Institute of Energy Technology
Encoderless Vector Control of PMSG for
Wind Turbine Applications
Conducted by group PED 1035
Master Thesis, 2010
Institute of Energy Technology
Pontoppidanstræde 101
Phone number 99 40 92 47
Fax 98 15 14 11
http://www.iet.aau.dk/
Title: Encoderless Vector Control of PMSG
for Wind Turbine Applications
Semester: 4th semester
Semester Theme: Master Thesis
Project period: 01.02.10 to 01.06.10
ECTS: 30
Project group: PED 1035
Members:
Andreea Cimpoeru
Supervisor: Kaiyuan Lu
Number of prints: 3
Number of pages: 62
Finished: 1.06.2010
Abstract:
The growing interest in wind turbine applications and the fast development of power electronics is making the manufacturers to find
the most suitable and low cost technologies
to put in practice. Permanent magnet synchronous generator are becoming more popular over the induction machine in wind turbine
applications, because of the increased power to
volume ratio, decreasing cost of magnets, and
increased efficiency. In this scope, the purpose
of this project is to find a solution in order
not to use the sensor mounted on the shaft of
the surface mounted PM for wind turbine applications. The control strategy used is Field
Oriented Control(FOC). First FOC is implemented and validated in Matlab/Simulink using measured speed and position. Next, the
investigation on methods to estimated the rotor position is done. With the chosen method
the validation of the control is performed.
The sensored Field Oriented Control is implemented in dSpace laboratory and the results have proved that the control is working
properly. The sensorless algorithm is working
in simulations and could not be implemented
in laboratory.
By signing this document, each member of the group confirms that all participated in the project work
and thereby all members are collectively liable for the content of the report.
Preface
This 10th semester report was conducted at the Institute of Energy Technology. It was written by Andreea Cimpoeru during the period from 1st of February to 01th of June 2010.
This report is a documentation for the project entitled Encoderless Vector Control of PMSG for Wind
Turbine Applications. This theme in particular was proposed by SIEMENS Wind Power. The purpose of the
project unit is to control a permanent magnet synchronous generator without using a sensor. The model of
this generator type and its implementation in Simulink is shown in this report.
The main report can be read as a self-contained work, while the appendixes contain details about measurements and other data. In this project the chapters are consecutive numbered while the appendixes are
assigned with letters
Figures, equations and tables are numbered in succession within the chapters, e.g. (3.4), where the first
number stands for the chapter and the second number stands for the equation number in the chapter.
Literature references are mentioned in square brackets by numbers. Detailed information about literature
is presented in the bibliography.
The figures (block diagrams, simulation plots, laboratory setup measurements plots, etc) included in this
report may be found ”‘List of figures”’ section in the beginning of the report.
A CD-ROM containing the simulation, main report and appendixes is attached to the project.
I would like to thank my supervisor Kaiyuan Lu for his guidance and advice forwarded during the progress
of the project. I will also like to acknowledge the help of my college Zihui Wang.
II
CONTENTS
Contents
1 Introduction
1.1 Background . . . . . . . .
1.2 Problem Statement . . . .
1.3 Objectives . . . . . . . . .
1.4 Limitations of the project
1.5 Overview of the project .
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1
1
3
3
4
4
2 Theoretical background
2.1 Overview of the system . . . . . . . . .
2.2 Voltage source converter . . . . . . . . .
2.3 Permanent magnet synchronous machine
2.3.1 Introduction to SPMSM . . . . .
2.3.2 Mathematical model of SPMSM
2.3.3 Validation of SPMSM . . . . . .
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5
5
5
7
7
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10
3 Field oriented control
3.1 Field oriented control . . . . . . . . . . .
3.2 Control properties . . . . . . . . . . . . .
3.3 Current and speed controller design . . .
3.3.1 Design of q axis current controller
3.3.2 Design of speed controller . . . . .
3.4 Simulation results . . . . . . . . . . . . .
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12
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18
21
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4 Sensorless control of PMSM
28
4.1 Presentation of the sensorlees control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Rotor position estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5 Laboratory work
5.1 Laboratory structure . . . . . . . . . . . .
5.2 Real time interface . . . . . . . . . . . . . .
5.3 Laboratory results . . . . . . . . . . . . . .
5.3.1 Control of PMSM with encoder . . .
5.3.2 Sensorless algorithm implementation
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37
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6 Conclusion
45
Bibliography
46
A Datasheet of PMSM
52
B PMSM laboratory test
54
IV
CONTENTS
C Test for the sensorless control
56
D Laboratory parameter specification
57
E Simulation blocks
59
V
LIST OF FIGURES
List of Figures
1.1
1.2
1.3
1.4
Growth in size of commercial wind turbine designs [7] . . . . . . . . . . . . . . .
World total installed capacity (MW)[5] . . . . . . . . . . . . . . . . . . . . . . . .
Costs of generated power on 2010 of wind power compared to conventional plants
Wind turbine configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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[4]
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1
2
2
3
2.1
2.2
2.3
2.4
2.5
2.6
Setup configuration . . . . . . . . . . . . . . . . . . . . .
Topology of a voltage source inverter with ideal switches
Clasification of permanent magnets machines . . . . . .
Stator voltage in reference frame transformation . . . .
Stator currents at nominal working point . . . . . . . .
Stator voltage at nominal working point . . . . . . . . .
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5
6
7
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11
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
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21
22
22
3.22
3.23
Scheme of Field Oriented Control strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vector diagram for constant torque per amper control in steady state . . . . . . . . . . . . . .
d and q axis control topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The structure of the q axis current controller . . . . . . . . . . . . . . . . . . . . . . . . . . .
Topology of the q axis current controller with unity feedback . . . . . . . . . . . . . . . . . .
Bode diagram of the q axis current controller . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step response for the q axis current controller . . . . . . . . . . . . . . . . . . . . . . . . . . .
Topology of the speed controller loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Speed controller loop with unity feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bode diagram of the speed controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Speed response of the speed controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Topology of the integrator antiwindup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reference and measured speed at no load . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reference and measured currents at no load and steep in speed a)Id current b)Iq current . . .
Stator currents and voltages at no load and step in speed a)Measured voltages b)Measured
currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reference and measured speed at 7 [Nm] load torque . . . . . . . . . . . . . . . . . . . . . . .
Reference and measured currents at 7 [Nm] load torque a)Id current b)Iq current . . . . . . .
Stator currents and voltages at 7 [Nm] load torque a)Measured voltages b)Measured currents
Reference and measured speed for different values of the speed and load torque . . . . . . . .
Reference and measured currents for different values of the speed and load torque a)Id current
b)Iq current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Measured stator currents and voltages for different values of the speed and load torque
a)Measured voltages b)Measured currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reference and measured speed in generator mode . . . . . . . . . . . . . . . . . . . . . . . . .
Electromagnetic torque in generator mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
4.2
4.3
Field Oriented Control of PMSM without the sensor . . . . . . . . . . . . . . . . . . . . . . .
Back EMF in stationary reference frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Representation of stator fix αβ reference frame . . . . . . . . . . . . . . . . . . . . . . . . . .
3.16
3.17
3.18
3.19
3.20
3.21
VI
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23
23
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26
27
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30
30
LIST OF FIGURES
4.4
4.5
4.6
4.7
4.8
Estimated and rotor position for PMSM in open loop system . . . . . . . . . . . . . . . . . . 32
Measured and estimated mechanical speed of PMSM in open loop system . . . . . . . . . . . 32
Estimated and rotor position of PMSM at 7 [Nm] load torque . . . . . . . . . . . . . . . . . . 33
Reference and measured speed with the estimated rotor position at 7 [Nm] load torque . . . . 33
Stator voltages and currents calculated with the estimated position a)Measured voltage b)Measured
current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.9 Estimated and rotor position of PMSM in generator mod . . . . . . . . . . . . . . . . . . . . 34
4.10 Estimated and measured speed of PMSM in generator mod . . . . . . . . . . . . . . . . . . . 35
4.11 Electromagnetic torque of PMSM in generator mod . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1
5.2
5.3
5.4
5.5
Description of laboratory setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Topology of the Real Time Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Control Desk layout of the PMSM simulation . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reference and measured speed at no load, step to rated speed . . . . . . . . . . . . . . . . . .
Stator currents and voltages at no load, step to rated speed a)Measured currents b)Measured
voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Reference and measured speed at different speeds and 7 [Nm] load torque . . . . . . . . . . .
5.7 Stator currents and voltages at different speeds and 7 [Nm] load torque a)Measured currents
b)Measured voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8 Reference and measured currents at different speeds and 7 [Nm] load torque a)Id current b)Iq
current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Electromagnetic torque of the PMSM at different speeds and 7 [Nm] load torque . . . . . . .
5.10 Estimated and rotor position of PMSM in open loop system . . . . . . . . . . . . . . . . . . .
5.11 Measured and estimated mechanical speed of PMSM in open loop system . . . . . . . . . . .
37
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41
42
42
43
43
44
A.1 Datasheet of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
B.1 Reference and measured speed at TL =7 [Nm] . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2 Stator currents and voltages a)Measured currents b)measured voltage . . . . . . . . . . . . .
54
55
E.1 Overall simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.2 Simulation of the mathematical model of PMSM . . . . . . . . . . . . . . . . . . . . . . . . .
E.3 FOC control of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
60
60
VII
CHAPTER 1. INTRODUCTION
Chapter 1
Introduction
The first chapter has the main scope to make an introduction to the presented report. It starts with a general
presentation about wind turbines and the problem formulation is presented. In order to have a way to go
through the research the objectives and the limitations of the project are defined. The chapter ends with the
report structure
1.1
Background
The wind energy is a pollution-free resource, in inexhaustible potential. The main drawback is the energy
production irregularity. In the recent years, because global warming and because the effects of carbon emissions had an important impact over the entire world, a demand for clean and sustainable energy sources
like wind, sea, sun and biomass have become an considerable alternative to the conventional resources. The
utilization of wind energy was used in the past mainly in the agriculture sector for pumping water and for
grinding. The research for wind power industry started to be improved in the last century, mainly due to the
oil crisis and natural resources ripening. By increasing the wind turbine size the electrical power production
is also increased. In Fig.1.1 can be seen that in the last forty years the wind turbine size have been increased
from 24 m to 114 m. Right now, the record for electric power production from wind is the Enercon E-126
wind turbine, produced by the German company Enercon, with a rated power of 6 MW [6]
Figure 1.1: Growth in size of commercial wind turbine designs [7]
1
1.1. BACKGROUND
Referring to generators for wind power-application, there can be two main classes considering the speed:
constant and variable speed. In the first steps of wind power development the constant speed wind turbines
and induction generators were used. Disadvantages of the fixed speed generators is the low efficiency, poor
power quality and high mechanical stress [3]. In order to maximize the wind energy capture, the extraction
of maximum power from wind at a large scale has become an important topic for wind companies. Running
the wind turbine generator at low and medium wind speeds the maximum power can be extracted. In Fig.1.2
can be seen the continue growing trend of wind power installation in the last decade. In 2008 wind energy
growth has reached a rate of 29%.
