Stator Copper Loss Research Articles

Open-Phase-Tolerant Online Current References for Maximum Torque Range and Minimum Loss With Current and Torque-Ripple Limits for n-Phase Nonsalient PMSMs With Nonsinusoidal Back EMF

Multiphase permanent-magnet synchronous machines (PMSMs) with nonsinusoidal back-electromotive force (back-EMF) offer high fault tolerance and torque density for electric vehicles. Most current-reference generation methods either minimize stator copper loss (SCL) or maximize achievable torque. Optimization of both goals is accomplished by full-torque-range minimum-loss (FRML) strategies, but so far just for sinusoidal back-EMF. Thus, FRML for nonsinusoidal back-EMF should be sought. Moreover, many methods are only suitable for healthy conditions or specific machines, harmonics, or open-phase-fault (OPF) scenarios. Additionally, the torque range may be extended by permitting torque ripple or (transiently) greater rms current, but this approach is not general nor FRML yet. This paper proposes online FRML current-reference generation for multiphase PMSMs with nonsinusoidal back-EMF: nonsinusoidal-back-EMF FRML (NSBE-FRML). When the torque reference is feasible, minimum SCL is attained while maximizing the achievable torque (i.e., FRML). For higher torque references, the instantaneous torque deviation is minimized, and the torque reference is saturated in consecutive samples limiting the torque ripple to a pre-specified threshold. Furthermore, the rms current is limited after transient overload by automatically decreasing the torque reference. The NSBE-FRML is suitable for any harmonics, healthy/OPF conditions, and multiphase PMSMs with negligible saliency ratio. Experiments are performed with a six-phase PMSM.

Research on the Influence of Different Winding Forms on the Performance of Induction Motor

Background: As a component of the motor’s electromechanical energy conversion, the winding is very important. When the winding design is improper, the harmonic content is increased, which leads to an increase in the motor loss and torque ripple. Therefore, winding design is very important for motor design. Objective: The effect of winding forms on the induction motor is analysed in this paper. The variation in performance parameters of different winding forms is invesitgated. Methods: This paper takes an 11 kW, 1500 r/min induction motor as the research object; the two- dimensional transient field finite element model has been established to calculate the basic parameters, which are then compared with the experimental data to verify the correctness of the model. Finally, the magnetizing reactance, starting performance, stator leakage reactance, various losses, and efficiency under different winding forms are calculated and compared. Results: When the motor adopts double-layer winding, the magnetizing reactance, stator slot leakage reactance, and harmonic leakage reactance are less than those of the motor with single-layer winding by 13.47%, 25.37% and 20.97%, respectively, while the end-leakage reactance, starting torque, and starting current rotor copper loss are higher than those of the motor with single-layer winding by 7.14%, 9.52%, 18.54%, and 15.23%, respectively. The core loss and stator copper loss of motors with different winding forms are almost unchanged. The efficiency of the motor with single-layer winding is higher than that of the motor with double-layer winding by 1.22%. Conclusion: When the winding form is different, the magnetizing reactance, stator slot leakage reactance, harmonic leakage reactance, and end-leakage reactance are different. Leakage reactance is the main factor that causes a difference in starting torque and starting current between the two winding forms. The core loss and stator copper loss of motor with different winding forms are almost unchanged, while the difference in the rotor copper loss is obvious. In addition, the efficiency of the motor with single-layer winding is higher than that of the motor with double-layer winding.

Response Analysis and Stator Optimization of Ultrahigh-Speed PMSM for Fuel Cell Electric Air Compressor

For the requirement of the complex dynamic performance for the fuel cell vehicle (FCV), the wide operation range and rapid dynamic response ability are essential to the fuel cell electric air compressor, which are limited by the output torque of the permanent magnet synchronous motor (PMSM) commonly used in FCV. The purpose of this study is to improve the output torque of the stators and its rapid dynamic response capacity of PMSM using the mathematical model, multi-objective optimization and experimental validation. Firstly, a mathematical model of speed regulation response of ultra-high speed PMSM is established, which provides a basis for taguchi legal sub-optimization in this study. Secondly, stator parameters were selected as optimization variables based on Taguchi method, and the optimal combination of optimization variables was selected with the maximum electromagnetic torque, minimum cogging torque, minimum stator copper loss and minimum stator iron loss as optimization objectives. Finally, the effectiveness of the optimization method is verified by simulation analysis and bench test. At the target speed of 110652rpm, 124364rpm and 146876rpm, the overall response times before optimization are 1.9386s, 2.3902s, and 2.7844s. Respectively, the overall response times after optimization are 1.8604s, 2.2856s, and 2.6132s. The speed response time after optimization is 0.0782s, 0.1046s and 0.1712s less than before optimization, respectively.

