Ahmed Hemeida

Analytical modeling of surface PMSM using a combined solution of Maxwell’s equations and magnetic equivalent circuit

This paper presents a complete analytical model for surface-mounted permanent magnet synchronous machines (PMSMs). A new simple and fast technique was developed to obtain accurate results in the calculation of machine parameters electromotive force (EMF), torque, and losses. This technique is based upon the combined solution of two models. The first model generates an exact solution of Maxwells equations in the air gap area applied to a very simple geometry. The second model gives an accurate solution in the detailed parts with complex geometry, based on a magnetic equivalent circuit (MEC) to obtain fast and accurate results in a simple way. The machines global quantities are then obtained and validated using the results of a finite element model (FEM) for different loading conditions and geometries. Compared with FEM, the proposed combined solution has the advantage of flexibility in the geometrical machine parameters, significantly less CPU time and an accuracy for the considered PMSM up to 4.85% in the EMF, 4.41% in the torque, and 4.44% in the iron losses. Finally, the relation between grid refinement in the MEC (coarse or fine grid of reluctances) and accuracy is pointed out, showing that the EMF can be accurately computed with a rather coarse grid, while accurate loss computation requires a fine grid.

A computationally efficient method to determine iron and magnet losses in VSI-PWM fed axial flux permanent magnet synchronous machines

For electrical machines with a 3-D geometry, such as axial flux permanent magnet machines, the computation of iron and magnet losses in the case of pulsewidth modulation (PWM) supply could be performed by a transient 3-D finite element model (FEM) coupled with an electrical circuit. To reduce the CPU time, in this paper, these losses are computed with acceptable accuracy without using a 3-D transient FEM. The multislice technique is used with a 2-D static FEM, combined with a state space model of the machine. A Preisach hysteresis model is considered to evaluate the iron loss during minor loops. The loss in the electrical steel and in the magnets is evaluated for several PWM frequencies as well as for different segmentations of the magnets.

Comparison of Methods for Permanent Magnet Eddy-Current Loss Computations With and Without Reaction Field Considerations in Axial Flux PMSM

This paper presents an analytical solution of the eddy currents in the permanent magnets (PMs) in the axial flux PM synchronous machine using a coupled solution of Maxwells equations and electric circuit network. This is based on calculating the axial field in an accurate way on the surface of the PM. This method is able to consider the effect of armature field and slots. The eddy currents are obtained by imposing this solution on the PM which is modeled by a simple electric network. This network is composed of simple resistances and inductances. The inductances are used to model the reaction field effect of the eddy currents flowing through the PM and also the skin effect. To show this effect, the machine is excited with different sources at different speeds. In addition, a variant of the model is made that neglects the inductances, in order to show in which conditions this low-frequency approximation is acceptable. It is concluded from this paper that inclusion of the reaction field is necessary when the machine is excited by a pulsewidth modulated (PWM) current, while for a sinusoidal excitation, the reaction field effect has minor contributions to the total eddy losses. In addition, the reaction field has major influence at higher speeds rather than lower speeds for PWM injection. In conclusions, for a preliminary design, the resistance model without the reaction field computation would be enough for the calculation of the PM losses. The circuit model is also capable of obtaining the solution with PM segmentation. In this paper, different PM segments were studied from the circuit model and the finite-element (FE) model point of view. Compared with the FE model, the circuit model has the advantage of flexibility in geometrical machine parameters, less CPU time, and accurate results for the PM losses up to 10%.

Analytical modeling of Eddy current losses in axial flux PMSM using resistance network

This paper presents an analytical modeling of eddy current losses of an Axial Flux Permanent Magnet Synchronous Machine (AFPMSM) using coupled solution of Maxwells equations and resistance network. The idea is based on calculating the flux density in an accurate way in the air gap area and on the magnet surface taking into account the effect of armature field and slotting effect. The resistance network for the magnet is then reconstructed by dividing it into a number of nodes and branches. The sources in the resistance network are based on the time derivative of the flux density on the permanent magnet (PM) surface. The field solution is analyzed in the frequency domain and the magnetic resistance network is solved for each frequency. Compared to the Finite Element Method (FEM), the analytical model has the advantage of flexibility in geometrical machine parameters, less CPU time, and accurate results.