Figure 1.2: World total installed capacity (MW)[5]
This fast development was possible because of the high price of oil and the reticence of using uranium,
gas or coal.
The price of wind energy is another important aspect for a wind turbine installed either on inland or
coastal place. As it can be seen in Fig.1.3 the price of wind energy is continuously decreasing in order to
compete with the price of conventional resources.
Figure 1.3: Costs of generated power on 2010 of wind power compared to conventional plants [4]
2
CHAPTER 1. INTRODUCTION
According to [4], the International Energy Agency (IEA) expects that wind power will be cheaper than
coal and gas in 2030.
1.2
Problem Statement
The variable speed wind turbine with full scale frequency converter is an attractive solution for research on
distributed power generation systems. The generator in this case can be double fed induction machine or
an permanent magnet synchronous generator(PMSG). The advantages of PMSG over induction machines
are the high efficiency and reliability, since there is no need of external excitation, smaller in size and easy
to control [9]. Also PMSG has some disadvantages like higher cost and a fix excitation. Over the years the
PMSG has become a more attractive solution to use it in variable wind turbine applications.
The generator is connected through a full scale voltage source converter: generator converter is used to
control the torque and the speed and grid side converter used to controll the power flow in order to keep
the DC-link voltage constant. The two converters are connected by a DC link capacitor in order to have a
separate control for each converter. In Fig.1.4 the PMSG and the full scale converter are presented.
Figure 1.4: Wind turbine configuration
Having an efficient and a reliable control is very important to have a better understanding of the system.
For controlling the PMSG is necessary to know the rotor position and speed. They can be known by using
a position or speed sensor, or they can be estimated. The use of sensor implies some drawbacks like the
increase cost of the system, a lower reliability, resulting that the sensorless solution for controlling the
PMSG is becoming a more attractive solution.
1.3
Objectives
The main goal of this project is to implement an sensorless control structure for a permanent magnet
synchronous generator for wind turbine applications, where the focus is set on position and speed estimation.
In order to have a better understanding of the system and the validation of the model a sensored control is
implemented. The objectives of the system are presented below:
• Implementation of a sensored control for surface mounted PMSM.
• Investigation of different sensorless methods.
• Selection of an optimal technique for determining the rotor position and implementation in Maltlab/Simulink.
• Laboratory implementation for sensored control of PMSM.
• After the sensorless control strategy shows good results in simulations implementation in dSpace laboratory.
3
1.4. LIMITATIONS OF THE PROJECT
• Implementation of the control on a 2-4 [MW] wind turbine generator.
1.4
Limitations of the project
Once the scope of the project is defined, some limitation arise in order to fulfill the scope of the project.
This limitation are as fallows:
• Just the surface mounted permanent magnet generator will be investigated
• The focus of this project is just the generator side inverter so the grid side converter is not implemented
in this report
• The wind turbine model, the wind model and the drive train model are not consider.
1.5
Overview of the project
The project is divided into six chapters. The first chapter it started with a small introduction about the wind
turbine background. The problem statement, the objective and the limitation of the project are presented.
The second chapter describe the system components and the purpose into the project. The voltage
source converter is described in details, the introduction and the mathematical model of permanent magnet
synchronous motor are also presented.
Chapter three has the main purpose to describe the chosen control strategy Field Oriented Control. The
design of the controllers in order to have a good performance of the machine are described next. Finally in
this chapter the validation of the machine model and control strategy is done.
In chapter four different sensorless control strategies are presented and finally one is chosen to implement
it. The simulation results are shown in the end of this chapter.
The implementation of the system in laboratory is described in chapter five. The results are presented
and discussed. Finally the conclusion and future work are taken in the end of this project, in chapter six.
4
CHAPTER 2. THEORETICAL BACKGROUND
Chapter 2
Theoretical background
In order to have an algorithm that can be implemented in real applications, the components have to be
determined by mathematical models. First voltage source converter is presented and described. A general
overview of permanent magnet synchronous machine is done in the fallowing part. Next the model of the
machine is expressed using mathematical formulas and finally the model is tested
2.1
Overview of the system
In this chapter every component of the system will be described and the model will be presented. The real
system that will be controlled is the one presented in Fig.2.1.
Figure 2.1: Setup configuration
The wind turbine and the gearbox from Fig.2.1 are replaced by an induction machine that is controlled
in torque mod. The generator side converter is controlled with Space Vector Modulation technique. Next
voltage source converter and permanent magnet synchronous machine will be presented.
2.2
Voltage source converter
In wind turbine application a back to back voltage source inverter (VSC) is widely used. The first inverter,
named generator side converter has the main purpose to transform the AC signal into DC, which is connected
to the DC-link, in this case the voltage source inverter is working as a rectifier. In the next step the DC
voltage is converted to AC signal with a desired frequency and voltage. In this case the grid side converter
is working as an inverter. The two inverters have different application for the wind turbine: the generator
5
2.2. VOLTAGE SOURCE CONVERTER
side inverter controls the torque and the speed while the grid side converter is keeping the DC link voltage
constant. The topology of a voltage source inverter is the one presented in Fig.2.2.
Figure 2.2: Topology of a voltage source inverter with ideal switches
The inverter is composed by three legs A, B, C each of the legs with two ideal semiconductors(IGBTs).
Only one switch from the leg can conduct at the same time once. The line to line voltages is expressed as in
the fallowing equations:
VAB = VAN − VBN
VBC = VBN − VCN
(2.1)
VAC = VAN − VCN
were N is the negative DC bus and VAN , VBN , VCN are the line to neutral voltage. Using Kirchhoff law it is
known that in a three phase, three wire system the voltage (currents) are equal zero.
VAN + VBN + VCN = 0
(2.2)
The two equations (2.1) and (2.2) can be rearrange in such a way that a new formula for the phase voltages
can be formulated:
 




VAB
1
0 −1
VAN
VBN  = 1 −1 1
0  · VBC 
(2.3)
3
0 −1 1
VAC
VCN
The switching states of each leg are representing by three variables: Da , Db , Dc named duty cycles. This
variables can have just two values ”1” when the switch is turn on and ”O” when is turn off. The switching
states together with the DC voltage can give an expression for the line two line voltages of the inverter:



  
VAB
1 −1 0
Da
VBC  = VDC  0
1 −1 ·  Db 
(2.4)
VAC
−1 0
1
Dc
After a few simplifications in the equations (2.4) and (2.3) the phase voltage is expressed with the help
of DC voltage and switching state as presented in equation (2.5):

  


2 −1 −1
Da
VAN
V
DC
−1 2 −1 ·  Db 
VBN  =
(2.5)
3
−1 −1 2
Dc
VCN
Having the duty cycles and the phase currents, the DC current can be deduct as in the fallowing:
 
Ia
IDC = Da Db Dc ·  Ib 
Ic
6
(2.6)
CHAPTER 2. THEORETICAL BACKGROUND
2.3
2.3.1
Permanent magnet synchronous machine
Introduction to SPMSM
Permanent magnet electric machine is a synchronous machine which is magnetized from permanent magnets
placed on the rotor instead of using a DC excitation circuit. In this case having the magnets on the rotor
the electrical losses of the machine are reduced and the absence of the field losses improves the thermal
characteristics of the PM machines. The absence of mechanical components such as slip rings and brushes
make the machine lighter, having a hight power to weight ratio which means a higher efficiency and reliability
[13]. With the advantages describe above permanent magnet synchronous generator is an attractive solution
for wind turbine applications. Like always, PM machines have some disadvantages: at high temperature the
PM are demagnetized, difficulties to handle in manufacture, high cost of PM material.
PM electric machines are classified into two groups PMDC machines and PMAC machines. The PMDC
machines are similar with the DC commutators machines, the only difference is that the field winding is
replaced by the permanent magnets. In case of PMAC the field is generated by the permanent magnets
located on the rotor and the brushes and the commutator does not exist in this machine type. For this
reason the machine is more simple and more attractive to use instead of PMDC [1]. Further on PMAC can
be classified depending on the type of the back electromotive force (EMF): trapezoidal and sinusoidal as
shown in Fig.2.3.
Figure 2.3: Clasification of permanent magnets machines
The trapezoidal machines, also called brushless DC motors, induce a trapezoidal back-EMF voltage
waveform in each stator phase winding during rotation, while the sinusoidal PMAC machines, called PM
synchronous machines, require sinusoidal current excitation of the stator [1].
Depending on the rotor configuration the PM synchronous machine can be classified in:
• Surface mounted magnet type (SPMSM). In this case the magnets are mounted on the surface of
the rotor. The magnets can be regarded as air because the permeability of the magnets is close to
unity(µ = 1) and the saliency is not present as a consequence of the same width of the magnets. From
this is resulting that the inductances expressed in the quadrature coordinates are equal (Lq = Ld ).
• Interior magnet type (IPMSM). For this case the magnets are place inside the rotor. In this configuration
of the machine appear the saliency and the airgap of d-axis is increased compared with the q axis
resulting that the q axis inductance has a different value than the d axis inductance.
In case of SPMSM the saliency is not present, making this machine more easy to design, becoming an
attractive solution for wind turbine application.
7
2.3. PERMANENT MAGNET SYNCHRONOUS MACHINE
2.3.2
Mathematical model of SPMSM
In order to design the PM machine in Matlab/Simulink is necessary to develop the mathematical model of
the motor that is derived from the space vector form of the stator voltage equation.
~ s = Rs I~s + d ~λs
V
abc
abc
dt abc
(2.7)
s
s
were Rs is the the stator winding resistance per phase, Iabc
is the stator phase current , Vabc
is the stator
phase voltage and λsabc is the flux linkage.
A transformation from abc to synchronous dq reference frame is needed in order to have a simpler model
that will be simulated in Matlab/Simulink. The model is derived in dq reference frame were q axis is rotating
with 90o ahead to the d axis with respect to the direction of rotation as shown in Fig.2.4.
