Virtual Vector Research Articles

Exponential Synchronization of Chaotic Lur'e Systems using Sampled-Data PI Control

In this paper, an exponential synchronization design method for chaotic Lur'e systems is developed. Firstly, a sampled-data based proportional-integral (PI) type controller is used in the slave system to achieve the synchronization. Next, the synchronization problem of the chaotic Lur'e system is transformed into the stabilization problem of the synchronization error system. Then, by introducing virtual vectors for reconstruction, a new augmented error system is obtained. As a result, the synchronization design based on sampled-data PI type controller can be achieved using the existing sampling system method. And based on this, a criterion for exponential synchronization design is obtained using the Lyapunov functional method. Finally, the effectiveness of the developed method is demonstrated by numerical example.

Research on the Coordination Suppression Strategy of Neutral Point Potential and Common Mode Voltage for NPC Three-Level Inverter

A Neutral Point Clamped (NPC) type three-level inverter has the advantages of a low switch voltage and a high-quality output waveform. However, there are inherent problems, such as neutral point potential asymmetry and common mode interferences, which easily affect the symmetry of the three-phase output voltage and the safe operation of the inverter. Firstly, according to the different modulation degrees, the fluctuation of midpoint potential can be suppressed by adding an action time correction factor to the traditional space vector pulse-width (SVPWM) modulation strategy and virtual space vector pulse-width (VSVPWM) modulation strategy, respectively. Secondly, considering the suppression of common mode voltage, a new virtual space vector pulse-width (NVSVPWM) modulation strategy is proposed, which uses a set of new vector synthesis methods. Finally, the simulation and experiment prove that the NVSVPWM strategy with an action time correction factor can suppress the fluctuation of the neutral point potential and common mode voltage at the same time, and the effect is significant.

Fault-Tolerant Predictive Current Control of Six-Phase PMSMs with a Single Isolated Neutral Configuration

Six-phase machines are increasingly used in safety-critical applications due to their inherent fault-tolerant capabilities. Due to the greater complexity of controlling six-phase machines and the fast dynamics required in safety-critical applications, finite control set model predictive control (FCS-MPC) emerged as an ideal candidate for the control of six-phase machines. However, most of the available FCS-MPC strategies only apply to six-phase machines where the two sets of three-phase windings are star-connected with isolated neutral points (2N). Nevertheless, the 2N configuration does not take full advantage of the machine’s capabilities in terms of fault tolerance. Hence, this paper proposes a predictive current control strategy based on virtual vectors for six-phase permanent magnet synchronous (PMSM) drives with a single isolated neutral point (1N) configuration. The proposed method reduces the current harmonic distortion, decreases the copper losses, and is suitable to operate the six-phase drive in fault-tolerant conditions. The included simulation and experimental results demonstrate the good performance obtained with the proposed strategy.

Direct Torque Control for Dual Three-Phase Permanent Magnet Motor With Improved Torque and Flux

The conventional duty ratio modulation based direct torque control (DR-DTC) for the dual three-phase permanent magnet (DTP-PM) motor reduces the torque ripple using duty ratio modulation in torque control. However, the flux was controlled by a hysteresis comparator, resulting in deficient steady-state performance. This paper proposes a novel DR-DTC strategy to improve torque and flux simultaneously. Firstly, a switching table with the multiple vector selection is newly established. Two adjacent virtual voltage vectors and a null vector are selected in each control period. Then, the duty ratios of selected adjacent virtual voltage vectors are optimized with the dual objective modulation considering torque performance and flux performance. In addition, the combination of adjacent virtual voltage vectors for the DTP-PM motor generates non-standard symmetrical switching sequences. Two switching sequences generated methods are further investigated to address the issue. So, the switching sequences of the proposed strategy can also be generated easily. Finally, the conventional strategy and the proposed strategy are compared through experiments, and the experimental results verify the effectiveness of the proposed strategy.

