In three-phase unbalanced systems, where the circulation of zero sequence current is necessary, four-leg converters provide a neutral connection for single-phase or other unbalanced loads typically utilized in three-phase distribution systems. In addition, control of the magnitude and phase of the zero-sequence voltage and/or current are also achieved using four-leg power converters. However, even when four-leg converters have become very important in several fields as for instance, four-leg microgrids and aerospace applications, a comprehensive review of the converter topologies, control methods, modulation methods and output filters have not been hitherto published. In this paper, a comprehensive overview of the state-of-the-art of four-leg converters is presented, based on the selection of over 400 papers published in journals and conferences, identifying mature and incipient topologies, modulation strategies, control schemes and applications. Each topic presented in this work is thoroughly discussed and reviewed, analyzing characteristics, implementation issues, and reported advantages and disadvantages to provide a comprehensive overview of the current research and future challenges in four-leg converters. The most important applications of four-leg converters are also discussed in this work, including stand-alone power supply, uninterruptible power supplies, grid-connected 4-leg inverters, ground power units for aerospace applications, active filtering for power quality enhancement, cooperative control of 4-leg converters for micro-grid applications, among others. Finally, future work and conclusions are highlighted in this paper. 

An Overview of Four-Leg Converters: Topologies, Modulations, Control and Applications

This article presents a model-free predictive current control (MFPCC) method for dual three-phase permanent magnet synchronous machines with an optimal modulation pattern. First, an ultralocal model based on the dq subspace is established, and a novel nonlinear disturbance observer is designed to effectively compensate for voltage distortion caused by inverter characteristics. Additionally, the introduction of an intermediate variable eliminates the estimation peaks in the high-frequency state, improving both steady-state and transient performance of the controller while suppressing the influence of parameter mismatch on control performance. Second, two candidate modulation patterns and their corresponding pulse synthesis patterns are predefined, and the closed-loop control of the xy subspace is realized through an efficient cost function. The switching mode with the best xy current performance at the current moment is then switched in real time to obtain improved steady-state performance and deeper harmonic current suppression. Finally, the experimental results have verified the effectiveness of the proposed MFPCC method.

Model-Free Predictive Current Control for Dual Three-Phase PMSM Drives With an Optimal Modulation Pattern

Model predictive control (MPC) has been widely applied to ac electric drives over the last decade. Despite the proposed solutions, researchers are still seeking to find more effective solutions for weighting factor (WF) design, parameter dependency, current/torque harmonics, variable switching frequency, and computational complexity. This article presents a comprehensive review of the WF design techniques for finite control set MPC strategies for ac electric drives. First, the article introduces the conventional MPC techniques for electric drives over permanent magnet synchronous motors. Second, WF design methods are discussed under two main headings: WF selection and WF elimination methods. Third, the ongoing challenges and future trends are addressed by considering the current literature. Based on this review, it is obvious that each WF design method still has problems that await more effective solutions. Finally, this article reviews various WF design methods for ac electric drives, reveals the advantages and disadvantages of existing methods in terms of control performance, flexibility, design complexity, and computational complexity, and highlights future trends.

A Review on Weighting Factor Design of Finite Control Set Model Predictive Control Strategies for AC Electric Drives

Model Predictive Torque Control (MPTC) is highly regarded for its simple structure, rapid dynamic response, and optimized control performance when applied to actual motor driving systems. However, conventional MPTC techniques often lead to undesirable effects in three-phase inverter-based surface-mounted permanent magnet synchronous motors (SPMSMs), such as high electromagnetic torque, stator flux ripples, and significant current harmonic distortion. Notably, the generalized MPTC approach generates a substantial common mode voltage (CMV) that can cause damage to the motor bearing and winding insulation in SPMSMs. To address these issues, this paper proposes a three-stage duty cycle-based deadbeat predictive torque control (DCDPTC) technique for SPMSMs. The proposed technique leverages the volt-second equilibrium theorem by aligning the duty cycles with the predicted electromagnetic torque, stator flux, and their respective target values while accounting for extreme cases, accordingly electromagnetic torque and stator flux ripples as well as the total harmonic distortion (THD) of the stator current are minimized. In order to improve the system robustness, the duty cycle is limited to avoid the overmodulation. Furthermore, optimized switching sequences are meticulously arranged to ensure the CMV is lowered and the minimum number of switching transitions is maintained while utilizing a fixed switching frequency. The proposed technique is simplified. Its resultant performance is validated by experimental results. 

Three-Stage Duty Cycle-Based Deadbeat Predictive Torque Control for Three-Phase SPMSMs With CMV Reduction

This article proposes a 27-level asymmetric cascade H-bridge multilevel topology for photovoltaic applications, which considers a predictive control strategy that allows minimization of the commutations of the converter. This proposal ensures a highly sinusoidal and stable photovoltaic injection when there are solar irradiance disturbances, generating a low distortion in the current waveform and low switching losses. To validate the performance of the control and the proposed topology, the dynamic model of the alternating current (AC) and direct current (DC) side system is first obtained, which is checked by computational simulations. Subsequently, the implementation of a master–slave control is carried out, focused on the control of DC voltage and AC current. The proposal is simulated, and the total harmonic distortion (THD) is obtained in the voltage and current waveforms. Undesired commutations, typical of the predictive control, are eliminated in the AC voltage waveform, and a proper DC voltage tracking is achieved for the high-power cell. In order to demonstrate the performance of the proposed control strategy, a low-power proof-of-concept prototype is implemented, in which the energy is injected to the grid, under the event of solar irradiance disturbances (with DC control).Then, the undesired switching in the main cell is eliminated, generating THDs in the voltage and current signal of 7.76% and 2.65%, respectively.