Figure 2.4: Stator voltage in reference frame transformation
Based on the reference frame theory, stator voltage equations in dq synchronous reference frame are
presented:
d
(2.8)
vds = Rs isd + λsd − ωe λsq
dt
d s
λ + ωe λsd
(2.9)
dt q
were vsd , vsq are the dq axis stator voltage, isd , isq are the dq axis stator current, λsd , λsq are the dq axis stator
flux linkages, Rs stator resistances and ωe is the electrical speed in rad/s.
vqs = Rs isq +
Flux linkage equations are expressed as presented in equations (2.10) and (2.11):
8
λsd = Ld isd + λm
(2.10)
λsq = Lq isq
(2.11)
CHAPTER 2. THEORETICAL BACKGROUND
with Ld =Lq =Ls dq axis inductances and λm permanent magnet flux linkage. With the help of flux linkage
equations, stator voltage equations in dq reference frame have the fallowing form:
disd
− ωe Lq isq
dt
(2.12)
disq
+ ωe (Ld isd + λm )
dt
(2.13)
vds = Rs isd + Ls
vqs = Rs isq + Ls
The torque equation of PMSG can be derived from the power balance equation. The power flowing into
the machine can be express in dq reference frame as presented in equation (2.14)
Pes =
3 ss
(v i + vqs isq )
2 dd
(2.14)
After substituting the stator voltage equations in dq reference frame into equation (2.14) and separating the
power quantities the power has the fallowing form:
Pe =
(isq )2
3 d
(is )2
d
3
3
(Rs isd 2 + Rs isq 2 ) + ( Ld d + Lq
) + (ωe λsd isq − ωe λsq isd )
2
2 dt
2
dt
2
2
(2.15)
The first term represents the power loss in the conductors, the second term indicates the time rate of change
for stored energy in the magnetic fields and the third term express the energy conversion, from electrical
energy to mechanical energy.[1] From the third term can be express the electromagnetic torque because the
power output from the motor shaft must be equal with the electromechanical power.
Pe = ωm Te =
3
[ωe λsd isq − ωe λsq isd ]
2
(2.16)
The relation between the electrical velocity and the mechanical angular velocity of the motor depends on
the number of pole pairs as presented below:
ωe = npp · ωm
(2.17)
If in equation (2.16) the expression of flux is replaced by the equations (2.10) and (2.11) then the torque will
have the fallowing form:
3
Te = npp[λm isq + (Ld − Lq )isq isd ]
(2.18)
2
In the final expression of the torque, equation (2.18), it can be observed that there are two terms, the first
one represents the synchronous torque and is produced by the flux of the permanent magnets and the second
term represents the reluctance torque and represents the torque produced by the difference of the inductances
in dq reference frame. In the project the motor is surface mounted permanent magnet and in this case the
inductances in dq reference frame are equal resulting a simpler expression of the electromagnetic torque,
without the reluctance torque. With the assumption express above, equation (2.18) has the fallowing form:
Te =
3
nppλm isq
2
(2.19)
The mechanical equation of the machine is express as a function of the electromagnetic torque (Te ), load
torque (Tl ) and electrical velocity of the machine:
Te = Tl + Bωm + J
d
ωm
dt
(2.20)
were J is the moment of inertia and B is the viscous friction.
9
2.3. PERMANENT MAGNET SYNCHRONOUS MACHINE
2.3.3
Validation of SPMSM
The mathematical equations of the machines are implemented in Matlab/Simulink in order to observed if
the motor model is reproducing the real machine. The parameters value of the machines used to control the
machine are presented in Table 2.1.
Parameter
Power
Phase Voltage
Rated current
Rated torque
Rated speed
Stator resistance
Synchronous inductance
Synchronous inductance
Permanent magnet flux linkage
Rotor moment of inertia
Nr. of pole pairs
Symbol
Pn
Vn
In
Tn
nn
Rs
Ld
Lq
λm
J
npp
Value
9.42
185
19.5
20
4500
0.18
2
2
0.123
0.48
4
Unit
[kW]
[V]
[A]
[Nm]
[rpm]
[Ω]
[mH]
[mH]
[Wb]
[mKgm2 ]
-
Table 2.1: Parameters of PMSM
The electrical and mechanical parameters of the generator presented in Table.2.1 were taken form the
datasheet of the machine presented in Appendix A. The simulation bloc is presented in Appendix E. The
validation of the model is made for the nominal load torque (Tl =20 [Nm]) and for the nominal speed
(nn =4500[rpm]). The machine is started at rated speed and after 0.4 seconds the nominal torque is applied.
The currents at nominal working point are present in Fig.2.5. It can be observed that at no load torque the
current is zero and at 0.4 [sec] when the load torque is applied the current has the rated value 27 [A] .
Figure 2.5: Stator currents at nominal working point
In Fig.2.6 the stator voltages of the machine is plotted. It can be observed that when the motor is
running at zero load torque the voltage has a smaller amplitude than when the load is applied. The value of
the voltage at nominal working point is the same that the nominal voltage described in datasheet.
10
CHAPTER 2. THEORETICAL BACKGROUND
Figure 2.6: Stator voltage at nominal working point
Conclusion
In this chapter introduction in the motor theory was made in order to familiarize with the concepts
and physical phenomenon that appear in an electric machine. Then the concept and the model of a voltage
source inverter is derived, fallowed by the description of the motor model in terms of mathematical equations.
Finally the mathematical model of the machine is implemented in Matlab/Simulink and is validated. With
the model of the voltage source inverter and PMSM working properly the control strategy and the designing
of the controllers can be chosen further on.
11
Chapter 3
Field oriented control
Field Oriented Control is the strategy chosen to be implemented in the PMSM control. The chapter starts
with a briefly introduction about FOC. Next the design of the current and speed controller is described. In
the end of this chapter the control is implemented in Matlab/Simulink and the results are presented.
3.1
Field oriented control
Field Oriented Control (FOC) is one of the most used technique for controlling the torque of a permanent
magnet synchronous motor. For a simpler implementation the strategy is using the synchronous reference
frame. FOC is a close loop strategy and is composed by two current controllers necessary for controlling the
torque and one speed controller. The controllers are PI’s (Proportional Integrator) due to theirs good steady
state errors. The diagram of the field oriented control strategy is the one presented in Fig.3.1.
Figure 3.1: Scheme of Field Oriented Control strategy
The measurement values necessary in the control are the DC voltage, the three phase stator current and
the rotor position of PMSM. In this case an encoder is used on the motor shaft in order to have the rotor speed.
12
CHAPTER 3. FIELD ORIENTED CONTROL
The integration of the speed will give the rotor position, necessary in the transformation of the measured
stator currents into dq reference frame axis. The d an q current component are the feedback currents for
the current controllers. The speed controller generates the torque, that will command the reference frame
currents isdr ef and isqr ef . From this torque command the reference currents isdr ef , isqr ef are set based on
the control strategies presented in details further on. The reference currents are compared with the actual
rotor currents in the dq reference frame and send to two current controllers. The output of the controllers
represents the required dq voltages. To control the current independently one of each other is necessary to
add the compensation term ωe λsd and to subtract ωe λsq term from the output of the current controllers.
The dq components of the voltage are transform to αβ reference frame in order to compute the duty cycles
necessary in Space Vector Modulation strategy. Finally the PWM generator block calculates the switching
signals for the inverter.
3.2
Control properties
In order to have a simpler control for PMSM some simplification have to be taken into consideration regarding
the produced torque. The load torque can be controlled by controlling the torque angle. Some control
strategies are described briefly in the fallowing:
Constant torque angle control
In this control strategy the d axis current is kept zero, while the vector current is align with the q axis in
order to maintain the torque angle equal with 90o . This is one of the most used control strategy because of
the simplicity, especially for SPMSM. In case of IPMSM, with a high saliency ratio it is not recommended
to use this control strategy because of the reluctance torque produced.
The torque equation for a PMSM, taking into account both isd and isq currents is the one derived in
equation (3.1).
3
(3.1)
Te = npp[λm isq + (Ld − Lq )isq isd ]
2
If the dq currents are substituting in equation (3.1) as presented in Fig.3.2 and after a few simplification the
torque value is the one presented in equation (3.2).
Figure 3.2: Vector diagram for constant torque per amper control in steady state
Te =
3
nppλm isq
2
(3.2)
From equation (3.2) it can be observed that the control property is very simple to implement, representing
the linearisation between the torque and current.
13
3.3. CURRENT AND SPEED CONTROLLER DESIGN
Maximum torque per ampere control
This control strategy has the main goal to keep the stator current as small as possible for a given
electromagnetic torque, in this way the maximum torque per ampere is obtain. In the case of surface mounted
permanent magnet machine this strategy is the same as CTAC but in case of IPMSM this control strategy
gives the highest torque output compared with the current, because is taken into consideration both electro
magnetic and the reluctance torque.
Unity power factor
One of the advantages of this control strategy is that between voltage and current vector is no phase
difference and the Volt Ampere (VA) rating of the machine is minimized.
Constant stator flux control
In this case the stator flux linkage magnitude is kept constant witch will result in limitation of the torque
capability of the machine.
The focus in this project is in implementation of a sensorlees control for PMSM and not in optimization of
the control strategy, so the constant torque angle control is implemented due to his simplicity, by controlling
only the iq current.
3.3
Current and speed controller design
In this section the speed and current controller design will be presented in details. d axis current controller
design is identical with q axis current controller so just one will be treat in this report. The structure of the
current and speed controllers is presented in Fig.3.3.
Figure 3.3: d and q axis control topology
were wref represents the reference speed in rpm and wm represents the mechanical speed of the rotor in
rpm. The error between the reference and the measured speed is send to a PI controller. The output of the
PI represents the electromagnetic torque from were the reference currents are subtract. The error between
the reference and the measured currents is the input to other two PI controllers necessary to determine the
dq reference stator voltages.
In order to have a simpler design of the current controllers and to controll the dq currents independently a
decoupling factor from the stator voltage equation must be done. The common part from the stator equations,
equations (2.8) and (2.9), is the back emf voltage. By subtracting ωe λsq from equation (2.8) and adding ωe λsd
to equation (2.9) the dq currents will be independently one of each other. The d and q current controller
design it has the same dynamics so the tuning of the PI controller is done just for the q axis.
14
CHAPTER 3. FIELD ORIENTED CONTROL
3.3.1
Design of q axis current controller
The diagram of the current controller is the one presented in Fig.3.4. The decoupling between the d and q
axis are performed.
