Zhaokai Li
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Zhaokai Li has a total of 84 co-authors. Here are the top co-authors by number of shared publications:
- Xiaoyan Huang
College of Electrical Engineering, Zhejiang University, Hangzhou, China
29 shared publications - Zhuo Chen
Zhejiang Provincial Key Laboratory of Electrical Machine Systems, College of Electrical Engineering, Zhejiang University, Hangzhou, China
13 shared publications - Lijian Wu
Zhejiang University
8 shared publications - Yelong Yu
Zhejiang Provincial Key Laboratory of Electrical Machine Systems, College of Electrical Engineering, Zhejiang University, Hangzhou, China
8 shared publications - Ang Liu
Zhejiang Provincial Key Laboratory of Electrical Machine Systems, College of Electrical Engineering, Zhejiang University, Hangzhou, China
7 shared publications - Luca Peretti
KTH Royal Institute of Technology, Stockholm, Sweden
7 shared publications
Latest Publications
- 17 December 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 14  (2) , 2527-2540
Model-Free Deadbeat Direct Speed Control With Adaptive Bandwidth Factor in Surface-Mounted Permanent Magnet Synchronous Motor
This paper presents a model-free deadbeat predictive direct speed control strategy for surface-mounted permanent magnet synchronous motors incorporating an adaptive-bandwidth extended state observer. Unlike conventional extended state observers with fixed bandwidth factors, which lack adaptability under varying conditions and introduce coordination difficulties between speed and current loops, the proposed method presents an observation-error-driven bandwidth adjustment mechanism. This method enables real-time and independent adjustment of the bandwidth factors for the lumped disturbance observers of speed and current, thereby dynamically balancing disturbance rejection and estimation accuracy under various operating conditions and enhancing the algorithm’s adaptability. To ensure theoretical stability, an integral-type Lyapunov function is constructed to guarantee the asymptotic convergence of the proposed adaptive bandwidth observer. Moreover, practical guidelines for parameter design principles are formulated to facilitate the implementation of the proposed method. Experimental results on a 750W SPMSM platform demonstrate that the proposed strategy significantly improves transient performance and adaptability compared to fixed-bandwidth observer-based approaches.
- 17 December 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 14  (2) , 2527-2540
Model-Free Deadbeat Direct Speed Control With Adaptive Bandwidth Factor in Surface-Mounted Permanent Magnet Synchronous Motor
This paper presents a model-free deadbeat predictive direct speed control strategy for surface-mounted permanent magnet synchronous motors incorporating an adaptive-bandwidth extended state observer. Unlike conventional extended state observers with fixed bandwidth factors, which lack adaptability under varying conditions and introduce coordination difficulties between speed and current loops, the proposed method presents an observation-error-driven bandwidth adjustment mechanism. This method enables real-time and independent adjustment of the bandwidth factors for the lumped disturbance observers of speed and current, thereby dynamically balancing disturbance rejection and estimation accuracy under various operating conditions and enhancing the algorithm’s adaptability. To ensure theoretical stability, an integral-type Lyapunov function is constructed to guarantee the asymptotic convergence of the proposed adaptive bandwidth observer. Moreover, practical guidelines for parameter design principles are formulated to facilitate the implementation of the proposed method. Experimental results on a 750W SPMSM platform demonstrate that the proposed strategy significantly improves transient performance and adaptability compared to fixed-bandwidth observer-based approaches.
- 27 November 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 74  (00189456) , 1-12
Improved Scalable Analytical Model for Predicting SPM Motor Performance Considering Magnet Shape and Magnetization Pattern
This paper develops the improved scalable analytical model (iSAM) for predicting the performance of the surface-mounted permanent-magnet (SPM) motor with the arbitrary magnet shape and magnetization direction. It extends the ability of the conventional analytical models. The database of the analytical model can store the electromagnetic information for the SPM motors, which enriches the scaling laws for electrical machines. As for the magnets with arbitrary shapes, they are divided into finite rectangles or fan-shaped segments based on their magnetization directions, which are then replaced by equivalent magnet currents along the magnet surfaces. Then, based on the iSAM, the air-gap field of the SPM motor can be obtained considering the iron nonlinearity. This method is beneficial for accelerating the optimization process aimed at reducing torque ripple in servo motor applications. The finite-element method (FEM) for eccentric magnetic pole servo motors is executed to verify the effectiveness of the proposed method. Additionally, a prototype with parallel magnetized PM is tested to demonstrate the accuracy of the iSAM. The proposed method is particularly useful for the modeling techniques and fault diagnosis of electrical machines.
