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Modeling and simulation of the switched reluctance machine
Introduction
As mentioned in the first chapter this thesis studies the SR rotating machine with radial flux [1]. As name implies the functioning of the machine is linked to a commutation sequence, provided through a full-bridge or half-bridge inverter. Because one of the aspects of this thesis is based on optimizing the SR machine an analytical model that considers the saturation effect and the machine geometry must be provided. Therefore, in this chapter the analytical model of this machine is developed along with a modality of computing the maximum and minimum inductance based on the magnetic flux lines. Finally the entire system implemented in Matlab/Simulink environment is presented together with the importance of the commutation angles.
Topologies of switched reluctance machine and associated power electronic converter
Classical SR machine topologies
For SR machine the number of stator poles and rotor teeth is chosen so that the sum of electromagnetic torque produced by each phase is never zero. Hence, the number of stator and rotor poles will never be equal and they can be calculated as follows:
Over the years several configurations have been proposed in literature; 3D views of different configurations with an increased number of stator teeth are presented in fig. 2.1. In general, multiphase SR machine benefits by reduction of the ripple torque, but exhibits higher manufacturing costs, since it requires a larger amount of electronic switching devices in the associated power converter for its operation. In order to have the guaranty for starting in both motion directions, at least three phases are required [2].
Novel SR machine topologies
For the SR machine topologies in which the number of rotor teeth are greater than the number of stator poles [3], it is possible to introduce a new relationship, i.e. =2 −2 (2.2) when > 4.
One results the configuration of fig. 2.2 (left side) with 6 stator poles and 10 rotor teeth. For this configuration the operation principle is simple and similar to classical topologies. In this case, if one rotor tooth is at 12o away and another is at 24o away, the one that is nearest with the energized stator pole will be attracted. Therefore the rotation will be continuous and without dead zones. According to [4] and [5] this configuration exhibits increased electro-magnetic torque density and smaller torque pulsations.
The three-phase SR machine having the configuration inspired from [6] and presented in fig. 2.2 (right side), i.e. 6 stator and 8 rotor teeth will be the SR machine topology studied in this thesis. The reasons for this choice are the advantages of larger available stator-windings space, higher average electromagnetic torque, and lower ripple torque due to the increased number of strokes compared to the 6 stator-pole /4 rotor-tooth topology [7].
Topologies of SR machine associated power electronic converters
Three-phase asymmetric half-bridge power converter
The commonly used power electronic converter associated to SR machine is of three-phase half-bridge topology (fig. 2.3). A bridge of this converter is based on two controllable IGBTs and two diodes used for demagnetization.
This type of converter provides the most control flexibility and fault tolerance. Using this converter, each phase can be supplied independently with positive and negative DC voltage. This independence between phases makes the converter reliable during fault conditions. If the machine works in motor operation mode during regenerative breaking the converter provides a maximum capacity of energy recovery [8].
When a three phase SR machine with 6 stator poles and 8 rotor teeth (6/8 SR machine) is considered, the electronic commutation pattern is that presented in the right part of fig. 2.3. Considering that the rotor is aligned with stator phase C, the operating principle is simple, as it is done on the positive slope of phase inductance (motor operation mode). In this case, stator phase A is in conduction, and transistors 1 and 2 are conducting; when the rotor reaches the aligned position, transistors 1 and 2 are blocked, and demagnetization is realized through diodes 1 and 2. The advantage of using this power electronic converter in this case is given by the possibility of prolonging the excitation of phase A more than one period ( = 2 ⁄ ∙ ) or continuing the supply of the second phase before rotor reaches the aligned position due to the phase independence.
Miller power converter
Another power converter topology associated to SR machine is Miller converter (fig.2.5). It has the advantage of requiring less (only four) power devices compared to the three-phase half-bridge asymmetric converter.
Its structure is built starting from a three-phase half-bridge inverter, the lower part being kept and the upper part being replaced by only one IGBT. The phase conduction period is provided by transistors 2 to 4 (fig.2.5), therefore if phase A is to be energized, one will have three operating stages:
magnetization stage when T1 and T2 are in conduction
demagnetization when T1 and T2 are closed to the current flow, in which case the current in phase decreases fast through the phase diode and the commune diode
period of freewheeling when T1 is in conduction and T2 is not, hence the phase current in this case is decreasing slowly
Miller power converter is disadvantageous when two phases are supplied in the same time, since in the conduction time the voltage of each phase will be half of the supplied DC-bus voltage [9].
Three-phase full bridge power converter
The three-phase full-bridge power converter is becoming common solution for many manufacturers, which offer the power module with the driver and protection circuits, as for three-phase AC machines. Given the fact that the price is less than for the above topologies, many authors have studied the electronic commutation and control of SR machines via such three-phase full-bridge power converters [10].
