Juha-Pekka Ström ACTIVE DU/DT FILTERING FOR VARIABLE

Juha-Pekka Ström

ACTIVE DU/DT FILTERING FOR VARIABLE-SPEED AC DRIVES

Thesis for the degree of Doctor of Science (Technology) to be presented with due permission for public examination and criticism in the Auditorium 1382 at Lappeenranta Uni-versity of Technology, Lappeenranta, Finland, on the 17th of December, 2009, at noon.

Acta UniversitatisLappeenrantaensis378

Supervisor Professor Pertti SilventoinenLaboratory of Applied ElectronicsLUT Institute of Energy Technology (LUT Energia)Faculty of TechnologyLappeenranta University of TechnologyFinland

Reviewers Professor Heikki TuusaLaboratory of Power ElectronicsTampere University of TechnologyFinland

Dr. Mika SippolaNidecon Technologies OyFinland

Opponent Dr. Mika SippolaNidecon Technologies OyFinland

ISBN 978-952-214-888-9ISBN 978-952-214-889-6 (PDF)

ISSN 1456-4491

Lappeenrannan teknillinen yliopistoDigipaino 2009

Abstract

Juha-Pekka Ström

Active du/dt Filtering for Variable-Speed AC Drives

Acta Universitatis Lappeenrantaensis 378

Dissertation, Lappeenranta University of Technology127 p.Lappeenranta 2009ISBN 978-952-214-888-9, ISBN 978-952-214-889-6 (PDF)ISSN 1456-4491

An oscillating overvoltage has become a common phenomenon at the motor terminal ininverter-fed variable-speed drives. The problem has emerged since modern insulated gatebipolar transistors have become the standard choice as the power switch component in low-voltage frequency converter drives. The overvoltage phenomenon is a consequence of thepulse shape of inverter output voltage and impedance mismatches between the inverter, mo-tor cable, and motor. The overvoltages are harmful to the electric motor, and may cause, forinstance, insulation failure in the motor. Several methods have been developed to mitigatethe problem. However, most of them are based on filtering with lossy passive components,the drawbacks of which are typically their cost and size.

In this doctoral dissertation, application of a new active du/dt filtering method based on alow-loss LC circuit and active control to eliminate the motor overvoltages is discussed. Themain benefits of the method are the controllability of the output voltage du/dt within certainlimits, considerably smaller inductances in the filter circuit resulting in a smaller physicalcomponent size, and excellent filtering performance when compared with typical traditionaldu/dt filtering solutions. Moreover, no additional components are required, since the activecontrol of the filter circuit takes place in the process of the upper-level PWM modulationusing the same power switches as the inverter output stage.

Further, the active du/dt method will benefit from the development of semiconductor powerswitch modules, as new technologies and materials emerge, because the method requires ad-ditional switching in the output stage of the inverter and generation of narrow voltage pulses.Since additional switching is required in the output stage, additional losses are generated inthe inverter as a result of the application of the method. Considerations on the application ofthe active du/dt filtering method in electric drives are presented together with experimentaldata in order to verify the potential of the method.

Keywords: Electric drive, output filter, active filterUDC 681.527.7 : 681.532.52

Acknowledgments

The research documented in this work was carried out at the LUT Institute of Energy Tech-nology (LUT Energia) at Lappeenranta University of Technology (LUT) during the years2006–2009. The research was funded by the Finnish Graduate School of Electrical Engineer-ing (GSEE), Vacon Plc., and Lappeenranta University of Technology.

The beginning of the active du/dt research came from Vacon Plc. during the fall 2006, as theauthor was invited to Vacon Plc. to discuss the topic of cable reflections and output filtering.Especially the contribution of Dr. Hannu Sarén and Dr. Kimmo Rauma on the researchtopic is most sincerely acknowledged, as is also the valuable support by the Vacon Companyduring the research projects. Without you and Vacon Plc. this research would not have beenpossible.

I would like to thank the preliminary examiners of this dissertation, Professor Heikki Tuusaand Dr. Mika Sippola for their valuable comments on the manuscript. I am very grateful foryour contribution and help in improving the thesis. I would like to express my gratitude to mysupervisor, Professor Pertti Silventoinen, and to Dr. Julius Luukko and Dr. Mikko Kuismafor their valuable guidance and help during the process.

I am very grateful to Dr. Hanna Niemelä for her help in improving the language of the text.I really appreciate your contribution, and your patience with my sometimes not-so-steadywriting schedule. It has been a huge help in the writing.

I express my deepest thanks to my collegues, Mr. Juho Tyster and Mr. Juhamatti Korho-nen for their contribution, many ideas, and uncompromising attitude towards the active du/dtresearch. Your work for the development of the method, for the prototypes, and in the lab-oratory has really been worthy. I also thank for your help during the preparation of themanuscript.

I would like to thank all the people I have worked with at the Deparment of Electrical Engi-neering here at LUT during these years; especially those who have been spending all thosecoffee breaks – sometimes even the longer ones – around the coffee table. All the sharedexperiences when we have hit the road – in the name of science, of course – have alwaysbeen something worth remembering. It has been a pleasure, thank you!

The financial support for this work by Emil Aaltonen Foundation, Walter Ahlström Founda-tion, Lahja and Lauri Hotinen Fund and the Foundation of the Finnish Society of ElectronicsEngineers is most sincerely appreciated.

Finally, I would like to express my deepest gratitude to my family; your support during allthe rush, and your understanding for my absence during all those hours at work have beenvery important. This is for you Tiina, Pietu, and Neela; you are my all.

Lappeenranta, December 1st, 2009

Juha-Pekka Ström

Contents

Abstract 3

Acknowledgments 5

List of Symbols and Abbreviations 9

1 Introduction 151.1 Background and motivation of the work . . . . . . . . . . . . . . . . . . . . 161.2 Objective of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4 Scientific contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2 Cable-reflection-induced terminal overvoltages in variable-speed drives 232.1 Frequency spectrum of the output voltage of a typical three-phase switching

mode inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Overvoltages caused by switching transients . . . . . . . . . . . . . . . . . . 26

2.2.1 Transmission line properties of the motor feeder cable in an electricdrive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.2 Transmission line discontinuities . . . . . . . . . . . . . . . . . . . . 302.2.3 Discontinuities in a typical inverter-fed electric drive . . . . . . . . . 31

2.3 Critical cable length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4 Fundamental properties of second-order systems . . . . . . . . . . . . . . . . 332.5 Typical output filtering solutions . . . . . . . . . . . . . . . . . . . . . . . . 35

2.5.1 Output du/dt filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5.2 Output du/dt filters with a clamping diode circuit . . . . . . . . . . . 362.5.3 Motor terminal cable terminators . . . . . . . . . . . . . . . . . . . . 372.5.4 Summary on typical topologies . . . . . . . . . . . . . . . . . . . . 372.5.5 More on PWM-inverter-based issues in electric drives . . . . . . . . 38

2.6 Effects of a converter drive on the electric motor . . . . . . . . . . . . . . . . 38

3 Output filtering in a frequency-converter-fed electric drive 413.1 Active du/dt filtering method . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.1.1 Active du/dt filter circuit . . . . . . . . . . . . . . . . . . . . . . . . 453.1.2 Active control of the active du/dt LC filter circuit . . . . . . . . . . . 463.1.3 Analysis of the active du/dt filtering method . . . . . . . . . . . . . . 493.1.4 Active du/dt filter current analysis . . . . . . . . . . . . . . . . . . . 55

3.1.5 Different charging schemes for active du/dt filter circuit . . . . . . . 563.1.6 Measured example of active du/dt operation . . . . . . . . . . . . . . 58

3.2 Active du/dt filter circuit component selection . . . . . . . . . . . . . . . . . 603.3 Selection of active du/dt rise time for various cable lengths . . . . . . . . . . 61

4 Applying active du/dt filtering to an electric drive 654.1 Effects of an electric motor on the active du/dt filtering method . . . . . . . . 65

4.1.1 Error caused by the induction motor current . . . . . . . . . . . . . . 664.1.2 Effect caused by resistive losses in the circuit . . . . . . . . . . . . . 76

4.2 Simulations of the error caused by the motor current . . . . . . . . . . . . . . 764.3 Measurements and experimental results . . . . . . . . . . . . . . . . . . . . 84

4.3.1 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.3.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 874.3.3 Additional switching losses caused by the application of the active

du/dt method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.3.4 Effect of active du/dt filtering method on common-mode voltages . . 99

5 Discussion and Conclusions 1015.1 Key results of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.2 Suggestions for future work . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

References 107

Appendices 113

A Simulation models 115

B Measurement equipment 123

C Asynchronous machine equivalent circuit parameters 127

List of Symbols and Abbreviations

Roman letters

A amplitude

A mains phase A

B mains phase B

C capacitance

CDCLINK DC link capacitor

C mains phase C

c speed of light

f frequency

fBW frequency bandwidth

fc switching frequency

fosc oscillation frequency

G conductance

H system transfer function in Laplace plane

Uout output voltage in Laplace plane

I current wave

i instantaneous current

icm common mode current

if filter current

IL load current

K active du/dt rise and fall time coefficients with respect to filter time constant

L inductance

l cable length

lc critical cable length

Lf filter inductance

LL load inductance

Lm magnetizing inductance of an asynchronous machine

L′s transient inductance of an asynchronous machine

Lrσ rotor leakage inductance of an asynchronous machine

Lsσ stator leakage inductance of an asynchronous machine

M number of charge periods

N number of charge pulses

n index in sum

P power

R resistance

Rloss equivalent loss resistance

Rr rotor resistance of an asynchronous machine

Rs stator resistance of an asynchronous machine

s Laplace variable, s = σ + jω

T period

t time

t1 charge sequence pulse turn-off time, same as t1/2

t2 time at which the charge sequence is complete, same as active du/dt tr

tcorr load current correction pulse length

tf fall time

tp cable propagation delay

tr rise time

t1/2 instant at which the system output voltage is half the applied step amplitude

u instantaneous voltage

uA mains voltage phase A

uB mains voltage phase B

ucm common mode voltage

uC mains voltage phase C

UDC DC link voltage

uinv inverter output voltage

uout output voltage

uU inverter output phase U voltage

u′U filtered inverter output phase U voltage

uV inverter output phase V voltage

u′V filtered inverter output phase V voltage

uW inverter output phase W voltage

u′W filtered inverter output phase W voltage

U inverter output phase U

V voltage wave

V− reflected voltage wave

V + incident voltage wave

Vp voltage peak value

V inverter output phase V

W inverter output phase W

XC capacitive reactance

XL inductive reactance

∆z differentially small increment in position

z position

Z0 characteristic impedance

Zc cable impedance

ZL load impedance

Zm motor impedance

Greek letters

α attenuation constant

β propagation constant

ε permittivity

εeff effective dielectric constant experienced by electromagnetic wave at a certaindielectric configuration at a certain frequency