- 27 November 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 74  (00189456) , 1-12
Improved Scalable Analytical Model for Predicting SPM Motor Performance Considering Magnet Shape and Magnetization Pattern
This paper develops the improved scalable analytical model (iSAM) for predicting the performance of the surface-mounted permanent-magnet (SPM) motor with the arbitrary magnet shape and magnetization direction. It extends the ability of the conventional analytical models. The database of the analytical model can store the electromagnetic information for the SPM motors, which enriches the scaling laws for electrical machines. As for the magnets with arbitrary shapes, they are divided into finite rectangles or fan-shaped segments based on their magnetization directions, which are then replaced by equivalent magnet currents along the magnet surfaces. Then, based on the iSAM, the air-gap field of the SPM motor can be obtained considering the iron nonlinearity. This method is beneficial for accelerating the optimization process aimed at reducing torque ripple in servo motor applications. The finite-element method (FEM) for eccentric magnetic pole servo motors is executed to verify the effectiveness of the proposed method. Additionally, a prototype with parallel magnetized PM is tested to demonstrate the accuracy of the iSAM. The proposed method is particularly useful for the modeling techniques and fault diagnosis of electrical machines.
- 31 July 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Transportation Electrification
- Vol. 11  (6) , 12898-12910
A Modified Deadbeat Predictive Current Control With Improved Dynamic Performance Under Insufficient Voltage Margin for IPMSM
Deadbeat predictive current control (DPCC) is well known for its excellent dynamic performance, which requires a sufficient voltage margin to achieve the theoretical tracking delay. However, there is still potential to improve its dynamic performance under conditions of insufficient voltage margin, such as at high speeds and under heavy loads. To address this, this article proposes a modified DPCC based on an exact discretized model of the interior permanent magnet synchronous motor (IPMSM). This model accounts for the zero-order hold effect of the inverter output voltage, providing better accuracy in long-step predictions at the cost of increased computational overhead. Additionally, the motor model is incrementalized to eliminate the need for rotor flux linkage. The proposed method extends the prediction horizon under insufficient voltage margin conditions to cover the entire dynamic process. The stator voltage vector is designed to lie on the hexagonal boundary of space vector pulsewidth modulation (SVPWM) and remain stationary in the $\boldsymbol {\alpha \beta }$ -reference frame throughout the entire dynamic process, thereby shortening the response time through quasitime-optimal control. Furthermore, a simplified iterative method is introduced to reduce the computational cost of voltage calculation, with the iteration number set to three to balance control performance and computational burden. Finally, experimental results validate the rationale for the iteration number selection and demonstrate the effectiveness of the proposed method in improving the dynamic performance of both current and torque compared to the conventional minimum-phase-error voltage limiting strategy. Nevertheless, despite the introduction of the simplified iterative method, the overall computational burden still limits the proposed method to systems with high-performance requirements and sufficient computational resources.
- 31 July 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Transportation Electrification
- Vol. 11  (6) , 12898-12910
A Modified Deadbeat Predictive Current Control With Improved Dynamic Performance Under Insufficient Voltage Margin for IPMSM
Deadbeat predictive current control (DPCC) is well known for its excellent dynamic performance, which requires a sufficient voltage margin to achieve the theoretical tracking delay. However, there is still potential to improve its dynamic performance under conditions of insufficient voltage margin, such as at high speeds and under heavy loads. To address this, this article proposes a modified DPCC based on an exact discretized model of the interior permanent magnet synchronous motor (IPMSM). This model accounts for the zero-order hold effect of the inverter output voltage, providing better accuracy in long-step predictions at the cost of increased computational overhead. Additionally, the motor model is incrementalized to eliminate the need for rotor flux linkage. The proposed method extends the prediction horizon under insufficient voltage margin conditions to cover the entire dynamic process. The stator voltage vector is designed to lie on the hexagonal boundary of space vector pulsewidth modulation (SVPWM) and remain stationary in the $\boldsymbol {\alpha \beta }$ -reference frame throughout the entire dynamic process, thereby shortening the response time through quasitime-optimal control. Furthermore, a simplified iterative method is introduced to reduce the computational cost of voltage calculation, with the iteration number set to three to balance control performance and computational burden. Finally, experimental results validate the rationale for the iteration number selection and demonstrate the effectiveness of the proposed method in improving the dynamic performance of both current and torque compared to the conventional minimum-phase-error voltage limiting strategy. Nevertheless, despite the introduction of the simplified iterative method, the overall computational burden still limits the proposed method to systems with high-performance requirements and sufficient computational resources.