An Improved Three-Vector-Based Model Predictive Current Control Method for Surface-Mounted PMSM Drives

The conventional model predictive control method suffers from large torque ripples and harmonic current. Moreover, the modulation range of output is limited, leading to the deterioration of performance. To address these problems, this article proposes an improved three-vector model predictive current control method for surface-mounted permanent magnet synchronous motor (SPMSM) drives. First, virtual vectors are introduced to increase the number of available voltage vectors, in which the voltage vector control set can be extended. Furthermore, a hierarchical multilevel optimization control algorithm is adopted to obtain the main control set and the extended control set. According to two different control sets, the first and second vectors can be obtained by the cost function, respectively, which can realize modulation range extension. Then, the zero vectors are added to adjust the magnitude of the output voltage vector, and the output vector action time is obtained based on the deadbeat principle. The ripples can be minimized, and the modulation range can be extended with the proposed method. Finally, a comparative analysis of both the simulation and experimental tests is investigated. The comparative investigation verifies the effectiveness and feasibility of the proposed method.

Design and Evaluation of a Virtual Vector Based Modulated Model Predictive Control for the Indirect Matrix Converters With Improved Performance

A virtual vector based modulated model predictive control (VV-M2PC) strategy is proposed for the indirect matrix converters (IMCs) in this article. Compared with the conventional M2PC, the VV-M2PC constructs and utilizes new virtual vectors to reduce the current control errors. Besides, the implementation and feasibility for the proposed strategy is discussed in detail. The comparative simulation and experimental results based on an experimental IMC prototype verify that the steady-state control performance can be improved under the VV-M2PC without affecting the dynamic-state control performance and increasing the computational burden.

Model Predictive Torque Control for a Dual Three-phase PMSM Using Modified Dual Virtual Vector Modulation Method

Single voltage vectors applied in the conventional model predictive torque control (MPTC) for multiphase motors do not only suffer from serious torque and stator flux ripples but also cause the large harmonic current. To address the aforementioned challenges, an MPTC using a modified dual virtual vector modulation method is proposed to improve the operational performance of a dual three-phase permanent magnet synchronous motor. Virtual voltage vectors are synthesized as the candidate control set to restrain the harmonic current. A transformation method is introduced to consider both the stator flux and torque in the duty cycle modulation. The torque and stator flux ripples are simultaneously reduced by addressing the limitations of nonuniform units. Furthermore, the null voltage vector is then inserted to expand the modulation range and improve the steady-state performance. Moreover, the sawtooth carrier is adopted to address the challenge of the asymmetric switch sequence caused by the modified modulation. Finally, the experimental results are presented to verify the effectiveness and superiority of the proposed MPTC method.

A Phase-Disposition PWM-Enabled Model Predictive Control for a Nine-Level Inner-Interleaved Hybrid Multilevel Converter

This article brings forward a phase-disposition pulsewidth modulation-enabled model predictive control (PDPWM-MPC) for a nine-level inner-interleaved hybrid multilevel converter (9L-IHMC). First, three layers of virtual space vector diagrams (VSVDs) are established based on the sign patterns of the original and virtual reference vectors in the abc-frame to achieve the phase-disposition pulsewidth modulation (PD-PWM) in a nonindependent three-phase way. Then, three adjacent virtual vectors in the third-layer VSVD, together with their optimized duty cycles, are applied to guarantee the optimal current tracking. Finally, through the use of the duty-cycle alternation approach, dc-link and floating capacitors voltages are balanced and circulating currents are mitigated as well. The proposed PDPWM-MPC can not only enable the decoupling of the low- and high-frequency stages in the 9L-IHMC but also reduce both output current ripples and computational burden. In addition, it can achieve a constant equivalent switching frequency and address the disproportion of power losses associated with the PD-PWM. Both simulations and experiments on a silicon carbide device-based prototype substantiate the effectiveness of the proposed control strategy.

Single-Loop Control for Single-Phase Dual-Boost Grid-Tied Inverter With Half Cycle Modulation and Feedforward Virtual-Vectors MPC

In this letter, a simplified single current loop control scheme for single-phase dual-boost inverter has been developed, combining half cycle modulation and virtual-vector (VV) based model predictive control (MPC). As the control reference can be slipped and allocated into two side boost, only a unified grid current reference is relied on in this proposed control method. Furthermore, with the concept of feedforward control, the global optimal solution space in MPC can be compressed, taking the duty ratio as boundary for the precompacted solution space. Thereby, the improved MPC can select the optimal VV in a smaller and closer subspace. Consequently, much finer control effect can be obtained. Experimental tests are provided to validate the proposed solution and its merits.

