control of permanent magnet synchronous generator for large wind turbines

Institute of Energy Technology

Encoderless Vector Control of PMSG forWind Turbine Applications

Conducted by group PED 1035Master Thesis, 2010

Institute of Energy TechnologyPontoppidanstræde 101Phone number 99 40 92 47Fax 98 15 14 11http://www.iet.aau.dk/

Title: Encoderless Vector Control of PMSGfor Wind Turbine ApplicationsSemester: 4th semesterSemester Theme: Master ThesisProject period: 01.02.10 to 01.06.10ECTS: 30Project group: PED 1035Members:

Andreea Cimpoeru

Supervisor: Kaiyuan Lu

Number of prints: 3Number of pages: 62Finished: 1.06.2010

Abstract:

The growing interest in wind turbine applica-

tions and the fast development of power elec-

tronics is making the manufacturers to find

the most suitable and low cost technologies

to put in practice. Permanent magnet syn-

chronous generator are becoming more popu-

lar 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 ap-

plications. The control strategy used is Field

Oriented Control(FOC). First FOC is imple-

mented and validated in Matlab/Simulink us-

ing measured speed and position. Next, the

investigation on methods to estimated the ro-

tor position is done. With the chosen method

the validation of the control is performed.

The sensored Field Oriented Control is im-

plemented in dSpace laboratory and the re-

sults 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 workand 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 An-dreea 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 WindTurbine Applications. This theme in particular was proposed by SIEMENS Wind Power. The purpose of theproject unit is to control a permanent magnet synchronous generator without using a sensor. The model ofthis 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 mea-surements and other data. In this project the chapters are consecutive numbered while the appendixes areassigned with letters

Figures, equations and tables are numbered in succession within the chapters, e.g. (3.4), where the firstnumber 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 literatureis presented in the bibliography.

The figures (block diagrams, simulation plots, laboratory setup measurements plots, etc) included in thisreport 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 progressof the project. I will also like to acknowledge the help of my college Zihui Wang.

II

CONTENTS

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Limitations of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Overview of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Theoretical background 52.1 Overview of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Voltage source converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Permanent magnet synchronous machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.1 Introduction to SPMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Mathematical model of SPMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3.3 Validation of SPMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Field oriented control 123.1 Field oriented control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Control properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Current and speed controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.1 Design of q axis current controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.2 Design of speed controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Sensorless control of PMSM 284.1 Presentation of the sensorlees control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Rotor position estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5 Laboratory work 375.1 Laboratory structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Real time interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.3 Laboratory results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.3.1 Control of PMSM with encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.3.2 Sensorless algorithm implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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 Growth in size of commercial wind turbine designs [7] . . . . . . . . . . . . . . . . . . . . . . 11.2 World total installed capacity (MW)[5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Costs of generated power on 2010 of wind power compared to conventional plants [4] . . . . . 21.4 Wind turbine configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Setup configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Topology of a voltage source inverter with ideal switches . . . . . . . . . . . . . . . . . . . . . 62.3 Clasification of permanent magnets machines . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Stator voltage in reference frame transformation . . . . . . . . . . . . . . . . . . . . . . . . . 82.5 Stator currents at nominal working point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.6 Stator voltage at nominal working point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 Scheme of Field Oriented Control strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Vector diagram for constant torque per amper control in steady state . . . . . . . . . . . . . . 133.3 d and q axis control topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 The structure of the q axis current controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.5 Topology of the q axis current controller with unity feedback . . . . . . . . . . . . . . . . . . 163.6 Bode diagram of the q axis current controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.7 Step response for the q axis current controller . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.8 Topology of the speed controller loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.9 Speed controller loop with unity feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.10 Bode diagram of the speed controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.11 Speed response of the speed controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.12 Topology of the integrator antiwindup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.13 Reference and measured speed at no load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.14 Reference and measured currents at no load and steep in speed a)Id current b)Iq current . . . 223.15 Stator currents and voltages at no load and step in speed a)Measured voltages b)Measured

currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.16 Reference and measured speed at 7 [Nm] load torque . . . . . . . . . . . . . . . . . . . . . . . 233.17 Reference and measured currents at 7 [Nm] load torque a)Id current b)Iq current . . . . . . . 243.18 Stator currents and voltages at 7 [Nm] load torque a)Measured voltages b)Measured currents 243.19 Reference and measured speed for different values of the speed and load torque . . . . . . . . 253.20 Reference and measured currents for different values of the speed and load torque a)Id current

b)Iq current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.21 Measured stator currents and voltages for different values of the speed and load torque

a)Measured voltages b)Measured currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.22 Reference and measured speed in generator mode . . . . . . . . . . . . . . . . . . . . . . . . . 263.23 Electromagnetic torque in generator mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Field Oriented Control of PMSM without the sensor . . . . . . . . . . . . . . . . . . . . . . . 284.2 Back EMF in stationary reference frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Representation of stator fix αβ reference frame . . . . . . . . . . . . . . . . . . . . . . . . . . 30

VI

LIST OF FIGURES

4.4 Estimated and rotor position for PMSM in open loop system . . . . . . . . . . . . . . . . . . 324.5 Measured and estimated mechanical speed of PMSM in open loop system . . . . . . . . . . . 324.6 Estimated and rotor position of PMSM at 7 [Nm] load torque . . . . . . . . . . . . . . . . . . 334.7 Reference and measured speed with the estimated rotor position at 7 [Nm] load torque . . . . 334.8 Stator voltages and currents calculated with the estimated position a)Measured voltage b)Measured

current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.9 Estimated and rotor position of PMSM in generator mod . . . . . . . . . . . . . . . . . . . . 344.10 Estimated and measured speed of PMSM in generator mod . . . . . . . . . . . . . . . . . . . 354.11 Electromagnetic torque of PMSM in generator mod . . . . . . . . . . . . . . . . . . . . . . . . 35