General Online Current-Harmonic Generation for Increased Torque Capability With Minimum Stator Copper Loss in Fault-Tolerant Multiphase Induction Motor Drives

This paper proposes a current-reference generation method including current harmonic injection (CHI) for enhancing the torque capability of multiphase induction machines (IMs) with negligible space-harmonic effects, which is useful, e.g., during transient overload in electric vehicles. The admissible torque is increased because the harmonics reduce the phase-current peaks, so that the instantaneous peak-current constraint of the drive, usually associated with the converter ratings, is respected. The harmonics are injected in the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x-y</i> subspaces of the IM, which do not produce torque, so that no torque ripple is introduced. The optimum harmonics are found online for each load, making it possible to minimize the stator copper loss (SCL) per torque in the entire torque range, ensuring full-range minimum loss (FRML). The method is suitable for healthy operation or open-phase faults, and for multiphase machines of any phase number and with either symmetrical or asymmetrical windings. Compared with FRML methods without CHI, higher torque is achieved. Although some techniques were available for increasing the torque capability by CHI, FRML was not attained, laborious offline optimization was needed, or they were only suitable for specific drives or for healthy conditions, unlike the proposal. Experimental results with a symmetrical six-phase IM are provided.

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.

Design and Analysis of a Novel High-Speed Permanent Magnet Machine With Dual Semi-Cage Winding

This article proposes a novel high-speed permanent magnet synchronous machine (HSPMSM) topology. The characteristics of the proposed machine are: 1) The stator winding is divided into two parts and each part is connected by the end ring at one end, which is helpful to solve the existing shortage of overlong end length in traditional HSPMSM. 2) The stator of the machine is designed with closed slot, which can greatly weaken the eddy current loss and the cogging torque of the machine. 3) The machine is driven by two separate three phase converter, which can improve the fault tolerance. In this article, the topology, and the corresponding control system is analyzed firstly. After that the electromagnetic performance, including back electromotive force, cogging torque, torque, etc. are analyzed with finite element analysis (FEA). In addition, the losses, including the stator copper loss, the stator iron loss and the eddy current loss of the permanent magnet and sleeve of the rotor, are calculated by FEA. The mechanical strength and dynamic performance of rotor is also checked. Finally, a prototype was designed and manufactured. The experimental results the validity of the topology.

Online Control Strategy for Tolerating Resistance Asymmetry With Minimum Copper Loss in the Full Torque Range for Symmetrical Six-Phase AC Drives

Multiphase drives exhibit remarkable advantages (e.g., fault tolerance) over three-phase ones. Six-phase drives are particularly attractive, given their moderate complexity and suitability for off-the-shelf three-phase converters. Regarding the stator winding arrangement, the symmetrical one offers superior postfault capabilities in most scenarios. On the other hand, resistance asymmetry in the stator phases or connections may arise due to different causes. The conventional full-range minimum-loss strategy (FRMLS) generates stator-current references under open-phase (infinite resistance) faults so that torque ripple is prevented while minimizing the losses for each torque ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{d}$</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">$\boldsymbol{q}$</tex-math></inline-formula> current) value and maximizing the torque range; however, this method is unsuitable for unequal resistances of finite value. This article proposes an FRMLS for setting the current references to reach these goals in symmetrical six-phase drives with any resistance asymmetry. The optimum references are found online depending on the resistances, without lookup tables. The phase currents are individually limited by an iterative algorithm, so that minimum stator copper loss (SCL) is achieved over the maximum admissible torque range. In this manner, unlike the conventional FRMLS, minimum SCL and maximum torque range are attained even for finite resistance imbalance. The currents in phases affected by high resistances are suitably reduced. Experimental results are provided.

Investigation of Electromagnetic Losses Considering Current Harmonics in High-Speed Permanent Magnet Synchronous Motor

This paper presents a characteristic analysis and experimental verification for predicting the electromagnetic losses in high-speed permanent magnet synchronous motors. To predict the operating characteristics (such as speed and input current), dynamic modeling is conducted that combines models for the space vector pulse width modulation (SVPWM) inverter and high-speed permanent magnet synchronous motor (HPMSM). By applying the predicted harmonic currents to the electromagnetic analysis, DC and AC copper losses of the stator winding, and eddy current loss of the rotor sleeve and rotor permanent magnet, are comprehensively analyzed using the finite element (FE) method. In particular, by analyzing the magnetic field behavior of magnetic flux density according to harmonics, a core loss analysis technique was presented. The validity of the hybrid analysis, which combines the stator copper loss and rotor eddy current loss derived from the FE analysis and the proposed core loss analysis, was verified through comparison with the experimental results under various operating conditions. Compared with the experimental results, the error of total losses using the hybrid analysis with a sinusoidal current was about 47.39%, and total losses using the hybrid analysis with a harmonic current was significantly improved to within 3.7%.

