Sensorless Control of Synchronous Machines by Linear Approximation of Oversampled Current

185 Pages·2015·6.14 MB·English

by  Peter Landsmann

Lehrstuhl für Elektrische Antriebssysteme und Leistungselektronik
der Technischen Universität München
Sensorless Control of Synchronous Machines by
Linear Approximation of Oversampled Current
Peter Landsmann
Vollständiger Abdruck der von der Fakultät für Elektrotechnik und
Informationstechnik der Technischen Universität München zur Erlangung
des akademischen Grades eines
Doktor-Ingenieurs
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr.-Ing. Hans-Georg Herzog
Prüfer der Dissertation:
1. Univ.-Prof. Dr.-Ing. Ralph Kennel
2. Univ.-Prof. Dr. techn. Manfred Schrödl
(Technische Universität Wien/Österreich)
Die Dissertation wurde am 10.06.2014 bei der Technischen Universität Mün-
chen eingereicht und durch die Fakultät für Elektrotechnik und Informations-
technik am 14.09.2014 angenommen.

Preface
The present work examines the potential of current oversampling for the sensorless control
of synchronous machines. Using linear regression, the current evolution during a switch-
ing state is approximated by a straight line. The approximated offset and slope represent
low-noise current and current derivative values. Upon this basis, three position estima-
tion techniques are developed and merged in two oppositional hybrid sensorless control
methods which demonstrate the advantages of the oversampling.
The research behind those contents has been enabled by and carried out at the Insti-
tute for Electrical Drive Systems and Power Electronics of the Technische Universitaet
Muenchen (Munich, Germany) in the period from 2012 to 2014 and under supervision of
Prof. Ralph Kennel. At this point in time the required hardware components were signifi-
cantly more expensive than conventional drive hardware. Hence, the reader is supposed to
gain a preview of the opportunities that are going to emerge for sensorless control as soon
as the prices of more elaborate components (e.g. DSP-FPGA combinations or magneto-
resistive current transducers) will drop into a range relevant for series production.
Foraccomplishingthisproject,includingallhardwareandsoftwaredevelopment,within
a period of 3 years the efficient collaboration with the following people has been essential:
During the work of his Diploma thesis Janos Jung developed the real time system capable
of current oversampling and the respective data processing. This development has been
broadly supported by the scientific employee Peter Stolze. As a part of his studies Math-
ias Kramkowski implemented the recursive linear regression algorithm in VHDL which
enabled the real time evaluation of the oversampling data. Based on the above works the
former student Tino Müller manufactured and commissioned a portable and reliable test
bench with which all experiments of this work have been realized.
Despite of the author’s aim to investigate thoroughly and provide comprehensible de-
ductions, he remains aware that no insight is ultimate - instead, the reader is welcome to
comment, ask critically or discuss new experience.
Munich, January 2015
Peter Landsmann

