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## Design of three LSPMSM rotor topologies

**Introduction**

The second chapter begins with a discussion about analytical methods used for LSPMSM transient d-q equivalent circuit. Further, the development of analytical models considering asynchronous and steady -state operations of the LSPMSM will be introduced. It will be discussed how to create a magnetic equivalent circuit for each of three rotor configurations selected in Chapter 1: series, radial magnetized and V-type. The obtained value of the air-gap flux will be used in the calculation of the flux linkage and steady-state performances.

The characteristics of each LSPMSM rotor configuration are described with aid of an analytical model which is verified by numerical software presented in a dedicated paragraph.

Finally, a general definition of the optimization problem is discussed and the results in the form of Pareto frontiers for two variants of rotor cage are shown.

### Analytical method of LSPMSM designing

In Chapter 1 it was concluded, that the most appropriate solution for the replying to the thesis objectives consists on the development of a multi-physical generic model is the usage of an analytical model. In this thesis the analytical model is based on d-q equivalent circuit.

The circuit based model is a good solution for evaluating and analyzing the transient and steady state performances of the LSPMSM. In spite of having calculation time extremely reduced, he analytical model have a comparatively low accuracy. For consolidation of the analytical models the F.E. modelling will be done using finite element models. In this thesis a specialized FEM software Ansoft/Maxwell is used for this purpose.

**Park transformation and transient d-q equivalent circuit of LSPMSM**

In electrical engineering, Park’s transformation is a mathematical direct–quadrature– zero (dq0) transformation that rotates the reference frame of three-phase systems in an effort to simplify the analysis of three-phase circuits.

The dqo transformation in matrix form applied to any three-phase quantities (e.g. voltages, currents, flux linkages, etc.) is given by eq. (2. 1)

When designing an LSPMSM there are two options available. The most popular one found in literature is an IM rotor retooling [SOULARD_02]. Since an LSPMSM can operate with the same stator and winding arrangement as an IM, the IM rotor can be replaced with an LSPMSM rotor [HENDERSHOT_10], [PYRHONEN_08], [DING_11], [HUNG_08], [TAKAHASHI_10]. The simplest way of the rotor modification is the embedding of PMs into the rotor core or onto its surface. This option expels the necessity of machine sizing from zero and permits to start the design process from a well-developed IM sizing procedure. The second option is to do a complete machine design like it has been demonstrated in [SORGDRAGER_14].

In order to reduce the number of discrete parameters and, hence, to limit the computation time, the design algorithm implemented to the LSPMSM models is based on the first method. presents the LSPMSM design procedure proposed in this thesis.

As it has already been mentioned above, for economic reasons, the stator and windings of the LSPMPM are identical to the induction motor of the same power used at present in the electrical applications [SOULARD_02]. As the air-gap flux density contains a large third harmonic due to the rectangular magnet flux density shape the stator winding is star-connected in order to avoid the presence of this third harmonic into the line currents.

In the first step of designing, the data concerning the power (see Fig.2. 2) and the stator of the motor is to be entered. In the same time a user has to choose a configuration of the PMs into the rotor.

The second step is the IM sizing for the same power range. At this stage the same design methodology as for an IM can be applied. This allows to define the stator and winding geometry and the number of rotor bars and to choose a structure of the squirrel cage for a first approximation that gives the value of the rotor cage resistance and the level of saturation in rotor teeth.

As soon as the geometry of the rotor and PMs is known, the d- and q-axis reactances and and the no-load EMF can be calculated either analytically or computed using FEM. Thanks to these parameters and taking into account the braking torque induced by the PMs, the start of the LSPMSM can be simulated. If the motor is not able to start, the designer has to go back either to the Stage 2 in order to change the rotor squirrel cage and, hence, to increase the starting torque or to the Stage 3 to resize the PMs and to reduce the breaking torque.

After the successful start of the LSPMSM, performances and steady-state characteristics are calculated and used for finding the optimal solution. Then, the design procedure must be repeated starting from the Stage 2. Every stage of the diagram will be more detailed below.

#### Algorithm of IM sizing

The LSPMSM contains both IM and PMSM component parts which can be designed separately. As it has been discussed in the previous chapters, once both rotor designs are done they can be combined into one rotor. According to Fig.2. 2, the first step for the design procedure is the sizing of an IM of the same power range that it is required by the specification. The slot number combinations follow the same concerns as in induction motors. Besides, it is generally favorable to have the number of rotor slots divisible by the number of poles, so that the poles are symmetric.