Research on the Influence of Temperature on the Performance of Induction Motor

Background: : Induction motor plays a major role in various industries, and its importance is increasing. Due to the environmental temperature or sealed working environment, heat generation is generally severe. The heat exchange with the outside environment does not take place smoothly, and the motor temperature increases. The performance of the induction motor is also significantly influenced by the temperature. Therefore, it is necessary to study the influence of temperature on the performance of induction motor. Objective: This study aimed to analyse the influence of temperature on induction motor. At different temperatures, variation in performance parameters has been observed. Methods: Taking an 11 kW 1500r/min induction motor as an example, a two-dimensional transient electromagnetic field model was established, and the correctness of the model was verified by experiments. The motor starting performance, various losses and efficiencies under different temperatures wereestimated. Results : As the stator and rotor resistance increased, the starting current decreased by 11.99% when the internal temperature rose from 25°C to 150°C. When the internal temperature rose from 25°C to 150°C, the stator copper loss increased by 32.83%, and the rotor copper loss increased by 28.79%. However, the core loss of the motor increased by 3W, and the motor efficiency decreased by 2.12%. Conclusion: When the temperature is different, the starting torque of the motor is almost unchanged, and the starting current decreases with an increase in temperature. The stator copper loss and rotor copper loss of the motor increase with the increase in temperature, while the core loss is almost unchanged. In addition, the efficiency of the motor gradually decreases with the increase in temperature.

Control of Permanent Magnet Synchronous Motor Using MPC–MTPA Control for Deployment in Electric Tractor

This study aims to evaluate the interior permanent magnet synchronous motor (IPMSM) drive performance for various load conditions under steady state and dynamic conditions. Therefore, this paper proposes finite set model-predictive control (FS-MPC) for IPMSM with maximum torque per ampere (MTPA) for electric tractor application. The MTPA control technique is used to obtain maximum torque while maintaining a minimum current constraint. In addition to MTPA control, the MPC scheme is used as the suitable alternative control strategy in the electric tractor application, which eliminates the occurrence of torque ripples during the dynamic speed tracking under variable load conditions. The MPC is used to improve the dynamic response of the motor drive and reduce torque ripples under variable load conditions. MPC–MTPA is developed in the MATLAB/SIMULINK and validated in the real-time environment using the hardware-in-the-loop (HIL) simulator (OPAL-RT OP5700). The results prove that MPC improves the dynamic performance and MTPA reduces the stator copper loss and increases the drive efficiency.

Torque Superposition Compensation Fault-Tolerant Control for Dual Three-Phase PMSM with an Inverter Single-Leg Open-Circuit Fault

Dual three-phase permanent-magnet synchronous motors (PMSM) have wide applications in electric vehicles due to advantages such as excellent control performance and outstanding fault tolerance capability. However, present fault-tolerant control of inverter single-leg open-circuit faults cannot make full use of each phase winding of the motor, which limits the torque-production capability. This paper proposes a torque superposition compensation (TSC) control which can minimize the stator copper losses while increasing the torque-production capability. The phase winding originally connected to the faulty inverter leg is then linked to the DC-link mid-point. Thus, the winding in the faulty phase can be utilized to generate an additional torque. The symmetric dual three-phase windings torque model and the asymmetric five-phase windings compensation torque model for Ud/2 voltage level are constructed according to the torque superposition, respectively. Then, the three-subplane decomposition transformation matrix for the post-fault dual three-phase PMSM is derived, and the decoupling model in the d-q subplane is constructed, which achieves the optimal enhancement of the torque-production capability. The simulation results verify the effectiveness of the proposed TSC fault-tolerant control.