Comparison of Three Analytical Methods for the Precise Calculation of Cogging Torque and Torque Ripple in Axial Flux PM Machines

A comparison between different analytical and finite-element (FE) tools for the computation of cogging torque and torque ripple in axial flux permanent-magnet synchronous machines is made. 2D and 3D FE models are the most accurate for the computation of cogging torque and torque ripple. However, they are too time consuming to be used for optimization studies. Therefore, analytical tools are also used to obtain the cogging torque and torque ripple. In this paper, three types of analytical models are considered. They are all based on dividing the machine into many slices in the radial direction. One model computes the lateral force based on the magnetic field distribution in the air gap area. Another model is based on conformal mapping and uses complex Schwarz Christoffel (SC) transformations. The last model is based on the subdomain technique, which divides the studied geometry into a number of separate domains. The different types of models are compared for different slot openings and permanent-magnet widths. One of the main conclusions is that the subdomain model is best suited to compute the cogging torque and torque ripple with a much higher accuracy than the SC model.

Analytical Model for Combined Study of Magnet Demagnetization and Eccentricity Defects in Axial Flux Permanent Magnet Synchronous Machines

A time-harmonic analytical model is presented for a combined study of demagnetization and rotor eccentricity in single-stator double-rotor axial flux permanent magnet synchronous machines (AFPMSM). Demagnetization defects are modeled by scaling the magnetization “square wave” by magnetization factors for each individual magnet on both rotors. Static, dynamic, and mixed rotor eccentricities are modeled using a permeance function. The original contribution of the model is that asymmetrical defects in the two air gaps of the machine can be described with acceptable accuracy and limited additional calculation time. The model is validated with a finite element method and experiments in both healthy and defected operations. Because the model has a short computation time, it is useful for real-time condition monitoring of any AFPMSM with double air gap and either concentrated or distributed windings.

Stator heat extraction system for axial flux yokeless and segmented armature machines

The torque density of electric motors strongly depends on the performance of the cooling system. In the axial flux yokeless and segmented armature machine, cooling inherently occurs through self-ventilation by both rotor discs. Nevertheless, an independent cooling system remains necessary for most applications. In the axial flux yokeless and segmented armature machine, the individual stator cores with concentrated windings are potted in the stator housing using an epoxy resin. These epoxy resins are relatively bad thermally conductive, and therefore, limit the heat transfer to the surface of the machine. Therefore, radially inward heat extraction fins are introduced in this paper. These fins provide an excellent thermal conduction path from the windings to the stator surface, where they can be abducted by conventional cooling techniques such as forced air or water jacket cooling. The focus of this paper is on the study of the radially inward heat extraction fins using thermal finite element modelling as well as experimental validation on a 4kW axial flux yokeless and segmented armature machine stator. At steady state and for the rated losses, the temperature difference between the winding and stator housing is less than 10 degrees Celcius.

Analytical modeling of axial flux PM machines with eccentricities

In this paper, an analytical quasi three-dimensional method is used to model an axial flux permanent magnet (AFPM) machine with various eccentricities. AFPM machines (AFPMMs) have various advantages but they are sensitive to geometrical imperfections for manufacturing aspect. The main aim of this paper is to propose a general analytical model to analyze the AFPMMs with various types of eccentricities. The radial and tangential magnetic flux densities in the air gap under healthy condition are obtained via combination of Maxwell’s equations and Schwarz-Christoffel (SC) mapping firstly. Next, in order to investigate the eccentricities, equations for air gap length and radii are deduced. The back electromotive force (EMF) is calculated and compared with those from healthy condition and finite element (FE) analysis, respectively. The results show that the analytical predictions agree well with the FE results. Moreover, using this method has a significantly less time consuming than the 3D FM simulation process, which is a great advantage of this method. Finally, the analytical model is verified via experimental results.

An optimal design of a 5MW AFPMSM for wind turbine applications using analytical model

In this paper an optimized design procedure for the axial flux permanent magnet synchronous machines (AFPMSMs) for large scale wind turbines is introduced. In this paper, the design for a 5MW wind turbine AFPMSM is introduced, analyzed, and validated. In this design, an efficient analytical model is used that is capable of obtaining all the electromagnetic parameters in a very accurate way. The structural mass is the most dominant mass in large wind turbines. Therefore, inclusion of this mass in the design is done. The effect of using multi-stages on the electromagnetic performance, the cost, and the the total mass of the machine is also introduced. Two types of structural mass are introduced. One with solid disk structure and another machine with ring type structure. The comparison of both structures on the electromagnetic performance is studied. Moreover, a comparison of different available market generators is proposed. In this comparison, the ring type AFPMSM has proven great robustness in terms of cost and mass to torque ratio. A complete 3D finite element (FE) validation has proven the robustness of the analytical model.