Direct Eigen Control for Induction Machines and Synchronous Motors

Jean Claude Alacoque

• Publisher: Wiley-IEEE Press
• Year: 2012
• Print ISBN: 9781119942702
• eBook ISBN: 9781118460634
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Power Resources
• Index: Technology & Engineering

Clear presentation of a new control process applied to induction machine (IM), surface mounted permanent magnet synchronous motor (SMPM-SM) and interior permanent magnet synchronous motor (IPM-SM)

Direct Eigen Control for Induction Machines and Synchronous Motors provides a clear and consise explanation of a new method in alternating current (AC) motor control. Unlike similar books on the market, it does not present various control algorithms for each type of AC motor but explains one method designed to control all AC motor types: Induction Machine (IM), Surface Mounted Permanent Magnet Synchronous Motor (SMPM-SM) (i.e. Brushless) and Interior Permanent Magnet Synchronous Motor (IPM-SM). This totally new control method can be used not only for AC motor control but also to control input filter current and voltage of an inverter feeding an AC motor.

• Accessible and clear, describes a new fast type of motor control applied to induction machine (IM), surface mounted permanent magnet synchronous motor (SM-PMSM) and interior permanent magnet synchronous motor (I-PMSM) with various examples
• Summarizes a method that supersedes the two known direct control solutions – Direct Self Control and Direct Torque Control – to be used for AC motor control and to control input filter current and voltage of an inverter feeding an AC motor
• Presents comprehensive simulations that are easy for the reader to reproduce on a computer. A control program is hosted on a companion website

This book is straight-forward with clear mathematical description. It presents simulations in a way that is easy to understand and to reproduce on a computer, whilst omitting details of practical hardware implementation of control, in order for the main theory to take focus. The book remains concise by leaving out description of sensorless controls for all motor types. The sections on "Control Process", "Real Time Implementation" and "Kalman Filter Observer and Prediction" in the introductory chapters explain how to practically implement, in real time, the discretized control with all three types of AC motors. In order, this book describes induction machine, SMPM-SM, IPM-SM, and, application to LC filter limitations. The appendixes present: PWM vector calculations; transfer matrix calculation; transfer matrix inversion; Eigen state space vector calculation; and, transition and command matrix calculation.

Essential reading for Researchers in the field of drive control; graduate and post-graduate students studying electric machines; electric engineers in the field of railways, electric cars, plane surface control, military applications. The approach is also valuable for Engineers in the field of machine tools, robots and rolling mills.

1

Induction Machine

The three-phase induction machine with non-salient poles is the most widespread electric motor because of its simple and robust construction; it is perhaps the electrical machine that has the least intuitive operation (Caron and Hautier, 1995). It has been the subject of very many technical publications.

1.1 Electrical Equations and Equivalent Circuits

Starting from the equivalent three-phase electrical circuit of the induction machine without neutral current, let us establish initially the relations between the various electrical variables.

1.1.1 Definitions and Notation

Definitions and notation of motor parameters:

stator resistance	Rs
rotor resistance	Rr
stator leakage inductance	ls
rotor leakage inductance	lr
mutual inductance	Lm
stator inductance	Ls = Lm + ls
rotor inductance	Lr = Lm + lr
stator time constant
rotor time constant
pole pair number	Np
dispersion coefficient

Definitions and notations of mechanical and electrical angular frequencies:

• mechanical angular frequency of the rotor Ω
• polar mechanical angular frequency¹ ω = N_p ⋅ Ω
• stator electrical angular frequency ω_s
• rotor electrical angular frequency ω_r
• relative slip
  

1.1.2 Equivalent Electrical Circuits

The reduced equivalent electrical circuit for each phase of the balanced three-phase induction machine is that of Figure 1.1.

The directed angular symbol of Figure 1.1 recalls that the coupling between stator and rotor windings is modified with the rotation of the rotor.

This circuit does not show the equivalent resistance of iron losses, in parallel with the mutual inductance; it would represent ohmic losses due to the hysteresis of the magnetic material and to eddy currents in magnetic steel sheets. These losses are in general minimized when designing an electric motor. Resistance values do not take into account the skin effect due to high frequency harmonic currents. Inductances are considered here to be unsaturated. It is nevertheless possible to modify the values of these elements according to the mode of motor feeding, the operation mode and the harmonic content of the voltage inverter output.

The electrical variables defined for this equivalent circuit are variables directly accessible by electrical measurement:

• the phase–neutral instantaneous voltage, per phase:

(1.1)

• the instantaneous current in each phase:

(1.2)

with three phases p ∈ {0 ; 1 ; 2}, and

is the phase lagging of the current compared to the phase voltage, under traction operation.

Figure 1.1 Equivalent circuit of one phase of the three-phase induction machine

Figure 1.2 Three-phase (a, b, c) and two-phase (α, β) fixed frames

The Concordia transformation (Owen, 1999) makes it possible to reduce the three-phase scalar representation in the phase plane, by introducing a vector representation into the ­orthonormal frame plane of Figure 1.2. The transfer matrix, from the balanced three-phase ­representation to the two-phase one, which preserves the instantaneous power, is the 2 × 3 matrix of the Concordia transformation (1.3).

(1.3)

The chosen positive sense for measuring angles, as well as for rotation sense and angular velocity, will be always counterclockwise.

After this transformation, the equivalent circuit of the induction machine takes the reduced vector form of Figure 1.3.

The circuits of Figures 1.1 and 1.3 seem identical, but they represent, respectively, just one phase in a three-phase fixed frame, and three phases in a two-phase fixed frame. Represented electrical variables are different and are linked by the Concordia transformation.

Figure 1.3 Two-phase equivalent circuit of the induction machine

Equations of the system (1.4), are relations between the magnitudes of vectorial variables and maximum values of electrical phase variables, in this transformation.

(1.4)

Phase parameter values of the motor remain unchanged.

1.1.3 Differential Equation System

The two meshes of the equi...

Table of contents

• Cover
• Title page
• Copyright page
• Dedication
• Foreword by Prof. Dr Ing. Jean-Luc Thomas
• Foreword by Dr Abdelkrim Benchaïb
• Acknowledgements
• Introduction
• 1 Induction Machine
• 2 Surface-Mounted Permanent-Magnet Synchronous Motor
• 3 Interior Permanent Magnet Synchronous Motor
• 4 Inverter Supply – LC Filter
• 5 Conclusion
• Appendix A: Calculation of Vector PWM
• Appendix B: Transfer Matrix Calculation
• Appendix C: Transfer Matrix Inversion
• Appendix D: State-Space Eigenvector Calculation
• Appendix E: F and G Matrix Calculations
• References
• Index