Enhanced Natural Fault-Tolerant Model Predictive Current Control in Nine-Phase Motor Drives Under Open-Phase Faults

For the open-phase fault (OPF) tolerant operation of multi-phase motors based on model predictive current control (MPCC), the fault diagnosis and control scheme reconfiguration are difficult to avoid, which leads to the increase of control complexity. A natural fault-tolerant (NFT) MPCC method based on virtual voltage vectors (V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{3}$</tex-math></inline-formula> ) can simplify this procedure and realize the fault-tolerant operation by using a unified control algorithm during pre- and post-faults. However, there is no effective control scheme to deal with the V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{3}$</tex-math></inline-formula> shifting after the fault, which will lead to the control errors. To overcome this problem, an enhanced NFT-MPCC strategy is proposed in this paper. Firstly, this paper analyzes the causes of the control error in NFT, and elaborates the influence of V <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{3}$</tex-math></inline-formula> shifting on the current tracking performance. Then, a duty ratio optimization based on an PI regulator is proposed for the first time. After the fault occurs, the PI regulator automatically corrects the duty ratio calculation result to eliminate the control error caused by vector shifting, and the proposed method is versatile to different OPF scenarios. Compared with existing NFT-MPCC technologies, the experimental results show that the proposed method significantly suppresses the torque ripple in post-fault, and provides a satisfactory control performance before and after fault without the need of software reconfiguration.

A Computationally Efficient Finite Control Set Model Predictive Control for Multiphase PMSM Drives

Finite control set model predictive control (FCS-MPC) has been widely studied and applied in power converters and machine drives. It takes advantage of the nonlinear finite switching states of the power converters, and a discrete model is used to predict the behavior of the system. The main advantages of FCS-MPC lie in easy inclusion of nonlinear constraints, simple structure and intuitive concept. However, FCS-MPC applied in multiphase machine drives will face with the challenge of heavy computation cost. In this article, a computationally efficient FCS-MPC method is proposed for multiphase drives. The concept of virtual voltage vector is introduced to eliminate low-order harmonic currents in open-loop mode, resulting in simplified prediction model and cost function. To further simplify the enumerative optimization process, the redundant vectors are eliminated, and only five evaluations are required. By this way, the computation complexity is considerably reduced and is approximately irrespective of phase number. Thus, it can be easily generalized to multiphase drives. Moreover, the merit of simple structure is kept, which is the most important characteristic of FCS-MPC. The proposed method is compared with the existing FCS-MPC methods to illustrate its effectiveness. The experimental results have verified that the proposed method can reduce computation complexity, achieve superior steady-state and dynamic performance.

Double-Vector-Based Finite Control Set Model Predictive Control for Five-Phase PMSMs With High Tracking Accuracy and DC-Link Voltage Utilization

Finite control set (FCS) model predictive control (MPC) has been widely emerged for the double-subspace control problem of five-phase permanent magnet synchronous motor (PMSM) drives thanks to the principles of the virtual voltage vectors (V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s), which improve the steady-state performance with low computational burden. However, the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s are designed offline to include one-subspace components, which is not considered as an optimized solution. Therefore, this article presents an improved double-vector-based FCS-MPC scheme for five-phase PMSM drives, considering the control objectives of the two subspaces. The proposed scheme remedies the limitations of the conventional V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s using online selection of the two vectors combination and duty ratio calculation. To keep low computational burden, ten possible double-vector combinations are examined during every sampling interval for each fundamental <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α–β</i> sector, which is defined using the deadbeat calculations. Compared with the standard FCS-MPC and the traditional FCS-MPC with V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> s schemes, the proposed double-vector-based FCS-MPC scheme can achieve improved tracking accuracy and high dc-link voltage utilization. The potentials of the proposed scheme over these existing FCS-MPC schemes are verified by simulation analysis and experimental test on a five-phase PMSM drive prototype.