- 15 January 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13  (2) , 2565-2579
Smooth Nonlinear ESO-Based Model-Free Predictive Current Control With an Extended Control Set for SPMSM Drives
This paper proposes an improved nonlinear extended state observer-based model-free predictive current control with an extended control set. First, the nonsmoothness problem of conventional nonlinear extended state observer model-free solutions is explained. By constructing a high-smoothness polynomial series at the transition points of the piecewise nonlinear function, an improved nonlinear extended state observer is designed to enhance the performance of the model-free predictive current control, and relevant stability proofs are derived by the Routh criterion. Furthermore, a newly designed extended control set based on the voltage vectors at the center of triangular subregions of the modulation area is proposed to improve the output voltage accuracy. Based on the geometrical characteristics of the subregion center voltage vectors, a fast-layering selection method is proposed to reduce the complexity of determining the optimal voltage vector. Finally, experimental results are presented to verify the proposed method’s feasibility and effectiveness.
- 15 January 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13  (2) , 2565-2579
Smooth Nonlinear ESO-Based Model-Free Predictive Current Control With an Extended Control Set for SPMSM Drives
This paper proposes an improved nonlinear extended state observer-based model-free predictive current control with an extended control set. First, the nonsmoothness problem of conventional nonlinear extended state observer model-free solutions is explained. By constructing a high-smoothness polynomial series at the transition points of the piecewise nonlinear function, an improved nonlinear extended state observer is designed to enhance the performance of the model-free predictive current control, and relevant stability proofs are derived by the Routh criterion. Furthermore, a newly designed extended control set based on the voltage vectors at the center of triangular subregions of the modulation area is proposed to improve the output voltage accuracy. Based on the geometrical characteristics of the subregion center voltage vectors, a fast-layering selection method is proposed to reduce the complexity of determining the optimal voltage vector. Finally, experimental results are presented to verify the proposed method’s feasibility and effectiveness.
- 11 December 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13  (2) , 1673-1686
Computational Efficient DSVM-Based Model Predictive Direct Speed Control for SPMSM Drives With Mechanical Disturbance Suppression
This paper proposes a simplified discrete space vector modulation-based model predictive direct speed control with an improved load disturbance observer for permanent magnet synchronous motor drives. Firstly, a simplified discrete space vector modulation method is used to improve the steady-state performance of model predictive direct speed control. In this discrete space vector modulation method, a novel geometric method relying only on three auxiliary lines in each sector is designed to simplify the algorithm’s complexity. In this way, the set of candidate vectors is quickly determined. Then, the current pulsation and speed of model predictive direct speed control are suppressed, and the computational burden of the discrete space vector modulation execution process is reduced. Secondly, the reasons that affect the dynamic performance of the conventional linear extended state observer-based mechanical disturbance observer are analyzed, and the observed error of the observer is derived. Based on the observer error, an improved mechanical disturbance observer is proposed to accelerate the convergence process. The Lyapunov theory proves the stability of the proposed observer. Finally, the feasibility of the proposed method is verified by experiments.
- 11 December 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13  (2) , 1673-1686
Computational Efficient DSVM-Based Model Predictive Direct Speed Control for SPMSM Drives With Mechanical Disturbance Suppression
This paper proposes a simplified discrete space vector modulation-based model predictive direct speed control with an improved load disturbance observer for permanent magnet synchronous motor drives. Firstly, a simplified discrete space vector modulation method is used to improve the steady-state performance of model predictive direct speed control. In this discrete space vector modulation method, a novel geometric method relying only on three auxiliary lines in each sector is designed to simplify the algorithm’s complexity. In this way, the set of candidate vectors is quickly determined. Then, the current pulsation and speed of model predictive direct speed control are suppressed, and the computational burden of the discrete space vector modulation execution process is reduced. Secondly, the reasons that affect the dynamic performance of the conventional linear extended state observer-based mechanical disturbance observer are analyzed, and the observed error of the observer is derived. Based on the observer error, an improved mechanical disturbance observer is proposed to accelerate the convergence process. The Lyapunov theory proves the stability of the proposed observer. Finally, the feasibility of the proposed method is verified by experiments.