γ complex propagation constant

Γi inverter reflection coefficient

ΓL load reflection coefficient

Γm motor reflection coefficient

λ wave length

µ permeability

ωn resonance frequency

ω angular frequency

φL load reflection phase angle

δs skin depth

σ conductivity

νp propagation velocity

ζ damping factor

Subscripts

max maximum value

Other symbols

δ (t) Dirac delta function, impulse function

ε(t) Heaviside step function

Acronyms

AC Alternating current

DC Direct current

DOL Direct-on-line

EMI Electromagnetic interference

ETD Ferroxcube ETD coil former cores and accessories product line

FIR Finite impulse response digital filter

FPGA Field programmable gate array

IEC International electrotechnical commission

IGBT Insulated gate bipolar transistor

LC Electrical circuit consisting of an inductive and capacitive component

MCMK Power cable type

NXP Vacon NX performance product line

PVC Polyvinyl chloride, insulating material used e.g. in power cables

PWM Pulse width modulation

RLC Electrical circuit consisting of an inductive, capacitive, and resistive component

TEM Transversal electromagnetic mode of wave propagation

VSI Voltage source inverter

15

Chapter 1

Introduction

The consumption of energy has considerably increased in the European Union during the pastyears, despite the efforts of union-wide and national policies and programmes to increase en-ergy efficiency. During the period of 1990–2005, the final electricity consumption in theEU-27 countries has increased by 29 %, at an annual growth rate of 1.8 %, and in Finland by37 %, at an annual growth rate of 2.3 % (Eurostat, 2007). In the future, even more pressurewill be put on cutting electricity consumption. The European Union has agreed on an inte-grated energy and environmental policy, and one of the main objectives is to save 20 % of theprojected energy consumption by the year 2020.

In order to rise to the challenge, modern electronic power converters and control of electricpower on the whole play a very important role in improving the energy efficiency of upcomingand present installations. A very typical and important application example of such a systemis an electric drive, in which electrical power is converted into mechanical torque, or viceversa. To control the electromechanical conversion process, in many cases, an electronicpower converter is essential in a modern electric drive. This is achieved by controlling theoutput voltage and frequency of the power converter to match the demands of the application.This leads to improvements in energy efficiency, especially for instance in pump, fan, andcompressor applications, and also in the control of the process in general, when comparedwith a noncontrolled drive. This is one of the main reasons why power-converter-controlledelectric drives have established themselves in the industry during the past decades. This hastaken place especially in the low-voltage segment (under one thousand volts) in both low- andhigh-power drives, because of the rapid development of low-voltage semiconductor powerswitches. Typically, the power converter in an electric drive is called a frequency converter,and the drive is called a variable-speed or a variable-frequency drive.

A major part of the produced electricity, over 40 % in the EU-27 countries, is consumed inthe industry (Bertoldi and Atanasiu, 2007), for example in the above-mentioned, numerouselectric drives. Even though frequency-converter-controlled electric drives have been appliedespecially in new electric drive installations, even more energy could be saved by installing a

16 Introduction

frequency converter to all suitable electric drives. In the industry, of all the installed electricdrives, induction motor drives are widely used in the industry, and are generally consideredvery reliable. However, the switched-mode operation of the frequency converter may causeadverse effects in the drive, as will be discussed later in this chapter. Therefore, variousfiltering solutions have been introduced to be used in conjunction with converter drives inorder to mitigate the effects.

In this dissertation, a new output filtering method consisting of a passive LC filter circuitand active control is developed for induction motor drives. Compared with more traditional,completely passive approaches, the filtering performance is improved. Further, the size ofthe electrical components is decreased in terms of both electrical and physical dimensions,thereby improving the integrability of the filter, decreasing filter losses, and reducing the costof the actual filter. However, extra losses are introduced as a result of extra switching of theoutput stage. The method is verified by both a theoretical analysis and measurements forinduction motor drives utilizing a modern frequency converter that uses fast switching IGBTpower switches. The focus of this dissertation is on the development and feasibility studyof the method, while the actual implementation on a real electric drive still requires furtherdevelopment.

The work documented in this doctoral dissertation focuses on induction motor drives only,because of their large number of installations in the industry. However, a frequency convertercan as well be applied to generator and synchronous motor drives. The number of converterdrives is also likely to increase in the future, because of the significant improvements inenergy efficiency for example in the above-mentioned motor drives, and in decentralized andrenewable energy production.

Further, there is no reason why the method should not be applicable also to other types ofmachines suitable for converter drives, because the developed output filtering method is inde-pendent of the electric motor properties present in the drive. Only the output voltage is shapedto achieve a more motor-friendly behavior by decreasing the du/dt value of the transients. Thefiltering method does not interfere with the upper-level control of the drive, because the con-trol of the filter circuit can be carried out as the lowest level of modulation. The developedmethod may even improve the control performance, since the motor terminal voltage, andtherefore motor flux, can now be accurately predicted, because the harmful cable oscillationis eliminated when the method is applied.

1.1 Background and motivation of the work

The voltage source inverter (VSI) based on insulated gate bipolar transistors (IGBT) applyingpulse width modulation (PWM) has established as the frequency converter in low-voltageAC drives. As a result of the remarkable advancements in the semiconductor power switchdevice generations, the switching losses have reduced significantly. This has made it possiblefor example to reduce the sizes of cooling profiles and device enclosures and to use higherswitching frequencies. Using a higher switching frequency results in a more sinusoidal motor

1.1 Background and motivation of the work 17

current with less ripple and less copper loss. However, both the switching losses in theinverter output stage and the iron losses caused by eddy current losses in the motor increaseas a function of switching frequency (Mohan et al., 2003).

The basic operating principle of a voltage source inverter using pulse width modulation ispresented in Figure 1.1.

0 0.005 0.01 0.015 0.02

−500

0

500

Time [s]a)

Vol

tage

[V]

0 0.005 0.01 0.015 0.02

−500

0

500

Time [s]b)

Vol

tage

[V]

Figure 1.1. Normal sine wave, 50 Hz, 400 V, three-phase, phase-to-phase AC voltages available fromthe standard European grid are shown in Figure 1.1a. In Figure 1.1b, the same voltages are constructedfrom rectified AC voltage applying pulse width modulation (PWM). The modulated voltage consistsof switched voltage pulses, which are modulated according to the reference, which is in this case the50 Hz three-phase sine voltages.

Figure 1.1a shows the standard 50 Hz, three-phase sine AC voltages available from the stan-dard European grid. These are the voltage waveforms for which most electric motors aredesigned. However, in an electric drive using a power converter, the output voltage waveformis quite different from the sine wave, as shown in Figure 1.1b. Because of the requirement tobe able to control the output frequency and voltage, the electrical power available from thegrid has to be constructed by using an inverter to produce the desired output voltage proper-ties. In the most common case, the output voltage is produced using pulse width modulationfrom rectified AC voltage, in which the width of the voltage pulse is modulated according tothe reference voltage. Therefore, the output voltage consists of steep rising and falling edgesof the DC voltage, instead of true sine wave behavior. This has a remarkable effect on thefrequency content of the output voltage. The properties of the output voltage edges dependon the properties of the power switches used in the output stage of the inverter.

18 Introduction

Although the IGBT has clear advantages when set against previous generations of semicon-ductor power switches, the remarkable advances in the switching times also manifest certaindrawbacks far more clearly than the older generations of power switches: The rise and fallswitching times of an IGBT are very short, at present in the order of tens of nanosecondsat best, and therefore the rate of change, namely du/dt, in the inverter output voltage pulseis very high. Hence, the output voltage contains a broad range of frequencies, including alot of high-frequency components (Skibinski et al., 1999). In the industry, a typical lengthof the interconnecting cable is tens or hundreds of meters, which is substantial comparedwith the wavelength of the high-frequency components present in the fast transient voltages.This leads to voltage reflections resulting in transient overvoltages at the motor terminals andelectromagnetic oscillation in the motor cable (Persson, 1992) and (Saunders et al., 1996).In order to suppress these effects of the fast switching transients, passive lowpass filtering istypically applied to the output voltage to narrow the frequency spectrum of the motor voltagebelow the natural oscillation frequency of the motor cable.

These effects have been mitigated by using many different passive filtering topologies, whichare typically somewhat large in size and therefore expensive, but not very effective in allrespects. The active du/dt filtering method presented in this dissertation is based on a passiveLC filter circuit and active control of the filter using pulse width modulation: each transientor edge in the fundamental modulation of the inverter has to be supplemented with additionaledge modulation to provide control for the filter circuit to produce output voltage of thedesired shape in a controlled way. Both the guidelines of pulse width modulation and thebehavior of a passive LC circuit are commonly known and documented, whereas combiningthese in the output filtering of an electric drive has novelty value.

However, there are publications considering active du/dt control in the inverter output voltage,see (Idir et al., 2006) and (Kagerbauer and Jahns, 2007). In these, the analysis is carried outfrom a different point of view, for example EMI reduction, and the switching transition speedof the power switch is reduced to decrease the EMI produced by the inverter output stage.Therefore, filtering is implemented on a totally different basis than the work carried out inthis study. By using the method presented in the publications for output filtering of the drive,where the required rise and fall times are in the order of microseconds, as discussed later inChapter 3, significant switching losses would be generated, and therefore the methods are notbeneficial for conducting output du/dt filtering.

1.2 Objective of the work

The main objective of the study was to develop an efficient source filter solution for electricdrives, in terms of both electrical performance and size. In this study, the goal is achievedby active control of the filter circuit, which is based on fast control of the circuit and fastswitching properties of the modern semiconductor power switches. This results in betterelectrical performance, but also in both electrically and physically smaller filter components.This in turn provides better electrical performance of the output filter and savings both interms of the filter size and cost, and therefore better integrability of the output filter. The

1.3 Outline of the thesis 19

inductor in particular is a costly component in a traditional passive du/dt filter, and it isthe component, in which major cost savings can be achieved in the total cost of the filter.Furthermore, the method presented will benefit from the development of faster and moreefficient power switch components, for example the development of silicon-carbide (SiC)technology for power switches. In addition, an advantage of active du/dt is that the faster thecomponents are and the less switching loss is generated, the more beneficial it will be for thedeveloped output filtering method.

1.3 Outline of the thesis

This doctoral dissertation studies output filtering needs arising from the switching-mode op-eration of a motor driven with a frequency converter. This is mainly a result of the advance-ments in semiconductor power switch transition times between the conducting and noncon-ducting states. Existing output filtering solutions and the problems caused by the fast tran-sitions are discussed, and a new output filtering method to be used in a frequency converterapplying fast power switches is introduced. The theoretical background for the method isdeveloped, and the feasibility of the method is verified by implementing it in a real inductionmotor drive, which consists of a standard industrial frequency converter with a custom-builtcontrol and an induction motor.