The switching decomposition pulse width modulation with reduced common mode voltage for reduced switch counts neutral point clamped inverter

Compared with a conventional three-levelconverter, a reduced switch counts three-level neutral point clamped (RSC-3LNPC) inverter uses only 10 switching devices to achieve three-leveloutput at a lower cost. However, in the RSC-3LNPC inverter, the common modevoltage (CMV) reduction and neutral point voltage (NPV) balance are mutuallycoupled, and the buck switching module eliminates medium vectors, making conventional modulation methods no longer applicable. To address this problem, this paperdevelops a generation mechanism of the voltage and switching vectors for RSC-3LNPC inverter and proposes a switching decomposition pulse width modulation (SDPWM) scheme. First, a virtual medium vector with two large vectors having the samedwell time is introduced. Then, the small and zero vectors with low CMV, along with the large and virtual medium vectors, are adopted, and by adjusting their dwell time, the NPV is balanced while reducing CMV. In addition, to reduce computational burden, the switching vector isdecomposed into a buck switching vector and a two-level switching vector. Both switching vector sequences with transformed duty cycles are carefully designed to achieve only three switching transactions per switching period. Finally, validation and correctness of the proposed SDPWM scheme for RSC-3LNPC inverterare verified by simulation and experiments.

Virtual Vector Optimal Selection Strategy for NPC Three‐Level Grid‐Tied Converter with Finite Control Set Model Predictive Control

Virtual vector is applied in neutral‐point‐clamped (NPC) three‐level converter finite control set model predictive control (FCS‐MPC) strategy due to its good performance of less current ripples and high power efficiency. However, in the process of adding virtual vectors, some redundant virtual vectors will be selected. Excessive virtual vector will increase the computational burden and affect grid‐tied current performance. A virtual vector optimal selection strategy for model predictive control to determine the vectors is proposed. The strategy calculates the fluctuation of grid‐tied current through theoretical analysis. Based on the analysis of amplitude fluctuation of grid‐tied current, the graphics of coverage angle visualization can be obtained under different virtual vector. The angle of the required virtual vectors is obtained through the graphics of coverage angle visualization. The number of virtual vector can be determined when the error current angle range covers the entire vector graph. The proposed control strategy was compared with the conventional control strategies, including excessive virtual vectors or with no any virtual vector. Experimental results show that the proposed control strategy can significantly reduce THD, grid‐tied current error and computational burden. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Zero Common-Mode Voltage Model Predictive Torque Control Based on Virtual Voltage Vectors for the Dual Three-Phase PMSM Drive

For the multiphase motor drive system, current harmonic components in stator windings and the common-mode voltage are the main factors affecting the control performance. In this paper, a novel model predictive torque control (MPTC) considering both harmonic and common-mode voltage suppression is proposed to improve the control performance. First, with the vector space decoupling (VSD) theory, 12 virtual voltage vectors are constructed based on the principle that the amplitudes of the vectors in the x-y harmonic subplace are zero to achieve the harmonic suppression. Then, these 12 virtual vectors are further simplified to six vectors to realize the common-mode voltage suppression, and they are taken as the candidate vectors to be rolling optimized to output the optimal voltage vector. This novel MPTC strategy can reduce the computational burden and avoid the weight factor design for the traditional multi-objective optimization. The effectiveness of this novel MPTC strategy was verified by simulations and experiments in comparison with normal MPTC methods, and it can save over 44% of the execution time of the traditional MPTC method and provide better suppression of the harmonic current components and the common-mode voltage.

An Improved Overmodulation Strategy for a Three-Level NPC Inverter Considering Neutral-Point Voltage Balance and Common-Mode Voltage Suppression

The three-level neutral-point clamped voltage source inverter (3L-NPC-VSI) is widely used in the maglev traction systems due to its high output voltage, large output capacity and low output current harmonics. In order to improve the utilization of the DC-bus voltage, an overmodulation strategy is necessary. This paper proposes an improved overmodulation strategy based on the minimum amplitude error method for a 3L-NPC-VSI. Compared with the conventional overmodulation strategy based on the minimum amplitude error method, the utilization of the DC-bus voltage is higher. Meanwhile, a virtual space vector modulation strategy is adopted for inverter neutral-point (NP) voltage balance and common-mode voltage (CMV) suppression. Furthermore, the suppression of leakage current also has been verified. Furthermore, the implementation details of the proposed overmodulation strategy based on minimum amplitude error method is elaborated. The effectiveness of the proposed method is verified by simulation and experimental results.

