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This study proposes an on-line minimum loss (ML) control strategy that considers the iron and copper losses of an interior permanent magnet synchronous motor in torque-controlled applications. The proposed ML control strategy utilizes a constrained optimization problem to satisfy torque reference tracking and loss minimization. An equivalent iron loss resistance circuit is adopted for the loss minimization. To solve the optimization problem, the Lagrange multiplier method is applied through a numerical analysis algorithm. The resulting solution provides the optimal current reference for every sampling instant. The Lagrange multiplier method needs parameters such as magnetic flux linkages, dynamic inductances, and iron loss resistance. Fundamental magnetic flux linkages are estimated using a flux observer, and the dynamic inductances are estimated with high-frequency voltage signal injection. The proposed iron loss resistance estimator estimates the equivalent iron resistance without any preliminary experiments. DC input power is measured using a current sensor for the accurate on-line estimation of iron loss resistance. To analyze the effectiveness of ML control compared with conventional maximum torque per ampere control, finite element analysis is used. The feasibility of the proposed ML control strategy is verified through simulation and experiments. [ABSTRACT FROM AUTHOR]

The torque ripple of an electrical machine will affect the control accuracy and trigger vibration and noise in the system. Consider only the motor itself, the torque ripple is mainly caused by the cogging torque at no load, the harmonic component of the induced electromotive force, and the saturation of the magnetic fields in load operation. In this paper, a two-stage optimization approach is used to reduce torque ripple and cogging torque for an integrated starter and generator(ISG) machine. The first level of optimization mainly adopts the appropriate pole-slot combinations, and for a machine with an initial model of 6-pole/36-slot, it is optimized to 8-pole/36-slot, which significantly reduces the cogging torque and torque ripple. The second level of optimization is rotor notching, and the notch strategy is classified into three types, Q-axis notch, magnetic bridge notch(MB notch), and Q-axis and magnetic bridge notch combination(QMC notch), and the selection of each notching parameters is analyzed respectively. For the Q-axis notch, the parameter sweep method is mainly used to determine the parameters, and for MB notch and QMC notch, the non-dominated sorting genetic algorithm-II(NSGA-II) is used for multi-objective optimization to determine the parameters. Then torque performance and total harmonic distortion(THD) are analyzed for each design. Finally, the rotor strength was analyzed. Simulation results show that suitable pole-slot combinations can reduce the cogging torque and torque ripple to a greater extent. Selection of suitable rotor notching can improve the torque performance again to some extent, in which the QMC notch design is preferred and recommended.

In this paper, circular area movement optimization (CAMO), a novel global search algorithm, and its hybridization with the pattern search method (PSM) are proposed to solve the multimodal optimization problem. The CAMO is an optimization technique that creates a circular search area, moves the area, and searches the entire search area. Depending on the type of samples inside the area, two strategies are used to quickly and efficiently find the optimal point across the area. Also, the hybridization with the PSM supports fast convergence on adjacent optima from the points that are discovered in the global search using the CAMO. The effectiveness of the algorithm was verified by applying the CAMO to two test functions, and its superiority was confirmed through comparison with existing optimization algorithms. In addition, by applying the proposed algorithm to the optimal design of the cogging torque of an interior permanent magnet synchronous motor for a hybrid electric vehicle, a design that reduces the cogging torque by 95.65% was successfully derived. Lastly, stress analysis and demagnetization analysis were performed to examine the structural and thermal stability of the motor.

This paper introduces a current sensorless speed control method for interior permanent magnet synchronous motors (IPMSMs) to track the maximum torque per ampere (MTPA) trajectory. Unlike traditional cascaded control structures, current measurements and inner regulation loops are eliminated. Instead, the MTPA is attained by directly adjusting the voltage vector amplitude and angle. An analytical formulation based on the motor voltage model is developed to extract the optimal voltage amplitude to run the motor within the MTPA operating points, disregarding any control law approximation or lookup tables-based numerical solutions. As a result of excluding current measurements and regulation loops, a one-speed controller is required. This leads to a significant reduction in control system complexity. Moreover, the simple structure of the control system highly qualifies it for cost-effective implementation of IPMSM applications. The validity of the designed control method is confirmed experimentally using a $5 Hp$ IPMSM. The experimentally obtained results are compared to the conventional field-oriented MTPA (FOC) to highlight the effectiveness of the suggested control system considering different operating conditions. Additionally, the MTPA trajectory tracking accuracy is quantitatively assessed using two performance metrics.

In order to extend motor operation range, a self-voltage-boosting AC motor drive is proposed in this paper. Compared with the traditional frontend DC-DC converters, the proposed topology reuses the power switches inherently involved within the three-phase inverter without using any additional active components. By modifying the time distribution of the two zero vectors in traditional seven-segment space vector pulse width modulation (SVPWM) technology, the inductor current and the flying capacitor voltage can be adjusted. The proposed topology has the advantage of a wider operating range without extra cost. Moreover, the performance of the motor drive is not affected. Experimental results demonstrate the correctness of the proposed topology.

This paper introduces a parameter-estimation-based sensorless adaptive direct voltage maximum torque per ampere (MTPA) control strategy for interior permanent magnet synchronous machines (IPMSMs). In direct voltage control, the motor's electrical parameters, speed, and rotor position are of great significance. Thus, any mismatch in these parameters or failure to acquire accurate speed or position information leads to a significant deviation in the MTPA trajectory, causing high current consumption and hence affecting the performance of the entire control system. In view of this problem, a fuzzy logic control-based cascaded model reference adaptive system (FLC-MRAS) is introduced to mitigate the effect of parameter variation on the tracking of the MTPA trajectory and to provide precise information about the rotor speed and position. The cascaded scheme consists of two parallel FLC-MRAS for speed and multiparameter estimation. The first MRAS is utilized to estimate motor speed and rotor position to achieve robust sensorless control. However, the speed estimator is highly dependent on time-varying motor parameters. Therefore, the second MRAS is designed to identify the quadratic inductance and permanent magnet flux and continuously update both the speed estimator and control scheme with the identified values to ensure accurate speed estimation and real-time MTPA trajectory tracking. Unlike conventional MRAS, which uses linear proportional-integral controllers (PI-MRAS), an FLC is adopted to replace the PI controllers, ensuring high estimation accuracy and enhancing the robustness of the control system against sudden changes in working conditions. The effectiveness of the proposed scheme is evaluated under different speed and torque conditions. Furthermore, a comparison against the conventional PI-MRAS is extensively investigated to highlight the superiority of the proposed scheme. The evaluation results and our quantitative assessment show the ability of the designed strategy to achieve high estimation accuracy, less oscillation, and a faster convergence rate under different working conditions. The quantitative assessment reveals that the FLC-MRAS can improve the estimation accuracy of speed, permanent magnet flux, and quadratic inductance by 19%, 55.8% and 44.55%, respectively. [ABSTRACT FROM AUTHOR]