Contents
1 Introduction 1
1.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Drive model 7
2.1 Nomenclature and definitions . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 Subscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 Reference frames (superscript) . . . . . . . . . . . . . . . . . . . . . 9
2.1.5 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Space vector representation . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Generic nonlinear synchronous machine model . . . . . . . . . . . . . . . . 17
2.3.1 Electrical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Anisotropy consideration . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Mechanical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.4 Nonlinear model for simulation . . . . . . . . . . . . . . . . . . . . 26
2.4 Linear PMSM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Linear reluctance synchronous machine (RSM) model . . . . . . . . . . . . 28
2.6 Eddy current model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Sensorless control – state of the art 33
3.1 Fundamental model based position estimation . . . . . . . . . . . . . . . . 34
3.1.1 Electromotive force observers . . . . . . . . . . . . . . . . . . . . . 35
3.1.2 Flux estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.3 Fundamental model based position estimation for the RSM . . . . . 38
3.2 Anisotropy-based position estimation . . . . . . . . . . . . . . . . . . . . . 40
I
Page II CONTENTS
3.2.1 Arbitrary Injection based anisotropy identification . . . . . . . . . . 44
3.2.2 Mean admittance estimation . . . . . . . . . . . . . . . . . . . . . . 48
3.2.2.1 Anisotropic voltage-current relation . . . . . . . . . . . . . 48
3.2.2.2 Geometrical approach . . . . . . . . . . . . . . . . . . . . 49
3.2.2.3 Extension with machine background information . . . . . 51
4 Current oversampling 55
4.1 Test bench hardware setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Analysis of the oversampled current response . . . . . . . . . . . . . . . . . 60
4.2.1 Dead time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.2 Cable recharging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.3 Machine recharging . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.4 Eddy currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.5 Summary of the oversampled current response analysis . . . . . . . 67
5 Linear approximation 69
5.1 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Recursive implementation on an FPGA . . . . . . . . . . . . . . . . . . . . 71
5.3 Noise suppression through linear regression . . . . . . . . . . . . . . . . . . 74
5.4 Experimental validation of the linear approximation . . . . . . . . . . . . . 79
5.4.1 Noise properties and components in idle condition . . . . . . . . . . 80
5.4.2 Linear approximation during injection . . . . . . . . . . . . . . . . 83
5.4.3 Linear approximation in the presence of rotor speed . . . . . . . . . 85
5.4.4 Comparison to the theoretical expectation . . . . . . . . . . . . . . 93
6 Position estimation 97
6.1 Position estimation close to standstill . . . . . . . . . . . . . . . . . . . . . 98
6.1.1 The passive switching state extension . . . . . . . . . . . . . . . . . 99
6.1.2 Elimination of the fundamental current slope . . . . . . . . . . . . . 101
6.1.3 Experimental evaluation of the regression based anisotropy identi-
fication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Position estimation in presence of rotor speed . . . . . . . . . . . . . . . . 108
6.2.1 Passive switching state EMF evaluation . . . . . . . . . . . . . . . . 109
6.2.1.1 Derivation of the estimation approach . . . . . . . . . . . 109
6.2.1.2 Influence of a present anisotropy . . . . . . . . . . . . . . 114
6.2.2 Active switching state current slope evaluation . . . . . . . . . . . . 115
6.2.2.1 EMF evaluation from the ASS current slope . . . . . . . . 116
CONTENTS Page III
6.2.3 Experimental validation of the current slope based electromotive
force (EMF) estimation . . . . . . . . . . . . . . . . . . . . . . . . . 119
7 Fusion of the position estimates 127
7.1 Parameter-free hybrid sensorless control for SPMSMs . . . . . . . . . . . . 128
7.1.1 Online SNR determination . . . . . . . . . . . . . . . . . . . . . . . 128
7.1.2 Adaptive fusion technique for noise minimization . . . . . . . . . . 132
7.1.3 Injection magnitude controller . . . . . . . . . . . . . . . . . . . . . 133
7.1.4 Initial identification of the load-dependent saliency displacement . . 134
7.1.5 Experimental validation of the parameter-free hybrid scheme . . . . 137
7.2 Generic high performance hybrid sensorless control . . . . . . . . . . . . . 142
7.2.1 Intelligent feedback design . . . . . . . . . . . . . . . . . . . . . . . 143
7.2.2 Dynamic limitation due to eddy currents . . . . . . . . . . . . . . . 145
7.2.3 Stabilized flux estimator for the RSM . . . . . . . . . . . . . . . . . 151
8 Conclusion 155
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Appendix 161
A Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
B Machines used in the experiments of this work . . . . . . . . . . . . . . . . 162
C Direct admittance matrix identification . . . . . . . . . . . . . . . . . . . . 164
D PSS current slope in presence of an anisotropy . . . . . . . . . . . . . . . . 165
E Minimum noise signal merging . . . . . . . . . . . . . . . . . . . . . . . . . 166
Page IV CONTENTS
Chapter 1
Introduction
The finite resources of our planet face a growing global development that already ex-
ceeds their sustainable limits [1]. The severity of the consequences of global resource
over-exploitation makes profound political changes inevitable [2–4], of which the recent
sustainability trend in industrialized nations, such as Germany, is just a beginning. Re-
garding energy production and consumption (as parts of the resource scarcity problem),
we already note an increased currency of "green" technical products, but the required
reduction of fossil fuel extraction and carbon emission is by far not reached yet [5]. A fur-
ther reduction can be facilitated, inter alia, by the increasing electrification of applications
and the improving efficiency of electro-mechanical power conversion.
Although power electronics and machine control strategies have made significant
progress in the past three decades, in practice still a major part of the generated electric
energy is used by machines in direct grid connection (Fig. 1.1(a)) - a simple operating
mode with low efficiency. However, the installation of a more efficient drive system,
consisting of inverter and machine, entails a higher initial investment. Especially when
utilizing the potential of inverters to employ (more efficient) synchronous machines, the
inverter requires the rotor position information.
Figure 1.1: Machine operation topologies.
1
Page 2 Chapter 1
This information is normally obtained by means of a rotor position sensor - a relatively
expensive and sensitive component that demands a free shaft end, construction space on
this side, an additional cable and an evaluation circuit (see Fig. 1.1(b)); and that increases
the (often manual) installation effort and aggravates the overall fault probability of the
drive system. This set of drawbacks obviously affects the attractiveness of inverter driven
synchronous machines, and thereby motivates the development of control strategies that
overcome the need for a position sensor (Fig. 1.1(c)).
In this sense, so called “sensorless control” strategies further the relevance and cur-
rency of synchronous machine drive systems, by making them cheaper, smaller, saver and
more robust - and do hence, in a broader sense, give a small contribution to the overall
electrification of applications and to the reduction of fossil energy consumption.
However, according to the state of the art in sensorless control, these strategies do also
entail drawbacks, difficulties and limitations:
(1.) Due to internal or subsequent filtering, the estimation bandwidth of most sensorless
methods is limited. Moreover, some injection-based methods require a reduction of
the current controller bandwidth which propagates into all above cascades. Hence,
a sensorless controlled drive will not fulfil very high dynamic requirements.
(2.) Sensorless control methods employ the machine as a sensor, despite its design for
energy conversion. Hence, manufacturing tolerances, age and temperature depen-
dences, nonlinearities and harmonics that may be negligible regarding energy con-
version, limit the accuracy of the position estimate in comparison a sensor signal.
(3.) Atlowspeedandstandstill, thepositioninformationiscommonlyobtainedfromthe
anisotropyorientation, usingsignalinjectiontechniques. Duetoswitchingfrequency
limitation for drives larger than 1kW, this injection is normally located in the
audible frequency range, resulting in an acoustic noise emission at low speed.
(4.) The anisotropy, exploited for low speed position estimation, shows harmonic and
load dependent deviations from the rotor position. Harmonics of very high magni-
tude, as for instance in discretely wound machines, and very high torques can both
lead to an assignment problem between anisotropy and rotor position. Especially
the latter cause is crucial, since it results in a general torque limitation for sensorless
control techniques at low speed.
(5.) The transition between the techniques for low and for high speed angle estimation
is based on the estimated speed, i.e. on the time derivative of the angle estimate,