The workflow summarizing the procedure of IM sizing is outlined in Fig.2. 3. Complete description of the analytical approach for IM and an example of calculations are presented in Appendix B. This approach can be applied for the design of a quite large range of IM. It was compiled using the methodologies proposed in [BOLDEA_10], [KOPILOV_86], [PYRHONEN_08].

Eq. (2. 31) shows that the period of the reluctance torque is one half of that of the PM generated torque. Fig.2. 8 proves that an interior magnet type LSPMSM can achieve higher torque than a surface mounted LSPMSM which does not have any reluctant torque component. However, the appearance of the reluctance torque does not mean that the interior magnet type can have higher power density than surface mounted LSPMSM because the magnet flux linkage in LSIPMSM is not the same as that in the surface mounted LSPMSM with the same magnet volume. Eq (2. 32) is another form of the torque equation (2. 31) and suggested by [HENDERSHOT_10] and showing that the total torque of a LSPMSM is increased due to the saliency of the rotor.

After every section devoted to one of three rotor topologies, the results of analytical models are compared with the results issued from a commercial software and providing from a finite element modeling.

**LSPMSM with radial magnetic circuit structure**

As it has already been discussed in the previous paragraph, the flux linkage and reluctance are the key parameters to determine the steady-state characteristics of a LSPMSM. Using the magnetic equivalent circuit is the most common method for the determination of these parameters [HENDERSHOT_10], [FODOREAN_09], [HEIKKILA_02], [CARPENTER_12].

**Table of contents :**

**Acknowledgments **

Résumé détaillé de la thèse

Introduction

**1 Context of the thesis **

1.1. Introduction

1.2. Environmental constraints and energy development

1.2.1. Global warming and its consequences

1.2.2. Part played by greenhouse gases in climate regulation

1.2.3. Global energy development

1.3. New efficiency standards for AC motors as measures against climate change

1.3.1. European Union plan on climate change

1.3.2. Shares of world electricity consumption by different sectors

1.3.3. New standard on efficiency classes for low voltage AC motors

1.4. Choice of an efficient electric motor for constant-speed application

1.4.1. Run-down on motor market

1.4.2. Induction motors

1.4.3. Permanent magnet synchronous motor

1.4.4. Line-start permanent magnet synchronous motor

1.4.5. Comparative technico-economic study of LSPMSM and IM

1.5. LSPMSM Design Challenges

1.5.1. Demagnetization

1.5.2. Pulsating torques

1.5.3. Braking torque

1.5.4. Manufacturing and sizing

1.6. Choice of an efficient LSPMSM rotor topology

1.6.1. Variants of LSPMSM rotor

1.6.2. Interior-magnet LSPMSM vs. surface-magnet LSPMSM

1.6.3. Choice of an efficient ILSPMSM topology

1.7. Choice of design and modeling techniques

1.7.1. Numerical methods

1.7.2. Analytical methods

1.7.3. Semi-analytical/ semi-numerical methods

1.7.4. Choice of method

1.8. Conclusion

1.9. References

**2 Design of three LSPMSM rotor topologies **

2.1. Introduction

2.2. Analytical method of LSPMSM designing

2.2.1. Park transformation and transient d-q equivalent circuit of LSPMSM

2.2.2. Study of LSPMSM asynchronous operation

2.2.3. Steady-State Model for the LSPMSM design

2.2.4. Analytical calculation of electromagnetic parameters

2.3. Optimization of LSPMSM

2.3.1. Organization of the design process

2.3.2. Optimization Problem

2.3.3. Optimization Technique

2.3.4. Functionality of software DEMO-LSPM

2.3.5. Results of optimization technique in the form of Pareto frontier for two variants of rotor cage

2.3.6. Advantage of rotor bar reduction

2.4. Conclusion

2.5. References

**3 Prototyping and experimental results **

3.1. Introduction

3.2. LSPMSM prototyping

3.3.1. Sizing of two LSPMSM rotors

3.3.2. Search of the optimal rotor configuration for the LSPMSM with V-type magnetic circuit structure

3.3.3. Dynamic analysis of the designed LSPMSM with V-type magnetic circuit structure

3.3.4. Demagnetization of the permanent magnets

3.3.5. Search of the optimal rotor configuration for the LSPMSM with series magnetic circuit structure

3.3.6. Dynamic analysis of the designed LSPMSM with series magnetic circuit structure

3.3.7. Demagnetization of the permanent magnets

3.3.8. Realization of the prototypes

3.3. Experimental results

3.3.1. Test strategy

3.3.2. Validation of asynchronous part in LSPMSM design

3.3.3. Validation of synchronous part in LSPMSM design

3.4. Thermal study

3.5. Conclusion

3.6. References

**Conclusion**