Asymmetrical Six-phase Induction Machine Research Articles

Natural Fault-Tolerant VV-DTC for Healthy and Postfault Operation of an Asymmetrical Six-Phase Induction Machine Drive System With Single Neutral

Natural Fault-Tolerant VV-DTC for Healthy and Postfault Operation of an Asymmetrical Six-Phase Induction Machine Drive System With Single Neutral

Data-Driven-Based Vector Space Decomposition Modeling of Multiphase Induction Machines

For contemporary variable-speed electric drives, the accuracy of the machine's mathematical model is critical for optimal control performance. Basically, phase variables of multiphase machines are preferably decomposed into multiple orthogonal subspaces based on vector space decomposition (VSD). In the available literature, identifying the correlation between states governed by the dynamic equations and the parameter estimate of different subspaces of multiphase IM remains scarce, especially under unbalanced conditions, where the effect of secondary subspaces sounds influential. Most available literature has relied on simple RL circuit representation to model these secondary subspaces. To this end, this paper presents an effective data-driven-based space harmonic model for n-phase IMs using sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover the IM governing equations. Moreover, the proposed approach is computationally efficient, and it precisely identifies both the electrical and mechanical dynamics of all subspaces of an IM using a single transient startup run. Additionally, the derived model can be reformulated into the standard canonical form of the induction machine model to easily extract the parameters of all subspaces based on online measurements. Eventually, the proposed modeling approach is experimentally validated using a 1.5 Hp asymmetrical six-phase induction machine.

Enhanced Reaching-Law-Based Discrete-Time Terminal Sliding Mode Current Control of a Six-Phase Induction Motor

This paper develops an inner stator current controller based on an enhanced reaching-law-based discrete-time terminal sliding mode. The problem of tracking stator currents with high accuracy while ensuring the robustness of a six-phase induction motor in the presence of uncertain electrical parameters and unmeasurable states is tackled. The unknown dynamics are approximated by using a time delay estimation method. Then, an enhanced power-reaching law is used to make each stage of the convergence faster. A stability analysis and the system controller’s finite-time convergence are demonstrated in detail. Practical work was conducted on an asymmetrical six-phase induction machine to illustrate the developed discrete approach’s robustness and effectiveness.

Operation and Testing of Indirect Field Oriented Control of Asymmetrical Six-Phase Open-Ended Winding Induction Machine Using Hardware-in-Loop (HIL) Emulator

This study deals with an asymmetrical six-phase open-ended winding induction machine in closed loop operation using indirect field-oriented control scheme. The closed loop scheme has been developed by using the two axis (d-q) modeling of six-phase induction machine in rotating synchronous reference frame and can be easily extended to any multiphase machine having the stator winding which are the multiple of three. Operation under steady-state is considered to develop the phasor diagram in closed loop operation of machine in the motoring mode. The performance of the asymmetrical six-phase induction machine (opened ended winding) is investigated in the entire four-quadrant operation. The complete machine drive system was developed by using MATLAB/Simulink, which was used to obtain analytical results in different modes. Furthermore, the analytical results in the motoring mode were experimentally validated through real-time simulation by using Typhoon hardware-in-loop (HIL) emulator.

Model Predictive Current Control of Six-Phase Induction Motor Drives Using Virtual Vectors and Space Vector Modulation

The use of multiphase machines has become a suitable choice in high-performance industry applications through advantages such as lesser torque ripple, enhanced current distribution per phase, and fault-tolerance capability. Among different control approaches for the regulation of multiphase drives, model-based predictive current control (MPCC) is one of the most analyzed strategies due to its adaptability and good dynamic response. However, this approach presents some disadvantages, e.g., high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents and increased harmonic content in the fundamental <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> stator currents. Modulation strategies have been combined with MPCC to overcome these shortcomings. This article proposes a modulated MPCC with virtual vectors and space vector modulation for the regulation of an asymmetrical six-phase induction machine to minimize the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents, reduce the harmonic content, and perform improved stator currents tracking compared with other MPCC versions. Experimental tests are provided to demonstrate the quality of the proposed current control strategy.

