A catalog record for this book is available from the British Library. Additional hard copy and PDF copies are available from [email protected] Modeling and Control of Switched Reluctance Machines. The past decade has seen a notable growth in the use of Switched Resistive Machines (SRMs) in a wide variety of consumer products and industrial applications.
Introduction
However, the doubly salient structure, deep magnetic saturation, supply switching shape and many nonlinearities make it very complicated to accurately model the magnetic characteristics of SRMs [1-4]. Several approaches are used to model the magnetic characteristics of SRMs including analytical models, artificial intelligent models, and lookup table-based models [5, 6].
Analytical modeling of SRM
The data can be obtained by FEA or measurements with efficient resolution to achieve a highly reliable model [ 20 , 21 ]. In [7], an analytical model is derived based on a piecewise analysis of machine fundamental geometry and turns per phase.
Artificial intelligence-based models
Finite element analysis of SRM
- Equations used for FEA
- Modeling of SRM using FEA
- Results of FE analysis
- Measuring method and platform
- Measurement results
- Error analysis and minimization
Then the properties of the previously defined 18 AWG blocks can be set to include the circuits. Better accuracy can be achieved if it is possible to measure a reasonable number of samples.
Model development using MATLAB/Simulink
Mathematical model of SRM
When considering mutual flux, flux coupling for incoming (λk) and outgoing (λk-1) phases can be expressed as:. The flux coupling can be represented as Eq. 18) in terms of self and mutual inductances.
Simulation of SRM drive
The most common converter for SRM is the asymmetric bridge converter as shown in Figure 12 for one phase of SRM. For high speeds, the phase voltage becomes a single pulse, the current limiting is no longer in use, the flux becomes a pure triangle as shown in Figure 21(b).
Experimental verification
The total torque is given in Fig. 20(b), as noted, it has a very noticeable ripple, which is a major drawback for SRMs. At low speed, the current is regulated by HCC, the phase voltage changes between +V and �V to achieve this control, the shape of the phase current is slightly off to form a triangular shape as shown in Figure 21(a) .
Conclusions
An accurate model of a switched reluctance motor based on the indirect measurement method and the support vector least squares machine. Switched reluctance machines (SRM) are an alternative to conventional and permanent magnet (PM) machines.
SRM characterization
- Reluctance machines (RM) and SRM basic features
- SRM background and development
- Geometric specifications
- Magnetic features
- SRM operation fundamentals
The rotor geometry also has a set of salient poles (Nr)—in this case Ns= 6 (two poles/phase), while Nr= 4. Torque development is clearly associated with todLs=dθ6¼0 (i.e. the overlapping pole regions); it is associated with motor (+) and generator (�) modes.
SRM modeling and energy balance
- Electromechanical energy conversion and torque production
- Linear magnetic circuit
- Overview on developed SRM loss estimation
- Copper losses
- Core losses
It should be noted that a corresponding harmonic content in the flux density waveform reflects a significant number of small loops. It should be noted that none of these are taken into account in the first term of Eq.
Conclusions
Optimal design of pulsed reluctance motor fed by asymmetric bridge inverter using experimental design method. Towards incorporating the effect of manufacturing processes into pre-estimated losses of a switched reluctance motor.
Structure and operation of SRM
The poles of the rotor tend to the diametrically opposite poles of the stator whenever they are excited by a current [6]. Calculating the torque is a problem due to the dependence of the inductance of the magnetic circuit on both the rotor angle and the stator current.
Design procedures
- Starting values
- Inner, outer, and shaft diameter and core length
- Air gap length
- Selection of number of phases and number of poles
- Stator and rotor pole arc
- Preliminary design
- Design verification
- Calculation of losses
It is necessary that the values of the polar arcs of the machine are within this triangle [24]. The iron thickness of the rotor back in terms of the stator pole width can be set in the range below:.
Dimensional effect analysis
Effects on average torque
Once the flux density and iron weight are known for each part of the machine, these data are used to calculate the core losses. Once the flux density and iron weight are known for each part of the machine, these data are used to calculate the core losses.
Effects on total losses
This chapter presents the results of research on the geometric optimization of the switched reluctance motor (SRM) magnetic circuit and optimization of the control algorithm. Recommendations for the practical implementation of the optimal control algorithm are given (using the most common half-bridge current circuit and modern electronic components).
Development of an optimization algorithm for the SRM magnetic circuit
Decreases the number of CF calculations for a more accurate calculation of the extremum coordinates. Increases the number of CF calculations for a more accurate calculation of the extremum coordinates.
Mathematical description of the pole curved shape
The area of possible contours of the rotor poles when setting the curved shape of the rod. An example of incorrect (a) and correct (b) setting of the coordinates of the boundary points of the polar contour.
Optimization of the curved shape of the rotor pole
The derivatives at boundary coordinates (х= 0 and х= 2π) become zero in the middle of this interval (forx=π); the derivative is equal to the derivative of the original function. The curved shape of the pole can be defined differently, for example by the set of.
The example of optimizing the geometric shape of a rotor pole As an example, consider the optimization of the curved shape of the rotor
The example of optimizing the geometric shape of a rotor bar As an example, consider the optimization of the curved shape of the rotor. The values of the torque for the full rotation of the rotor were measured in 0.5°.
Development of the SRM optimal control algorithm
The rotation angle of the rotor is read from the encoder (both incremental and absolute encoders can be used) and it can also be obtained by processing test pulses sent to the SRM stage (without encoder control system). One of the microcontroller's control subroutines solves Eqs. 15) and (20) based on ADC data obtained using the built-in direct memory access controller (DMA).