Figure 3.4: The structure of the q axis current controller
The blocks from the figure are explained in details in the fallowing part:
• The controller block is chosen to be a PI controller because its offer a zero error in steady state. The
transfer function of a PI controller is the ratio between the output signal and the error signal as shown
in equation (3.3):
kii
U (s)
1 + Tii s
= kpi +
= kpi
(3.3)
Gc (s) =
E(s)
s
Tii s
were kpi represent the proportional gain, kii the integrator gain and Tii is called the integrator time
and represents the ratio between kpi and kii .
Tii =
kpi
kii
(3.4)
• The control algorithm block represents the delay introduced by the digital calculations. It has the form
1
= 0.2[ms] (were fs is the sampling
of a first order system, with a time constant equal with Ts = f1s = 5k
frequency).
GCA (s) =
1
Ts s + 1
(3.5)
• The plant transfer function is determine from the dq voltage equations after the decoupling term has
d
been removed, were s = dt
and considering current as input and voltage as output as shown in equation
(3.6):
Gpl (s) =
1
1
1
iq (s)
K
=
=
=
L
s
uq (s)
Rs + sLs
Rs 1 + s R
1 + sTq
(3.6)
s
were Tq is the time constant of the motor and K is a notation for the inverse of the stator resistance:
K=
Tq =
1
Rs
Ls
= 0.0116[sec]
Rs
(3.7)
• The sampling block is the delay introduced by the digital to analog conversion. It is also a first order
transfer function with the time constant Ts .
Gsam (s) =
1
0.5Ts s + 1
(3.8)
15
3.3. CURRENT AND SPEED CONTROLLER DESIGN
In order to have a simpler control loop the feedback path is moved to the forward path as shown in
Fig.3.5.
Figure 3.5: Topology of the q axis current controller with unity feedback
The open loop transfer function of the current controller is the one presented in equation (3.9).
GOL (s) = Gsam (s) · Gc (s) · GCA (s) · Gpl (s)
1
1 + Tii s
1
K
GOL (s) =
· kpi
·
·
0.5Ts s + 1
Tii s
Ts s + 1 1 + sTq
(3.9)
The slowest pole is the one of the PMSM transfer function and is meant to cancel the zero of the controller,
making the system more stable. This implies:
Ls
= 0.0116[sec]
(3.10)
Rs
In order to simplify the transfer function a time constant is introduced, who represents the approximation
of all first order transfer functions that introduce delays because their values are very small compared with
the electrical motor time constant, resulting that their dynamics are smaller. This implies that the transfer
function of the delays will be replaced by a unique transfer function of first order, having the time constant
equal with the sum of all time constants from the system.
1 + Tii s = 1 + Tq s ⇒ Tii = Tq =
Tsi = 1.5Ts = 0.3[ms]
(3.11)
With the assumptions made about the open loop transfer function the equation (3.9) will have a simpler
form as fallows:
kpi
1
GOL (s) =
K
(3.12)
Tii s Tsi s + 1
To determine the value of kp is necessary to
use a controller design criterion called Optimal Modulus (OM),
√
2
with the damping factor chosen to be ζ = 2 . The open loop transfer function of a second order system has
the form:
1
GOM (s) =
(3.13)
2τ s(τ s + 1)
If the analogy between the equation (3.12) and (3.13) is made the fallowing relations are deducted in oder
to determine the gains of the PI controller:
kpi K
1
Tii Rs
=
⇒ kpi =
= 3.333
Tii
2Tsi
2Tsi
The PI transfer function in ’s’ domain has the fallowing form:
Gc (s) = 3.33 +
300
s
(3.14)
(3.15)
In order to implement the controllers in real system the transfer function of the PI current controller is
transform in ’z’ domain, as presented in the fallowing equation:
Gc (z) = 3.333 +
16
0.06
z−1
(3.16)
CHAPTER 3. FIELD ORIENTED CONTROL
The bode diagram of the q axis current controller is the one presented in Fig.3.6. It can be observed that it
has a phase margin of PM=63.6 [deg], a gain margin equal with GM=19.1 [dB] and it can be observed that
the system is stable.
Figure 3.6: Bode diagram of the q axis current controller
The step response of the system is also presented in Fig.3.7 with the fallowing characteristics:
Figure 3.7: Step response for the q axis current controller
• Maximum overshoot Mp =4.32%
• Settling time ts =2.53 [ms]
17
3.3. CURRENT AND SPEED CONTROLLER DESIGN
• Rise time tr =0.912 [ms]
3.3.2
Design of speed controller
The loop from were the speed controller will be design is the one presented in Fig.3.8.
Figure 3.8: Topology of the speed controller loop
The blocks from the figure are described in the fallowing:
• The PI speed controller with the transfer function presented in equation (3.17)
Gc (s) = kps
1 + Tis s
Tis s
(3.17)
were kps is the proportional gain of the speed controller and Tis is the time integral.
• The delay introduced by the digital calculations is representing the control algorithm block. Transfer
1
function has the form of a first order system with a time constant Ts = f1s = 5k
= 0.2[ms] (were fs is
the sampling frequency)
1
(3.18)
GCA (s) =
Ts s + 1
• The current control loop can be expressed like a first order system with the time constant Tiq =
with the transfer function presented in equation (3.19)
GCCL (s) =
1
Tiq s + 1
Tii Rs
Kpi
(3.19)
• The plant block is calculated from the mechanical equation of the PMSM as shown in equation (3.20)
Te − Tl − Bωm = J
d
ωm
dt
(3.20)
were
3
nppλm isq
2
If the viscous friction coefficient is neglected then the mechanical equation will become:
Te =
Te − Tl = J
d
ωm
dt
(3.21)
(3.22)
The load torque from the point of view of controller is consider as a disturbance and will not be
consider. From equation (3.22) the transfer function of the machine in ’s’ domain has the fallowing
form:
ωm (s)
npp
=
(3.23)
Te (s) − Tl (s)
Js
18
CHAPTER 3. FIELD ORIENTED CONTROL
• The filter block represents the delay introduced by the filtering of the measured speed, from an encoder
1
1
mounted on the shaft of the machine. The filter has a time constant Tf = ω1c = 2πf
= 2π200
= 0.796[ms]
GF L (s) =
1
Tf s + 1
(3.24)
• The sampling block is the delay introduced by the digital to analog conversion and his time constant
is equal with Ts
1
(3.25)
Gsam (s) =
0.5Ts s + 1
To simplify the close loop transfer function the disturbances are not taken into consideration and the feedback
path is moved on the forward part as in the case of current controller. The close loop system in presented in
the next figure.
Figure 3.9: Speed controller loop with unity feedback
The open loop transfer function is the one presented in equation (3.26)
GOL (s) =
1
1
1
1
3nppλm npp
1 + Tis s
·
· kps
·
·
·
0.5Ts s + 1 Tf s + 1
Tis s
Ts s + 1 Tiq s + 1
2
Js
(3.26)
In order to simplify the transfer function, all the time constants of the delays are approximated with one
time constant as presented in equation (3.27)
Tss = 1.5Ts + Tf + Tiq = 1.8[ms]
(3.27)
The open loop transfer function becomes:
GOL (s) =
nppKc kps (Tis s + 1)
JTis s2 (Tss s + 1)
(3.28)
with Kc = 23 nppλm . In order to obtain an optimal response is necessary to tune the regulator according to
the Optimum Symmetric Method(OSM) [10]. The open loop transfer function of OS method has the form
presented below:
k1 kp Ti s + k1 kp
GOSM
(3.29)
OL (s) = 2
s (T1 Ti s + T1 )
In order to find the gains for the PI controller is necessary to arrange the equation of the open loop transfer
function of the speed controller in the same manner as equation (3.29).
GOL (s) =
nppKc
c
kps Tis s + nppK
kps
J
J
s2 (Tis Tss s + Tis )
(3.30)
With the help of equations (3.30) and (3.28) the gains of the PI controller are find out as presented below:
kps =
1
1
= nppKc
= 0.462
2k1 T1
2 J Tss
Tis = 4T1 = 4Tss = 7[m]
(3.31)
(3.32)
19
3.3. CURRENT AND SPEED CONTROLLER DESIGN
To implement the control in real system is necessary also to transform the PI speed controller form ’s’ domain
in ’z’ domain. The transfer function of the speed PI controller in ’z’ domain is the one presented in equation
(3.33).
0.0132
Gc (z) = 0.462 +
(3.33)
z−1
The bode diagram is presented in Fig.3.10 and can be observed that has a phase margin of PM=34.8 [deg],
a gain margin equal with GM=13 [dB].
Figure 3.10: Bode diagram of the speed controller
The step response of the speed controller is presented in Fig.3.11. It is characterized by the fallowing
parameter:
Figure 3.11: Speed response of the speed controller
20
CHAPTER 3. FIELD ORIENTED CONTROL
• Maximum overshoot Mp =43.3%
• Settling time ts =2.91 [ms]
• Rise time tr =3.77 [ms]
One of the characteristics of the speed controller is to be slower than the current controller and seeing the
characteristics it is noticeable that the current controller acts faster. From the step response of the speed
controller figure it can be observed that it has a very big overshoot, which mean that when starting the
machine it will have a very big torque command, making the currents to have a very big amplitude, above
the maximum allowed. For this reason the anti-windup circuit is implemented in order to limit the response
of the speed controller.
Anti-windup circuit
When designing the current and speed controllers in FOC it is necessary to have in mind the limitation of
their outputs in order to prevent the system from overcurrents or overvoltages appearance.When the output
of the controlled signal (current, voltage) has a very big value the input of the controller has a saturated
value. This has the consequence that the integral part is integrating the provided error. Because of this the
output of the controller may drift to very large values and to a poor transient response. The overshoots in
the controlled signal can be avoided by keeping the integral to a proper value when the controller saturates,
so when the control error changes the controller is ready to act [15]. The anti-windup circuit is the one
presented in Fig.3.12.
Figure 3.12: Topology of the integrator antiwindup
The output of the controller is limited to a certain value given by the limitation of the voltages and
currents. The input to this limitation gain is subtract from the output and the difference is fed back to the
integrator through the gain Ta . This signal is becoming non zero when the limiter saturates and prevents
the integrator to have a very big value. The reduction in the integration winding up is set by the value of
the time constant Ta . The value of time constant must be chosen as small as possible but also a very small
value may decrease the system performances [17]. The gains chosen for the anti-windup circuit are kai =0.1
for the currents controllers and kas =5 for the speed controller.