The rest of the dissertation is divided into the following chapters:

Chapter 2 gives general information about the background and the problems evolved infrequency-converter-fed electric drives as a result of the development of the powerswitch components. Common solutions to the problems presented in the literature arealso discussed in brief.

Chapter 3 discusses output filtering of a frequency-converter-fed electric drive and intro-duces issues to be taken into account in the design of output filtering for a certainelectric motor drive. The developed active output filtering method is presented, andthe theory for application of the method is provided. Design considerations for theimplementation of the method are presented.

Chapter 4 introduces issues related to the developed active output filtering method in anactual electric drive. Guidelines are given for solving these issues, when the outputfiltering method is applied to a drive. Measurements using a prototype equipment arepresented. The objective of the measurements is to show that the theory developed isfeasible and the narrow pulses required by the method are in fact achievable in stan-dard industrial electric drive hardware. Considerations especially for the selection ofcomponents are presented.

Chapter 5 concludes the work covered in this dissertation and discusses the results obtained.The usability of the results is evaluated and suggestions for future work are given.

20 Introduction

1.4 Scientific contribution

The scientific contributions of this doctoral dissertation are:

• Development of a new active output filtering method, which consists of a passive LCcircuit and a specific control of the circuit in order to produce voltage slopes of de-signed length to suppress the effects of fast transients in an electric drive.

• Formulation of the theoretical background for the application of the active du/dt filter-ing method in an electric drive.

• Development of guidelines for the filter component value selection and the basis for thecorresponding control sequences for the application of the method in an electric drive.

• A method is introduced for correction of the error caused by the load current of themotor present in the drive.

• The method is proven to be a potential output du/dt filtering solution by a series ofexperimental measurements.

The author has published research results related to the subjects covered in the dissertation asa co-author in the following publications:

1) J.-P. Ström, J. Tyster, J. Korhonen, K. Rauma, H. Sarén and P. Silventoinen, "Activedu/dt Filtering for Variable Speed AC drives," in 13th European Conference on PowerElectronics and Applications, EPE 2009, 8–10 September, Barcelona, Spain, 2009,(Ström et al., 2009).

2) J. Korhonen, J.-P. Ström, J. Tyster, H. Sarén, K. Rauma and P. Silventoinen, "Control ofan Inverter Output Active du/dt Filtering Method", in The 35th Annual Conference ofthe IEEE Industrial Electronics Society, IECON 2009, 3–5 November, Porto, Portugal,2009, (Korhonen et al., 2009).

3) J. Tyster, M. Iskanius, J.-P. Ström, J. Korhonen, K. Rauma, H. Sarén and P. Silventoinen,"High-speed gate drive scheme for three-phase inverter with twenty nanosecond mini-mum gate drive pulse," in 13th European Conference on Power Electronics and Appli-cations, EPE 2009, 8–10 September, Barcelona, Spain, 2009, (Tyster et al., 2009).

4) J.-P. Ström, H. Eskelinen and P. Silventoinen, "Manufacturability and Assembly Aspectsof an Advanced Cable Gland Design for an Electrical Motor Drive," Intl. Journal ofDesign Engineering, Vol. 1, Issue 4, 2009.

5) J.-P. Ström, M. Koski, H. Muittari and P. Silventoinen, "Analysis and filtering of commonmode and shaft voltages in adjustable speed AC drives," in 12th European Conferenceon Power Electronics and Applications, EPE 2007, 2–5 September, Aalborg, Denmark,2007.

6) J.-P. Ström, M. Koski, H. Muittari and P. Silventoinen, "Transient Over-Voltages in PWMVariable Speed AC Drives - Modeling and Analysis," in Nordic Workshop on Powerand Industrial Electronics, 12–14 June, Lund, Sweden, 2006.

1.4 Scientific contribution 21

J.-P. Ström has been the primary author in publications 1 and 4–6. The background researchfor publications 1–3 has been done together by J.-P. Ström, Mr. J. Korhonen, and Mr. J.Tyster. The prototype used in the measurements of publications 1–2 was developed by Mr.J. Tyster and Mr. J. Korhonen. The prototype used in publication 3 was developed by Mr. J.Tyster and Mr. M. Iskanius. Measurements for publications 1–3 were carried out by the firstauthors of the corresponding publications.

Background research for publication 4 was carried out by the authors. The research on themanufacturability and assembly aspects in publication 4 was carried out by Dr. H. Eskelinen.The cable gland prototypes were constructed by the Department of Mechanical Engineeringat Lappeenranta University of Technology and the measurements were carried out by J.-P.Ström.

For publication 5, background research was carried out by Ms. H. Muittari. Filter prototypeconstruction and the measurements were carried out by J.-P. Ström and Ms. H. Muittari. Forpublication 6, J.-P. Ström was in the major role in the background research, measurementsand writing, with the help of the co-authors.

The author is designated as a co-inventor in the following patents or patent applications con-sidering the subjects presented in this dissertation:

FI Patent 119669 B "Jännitepulssin rajoitus". Patent granted Jan 30 2009, (Sarén et al.,2009).

EU Patent application 08075493.0 - 1242 "Limitation of voltage pulse". Application filedMay 19 2008, (Sarén et al., 2008a).

US Patent application 20080316780 "Limitation of voltage pulse". Application filed Dec25 2008, (Sarén et al., 2008b).

22 Introduction

23

Chapter 2

Cable-reflection-induced terminalovervoltages in variable-speed drives

Along with the development of new power semiconductor switching components and identi-fication of the side effects produced by the frequency converters applying these components,the topic of cable reflection has been under extensive research, and numerous scientific pub-lications can be found considering both the phenomenon itself and various means to mitigateits effects. Some key publications on cable reflections are for example (Persson, 1992) and(Saunders et al., 1996).

As presented in the introductory chapter, three-phase motors are controlled by means ofvariable voltage and frequency, and in a very typical case, this is implemented by using aswitching-mode DC to a three-phase AC converter, typically a voltage source inverter (VSI)applying pulse width modulation (PWM). The energy from the utility source is rectified intoa DC link capacitor by using a rectifying bridge, and the DC link capacitor acts as the low-impedance voltage source for the inverter bridge.

The AC voltage is formed from the DC link voltage by the inverter bridge as a series ofpulses, which have a constant amplitude – neglecting the DC link fluctuations – and a varyingwidth, the output of the phases being connected either to the positive or negative DC linkrail; therefore, the phase-to-phase voltage between two phases can be either the positive ornegative DC bus voltage. A schematic of a main circuit of a frequency converter is shown inFigure 2.1. Further, a possible output filter connection is shown along with a typical motorcommon-mode current path.

In order to keep the losses produced in the switching operation of a single power semiconduc-tor component in the inverter bridge to a minimum, the transition time between the on- andoff-states (and vice versa) of the switching component should be made as short as possible.This is because the voltage across the component is larger than the on-state saturation voltage

24 Cable-reflection-induced terminal overvoltages in variable-speed drives

Figure 2.1. Frequency converter main circuit. Power from the grid is rectified into the DC link. Themotor AC voltage of variable frequency and voltage is generated from the DC link voltage using thethree-phase inverter bridge shown. A possible output du/dt filter, and a typical motor common-modecurrent path are also presented.

of the component and a possible current flowing through the component will generate powerloss (heat) during the transition according to the following equation

P =1T

∫uidt. (2.1)

On this account, the transitions in the voltage pulses generated by the DC to AC converter inthe adjustable speed drive are kept as short as possible, leading to the fact that the steepnessof the edges of the voltage pulses is high. In an inverter power switch component generallyapplied, that is, the insulated gate bipolar transistor (IGBT), the transition time between thestates is at fastest in the order of tens of nanoseconds, as can be seen for instance in thenext section. In addition to the benefits presented above, the fast switching voltage transientand thereby the output voltage of the inverter contains a lot of high-frequency componentsas a byproduct of the switching mode operation. The frequency components beside the basefrequency of the electric drive are by definition unnecessary and even harmful to the operationof the drive, but are not irrelevant for the operation of the drive. This is the key differencebetween the voltage waveforms in a traditional direct-on-line (DOL) and VSI-converter-feddrives.

The switching transients occuring in the inverter are – and have to be – fast, when comparedwith the fundamental and switching frequencies. Therefore, the output voltage waveformcontains in addition to the fundamental base frequency, switching frequency, and their har-monics, high-frequency components resulting from the steep voltage pulse edges extendingup to the megahertz range (Skibinski et al., 1999). If the speed of propagation in the mo-tor cable is for example in the order of 0.5c, see for example (Skibinski et al., 1997; Ahola,2003), the wavelength of a 50 Hz signal is in the order of thousands of kilometers, whereasthe wavelength of a signal of 1 MHz is only 300 meters.

2.1 Frequency spectrum of the output voltage of a typical three-phase switching modeinverter 25

Hence, the lengths of a typical motor cable, which are in the order of tens to a few hundredmeters, are substantial compared with the high-frequency components present in the inverteroutput voltage. Therefore, each switching in the inverter output stage induces a travelingwave into the motor cable, and the transmission line theory must be applied in the analysis ofthe behavior of the traveling waves in the motor cable (Persson, 1992); see Chapter 4 for mea-surements of the propagation speed for the MCMK power cables used in the measurementsof this dissertation.

This also sets special requirements for the motor cabling and the insulations in the electricmotor, because the motor and the motor cable are typically designed for low operating fre-quencies, and also the effects caused by the high frequency content in the output voltagemust be taken into account in a converter drive, for example the overvoltages caused by wavereflections, as will be discussed later in this chapter.

2.1 Frequency spectrum of the output voltage of a typicalthree-phase switching mode inverter

As presented in (Skibinski et al., 1999), the output voltage of a pulse-width-modulated(PWM) voltage source inverter can be approximated as a series of trapezoids of varyingwidth, and the frequency spectrum of the signal can be approximated by means of Fourieranalysis (Zhong et al., 1998). An example of an inverter output voltage and correspondingdifferential-mode voltage spectrum presented in (Skibinski et al., 1999) are shown in Fig-ures 2.2a and 2.2b.

Figure 2.2. a) Inverter phase output voltage and b) corresponding voltage spectrum. In this example,from (Skibinski et al., 1999), the switching frequency fc is 500 Hz, the duty cycle 50 % and tr 200 ns.The frequency axis is logarithmic.