5.1 Description of laboratory setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Topology of the Real Time Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.3 Control Desk layout of the PMSM simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.4 Reference and measured speed at no load, step to rated speed . . . . . . . . . . . . . . . . . . 405.5 Stator currents and voltages at no load, step to rated speed a)Measured currents b)Measured

voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.6 Reference and measured speed at different speeds and 7 [Nm] load torque . . . . . . . . . . . 415.7 Stator currents and voltages at different speeds and 7 [Nm] load torque a)Measured currents

b)Measured voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.8 Reference and measured currents at different speeds and 7 [Nm] load torque a)Id current b)Iq

current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.9 Electromagnetic torque of the PMSM at different speeds and 7 [Nm] load torque . . . . . . . 435.10 Estimated and rotor position of PMSM in open loop system . . . . . . . . . . . . . . . . . . . 435.11 Measured and estimated mechanical speed of PMSM in open loop system . . . . . . . . . . . 44

A.1 Datasheet of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

B.1 Reference and measured speed at TL=7 [Nm] . . . . . . . . . . . . . . . . . . . . . . . . . . . 54B.2 Stator currents and voltages a)Measured currents b)measured voltage . . . . . . . . . . . . . 55

E.1 Overall simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59E.2 Simulation of the mathematical model of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . 60E.3 FOC control of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 generalpresentation about wind turbines and the problem formulation is presented. In order to have a way to gothrough the research the objectives and the limitations of the project are defined. The chapter ends with thereport structure

1.1 Background

The wind energy is a pollution-free resource, in inexhaustible potential. The main drawback is the energyproduction irregularity. In the recent years, because global warming and because the effects of carbon emis-sions had an important impact over the entire world, a demand for clean and sustainable energy sourceslike wind, sea, sun and biomass have become an considerable alternative to the conventional resources. Theutilization of wind energy was used in the past mainly in the agriculture sector for pumping water and forgrinding. The research for wind power industry started to be improved in the last century, mainly due to theoil crisis and natural resources ripening. By increasing the wind turbine size the electrical power productionis also increased. In Fig.1.1 can be seen that in the last forty years the wind turbine size have been increasedfrom 24 m to 114 m. Right now, the record for electric power production from wind is the Enercon E-126wind 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 turbinesand induction generators were used. Disadvantages of the fixed speed generators is the low efficiency, poorpower quality and high mechanical stress [3]. In order to maximize the wind energy capture, the extractionof maximum power from wind at a large scale has become an important topic for wind companies. Runningthe wind turbine generator at low and medium wind speeds the maximum power can be extracted. In Fig.1.2can be seen the continue growing trend of wind power installation in the last decade. In 2008 wind energygrowth 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 orcoastal place. As it can be seen in Fig.1.3 the price of wind energy is continuously decreasing in order tocompete 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 thancoal and gas in 2030.

1.2 Problem Statement

The variable speed wind turbine with full scale frequency converter is an attractive solution for research ondistributed power generation systems. The generator in this case can be double fed induction machine oran permanent magnet synchronous generator(PMSG). The advantages of PMSG over induction machinesare the high efficiency and reliability, since there is no need of external excitation, smaller in size and easyto control [9]. Also PMSG has some disadvantages like higher cost and a fix excitation. Over the years thePMSG 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 tocontrol the torque and the speed and grid side converter used to controll the power flow in order to keepthe DC-link voltage constant. The two converters are connected by a DC link capacitor in order to have aseparate 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 usinga position or speed sensor, or they can be estimated. The use of sensor implies some drawbacks like theincrease cost of the system, a lower reliability, resulting that the sensorless solution for controlling thePMSG 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 magnetsynchronous 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 isimplemented. 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 Malt-lab/Simulink.

• Laboratory implementation for sensored control of PMSM.

• After the sensorless control strategy shows good results in simulations implementation in dSpace lab-oratory.

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 implementedin 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 windturbine 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 voltagesource converter is described in details, the introduction and the mathematical model of permanent magnetsynchronous motor are also presented.

Chapter three has the main purpose to describe the chosen control strategy Field Oriented Control. Thedesign of the controllers in order to have a good performance of the machine are described next. Finally inthis 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 implementit. 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 presentedand 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 bedetermined by mathematical models. First voltage source converter is presented and described. A generaloverview of permanent magnet synchronous machine is done in the fallowing part. Next the model of themachine 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 realsystem 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 controlledin torque mod. The generator side converter is controlled with Space Vector Modulation technique. Nextvoltage 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 connectedto the DC-link, in this case the voltage source inverter is working as a rectifier. In the next step the DCvoltage is converted to AC signal with a desired frequency and voltage. In this case the grid side converteris 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 voltageconstant. 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 inthe fallowing equations:

VAB = VAN − VBNVBC = VBN − VCNVAC = VAN − VCN

(2.1)

were N is the negative DC bus and VAN , VBN , VCN are the line to neutral voltage. Using Kirchhoff law it isknown 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 voltagescan be formulated: VANVBN

VCN

=13

1 0 −1−1 1 00 −1 1

·VABVBCVAC

(2.3)

The switching states of each leg are representing by three variables: Da, Db, Dc named duty cycles. Thisvariables can have just two values ”1” when the switch is turn on and ”O” when is turn off. The switchingstates together with the DC voltage can give an expression for the line two line voltages of the inverter:VABVBC

VAC

= VDC

1 −1 00 1 −1−1 0 1

·Da

Db

Dc

(2.4)

After a few simplifications in the equations (2.4) and (2.3) the phase voltage is expressed with the helpof DC voltage and switching state as presented in equation (2.5):VANVBN

VCN

=VDC

3

2 −1 −1−1 2 −1−1 −1 2

·Da

Db

Dc

(2.5)

Having the duty cycles and the phase currents, the DC current can be deduct as in the fallowing:

IDC =[Da Db Dc

]·

IaIbIc

(2.6)