Conclusions
Applications of SRM such as SRG are in the fields of aerospace, automotive, and wind energy [6]. However, the fluctuating cost of neodymium (NdFeB), which makes up the magnets, has raised some reservations in the consensus opinion for these generators [9].
Formulation of similarity laws
Rated power and losses
Finally, Section 5 offers some conclusions and points out some of the implications of the scale model methodology in the design process. Thus, the time rate of change of the magnetic energy is given by (7), and Te can be obtained from the coenergy as given in (8):
Multi-machine topology
For a multi-machine topology SRM module, the rated power can be expressed by Taking the regular monolithic machine as a reference, each SRM unit provides only a part of the rated power and enables to deduce a new relationship between the relative dimensions of the SRM and the number of modules.
Machine design
Short flux-path topology
To compare the flux path lengthFsf of a short flux path (SFP) topology with the length of the regular machinelF, an external radiusR2, similar for both topologies, is considered. PJ∝mJ2lCu3∝mlCu2∝m Blð FÞ4=3 (41) The copper losses depend on the length of the flux path, which becomes lower in the SFP topology.
Field-based model for dimensional analysis
Therefore, similarly to common topologies, the mutual flux connection between two phase windings of the magnetic SFP topology is negligible. Therefore, similarly to common topologies, the mutual flux connection between two phase windings of the magnetic SFP topology is negligible.
Design study results and discussion
Two angular coordinates are sufficient to determine the position of the rotor pole and the quantities involved in the system. Parameters of the compared topologies (the base power is peak power), m (number of phases), NR (number of rotor poles), τR (rotor pole pitch), βR (rotor pole arc), P (rated power) .
Mathematical model of LSRM
Thus, it is necessary to know, at any moment, the position of the secondary or moving part, for which a linear encoder is usually used. Thus, it is necessary to know, at any moment, the position of the secondary or moving part, for which a linear encoder is usually used.
LSRM design procedure
- Design specification
- Output equation
- Selection of magnetic loading, current density and normalized geometric variables
- Number of turns and wire gauge
- Finite element analysis
- Thermal analysis
- Discussion of results
In the second approach, the LSRM design is performed using an analytical formulation of the average translational force determined by means of an idealized energy conversion loop [12, 13]. In order to verify and compare the results, the prototype was analyzed using the finite element method (FEM) described in Section 3.5 modified to account for end effects.
![Figure 5 shows a flowchart with the different steps of the design process [9].](https://thumb-ap.123doks.com/thumbv2/1libvncom/9201819.0/143.765.127.652.294.466/figure-shows-flowchart-different-steps-design-process.webp)
Simulation model and experimental results of an LSRM actuator The simulation of an LSRM force actuator is presented [27]. This linear actuator
The LSRM block must solve the mathematical model of the SRM, i.e. the space-state equations (7). The phase currents are obtained directly from the electronic power converter output, and the position is from the firing position generator module of the digital control block.
Conclusion
Modeling of a linear switched reluctance machine and wave energy conversion drive using a matrix and tensor approach. Switched reluctance machines (SRMs) are very competitive candidates for high-speed applications in high-temperature environments due to their single-material rotor with no permanent magnets (PMs).
Control of ultrahigh-speed SRMs (UHSSRMs) over 100,000 rpm Extensive research has been conducted in the literature for high-speed SRMs up
As shown in Figure 1(iii) (a), when the rotor is θ1 degrees from the non-aligned position (θ= 0°, which is also the aligned position for the other phase), the optical sensor detects the black mark and gives a rising edge of the output signal. It can be read from the oscilloscope that the frequency of the current profile of phase A (magenta waveform) is 3.353 kHz.
Rotor design of ultrahigh-speed SRMs over 1,000,000 rpm
Problem of conventional rotor designs
Higher speeds could be achieved, but due to bearing safety concerns, the final speed was stopped at 100,000 rpm.
Possible solutions in the literature .1 Using bolts rather than a shaft
A typical value of the air gap of ultra-high-speed SRMs is 0.1–0.25 mm to increase the torque density [26]. From the stress analysis of the finite elements, it can be seen that at 1.2 million rpm the maximum stress is 1055 MPa, which is located at the connection points of the flow bridge.
A novel rotor geometry for ultrahigh-speed SRMs over 1,000,000 rpm From the analysis above, it can be concluded that a new geometry has to be
In addition, there is no shaft in the middle of the rotor lamination, which significantly reduces the higher stress caused by the large centrifugal force. A detailed 3D FEA of the stress distribution of the rotor stack and clamping shaft can be found in [36, 42].
Electromagnetic design of an ultrahigh-speed SRM over 1,000,000 rpm
- Air gap design
- Stator winding design
- Windage torque estimation
- Finite element analysis
- Prototype
- Experimental result
However, the equivalent air gap length is greater due to the use of the retaining sleeve. The control of the switched solidification motor is not as easy as other traditional machines.
Switched reluctance motors
Torque characteristic
In the description of the theory and in the simulation results, the parameters of the SRM model described in [8] were used. This characteristic of the motor makes it possible to create a rotary motion of the rotor by magnetizing and demagnetizing each phase in the correct position of the rotor.
Control techniques
Voltage impulse control
Current control
And in the third part, the negative source voltage is applied so that the current decreases to zero before it starts producing negative torque. The voltage is kept constant in the last controller, with the expectation that the current will also be constant.
Torque control
Linear controller design
Model equations
Laplace model
To solve the rest of the non-linearities, it is necessary to linearize the model. It is also possible to design adaptive controllers where the gains are a function of the inductance and operating point.
- Constant current
- Constant torque
- Current dynamic constraints
- Deaccelerating and speed inverting
Also, the currents must be converted to the function of the rotor position so that the rotor has a constant motion. This second term is non-linear, so torque is not a direct calculation of current.
