We present an analytical method for calculation of no-load magnetic field distribution in the slotted air gap of a surface permanent-magnet (PM) motor with radial or parallel magnetization. The method introduces the notion of complex relative air-gap permeance, calculated from the conformal transformation of the slot geometry, to take into account the effect of slotting. As a result, an accurate solution of both radial and tangential components of the flux density can be obtained which shows excellent agreement with the results of finite-element simulations. As an example of the effectiveness of the model, we present calculations of the back electromotive force and the cogging torque waveforms in a surface PM motor.

Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance

Artificial intelligence (AI) techniques, particularly the neural networks, are recently having significant impact on power electronics and motor drives. Neural networks have created a new and advancing frontier in power electronics, which is already a complex and multidisciplinary technology that is going through dynamic evolution in the recent years. This paper gives a comprehensive introduction and perspective of neural network applications in the intelligent control and estimation for power electronics and motor drives area. The principal topologies of neural networks that are currently most relevant for applications in power electronics have been reviewed including the detailed description of their properties. Both feedforward and feedback or recurrent architectures have been covered in the description. The application examples that are discussed in this paper include nonlinear function generation, delayless filtering and waveform processing, feedback signal processing of vector drive, space vector PWM of two-level and multilevel inverters, adaptive flux vector estimation, and some of their combination for vector-controlled ac drive. Additional selected applications in the literature are included in the references. From the current trend of the technology, it appears that neural networks will find widespread applications in power electronics and motor drives in future

Neural Network Applications in Power Electronics and Motor Drives—An Introduction and Perspective

The paper presents an accurate analytical subdomain model for computation of the open-circuit magnetic field in surface-mounted permanent-magnet machines with any pole and slot combinations, including fractional slot machines, accounting for stator slotting effect. It is derived by solving the field governing equations in each simple and regular subdomain, i.e., magnet, air-gap and stator slots, and applying the boundary conditions to the interfaces between these subdomains. The model accurately accounts for the influence of interaction between slots, radial/parallel magnetization, internal/external rotor topologies, relative recoil permeability of magnets, and odd/even periodic boundary conditions. The back-electromotive force, electromagnetic torque, cogging torque, and unbalanced magnetic force are obtained based on the field model. The relationship between this accurate subdomain model and the conventional subdomain model, which is based on the simplified one slot per pole machine model, is also discussed. The investigation shows that the proposed accurate subdomain model has better accuracy than the subdomain model based on one slot/pole machine model. The finite element and experimental results validate the analytical prediction.

An Accurate Subdomain Model for Magnetic Field Computation in Slotted Surface-Mounted Permanent-Magnet Machines

Cogging torque in permanent-magnet machines causes torque and speed ripples, as well as acoustic noise and vibration, especially in low speed and direct drive applications. In this paper, a general analytical expression for cogging torque is derived by the energy method and the Fourier series analysis, based on the air gap permeance and the flux density distribution in an equivalent slotless machine. The optimal design parameters, such as slot number and pole number combination, skewing, pole-arc to pole-pitch ratio, and slot opening, are derived analytically to minimize the cogging torque. Finally, the finite-element analysis is adopted to verify the correctness of analytical methods.

Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines

Load modeling has significant impact on power system studies. This paper presents a review on load modeling and identification techniques. Load models can be classified into two broad categories: 1) static and 2) dynamic models, while there are two types of approaches to identify model parameters: 1) measurement-based and 2) component-based. Load modeling has received more attention in recent years because of the renewable integration, demand-side management, and smart metering devices. However, the commonly used load models are outdated, and cannot represent emerging loads. There is a need to systematically review existing load modeling techniques and suggest future research directions to meet the increasing interests from industry and academia. In this paper, we provide a thorough survey on the academic research progress and industry practices, and highlight existing issues and new trends in load modeling.