6


2.3 Permanent magnet synchronous machine

2.3.1 Introduction to SPMSM

Permanent magnet electric machine is a synchronous machine which is magnetized from permanent magnetsplaced on the rotor instead of using a DC excitation circuit. In this case having the magnets on the rotorthe electrical losses of the machine are reduced and the absence of the field losses improves the thermalcharacteristics of the PM machines. The absence of mechanical components such as slip rings and brushesmake 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 solutionfor wind turbine applications. Like always, PM machines have some disadvantages: at high temperature thePM 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 PMDCmachines are similar with the DC commutators machines, the only difference is that the field winding isreplaced by the permanent magnets. In case of PMAC the field is generated by the permanent magnetslocated on the rotor and the brushes and the commutator does not exist in this machine type. For thisreason the machine is more simple and more attractive to use instead of PMDC [1]. Further on PMAC canbe classified depending on the type of the back electromotive force (EMF): trapezoidal and sinusoidal asshown 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 voltagewaveform in each stator phase winding during rotation, while the sinusoidal PMAC machines, called PMsynchronous 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 ofthe rotor. The magnets can be regarded as air because the permeability of the magnets is close tounity(µ = 1) and the saliency is not present as a consequence of the same width of the magnets. Fromthis 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 configurationof the machine appear the saliency and the airgap of d-axis is increased compared with the q axisresulting 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 anattractive 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 ofthe motor that is derived from the space vector form of the stator voltage equation.

~V sabc = Rs~Isabc +

d

dt~λsabc (2.7)

were Rs is the the stator winding resistance per phase, Isabc is the stator phase current , V sabc is the statorphase voltage and λsabc is the flux linkage.

A transformation from abc to synchronous dq reference frame is needed in order to have a simpler modelthat will be simulated in Matlab/Simulink. The model is derived in dq reference frame were q axis is rotatingwith 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 arepresented:

vsd = Rsisd +

d

dtλsd − ωeλsq (2.8)

vsq = Rsisq +

d

dtλsq + ωeλ

sd (2.9)

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.

Flux linkage equations are expressed as presented in equations (2.10) and (2.11):

λsd = Ldisd + λm (2.10)

λsq = Lqisq (2.11)

8


with Ld=Lq=Ls dq axis inductances and λm permanent magnet flux linkage. With the help of flux linkageequations, stator voltage equations in dq reference frame have the fallowing form:

vsd = Rsisd + Ls

disddt− ωeLqisq (2.12)

vsq = Rsisq + Ls

disqdt

+ ωe(Ldisd + λm) (2.13)

The torque equation of PMSG can be derived from the power balance equation. The power flowing intothe machine can be express in dq reference frame as presented in equation (2.14)

P se =32

(vsdisd + vsqi

sq) (2.14)

After substituting the stator voltage equations in dq reference frame into equation (2.14) and separating thepower quantities the power has the fallowing form:

Pe =32

(Rsisd2 +Rsi

sq2) +

32

(d

dtLd

(isd)2

2+d

dtLq

(isq)2

2) +

32

(ωeλsdisq − ωeλsqisd) (2.15)

The first term represents the power loss in the conductors, the second term indicates the time rate of changefor stored energy in the magnetic fields and the third term express the energy conversion, from electricalenergy to mechanical energy.[1] From the third term can be express the electromagnetic torque because thepower output from the motor shaft must be equal with the electromechanical power.

Pe = ωmTe =32

[ωeλsdisq − ωeλsqisd] (2.16)

The relation between the electrical velocity and the mechanical angular velocity of the motor depends onthe 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 willhave the fallowing form:

Te =32npp[λmisq + (Ld − Lq)isqisd] (2.18)

In the final expression of the torque, equation (2.18), it can be observed that there are two terms, the firstone represents the synchronous torque and is produced by the flux of the permanent magnets and the secondterm represents the reluctance torque and represents the torque produced by the difference of the inductancesin dq reference frame. In the project the motor is surface mounted permanent magnet and in this case theinductances 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 =32nppλmi

sq (2.19)

The mechanical equation of the machine is express as a function of the electromagnetic torque (Te), loadtorque (Tl) and electrical velocity of the machine:

Te = Tl +Bωm + Jd

dtωm (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 ifthe motor model is reproducing the real machine. The parameters value of the machines used to control themachine are presented in Table 2.1.

Parameter Symbol Value UnitPower Pn 9.42 [kW]

Phase Voltage Vn 185 [V]Rated current In 19.5 [A]Rated torque Tn 20 [Nm]Rated speed nn 4500 [rpm]

Stator resistance Rs 0.18 [Ω]Synchronous inductance Ld 2 [mH]Synchronous inductance Lq 2 [mH]

Permanent magnet flux linkage λm 0.123 [Wb]Rotor moment of inertia J 0.48 [mKgm2]

Nr. of pole pairs npp 4 -

Table 2.1: Parameters of PMSM

The electrical and mechanical parameters of the generator presented in Table.2.1 were taken form thedatasheet of the machine presented in Appendix A. The simulation bloc is presented in Appendix E. Thevalidation 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 thecurrent 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 isrunning at zero load torque the voltage has a smaller amplitude than when the load is applied. The value ofthe voltage at nominal working point is the same that the nominal voltage described in datasheet.

10


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 conceptsand physical phenomenon that appear in an electric machine. Then the concept and the model of a voltagesource 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. Withthe model of the voltage source inverter and PMSM working properly the control strategy and the designingof 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 startswith a briefly introduction about FOC. Next the design of the current and speed controller is described. Inthe 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 permanentmagnet synchronous motor. For a simpler implementation the strategy is using the synchronous referenceframe. FOC is a close loop strategy and is composed by two current controllers necessary for controlling thetorque and one speed controller. The controllers are PI’s (Proportional Integrator) due to theirs good steadystate 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 andthe 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 measuredstator currents into dq reference frame axis. The d an q current component are the feedback currents forthe current controllers. The speed controller generates the torque, that will command the reference framecurrents isdref and isqref . From this torque command the reference currents isdref , isqref are set based onthe control strategies presented in details further on. The reference currents are compared with the actualrotor currents in the dq reference frame and send to two current controllers. The output of the controllersrepresents the required dq voltages. To control the current independently one of each other is necessary toadd the compensation term ωeλ

sd and to subtract ωeλsq 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 cyclesnecessary in Space Vector Modulation strategy. Finally the PWM generator block calculates the switchingsignals for the inverter.

