Georges Barakat

Quasi-3-D analytical modeling of the magnetic field of an axial flux permanent-magnet synchronous machine

A quasi-three-dimensional (3-D) analytical model of the magnetic field in an axial flux permanent-magnet synchronous machine is presented. This model is derived from an exact two-dimensional analytical solution of the magnetic field extended to the 3-D case by a simple and effective radial dependence modeling of the magnetic field. The obtained quasi-3-D solution allows rapid parametric studies of the air-gap magnetic field. Then, analytical modeling of the cogging torque is presented. It is based on the obtained quasi-3-D analytical solution. Results issued from the proposed model in the air gap are compared with those stemming from a 3-D finite-element method simulation as well as with prototype measured values.

Two-Dimensional Exact Analytical Solution of Armature Reaction Field in Slotted Surface Mounted PM Radial Flux Synchronous Machines

This paper presents an analytical solution for prediction of the armature reaction magnetic field in slotted surface mounted permanent magnet radial flux synchronous machines. This technique is used in the case of internal and external rotor radial-field machines. The magnetic field expressions are developed in both slots regions and magnetic airgap region leading to an exact calculation of the effects of slotting on the airgap magnetic quantities. Results from this analytical model are compared to corresponding finite element analyses. This analytical model is then used to estimate the self and mutual inductances.

Analytical Prediction of Eddy-Current Loss in Armature Windings of Permanent Magnet Brushless AC Machines

This paper presents an analytical model for prediction of eddy current loss in armature windings of permanent magnet brushless AC machines. The developed model can either be used in the case of internal or external rotor radial-field machines topologies. First, a 2-D exact analytical solution of magnetic field distribution in an actual geometry of slotted surface mounted PM radial flux synchronous machines is established. It involves solution of Maxwells equations in slots, airgap and PMs region. Then, magnetic vector potential solution in the slots is used for prediction of resistance limited eddy current in armature windings. Finally, results from this analytical model are compared to corresponding finite element analyses.

Modeling and optimal sizing of hybrid renewable energy system

This paper presents a new methodology of sizing optimization of a stand-alone hybrid renewable energy system. The developed approach makes use of a deterministic algorithm to minimize the life cycle cost of the system while guaranteeing the availability of the energy. Firstly, the mathematical modeling of the principal elements of the hybrid wind/PV system is exposed showing the main sizing variables. Then, the deterministic algorithm is presented and implemented to minimize the objective function which is equal to the life cycle cost of the hybrid system and finally, the obtained results are exposed and discussed.

Analytical Modeling of the Open-Circuit Magnetic Field in Axial Flux Permanent-Magnet Machines With Semi-Closed Slots

This paper presents a multi-slice analytical model for prediction of the open-circuit magnetic field in slotted semi-closed permanent-magnet axial flux synchronous machines. The technique is based on 2-D exact solution of the Maxwells equations using the separation of variables method. The magnetic field expressions are developed in slots regions, slot opening regions, magnetic air gap regions, and permanent magnet regions leading to an exact calculation of the slot effects on the air gap magnetic field. The model is established considering that ferromagnetic parts are infinitely permeable, and end effects at inner and outer radii are neglected. The open circuit machines global quantities (electromotive force and cogging torque) are then deduced from the local magnetic field expressions. Finally, the accuracy of the presented analytical model is validated by comparing its results to corresponding finite-element analyses for two different axial flux machines.

Comparison of Open Circuit Flux Control Capability of a Series Double Excitation Machine and a Parallel Double Excitation Machine

Double excitation synchronous machines combine permanent-magnet (PM) excitation with wound field excitation. The goal behind the principle of double excitation is to combine the advantages of PM-excited machines and wound field synchronous machines. These machines can constitute an energy-efficient solution for vehicle propulsion. This paper presents a comparison of the open circuit flux control capability of two structures of double excitation synchronous machines. First, a review of the state of the art of double excitation machines is presented. Then, the structures of these two machines are presented: one is a series double excitation synchronous machine and the other is a parallel double excitation synchronous machine. Finally, the open circuit flux control capabilities of both structures are compared.

Optimal sizing of stand-alone hybrid wind/PV system with battery storage

In this paper, a new methodology developed to design a hybrid wind/photovoltaic (wind/PV) system, is presented. Based on an optimization process using a deterministic algorithm, the developed methodology helps the authors to obtain the optimal number and type of PV panels, wind turbines and storage units ensuring that the system total cost is minimized while guaranteeing the permanent availability of energy to cover the load energy requirements. The hybrid system configuration and modeling are presented and the used deterministic algorithm (DIRECT algorithm) is described and implemented in MATLAB environment to optimize the hybrid wind/PV system.

Analytical Modeling of Magnetic Field in Surface Mounted Permanent-Magnet Tubular Linear Machines

We present an exact 2-D analytical model for predicting the magnetic field in idealized structures of surface mounted permanent-magnet tubular linear machines that account for the stator slotting effect. The open-circuit and armature reaction magnetic field distributions are analytically derived and compared to finite-element analyses. The on-load magnetic field calculation is based on the superposition of the component fields due to permanent magnets and armature field reaction. Our model can be advantageously used for the analysis and design of a class of linear tubular machines.

Original article: Overview of analytical models of permanent magnet electrical machines for analysis and design purposes

Generally, accurate modelling of electrical machines requires the use of finite-element method. However, FE analysis is too time consuming, especially at firsts design stages, from the point of view of engineers working in R&D departments in the electrical machine industry. To reduce pre-design stages duration, analytical models are often preferred. Two types of analytical models are often used: magnetic equivalent circuits (MEC) and analytical models based on the formal solution of Maxwells equations in constant permeability regions. However, MEC method is not as generic as the finite element method. In fact, even in the case of a given structure geometry, MEC method has to be adapted if the geometric parameters vary in a large scale. Analytical models based on the formal solution of Maxwells equations help overcome aforementioned problem. This paper is intended as a tutorial overview based on a review of the state of the art, describing recent developments in the field of analytical modelling of permanent magnet machines.

Analytical Modeling of Open Circuit Magnetic Field in Wound Field and Series Double Excitation Synchronous Machines

We describe an exact 2-D analytical model for predicting the open circuit magnetic field in idealized structures of wound field and series hybrid excitation permanent-magnet synchronous machines. This technique can be used for either internal or external rotor radial-field machine topologies. It involves analytical solution of Maxwells equations in stator and rotor slots and annular air-gap/magnet regions. We compare results from this analytical model to corresponding finite-element analyses. We then use it to estimate the cogging torque, induced back-electromotive force, and to study the effects of rotor skewing.