Improvement of the low-speed sensorless position control for an interior permanent magnet synchronous motor (IPMSM), which drives a horizontal axis washing machine drum, extended-flux (EF) model-based PI observer (PIO) system is proposed. This control is designed to estimate the derivatives of the EF components, which are voltage components, from which the rotor position information is extracted. Motor parameters change during the operation because of the load and temperature, and those changes affect the performance of sensorless IPMSM drive, especially at low-speed operation. For satisfactory low-speed operation, observer gains should be carefully selected to reduce the influence of measurement noise and un-modeled dynamics. Linear quadratic (LQR) control method is used to calculate the optimal coefficients of a PIO to improve low-speed performance. The PI observer is chosen for its capability to decouple modeling uncertainties and measurement noise. The effectiveness of the proposed sensorless method is verified by the simulation on MATLAB/Simulink and experimental results in a 900W IPMSM drive for washing machine. The proposed estimator achieves stable operation at 87 rpm 100% and 45 rpm 25% load torque conditions. It has a much better dynamic performance and improved capability and is robust for speed and torque variations in the system. [ABSTRACT FROM AUTHOR]

To solve the problem of PI control cannot achieve satisfactory dynamic performance under complex operating conditions, an improved model-free continuous super-twisting non-singular fast terminal sliding mode control (NFTSM) algorithm (INFTSMC) for IPMSM based on improved extended higher-order sliding mode disturbance observer (IESMDO) is proposed. Firstly, the speed-current hyperlocal models of IPMSM are developed; Then, the speed-current controllers for INFTSMC are designed to optimize the current-speed dual closed-loops; where the jitter of system is effectively attenuated by combining third-order super-twisting with NFTSM; At the same time, IESMDO feeds back the disturbance of the speed and current loops to the controllers, it can effectively improve the performance for system control, and achieve fast-tracking of speed and d-q axis currents without overshoot; Finally, the algorithm is experimentally compared with PI and traditional NFTSMC to verify that the algorithm effectively improves the dynamic steady-state response and robustness of IPMSM.

To solve the problems that control performance of high torque traction interior permanent magnet synchronous motor (IPMSM) is degraded by parameter perturbation and unknown disturbance, this paper proposes a novel Improved Super-Twisting non-singular fast terminal sliding mode control strategy (IST-NFTSMC) for IPMSM based on Extended Nonsingular Fast Terminal Sliding Mode Disturbance Observer (ENFTSMDO). Firstly, the mathematical model of IPMSM under parameter perturbation is established; Then, an improved Super-Twisting nonsingular fast terminal sliding mode speed controller (IST-NFTSMC) based on extended nonsingular fast terminal sliding mode disturbance observer (ENFTSMDO) is designed, in which the improved Super-Twisting control law designed can effectively weaken the chattering of traditional NFTSMC, and ENFTSMDO can more accurately observe the unknown disturbance part of the system in real-time than ESMDO; Finally, compared with PI control and traditional NFTSMC control by simulations and experiments, the method proposed has merits of accelerating convergence, improving steady-state accuracy and minimizing the current and torque pulsation.

An IPMSM with I2V type rotor topology structure is proposed, its loss, efficiency and torque are analyzed and compared with V and IV type. Firstly, the optimized rotor topology structures are used to analyze the no-load air-gap flux density waveform and harmonic contents of the IPMSM. The results show that the THD of the no-load air-gap flux density with the I2V type is the smallest and the sinusoidal degree of the waveform is the highest. Secondly, the loss of the IPMSM with optimized rotor topology structures are analyzed and compared. Compared with the other two rotors, the results show that the iron loss of the IPMSM with the I2V type is the smallest. The iron loss of the IPMSM with I2V type is significantly less than that of the other two rotors especially under the deep flux weakening conditions. The output torque of the IPMSM under different current angles, current densities and speed are analyzed and compared. The results show that the torque performance of the IPMSM with I2V type is better than the other two rotors. this paper proposes a simple and effective method to optimize the position and diameter of the magnetic isolation holes by establishing a parameterized model. The results show that the torque ripple and cogging torque with the further optimized I2V type rotor topology structure are greatly reduced, the iron loss and magnet loss are also effectively reduced. Finally, the von Mises stress and the total displacement of the rotor deformation of the IPMSM with the further optimized I2V type under different working conditions are verified by finite element analysis. The results show that the rotor will not rupture, the displacement is small enough to avoid the touch between stator and rotor.

An interior permanent magnet synchronous motor (IPMSM) with "VV—" shape rotor topology structure is proposed, and its performances are compared with "V" shape and "V—" shape rotor topology structure. The results show that the performances including output average torque, reluctance torque, torque ripple, cogging torque, iron loss of the IPMSM with "VV—" shape is better than the other two rotors. Firstly, the parameters which have great influence on the torque and the efficiency of the IPMSM are analyzed and optimized. The no‐load back electromotive force (EMF) of three different optimized rotor topology structures are analyzed and compared, the results show that the no‐load back EMF of the IPMSM with "VV—" shape topology structure has the lowest total harmonic distortion rate (THD). Secondly, the torque of the IPMSM with "VV—" shape under different current angles, current densities and speeds are analyzed and compared with the other two rotors. The results show that the torque performance of the IPMSM with "VV—" shape rotor topology structure is better than that of the other two. Finally, aiming at the problems that the torque ripple and cogging torque of the IPMSM with "VV—" shape rotor topology structure are greatly increased when the iron loss is reduced, This paper proposes to add a set of circular flux isolation holes between the second layer and the third layer of permanent magnets, and the position and diameter of this set of circular flux isolation holes are optimized and adjusted. The results show that the torque ripple and cogging torque of the IPMSM with the further optimized "VV—" shape rotor topology structure are greatly reduced, and the THD of no‐load back EMF is also further reduced, which has great significance to reduce vibration and noise, improve the control accuracy of the IPMSM. [ABSTRACT FROM AUTHOR]