- 10 July 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industrial Electronics
- Vol. 72  (1) , 756-767
Investigation and Comparative Study of Double-Sided Yokeless Asymmetric Flux Reversal Permanent Magnet Linear Machine
This article proposes two types of double-sided yokeless asymmetric flux reversal permanent magnet linear machines (DYAFR-PMLM) for long-distance application. By employing asymmetric excitation, the second-order harmonic magnetomotive force (MMF) arises with significant amplitude, making it a valuable resource for enhancing thrust force density. The article starts by introducing the machine topology and working mechanism under both asymmetric excitation and a complementary secondary structure. Subsequently, the mechanism for thrust force generation under multiple MMFs is analytically calculated and validated by using finite element analysis. Then, some crucial electromagnetic performance metrics, including the open-circuit performances, thrust force performances, power factor, and demagnetization risk, are comparatively analyzed. The results reveal that the proposed DYAFR-PMLM with a consequent pole (CP) structure can achieve a thrust force density 59% higher than conventional FR-PMLM. Additionally, the power factor can be increased to 0.89, and the normal force can be significantly reduced from kilo-newtons to under 10 newtons. More notably, DYAFR-PMLM attains a thrust force density of 78.2% while substantially reducing the PM volume to about 1/74 over a 10-m distance in comparison to conventional PMLM. Finally, a prototype of DYAFR-PMLM with a CP structure is fabricated and validated through experimental testing.
- 10 July 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industrial Electronics
- Vol. 72  (1) , 756-767
Investigation and Comparative Study of Double-Sided Yokeless Asymmetric Flux Reversal Permanent Magnet Linear Machine
This article proposes two types of double-sided yokeless asymmetric flux reversal permanent magnet linear machines (DYAFR-PMLM) for long-distance application. By employing asymmetric excitation, the second-order harmonic magnetomotive force (MMF) arises with significant amplitude, making it a valuable resource for enhancing thrust force density. The article starts by introducing the machine topology and working mechanism under both asymmetric excitation and a complementary secondary structure. Subsequently, the mechanism for thrust force generation under multiple MMFs is analytically calculated and validated by using finite element analysis. Then, some crucial electromagnetic performance metrics, including the open-circuit performances, thrust force performances, power factor, and demagnetization risk, are comparatively analyzed. The results reveal that the proposed DYAFR-PMLM with a consequent pole (CP) structure can achieve a thrust force density 59% higher than conventional FR-PMLM. Additionally, the power factor can be increased to 0.89, and the normal force can be significantly reduced from kilo-newtons to under 10 newtons. More notably, DYAFR-PMLM attains a thrust force density of 78.2% while substantially reducing the PM volume to about 1/74 over a 10-m distance in comparison to conventional PMLM. Finally, a prototype of DYAFR-PMLM with a CP structure is fabricated and validated through experimental testing.
- 3 June 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Magnetics
- Vol. 60  (9) , 1-7
Design and Quantitative Analysis of Asymmetric Flux Reversal Permanent Magnet Linear Machine With Reduced Leakage Flux
This article introduces an asymmetric flux reversal permanent magnet linear machine (AFR-PMLM) designed to minimize the leakage flux. By employing asymmetric Halbach PM array, it effectively generates and fully exploits the second-order harmonic magnetomotive force (MMF), leading to substantial improvements in both thrust force density and power factor compared to conventional FR-PMLM. First, the machine topology and operation principle are introduced. Subsequently, the thrust force generation mechanism under multi MMFs is analytically calculated based on MMF-permeance model. Furthermore, various electromagnetic performances are thoroughly illustrated and comprehensively studied. It reveals that the proposed AFR-PMLM with Halbach PM array has the capability to provide 12.8% and 55.4% higher average force than that in AFR-PMLM with conventional asymmetric PM excitation and conventional FR-PMLM, respectively. Additionally, it achieves a power factor exceeding 0.77 under a current density of 6 A/mm2, representing a notable improvement of 36.8% compared to conventional FR-PMLM with symmetric PM excitation. Compared with conventional PMLM, it can provide nearly 72.1% of the thrust force density while consuming only 1/81 of the PMs over a 10 m distance.