Six-Step Operation of a Symmetric Dual Three-Phase PMSM With Minimal Circulating Currents for Extended Speed Range in Electric Vehicles

Automotive applications demand high efficiency, good reliability, and a wide operating speed range within limited dc bus voltage constraints. In this article, a zero degree displacement dual three-phase permanent magnet synchronous machines (PMSM) is derived from an original three-phase PMSM to enhance the power rating as well as the operating speed range. The proposed topology can be used as an alternative to the conventional configuration of three-phase PMSM with a bidirectional dc–dc converter for electric vehicles. Even though the commonly used dual three-phase PMSM with split-phase winding eliminates the sixth harmonic torque pulsation, a large circulating current is generated during six-step operation, which results in additional stator copper loss. In this article, six-step operation of the symmetric dual three-phase PMSM with zero degree winding displacement is proposed to achieve maximum inverter utilization. Both harmonic circulating current and torque pulsation were observed to be within satisfactory levels using this configuration. A changeover algorithm is also proposed to enable a smooth transition between closed-loop current vector control during low and medium speed operation to open-loop six-step voltage angle control for high speed operation. The performance of the proposed method is experimentally validated on a 3-kW dual three-phase PMSM drive.

Treatment Strategy Research on a Squirrel-Cage Induction Motor with Broken Rotor Bar Faults.

Squirrel-cage induction motors are increasingly displaying a broken rotor bar fault, which represents both a technical problem and an economic problem. After confirming that the broken rotor bars do not affect the normal start-up and basic working performance of the squirrel-cage induction motor, this paper focuses on the loss and efficiency changes of the motor brought about by the broken rotor bar fault. Using finite element simulation and experimentation, various losses like stator copper loss, iron loss, rotor copper loss, mechanical loss and additional losses, total loss and efficiency are obtained. By combining price and cost factors, the cost-effective measures that can be taken after the occurrence of different degrees of broken bars are evaluated here to provide guidance for correctly handling this problem.

Study on performance of low-speed high-torque permanent magnet synchronous motor with dynamic eccentricity rotor

In actual production, errors in manufacturing and assembly may lead to misalignment of the stator and rotor and uneven air gap magnetic density, which affects the running performance of the motor. The influence of rotor dynamic eccentricity on air-gap flux density, cogging torque and loss is studied by combining analytical method and finite element analysis. The eccentric rotor model of low-speed high-torque permanent magnet synchronous motor (LHPMSM) is established on Maxwell 2D. The results show that with the increase of the rotor eccentricities, the back EMF and stator iron loss changeless, the cogging torque decreases slightly. The output torque increases slightly, but the harmonic distortion rate of air gap magnetic density and stator copper loss increase significantly.

COMPARATIVE ANALYSIS OF SIX PHASE INDUCTION MOTOR

In recent years, AC induction motors have replaced DC motor. The most important reason for this is that DC motors have a mechanical brush and commutator system that is subject to wear and tear over time. While DC motor drivers need a lot of maintenance due to this system, induction motors do not require almost any maintenance since this system is not available. In recent years, technological advances in the field of multiphase induction motors have led to a significant evolution. A lot of research has been done around the world and a lot of new and interesting developments have been reported to the literature. This paper provides information about six-phase induction. In addition, what kind of advantages the concept of multiphase provides and how this structure is formed contains information about them. The six-phase induction motor will be simulated through the MATLAB/SIMULINK package program and compare with three phase induction motor. Both motors were run in simulation using the same parameters. At the end of the simulation, current, moment and speed graphs of the six-phase induction motor and three-phase induction motor will be drawn according to time. The study also included equations used during modeling and equivalent circuits belonging to a six-phase induction motor. It has been graphically shown that a six-phase induction motor is more advantageous than a three-phase motor. For example, in six-phase induction motors, the transition time to a continuous state is shorter. In addition, while the frequency of torque vibration increases, its amplitude decreases, the current value of each phase decreases, the stator copper losses are less than the three-phase induction motor. In motors, usually the power needed is divided by the number of phases. So the more phases there are, the greater the power carrying capacity. Today, multi-phase induction motor drives are used in special applications such as electric vehicles, space technology, aerospace applications, as moving power on ships, electric trains, which require high reliability and power.

Comparative Study of 6-Slot/2-Pole High-Speed Permanent Magnet Motors With Different Winding Configurations

In this article, three 6-slot/2-pole high-speed permanent magnet motors with 1, 2, and 3 coil-pitch windings are optimized by the finite element method taking into account stator copper loss and iron loss. Their electromagnetic performances are analyzed and compared, including air-gap flux density, back electromagnetic force, electromagnetic torque, winding inductances, and various loss components. For high-speed application, compared with 1 and 3 coil-pitch windings, the proposed 2 coil-pitch windings have a good tradeoff between winding factor and end-winding axial length which are attractive for improved torque density. Finally, the experimental results are given to validate some of the finite element predicted results.