Although it is crucial to design the magnetic flux path and the maximum torque per ampere (MTPA) current reference under the current limitation, it is challenging to simultaneously consider these features in developing an interior permanent magnet synchronous motors (IPMSM) due to complicated coupling effects. In this article, to overcome the above issue, the motor-design parameters are estimated by conducting electromagnetic finite element (FE) analysis two times at every iteration of topology optimization. Then, the MTPA current phase angle can be analytically expressed in terms of an elementwise relative density (i.e., design variable in topology optimization). In addition, the structural safety is assessed by conducting the structural FE analysis under design-dependent loads to reflect a high-speed rotation. The proposed two-stage topology optimization enables us to simultaneously optimize both a structural design and current phase angle to achieve the maximum electromagnetic performance. Structural safety and manufacturability are also considered to obtain a practically meaningful design. With two different types of permanent magnets, the optimized IPMSMs are obtained and manufactured to validate the proposed method. Simulation and experimental results demonstrate the validity and potential of this work. [ABSTRACT FROM AUTHOR]

To extend the lifetime, improve the power density and reduce the system cost, the film capacitor is applied to replace the large-volume electrolytic capacitor in motor drives. As the dc-link voltage fluctuates periodically, the rotor position estimation error and operation stability are necessary to be concerned in the position sensorless control methods. A cross-decoupling complex filtering-based position estimation method is investigated for the reduced capacitance interior permanent magnet synchronous motor drive system. Harmonic components of the extended back electromotive force (EEMF) caused by the dc-link voltage fluctuation are analyzed to evaluate the additional rotor position error. A cross-decoupling complex filter realized by the multiple first-order complex filters with different center frequencies is designed to improve the position estimation precision. Harmonics of the EEMF are suppressed and the position error can be eliminated. The estimation precision and operation ability are improved. Experimental results are performed to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The conventional direct torque control (DTC) has high torque and stator flux fluctuation that causes the stator current distortion. This paper presents an efficient control method based on the feedback-linearization direct torque control (FL-DTC) method for an interior permanent magnet synchronous motor (IPMSM) drive by using an improved firefly algorithm. The proposed approach can greatly restrain the poor performance of torque and stator flux. Thus, it is suitable for IPMSM drives in electric vehicles. First, a decoupled linear model is derived to implement the proposed efficient feedback linearization control for the IPMSM. Two phase voltages in d-q axes and two additional control inputs take shape into an isomorphism mapping with the concept of orthogonal transformation. The torque generation is related to the additional control. Second, the Hamiltonian efficient control theory combined with an improved firefly algorithm is applied to obtain an analytical solution. An efficient linearization controller is designed with a cost function considering the maximum voltage of the inverter. Finally, simulation and experiment are carried out to compare the performance of the proposed efficient FL-DTC with the improved firefly algorithm and the conventional direct torque control. The results show that the proposed control method can reduce the torque and flux ripples at a steady state and maintains a good dynamic response with the variations of speed and torque. • To restrain the poor performance of torque and stator flux, this paper presents an optimal control method based on feedback-linearization direct torque control (FL-DTC) method for an interior permanent magnet synchronous motor (IPMSM) drive by using an advanced firefly algorithm. • A decoupled linear model is derived to implement the proposed optimal feedback linearization control for the IPMSM. Two phase voltages in d-q axes and two additional control inputs take shape into an isomorphism mapping with the concept of orthogonal transformation. • The Hamiltonian of optimal control theory based on an advanced firefly algorithm is applied to obtain an analytical solution. • An optimal linearization controller is designed with a cost function considering the maximum voltage of the inverter. • The proposed control method has faster torque response and smaller torque and stator flux fluctuation. [ABSTRACT FROM AUTHOR]

An interior permanent magnet synchronous motor (IPMSM) with 'VV—' shape rotor topology structure is proposed. The established two‐dimensional (2D) parameterized finite element analysis (FEA) models are used to analyze and compare the output average torque, torque density, air‐gap flux density and back electromotive force (EMF) of the IPMSM with 'V' shape, 'V—' shape, 'VV—' shape for electric vehicle (EV) applications. The rotor topology structure has a great influence on the performance of the IPMSM, especially the first layer of permanent magnet of the multi‐layers permanent magnet structure has the greatest influence on the performance of the IPMSM. Therefore, firstly, this paper mainly analyzes and optimizes the opening angle of permanent magnet and the pole arc angle of the first layer, which have a great influence on the electromagnetic performance of the IPMSM. Secondly, the d‐axis and q‐axis inductance, saliency ratio, output average torque, reluctance torque under different current angles are analyzed and compared. The results show that the output average torque and reluctance torque of the IPMSM for EV applications with 'VV—' shape rotor topology structure proposed in this paper are larger than that of the other two rotor topology structures as the amount of permanent magnet with 'VV—' shape rotor topology structure is slightly reduced. Finally, the torque density versus current density of the IPMSM with three different rotor topology structures is analyzed and compared. The results show that the torque density of the IPMSM with 'VV—' shape proposed in this paper is higher than that of the other two rotor topology structures under different current densities. [ABSTRACT FROM AUTHOR]

We are concerned with the problem of fast and accurate tracking of currents in the general synchronous drive. The problem becomes complicated with decreasing available voltage, which is common in high-speed and field weakening regimes. The existing time-optimal controllers rely on a simplified model, ignoring stator resistance and differences in inductances. We derive a solution for the general model considering all parameters and show how the parameters affect the current trajectory. One simplifying assumption had to be made, but we show in simulation that it has a negligible impact on accuracy. The simplification allowed for the design of a feed-forward controller that has a low computational cost and can be easily implemented in realtime. We provide experimental validation of the controller on the developed IPMSM drive prototype of the rated power of 4.5 kW using conventional industrial DSP. The controller is compared to conventional PI and deadbeat solutions, demonstrating that the time-optimal controller can reach the required setpoint four times faster than the competitors at the field weakening regime of the drive. The proposed feed-forward control can be seen as a universal building block that can be combined with existing feedback controllers and observers and thus incorporated into existing control solutions. [ABSTRACT FROM AUTHOR]