A Hybrid Multivector Model Predictive Control for an Inner-Interleaved Hybrid Multilevel Converter

A hybrid multivector model predictive control strategy for an inner-interleaved hybrid multilevel converter is brought forward in this article, which can enable the separation of the low- and high-frequency stages. It initiates with the use of sign patterns of the reference vector in the stationary reference frame to determine switching states of the low-frequency stage. Then, the reference vector is converted to the inner virtual space vector diagram, which is further transformed into a 120° oblique coordinate system, where the adjacent vectors are selected. Further, the current tracking is realized through the duty cycle optimization of the chosen vectors. Finally, a symmetric switching sequence (SS), which serves as the best one for dc capacitors voltages balancing and circulating current suppression, is selected among all the SSs that belong to the three chosen vectors with optimal duty cycles. The proposed method reduces both current ripples and computational burden while achieving a constant equivalent switching frequency. Comprehensive experimental results performed on an all silicon-carbide prototype verify the effectiveness of the proposed control.

A Hybrid Two-Stage Control Solution for Six-Phase PMSM Motor With Improved Performance

This article proposes a hybrid two-stage control solution for a six-phase permanent magnet synchronous machine (PMSM) motor with enhanced control performance. The original direct torque control (DTC) and model predictive control (MPC) are artfully integrated together to alleviate the computational burden and the harmonic currents. The proposed method is implemented in two steps. First, the original DTC method is adopted to determine the orientation vector from six existing vectors. It is worthy to mention that the orientation vector is different from the commonly used reference vector calculated through the deadbeat control theory. Second, the prediction vectors located in the same sector with the orientation vector will be evaluated in the original MPC manner. In this way, the enumeration of all the prediction vectors is avoided and the computational burden is avoided. In addition, discrete duty ratios are assigned to define other two groups of virtual vectors to enhance the current quality. In this way, high-performance control of a six-phase motor can be achieved by simply combining the standard DTC and MPC control structure. Experimental results have been used to assess the goodness of the proposed method.

Virtual Voltage Vector-Based Model Predictive Current Control for Five-Phase Induction Motor

The high-performance control technology of multi-phase motors is a key technology for the application of multi-phase motors in many fields, such as electric transportation. The model predictive current control (MPCC) strategy has been extended to multi-phase systems due to its high dynamic performance. Model-predictive current control faces the problem that it cannot effectively regulate harmonic plane currents, and thus cannot obtain high-quality current waveforms because only one switching state is applied in a sampling period. To solve this problem, this paper uses the virtual vector-based MPCC to select the optimal virtual vector and apply it under the premise that the average value of the harmonic plane voltage in a single switching cycle is zero. Taking a five-phase induction motor as an example, the steady-state and dynamic performance of the proposed virtual vector MPCC and the traditional model predictive current control were simulated, respectively. Simulation results demonstrated the effectiveness of the proposed method in improving waveform quality while maintaining excellent dynamic performance.

Improved Model Predictive Control for Single-Phase Grid-Tied Inverter With Virtual Vectors in the Compacted Solution-Space

In this letter, an improved model predictive control (MPC) has been proposed for single-phase grid-tied converter with virtual vectors in a reshaped and compacted solution space, while improving ac power quality, without increase of the virtual vectors number. Combining linear solution space reconstruction method, the global optimization solution space can be shrunken and reshaped in real-time, only relying on grid angle information. Therefore, MPC can select the optimal virtual-vector in a finer and closer solution subspace, then, much finer control effect can be obtained. Implemented by finite-control set MPC with an integrated difference modulator, equivalent fixed double switching frequency at the output can be achieved. Experimental results validate the effectiveness of the proposed methods.