3.4
Simulation results
After the description of Field Oriented Control strategy with the determination of all parameters, is necessary
to be implement it in Matlab/Simulink. In order to go further and test the simulations in real system all
the calculation are represented in discrete domain. The electrical parameters of the system are the one
presented in Table 2.1 in Section 2.3 and the simulation blocks are presented in Appendix E. In laboratory
the induction machine M2AA100LA, with the parameters presented in Appendix D, is used to load the
permanent magnet machine. For this reason for now one it will be considered that the nominal speed of
PMSM is nn = 1400[rpm] and the rated torque will be consider equal with TL = 14 [Nm].
The sampling time of the simulation model was chosen to be Ts = 5[kHz]. The duty cycles generation for
the voltage source inverter are done with the Space Vector Modulation block and it was taken from dSpace
21
3.4. SIMULATION RESULTS
laboratory, IET. In this part of the chapter the behavior of the system in different circumstances will be
observed: step in speed and no load, step in speed and step in load, motor and generator operation.
Test of PMSM at no load
For this test the PMSM is started at 50% rated speed (nn = 700 [rpm]) and no load, at second 1 a step
of 700 [rmp] is applied to the reference speed. The response of the measured speed is shown in Fig.3.13.
Figure 3.13: Reference and measured speed at no load
As seen in the figure the measure speed is fallowing with good accuracy the reference speed. The measured
speed it reaches 700 [rpm] in 0.045 [sec], slower in comparison with the designed PI controllers but without
any overshoot. This is the contribution of the anti-windup circuit.
The dq measured currents are compared with the dq reference currents in Fig.3.14. It can be observed
that the d current is zero imposed by the control strategy. From Fig.3.14 (b) it can be observed that the
current is limited in FOC to value I=24 [A]. After the motor is reaching the reference speed the currents are
stabilized at zero, because the machine is working just in speed mode and the load torque is equal with zero.
Figure 3.14: Reference and measured currents at no load and steep in speed a)Id current b)Iq current
The phase voltages and the stator currents of the machine are presented in Fig.3.15. In Fig.3.15 b) at
start up and until the speed is reached the reference speed the currents are limited to value 24 [A] and at no
22
CHAPTER 3. FIELD ORIENTED CONTROL
load the currents are zero. The stator voltages at no load and 50 % rated speed has the amplitude equal with
36.06 [V] and at the rated speed equal with 72.08 [V]. In the zoom made can be observed that the signals
are sinusoidal.
Figure 3.15: Stator currents and voltages at no load and step in speed a)Measured voltages b)Measured currents
Test of PMSM at 7 [Nm] load torque
For this test the motor is loaded with 50% rated load torque (TL = 7 Nm) and the reference speed has
a value equal with 700 [rpm]. At time 1 [sec] another step to rated speed is applied to the machine. The
response of the speed is presented in Fig.3.16.
Figure 3.16: Reference and measured speed at 7 [Nm] load torque
It can be observed that the response of the speed when the load torque is applied is slower than in the case
were the machine is working at zero load torque, but without overshoots. The settling time of the measured
speed is 0.05 [sec].
Similar with the case without the load torque the dq currents are fallowing the reference currents, presented in Fig.3.17. The q axis current is limited to 24 [A] as in the previous case and the d axis is zero as
expected.
23
3.4. SIMULATION RESULTS
Figure 3.17: Reference and measured currents at 7 [Nm] load torque a)Id current b)Iq current
The stator currents and voltages are presented in Fig.3.18. The stator currents at 50% rated torque and
50% rated speed have the value 9.476 [A] while the voltages have the value 38.35 [V].
Figure 3.18: Stator currents and voltages at 7 [Nm] load torque a)Measured voltages b)Measured currents
Test of PMSM at nominal speed, nominal torque
In this test the machine is started in motor mode at 50% rated speed (nn = 700 [rpm]) and no load. At
0.5 [sec] a load torque of 7 [Nm] is applied to the system, fallowed by a step in speed to the rated speed at
t=1 [sec], and a step to nominal load torque at 1.5 [sec]. The reference and measured speed is presented in
Fig.3.19. It can be observed that the measured speed is fallowing with good accuracy the reference one and
without any overshoots. In the zoom made on the graphic it can be observed that when the load torque is
applied to the system small back overshoots appear. Also it can be observed that the settling time of the
measured speed when the machine is loaded is bigger that when is no load applied to the motor.
24
CHAPTER 3. FIELD ORIENTED CONTROL
Figure 3.19: Reference and measured speed for different values of the speed and load torque
The dq currents are plotted for this test in order to observed the correctness of the chosen control. In
Fig.3.20 the d current has the value 0 and the q current can be calculated from the torque equation (2.19).
The value of the q current when the load torque is applied is 18.9 [A] as expected. When the load torque is
applied small overshots appear in the d current as presented in the zoom made on Fig.3.20(a).
Figure 3.20: Reference and measured currents for different values of the speed and load torque a)Id current b)Iq
current
In Fig.3.21 stator voltages and currents are plotted. The amplitude of the voltages at nominal speed and
nominal torque is 79.46 [V]. For simplicity in the control Id current was chosen to be zero, so the magnitude
of Iq current is giving the magnitude of the stator currents resulting that at 50% rated torque the value of
the currents is 9.48 [A] and at rated torque 18.95 [A]. From the zoom in both plots it can be observed that
the signals are sinusoidal.
25
3.4. SIMULATION RESULTS
Figure 3.21: Measured stator currents and voltages for different values of the speed and load torque a)Measured
voltages b)Measured currents
Test of PMSM in generator mod
For this test the machine is started in motor mode at rated speed (nn =1400 [rpm]). At t=0.5 [sec] the
load torque is applied to the machine and at t=1.5 [sec] the motor is run in generator mode. The reference
and the measured speed is presented in Fig.3.22, and it can be observed that the measured speed fallows
with good accuracy the reference one. In the zoom made on the plot can be observed the behavior of the
speed when the positive and negative torque is applied.
Figure 3.22: Reference and measured speed in generator mode
The behavior of the electromagnetic torque in generator mode is shown in Fig.3.23. When positive torque
is applied to the motor, positive electromagnetic torque is generated, and when motor is working in generator
mode the electromagnetic torque is responding in the same way.
26
CHAPTER 3. FIELD ORIENTED CONTROL
Figure 3.23: Electromagnetic torque in generator mode
With this test it was proven that the controll is working also in the generator mode of the machine.
Conclusion
In this chapter Field Oriented Control was presented and described in details. The design of the speed
and current controllers were made, necessary in a good implementation of the control strategy. To prove the
correctness of the system different plots are done for different speeds and load torque. As the controllers show
satisfactory results in both motor and generator mode Field Oriented Control was chosen to be implement
in real system. Next step in the project is to find the proper method to estimate the position and speed of
the PMSM in order not to use the encoder mounted on the shaft of the motor.
27
Chapter 4
Sensorless control of PMSM
This chapter starts with the presentation of the sensorlees algorithm fallowed by the description of different estimation strategies for the rotor position. The chosen sensorless strategy is described and finally is
implemented in simulation. The results and the conclusion are presented in the end of the chapter
4.1
Presentation of the sensorlees control
In the last years the induction machine has been a nice solution for applications but PMSM motor has
become a very important competitor because of the high efficiency. To control the motor in a robust way
is necessary to know the rotor position. The most used technique to determine the rotor position is to use
an encoder or a resolver on the motor shaft, but this will add additional cost to the system, the size of the
system will increase and the reliability will degrease. In the last years have been an intense research about
finding the most reliable position sensorlees method. The Field Oriented Control strategy scheme with rotor
position estimation is presented in Fig.4.1.
Figure 4.1: Field Oriented Control of PMSM without the sensor
The research on surface mounted PMSM is more difficult that on interior PMSM because of the equality
between the d and q inductances. Also at zero and low speed is very difficult to determine the rotor position
28
CHAPTER 4. SENSORLESS CONTROL OF PMSM
but the advantages like the simplicity in the motor structure and lower cost of the machine are significant
reasons for starting the investigations on the estimation position of the rotor. Further on some position
estimation strategy will be briefly presented.
Position Estimation Based on Back EMF
The most easiest and frequent method to estimate the position of the rotor is the one based on back
electromotive force (EMF). In this strategy the variables necessary to compute the back EMF are estimated
from the electrical parameter of the machines. The mechanical components are deducted from the estimated
values from the back EMF. Even this strategy is very easy to implement, it has some drawbacks regarding
the sensitivity to the parameters uncertainties, especially with the stator resistance variation and model of
the machine in case of zero and low speed [16]. For the case of wind turbine application were the generator
is working at variable speeds this strategy is very suitable, also because at high speeds the voltage drop on
the stator resistance is very small.
Position Estimation Based on Stator Flux Linkage Estimation.
The flux linkage is estimated from the stationary reference frame as presented in equations (4.1) and
(4.2).
Z
λα =
(uα − Rs iα )dt
(4.1)
(uβ − Rs iβ )dt
(4.2)
Z
λβ =
In order to determine the flux linkage it can be observed that some parameters have to be known: phase
current, phase voltage and stator resistance either by measurements or estimated. With this technique some
problems can appear due to the integration drift and variation of the parameters with the temperature.
Another disadvantage with this method is that the initial position is not detectable unless another control
strategy is implemented for this purpose.
Position Estimation Based on Observer Methods
The idea behind the observer method is to construct a model that has the same inputs than the real
machine and the states of the model fallows the values of the real model (velocity, rotor position). If errors
appear in the estimated states of the observed, they can be reduced by the correction of the error at the
output of the real machine (which is measurable) and the output of the modeled machine. As this method
is a parameter dependent method, variations in parameters of the machine can have a big influence in the
estimation position
Position estimation using high frequency signal injection.
This method is more attractive for IPMSM because they present saliency. This strategy can work also
at zero and low speed. But in case of direct drive wind turbine, were the switching frequency is low this
strategy is not so suitable.
4.2
Rotor position estimation
The chosen strategy to determinate the estimation position of the rotor is the one based on back EMF.
In case of a permanent magnet synchronous motor the rotor permanent magnet flux is align with d axis,
resulting that the induced voltage of permanent magnet flux (back EMF) is align with the q axis. Rotor
position is the same with the position of back EMF vector as shown in Fig.4.2. The position of the back
EMF vector, respectively rotor position is determined as shown in equation (4.3).