Abstract An interior permanent magnet synchronous motor (IPMSM) with “VV—” shape rotor topology structure is proposed, and its performances are compared with “V” shape and “V—” shape rotor topology structure. The results show that the performances including output average torque, reluctance torque, torque ripple, cogging torque, iron loss of the IPMSM with “VV—” shape is better than the other two rotors. Firstly, the parameters which have great influence on the torque and the efficiency of the IPMSM are analyzed and optimized. The no‐load back electromotive force (EMF) of three different optimized rotor topology structures are analyzed and compared, the results show that the no‐load back EMF of the IPMSM with “VV—” shape topology structure has the lowest total harmonic distortion rate (THD). Secondly, the torque of the IPMSM with “VV—” shape under different current angles, current densities and speeds are analyzed and compared with the other two rotors. The results show that the torque performance of the IPMSM with “VV—” shape rotor topology structure is better than that of the other two. Finally, aiming at the problems that the torque ripple and cogging torque of the IPMSM with “VV—” shape rotor topology structure are greatly increased when the iron loss is reduced, This paper proposes to add a set of circular flux isolation holes between the second layer and the third layer of permanent magnets, and the position and diameter of this set of circular flux isolation holes are optimized and adjusted. The results show that the torque ripple and cogging torque of the IPMSM with the further optimized “VV—” shape rotor topology structure are greatly reduced, and the THD of no‐load back EMF is also further reduced, which has great significance to reduce vibration and noise, improve the control accuracy of the IPMSM.

Referring to the sensorless control of interior permanent magnet synchronous motor (IPMSM), the initial rotor polarity is normally estimated based on the motor saturation effect. However, for certain special IPMSMs, the saturation effect is weak even at the rated point, making the saturation-based rotor polarity detection methods invalid. Therefore, this paper proposes a novel rotor polarity detection method based on torque-pulse injection. Two current pulses are imposed on the positive and negative directions of the q-axis estimated by the high-frequency injection (HFI) method, respectively; the signs of speed peaks indicate the rotor polarity. To derive the rotor polarity from the tiny speed signal, a new speed estimation method is presented. To improve the dynamic performance of speed estimation, a special current filter is adopted in the HFI method. To choose the proper width and amplitude of the current pulse under different load and inertia conditions, an automatic program is designed. The proposed method has the advantages of high accuracy, short identification time, tiny movement, and automatic operation, making it applicable to various load and inertia conditions. The effectiveness of the proposed method is validated by experiments on an IPMSM with low saturation effect. [ABSTRACT FROM AUTHOR]

A voltage balancer remains a good solution of power transfer for bipolar dc grids, which, however, would increase the costs due to its requirement for additional hardware support. In this article, an auxiliary power transfer strategy is proposed by using the inactive motor drives affiliated with the bipolar dc grid. During idle periods of the motor drive, one inverter bridge arm is connected with the bipolar dc grid at their neutral points, allowing bidirectional power transfer between the upper and lower dc-bus sources. The proposed strategy share part of the voltage balancer's power transfer burden without requiring additional hardware and affecting the normal operations of the motor drive. In addition, its effectiveness is verified by experimental results on an interior permanent magnet synchronous motor drive, showing that the power flows among the upper and lower dc-bus power supplies are controlled effectively. Also, the active control of the dc-bus voltages could be achieved by modulation of the phase currents. [ABSTRACT FROM AUTHOR]

The trend in the industrial power electronics electrical drives is to reach high power density and high efficiency in variable load conditions at cost-effective unwasteful designs. Currently, motors with permanent magnets (such as IPMSM and PMaSynRM) are of great interest because of compactness, low losses, and high-torque capability. The performance of a drive system can be predicted with a motor electromagnetic authentic nonlinear model. In this article, a novel, fast, and precise motor model of PMaSynRM based on virtual reluctance (VR) is proposed. It takes into account the cross saturation, winding distribution, space harmonics, slotting effect, and stepped skewing. The VRs are identified by finite element analysis (FEA) and implemented in the time-stepping simulation. The flux inversion is not required. The proposed concept is useful in the rotating field or phase quantities (for open phase simulation). The model is also discretized for SiL and HiL applications. Finally, the validation in FEA and experimental setup was performed. [ABSTRACT FROM AUTHOR]

Interior permanent magnet synchronous motor (IPMSM) with back electromotive-force (EMF) based sensorless field-oriented control (FOC) is widely used in medium-high speed applications. Unfortunately, the back EMF is too small to be estimated accurately during low speed operation. Hence, the current-frequency (I–f) control with controllable current vector is used for startup. However, the conventional I–f control is hard to realize the tradeoff between startup speed and load capacity, suffering high-acceleration and high-load startup failure. In this article, a current vector angle controller for sensorless IPMSM startup is proposed to adjust speed-up-stage current acceleration and constant-speed-stage current amplitude with load automatically. The proposed angle controller guarantees the current vector angle close to the maximum torque per ampere angle, which contributes to large startup torque, high operating efficiency and smooth transition from I–f startup to sensorless FOC. Furthermore, the robustness against parameters variation of angle controller is evaluated quantitatively. These theoretical advantages are verified in experiments with a 380 V, 1.5 kW IPMSM. In particular, the experimental results demonstrate that the proposed I–f control realizes full-load startup even with ${\rm{ \pm }}$ 50% flux linkage and ${\rm{ \pm }}$ 30% inductance variation. Furthermore, the startup acceleration auto-adjusts with load to reconcile startup speed and load capacity. [ABSTRACT FROM AUTHOR]

Accurate rotor position is significant for the back electromotive force (EMF)-based sensorless interior permanent-magnet synchronous motor (IPMSM) control. However, the ±(6 h±1)th harmonics will appear obviously in the estimated back-EMF due to the effect of the inverter nonlinearity and flux spatial harmonics. These harmonics will subsequently result in the ±(6 h)th harmonic pulsation in the estimated rotor position. In order to deal with this issue, a new complex-coefficient synchronous frequency filter (CCSFF)-based sliding mode observer combined with a quadrature phase-locked loop (PLL) is proposed to mitigate the back-EMF voltage distortion. Therefore, the performance of the position estimation is remarkably improved. The proposed CCSFF possesses both bandpass-filtering and frequency-adaptability characteristics. It can pass the fundamental component without magnitude attenuation and phase delay in different frequency scenarios. Moreover, the linearized model of the proposed CCSFF-PLL-based position estimation system is established and a systematic parameter design is presented to obtain promising dynamic performance. The effectiveness and feasibility of the proposed method are confirmed by experiments on a 1.5-kW IPMSM test platform. [ABSTRACT FROM AUTHOR]