3.2 Control properties

In order to have a simpler control for PMSM some simplification have to be taken into consideration regardingthe produced torque. The load torque can be controlled by controlling the torque angle. Some controlstrategies 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 inorder to maintain the torque angle equal with 90o. This is one of the most used control strategy because ofthe simplicity, especially for SPMSM. In case of IPMSM, with a high saliency ratio it is not recommendedto 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 inequation (3.1).

Te =32npp[λmisq + (Ld − Lq)isqisd] (3.1)

If the dq currents are substituting in equation (3.1) as presented in Fig.3.2 and after a few simplification thetorque value is the one presented in equation (3.2).

Figure 3.2: Vector diagram for constant torque per amper control in steady state

Te =32nppλmi

sq (3.2)

From equation (3.2) it can be observed that the control property is very simple to implement, representingthe 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 givenelectromagnetic torque, in this way the maximum torque per ampere is obtain. In the case of surface mountedpermanent magnet machine this strategy is the same as CTAC but in case of IPMSM this control strategygives the highest torque output compared with the current, because is taken into consideration both electromagnetic and the reluctance torque.

Unity power factor

One of the advantages of this control strategy is that between voltage and current vector is no phasedifference 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 torquecapability of the machine.

The focus in this project is in implementation of a sensorlees control for PMSM and not in optimization ofthe control strategy, so the constant torque angle control is implemented due to his simplicity, by controllingonly 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 controllerdesign is identical with q axis current controller so just one will be treat in this report. The structure of thecurrent 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 inrpm. The error between the reference and the measured speed is send to a PI controller. The output of thePI represents the electromagnetic torque from were the reference currents are subtract. The error betweenthe reference and the measured currents is the input to other two PI controllers necessary to determine thedq reference stator voltages.

In order to have a simpler design of the current controllers and to controll the dq currents independently adecoupling 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 ωeλsq from equation (2.8) and adding ωeλsdto equation (2.9) the dq currents will be independently one of each other. The d and q current controllerdesign it has the same dynamics so the tuning of the PI controller is done just for the q axis.

14


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 qaxis 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. Thetransfer function of a PI controller is the ratio between the output signal and the error signal as shownin equation (3.3):

Gc(s) =U(s)E(s)

= kpi +kiis

= kpi1 + Tiis

Tiis(3.3)

were kpi represent the proportional gain, kii the integrator gain and Tii is called the integrator timeand represents the ratio between kpi and kii.

Tii =kpikii

(3.4)

• The control algorithm block represents the delay introduced by the digital calculations. It has the formof a first order system, with a time constant equal with Ts = 1

fs= 1

5k = 0.2[ms] (were fs is the samplingfrequency).

GCA(s) =1

Tss+ 1(3.5)

• The plant transfer function is determine from the dq voltage equations after the decoupling term hasbeen removed, were s = d

dt and considering current as input and voltage as output as shown in equation(3.6):

Gpl(s) =iq(s)uq(s)

=1

Rs + sLs=

1Rs

11 + sLsRs

=K

1 + sTq(3.6)

were Tq is the time constant of the motor and K is a notation for the inverse of the stator resistance:

K =1Rs

Tq =LsRs

= 0.0116[sec] (3.7)

• The sampling block is the delay introduced by the digital to analog conversion. It is also a first ordertransfer function with the time constant Ts.

Gsam(s) =1

0.5Tss+ 1(3.8)

15


In order to have a simpler control loop the feedback path is moved to the forward path as shown inFig.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)

GOL(s) =1

0.5Tss+ 1· kpi

1 + Tiis

Tiis· 1Tss+ 1

· K

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:

1 + Tiis = 1 + Tqs⇒ Tii = Tq =LsRs

= 0.0116[sec] (3.10)

In order to simplify the transfer function a time constant is introduced, who represents the approximationof all first order transfer functions that introduce delays because their values are very small compared withthe electrical motor time constant, resulting that their dynamics are smaller. This implies that the transferfunction of the delays will be replaced by a unique transfer function of first order, having the time constantequal with the sum of all time constants from the system.

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 simplerform as fallows:

GOL(s) =kpiTiis

K1

Tsis+ 1(3.12)

To determine the value of kp is necessary to use a controller design criterion called Optimal Modulus (OM),with the damping factor chosen to be ζ =

√2

2 . The open loop transfer function of a second order system hasthe form:

GOM (s) =1

2τs(τs+ 1)(3.13)

If the analogy between the equation (3.12) and (3.13) is made the fallowing relations are deducted in oderto determine the gains of the PI controller:

kpiK

Tii=

12Tsi

⇒ kpi =TiiRs2Tsi

= 3.333 (3.14)

The PI transfer function in ’s’ domain has the fallowing form:

Gc(s) = 3.33 +300s

(3.15)

In order to implement the controllers in real system the transfer function of the PI current controller istransform in ’z’ domain, as presented in the fallowing equation:

Gc(z) = 3.333 +0.06z − 1

(3.16)

16


The bode diagram of the q axis current controller is the one presented in Fig.3.6. It can be observed that ithas a phase margin of PM=63.6 [deg], a gain margin equal with GM=19.1 [dB] and it can be observed thatthe 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


• 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) = kps1 + Tiss

Tiss(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. Transferfunction has the form of a first order system with a time constant Ts = 1

fs= 1

5k = 0.2[ms] (were fs isthe sampling frequency)

GCA(s) =1

Tss+ 1(3.18)

• The current control loop can be expressed like a first order system with the time constant Tiq = TiiRsKpi

with the transfer function presented in equation (3.19)

GCCL(s) =1

Tiqs+ 1(3.19)

• The plant block is calculated from the mechanical equation of the PMSM as shown in equation (3.20)

Te − Tl −Bωm = Jd

dtωm (3.20)

wereTe =

32nppλmi

sq (3.21)

If the viscous friction coefficient is neglected then the mechanical equation will become:

Te − Tl = Jd

dtωm (3.22)

The load torque from the point of view of controller is consider as a disturbance and will not beconsider. From equation (3.22) the transfer function of the machine in ’s’ domain has the fallowingform:

ωm(s)Te(s)− Tl(s)

=npp

Js(3.23)

18


• The filter block represents the delay introduced by the filtering of the measured speed, from an encodermounted on the shaft of the machine. The filter has a time constant Tf = 1

ωc= 1

2πf = 12π200 = 0.796[ms]

GFL(s) =1

Tfs+ 1(3.24)

• The sampling block is the delay introduced by the digital to analog conversion and his time constantis equal with Ts

Gsam(s) =1

0.5Tss+ 1(3.25)

To simplify the close loop transfer function the disturbances are not taken into consideration and the feedbackpath is moved on the forward part as in the case of current controller. The close loop system in presented inthe 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

0.5Tss+ 1· 1Tfs+ 1

· kps1 + Tiss

Tiss· 1Tss+ 1

· 1Tiqs+ 1

· 3nppλm2

npp

Js(3.26)

In order to simplify the transfer function, all the time constants of the delays are approximated with onetime 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) =nppKckps(Tiss+ 1)JTiss2(Tsss+ 1)

(3.28)

with Kc = 32nppλm. 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 formpresented below:

GOSMOL (s) =k1kpTis+ k1kps2(T1Tis+ T1)

(3.29)

In order to find the gains for the PI controller is necessary to arrange the equation of the open loop transferfunction of the speed controller in the same manner as equation (3.29).

GOL(s) =nppKcJ kpsTiss+ nppKc

J kps

s2(TisTsss+ 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

2k1T1=

12nppKcJ Tss

= 0.462 (3.31)

Tis = 4T1 = 4Tss = 7[m] (3.32)

19


To implement the control in real system is necessary also to transform the PI speed controller form ’s’ domainin ’z’ domain. The transfer function of the speed PI controller in ’z’ domain is the one presented in equation(3.33).

Gc(z) = 0.462 +0.0132z − 1

(3.33)

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 fallowingparameter:

Figure 3.11: Speed response of the speed controller

20


• 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 thecharacteristics it is noticeable that the current controller acts faster. From the step response of the speedcontroller figure it can be observed that it has a very big overshoot, which mean that when starting themachine it will have a very big torque command, making the currents to have a very big amplitude, abovethe maximum allowed. For this reason the anti-windup circuit is implemented in order to limit the responseof the speed controller.

Anti-windup circuit

When designing the current and speed controllers in FOC it is necessary to have in mind the limitation oftheir outputs in order to prevent the system from overcurrents or overvoltages appearance.When the outputof the controlled signal (current, voltage) has a very big value the input of the controller has a saturatedvalue. This has the consequence that the integral part is integrating the provided error. Because of this theoutput of the controller may drift to very large values and to a poor transient response. The overshoots inthe 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 onepresented 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 andcurrents. The input to this limitation gain is subtract from the output and the difference is fed back to theintegrator through the gain Ta. This signal is becoming non zero when the limiter saturates and preventsthe integrator to have a very big value. The reduction in the integration winding up is set by the value ofthe time constant Ta. The value of time constant must be chosen as small as possible but also a very smallvalue may decrease the system performances [17]. The gains chosen for the anti-windup circuit are kai=0.1for 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 necessaryto be implement it in Matlab/Simulink. In order to go further and test the simulations in real system allthe calculation are represented in discrete domain. The electrical parameters of the system are the onepresented in Table 2.1 in Section 2.3 and the simulation blocks are presented in Appendix E. In laboratorythe induction machine M2AA100LA, with the parameters presented in Appendix D, is used to load thepermanent magnet machine. For this reason for now one it will be considered that the nominal speed ofPMSM 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 forthe 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 beobserved: 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 stepof 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 measuredspeed it reaches 700 [rpm] in 0.045 [sec], slower in comparison with the designed PI controllers but withoutany 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 observedthat the d current is zero imposed by the control strategy. From Fig.3.14 (b) it can be observed that thecurrent is limited in FOC to value I=24 [A]. After the motor is reaching the reference speed the currents arestabilized 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) atstart up and until the speed is reached the reference speed the currents are limited to value 24 [A] and at no

22


load the currents are zero. The stator voltages at no load and 50 % rated speed has the amplitude equal with36.06 [V] and at the rated speed equal with 72.08 [V]. In the zoom made can be observed that the signalsare 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 hasa value equal with 700 [rpm]. At time 1 [sec] another step to rated speed is applied to the machine. Theresponse 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 casewere the machine is working at zero load torque, but without overshoots. The settling time of the measuredspeed is 0.05 [sec].

Similar with the case without the load torque the dq currents are fallowing the reference currents, pre-sented in Fig.3.17. The q axis current is limited to 24 [A] as in the previous case and the d axis is zero asexpected.

23


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 and50% 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. At0.5 [sec] a load torque of 7 [Nm] is applied to the system, fallowed by a step in speed to the rated speed att=1 [sec], and a step to nominal load torque at 1.5 [sec]. The reference and measured speed is presented inFig.3.19. It can be observed that the measured speed is fallowing with good accuracy the reference one andwithout any overshoots. In the zoom made on the graphic it can be observed that when the load torque isapplied to the system small back overshoots appear. Also it can be observed that the settling time of themeasured speed when the machine is loaded is bigger that when is no load applied to the motor.

24


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. InFig.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 isapplied 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 andnominal torque is 79.46 [V]. For simplicity in the control Id current was chosen to be zero, so the magnitudeof Iq current is giving the magnitude of the stator currents resulting that at 50% rated torque the value ofthe currents is 9.48 [A] and at rated torque 18.95 [A]. From the zoom in both plots it can be observed thatthe signals are sinusoidal.

25


Figure 3.21: Measured stator currents and voltages for different values of the speed and load torque a)Measuredvoltages 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] theload torque is applied to the machine and at t=1.5 [sec] the motor is run in generator mode. The referenceand the measured speed is presented in Fig.3.22, and it can be observed that the measured speed fallowswith good accuracy the reference one. In the zoom made on the plot can be observed the behavior of thespeed 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 torqueis applied to the motor, positive electromagnetic torque is generated, and when motor is working in generatormode the electromagnetic torque is responding in the same way.