- 3 June 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Magnetics
- Vol. 60  (9) , 1-7
Design and Quantitative Analysis of Asymmetric Flux Reversal Permanent Magnet Linear Machine With Reduced Leakage Flux
This article introduces an asymmetric flux reversal permanent magnet linear machine (AFR-PMLM) designed to minimize the leakage flux. By employing asymmetric Halbach PM array, it effectively generates and fully exploits the second-order harmonic magnetomotive force (MMF), leading to substantial improvements in both thrust force density and power factor compared to conventional FR-PMLM. First, the machine topology and operation principle are introduced. Subsequently, the thrust force generation mechanism under multi MMFs is analytically calculated based on MMF-permeance model. Furthermore, various electromagnetic performances are thoroughly illustrated and comprehensively studied. It reveals that the proposed AFR-PMLM with Halbach PM array has the capability to provide 12.8% and 55.4% higher average force than that in AFR-PMLM with conventional asymmetric PM excitation and conventional FR-PMLM, respectively. Additionally, it achieves a power factor exceeding 0.77 under a current density of 6 A/mm2, representing a notable improvement of 36.8% compared to conventional FR-PMLM with symmetric PM excitation. Compared with conventional PMLM, it can provide nearly 72.1% of the thrust force density while consuming only 1/81 of the PMs over a 10 m distance.
- Open Access
- 21 February 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industrial Electronics
- Vol. 71  (10) , 12770-12780
The Scalable Analytical Model for Calculating the Magnetic Field of Surface-Mounted Permanent Magnet Motor
This article develops a scalable analytical model that builds a relationship between any surface-mounted permanent magnet (SPM) motor and a general motor with variable slot-opening and air-gap length, considering both the saturation effect and slotting effect. It can not only give the performance of the single SPM motor but also show internal connection among different SPM motors regardless of the motor power and dimension. To account for the iron saturation, the equivalent saturation current combined with simplified BH curves of iron is introduced to directly present the iron magnetic potential distribution without an iterative process. Thus, the proposed model can be used as the surrogate model in the motor design with little computation and provide great insight into the relationship among motors with different power and dimension. Both finite-element analysis and experiment are carried out to validate the proposed model.
- 21 February 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industrial Electronics
- Vol. 71  (10) , 12770-12780
Open AccessThe Scalable Analytical Model for Calculating the Magnetic Field of Surface-Mounted Permanent Magnet Motor
This article develops a scalable analytical model that builds a relationship between any surface-mounted permanent magnet (SPM) motor and a general motor with variable slot-opening and air-gap length, considering both the saturation effect and slotting effect. It can not only give the performance of the single SPM motor but also show internal connection among different SPM motors regardless of the motor power and dimension. To account for the iron saturation, the equivalent saturation current combined with simplified BH curves of iron is introduced to directly present the iron magnetic potential distribution without an iterative process. Thus, the proposed model can be used as the surrogate model in the motor design with little computation and provide great insight into the relationship among motors with different power and dimension. Both finite-element analysis and experiment are carried out to validate the proposed model.
- Open Access
- 16 January 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Energy Conversion
- Vol. 39  (3) , 2008-2017
Hybrid Analytical Model of Permanent Magnet Linear Motor Considering Iron Saturation and End Effect
This paper proposed a hybrid analytical model for predicting the magnetic field distribution of slotted surface-mounted permanent magnet linear motor considering both iron saturation and end effect. In the proposed model, the segmented conformal mapping is developed to reduce the computation time while keeping same accuracy, especially when the end effect significantly affects the motor performance. Then, with the help of the magnetic circuit model in the primary and secondary iron, the magnetic potential drop of iron is obtained from the iterative calculation. The equivalent saturation current is introduced to represent the iron saturation and finally the performance of permanent magnet linear motor can be obtained considering both iron saturation and end effect. The proposed model expands the scope of the analytical models for the analysis of linear motors. The finite element analysis and experimental validation are carried out to show the effectiveness of the proposed model.
- 16 January 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Energy Conversion
- Vol. 39  (3) , 2008-2017
Open AccessHybrid Analytical Model of Permanent Magnet Linear Motor Considering Iron Saturation and End Effect
This paper proposed a hybrid analytical model for predicting the magnetic field distribution of slotted surface-mounted permanent magnet linear motor considering both iron saturation and end effect. In the proposed model, the segmented conformal mapping is developed to reduce the computation time while keeping same accuracy, especially when the end effect significantly affects the motor performance. Then, with the help of the magnetic circuit model in the primary and secondary iron, the magnetic potential drop of iron is obtained from the iterative calculation. The equivalent saturation current is introduced to represent the iron saturation and finally the performance of permanent magnet linear motor can be obtained considering both iron saturation and end effect. The proposed model expands the scope of the analytical models for the analysis of linear motors. The finite element analysis and experimental validation are carried out to show the effectiveness of the proposed model.