The high-frequency (HF) signal injection method has been widely used in sensorless control for IPMSM drives. However, the audible noise caused by HF injection restricts the sensorless application. Moreover, the control bandwidth of systems based on sinusoidal multifrequency injection or variable-frequency injection for audible noise reduction is limited due to the need for filters. This article proposes a novel amplitude modulation multirandom frequency injection (AMMRI) method to improve control bandwidth and reduce audible noise. First, the detailed message signal modulation, error extraction, position tracking, and position estimation error compensation based on amplitude-modulated voltage signal are derived and analyzed. Because the filters for HF current and error extractions are removed, the control bandwidth is improved. Second, in order to reduce audible noise, the proposed AMMRI is derived by selecting the message signal according to equal-loudness contour. The proposed method improves the control bandwidth compared to conventional multifrequency injection and reduces audible noise compared to conventional square wave injection. Finally, experimental results verify the proposed method on a 1.5-kW IPMSM platform. [ABSTRACT FROM AUTHOR]

The dq-axis inductance parameter value of the Internal Permanent Magnet Synchronous Motor (IPMSM) will change with the dq-axis current. The Virtual Constant Signal Injection Method (VCSIM)-based Maximum Torque Per Ampere (MTPA) control ignores the partial derivative term of the dq-axis inductance to the dq-axis current when extracting the partial derivative information of the torque to the dq-axis current. This will cause the current to deviate from the MTPA point, which will have a certain impact on the output capacity and efficiency of the motor torque. To solve the above problems, this paper proposes a simple and feasible compensation method by solving the partial derivative information between the dq-axis inductance and the dq-axis current. The experimental results show that the motor efficiency and torque output capability are significantly improved after applying the proposed strategy. [ABSTRACT FROM AUTHOR]

A wide-speed-range sensorless control for an IPMSM is deeply studied in this paper, which combines the high-frequency injection (HFI) method and sliding-mode observer (SMO) method. At low-speed range, a rotating high-frequency voltage signal is injected into the IPMSM; the rotor position can be estimated by the HFI method based on the saliency of the IPMSM. At high-speed range, an SMO method based on the extended back electromotive force (EMF) of the IPMSM is utilized to estimate the rotor position. Furthermore, to blend the positions estimated by these two methods, a speed-dependent weight function is designed. The steady-state and dynamic performance of the wide-speed sensorless control are investigated by experiments. In high-speed range, the position estimation errors of the SMO method at different operation points are smaller than 6 el.deg.; in low-speed range, the position estimation errors of the HFI method at different operation points are smaller than 15 el.deg.; and during the transition process, the IPMSM can switch smoothly between the HFI-based and SMO-based sensorless control methods. [ABSTRACT FROM AUTHOR]

In this article, considering the influence of iron core saturation and complex boundary conditions, a novel no-load magnetic field analytical method and system multiobjective optimization model for interior permanent magnet synchronous motor (IPMSM) are proposed. First, an analytical method based on magnetic potential permeance method is proposed. The complex cogging effect and equivalent air gap permeability function are fully considered in this method. Furthermore, on the basis of Taguchi optimization design based on Fuzzy theory, an improved optimization model considering multivariable interaction is proposed. Among them, in order to comprehensively consider the performance of electromagnetic, vibration, and temperature rise, five optimization objectives including torque, pulsation, cogging torque, loss, and flux density are optimized. The sensitivity of design variables and the interaction between variables are not ignored. Finally, a 6-pole 36-slot IPMSM is manufactured for prototype experiments. A large number of prototype experiments, finite element, and computational fluid dynamics simulation analysis including no-load magnetic field, back electromotive force, temperature rise, electromagnetic torque, and so on are carried out. The accuracy and rationality of the proposed no-load magnetic field analysis method and global optimization model are well-verified. [ABSTRACT FROM AUTHOR]

Position sensorless control of interior permanent magnet synchronous motors (IPMSMs) is of great importance for the sake of the cost reduction and robustness improvement. An improved position sensorless method based on adjustable high-frequency (HF) square-wave voltage injection has been proposed for the IPMSM drive under zero- and low-speed regions. The general detection method of position from positive- and negative-sequence HF current response has been developed by the simple algebraic operations of data at some adjacent sampling instants. In addition, the proposed method not only can retain the advantage of the removal of low-pass filters in current feedback but also can increase the voltage margin of inverter with adjustable frequency setting of HF signal compared with existing square-wave voltage injection methods. Comprehensive experimental results have been given to verify the proposed theoretical analysis. [ABSTRACT FROM AUTHOR]

This article presents a sensorless control strategy by injecting high-frequency (HF) voltage into the d-axis for the interior permanent magnet synchronous motor (IPMSM) in the full speed range. The defined quadratic virtual back electromotive force model can be adopted in the full speed range, and thus, there is no need to design a transition algorithm from the zero–low speed to the medium–high speed. Besides, the accurate model of IPMSM is applied to eliminate the error caused by ignoring the stator resistance. Furthermore, the estimation error caused by the filter and system delay during demodulating the HF current in the conventional HF voltage injection method is avoided. Compared with the method of injecting HF voltage into the q-axis, the proposed method has smaller torque ripple and smaller injected voltage. The effectiveness of the proposed method is verified by experimental results. [ABSTRACT FROM AUTHOR]

To realize the smooth transition from the partial flux weakening zone I (FW-I Zone) to the deep flux weakening zone II (FW-II Zone) and avoid the current loop saturation during the deep flux weakening control for an interior permanent magnet synchronous motor, a novel deep flux weakening control strategy with variable direct axis (d-axis) current limitation (VDL-FWC) is proposed. In the framework of the traditional voltage closed-loop feedback regulation flux weakening control (FB-FWC) strategy, the d-axis flux weakening current is limited by the maximum torque per voltage, which is quickly obtained through a parabolic approximation that varies with the quadrature axis (q-axis) current. Therefore, when the d-axis weakening current exceeds its limitation, a closed-loop voltage feedback proportional-integral controller is used to adjust the q-axis current increment, which transfers the exceeding d-axis current to the q-axis current to prevent voltage saturation. This process helps the current loop avoid becoming out of control. The proposed deep flux weakening control strategy is compared with the FB-FWC strategy and flux weakening control strategy with a fixed direct d-axis current limitation (FDL-FWC). Studies show that the proposed strategy is effective and has a higher load capacity in the deep flux weakening zone. [ABSTRACT FROM AUTHOR]