The main parameters that the spectral width of the signal depends on are the rise time tr andthe switching frequency fc. According to (Zhong et al., 1998), the theoretical spectrum isflat until fc, and it begins to attenuate after this frequency by 20 dB/decade and after fBW by


40 dB/decade. Therefore, fBW can be used as a rough approximate for the spectral width ofthe inverter output voltage waveform (Skibinski et al., 1999):

fBW ≈1

πtr. (2.2)

When IGBT power switches with typical transition times between 50 and 400 ns (Saunderset al., 1996; IEC, 2007) are employed in the inverter output stage, the frequency spectrum ofthe output voltage extends up to the radio frequency region, from hundreds of kilohertz upto several megahertz. As an example, the rise and fall times and the calculated bandwidthestimate using (2.2) for some Semikron Semitrans packaged IGBT modules are presented inTable 2.1. These modules are selected as an example, because they fit in the Vacon NXP seriesframe size 6 industrial frequency converter, which is also used in the prototype equipment andtests. The total switching energy at the rated, continuous collector current is also presented.

Table 2.1. Rise and fall times, the total switching energies and the calculated bandwidth estimates ofsome Semikron Semitrans packaged IGBT modules, as stated by the manufacturer

Module Typical Typical Total switching Bandwidth

type rise time fall time energy estimate

tr tf @100 A Eq. (2.2)

Semikron SKM

100GB123D 70 ns 70 ns 27 mJ 4.5 MHz

1200 V Standard

Semikron SKM

100GB125DN 40 ns 20 ns 22 mJ 16 MHz

1200 V Ultra fast

Semikron SKM

100GB176D 40 ns 145 ns 100 mJ 10.6 MHz

1700 V Trench

Spectrum measurements of an inverter output voltage are presented for example in (Skibinskiet al., 1999), in which the spectral width was found to reach up to the megahertz range. Inthe example, rise time was 200 ns and the spectral width was more than 1 MHz.

2.2 Overvoltages caused by switching transients

In a centralized industrial installation, typical motor feeding cable lengths vary from tens ofmeters up to a few hundred meters. Unless the converter is installed immediately next to

2.2 Overvoltages caused by switching transients 27

the motor, the motor cable has to be regarded as a transmission line, if the electric drive isconverter fed. In this case, the voltages and currents are not only functions of time, but haveto be regarded also as functions of position along the motor cable. This is because the inverteroutput voltage contains frequency components that have wavelengths in the order of the motorcable length, as pointed out above. As a consequence, voltage and current oscillations mayoccur along the power cable. Providing that the physical length of the motor cable length lis less than λ/16 of a frequency component in the output voltage, the voltages and currentscan be assumed to be constant along the transmission line, and hence no transmission lineanalysis is required, nor cable oscillations or overvoltage caused by it have to be taken intoaccount. λ is the wave length of a certain frequency in the cable. Equation (2.2) can be usedto roughly approximate the spectral bandwidth of the inverter output voltage.

The transmission line theory, see (Heaviside, 1893, 1899), which describes the propagationof an electromagnetic wave along a transmission line, has been succesfully applied to theanalysis of cable oscillations and voltage reflections, as pointed out above. In general, themotor cable consists of several phase conductors and a ground conductor, since the three-phase AC system is used in most installations. Therefore, the motor cable is generally amulticonductor transmission line.

However, the motor cable is typically presented as a two-wire transmission line model, be-cause the analysis is simplified and the use of multiple phase transmission line models isavoided. In addition, since the cable oscillation phenomenon takes place at each transition ofthe inverter output stage, the use of a one-phase equivalent circuit is justified. Nonetheless,the limitations of the simplification have to be taken into account in the analysis: only onephase can be considered at a time, and the other phases have to be assumed stationary and ina steady state during the analysis.

In the two-wire transmission line model, the electromagnetic wave is assumed to propagatein the pure transverse electromagnetic (TEM) mode. However, in an actual motor cable, themode of propagation is not pure TEM, as the wave also has small longitudinal components,for example because of the finite conductivity of the conductors. In practice, the structures ofthe fields are similar to pure TEM, and the wave can be approximated as a TEM wave (Ahola,2003). This kind of a propagation mode is called a quasi-TEM mode.

2.2.1 Transmission line properties of the motor feeder cable in an elec-tric drive

The electrical length of the transmission line depends on the phase velocity (propagation ve-locity) and the frequency of the electromagnetic wave. The relation between the phase speed,νp, the wave length, λ , and the frequency, f , of the wave is described by the fundamentalequation:

νp = λ f . (2.3)


The equivalent circuit of a two-wire transmission line of an infinitesimal length ∆z is pre-sented in Figure 2.3, which consists of the distributed parameters inductance, capacitance,resistance, and conductance per unit length of the transmission line. These parameters de-scribe the properties of the transmission line and depend on the geometry and the dielectricsused in the physical conductor. Series inductance describes the self-inductivity of the conduc-tor, capacitance refers to the natural capacitance in the proximity of the conductors, resistancerepresents the resistive losses caused by the finite conductivity of the conductor, and finally,conductance describes the losses owing to the conductivity and the dielectric losses causedby the polarization of dipoles in the insulating material. The inductance and capacitance rep-resent delay, whereas resistance and conductance express losses (or attenuation) along thetransmission line. A transmission line of finite length can be thought to consist of a group ofelements, as presented in Figure 2.3, connected in series.

Figure 2.3. Equivalent circuit of a two-wire TEM transmission line of an infinitesimal length. R, L,G, and C are the distributed resistance, inductance, conductance, and capacitance of the line per unitlength. The voltages v and currents i indicated in the figure describe the voltages and currents in thetransmission line at z and ∆z at the time instant t.

It can be derived that on a transmission line of this kind, the voltages and currents may varynot only as a function of time, but also as a function of position z, according to the telegra-pher’s equations (Heaviside, 1899). The voltages and currents consist of a superposition ofincident and reflected waves. Therefore, standing waves may occur on the line. The prop-erties of the transmission line are defined by the complex propagation constant γ and thecharacteristic impedance Z0. The propagation constant is defined by the equation (Collin,1992) p. 88

γ =√

(R+ jωL)(G+ jωC) = α + jβ , (2.4)

where α is the attenuation constant, and β is the propagation constant, which describe thedamping and the wavelength as a function of the length of the transmission line with thedistributed circuit parameters resistance R, inductance L, conductance G and capacitance Cper unit length. The characteristic impedance of a transmission line is defined as (Collin,1992) p. 88


Z0 =

√R+ jωLG+ jωC

. (2.5)

If the transmission line is assumed lossless or the losses are negligible, the characteristicimpedance can be approximated with the following equation:

Z0 =

√LC

. (2.6)

The characteristic impedance defines the relation between the amplitudes of the correspond-ing voltage and the current waves on the transmission line, thus

Z0(z) =V (z)I(z)

, (2.7)

for every position z. In general, all the distributed parameters are functions of frequency,and therefore the propagation constant and the characteristic impedance are also frequencydependent.

The propagation velocity of the wave can be calculated using the following equation:

νp =ω

β=

1√

εµ=

1√LC

, (2.8)

where ε and µ depend on the dielectric material used in the power cable. The propagationvelocity of the wave depends only on the properties of the dielectric materials, if the currentspropagate only along the surface of the conductor. However, because of the finite conduc-tivity of the conductor, the currents flow also inside the conductive material. The currentdistribution on the cross-section of the conductor at a certain frequency is described by skindepth, which depends on the angular frequency ω , permeability µ , and conductivity σ asfollows (Wheeler, 1942)

δs =

√2

ωµσ. (2.9)

The skin-effect also increases the resistive losses, because the current density near the surfaceof the conductor increases, increasing the ac resistance of the conductor. In addition, theproximity effect increases the ac resistance even further in budled cables.


2.2.2 Transmission line discontinuities

A discontinuity along a transmission line means a change in the characteristic impedance.The characteristic impedance is the proportion of voltage and current waves. At a disconti-nuity, part of the incident power passes through the interface while part reflects back to theoriginal direction, because the potential has to be equal at the point of mismatch. Generally,any variation in the geometry of the dielectrics along a propagation path causes a change inthe characteristic impedance and therefore a reflection. Typically, a change in the characteris-tic impedance is a consequence of a mismatched load impedance at the end of a transmissionline, or changes in the type of the transmission lines along the propagation path. In addition,connectors, connections, and junction boxes typically employed in electrical power engineer-ing cause a significant change in the geometry of the propagation path and therefore in thecharacteristic impedance.

The relationship between the incident wave and the reflected wave depends on the differenceof the characteristic impedances at the discontinuity: the greater the difference, the more ofthe incident wave is reflected. The reflection coefficient is defined at the impedance mismatchas follows (Heaviside, 1899), p. 375:

ΓL =V−

V + =Z0−ZL

Z0 +ZL= |ΓL| · e jφL , (2.10)

where V + is the incident wave, V− is the reflected wave at the discontinuity, Z0 is the char-acteristic impedance of the transmission line, and ZL is the loading impedance seen at thediscontinuity in the direction of the incident wave. |ΓL| defines the magnitude of the reflectedwave and φL defines the phase angle shift of the reflected wave with respect to the incidentwave at the mismatch point. If the transmission line is perfectly matched, ZL = Z0, no reflec-tion takes place, as can be seen from the above equation. If the transmission line is terminatedto a short circuit (ZL = 0) or an open circuit (ZL = ∞), all the incident wave is reflected ata phase angle of 0 or 180 degrees, correspondingly. During the transient, the electric motorresembles an open circuit at the end of the motor cable, leading to an in-phase reflection andovervoltage as an outcome of the superposition of the incident and reflected waves.

The voltages and currents can be written as a function of the length of the motor cable apply-ing the reflection coefficient as follows:

V (z) = V +0 e jγz (1+ΓLe− j2γz) (2.11)

I(z) =V +

0Z0

e jγz (1−ΓLe− j2γz) . (2.12)

The above equations show that if the transmission line is not terminated at the characteristic


impedance Z0, the amplitudes of the voltage and current waves become functions of position,and standing waves occur at the transmission line.

2.2.3 Discontinuities in a typical inverter-fed electric drive

The main factors contributing to the overvoltages are the magnitude and rise time of the outputvoltage pulses, the interconnecting power cable length, the motor characteristic impedance,and the impedance mismatch between the characteristic impedances of the cable and themotor.

As the inverter output stage is operated, switching transient injects an incident voltage wave inthe interconnecting power cable that propagates toward the electric motor. In the inverter-fedelectric drive, there are at least two significant impedance mismatches between the inverteroutput stage and the motor: the interfaces between the inverter and the motor cable andbetween the cable and the motor, if the cable is solid and there are no additional connectionsalong the cable. Because of the geometry and the construction, the characteristic impedancesof the motor and the motor cable are usually significantly mismatched.