26


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 speedand current controllers were made, necessary in a good implementation of the control strategy. To prove thecorrectness of the system different plots are done for different speeds and load torque. As the controllers showsatisfactory results in both motor and generator mode Field Oriented Control was chosen to be implementin real system. Next step in the project is to find the proper method to estimate the position and speed ofthe 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 differ-ent estimation strategies for the rotor position. The chosen sensorless strategy is described and finally isimplemented 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 hasbecome a very important competitor because of the high efficiency. To control the motor in a robust wayis necessary to know the rotor position. The most used technique to determine the rotor position is to usean encoder or a resolver on the motor shaft, but this will add additional cost to the system, the size of thesystem will increase and the reliability will degrease. In the last years have been an intense research aboutfinding the most reliable position sensorlees method. The Field Oriented Control strategy scheme with rotorposition 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 equalitybetween 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 significantreasons for starting the investigations on the estimation position of the rotor. Further on some positionestimation 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 backelectromotive force (EMF). In this strategy the variables necessary to compute the back EMF are estimatedfrom the electrical parameter of the machines. The mechanical components are deducted from the estimatedvalues from the back EMF. Even this strategy is very easy to implement, it has some drawbacks regardingthe sensitivity to the parameters uncertainties, especially with the stator resistance variation and model ofthe machine in case of zero and low speed [16]. For the case of wind turbine application were the generatoris working at variable speeds this strategy is very suitable, also because at high speeds the voltage drop onthe 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).

λα =∫

(uα −Rsiα)dt (4.1)

λβ =∫

(uβ −Rsiβ)dt (4.2)

In order to determine the flux linkage it can be observed that some parameters have to be known: phasecurrent, phase voltage and stator resistance either by measurements or estimated. With this technique someproblems 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 controlstrategy 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 realmachine and the states of the model fallows the values of the real model (velocity, rotor position). If errorsappear in the estimated states of the observed, they can be reduced by the correction of the error at theoutput of the real machine (which is measurable) and the output of the modeled machine. As this methodis a parameter dependent method, variations in parameters of the machine can have a big influence in theestimation position

Position estimation using high frequency signal injection.

This method is more attractive for IPMSM because they present saliency. This strategy can work alsoat zero and low speed. But in case of direct drive wind turbine, were the switching frequency is low thisstrategy 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. Rotorposition is the same with the position of back EMF vector as shown in Fig.4.2. The position of the backEMF 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 integrationof 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 phaseaxis can be expressed as following:

fsabc =23

(fsa + afsb + a2fsc ) (4.4)

were the coefficient 23 gives the same magnitude of the space vector as the amplitude of the phase waveforms,

fa, fb, fc represents the instantaneous values for the machine variables for phase a, b and c and a = ej2π3

[1]. In order to have a simpler model for computing the variables of the machine a new reference frame isdescribed. 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 andαβ 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


dependence between αβ and abc phase coordinates is expressed matriceal as presented below:

[vαvβ

]=

23

[1 − 1

2 − 12

0√

32 −

√3

2

]·

vavbvc

(4.5)

Knowing the stator voltages in the fixed reference frame αβ it is possible to calculate the stator angle θv aspresented in equation (4.6).

θv = atanVβVα

(4.6)

Now all the variables necessary to calculate the electrical parameters of the machine in the new coordinates arededuct. The transformation from αβ to δϕ is based on Park Transformation and represents the transformationfrom the stator equations to the machines rotor equations and is expressed as described below:[

vδvϕ

]=[cosθv sinθv−sinθv cosθv

]·[vαvβ

](4.7)

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 = Rsiδ + Lsdiδdt− ωevLsidelta + eδ (4.8)

vϕ = Rsiϕ + Lsdiϕdt

+ ωevLsiϕ + eϕ (4.9)

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:

eδ = ωeλmsinθn

eϕ = ωeλmcosθn(4.10)

were ωe is the electrical speed, λm is the magnetic flux linkage of the motor and θn is estimated angle in δϕcoordinated

The simplicity with this strategy, in determining the position of the rotor is coming from the fact thatno integration is needed. In steady state iδ, iϕ currents are constant resulting that the derivative term fromequations (4.8) and (4.9) may be simply omitted. With this assumption made some problems are solved likethe ones that appear with the ideal integration affected by the dc-link or dc-offset, because of the initialconditions of the integral and from non-perfect measurements of current or/and voltages [2]. With thissimplifications made in the chosen control strategy the rotor position in δϕ coordinated is determined fromequations (4.8) and (4.9)and presented in the following:

θn = tan−1 vδ −Rsiδ + ωevLsiδvϕ −Rsiϕ − ωevLsiϕ

(4.11)

The estimated rotor position is determinate as shown in the fallowing equation:

θ = θv − θn (4.12)

Next the sensorless algorithm is implemented in Maltlab/Simulink and the simulation results are presentedand discussed.

31


4.3 Simulation results

In this section, simulation results of the position and speed estimation algorithm are presented. The sensorlessmethod 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 to50% rated load torque (TL = 7 [Nm]) is applied to the system. At time 1.4 [sec] the machine is running ingenerator mode at rated torque (TL = 14 [Nm]). The estimated and measured rotor position are presentedin Fig.4.4. It can be observed that at rated load torque the error between the estimated and rotor positionis the same than in the case were the motor is running with zero torque and it has the value equal with 3.29degrees.

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 goodaccuracy the mechanical speed in case of motor operation as well as in the case were the machine is drivenin generator mod.

Figure 4.5: Measured and estimated mechanical speed of PMSM in open loop system

32


Test of PMSM in close loop

The sensorless algorithm is tested in closed loop at different conditions to see the behavior of the estimatedrotor position. The switch between the rotor position and the estimated position is made at time 0.01 sec, ataround 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]. Therotor 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. Atfull load torque and rated speed the error between the estimated and rotor position has the value equal with3.51 [degrees] and in the case when the motor is driven at zero load torque has the value 3.36 [degrees]. Thereference and the measured speed of the motor are plotted in Fig.4.7. It can be observed that the estimatedspeed is fallowing with good accuracy the reference speed when the sensor is not used in the system and therotor position is estimated. There are no overshoots and the settling time of the speed response is around0.04 [sec].