Calculation of Rotor Harmonic Losses in Multiphase Induction Machines

The topic of this paper is the determination of rotor harmonic losses in multiphase machines. Specifically, harmonic losses occur in the rotor winding and core due to higher-order spatial harmonics of the flux density. This phenomenon influences machine parameters and overall performance and increases temperature rise in parts of the rotor. The flux density distribution is determined by the stator magnetomotive force harmonic content, which is directly related to the winding distribution. A cage-rotor asymmetrical six-phase induction machine is selected for this case study. An analysis of different stator winding topologies and their influence on harmonic losses is presented. A finite element-based method for calculating the contribution of individual stator magnetomotive force harmonics to the rotor losses is developed and described in the paper. The analysis includes scenarios with different phase current waveforms to emphasize the issues specific to the asymmetrical six-phase machine. It is found that the magnetomotive force components generated by non-torque-producing current components contribute significantly to harmonic losses. The obtained results can represent a foundation for optimal stator winding topology selection. This work is intended to motivate the development of new and the modification of existing models to properly include rotor harmonic losses during the design, performance prediction, and control of multiphase machines.

A Computationally Efficient Model Predictive Control of Six-Phase Induction Machines Based on Deadbeat Control

Model predictive current control (MPCC) has recently become a viable alternative for multiphase electric drives, because it easily exploits the inherent advantages of multi-phase machines. However, the prediction in MPCC requires a high number of voltage vectors (VVs), being therefore computationally demanding. In that regard, this paper proposes a computationally efficient MPCC of an asymmetrical six-phase induction machine drive (ASIMD) that reduces the number of VVs used for prediction. By using the characteristics of the deadbeat control (DB), the proposed method obtains a reference voltage vector (RVV), where its position will serve as a reference and integrates the MPCC scheme. Only 4 out of 13 predictions are needed to determine the best VV, dramatically reducing the algorithm computation. Experimental results for a six-phase case study compare the standard MPCC with the suggested method, confirming that deadbeat model predictive current control (DB-MPCC) shows that the execution time can be shortened by 48.8% and successfully improve the motor performance and efficiency.

Predictive current control based pseudo six-phase induction motor drive

Asymmetrical six-phase induction machines are widely used in high-power safety-critical applications. The so-called pseudo six-phase winding layout has recently been proposed as a promising contender for high power medium voltage applications in terms of torque density, phase current quality, simple single-layer-based stator winding design, and fault-tolerant capability. This winding layout employs quadruple three-phase stator winding sets connected to provide only six terminals, while being fed from two three-phase inverters. Therefore, the same conventional six-phase-based control structure can still be employed. Among the different control techniques, model predictive current control is considered as one of the cutting-edge technologies for multiphase drive systems, thanks to its simplicity and flexibility in defining new control objectives. This paper investigates how the available 64 voltage vectors of a six-phase inverter are classified among different subspaces when employing a pseudo six-phase stator winding. Moreover, the required modifications to classical predictive current control (PCC) are introduced in order to properly control the machine in a manner similar to conventional asymmetrical six-phase machines while ensuring minimum circulating xy current components. The concept of virtual voltage vectors (VVVs) has also been employed to further enhance the stator current quality. The proposed controller is validated using a 2Hp prototype pseudo six-phase machine under different operating conditions. An experimental comparative study with an asymmetrical six-phase machines is also carried out to verify the claimed equivalence.

Experimental Stability Study of Modulated Model Predictive Current Controllers Applied to Six-Phase Induction Motor Drives

Modulated model predictive current control techniques are considered an interesting option to control multiphase drives due to their control flexibility and fast dynamic response. However, a practical stability study of those techniques is still missing. This article presents an experimental stability study, to quantify the limits of stability, to modulated predictive current controllers applied to an asymmetrical six-phase induction machine. Experimental results are presented to verify the theoretical analysis results in terms of stability ranges regarding sampling frequency and rotor speed.

Improved Mathematical Modeling of Six Phase Induction Machines Based on Fractional Calculus

Multiphase induction machine modelling represents a crucial research topic for both machine control and performance evaluation purposes. Generally, multiphase induction machines are preferably modelled using the vector space decomposition technique with some assumptions to simplify the mathematical model. However, different sources of non-linearities, including low order harmonics mapped to secondary subspaces, cross-coupling saturation and iron losses result in a notable deviation from the experimentally measured waveforms. Furthermore, considering full symmetry amongst motors phases seems to be a rather idealistic assumption. Fractional order modelling has recently emerged as a promising mathematical technique to model highly nonlinear electrical and mechanical systems. This paper proposes an improved vector space decomposition (VSD)-based fractional order model of an asymmetrical six-phase induction machine under both healthy and open phase fault conditions with different neutral arrangements. The appropriate differentiation orders have been obtained by optimizing the error function between simulated and experimental waveforms. The results are compared with the conventional integral order-based model. Experimental validation has been carried out using a 1.5Hp prototype induction machine.