The amplitude of the reflected wave in proportion to the incident wave is defined by thevoltage reflection coefficient Γm at the motor terminal:

Γm =Zm−Zc

Zm +Zc, (2.13)

where Zm is the motor characteristic impedance and Zc is the characteristic impedance of theinterconnecting power cable. The maximum peak voltage at the motor terminal expressedusing (2.13) results in (Saunders et al., 1996)

Vp∣∣(z=l) = (1+Γm) ·UDC, (2.14)

where the amplitude of the incident wave equals the amplitude of the voltage at the driveoutput, UDC, and the motor reflection coefficient is Γm. Because the impedance of the mo-tor resembles an open end compared with a typical cable impedance, the incident wave isreflected back in-phase from the interface of the motor and the cable. Therefore, the volt-age reflection can cause overvoltages up to twice the bus voltage at the motor terminal. Theovervoltage may degrade the insulation and potentially produce destructive stress on the in-sulation system of the motor. Typically, the voltage is not evenly distributed in the statorwinding; a major part of the voltage is across the first few coil rounds before the voltagedistribution is balanced in the winding. Furthermore, the faster the transient, the more of thevoltage occurs across the first coil round, which adds to the stress caused to the insulation ofthe stator winding (Suresh et al., 1999), (Hwang et al., 2005), and (IEC, 2007).


The load reflection coefficient at the motor end depends on the size of the motor. As thesize of the motor increases, the reflection coeffient decreases, for example because of largerstray capacitances, and the theoretical maximum value of the overvoltage decreases fromthe double voltage. Typically, in the literature, the reflection coefficient is reported to varybetween 0.65 and 0.95, which causes a theoretical overvoltage of 1.65 to 1.95 times the DClink voltage. Typical motor reflection coefficients for various motor sizes are presented forexample in (Saunders et al., 1996) and (Skibinski et al., 1998). However, it has to be takeninto account that the motor impedance, and the load reflection coefficient, similarly as othertransmission line parameters, are frequency dependent.

As the incident voltage wave is reflected back from the motor terminal, the reflected wavestarts to propagate back towards the frequency converter. A new reflection takes place atthe interface of the motor cable and the inverter, the magnitude of which depends on thereflection coefficient at that interface. The reflection coefficient can be obtained from Eq.(2.10), if the characteristic impedances are known. The characteristic impedance of the cablecan be determined by measurements as presented in (Ahola, 2003). The impedance of theoutput stage depends on the state of the switches; measurements of the inverter output stageimpedances as a function of switching state are presented for example in (Kosonen, 2008).Generally, the reflection coefficient of the inverter end is approximated as a short circuit inthe literature, because the DC link capacitor and freewheeling diodes are assumed to act as ashort circuit to the steep-edged switched voltages (Skibinski et al., 1997, 1998).

The voltage wave is reflected from the inverter towards the motor, but now out of phase,because the reflection coefficient Γi ≈ −1. The voltage wave remains in the motor cable re-flecting back and forth between the inverter and the motor, and after each switching transient,a decaying cable oscillation may build up. The frequency of the cable oscillation dependson the propagation velocity of the wave and the length of the motor cable. The oscillationdecays mainly as a result of the high-frequency attenuation of the cable, and also if the motorreflection coefficient is smaller than one, part of the incident wave is transmitted to the motor.The propagation delay of the incident wave depends on the propagation speed of the wave inthe cable and the cable length. Therefore, the frequency of the cable oscillation can be solvedas follows (Skibinski et al., 1997):

fosc =1

4tp=

νp

4l, (2.15)

where tp is the propagation delay of the cable, νp the propagation velocity, and l the length ofthe cable.

The cable oscillation frequency and decaying time are also important factors in the origin ofovervoltages that are greater than the theoretical maximum of twice the voltage for a singletransition discussed so far. If a new transient occurs before the oscillation caused by the pre-vious transient has decayed, overvoltages above twice the DC link voltage are also possible,see (Skibinski et al., 1997). This condition is called double pulsing.

2.3 Critical cable length 33

Yet another important factor in the origin of overvoltages greater than twice the DC linkvoltage is called polarity reversal, where two of the inverter phases are switched from oppositestates at the same time.

The key in reducing the overvoltage at the motor end is to slow down the rising and fallingtimes of the modulated voltage pulses according to the cable length, see (Persson, 1992).The longer the feeding motor cable, the longer the rise or fall time should be. The switchingtime can be prolonged by slowing down the switching operation of the semiconductor powerswitch, as previously mentioned, or by filtering. Slowing down the power switch generatesexcessive switching losses, and therefore it is not an optimal solution. Different filteringsolutions will be discussed in more detail later in this chapter. Further, a conventional LCfilter can be used to produce rising and falling slopes of desired length, if the active control isused, as will be shown in the next chapter.

2.3 Critical cable length

As presented earlier, a propagation delay is introduced to the incident voltage and currentwaves by the motor cable. The rise time of the injected voltage affects the maximum value ofthe overvoltage. If the propagation delay is smaller than half the rise time, the voltage wavereflected from the inverter end reduces the overvoltage at the motor end before it has reachedits full value. This is the definition for the critical cable length in an electric drive (Persson,1992), and full overvoltage is induced by the voltage reflection at this cable length. The keyin mitigating the motor-end overvoltage is to increase the critical cable length by decreasingthe du/dt in the voltage injected to the cable. The critical cable length is defined as

lc =tr2·νp, (2.16)

where tr is the rise time of the voltage pulse and νp the propagation velocity in the motorcable.

2.4 Fundamental properties of second-order systems

Systems that can be described by second-order differential equations are called second-ordersystems, such as most output filtering circuits are. The differential equation of the second-order system in the general form is

A f (t) =d2ydt2 +2ζ ωn

dydt

+ω2n y, (2.17)


where ωn is the undamped resonance frequency of the system and ζ is the damping factor,which describes how the system responds to a step input. The resonance frequency is thenatural frequency at which the output of the system resonates if not damped. Critical damping(ζ = 1) provides the fastest system response in the absence of overshoot. The greater thedamping factor is, the slower the system responds to the input. A damping factor belowthe critical value provides a faster system response, but in this case there is overshoot in theoutput, the amount of which depends on how close the damping factor is to zero. If thedamping factor is zero, the oscillation at the system output does not decay, and the amount ofovershoot is equal to the magnitude of the input step. Hence, an undamped system resonatesbetween zero and two times the input step at the natural frequency of the system. The stepresponses of second-order systems with various damping factors are presented in Figure 2.4.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Step response of a second order system as a function of damping factor

ζ=0ζ=0.2ζ=0.5ζ=1ζ=2ζ=5

Figure 2.4. Second-order system step response for various damping factors ζ with a constant undampedresonance frequency ωn.

Typically, in a passive output filter the inductance and capacitance define the resonance fre-quency of the filter. In addition to these, the damping factor is defined by the resistance ofthe circuit. In a passive filter design, and in filter design on the whole, the step response ofthe filter circuit is an important design consideration, in addition to the frequency response ofthe system.

2.5 Typical output filtering solutions 35

2.5 Typical output filtering solutions

The reflection from the motor and motor cable interface can cause exceeding of the motorimpulse voltage rating, which is harmful to the insulation system of the motor. Furthermore,in addition to the differential-mode line-to-line voltages, steep common mode voltages ofhigh du/dt are coupled to the motor as a result of the operating principle of the two-levelinverter, see for example (Skibinski et al., 1999). These phase-to-ground common-modevoltages have been shown to cause a high-frequency current in the grounding system of thedrive and are a major cause of shaft voltages, which are among the factors causing bearingcurrents (Erdman et al., 1996; von Jouanne et al., 1998).

The overvoltages and adverse effects caused by voltage reflections in electrically long cableshave been mitigated by applying various different filtering solutions: output reactors, outputfilters, such as sine wave and du/dt filters, and cable terminators.

2.5.1 Output du/dt filters

The most typical solutions are different kinds of passive output filtering approaches, in whichthe du/dt of the output voltage is decreased. A very typical du/dt filter, see Figure 2.5, consistsof a series inductance and a parallel capacitance, and the losses in the circuit are tuned in orderto obtain the desired transient output response for the drive (Finlayson, 1998). This kind ofa system consisting of inductance, capacitance, and resistance is generally a second ordersystem.

Figure 2.5. Schematic of a conventional du/dt output filter. Damping resistors or equivalent losses inthe inductors are not illustrated in the figure.

However, since a second order system itself is a resonance circuit, it easily becomes a sourceof overvoltage and oscillation instead of the inverter-power cable electric motor resonator, ifnot sufficiently damped. The du/dt is decreased according to the LC constant value, but inorder to obtain a good transient response, damping is necessary, which means losses. In the


design procedure of the passive du/dt, the most essential design parameters are the resonanvefrequency ωn and the damping factor ζ . In addition to the transient response, the frequencyplane response is important. At the cable oscillation frequencies the filter is designed for, thefilter attenuation should be maximized. The du/dt filter design is a compromise between thesekey features. Also, if the resonance frequency is below the inverter switching frequency fc,the filter is a sinewave filter, and if it is above this frequency, it is called a du/dt filter. Designswith resonance frequencies close to possible switching frequencies should be avoided, sincea strong filter resonance is induced.

Output du/dt filters based on inductors and capacitors have been introduced for examplein (Finlayson, 1998), (Moreira et al., 2005), (Moreira et al., 2002), (Rendusara and Enjeti,1998), (Rendusara and Enjeti, 1997), (Sozey et al., 2000), (Palma and Enjeti, 2002), (vonJouanne and Enjeti, 1997), (von Jouanne et al., 1996b), and (Steinke, 1999), and sinewavefilters in (Skibinski, 2002) and (Skibinski, 2000).

2.5.2 Output du/dt filters with a clamping diode circuit

Some of the output filters use clamping diodes to limit the overshoot in the filter circuit tothe positive and negative DC link voltage, see Figure 2.6. The clamping diodes are effectivein preventing the filter oscillation, but they provide an alternative path for the reactive motorcurrent, which is thus not seen by the current measurements of the output phases. As a result,part of the low-du/dt LC resonance sine wave is fed to the motor cable, but the natural LCovershoot is removed by the clamping circuit. However, current spikes through the diodes areintroduced along with losses. The current amplitude of the current spikes can be decreased byadding resistance between the clamping circuit and the DC link, but at the expense of losses.

Figure 2.6. Schematic of a conventional du/dt output filter with clamping diodes. The natural LCovershoot is removed by the clamping circuit.

Filters utilizing clamping diodes are presented in (Moreira et al., 2002), and (Habetler et al.,2002), and a clamping filter to be placed at the motor end in (Chen and Xu, 1998).