A three-phase star-connected 6/8 SR machine with ideal waveforms of phase inductance and current is presented in fig. 2.6. The three-phase full-bridge power converter entails three operating stages:
if transistors T3 and T2 are conducting, the current in phase B is positive and in phase A is negative
when T3 is blocked, the phase current decreases slowly through diode D3 and transistor T4
if both transistors T3 and T4 are blocked, the phase current decreases fast thanks to the negative voltage applied via diodes D3 and D4
As pointed out in [9] the major advantage of using three-phase full-bridge power converter associated to SR machines is justified by the low overall cost. By using this converter the number of switching pulses is reduced, therefore the switching losses are decreasing.
SR machine prototype under study
The SR machine studied in this thesis is of three-phase 6/8 topology with the expedient features of more machine-sizing flexibility, larger available stator-winding space, lesser mass for stator and rotor laminations, higher average electromagnetic torque and lower torque ripple due to increased number of strokes, and hence faster rate of change of the stator phase-winding inductance, when compared to conventional 6/4 and 12/8 SR machine topologies with similar volume constraints [3] [4] [5]. A detailed view in SolidWorks environment of the studied SR machine is presented in fig. 2.7.
Table of contents :
Notations and definitions
General introduction
Ch. 1 Switched reluctance machine as integrated starter-alternator
1.1 Introduction
1.2 Main features of switched reluctance machines
1.3 SR machine as integrated starter-alternator
1.4 Conclusions
Selected references
Ch. 2 Modeling and simulation of the switched reluctance machine
2.1 Introduction
2.2 Topologies of switched reluctance machine and associated power electronic converter
2.2.1 Classical SR machine topologies
2.2.2 Novel SR machine topologies
2.2.3 Topologies of SR machine associated power electronic converters
2.2.3.1 Three-phase asymmetric half-bridge power converter
2.2.3.2 Miller power converter
2.2.3.3 Three-phase full bridge power converter
2.2.4 SR machine prototype under study
2.3 Analytical modeling of the SR machine prototype
2.3.1 Analysis of voltage equations
2.3.2 Instantaneous electromagnetic torque
2.3.3 Phase inductance vs. rotor position
2.3.3.1 Analytical calculation of the phase inductance for aligned rotor position
2.3.3.2 Analytical calculation of the phase inductance for unaligned rotor position
2.4 Validation of the analytical model by finite-element magnetic field analysis
2.4.1 Finite element software used for validation
2.4.2 Comparative FE-computed and analytical results
2.4.2.1 Validation of the voltage equations
2.4.2.2 Validation of electromagnetic torque equations
2.4.2.3 Phase inductance validation
2.5 Simulations of the SR machine model
2.5.1 MATLAB/Simulink model
2.5.2 Influence of commutation angles
2.5.2.1 Simulations with theoretical angle
2.5.2.2 Simulations when commutation angles change
2.6 Conclusions
Selected references
Ch. 3 Optimization of switched reluctance machine using space mapping technique
3.1 Introduction
3.2 General aspects of optimization
3.2.1 Optimization
3.2.2 Design provided by optimization
3.2.3 Space mapping method
3.3 Space mapping at the output level
3.3.1 Space mapping function
3.3.2 Optimization using a mathematical model
3.3.2.1 Optimization on the fine model
3.3.3 Output space mapping proportional
3.3.3.1 General function calculation
3.3.3.2 Mathematical based problem
3.3.4 Manifold mapping
3.3.4.1 Mathematical problem
3.3.5 Comparison between the OSMP and MM methods applied to the mathematical model
3.4 Optimization of the SR machine by using SM technique
3.4.1 Description of the parameter control optimization
3.4.2 Approach used in fine and coarse models selection
3.4.3 Output space mapping proportional applied to machine optimization
3.4.4 Manifold mapping applied to SR machine optimization
3.4.5 Comparative optimal results
3.5 Space mapping technique applied to design and control optimization of SR machine for ISA applications
3.5.1 Optimization problem description
3.5.2 Selection of the fine and coarse models
3.5.3 Output space mapping proportional applied to SR machine optimization
3.5.4 Manifold mapping applied to SR machine optimization
3.5.5 Comparative optimal design
3.6 Simulation of the optimally-designed SR machine used in ISA application
3.7 Conclusions
Selected references
Ch. 4 Experimental study and control of a three-phase 6/8 SR machine
4.1 Introduction
4.2 Experimental test bench
4.2.1 Hardware components
4.2.1.1 Three-phase half-bridge inverter
4.2.1.2 Testing equipment dSpace 1104
4.2.1.3 Auxiliary equipment
4.2.2 Software components
4.2.2.1 Real-time control software
4.2.2.2 Real-time software
4.3 Steady-state tests for motor and generator operation modes of the studied SR machine and dynamic tests for a part of ISA driving cycle
4.3.1 Phase inductance measurement
4.3.2 Commutation angles validation for motor operation mode
4.3.3 Steady-state tests under motor and generator operation mode
4.3.3.1 Motor operation mode
4.3.3.2 Generator operation mode
4.3.4 SR machine tests as part of automotive ISA operation cycle
4.4 Conclusions
4.5 Selected references
General conclusions, original contributions and prospects