Improved Predictive Control for an Asymmetric Multilevel Converter for Photovoltaic Energy

This paper presents a feedback linearization (FL) based direct torque control (DTC) for an asymmetrical six-phase permanent magnet synchronous motor (PMSM). The decoupled linear model of PMSM is yielded using the feedback linearization approach. In this way, the advantages of classical hysteresis comparator based DTC, such as fast dynamic response is preserved. The output of the feedback linearization, namely the desired vector is synthesized by four active vectors for the sake of harmonics mitigation in the secondary subspace. The existing work usually adopts the synthetic vectors with zero voltage in the secondary subspace to suppress the harmonic currents. While this practice ignores the back electromotive force (EMF) harmonics. Thus, the four-vector based space vector pulse width modulation (SVPWM) with and without considering the back EMF harmonics is investigated, respectively. The effectiveness of the proposed method is validated through experimental results. Compared with the classical switching table based DTC, the proposed FL-DTC method achieves less torque & flux ripple in the primary subspace and less harmonic currents in the secondary subspace. 

Feedback Linearization Based Direct Torque Control for Asymmetrical Six-Phase PMSM Motor with Back EMF Harmonics Compensation

This paper explores the feasibility of multilevel dual-active bridge-inverter (DABMI) applications for grid-connected applications of a modern Model of Predictive Direct Power Control (MPDPC) based on the conservative power theory (CPT). In the case of unbalanced grid voltages, the objective of the study is to promote continued active and reactive energy in MPDPC without reducing efficiency such as transient response and current harmonics. The nature of the instantaneous p-q theory permits only one out of three control targets to be fulfilled. The proposed control approached directly regulates the instantaneous active and reactive power to achieve three particular control objectives namely sinusoidal and symmetrical grid current, cancelling twice of fundamental grid frequency reactive power ripples, and removing twice grid frequency active power ripple. The techniques of complicated Grid part sequence extraction are unnecessary and improved at no extra expense, as is the case with current MPDPC fault-tolerant approaches. The instantaneous power at the next sampling instant is predicted with the newly developed discrete-time model. Each possible switching state will then be evaluated in the cost function defined until the optimal state which lead to the minimum power errors is determined. In MATLAB/Simulink simulation, the proposed CPT-based MPDPC measures reliability and performance at balanced and unbalanced grid voltages then compared with the conventional and existing MPDPC The proposed method manages to achieve all of three control targets which generates sinusoidal grid currents and attenuates active and reactive power ripple of twice the grid frequency exactly at the same time without losing its critical efficiency including transient reaction and current harmonics.

Predictive Direct Power Control for Dual-Active-Bridge Multilevel Inverter Based on Conservative Power Theory

The current loop is significant for disturbance rejection performance in interior permanent magnet synchronous motor (IPMSM) drive system. This article presents a robust current model predictive control method which significantly expands the bandwidth of the current loop. The proposed method is based on an incremental model which can avoid the disturbance of inaccurate flux linkage. However, disturbance from inaccurate inductors and resistors in the motor model can also affect predictive control. To cope with this problem, the proposed method combines with an extended state observer (ESO) which is used to estimate disturbance and compensate for it. Finally, the effectiveness of the proposed method is verified in Simulink.

An Extended State Observer-Based Model Predictive Current Control Strategy for IPMSM Drive System

The traditional auto disturbance rejection controller (ADRC) can’t effectively suppress the torque ripple of the permanent magnet synchronous motor (PMSM) caused by current sampling errors. A speed loop generalized integral-decoupled auto disturbance rejection controller (GI-DADRC) is proposed, which utilizes the high gain characteristics of quasi-resonant integrators at resonant frequencies to enhance the observation accuracy of extended state observer (ESO) against harmonics disturbance. This method not only retains the ability of traditional ADRC in suppressing the DC disturbance, but also improves its performance to suppress harmonics disturbance. Simulation results prove the feasibility of the proposed method.

Torque Ripple Suppression of Permanent Magnet Synchronous Motor Based on Improved Active Disturbance Rejection Controller

Model predictive current control (MPCC) has become one of the most promising control strategies for synchronous reluctance motor (SynRM) drive system. However, the parameters sensitivity is still a bottleneck problem for MPC, and the existing methods are not suitable for sensorless control. This paper proposes a sensorless MPCC strategy based on alternative high-frequency square-wave voltage injection (AHFSVI). The proposed methods inject an alternative high-frequency signals on dq-axis of the stator voltage, estimating rotor position, rotor speed and inductance simultaneously. By updating the inductance used in MPC per injection cycle, the proposed method can effectively suppress the impact caused by parameter mismatches. Finally, the effectiveness of the proposed method is verified by Simulink.

Sensorless Model Predictive Current Control for SynRM Based on Alternate High-Frequency Square-wave Voltage Injection

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