2.5 Typical output filtering solutions 37

2.5.3 Motor terminal cable terminators

Cable terminators have also been used to mitigate the overvoltages (Skibinski, 1996; Chenand Xu, 1998; Moreira et al., 2005). These are based on the fact that if the transmission lineis terminated to the characteristic impedance Z0, no reflection takes place. In these solutions,the terminating resistors are chosen close to the assumed cable characteristic impedance via acapacitive coupling interface. The actual terminating impedances are the terminator and theelectric motor in parallel. However, the impedance of the motor is assumed to be far higherthan the cable characteric impedance, and therefore the effect of the motor on the terminatingimpedance can be neglected (Skibinski, 1996), which is also a typical case in reality. Thecable terminator, see Figure 2.7, is very effective in limiting the overvoltage in the motorterminal, but it does not limit the du/dt value, creates power loss, since resistors in the orderof the cable characteristic impedance are used (in the order of 102 Ω), even if capacitivecoupling is used.

Figure 2.7. Schematic of a cable terminator. The motor cable is matched to the characteristic impedanceusing a terminator via a capacitive coupling interface. The purpose of the interface is to reduce lossesin the circuit.

2.5.4 Summary on typical topologies

Drawbacks of the typical filtering solutions are often their large physical size, resulting in dif-ficulties in the integrability. As can be seen from the well-known equation for the resonancefrequency of a second-order system, the lower is the resonance frequency, the greater thecomponent values are. A more thorough summary of the commonly used filtering solutionsin frequency-converter-fed electric drives is provided for example in (Moreira et al., 2005).


2.5.5 More on PWM-inverter-based issues in electric drives

The cable reflection and oscillation and their effects on the whole drive caused by a modern,fast switching IGBT-based frequency converter applying pulse width modulation techniqueshave been studied extensively, and the basic mechanism of the phenomenon is quite wellknown and documented, see (Persson, 1992), (Saunders et al., 1996), (Skibinski et al., 1997),(Kerkman et al., 1997), (Leggate et al., 1999), (Takahashi et al., 1995), (von Jouanne et al.,1995), (von Jouanne et al., 1996a), and (Kerkman et al., 1998).

Modeling of the system in order to analyze, test, and develop new solution approaches hasalso been discussed in the literature, for example in (von Jouanne and Enjeti, 1997), (vonJouanne et al., 1996b), (Skibinski et al., 1998), (Ström et al., 2006), (Tarkiainen et al., 2002),(Boglietti and Carpaneto, 2001), and (Boglietti et al., 2005).

Issues on the cabling of a frequency converter-fed drive are addressed in (Bartolucci andFinke, 2001). On the detrimental effects of a switching-mode inverter on the electric motoritself are presented for example in (Erdman et al., 1996), (Skibinski et al., 1996), (Melfi et al.,1998), (Suresh et al., 1999), (von Jouanne et al., 1998), (Busse et al., 1997c), (Busse et al.,1997a), and (Busse et al., 1997b); these are for example the effects of motor overvoltagescaused by the voltage reflection on the insulation system of the motor, and bearing currentscaused by the frequency converter.

2.6 Effects of a converter drive on the electric motor

Voltage pulses with a high du/dt value and a high voltage are harmful to the stator windinginsulations, and therefore it is a common practice to use filtering between the frequencyconverter and the motor, especially when the supply voltage is higher than 400 V. This isbecause the maximum phase-to-phase voltage as a result of cable reflection is double the DClink voltage, and the higher is the supplying grid voltage, the higher is the maximum voltageat the motor terminal. As an example, the maximum motor phase-to-phase potential peak isapproximately 1 kV for a 400 V drive, but almost 2 kV for a 690 V drive. Therefore, theproblems and stress on the motor insulation system are more evident on higher grid voltages,and a higher insulation strength is required of the motor. The situation gets even worse whenthe du/dt value of the voltage pulse increases, since the insulating properties of the insulationsystem become more vulnerable to dielectric breakdown as the rise time decreases (Saunderset al., 1996), (IEC, 2007).

The output voltage rise and fall times in a frequency converter applying IGBT semiconductorsin the output stage of the inverter are typically in the order of tens of nanoseconds at best,as shown previously in this chapter. The switching times are kept to minimum in order tominimize the switching losses. The switching operation produces overvoltage in the motorterminals, and this operation can reduce the life of the motor insulation system, if the voltagestrength is repeatedly exceeded. The risk to the insulation caused by partial discharges is

2.6 Effects of a converter drive on the electric motor 39

pronounced with voltage pulses of a high voltage and a fast rise time. The rise and fall timesof the voltage pulses depend on the switching properties of the semiconductor power devicesused, but eventually on the gate driver circuit and snubber circuits.

Further, if the pulse width matches the propagation delay between the converter and the mo-tor, an overvoltage higher than twice the voltage may be generated, in addition to the doublepulsing and polarity reversal already mentioned. Cablings consisting of several cable sectionscan also lead to overvoltage problems, because at each switching instant, the voltage reflec-tion will eventually take place at each point of impedance discontinuity, and the system willthereby consist of a large number of incident and reflected waves oscillating in the cabling. Ifthis is the case, output filtering should be considered (Skibinski et al., 1997), (Leggate et al.,1999), (IEC, 2007).

In (IEC, 2007), in addition to the above-mentioned filtering approaches, several measuresare suggested to reduce voltage stress on the motor. Decentralized topologies are proposed,where converters are placed close to the motor or they are integrated to the motor. However,these may be impractical in existing or even in new installations. Moreover, special cablingis proposed in order to increase high-frequency loss in the cable to attenuate the cable oscil-lation. However, in this case, standard cables cannot be used, which will result in extra costs,and extra losses in the cable are introduced. Changing the cable of an existing installation isnot feasible either. The use of a multilevel converter has also been suggested, but it seldom isa likely solution to overvoltages in low-voltage drives.

The oscillating voltage as a result of the wave reflections cause stress on the main insulationof the windings, both on the phase-to-phase and phase-to-ground insulations. Furthermore,voltage pulses of a fast rise time (<1 µs), (IEC, 2007) cause uneven voltage distribution in thestator windings, resulting in a high voltage stress on the first few turns at the individual phasewindings. Examples of the voltage distribution as a function of the voltage peak rise timeare given in (IEC, 2007). As the rise time shortens, into the order of tens of nanoseconds,more of the voltage peak will occur across the first turn of the coil, approaching 40–50 % ofthe voltage peak over the first turn. Therefore, there will be a high voltage peak between thewires in a single coil, which may lead to a breakdown in the insulation system of the motorbecause of an insufficient voltage strength in the insulative coating of the coil wire. The levelsat which the stress caused by the overvoltage becomes harmful are the voltage levels at whichpartial discharges start to occur. The deterioration of the insulation depends on the frequencyand the energy of the partial discharges (IEC, 2007).

41

Chapter 3

Output filtering in afrequency-converter-fed electricdrive

In this chapter, considerations for the design of output filtering in an electric drive are pre-sented. Furthermore, the theoretical basis for a new active du/dt filtering method suitablefor the output filtering of an electric drive is introduced. As discussed earlier in the previouschapters, the advancements in the switching times of semiconductor power switches, espe-cially in the latest generations of IGBT devices, introduced new problems into electric drives,and as described above, output filtering is required to slow down the du/dt of the edges of theoutput voltage pulses in some cases.

In terms of output filtering analysis, the frequency-converter drive can be considered as a sys-tem consisting of several major components, which have an effect on the drive as it operates.In particular, these components influence the side effects. In Figure 3.1, the electric drive ispresented as a block diagram from the viewpoint of analyzing output filtering.

In analyzing output filtering, the most relevant components of the electric drive are the in-verter output stage, electric motor, motor cable, DC link, and their high-frequency properties,far above the typical switching and fundamental frequencies of the drive, as was presentedin the previous chapter. The system forms a resonating structure that has a natural resonancefrequency depending on the velocity of propagation in the cable and the cable length. In termsof high frequencies, the inverter, motor cable, and the motor system form a transmission lineresonator.

The propagation speed in the medium depends on the dielectric properties of the motor ca-ble. When a pulse-shaped stimulus is fed to the system, the system resonates at its naturalfrequency, which in this case is typically called the cable resonance or oscillation frequency.

42 Output filtering in a frequency-converter-fed electric drive

Figure 3.1. Electric drive presented as a block diagram from the viewpoint of analyzing output filter-ing. The most relevant components of the system include the output stage of the frequency converter(inverter in the figure), the DC link, electric motor, interconnecting motor cable, and a possible filtercircuit performing output filtering.

In order to eliminate the oscillation in the system, the natural cable resonance frequency,if present, must be removed from the inverter output voltage by filtering. Because of theimpedance mismatches in the system, the resonance effect is strong. In the output filter de-sign and the frequency domain analysis, the cable oscillation frequency range is an importantdesign parameter.

As presented above, the frequency content in the inverter output extends to the megahertz re-gion, as typical cable oscillation frequencies are in the order of tens of kilohertz to hundredsof kilohertz; see for example the measurements presented in the next chapter. Therefore,output filtering must be carried out using a lowpass type filter, because the cable oscillationfrequency must be filtered out, but the fundamental operation of the drive and power trans-mission from the converter to the motor may not be interfered with. In addition, the cableoscillation frequency increases as the cable length decreases, and the filter cut-off frequencymust be designed for a certain cable type and the longest cable length allowed.

It should be noted that for a certain voltage rise time, by decreasing the cable length enoughto increase the cable oscillation frequency to a region where the inverter output voltage con-tains little stimulus or no stimulus at all at the cable resonance frequency, the oscillation andovervoltage at the motor terminal can be eliminated. Moreover, limiting the frequency spec-trum of the inverter output voltage to contain no stimulus at the cable resonance frequencywill provide the same result. Effectively, this corresponds to lowpass filtering in the inverteroutput. Eventually, from a practical point of view, it is not feasible to replace the IGBT de-vices by older, slower power switches in a modern low-voltage AC drive. Furthermore, in anindustrial envinronment, the motor cable length cannot be selected arbitrarily, but it is limitedby the installation options of the electric drive.

Hence, in order to succesfully prevent cable oscillation and motor terminal overvoltage, themost reasonable solution is efficient lowpass filtering, which is analogous to slowing downthe switching operation and limiting the output voltage spectrum below the cable oscillationfrequency. This analysis is also well in line with the propositions discussed for example in(Persson, 1992) and (Saunders et al., 1996). Moreover, the filter cut-off frequency must bedesigned according to the longest motor cable to be used with the filter. As the cable oscil-

3.1 Active du/dt filtering method 43

lation frequency increases as the cable length decreases, minimum filter stop-band ripple isalso preferred for the filter topology. An ideal frequency response for output filtering is illus-trated in Figure 3.2. For example, a digital FIR filter, whose impulse response is a Gaussianfunction, has a step and frequency plane response similar to the Figure 3.2. However, as forother FIR filters, there is no analog representation of the filter.