Figure 4.7: Reference and measured speed with the estimated rotor position at 7 [Nm] load torque

33


Stator voltages and currents are presented in Fig.4.8 It can be observed in Fig.4.8 a) that the voltagessignals are sinusoidal and have the same values as in the case were the encoder was used. In Fig.4.8 b) statorcurrents are shown and at rated load torque, the currents magnitude have the value almost 18.94 [A] thesame 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 startedat rated speed (nn=1400 [rpm]) and zero load torque. At time 0.7 [sec] a step to 50% rated load torque isapplied and at time 1.4 [sec] the motor is run in generator mod at rated load torque. The estimated positionin this case is presented in Fig.4.9. It can be observed that when the machine is running in motor mode theposition error is almost the same as in the case where the motor is running in generator mode and has thevalue around 3.5 [degrees]

Figure 4.9: Estimated and rotor position of PMSM in generator mod

34


The measured and estimated speed are presented in Fig.4.10. The estimated speed is in very goodaccordance with the measured speed. In the zoom made on the plot it can be observed the overshoots thatappear 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 torqueis responding very well in the load changes, when a positive load torque is applied the electromagnetic torqueis 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


Conclusions

This chapter had the main purpose to find a suitable control strategy for estimating the rotor position ofPMSM. First several algorithms were described and one method was chosen to be implemented. The methodwas tested at different conditions to observed the behavior of the machine without the sensor. The positionerror is almost the same in the case when the machine is running with zero load torque as in the case whenis 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 correctnessof 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 correctand in accordance with the real system. First the test setup and the real time interface are presented. Nextin 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 PMSMis fed by a frequency inverter (Danfoss FC300VLT). The inverter is IGBT based converter whose interfacecard has been removed and replaced by a Interface and Protection Card (IPC), that enables the IGBTdrivers 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 regenerativeline rectifier (SIMOVERT RRU) is used to provide the DC bus. The digital controller DS1103 PPC is usedto control the inverter. It represents the main process unit and has the advantage that it has a softwareinterface in Simulink from were all the applications can be developed and compiled automatically in thebackground. 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 necessaryto 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 anonline computation and updating are carried out in the background in order to fulfill the demands that aretest for. Another advantage is the online computation of the program when the data and the real time codeare generated.

The real time application is done like a Simulink blockset. It consist of two parts: Data Acquisition blockand 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 isrunning properly. In Data Acquisition block there are five blocks that will be described further on.

38


The control block manages the entire acquisition block, and has the commands for enabling or disablingthe 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 ofovercurrent, overspeed and undervoltage the signal FAULT is sent to the enabling controlling block, stoppingthe entire system.

The currents from the inverter are found in the Currents block and the DC voltage measurement thatwill 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 withthe help of an encoder. All this blocks are necessary in order to control the permanent magnet synchronousmachine. 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 inControl Desk software which is able to provide a real time control and evaluation of the system. The ControlDesk 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: measuredthree phase currents; measured and reference d,q components of the currents and voltage, measured DCvoltage, 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 theresults 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 theinverter has the same value than in simulations: fs = 5kHz. The space vector modulation block is the oneavailable 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 inmotor mode.

5.3.1 Control of PMSM with encoder

This section presents different results for permanent magnet synchronous motor controlled with Field Ori-ented 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 astep 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 inthe 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 canbe observed that it has no overshoots and has settling time equal with 0.2 [sec] The stator voltages andcurrents 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 areapplied the currents have the limited value. At 50% rated speed the currents have the value 0.146 [A] and at

40


rated speed the currents amplitude is equal with 0.22 [A]. The value of the currents is not equal with zero inthis case because the machine has to produce a minimum torque to overcome the viscous friction and the dryfriction 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 samecondition in simulations, 36.06 [V]. At rated speed the voltages have the value 75.97 [V] which is closed tothe one from the Matlab simulation 72.08 [V]. The difference between the values from the laboratory and thevalues from the simulations may be due to the fact that the values of the machine parameters in simulationare 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 loadtorque. The machine is started at 50% rated speed (nn = 73.3 [rpm]), at time 6.2 [sec] a load of 7 [Nm] isapplied to the motor, fallowed by a step to rated speed at time 11.57 [sec]. The reference and the measuredspeed are shown in Fig.5.6. In the zoom made in the picture it can be observed the moments were the steps inspeed and the load torque are applied. It can be observed that the measured speed is fallowing the referencespeed 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.5.7a) and it can be observed that the currents are increasing with the load torque and at 50% rated speedand 50% rated torque the currents have the amplitude equal with 7.95 [A]. This value is smaller than theone from the simulations 9.48 [A]. When keeping the load torque constant to 7 [Nm] and increasing thespeed to rated speed, stator currents are decreasing. Because the speed response of the machine is showinggood performances the problem may be that the load is not properly controlled and the measured value isdifferent than the real one. Other reason for this situation may be that the values of the machine parametersare different than the one used in the simulations. Some other tests are done in order to observe the behaviorof machine at different load torque command. The tests are presented in Appendix B. The stator voltagesat 50% rated speed and 50% torque is 51.03 [V] and at rated speed 81.78 [V]. This are comparable with thevalues from simulations 38.35 [V] respectively 74.89 [V].

41


Figure 5.7: Stator currents and voltages at different speeds and 7 [Nm] load torque a)Measured currents b)Measuredvoltages

The real and imaginary current axis are shown in Fig.5.8. In Fig.5.8 a) d axis current is presented andit can be observed that the current has the magnitude almost zero fallowing the reference Id current that isequal with zero, imposed by the control property. In Fig.5.8 b) Iq current is fallowing the reference currentand when the load torque is applied at 50% rated speed the current is increasing with the increased in torqueand 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 electromagnetictorque has the value 6.12 [Nm]. The reason may be the same as for the current.