29
4.2. ROTOR POSITION ESTIMATION
Figure 4.2: Back EMF in stationary reference frame
θr = tan−1
esd
esq
(4.3)
To have a simpler control strategy and to get rid of the problems that may appear with the integration
of the current a new method to determine the back EMF is describe further on.
The space vector of the machine variables (current, voltage, flux linkage) represented along the phase
axis can be expressed as following:
2
s
fabc
= (fas + afbs + a2 fcs )
(4.4)
3
were the coefficient 32 gives the same magnitude of the space vector as the amplitude of the phase waveforms,
2π
fa , fb , fc represents the instantaneous values for the machine variables for phase a, b and c and a = ej 3
[1]. In order to have a simpler model for computing the variables of the machine a new reference frame is
described. The only information that are available until now are the three phase stator voltage and current,
with the help of Clark Transformation the two variables αβ can be computed. The relation between abc and
αβ reference frame are represented in the Fig.4.3.
Figure 4.3: Representation of stator fix αβ reference frame
It can be observed that α axis is align with the phase a and β is the orthogonal imaginary axis. The
30
CHAPTER 4. SENSORLESS CONTROL OF PMSM
dependence between αβ and abc phase coordinates is expressed matriceal as presented below:
 
va
1
1 1
−
−
2
vα
√2
√2
 vb 
=
·
3
vβ
3 0
− 23
2
v
(4.5)
c
Knowing the stator voltages in the fixed reference frame αβ it is possible to calculate the stator angle θv as
presented in equation (4.6).
Vβ
(4.6)
θv = atan
Vα
Now all the variables necessary to calculate the electrical parameters of the machine in the new coordinates are
deduct. The transformation from αβ to δϕ is based on Park Transformation and represents the transformation
from the stator equations to the machines rotor equations and is expressed as described below:
vδ
cosθv sinθv
v
=
· α
(4.7)
vϕ
−sinθv cosθv
vβ
With the new transformation the stator voltage will be aligned on δ axis while the vϕ component is zero.
The electrical equations of PMSM in the new coordinates system are the one present in the following:
vδ = Rs iδ + Ls
diδ
− ωev Ls idelta + eδ
dt
(4.8)
diϕ
+ ωev Ls iϕ + eϕ
(4.9)
dt
were vδ , vϕ , iδ , iϕ are the stator voltages and currents in δϕ reference frame, ωev is the rotating speed of is ,
eδ , eϕ are the stator back EMF in δϕ reference frame were:
vϕ = Rs iϕ + Ls
eδ = ωe λm sinθn
eϕ = ωe λm cosθn
(4.10)
were ωe is the electrical speed, λm is the magnetic flux linkage of the motor and θn is estimated angle in δϕ
coordinated
The simplicity with this strategy, in determining the position of the rotor is coming from the fact that
no integration is needed. In steady state iδ , iϕ currents are constant resulting that the derivative term from
equations (4.8) and (4.9) may be simply omitted. With this assumption made some problems are solved like
the ones that appear with the ideal integration affected by the dc-link or dc-offset, because of the initial
conditions of the integral and from non-perfect measurements of current or/and voltages [2]. With this
simplifications made in the chosen control strategy the rotor position in δϕ coordinated is determined from
equations (4.8) and (4.9)and presented in the following:
θn = tan−1
vδ − Rs iδ + ωev Ls iδ
vϕ − Rs iϕ − ωev Ls iϕ
(4.11)
The estimated rotor position is determinate as shown in the fallowing equation:
θ̂ = θv − θn
(4.12)
Next the sensorless algorithm is implemented in Maltlab/Simulink and the simulation results are presented
and discussed.
31
4.3. SIMULATION RESULTS
4.3
Simulation results
In this section, simulation results of the position and speed estimation algorithm are presented. The sensorless
method is first tested in open loop and then in close loop to see if the system is working properly.
Open loop test of the sensorless strategy
The machine is started at nominal rated speed (nn =1400 [rpm]) and no load. At 0.7 [sec] a step to
50% rated load torque (TL = 7 [Nm]) is applied to the system. At time 1.4 [sec] the machine is running in
generator mode at rated torque (TL = 14 [Nm]). The estimated and measured rotor position are presented
in Fig.4.4. It can be observed that at rated load torque the error between the estimated and rotor position
is the same than in the case were the motor is running with zero torque and it has the value equal with 3.29
degrees.
Figure 4.4: Estimated and rotor position for PMSM in open loop system
The measured and estimated speed is shown in Fig.4.5. The estimated speed is fallowing with good
accuracy the mechanical speed in case of motor operation as well as in the case were the machine is driven
in generator mod.
Figure 4.5: Measured and estimated mechanical speed of PMSM in open loop system
32
CHAPTER 4. SENSORLESS CONTROL OF PMSM
Test of PMSM in close loop
The sensorless algorithm is tested in closed loop at different conditions to see the behavior of the estimated
rotor position. The switch between the rotor position and the estimated position is made at time 0.01 sec, at
around 400 [rpm]. The machine is running at nominal speed and no load. At time 0.7 [sec] a step to 7 [Nm]
is applied to the machine fallowed by another one, to rated load torque(TL =14 [Nm]) at time 1.4 [sec]. The
rotor and estimated position are presented in Fig.4.6.
Figure 4.6: Estimated and rotor position of PMSM at 7 [Nm] load torque
It can be observed that the estimated position is in accordance with the real position of the motor. At
full load torque and rated speed the error between the estimated and rotor position has the value equal with
3.51 [degrees] and in the case when the motor is driven at zero load torque has the value 3.36 [degrees]. The
reference and the measured speed of the motor are plotted in Fig.4.7. It can be observed that the estimated
speed is fallowing with good accuracy the reference speed when the sensor is not used in the system and the
rotor position is estimated. There are no overshoots and the settling time of the speed response is around
0.04 [sec].
Figure 4.7: Reference and measured speed with the estimated rotor position at 7 [Nm] load torque
33
4.3. SIMULATION RESULTS
Stator voltages and currents are presented in Fig.4.8 It can be observed in Fig.4.8 a) that the voltages
signals are sinusoidal and have the same values as in the case were the encoder was used. In Fig.4.8 b) stator
currents are shown and at rated load torque, the currents magnitude have the value almost 18.94 [A] the
same as in the simulations made at the same conditions.
Figure 4.8: Stator voltages and currents calculated with the estimated position a)Measured voltage b)Measured current
Next test is made to observed the behavior of the machine in generator mode. The machine is started
at rated speed (nn =1400 [rpm]) and zero load torque. At time 0.7 [sec] a step to 50% rated load torque is
applied and at time 1.4 [sec] the motor is run in generator mod at rated load torque. The estimated position
in this case is presented in Fig.4.9. It can be observed that when the machine is running in motor mode the
position error is almost the same as in the case where the motor is running in generator mode and has the
value around 3.5 [degrees]
Figure 4.9: Estimated and rotor position of PMSM in generator mod
34
CHAPTER 4. SENSORLESS CONTROL OF PMSM
The measured and estimated speed are presented in Fig.4.10. The estimated speed is in very good
accordance with the measured speed. In the zoom made on the plot it can be observed the overshoots that
appear when the load torque is applied.
Figure 4.10: Estimated and measured speed of PMSM in generator mod
The electromagnetic torque is presented in Fig.4.11. It can be observed that the electromagnetic torque
is responding very well in the load changes, when a positive load torque is applied the electromagnetic torque
is positive and when the machine is working in generator mode the load torque is negative.
Figure 4.11: Electromagnetic torque of PMSM in generator mod
35
4.3. SIMULATION RESULTS
Conclusions
This chapter had the main purpose to find a suitable control strategy for estimating the rotor position of
PMSM. First several algorithms were described and one method was chosen to be implemented. The method
was tested at different conditions to observed the behavior of the machine without the sensor. The position
error is almost the same in the case when the machine is running with zero load torque as in the case when
is running at rated load torque. Also in generator mode the estimated rotor position is working properly.
Next, the simulations are implemented in laboratory, in dSpace application, in order to see the correctness
of the system.
36
CHAPTER 5. LABORATORY WORK
Chapter 5
Laboratory work
This chapter has the main purpose to assure that the models and simulations done until know are correct
and in accordance with the real system. First the test setup and the real time interface are presented. Next
in the chapter the experimental results for different condition are presented and the conclusion are taken.
5.1
Laboratory structure
The setup used in the laboratory in order to test the simulations is the one presented in Fig.5.1.
Figure 5.1: Description of laboratory setup
The main components of the system are:
• DC power supply
• Danfoss VLT5004 inverter
• Siemens PMSM type ROTEC 1FT6084-8SH7
• Danfoss FC300VLT (FC 302) frequency inverter
• ABB three phase induction motor type M2AA100LA
• dSpace control system
37
5.2. REAL TIME INTERFACE
• current and DC voltage measurement boxes
• encoder
The characteristics of the laboratory setup components are the one presented in Appendix.D. The PMSM
is fed by a frequency inverter (Danfoss FC300VLT). The inverter is IGBT based converter whose interface
card has been removed and replaced by a Interface and Protection Card (IPC), that enables the IGBT
drivers to be controlled from an external digital controller providing reliable short-circuit, shoot-through,
dc-overvoltage and over temperature protections [12]. The IM is fed by a torque controlled DC-inverter
(Danfoss VLT5004 inverter) so a great deal of loading-torque characteristics can be achieved. A regenerative
line rectifier (SIMOVERT RRU) is used to provide the DC bus. The digital controller DS1103 PPC is used
to control the inverter. It represents the main process unit and has the advantage that it has a software
interface in Simulink from were all the applications can be developed and compiled automatically in the
background. The management of the process in real time is carried out in a software called Control Desk,
from were a virtual control panel with scopes and instruments are developed.
5.2
Real time interface
In order to determine if the simulation are correct and are in accordance with the real system is necessary
to be checked in the real time application. One solution for this purpose is to check them in dSpace board.
One feature of this interface is that allows the user to create the control in Matlab/Simulink and then an
online computation and updating are carried out in the background in order to fulfill the demands that are
test for. Another advantage is the online computation of the program when the data and the real time code
are generated.
The real time application is done like a Simulink blockset. It consist of two parts: Data Acquisition block
and the Control block as shown in Fig.5.2
Figure 5.2: Topology of the Real Time Interface
The Data Acquisition is the block were all the inputs signals necessary in the control block are managed.
It consists of different blocks each of them with a precise purpose in order to guaranty that the program is
running properly. In Data Acquisition block there are five blocks that will be described further on.