Figure 3.2. a) Time domain step response and b) the frequency response magnitude of a filter, whichwould be ideal for output filtering.

A frequency response illustration is provided in Figure 3.3, which shows the shape of thefrequency content of a linear ramp as an example of a typical approximation of an inverteroutput voltage shape. For instance, the linear ramp is the response of a system, the coefficientsof which are a discrete-time rectangular pulse, such as a moving-average filter. The frequencyresponse for a signal of this kind is presented for instance in (Proakis and Manolakis, 2007),p. 242.

The slower the slope is, the less frequency content is generated. Therefore, for a steep tran-sition as the inverter output voltage, by applying a filter with a similar frequency response,the transient response in the time domain is a step with a constant slew rate. In addition,a frequency response that contains zeros (e.g. the linear ramp presented), it is beneficial toplace the zeros at the cable oscillation frequency, if it is known. If the voltage fed to thecable contains stimulus at the cable resonance frequency, oscillation is induced to the extentprovided by the amplitude of the cable oscillation frequency component present in the outputvoltage. In the context of cable resonances, the first minimum response is achieved, when theramp length is four times the cable propagation delay, td (Persson, 1992).

3.1 Active du/dt filtering method

In this dissertation, the term active du/dt filtering is used to refer to the actively controlledoutput filtering method developed. Active du/dt is a method that is capable of forming ris-ing and falling voltage slopes of desired rise and fall times. This operation is achieved byselecting the filter component values appropriately and by active control of the filter. The


Figure 3.3. a) Time domain step response and b) the frequency response magnitude of a linear ramp.

proposed filter circuit consists of an LC circuit, and hence, the shapes in the produced slopeare sinusoidal. The basic idea in the active control is to succesfully charge and discharge thecapacitor in the filter, and handle the transient response of the LC filter circuit. The capac-itor on the filter circuit is considered to act as a voltage source towards the load during thetransients. The function of the reactor in the filter is to limit the charging and dischargingcurrent of the capacitor, and eventually the peak current of the filter serial resonance circuitseen in the inverter output stage. Moreover, the charging and discharging sequences haveto be accurately timed so that the natural resonance of the LC circuit at the filter resonancefrequency is avoided.

In a passive output filter, the reduction in the filter output du/dt and the filtering of the cableresonance frequency depend on the transition frequency, which has to be low enough in orderfor the filter to function properly in the task it is designed for. However, as it is well known,decreasing the cut-off frequency of the filter means electrically and physically larger filtercomponents. One of the benefits of the active du/dt method is that the active du/dt filter com-ponent values are selected based on the voltage slope transition period, and also on the filterpeak current specification, which results in far smaller inductance values than in a conven-tional passive output filtering approach. The active du/dt LC filter is not solely responsiblefor the filtering of the inverter voltage, but the filtering result is a combined effect of the LCcircuit and the control, charging and discharging the filter by voltage pulses.

Yet another benefit of the method is that the performance of the motor control in the ACdrive improves, because the motor flux estimation accuracy is improved. The active du/dtvoltage causes, if correctly designed, no motor overvoltage. Therefore, the motor flux canbe estimated more accurately in the motor control of the frequency converter. Because ofthe cable oscillation, the motor terminal voltage differs considerably from the inverter outputvoltage, which affects the performance of the control. A correct filter design attenuates thecable resonance and very effectively removes terminal overvoltages.

In the analysis presented in this chapter, the filter (or more specifically the capacitor in thefilter) is assumed to be an ideal voltage source. This assumption is very close to reality, if theonly load driven by the filter is the long motor cable without any motor connected at the end


of the cable, or there is no load at all at the filter output. This assumption enables a simplifiedanalysis of the active du/dt filter, and the basic operation and design of the filter can be ana-lyzed. However, in practice, when the motor is added to the drive, the load currents interferethe operation of the filter, depending mostly on the rated current of the motor compared withthe filter charging current. In order to correct the errors caused by the motor current, correc-tive actions must be taken depending on the direction and magnitude of the motor current.This topic is discussed in more detail in Chapter 4.

3.1.1 Active du/dt filter circuit

As presented above, the active filter circuit topology of one inverter output phase is an LCfilter, which consists of an inductor in series with the main current path of the output phaseand a capacitor in parallel with the output phase. The idea in active du/dt filtering is to slowdown the rising and falling edges of the inverter pulses by controlling a specifically designedLC circuit to produce the desired voltage slope. The LC filter topology for active du/dt controlis presented in Figure 3.4. The topology of the filter circuit in active du/dt is an LC output

Figure 3.4. Proposed LC filter topology for active du/dt control, consisting of a series inductance andcapacitance at each of the inverter output phases. The capacitor is in parallel with the load (motor andmotor cable) and acts as a voltage source in the circuit. The capacitors are wye connected, and the wyepoint is connected to the negative DC bus of the inverter, as the operation of the inverter is based on thenegative DC bus in the context of this research. The filters designed for active du/dt do not function bythemselves, i.e., passively; active control is required to produce the desired voltage slopes. The transientresponse of the filter circuit is not suitable for output filtering without the control because of tendencyto oscillate.

filter, with the capacitors wye connected to the negative DC link rail. The DC link connectionis not necessary for the active du/dt operation, but since the negative DC link is the referencepotential for the inverter stage, it stabilizes the capacitor wye point to a known potential.

However, the component values of the filter are designed from a different viewpoint thanin passive du/dt filters because the control of the filter significantly affects the behavior ofthe active du/dt. In a typical case, the filter inductance value can be selected to be notably


smaller than in conventional output filter designs, because only the LC constant of the circuitaffects the output du/dt. The damping factor ζ is designed as to close to zero as possible byfilter component selection and design, because the transition behavior of the filter is activelycontrolled. The operation is achieved by using extra voltage pulses. Further, the losses in thefilter circuit can be minimized because there is no need to stabilize the transient response byincreasing the damping factor in the circuit.

This is a significant difference compared with passive du/dt filter design, since the control ofboth the resonance frequency and the damping factor is necessary in passive filters, becausethe inverter output voltage consists of voltage steps, and hence the step response of the filteris important. However, in a passive filter, damping causes losses, and the losses take placemainly in the iron cores of the inductors or in external damping resistors. In active du/dt,control of the filter circuit is required, because the response of the filter to plain voltage stepsis that of the case ζ = 0 shown in Figure 2.4. Hence, using the active du/dt filter circuitwithout any control is disadvantageous, because the filter output response to voltage steps isan oscillation. The filter oscillates at the resonance frequency of the filter at an amplitudetwice the fed voltage step, and decays very slowly. A measured example of such a case ispresented later in Chapter 4. In the case of an electric drive, this is a worse scenario than nooutput filtering at all.

In active du/dt, the filter losses are considerably smaller than in convential passive outputfilters, but the required control of the filter circuit introduces extra switching losses in theoutput stage of the inverter. Therefore, in active du/dt, the filtering losses are transferredfrom the filter circuit to the inverter output stage. However, the development of the powerswitch components also improves du/dt loss performance, which is not the case with passiveoutput filters. More loss considerations are presented in Chapter 4, in the measurementssection.

3.1.2 Active control of the active du/dt LC filter circuit

The basic principle behind charging and discharging the output filter, that is, the active du/dtcontrol, is illustrated in Figures 3.5 and 3.6.

The ideal step response of an LC circuit with a zero damping factor doubles the input voltageof an amplitude A to 2A, and resonance is induced at the frequency determined by the L andC component values. This property of the LC circuit can be used to produce desired voltageslopes using pulse width modulation: to produce a voltage level, half the voltage of the targetvoltage level is fed to the LC circuit. In this case, the aimed output voltage is the DC linkvoltage. Hence, the feeding voltage is switched off at the moment t1/2, when the outputvoltage of the LC circuit is half, A/2, of the inverter voltage. However, the filter LC circuit,and therefore the output voltage of the circuit, is very susceptible to oscillate if not stabilized.In order to prevent the resonance, the feeding voltage must be switched on at the momentat which the target voltage is reached, which is twice the time t1/2. Therefore, no switchingtransient occurs because the filter and supplied voltages are the same. This also equals a dutycycle of 50 % during the charging period.


Figure 3.5. Ideal step response of an LC circuit with a small damping factor. a) A step of amplitude Ainduces b) an oscillation of amplitude 2A at the LC circuit natural resonance frequency.


!

! !

Figure 3.6. Operation principle of the presented control scheme for active du/dt control. a) Additionaledge modulation is applied to the original inverter pulse, in order generate half of the voltage A usingPWM, b) gate control signals of the inverter leg. c) Voltage A/2 is doubled to A in the LC circuit, andthe pulse can be switched on without transient.


The rising and falling voltage slopes of the filter are determined by the LC constant of thecircuit. By feeding the filter with a voltage greater than half the supplying voltage, that is,using a longer than 50 % duty cycle, creates overshoot and is therefore an unwanted situation,if all the losses are neglected in the DC link, inverter bridge, and LC filter circuit.

In a typical three-phase, two-level inverter, the rising voltage step is modulated using theupper switch of the inverter leg of the corresponding phase, and the falling voltage slope ismodulated using the lower switch of the leg, see Figure 3.4. Therefore, also the modulationof the original inverter pulse edges required by active du/dt control is carried out for therising and falling slopes by using the corresponding inverter leg switches. The pulse edgeis modulated only at the turn-on of the transistor, not at the turn-off, since the output stageoperates at the freewheel mode.

Further, the number of pulses used in the charging of the filter affects the rising and fallingtimes generated by the output filter, as will be discussed later in this chapter. However, ifmore than one required extra pulse is used during a charge or discharge period, additionalswitching losses are generated. Therefore, from a practical point of view, with the presentIGBT power switches, these charging schemes are not as useful as the single pulse chargepresented.

Furthermore, the filter charging current, flowing through the inductor, rises during the firsthalf of the charging sequence, as charge flows to the capacitor. As the feeding voltage isrestored to the previous potential at the moment t1/2, at which the filter output voltage isA/2, the charging current will start to decrease, and the remaining energy in the inductor willcharge the capacitor to the full voltage 2 ·A/2 = A. In addition, during a discharge, a similarpulse pattern is required to slow down the falling voltage in order to prevent undershootand oscillation of the filter circuit after the falling voltage slope. Additionally, if the currentflowing through the inductor is not at the level preceding the sequence at the end of thesequence at moment 2t1/2, overshoot and oscillation will be present in the output voltage, aswill be shown in Chapter 4.

3.1.3 Analysis of the active du/dt filtering method

The rise time tr for the single pulse charge described previously can be derived from the singlephase equivalent circuit of the three-phase filter, Figure 3.7.