In order to solve the problem that the three-phase current of the interior permanent magnet synchronous motor (IPMSM) contains the 11th and 13th current harmonics, a multiple synchronous rotating frame transformation (MSRFT)-based current harmonic suppression method is established. Firstly, the influencing factors of current harmonics in IPMSM vector control are analyzed, and the influence mechanism of the inverter's dead-time effect and the permanent magnet flux linkage harmonics on the current harmonics is described. Secondly, a simple current harmonic extraction method is proposed by optimizing the traditional current harmonic extraction method based on MSRFTs. The proposed method achieves the accurate extraction of the current harmonic components. Thirdly, a harmonic voltage generation method is established and is combined with the proposed current harmonic extraction method to form a current harmonic suppression strategy. Finally, the feasibility and effectiveness of the proposed method are verified via MATLAB/Simulink simulations and experiments. The simulation and experimental results show that the proposed current harmonic extraction method can extract the current harmonic components accurately, and the proposed current harmonic suppression strategy can suppress the 11th and 13th current harmonics effectively. [ABSTRACT FROM AUTHOR]

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The dynamic eccentricity fault (DEF) of the interior permanent magnet synchronous motor (IPMSM) is mainly caused by external mechanical shock. In the case of DEF, an unbalanced magnetic force occurs because the length of the air gap is not constant. Noise and vibration of the motor occur due to unbalanced magnetic force. In addition, since the length of the air gap is not constant, the distribution of magnetic flux density is distorted, and iron loss is increased. As the iron loss increases, the temperature rises, and an irreversible demagnetization fault (IDF) of the permanent magnet occurs due to overheating. Therefore, in this paper, the fault mechanism of IDF due to DEF of IPMSM for electric vehicle (EV) traction is analyzed. Initially, the magnetic flux density and iron loss characteristics according to the healthy condition and DEF condition are analyzed using the finite element method (FEM). Then, the detailed iron loss analysis is performed based on the phase current waveform measured through the load test of the motor. Finally, the fault mechanism of IDF due to DEF was verified through an electric-axle load test on a manufactured motor having eccentricity.

Interior permanent magnet synchronous motor (IPMSM) is applied in automotive drive because of its high efficiency and high power density. The accurate torque control of motor, however, is still subject to further investigation and improvement. In order to improve the performance of IPMSM applied in electric vehicles, a feedback torque control method based on online parameter identification is developed in this research. In order to control the instantaneous electromagnetic torque accurately, stator resistance, rotor flux, and dq-axis inductance are identified simultaneously with a recursive least square algorithm. In this process, sinusoidal disturbance current is injected into d-axis to solve the rank-deficient problem. Furthermore, a simulation model is developed based on this torque control method. The simulation results show that the torque control method developed in this research can perform better than the torque control method based on fixed parameters. On the other hand, a test rig is developed in this research to verify the feasibility of torque control method and the effectiveness of simulation model. The measured results show that these parameters can be identified accurately with the online parameter identification method developed in this research, and the robustness of this online parameter identification method can be verified in the experiment. Furthermore, the torque control method is verified with this test rig, and the results show that the measured torque can accurately follow the torque command rapidly with little fluctuation, indicating that the method developed in this research has the features of high accuracy, high robustness and short response time.

A novel voltage control scheme for an interior permanent magnet synchronous motor (IPMSM) servo drive in the constant power region with intelligent estimation of the motor parameter is proposed in this study. In the novel voltage control scheme, a feedforward voltage angle controller is proposed where an intelligent parameter estimation method by using a wavelet fuzzy neural network (WFNN) is developed to estimate the $q$ -axis inductance online. In this study, in order to minimize the copper loss, a flux-weakening (FW) control scheme under maximum phase voltage is developed first. Then, an adaptive backstepping based nonlinear controller (ABNC) considering nonzero $d$ -axis current is developed to improve the robustness of the speed control. The Lyapunov stability theorem is used to derive the adaptive law of the online estimation of the lumped uncertainty to ensure the asymptotical stability of the ABNC. Moreover, a feedforward voltage angle controller is developed for the voltage control where the $q$ -axis current controller is retained in order to ensure the steady-state performance of the control system. Furthermore, the WFNN is adopted to estimate the actual $q$ -axis inductance value online for the feedforward voltage angle controller to improve the dynamic response. In addition, some experimental results are demonstrated to verify the effectiveness of the proposed voltage control scheme with ABNC in the constant power region.

This paper presents a detailed process for the design of interior permanent magnet synchronous machines (IPMSMs) for electric vehicle (EV) applications. First, a comprehensive design process featuring two objectives and three constraints is proposed to realize an optimal IPMSM design that can satisfy the key performance requirements for an EV application. The objectives and constraints were carefully selected and designed to obtain a balance between performance, efficiency, and cost. Because the inductances and magnet flux linkage of the machine are key design parameters for attaining optimal flux-weakening capability, the impact of the machine dimensions on these two parameters is thoroughly investigated and explained using both analytical and numerical techniques. Additional analyses including normalized key performance metrics and the impact of short-circuit faults in PM machines with three different characteristic current values (1, 1.3, and 2.6 pu) are also provided, highlighting the advantages and limitations of the three baseline designs.

A novel control approach based on Linear Parameter Varying (LPV) is designed for Electric Vehicles (EVs) to address the crucial challenge of torque derating. A high fidelity Interior Permanent Magnet Synchronous Motor (IPMSM) based EV is modelled by taking into account the influence of temperature. A closed loop torque compensation control architecture with LPV based Field Oriented Control (FOC) has been designed to mitigate the thermal effects. In order to curtail deteriorating of FOC due to parameter variation, a robust LPV observer has been proposed to estimate the degraded Permanent Magnet (PM) flux linkage and instantaneous torque production caused by uncertainties in stator resistance arises due to thermal effects. A LPV gain scheduling robust current controller for inner control loop of FOC has also been designed which ensures internal stability. The LPV observer-controller gains are computed by solving Linear Matrix Inequalities (LMIs) using convex optimization and singular value decomposition. The experiments simulations have been performed for EV operation against the Worldwide Harmonized Light Vehicles Test Procedure (WLTP) class 3, New European Driving Cycle (NEDC) and Federal Test Procedure (FTP) driving cycles considering thermal effects in Matlab/Simulink. The efficacy of proposed control architecture for managing the derating torque of IPMSM based EV is demonstrated through the validity of results and detailed data analysis. The LPV based FOC is compared with conventional FOC control counterpart. The comparative experiments simulation results show that the overall Mean Square Error (MSE) value is exponentially reduced which establish superiority of the proposed control scheme.