38
CHAPTER 5. LABORATORY WORK
The control block manages the entire acquisition block, and has the commands for enabling or disabling
the inverter. If any faults occur in the system then the converter is stopped.
The protection block is the one in charge of keeping the system in the safety boundaries. In case of
overcurrent, overspeed and undervoltage the signal FAULT is sent to the enabling controlling block, stopping
the entire system.
The currents from the inverter are found in the Currents block and the DC voltage measurement that
will be transform into three phase voltage, necessary to supply the machine is found in Voltage block.
Finally the Encoder Interface block will give information about the position and the speed of the shaft with
the help of an encoder. All this blocks are necessary in order to control the permanent magnet synchronous
machine. The control block is composed by the control of the PMSM.
Another feature of the dSpace implementation of the control is the Graphical User Interface, build in
Control Desk software which is able to provide a real time control and evaluation of the system. The Control
Desk layout is presented in Fig.5.3.
Figure 5.3: Control Desk layout of the PMSM simulation
The inputs that can be controlled with the help of the interface are: the start/stop of the system,
mechanical reference speed, controlled method. Also, it can be used to view different outputs like: measured
three phase currents; measured and reference d,q components of the currents and voltage, measured DC
voltage, rotor position, duty cycles.
Next the results from the simulation of the controlled PMSM algorithm is presented and described.
5.3
Laboratory results
In this section the simulations held in Matlab/Simulink were implemented in real time application and the
results are shown and described. First the Field Oriented Control with the sensor is implemented and tested.
Further on the sensorless algorithm is activated and results are presented. The switching frequency of the
inverter has the same value than in simulations: fs = 5kHz. The space vector modulation block is the one
available in Flexible Drive System Laboratory. In order to run the PMSM in generator mode some changes
39
5.3. LABORATORY RESULTS
in the setup has to be done and due to the time limit the simulation were carried out just with PMSM in
motor mode.
5.3.1
Control of PMSM with encoder
This section presents different results for permanent magnet synchronous motor controlled with Field Oriented Control strategy using the encoder.
Test of PMSM at no load and steps in speed
This test is done to see the response of the motor at different speed steps. The machine is started with a
step of 50% rated speed (nn = 73.3 [rps]) fallowed at time 5.3 [s] by a step to rated speed. At time 15.3 [sec]
a step down to 73.3 [rps] is applied to the machine. Fig.5.4 shows the reference and the mechanical speed in
the presented case.
Figure 5.4: Reference and measured speed at no load, step to rated speed
It can be observed that the mechanical speed is fallowing the reference speed with good accuracy. It can
be observed that it has no overshoots and has settling time equal with 0.2 [sec] The stator voltages and
currents are presented in Fig.5.5
Figure 5.5: Stator currents and voltages at no load, step to rated speed a)Measured currents b)Measured voltages
In Fig.5.5 a) stator currents are presented. During the acceleration time when the steps in speed are
applied the currents have the limited value. At 50% rated speed the currents have the value 0.146 [A] and at
40
CHAPTER 5. LABORATORY WORK
rated speed the currents amplitude is equal with 0.22 [A]. The value of the currents is not equal with zero in
this case because the machine has to produce a minimum torque to overcome the viscous friction and the dry
friction and also because of the non linearity of the inverter. The stator voltages are presented in Fig.5.5 b)
and at 50% rated speed the value of the voltages is 42.23 [V], which is closed to the value obtain at the same
condition in simulations, 36.06 [V]. At rated speed the voltages have the value 75.97 [V] which is closed to
the one from the Matlab simulation 72.08 [V]. The difference between the values from the laboratory and the
values from the simulations may be due to the fact that the values of the machine parameters in simulation
are different from the real ones.
Test of PMSM at load torque and different speed steps
To see if the simulation is working properly the machine should be tested at different steps in the load
torque. The machine is started at 50% rated speed (nn = 73.3 [rpm]), at time 6.2 [sec] a load of 7 [Nm] is
applied to the motor, fallowed by a step to rated speed at time 11.57 [sec]. The reference and the measured
speed are shown in Fig.5.6. In the zoom made in the picture it can be observed the moments were the steps in
speed and the load torque are applied. It can be observed that the measured speed is fallowing the reference
speed with very good approximation and without any overshoots.
Figure 5.6: Reference and measured speed at different speeds and 7 [Nm] load torque
The stator voltages and currents are presented in Fig.5.7. The stator currents are presented in Fig.5.7
a) and it can be observed that the currents are increasing with the load torque and at 50% rated speed
and 50% rated torque the currents have the amplitude equal with 7.95 [A]. This value is smaller than the
one from the simulations 9.48 [A]. When keeping the load torque constant to 7 [Nm] and increasing the
speed to rated speed, stator currents are decreasing. Because the speed response of the machine is showing
good performances the problem may be that the load is not properly controlled and the measured value is
different than the real one. Other reason for this situation may be that the values of the machine parameters
are different than the one used in the simulations. Some other tests are done in order to observe the behavior
of machine at different load torque command. The tests are presented in Appendix B. The stator voltages
at 50% rated speed and 50% torque is 51.03 [V] and at rated speed 81.78 [V]. This are comparable with the
values from simulations 38.35 [V] respectively 74.89 [V].
41
5.3. LABORATORY RESULTS
Figure 5.7: Stator currents and voltages at different speeds and 7 [Nm] load torque a)Measured currents b)Measured
voltages
The real and imaginary current axis are shown in Fig.5.8. In Fig.5.8 a) d axis current is presented and
it can be observed that the current has the magnitude almost zero fallowing the reference Id current that is
equal with zero, imposed by the control property. In Fig.5.8 b) Iq current is fallowing the reference current
and when the load torque is applied at 50% rated speed the current is increasing with the increased in torque
and at time 11.75 [sec] when the speed is increased to rated speed the current is decreasing to the value 5.7
[A] this is also due to the wrong control of the load.
Figure 5.8: Reference and measured currents at different speeds and 7 [Nm] load torque a)Id current b)Iq current
The electromagnetic torque of the machine is shown in Fig.5.9. At 7 [Nm] load torque the electromagnetic
torque has the value 6.12 [Nm]. The reason may be the same as for the current.
42
CHAPTER 5. LABORATORY WORK
Figure 5.9: Electromagnetic torque of the PMSM at different speeds and 7 [Nm] load torque
5.3.2
Sensorless algorithm implementation
First the sensorless algorithm is implemented in open loop. The PMSM is started at 50% rated speed and
no load, at time 6.38 [s] a step to rated speed is applied to motor, fallowed by a step down to 73.3 [rpm] at
time 12.78 [sec]. The estimated and the real position of the machine is shown in Fig.5.10. It can be observed
that at 50% rated speed the error between the rotor position and estimation has the value 11.45 [degrees]
and at the rated speed the error has the value equal with 17.64 [degrees]. The increase in the position error
at rated speed may be due to the introduced software delays.
Figure 5.10: Estimated and rotor position of PMSM in open loop system
The measured and estimated speed is presented in Fig.5.11. It can be observed that the estimated speed
is fallowing with good accuracy the mechanical speed of the machine, without any overshoots.
43
5.3. LABORATORY RESULTS
Figure 5.11: Measured and estimated mechanical speed of PMSM in open loop system
Closed loop
In order to see if PMSM is working without the encoder mounted on the shaft of the motor, the estimation
algorithm must be tested in closed loop. The sensorless algorithm based on back EMF calculations is not
working at zero and low speeds so until the motor has reached a given speed is running based on the encoder
informations. In order to use the estimated rotor position a switch is used, but the system was not able to
work based on the new algorithm. In order to find out were may be the problem some tests have been done.
The system was driven at 100 [rpm] and no load in order to see the influence of the inductances changes in
the estimation error.
The error between the rotor and estimated position at 100 [rpm] and zero load torque is around 6 [degrees].
The inductance was changed to almost 100% of the inductance value given in datasheet resulting a change
in position error around 2%.The inductance changes and the error values are shown in Appendix.C. After
this test it can be noted that the algorithm is not effected by the parameters change. More investigations
have to be done regarding the problems that may appear in the implementation of the sensorless algorithm
in closed loop.
Conclusion
In this chapter laboratory work was presented. First the test setup and Real Time Application were
described. Field Oriented Control strategy was tested with the necessary informations taken from the encoder,
and the results are showing that the control is working in good accordance with the simulations. When loading
the machine in order to fully test the motor some differences in the current and voltage values are presented.
These problems may appear since the load is not properly controlled and also because the parameters used in
the simulation may be different than the real ones. Next sensorless algorithm was implemented in open loop.
The position and speed estimation shows good accordance with the real one. When testing the algorithm in
closed loop some problems are appeared and the sensorless method could not be implemented.
44
CHAPTER 6. CONCLUSION
Chapter 6
Conclusion
This project has the main scope to eliminate the encoder mounted on the shaft of a PMSG for wind turbine
applications by implementing an algorithm from were the position and speed will be determinated. In order
to fulfill the scope of the project some objectives were presented in Chapter 1, Section 1.3:
• Implementation of a sensored control for surface mounted PMSM.
• Investigation of different sensorless methods.
• Selection of an optimal technique for determining the rotor position and implementation in Maltlab/Simulink.
• Laboratory implementation for sensored control of PMSM
• After the sensorless control strategy shows good results in simulations implementation in dSpace laboratory.
• Implementation of the control on a 2-4 [MW] wind turbine generator.
Before implementing the algorithm in the laboratory and test the corecteness is necessary to test the
theoretical performance by using the simulations. So first the mathematical model of the PMSM was tested
in simulations, then Field Oriented Control strategy with the sensor was implemented. In order to achieve a
stable system the PI controllers have to be tunned properly. For the PI current controller the optimal criterion
for adjusting the gains is the magnitude optimum while for the speed controller is symmetry optimum. Finally
the entire model was tested in Matlab/Simulink and results were presented. For different test conditions the
model shows good performance.
Next different position estimation methods were investigated. The method chosen in this case is based on
back EMF calculation with a few changes in the voltage and current generation. For wind turbine application
is a suitable control strategy due to the simplicity and good performances.
Field Oriented Control with the sensor was implemented in dSpace laboratory. The results from the
laboratory work shows good performance when the machine is running at zero load. When the machine is
loaded and reference speed is increased the current is decreasing, this situation may be because the load is
not properly controlled. The speed response of the motor is fallowing the reference in all presented cases.
The position estimation was tested also in laboratory. When the estimation algorithm was working in
open loop it shows that that estimation and rotor position are in good accordance. When the algorithm was
tested in closed loop, the system could not work.
