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

An induction motor is the most frequently used electric machine in high-performance drive applications. Control schemes of such drives require an exact knowledge of at least some of the induction motor parameters. Any mismatch between the parameter values used within the controller and actual parameter values in the motor leads to a deterioration in the drive performance. Numerous methods for induction machine on-line and off-line parameter estimation have been developed exclusively for application in high-performance drives. This paper aims at providing a review of the major techniques used for the induction motor parameter estimation. The paper is illustrated throughout with experimental and simulation examples related to various parameter estimation techniques.

A review of RFO induction motor parameter estimation techniques

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

This paper proposes a coaxial magnetic gear that offers higher torque density, lower cogging torque, and lower iron losses than its counterparts. The key is to newly employ a Halbach permanent-magnet (PM) array to constitute the PM poles in the inner rotor and a partial Halbach array (two segments per pole) for the outer rotor. The corresponding magnetic field distributions, torque transmission, and torque ripples are analytically discussed. Then, the corresponding performances are quantitatively assessed by using the finite-element method.

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A Coaxial Magnetic Gear With Halbach Permanent-Magnet Arrays

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

Field orientation techniques without flux measurements depend on the parameters of the motor, particularly on the rotor resistance or rotor time constant (for rotor field orientation). Since these parameters change continuously as a function of temperature, it is important that the value of rotor resistance is continuously estimated online. A fourth-order sliding-mode flux observer is developed in this paper. Two sliding surfaces representing combinations of estimated flux and current errors are used to enforce the flux and current estimates to their real values. Switching functions are used to drive the sliding surfaces to zero. The equivalent values of the switching functions (low-frequency components) are proven to be the rotor resistance and the inverse of the rotor time constant. This property is used to simultaneously estimate the rotor resistance and the inverse of the time constant without prior knowledge of either the rotor resistance or the magnetizing inductance. Simulations and experimental results prove the validity of the proposed approach

http://www.diegm.uniud.it/petrella/Azionamenti%20Elettrici%20II/Tesine/04118391%20-%20Proca%20et%20al.%20-%20Sliding-Mode%20Flux%20Observer%20With%20Online%20Rotor%20Parameter%20Estimation%20for%20Induction%20Motors.pdf

Sliding-Mode Flux Observer With Online Rotor Parameter Estimation for Induction Motors

A three-phase squirrel-cage induction motor is used as the propulsion system of an electric vehicle (EV) The motor is controlled at different operating conditions using a direct torque control (DTC) technique combined with a new switching pattem producing low harmonics The operating flux of the motor is chosen optimally for both loss minimization and good dynamic response Since speed estimation is sensitive to rotor resistance variations, the rotor resistance value is calculated and modified in real-time continuously Simulation and experimental results show that the proposed DTC is able to follow the reference speed (which may be only input reference of the system) with a reasonable dynamic and relatively low error

/pdf/sensorless-direct-torque-control-of-induction-motors-used-in-2gaoz4vd4m.pdf

Sensorless direct torque control of induction motors used in electric vehicle

The parameters of the induction motor model vary as operating conditions change. Accurate knowledge of these parameters and their dependency on operating conditions is critical for optimal field oriented control. This paper presents a systematic approach to modeling an induction motor considering operating conditions. All parameters are assumed to vary as a function of the operating conditions. The parameters are estimated from transient data using a constrained optimization algorithm. The parameters are mapped to the operating conditions using polynomial functions and artificial neural networks. The model is validated for both steady state and transient conditions.

Identification of Variable Frequency Induction Motor Models from Operating Data

This paper presents an analytical method of modeling permanent magnet motors. The model is dependent only on geometrical and materials data making it suitable for insertion into design programs, avoiding long finite element analysis. Modeling is based on the calculation of the air gap field density waveform at every time instant. 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.

A.B. Proca

Papers

Analytical model for permanent magnet motors with surface mounted magnets

Sliding-Mode Flux Observer With Online Rotor Parameter Estimation for Induction Motors

Sensorless direct torque control of induction motors used in electric vehicle

Identification of Variable Frequency Induction Motor Models from Operating Data

Analytical model for permanent magnet motors with surface mounted magnets