This paper introduces a parameter-estimation-based sensorless adaptive direct voltage maximum torque per ampere (MTPA) control strategy for interior permanent magnet synchronous machines (IPMSMs). In direct voltage control, the motor’s electrical parameters, speed, and rotor position are of great significance. Thus, any mismatch in these parameters or failure to acquire accurate speed or position information leads to a significant deviation in the MTPA trajectory, causing high current consumption and hence affecting the performance of the entire control system. In view of this problem, a fuzzy logic control-based cascaded model reference adaptive system (FLC-MRAS) is introduced to mitigate the effect of parameter variation on the tracking of the MTPA trajectory and to provide precise information about the rotor speed and position. The cascaded scheme consists of two parallel FLC-MRAS for speed and multiparameter estimation. The first MRAS is utilized to estimate motor speed and rotor position to achieve robust sensorless control. However, the speed estimator is highly dependent on time-varying motor parameters. Therefore, the second MRAS is designed to identify the quadratic inductance and permanent magnet flux and continuously update both the speed estimator and control scheme with the identified values to ensure accurate speed estimation and real-time MTPA trajectory tracking. Unlike conventional MRAS, which uses linear proportional-integral controllers (PI-MRAS), an FLC is adopted to replace the PI controllers, ensuring high estimation accuracy and enhancing the robustness of the control system against sudden changes in working conditions. The effectiveness of the proposed scheme is evaluated under different speed and torque conditions. Furthermore, a comparison against the conventional PI-MRAS is extensively investigated to highlight the superiority of the proposed scheme. The evaluation results and our quantitative assessment show the ability of the designed strategy to achieve high estimation accuracy, less oscillation, and a faster convergence rate under different working conditions. The quantitative assessment reveals that the FLC-MRAS can improve the estimation accuracy of speed, permanent magnet flux, and quadratic inductance by 19%, 55.8% and 44.55%, respectively.

Conventional active disturbance rejection controller (ADRC) for interior permanent magnet synchronous motor (IPMSM) drives suffers deteriorated performance in dealing with low-order harmonic disturbances. To enhance the capability of ADRC in rejecting such disturbances, this article proposes a complex coefficient active disturbance rejection controller (CCF-ADRC). The complex coefficient filter (CCF), which is capable of extracting signals with selective frequency and selective phase sequence from the input orthogonal signals, is incorporated into the extended state observer to enhance its estimation accuracy on the d-q-axis harmonic disturbances. With the harmonic disturbances accurately estimated, the subsequently designed CCF-ADRC can achieve enhanced performance in rejecting such disturbances. Theoretical analysis on the stability, the harmonics rejection capability, the command tracking capability, and the influence of parameter mismatches are systematically conducted. Comprehensive experiments on a 1.0-kW IPMSM verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

There is a certain amount of current harmonics in interior permanent magnet synchronous motor. In order to accurately control the current harmonic, this article focuses on three aspects: establishing current harmonic calculation model, extracting current harmonic, and designing current harmonic regulator. A current harmonic calculation model, which considers the effect of voltage harmonics induced by current controllers and digital control delay on the initial phase angle of voltage harmonics, is established for the first time. With the help of multiple synchronous rotating frame transformation, a current harmonic extraction method more suitable for motor drive field, which aims to extract the current harmonic characteristics of d-axis and q-axis currents, is proposed. On this basis, the controlled quantity and control quantity are unified in d–q coordinate frame for analyzing the coupling relationship of current harmonic characteristics. And then a PI current harmonic regulator, including current harmonic decoupling and voltage harmonic initial phase angle compensation, is constructed, so as to realize the effective control of current harmonics. Finally, the effectiveness and superiority of the proposed method are verified by simulation and experiments. [ABSTRACT FROM AUTHOR]

Owing to the importance of environmental issues, a prevalent global challenge, the use of permanent magnet synchronous motors has increased significantly in several industries. Motor efficiency is important because of environmental regulations. As an approach to increase the efficiency of a motor, a method has been presented to increase efficiency via a motor design. Although the design is important, the method for controlling the actually developed motor also significantly affects efficiency. As a method for controlling the existing motor, current control was adopted. Speed–torque control is widely used as a method commonly adopted in conventional motor control. As the motor control method proposed in this study, flux–torque control was employed. Although flux–torque control is not a novel technology, in the case of the control method proposed in this study, a method for interpolating values after comparison with actual data via the finite element analysis (FEA) of the motor is applied. In this study, a method for interpolating inductance among important factors for motor torque control is proposed. Therefore, regarding the proposed flux–torque control, the validity of the study was verified based on the actual data obtained from the FEA and actual manufactured motor shape. [ABSTRACT FROM AUTHOR]

In view of the lack of the role of reluctance torque in the electromagnetic torque output of the motor under the previous control logic with id=0, only the excitation torque component is working. Therefore, on the premise of inputting unit current, the output electromagnetic torque cannot reach the maximum value, resulting in low energy utilization, reduced load capacity and low operation efficiency. The maximum torque control of unit current output is proposed to control id to pursue the maximum torque. This control method studies the mathematical model of the Interior Permanent Magnet Synchronous Motor (IPMSM) in the rotating d-q-O coordinate system, and establishes the relationship between the current and torque of IPMSM through mathematical formula derivation, so as to realize the Maximum Torque Per Ampere (MTPA) control of the IPMSM. Through Simulink simulation, compared with the previous control logic with id=0, when MTPA control logic outputs the same electromagnetic torque value, the stator current value of IPMSM is smaller and the energy utilization rate is the highest, thus improving the operation efficiency. [ABSTRACT FROM AUTHOR]

When the interior permanent magnet synchronous motor (IPMSM) is running, there are abundant harmonics in the stator current. In order to achieve the suppression of current harmonics, the current harmonic extraction method and current harmonic controller are studied in this paper. Firstly, a simple and accurate method for extracting current harmonics is proposed by means of multiple synchronous rotating frame transformation (MSRFT). Secondly, an improved deadbeat predictive control (IDPC) based current harmonic controller is designed after analyzing the advantages and disadvantages of traditional current harmonic controllers. Thirdly, IDPC-based current harmonic suppression strategy is proposed by combining the proposed current harmonic extraction method and the proposed current harmonic controller. The proposed strategy can still effectively achieve current harmonic suppression when the motor runs at low speed, medium speed and high speed and the controller parameters are mismatched with the motor parameters. Finally, the feasibility and effectiveness of the proposed strategy are verified by simulation and experiments. [ABSTRACT FROM AUTHOR]