Load Modeling—A Review

This paper presents an analytical method of modeling permanent magnet (PM) motors. The model is dependent only on geometrical and materials data which makes it suitable for insertion into design programs, avoiding long finite element analysis (FEA) calculations. The modeling procedure is based on the calculation of the air gap field density waveform at every time instant. The waveform is the solution of the Laplacian/quasi-Poissonian field equations in polar coordinates in the air gap and takes into account slotting. The model allows the rated performance calculation but also such effects as cogging torque, ripple torque, back-EMF form prediction, some of which are neglected in commonly used analytical models.

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Analytical model for permanent magnet motors with surface mounted magnets

Phase windings of switched reluctance machines are modeled by a nonlinear inductance and a resistance that can be estimated from standstill test data. During online operation, the model structures and parameters of SRMs may differ from the standstill ones because of saturation and losses, especially at high current. To model this effect, a damper winding is added into the model structure. This paper proposes an application of artificial neural network to identify the nonlinear model of SRMs from operating data. A two-layer recurrent neural network has been adopted here to estimate the damper currents from phase voltage, phase current, rotor position, and rotor speed. Then, the damper parameters can be identified using maximum likelihood estimation techniques. Finally, the new model and parameters are validated from operating data.

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Neural network-based modeling and parameter identification of switched reluctance motors

Proper load models are essential to power system stability analysis. This paper proposes a methodology for the development of neural network (NN) based composite load models for power system stability analysis. A two-step modeling procedure is proposed. First knowledge is acquired from a test bed of power systems based on detail load models of a bus to the distribution level. Then, the test bed data is used to develop a composite NN model. The developed NN model is updated based on measurements. A case study on a power inverter controling an induction motor load is presented.

Composite neural network load models for power system stability analysis

In this paper, we propose robust nonlinear force controllers for a switched-reluctance-motor (SRM) electromechanical brake system which is a promising replacement for hydraulic brakes in the automotive industry. A torque-level control law is first designed using robust backstepping. The backstepping proceeds via the force and the velocity states. The voltage-level control laws are obtained from the virtual control law for the torque using either an additional step of backstepping incorporating a novel voltage-commutation scheme or a torque-ripple-minimizing algorithm based on a design of turn-on/turn-off angles and torque factors. The controllers do not require knowledge of the motor mechanical parameters and the functional forms of the relationships among the motor position, the brake force, and the motor load torque. A detailed model of the motor including current-dependent inductance coefficients is used. The load exerted on the motor by the caliper may be modeled as a spring; however, the actual load model is taken to be an unknown nonlinear function of position to allow for uncertainties in the model. Hence, the developed controllers work for a wide variety of loads including brake systems. Moreover, the controllers provide significant robustness to uncertainty in the inductances and address practical current and voltage constraints. The performance of the proposed controllers is demonstrated through both simulation and experimental studies.

Robust Force Control of an SRM-Based Electromechanical Brake and Experimental Results

In this paper, we propose a robust nonlinear force controller for a switched reluctance motor (SRM) electromechanical brake system which is a promising replacement for hydraulic brakes in the automotive industry. A detailed model of the motor including current dependent inductance coefficients is used. The load exerted on the motor by the caliper may be modeled as a spring; however, the actual load model is taken to be an unknown nonlinear function of position to allow for uncertainties in the model. Hence, the developed controller works for a wide variety of loads including brake systems. The controller is designed using backstepping and incorporates a novel voltage commutation scheme. The controller does not require knowledge of the mechanical parameters of the motor and the functional forms of the relationships among the motor position, the brake force, and the motor load torque. Moreover, the controller provides significant robustness to uncertainty in the inductances. Furthermore, practical current and voltage constraints are addressed. The performance and robustness of the controller are demonstrated through simulation studies.

Wenzhe Lu

Papers

Analytical model for permanent magnet motors with surface mounted magnets

Neural network-based modeling and parameter identification of switched reluctance motors

Composite neural network load models for power system stability analysis

Robust Force Control of an SRM-Based Electromechanical Brake and Experimental Results

A Robust Force Controller for an SRM Based Electromechanical Brake System