Finite control set model predictive control (FCS-MPC) is a control strategy with fast response and a simple and flexible structure. However, when the control plant is complicated such as a multiphase electric machine, the application of FCS-MPC faces clear challenges. This article for the first time investigates the FCS-MPC for a nine-phase open-end winding (OW) permanent magnet synchronous machine, which is powered by nine H-bridge inverters with a common dc bus. First, in order to solve the challenge of substantial iterations in the conventional FCS-MPC, the number of control sets is simplified by reconfiguring the high level in switching states. Then, to eliminate the zero-sequence current caused by the common dc bus, the zero common-mode voltage (CMV) vector is selected. Subsequently, duty-ratio optimization is used to further reduce the available vectors. By the abovementioned measures, the number of iterations is reduced from 19 171 to 18. In order to suppress the harmonic current, the virtual voltage vectors (VVs) are designed. Each VV is synthesized by two zero CMV vectors, which can eliminate all the third and fifth harmonics in the output voltage. In addition, to achieve symmetrical pulsewidth modulation pulse sequences, a general pulse generation method for OW drive systems is proposed. Finally, the control performance of different control sets and harmonic weighting factors are evaluated and compared, and the experimental results have verified the effectiveness of the proposed methods.

The current error is hard to avoid for finite control set model predictive current control (FCS-MPCC) in nine-phase open-end winding permanent magnet synchronous motors. To overcome this problem, an online virtual voltage vector (V $^{3}$ ) synthesis strategy is proposed in this article. First, a group of V $^{3}$ s without harmonic voltage components are designed as the basic vectors for online synthesis. Then, two adjacent basic V $^{3}$ s and a zero vector are used to synthesize a new V $^{3}$ , which can output arbitrary amplitude and phase angle in the fundamental space. The two basic V $^{3}$ s are directly selected from the located sector of the predicted reference voltage vector (RVV), and their duration ratio can be simply calculated according to the angle of the RVV in the sector. In this way, the zero error is realized between the new V $^{3}$ and RVV. Moreover, an online pulse generation algorithm corresponding to the new V $^{3}$ is proposed, which can calculate the symmetrical pulse sequences in real-time for the multiphase OW drive system without the space vector modulator. Finally, experimental results have verified the effectiveness and superiority of the proposed strategy, in comparison to existing FCS-MPCC in multiphase OW motor drive systems.

Due to the large number of candidate voltage vectors, there is heavy calculation burden of finite control set-model predictive control (FCS-MPC) in multi-phase open-winding (OW) motor drive systems. Though low-complexity FCS-MPC schemes exist, they are sensitive to motor parameters. In this article, a robust FCS-MPC with high computational efficiency is proposed for the nine-phase OW-PMSM. Firstly, based on the virtual voltage vector scheme synthesized by three active vectors, harmonic voltage components are eliminated. Then, the deadbeat current control (DBCC) is introduced to calculate the reference voltage vector (RVV), and the optimal voltage vector is determined by the location of the RVV, which successfully reduces the number of iterations in selecting the voltage vectors and improves the computational efficiency. In addition, in order to mitigate the sensitive of the proposed scheme to motor parameters, a parameter extraction method based on a sliding mode observer is designed to enhance the robustness of the FCS-MPC. Moreover, the corrected parameters can also be used for other calculations to achieve satisfactory steady-state performance, such as duty cycle optimization. Finally, experimental results verify the feasibility and superiority of the proposed method.

The heavy computational burden and the complexity in pulse generation based on multivector synthesis represent serious challenges for applying finite control set model-predictive control (FCS-MPC) in multiphase open-end winding (OW) drive systems. In this article, a low-complexity model-predictive control with dead-time compensation is proposed for the nine-phase OW permanent magnet synchronous machine drive system. First, to simultaneously eliminate voltage vectors on the third, fifth, and seventh harmonic planes, three vectors in the same direction are selected to synthesize the virtual vector (VV). In addition, a multivector synthesis algorithm is designed to generate a symmetrical pulse sequence. Then, in order to suppress the harmonic voltage vector caused by the dead time, an additional voltage vector was added to the VV. Finally, the deadbeat principle was introduced to calculate the reference voltage vector, and the optimal voltage vector is determined according to the position of the reference voltage vector, which reduces the computational burden successfully. The proposed method is studied and compared with traditional FCS-MPC schemes. Simulation and experimental results have verified the effectiveness of the proposed method, which reduces the computational burden and complexity and enables the use of FCS-MPC for multiphase OW drive systems.

In this article, an improved conformal mapping (ICM) method based on a complex potential function is proposed. It can improve the calculation speed and accuracy of magnetic fields for surface-mounted permanent magnet synchronous motors (SPMSMs). The eccentric-shaped poles are replaced by equivalent currents, and the improved conformal mapping method is adopted to transform an actual slotted motor air gap to an equivalent rectangular regular slotless air gap. The ICM method improves the speed of calculation because its number of mapping times is less than the traditional conformal mapping (TCM) method. By solving the complex potential generated by the equivalent current in the rectangular regular air-gap region, the air-gap magnetic field of the SPMSM under no-load, armature reaction and loaded conditions can be solved. Then, the no-load back-EMF and loaded torque performance under different load conditions are calculated. The accuracy of the ICM method is verified by finite-element simulation. In addition, the fast speed and high accuracy of the proposed ICM method incorporating the complex potential function for solving the air-gap magnetic field has been demonstrated in comparison to the TCM method with the Hague equation. An eccentric-shaped-pole permanent magnet motor prototype is also built and tested in experiment and the results agree with those calculated by the proposed ICM method.

Nowadays, various analytical models (AMs) have been developed to analyze SPM machines with magnet shaping technique consideration, but their mechanism are all based on division and superposition theory, and numerous repetitive model calculations are required, which greatly attenuates the inherent speed superiority of AMs. In this article, a new fast AM is proposed, which can analytically solve the magnetic field generated from an arbitrary number of currents to obtain the magnetic field solution for shaping PM without any repetitive model calculation. Besides, five existing typical AMs considering shaping PMs are implemented and compared with the new model, viz., radial and tangential PM segmented method, traditional equivalent current method, and conformal mapping models. The comparison study investigates the adjustable model parameters, the dimension of the stiffness matrix, the number of repetitive model calculations, and the actual time consumption. Then, by finite element model validation, the new proposed model can maintain high accuracy and breakneck computational speed simultaneously. Ultimately, the broad application scope and rich added value of new AM are also expounded.