuscript presents a simple formulation of the original virtual-vector-based PWM, which enables capacitor voltage balance in every switching cycle. The formulation is presented, for the general case, in terms of basic phase voltage modulating signals, with no reference to space vectors, involving any number of levels and for any operating conditions, including the overmodulation region. The equivalence of the presented formulation to the original PWM strategy is demonstrated through simulation under different scenarios and operating conditions. Thus, this manuscript offers in a one-stop source a simple, effective, and comprehensive PWM formulation to operate multilevel three-phase NPC DC–AC converters with any number of levels in any operating condition.

A Survey on Capacitor Voltage Control in Neutral-Point-Clamped Multilevel Converters

Neutral-point-clamped multilevel converters are currently a suitable solution for a wide range of applications. It is well known that the capacitor voltage balance is a major issue for this topology. In this paper, a brief summary of the basic topologies, modulations, and features of neutral-point-clamped multilevel converters is presented, prior to a detailed description and analysis of the capacitor voltage balance behavior. Then, the most relevant methods to manage the capacitor voltage balance are presented and discussed, including operation in the overmodulation region, at low frequency-modulation indexes, with different numbers of AC phases, and with different numbers of levels. Both open- and closed-loop methods are discussed. Some methods based on adding external circuitry are also presented and analyzed. Although the focus of the paper is mainly DC–AC conversion, the techniques for capacitor voltage balance in DC–DC conversion are discussed as well. Finally, the paper concludes with some application examples benefiting from the presented techniques.

Extending DC Bus Utilization for Induction Motors with Stator Flux Oriented Direct Torque Control

This paper presents a method to extend the DC bus utilization on an induction motor (IM) by using a combination of Space-Vector Modulated Direct Torque Control (DTC–SVM) and conventional DTC. The scheme proposed in this paper exploits the advantages of both control methods. During the linear region, it allows for a low torque ripple and low current harmonic distortion (THD). During the overmodulation region, it allows for the fastest torque response up to the six-step operation region. In both regions, there is complete independence of the motor parameters. The paper describes a way to provide a smooth transition between the two control schemes. Non-linearities affect the stator flux angle estimation, which leads to the inability to decouple torque and flux. To overcome this problem, a novel PI-based control scheme as well as a simplification on the decoupling terms’ calculation are proposed. Simulation and experimental results are presented to verify the feasibility of the proposed method.

An Over-Modulated Model Predictive Current Control for Permanent Magnet Synchronous Motors

To improve the voltage utilization rate of DC bus and reduce the voltage vector tracking error, a finite-control-set modulated model predictive control (FCS-M2PC) with overmodulation capacity for permanent magnet synchronous motor (PMSM) incorporating penalty function is proposed in this paper. Firstly, three modulation regions are determined according to the combined action of dead-beat control and model predictive control (MPC). Secondly, three, two and one voltage vectors are applied to linear modulation region (LMR), overmodulation region I (OMR-I) and overmodulation region II (OMR-II), respectively, to synthesize the reference voltage vector. Thirdly, to obtain better steady-state performance in the whole modulation region, the optimal vector dwell-times can be obtained from the uniform penalty function defined by a set of mode parameters to minimize the error between the current references and the current predictions, rather than applying a single voltage vector in the conventional finite-control-set model predictive control (FCS-MPC). The effectiveness and superiority of the proposed method are validated experimentally.

Investigated Analysis and New Zero-Sequence Harmonic Injection Pulsewidth Scheme for Overmodulation Region

Pulswidth modulation (PWM) methods were developed to grant the voltage source inverter (VSI) output signal better quality measures. The PWM method that VSI relies on must consider the utilization of the direct current (DC) source, especially when the drive system works in the overmodulation region. In this paper, different zero-sequence harmonic injection PWM methods are proposed. Two essential objectives are optimized by minimizing total harmonic distortion and maximizing the DC bus utilization. All schemes’ results are compared with each other and with some of the commonly used PWM schemes. This paper concludes the usage of third, ninth, and fifteenth harmonic injections and any combination of them to reach a new PWM method that overtakes the disadvantages of other methods. Meanwhile, it provides a handy tool to operate VSI optimally. Ultimately, this work concludes to what extent is the zero-sequence injection is helpful. The work is evaluated experimentally, and the practical results match the simulation outcomes.