Saturated VSD model of a six‐phase induction machine

In this study, a saturated model of an asymmetrical six-phase induction machine is presented. The model is based on the vector space decomposition approach, and it includes main and leakage flux saturation, as well as the mutual coupling between orthogonal planes while using the Gamma equivalent circuit approach. The accuracy of the proposed model in unbalanced operating modes that are characteristic for multiphase machines, such as post-fault and power-sharing operation, makes it advantageous compared to existing models. The model is developed assuming that the machine operates in asymmetrical conditions and that, therefore, there is fundamental frequency excitation in both planes. The inter-plane coupling effect is examined using finite element analysis and an experimental procedure for its quantification is developed. The model is verified by comparison with the experimental results obtained from a prototype asymmetrical six-phase induction machine, and its advantages compared to existing models are emphasised.

A Three-Phase Inverter Based Overmodulation Strategy of Asymmetrical Six-Phase Induction Machine

Overmodulation (OVM) techniques of asymmetrical six-phase induction machine (ASIM) achieve higher dc-bus utilization by applying nonzero average voltage in nonenergy transfer plane. This results into unwanted current and associated copper loss. Existing OVM techniques reduce this loss with pulsewidth modulation (PWM) techniques from six-dimensional space vector perspective, which is both conceptually difficult and computationally challenging. The computational complexity of space vector based techniques is reduced by few existing PWM techniques in linear region by splitting the six-phase inverter as two three-phase inverters and modulate these inverters with linear PWM techniques in 30° phase shifted. This is referred as three-phase inverter based technique in the title. But, three-phase inverter based OVM technique does not exist in the literature due to lack of knowledge of the relationship between six-dimensional space vectors and space vectors of two three-phase inverters. This article first establishes this relation. Based on this relation, an OVM technique is proposed where the reference voltage vectors of two inverters are phase shifted by 30° but of different magnitudes. The proposed technique achieves THD and WTHD performances similar to space vector based best technique of ASIM with reduced computational complexity, as shown in details. The proposed strategy is validated through experiments and simulations on six-phase induction machine at 4.2 kW.

Fault tolerance of asymmetrical six-phase induction machine during single open circuit fault to three open circuit faults using GUI

The fault tolerance of multiphase drive is favourable in the industry for its reliability and safety reasons. However, from the educational point of view, the post-fault capability of six-phase machine is still unclear. This paper presents the fault tolerance of asymmetrical six-phase induction machine (A6-IM) under one to three open-circuit faults using Graphical User Interface (GUI). In this study, the capability of A6-IM has been interpreted through a simple and user-friendly GUI helping students to have a better understanding on the current limits of A6-IM. The optimization of post-fault current references is based on maximum torque (MT) and minimum loss (ML). This work provides GUI highlighting the post-fault derating of A6-IM with single isolated neutral (1N) in two different modes namely MT and ML for educational purposes.

A Novel Modulated Model Predictive Control Applied to Six-Phase Induction Motor Drives

Model-based predictive control techniques, with finite set control, are considered an interesting option to control multiphase drives due to their control flexibility and fast dynamic response. However, those techniques have some drawbacks such as a high computational cost, poor ( $x-y$ ) currents reduction, and steady-state error, especially at high speeds. To improve some of these drawbacks, modulation stages have been presented as an alternative. However, some of those drawbacks have not been improved. This article proposes a novel approach to the classic predictive current control (PCC) applied to an asymmetrical six-phase induction machine, where a space vector modulation with specific vectors is used in order to improve the ( $x-y$ ) currents, the steady-state error and total harmonic distortion (THD) at high operation speeds. Experimental results are presented to demonstrate the characteristics of the proposed control technique in terms of current tracking, ( $x-y$ ) currents reduction and THD of stator currents compared to the classic PCC.

Discrete sliding mode control based on exponential reaching law and time delay estimation for an asymmetrical six‐phase induction machine drive

This study deals with the problem of controlling rotor speed and stator currents of an asymmetrical six-phase induction machine with uncertain dynamics, disturbances, and unmeasurable rotor currents and proposes a robust non-linear variable structure controller. First of all, an outer control loop based on a proportional–integral regulator is performed to control the rotor speed and to construct the desired stator current references. Then, the inner loop is performed based on the proposed method that combines the time delay estimation method and discrete sliding mode control based on exponential reaching law. This structure allows an accurate and simple estimation of uncertainties and rotor currents, a high-tracking precision, a convergence of the stator currents to their known desired references in finite-time and chattering reduction. The design procedure is detailed step by step and the stability analysis and the convergence time are established for the current closed-loop system. Experimental work was carried out on an asymmetrical six-phase induction motor drive to show the effectiveness and performance of the proposed robust non-linear discrete method. The results obtained highlighted the good tracking performance of the stator currents.