Fault tolerant control of a three‐phase PMSM by limiting the heat of an inter‐turn fault

Inter-turn faults are most commonly the initial stator winding fault in power trains with Voltage Source Inverters. Without counteractions, these faults can propagate and cause catastrophic failures in safety critical applications like all-electric aircraft. The propagation of an inter-turn fault can be reduced, by limiting the local temperature at the fault. In this article, a fault tolerant control scheme is designed and validated, which reduces the heat of an inter-turn fault by a controlled adaption of the operating point. The control strategy utilizes the hyperbolas of constant torque and the controller design is based on a linear time-invariant system description. A machine learning regression is used for the online heat estimation and a 3D lumped-parameter model to evaluate the thermal effectiveness. To test the control scheme, an inter-turn fault is actively switched, which generates the local heat equal to 13 % of the overall stator copper losses. The control scheme adopts the operating point within 30 electric periods, which reduces the generated heat of the inter-turn fault by 70 %. This causes a temperature reduction at the fault locally from 367°C to 175°C, which extends the approximated insulation life from 30 s to 5000 h.

Minimization of torque ripple in switched reluctance motor based on MPC and TSF

In this paper, a novel control method based on model predictive control (MPC) and torque sharing function (TSF) is addressed to minimize the torque ripple of switched reluctance motor (SRM). Firstly, an accurate SRM model is established based on flux‐linkage characteristic curves obtained from the locked rotor test, which can predict the future operation state of the SRM drive system. Secondly, an improved TSF curve is proposed, and genetic algorithm is used to optimize TSF parameters to reduce torque ripple in commutation region. Besides, the MPC is integrated into the TSF control framework to replace the traditional hysteresis controller, and establishes a new TSF‐based model predicted torque control (MPTC) method, which avoids the frequency conversion problem caused by torque or current hysteresis controller. Further, a sector division scheme is addressed to decrease the number of candidate voltage states, whereby the computation of the controller in each sampling period is effectively reduced. Finally, in order to verify the correctness of the MPTC method, it is compared with the traditional direct instantaneous torque control (DITC). Both simulations and experiments on a three‐phase 12/8 pole SRM have confirmed that MPTC scheme can not only decreases torque ripple and stator copper losses, but also has higher efficiency than DITC. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Study on No‐Load Loss and Rotor Contact Resistance of Asynchronous Motor

In induction motor no‐load test, the no‐load losses usually include the stator copper loss, iron loss, the friction, and the windage losse, and the stray loss, and the rotor aluminum loss often is ignored. In this paper, a new method that separates the rotor aluminum loss from the no‐load losses is mentioned. Although, in IEEE Standard 112 and IEC34‐2, the rotor aluminum loss is neglected in no‐load test. However, in proposed method, the rotor aluminum loss is considered as an important part of the no‐load loss. Therefore, this paper intends to develop a new testing method to obtain the rotor aluminum loss under no‐load condition. In this case, six induction motors of the same kind (3 kW, four‐poles) are chosen to carry out no‐load and ideal no‐load tests. Through the comparative analysis of experimental data, the no‐load rotor aluminum loss accounts for about 13.4% of the no‐load loss, and the test approach can also explain that this part loss is not generated by higher harmonics. Based on these results, this paper demonstrates that the rotor contact resistance has great influence for the no‐load rotor aluminum loss, and a rotor resistance analysis model with rotor contact resistance is proposed. Final, the proposed method offers the possibility of taking measures on rotor resistance to improve motor efficiency. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Overmodulation Method With Adaptive $x$-$y$ Current Limitation for Five-Phase Induction Motor Drives

Five-phase induction machines are attractive due to inherent benefits such as lower current rating than three-phase ones. On the other hand, ac motor drives often need to operate in the overmodulation (OVM) region, e.g., to increase the maximum speed or to work with reduced dc-link voltage. Most of the existing OVM strategies for five-phase drives are based on injecting low-order harmonics in the no-torque <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> plane while avoiding low-order <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> harmonics (at least up to a modulation index of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{1.2311}\,{\;}\text{p.u.}$</tex-math></inline-formula> ), so as to prevent the torque ripple associated with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</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> components. However, in practice the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</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> impedance is very small, and hence, this approach can easily lead to overcurrent. This article proposes an OVM method for five-phase induction motors that adaptively modifies the injected components so that at each moment the addition of low-order <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 is favored over <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> ones but without surpassing the maximum current rms of the drive. In case the total stator copper loss (SCL) tends to exceed its rating during OVM in a given scenario, the proposed scheme automatically reduces the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</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> injection to keep the SCL at its rated value. Experimental results verify the theory.