Field Oriented Control was implemented on 2.2 [kW] machine. The machine was tested in laboratory
and good performances were achieved. The estimation position of the rotor shows good performances in
simulations but could not be implemented in laboratory.
45
Future work
Because not all the objectives of the project were fulfilled, some future work is necessary to be done:
• The chances in the setup should be made in order to run the PMSM in generator mod.
• More investigations on the estimation position in the laboratory should be done, in order to be able to
have the motor working without the sensor.
• With all the system working properly, the algorithm should be tested on a 2-4 [MW] generator.
46
BIBLIOGRAPHY
Bibliography
[1] Sensorless Control of Permanent Magnet Synchronous Motor Drives, Chandana Perera, PHD Thesis,
December 2008, Aalborg University.
[2] A Comparative Study Between Three Philosophies of Stator Flux Estimation for Induction Motor Drive,
A. W. Silveira,IEEE Article, 2007, p. 1171-1176
[3] Modeling of the Wind Turbine with a Permanent Magnet Synchronous Generator for Integration, Ming
Yin et all, 2007
[4] The economics of wind energy, European Wind Energy Association, 2003
[5] World wind energy report, Association W. W. E., 2008
[6] Enercon, Windblatt - enercon magazine for wind energy, www.enercon.de, 04/2007
[7] Wind energy-the facts, European Wind Energy Association, http://www.ewea.org, 2003-2004
[8] Control of permanent magnet synchronous generator for large wind tubines, Groupe WPS3-950, Aalborg
Universitet, winter 2009
[9] PM Wind Generator Comparison of Different Topologies, Yicheng Chen, Pragasen Pillay, Azeem Khan,
IEEE Article
[10] Modification of Symmetric Optimum Method, MIZERA R., 2005
[11] World wind energy report 2008, tech. rep., World Wind Energy Association, 2008
[12] Getting started with dSPACE system, R. Teodorescu, Aalborg University, Institute of Energy Technology, Department of Electrical Energy Conversion, Version 2009
[13] Electrical Machines and Drives, Peter Vas, Oxford University Press, 1992
[14] Sensorless control of surface permanent magnet synchronous motor using a new method, Z. Song et al.
Energy Conversion and Management, 2006
[15] Feedback Control of Dynamic Systems, Gene F. Franklin, J.D. Powell, A. Emami-Naeini, Fifth Edition,
Prentice Hall, USA, 2006, ISBN 0-13-149930-0
[16] Back EMF estimation based sensorless control of PMSM: Robustness with respect to Measurement errors
and inverter irregularities, Babak N., Farid M., Francois M. IEEE Transactions and applications,2007
[17] Speed anti-windup PI strategies review for Field Oriented Control of permanent magnet synchronous
machines, Jordi E., Antoni A., Josep.et all, IEEE Article, 2009
[18] Adaptive observer for speed sensorless PM motor control, H. Rasmussen, P. Vadstrup and H. Børsting,
IEEE Article, 2003
[19] Automatic Control of Converter-Fed Drives, M. P. Ka´zmierkowski, H. Tunia, PWN Polish Scientific
Publishers, 1994, ISBN: 83-01-11228-X
47
BIBLIOGRAPHY
[20] Pulsewidth Modulation for Electronic Power Conversion, J. Holtz, IEEE, Vol. 82, No.8, August 1994,
p. 1194-1214
[21] Direct torque control of permanent magnet synchronous machines analysis and implementation, Julius
Lukko, Lappeenranta, 2000, ISBN 951-764-438-8
48
BIBLIOGRAPHY
49
BIBLIOGRAPHY
Nomenclature
Variable
Abbreviations
AC
DC
FOC
EMF
IEA
IPMSM
OM
OSM
PI
PMSM
PMSG
PWM
SPMSM
SVM
VSI
Symbols
VAB
VAN
VBC
VBN
VCA
VCN
VDC
VA , VB , VC
IA , IC , IC
s
I~abc
s
~
Vabc
~s
Ψ
abc
vds , vqs
isd , isq
isdref , isqref
λsd , λsq
Rs
Ls
Pn
Tl
Te
Bm
J
ωe
50
Parameter
Alternative Current
Direct current
Field oriented control
Back electromotive force
International Energy Agency
Interior permanent magnet synchronous machine
Optimal Modulus
Optimum Symmetric Method
Proportional Integral
Permanent magnet synchronous machine
Permanent magnet synchronous generator
Pulse width modulation
Surface permanent magnet synchronous machine
Space vector modulation
Voltage source inverter
Line A to line B voltage
Line A to neutral N voltage
Line B to line C voltage
Line B to neutral N voltage
Line C to line A voltage
Line C to neutral N voltage
DC voltage
Phase voltages
Phase currents
Stator phase current
Stator phase voltage
Flux linkage
Stator voltage in dq stationary reference frame
Stator current in dq stationary reference frame
Reference current in dq stationary reference frame
Stator flux linkages in dq stationary reference frame
Stator resistance
Synchronous inductance
Power
Load torque
Electromagnetic torque
Dry friction coefficient
Moment of inertia
Electrical speed
BIBLIOGRAPHY
Variable
ωm
wref
npp
λm
kpi
kii
Tii
kps
kis
Tis
G(s)
Ts
fs
Tiq
Tsi
Tss
Parameter
Mechanical speed
Reference speed
Number of pole pairs
Permanent magnet flux linkage
Proportional gain for PI current controller
Integrator gain for PI current controller
Time integral of PI current controller
Proportional gain for PI speed controller
Integrator gain for PI speed controller
Time integral of PI speed controller
Transfer function of the current/speed controller
Sampling time
Sampling frequency
Time constant of the current controller
Equivalent time constant
Time constant of the speed controller
51
52
APPENDIX A. DATASHEET OF PMSM
Appendix A
Datasheet of PMSM
53
Appendix B
PMSM laboratory test
This part is meant to investigate the response of PMSM at different load conditions in order to find out were
may be the problem.
For this test the machine was driven at 50% rated speed (nn = −73.3 [rpm]) and at time 6.4 [sec] the
machine was loaded to 7 [Nm], fallowed at time 12.34 [sec] with a step to rated speed. Sign plus or minus in
the speed represent the rotation of the machine, clockwise or anti clockwise, and for this test the machine
is running in opposite direction than in the test made in Section 5.3.1 in order to observed the behavior of
the machine in this case. The reference and measured speed is shown in Fig.B.1.
Figure B.1: Reference and measured speed at TL =7 [Nm]
It can be observed that the mechanical speed is fallowing the reference speed with good accuracy and no
overshoots appear during the transient period. The stator voltage and current are presented in Fig.B.2
54
APPENDIX B. PMSM LABORATORY TEST
Figure B.2: Stator currents and voltages a)Measured currents b)measured voltage
s
In Fig.B.2 a) stator currents are present. At 50% rated speed and 50% rated toque, stator currents have
the amplitude equal with 10.16 [A] and at rated speed the currents are increased to the value 13.19 [A]. The
currents value obtained in the simulation in the same conditions (50%rated load torque and rated speed) is
9.4 [A], so the values are different from the simulation. In Fig.B.2 b) stator voltages are presented. At 50%
rated speed and no load torque the amplitude of the stator voltages have the value 43.47 [V], closed to the
value from simulation 36.05 [V]. When the machine is running at 73.3 [rps] and 50% rated load torque is
applied to the machine, stator voltages are decreasing to value 25.42 [V],and when the a step in speed to
rated speed is applied at time 12.34 [sec] the amplitude of the stator voltages has the value 60.4 [V].
The big differences in the values of the currents and voltages, at different speeds and load torque it may
be a consequence of the fact that the load is not properly controlled and also it may be a difference in the
measured and real load torque applied to machine.
55
Appendix C
Test for the sensorless control
Inductance [mH]
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
Position Error
5.7
5.8
6
6.1
5.9
6
6
6
5.8
5.7
5.9
6
5.8
6.1
5.9
6
5.5
6.1
5.7
6
5.9
6
6
5.1
6.1
6.1
Table C.1: Parameters of PMSM
56
APPENDIX D. LABORATORY PARAMETER SPECIFICATION
Appendix D
Laboratory parameter specification
Specifications of the components
• Siemens PMSM type ROTEC 1FT6084-8SH7:
-rated power: 9.4 kW
-rated torque = 20 Nm
-rated current = 24.5 A
-rated frequency = 300 Hz
-rated speed = 4500 rpm.
• Danfoss VLT5004 frequency inverter:
-rated voltage: input =3 phase AC 380 V, output = 3 phase AC 380 V
-rated output frequency = 0 .. 132 Hz
-rated current: input = 5.3 A , ouput=5.6 A
-rated power = 4.3 kVA
-switching frequency = 3 .. 5 kHz
• ABB three phase induction motor type M2AA100LA:
-rated power = 2.2 kW
-rated voltage = 380 .. 420 V rms (Y)
-rated frequency = 50 Hz
-rated current = 5.0 A rms
-power factor = 0.81
-rated speed = 1430 rpm
-poles pair number = 2
• Danfoss FC300VLT (FC 302) frequency inverter:
-rated voltage: input =3 phase AC 380 V, output = 3 phase AC 380 V
-rated output frequency = 0 .. 1000 Hz
-rated current: input = 5.3 A , ouput=5.6 A
-rated power = 4.3 kVA
-switching frequency = 3 .. 5 kHz
• Siemens SIMOVERT MC RRU regenerative rectifier type 6SE7028-6EC85-1AA0
-rated voltage: input=380..460VAC ±15%, output=510..620VDC±15% (1.35x input)
-rated current: input = 68 ADC, output= 86 ADC (79 ADC in regeneration mode)
57
• DS1103 PPC -Motorola PowerPC 604e running at 333 MHz
-Slave DSP TI’s TMS320F240 Subsystem
-16 channels (4 x 4ch) ADC, 16 bit , 4 µs, ±10 V
-4 channels ADC, 12 bit , 800 ns, ± 10V
-8 channels (2 x 4ch) DAC, 14 bit , ±10 V, 6 µs
-Incremental Encoder Interface -7 channels
-32 digital I/O lines, programmable in 8-bit groups
-Software development tools (Matlab/Simulink, RTI, RTW, TDE, Control Desk)
58
APPENDIX E. SIMULATION BLOCKS
Appendix E
Simulation blocks
Figure E.1: Overall simulation model
59
Figure E.2: Simulation of the mathematical model of PMSM
Figure E.3: FOC control of PMSM
60