Magnetizing Inductance Determination in a Six-Phase Induction Machine

A simple offline method for measuring the magnetizing inductance of an asymmetrical six-phase induction machine is presented in this paper. The measurement procedure is based on dc excitation and it is performed at standstill. As opposed to the standard no load test, the magnetizing inductance is measured solely with the stator leakage influence significantly diminished. Additionally, the iron losses in the machine and their influence on the measurement are reduced considerably. The proposed method is applicable regardless of whether the neutral point of the machine is accessible or not. The method is verified through finite element analysis and experimentally. The obtained test results confirm the accuracy of the proposed approach.

Interplane cross‐saturation in multiphase machines

The use of electrical machines in electric vehicles and high-power drives frequently requires multiphase machines and multiphase inverters. While appropriate mathematical models under the linear magnetic conditions are readily available for multiphase machines, the same cannot be said for the models of the saturated multiphase machines. This study examines the saturation in an asymmetrical six-phase induction machine under different supply conditions and addresses the applicability of the existing saturated three-phase machine models for the representation of saturated multiphase machines. Specifically, the mutual coupling between different sequence planes in the vector space decomposed model under saturated conditions is analysed. The study relies on analytical considerations, finite element analysis and experimental results. It is shown that the saturation of the main flux path is influenced by the current components in the orthogonal (non-fundamental) sequence plane. This implies the need to develop new multiphase machine models which take this effect into account.

Low-Order Space Harmonic Modeling of Asymmetrical Six-Phase Induction Machines

Multiphase machines are commonly analyzed using vector space decomposition modeling technique, where the original phase variables are decomposed into multiple orthogonal subspaces. The machine torque production and, therefore, its dynamic response are mainly decided from the $\alpha $ – $\beta $ fundamental subspace. In the available literature, other non-fundamental subspaces are commonly regarded as the non-flux/torque producing subspaces while mainly contributing to the extra winding joule losses. Although the primitive harmonic-free models are usually assumed for these secondary subspaces in the asymmetrical six-phase induction machines, a clear evidence to include or discard the effect of the low-order space harmonics of the air gap flux distribution under different neutral configurations has not been established so far. To this end, this paper investigates the effect of the induced air gap harmonics mapped to the $x$ - $y$ and zero subspaces on the dynamic modeling and, hence, the dynamic response of an asymmetrical six-phase induction machine. An improved space harmonic model is, then, proposed to better explore/simulate their effect under both healthy as well as fault conditions. The proposed model is experimentally validated using a 1.5-kW prototype induction machine.

Effect of DC-Link Voltage Limitation on Postfault Steady-State Performance of Asymmetrical Six-Phase Induction Machines

The asymmetrical six-phase induction machine represents the most common multiphase machine type used in many high-power industrial applications. While a body of research covering control of the machine under fault conditions has been published in the literature, corresponding studies to investigate the dc-link voltage design requirements under postfault operation in a simple and efficient manner have not met the same interest. To this end, this paper first introduces the machine steady-state equivalent circuit under one open-phase fault, which simplifies the estimation of different machine characteristic curves instead of using tedious mathematical techniques. As far as the machine parameters are concerned in this paper, a modified locked-rotor test based on the derived equivalent circuit is also proposed to fully estimate the parameters of different subspaces using a simple technique without the need for additional tests. The proposed steady-state circuit is also used to understand the effect of the secondary subspace impedance, neutral configuration, and the postfault control strategy on the maximum achievable torque for a limited dc-bus voltage. The minimum dc-link voltage magnitude to provide rated output under postfault operation is also given. The proposed concepts have been experimentally verified using a prototype asymmetrical six-phase machine.

Postfault Control of Scalar (V/f) Controlled Asymmetrical Six-Phase Induction Machines

With the accelerated development in semiconductor power devices along with the dictated rigorous reliability standards in some industrial sectors, the application of a medium-voltage high-power multiphase induction machine with multiple three-phase windings is now considered as a leading technology in high-power safety-critical applications. This paper proposes a parameter-independent postfault control scheme for an asymmetrical six-phase induction machine based on simple scalar V/f control, which can successfully ensure the most common postfault scenarios used in this respect, namely, equal stator copper loss and minimum copper loss modes. Moreover, the proposed controller can effectively be used in either open-loop or closed-loop speed control modes. The proposed controller is experimentally validated using a 1.5-kW prototype induction machine. The effect of the neutral arrangement on the dynamic performance is also explored.