42


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 andno load, at time 6.38 [s] a step to rated speed is applied to motor, fallowed by a step down to 73.3 [rpm] attime 12.78 [sec]. The estimated and the real position of the machine is shown in Fig.5.10. It can be observedthat 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 errorat 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 speedis fallowing with good accuracy the mechanical speed of the machine, without any overshoots.

43


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 estimationalgorithm must be tested in closed loop. The sensorless algorithm based on back EMF calculations is notworking at zero and low speeds so until the motor has reached a given speed is running based on the encoderinformations. In order to use the estimated rotor position a switch is used, but the system was not able towork 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 inthe 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 changein position error around 2%.The inductance changes and the error values are shown in Appendix.C. Afterthis test it can be noted that the algorithm is not effected by the parameters change. More investigationshave to be done regarding the problems that may appear in the implementation of the sensorless algorithmin closed loop.

Conclusion

In this chapter laboratory work was presented. First the test setup and Real Time Application weredescribed. 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 loadingthe 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 inthe 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 inclosed 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 turbineapplications by implementing an algorithm from were the position and speed will be determinated. In orderto 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 Malt-lab/Simulink.

• Laboratory implementation for sensored control of PMSM

• After the sensorless control strategy shows good results in simulations implementation in dSpace lab-oratory.

• 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 thetheoretical performance by using the simulations. So first the mathematical model of the PMSM was testedin simulations, then Field Oriented Control strategy with the sensor was implemented. In order to achieve astable system the PI controllers have to be tunned properly. For the PI current controller the optimal criterionfor adjusting the gains is the magnitude optimum while for the speed controller is symmetry optimum. Finallythe entire model was tested in Matlab/Simulink and results were presented. For different test conditions themodel shows good performance.

Next different position estimation methods were investigated. The method chosen in this case is based onback EMF calculation with a few changes in the voltage and current generation. For wind turbine applicationis 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 thelaboratory work shows good performance when the machine is running at zero load. When the machine isloaded and reference speed is increased the current is decreasing, this situation may be because the load isnot 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 inopen loop it shows that that estimation and rotor position are in good accordance. When the algorithm wastested in closed loop, the system could not work.

Field Oriented Control was implemented on 2.2 [kW] machine. The machine was tested in laboratoryand good performances were achieved. The estimation position of the rotor shows good performances insimulations 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 tohave 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, MingYin 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, AalborgUniversitet, 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 Technol-ogy, 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 errorsand 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 synchronousmachines, 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 ScientificPublishers, 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, JuliusLukko, Lappeenranta, 2000, ISBN 951-764-438-8

48

BIBLIOGRAPHY

49

BIBLIOGRAPHY

Nomenclature

Variable ParameterAbbreviationsAC Alternative CurrentDC Direct currentFOC Field oriented controlEMF Back electromotive forceIEA International Energy AgencyIPMSM Interior permanent magnet synchronous machineOM Optimal ModulusOSM Optimum Symmetric MethodPI Proportional IntegralPMSM Permanent magnet synchronous machinePMSG Permanent magnet synchronous generatorPWM Pulse width modulationSPMSM Surface permanent magnet synchronous machineSVM Space vector modulationVSI Voltage source inverterSymbolsVAB Line A to line B voltageVAN Line A to neutral N voltageVBC Line B to line C voltageVBN Line B to neutral N voltageVCA Line C to line A voltageVCN Line C to neutral N voltageVDC DC voltageVA, VB , VC Phase voltagesIA, IC , IC Phase currents~Isabc Stator phase current~V sabc Stator phase voltage~Ψsabc Flux linkage

vsd, vsq Stator voltage in dq stationary reference frame

isd, isq Stator current in dq stationary reference frameisdref , isqref Reference current in dq stationary reference frameλsd, λ

sq Stator flux linkages in dq stationary reference frame

Rs Stator resistanceLs Synchronous inductancePn PowerTl Load torqueTe Electromagnetic torqueBm Dry friction coefficientJ Moment of inertiaωe Electrical speed

50

BIBLIOGRAPHY

Variable Parameterωm Mechanical speedwref Reference speednpp Number of pole pairsλm Permanent magnet flux linkagekpi Proportional gain for PI current controllerkii Integrator gain for PI current controllerTii Time integral of PI current controllerkps Proportional gain for PI speed controllerkis Integrator gain for PI speed controllerTis Time integral of PI speed controllerG(s) Transfer function of the current/speed controllerTs Sampling timefs Sampling frequencyTiq Time constant of the current controllerTsi Equivalent time constantTss Time constant of the speed controller

51

APPENDIX A. DATASHEET OF PMSM

Appendix A

Datasheet of PMSM

Figure A.1: 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 weremay be the problem.

For this test the machine was driven at 50% rated speed (nn = −73.3 [rpm]) and at time 6.4 [sec] themachine was loaded to 7 [Nm], fallowed at time 12.34 [sec] with a step to rated speed. Sign plus or minus inthe speed represent the rotation of the machine, clockwise or anti clockwise, and for this test the machineis running in opposite direction than in the test made in Section 5.3.1 in order to observed the behavior ofthe 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 noovershoots 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 havethe amplitude equal with 10.16 [A] and at rated speed the currents are increased to the value 13.19 [A]. Thecurrents value obtained in the simulation in the same conditions (50%rated load torque and rated speed) is9.4 [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 thevalue from simulation 36.05 [V]. When the machine is running at 73.3 [rps] and 50% rated load torque isapplied to the machine, stator voltages are decreasing to value 25.42 [V],and when the a step in speed torated 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 maybe a consequence of the fact that the load is not properly controlled and also it may be a difference in themeasured and real load torque applied to machine.

55

Appendix C

Test for the sensorless control

Inductance [mH] Position Error1.5 5.71.6 5.81.7 61.8 6.11.9 5.92 6

2.1 62.2 62.3 5.82.4 5.72.5 5.92.6 62.7 5.82.8 6.12.9 5.93 6

3.1 5.53.2 6.13.3 5.73.4 63.5 5.93.6 63.7 63.8 5.13.9 6.14 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

control of permanent magnet synchronous generator for large wind turbines

Documents