Sensorless schemes are mainly used in fault-tolerant control of interior permanent magnet synchronous motor (IPMSM) drives. Traditional sensorless methods with injection of high-frequency (HF) carrier signals into the stationary reference frame have a stable performance. However, phase shifts caused by conventional high-pass filters (HPFs) decrease the estimation accuracy. Besides, the demodulation process is usually complicated, which increases the difficulty of application. To solve these problems, this study presents an HF-induced current direct demodulation method. Rotor position angle can be solved from the sampled currents at adjacent moments without demodulation signals. Therefore, the errors related to filters in the rotor position estimation are eliminated. Besides, the efficiency of the demodulation algorithm is improved. Furthermore, an online compensation method for cross-saturation effect is proposed. Experimental results verify that the proposed strategy can obtain an accurate rotor position with good steady-state and dynamic performance. [ABSTRACT FROM AUTHOR]

Among various maximum torque per ampere (MTPA) control schemes for interior permanent magnet synchronous motor (IPMSM) drives, the signal-injection-based methods exhibit relatively high overall performance due to their high control accuracy and satisfactory dynamic performance. However, the high current spectrum peaks induced by the fixed-frequency signal injection may cause electromagnetic interference and even audible noise problems in applications, such as electric vehicles, vessels, and aircraft. To address this problem, an MTPA control method using pseudorandom frequency-switching sinusoidal signal injection is proposed in this paper. The sinusoidal signals with two different frequencies are randomly injected into the d- and q-axis currents and the MTPA points can be tracked according to the resultant system response. In this way, a high-performance MTPA control can be achieved regardless of motor parameter variations. Since the injection frequency of the proposed method varies randomly, the induced harmonic components in phase currents no longer concentrate at certain frequencies, and the current spectrum peaks caused by signal injection can be reduced accordingly. The experimental results demonstrate the validity of the presented method. [ABSTRACT FROM AUTHOR]

In this article, a novel global search algorithm tornado optimization (TO) and its hybridization with pattern search method (PSM) are proposed to solve the multimodal optimization problem. The TO enhances the capability of global searching with two strategies: intensification strategy and diversification strategy. The hybridization with PSM supports the exact and fast convergence on adjacent optima from the points that are discovered in global search using TO. The outstanding performance of the proposed algorithm is verified by comparison with niching genetic algorithm at the two test functions, and the algorithm is applied to the optimal design of the interior permanent magnet synchronous motor for electric vehicles. [ABSTRACT FROM AUTHOR]

This paper presents the dynamic analysis and computer simulation of interior permanent magnet synchronous motor (IPMSM) with intermittent loading. This objective was realized with the aid of MATLAB m.file function program, which is based on an explicit Runge-Kutta fourth order numerical method to solve a set of first order differential system of equations describing electrical and mechanical models of IPMSM. The IPMSM used in this research is of specifications 3-phase, 2 KW, 50 Hz, 4 poles, 240 V. The IPMSM differential equations are expressed in rotor reference frame with q- and d-axes stator currents, mechanical rotor speed, and rotor angular position as state variables. The analysis and simulation of the motor is initially done with no-load and with the parameters as given in Table 1. Subsequently, the motor was loaded and parameter variations were carried out. The result of a typical responses of the motor were obtained which showed that IPMSM has more ripples, overshoot, slower response but can carry load of up to 90 Nm. The effect of higher stator resistance shows that it minimizes the magnitude of ripple of the output characteristics (torque and power) but takes more time to attain the same steady state value. In the same vein, variation of moment of inertia has little or no effect on the output characteristics of the motor. The findings obtained in this research work as compared to other literatures showed that with the parameters recommended, an improved design and operation of IPMSM will be obtained for best performance and without unsynchronous operation due to overloading. [ABSTRACT FROM AUTHOR]

In this article, a new frequency adaptive second-order disturbance observer (FASODO) for back electromotive force (EMF) and active flux estimation is proposed using the active flux model of interior permanent magnet synchronous motors. FASODO is a frequency adaptive approach and eliminates the phase delay compensator demand of the traditional sliding mode observer-based back EMF estimator. Besides, FASODO estimates the active flux and the back EMF simultaneously. As a result, a quadrature phase-locked loop (Q-PLL) using either the back EMF or the active flux and a tan inverse approach can be used for speed–position identification. Meanwhile, an integrally compensated Q-PLL is designed to overcome the traditional Q-PLL position estimation error during ramp frequency tracking. The design guideline of FASODO and the integrally compensated Q-PLL are provided. A comparative analysis with traditional SMO shows that the proposed approach can deliver a better sensorless control performance. Furthermore, a comparison with a frequency adaptive complex coefficient filter enhanced SMO shows a comparable result, while the proposed approach additionally delivers the active flux. The approach is verified using the Texas Digital Signal Processor (TMS320F28335) and RT-LAB Real-Time Simulator, taking into account different operating conditions. [ABSTRACT FROM AUTHOR]

This article proposes an online torque ripple minimization (TRM) technique using a fuzzy system (FS)-based d-axis current design for interior permanent magnet synchronous motor (IPMSM) drives. Existing control-based TRM techniques generally employ optimization algorithms to design the dq-axis currents that attenuate the torque ripples. However, complex iterations applied for the optimization algorithms increase computational complexity, which limits the applicability of such TRM techniques under transient state of the IPMSM drives. Unlike with existing methods, the proposed TRM technique designs reference d-axis current using a computationally efficient algorithm and remarkably minimizes the torque ripples. Moreover, the reference d-axis current is designed online based on an FS to keep the stator current of the IPMSM inside the rated value, especially at the transient state. The proposed TRM strategy is validated through simulation and experimental investigations by using a MATLAB/Simulink software and a prototype IPMSM drive with TI TMS320F28335 digital signal processor. Comparative theoretical and experimental investigations prove that the proposed TRM technique is computationally efficient and ensures more reduced ripples in the electromagnetic torque and dq-axis currents with d-axis current significantly close to zero than conventional maximum torque per ampere based technique without TRM and conventional current control-based TRM technique under critical load conditions. [ABSTRACT FROM AUTHOR]