Figure 3.7. Single-phase ideal equivalent circuit of the proposed LC filter for active du/dt control.


As presented above, the filter circuit is an LC filter, in which the inductor L and the capacitorC are in series. The output voltage of the filter is the voltage of the capacitor, and both theload and filter current flow through the inductor. Before the theory for the control of activedu/dt can be developed, the operation of the LC circuit during transients must be analyzed.

First, the response of the LC circuit shown in Figure 3.7 is analyzed. Deriving from thes-plane transfer function H(s) of a second-order system

H(s) =ω2

n

s2 +2ζ ωns+ω2n, (3.1)

yields that the s-plane transfer function for the active du/dt filter circuit shown in Figure 3.7is

H(s) =1

LC

s2 + 1LC

, (3.2)

since in this case, ωn = 1/√

LC and ζ = 0, because in this simplified analysis, resistance isassumed R = 0 and the circuit is at resonance at the frequency when the reactances of boththe inductor and the capacitor are the same, that is, when the condition XL = XC is satisfied.

As presented, the feeding voltage must be switched off, when the output voltage of the filterreaches half the DC link voltage. Based on (3.2), the step response of the presented LC circuitfor the step of an amplitude A can be transformed into the time domain. The output voltageof an ideal LC circuit for a step of an amplitude A is

uout(t) = A ·(

1− cost√LC

), (3.3)

see Figure 3.5.

The output voltage uout(t) of the circuit is half the DC link at the instant t1 = t1/2, that is

uout(t1/2) =12

A. (3.4)

Combining (3.3) and (3.4) yields t1/2 = t1 = π√

LC/3. Because the instant at which thecharge, that is, the rising voltage slope, is complete and the feeding voltage is switched onagain is t2 = 2t1/2, the rise time tr of the charge is

tr = t2 =2π

3

√LC ≈ 2.094 ·

√LC. (3.5)


At the moment t2, uout equals the amplitude A of the output voltage pulse, which in this caseis equal to the DC link voltage. As we can see from (3.5), the voltage slope rise time dependson the LC constant of the circuit. The pulse widths of the charge sequence also depend onthe LC constant of the circuit and thereby on the target voltage transition time. It can also benoted that for fast voltage transition times, the inverter output stage must be able to producepulses in the order of the desired transition time. For example, if the target is a 2 µs voltageslope, the output pulse width in the charge sequence equals 1 µs. However, as the motorcable length increases, the longer are the required voltage slopes, and therefore the situationis easier for the inverter output stage. This is also the situation at which the motor overvoltageproblems are most evident.

Because of the symmetricity of the charging and discharging sequences, the pulse widths arethe same for both the sequences in an ideal case. In a real implementation, various delaysbetween the control logic, gate drivers, output stage power modules, and also the dead times,turn-on and turn-off delays of the actual power switches have to be taken into account in asuccessful implementation. However, a sufficient requirement is that the pulses produced bythe inverter output stage are of correct length and pulse width, despite the internal implemen-tation of the charge and discharge pulse generation.

Because a common two-level inverter has only two voltage levels, it is the positive and neg-ative DC bus rails, to which the output phase can be connected through the inverter bridge.Thus, half of the DC voltage cannot be directly generated. However, half the DC link voltagecan be generated in the same way as different voltage levels are normally generated usingpulse width modulation in the inverter, as stated earlier. This introduces a new edge modula-tion in a faster time domain compared with the normal inverter PWM modulation. In additionto the normal phase voltage modulation at the switching frequency, at every turn-on switchingaction of the inverter output stage, the edge modulation has to be carried out for the voltagestep for successful active du/dt filtering.

Based on Figure 3.5, if the voltage applied to the LC circuit is cut at the moment when thevoltage is at the half of the DC link voltage, the LC circuit will double the output voltage tothe full DC link voltage. By solving from Eq. (3.2) and by using the stimulus described, theoutput of the LC filter circuit in the time domain can be obtained from

uout(t) = A[

1− cost√LC− ε (t− t1) ·

[1− cos

t− t1√LC

]], (3.6)

where A equals the DC link amplitude, ε is the Heaviside step function, ε (t− t1) is the stepfunction delayed by t1, and t1 is the moment, at which the output voltage of the LC circuit ishalf the DC link step applied to the circuit. The stimulus and the output voltage of the LCcircuit are presented in Figure 3.8 for an amplitude of A = 1, which can be considered to be1 pu UDC.

The behavior presented in Figure 3.8 can be explained by the fact that the voltage is cut at themoment when the output voltage is at the half of the voltage step, and the LC circuit doubles


−2

−1

0

1

2

Out

put V

olta

ge

a)

The response of the LC circuit for a single charge pulse

0

0.5

1

1.5

2

Stim

ulus

Timeb)

Single charge pulse

LC circuit impulse response

Figure 3.8. a) Response of the LC circuit for a single pulse, the pulse width of which is adjusted sothat the pulse is turned off at the instant when the output voltage of the LC circuit is half the DC linkamplitude. Therefore, the output voltage of the LC circuit increases to the potential of the DC link, at arise time set by the time constant of the LC circuit, as presented. b) The LC circuit impulse response isalso shown as a comparison.

the voltage applied. Hence, the voltage maximum is the amplitude of the DC link voltage, nottwice the DC link voltage as for a plain step as in Figure 3.5. However, as previously noted,the LC circuit will resonate at twice the amplitude of the voltage step, if the damping factor ζ

is zero. Therefore, the oscillation amplitude in this case is twice the amplitude of the appliedvoltage step, as in Figure 3.5, but now the output voltage resonates around zero instead insteadbetween zero and twice the DC link voltage. Further, the stimulus approximates roughly theDirac delta (impulse) function, δ (t). The impulse response of the LC circuit can be solvedfrom Eq. (3.2):

uout(t) =1√LC

sint√LC

, (3.7)

which is also presented in Figure 3.8.

It can be noted that the curves in Figure 3.8 have a similar form, but neither of the voltagewaveforms are useful in the generation of the filter output voltage. However, we can see fromFigure 3.8 that if the stimulus voltage to the LC circuit is switched back on exactly at theinstant when the output voltage of the circuit is at the same voltage as the DC link voltage,no transient will occur, and the output voltage will remain at the DC link voltage applied.


Based on (3.2) and (3.5), the output voltage of the filter can be solved for the pulse sequencedescribed. The stimulus consists of a sum of step functions of amplitude A, of which two aredelayed by t1 and t2

Uout(s) = H(s) ·Uin(s) =1

LC

s2 + 1LC

·A(

1s− e−t1s

s+

e−t2s

s

)︸︷︷︸

charge pulse

. (3.8)

By transforming (3.8) into the time domain, the output voltage of the filter can be written as

uout(t) = A ·[

1− cost√LC− ε (t− t1)

[1− cos

t− t1√LC

]+ ε (t− t2)

[1− cos

t− t2√LC

]], (3.9)

where A again equals the DC link voltage and ε is the Heaviside step function. t2 is the instantat which the output voltage of the LC circuit has doubled to the full step voltage. Ideally, t2 istwo times t1, because at t1 the output voltage of the LC circuit is at half the DC link voltage.The waveform is presented in Figure 3.9.

0

0.5

1

1.5

2

Out

put V

olta

ge

a)

The response of the LC circuit for active du/dt charge

0

0.5

1

1.5

2

Stim

ulus

Timeb)

Figure 3.9. a) Response of the LC circuit. b) Charge sequence, according to the active du/dt method isapplied.

As can be seen from Figure 3.9, the LC circuit can be employed in generation of an outputvoltage, which consists of several delayed step responses of the LC circuit in order to produce


a rising voltage slope. The rise time of the slope depends on the time constant of the LCcircuit.

By definition, the LC circuit doubles the modulated voltage applied to full voltage, but inthis case the resonance of the LC circuit is avoided, if the switching instants are conductedexactly as described. If there is variation from the ideal timing of the switching instants,resonance will be induced in the LC circuit, resulting in residual oscillation. The amplitudeof the residual oscillation depends on the amount of inaccuracy, as will be presented later inthis chapter. Therefore, accurate control of the voltage pulses fed to the LC circuit is essential,since inaccurate control does not bring any benefits.

The method described above is called charging the filter, and the pulse sequence in Figure 3.9is known as the charge pulse. In addition to this, generation of the charging pulse can bethought to consist of several delayed steps, in this analysis unit steps (1 pu UDC). If the stepsare correctly timed, the step responses, as in Figure 3.5, are superimposed in the LC circuit ina way that produces a voltage slope of desired length. This idea is illustrated in Figure 3.10.

−2

0

2

Ste

p re

spon

ses

a)

The response of the LC circuit for active du/dt charge

−2

0

2

Stim

ulus

b)

0

1

2

Com

bine

d re

spon

se

Timec)

First step

Second step

Third step

Figure 3.10. a) Individual step responses of the LC circuit for the steps applied as presented in the activedu/dt theory. b) The delayed steps are shown to produce c) a voltage slope as a combined response.The rise time of the slope depends on the resonance frequency of the LC circuit, as seen from a), andthereby on the actual L and C component values.

As stated before, t1 and t2 correspond to π/3 and 2π/3, respectively. Therefore, the phaseshift between the individual responses has to be π/3 for zero residual oscillation. Inaccuratetiming causes error in the phase shift and, therefore, oscillating filter voltage.

In addition, the pulse sequence can also be applied to produce a falling voltage slope inaddition to the presented rising voltage slope. The falling slope is achieved by using a similar


but reversed pulse pattern as in the charge pulse, as was presented above in Figure 3.6. Ifthe filter circuit is not succesfully discharged, LC circuit resonance will occur, as presentedin Figure 3.11. An example of a successful charge and discharge sequence is presented inFigure 3.12.

−2

−1

0

1

2

Out

put V

olta

ge

a)

The response of the LC circuit for a falling voltage step

0

0.5

1

1.5

2

Stim

ulus

Timeb)

Figure 3.11. a) The response of the LC circuit. The effect of an unmodulated falling step is alsopresented. b) Charge sequence according to the active du/dt method is applied.

3.1.4 Active du/dt filter current analysis

The filter current flowing in the LC circuit during the charge and discharge periods can besolved using the same principle as in solving (3.8), that is, by determining the s-plane LCcircuit voltage equation and solving for the current in the LC filter circuit caused by thecharging pulse. In the time domain, this analysis yields for the filter current

if(t) =A√L/C

[sin

t√LC− ε (t− t1)sin

t− t1√LC

+ ε (t− t2)sint− t2√

LC

](3.10)

The maximum filter current during the charging period is at the moment t1/2, as the supplyingvoltage is switched off; after that instant the charging current of the inductor L begins todecrease. Based on (3.5) and (3.10), the charging current maximum value can be solved

if(t)max = i(t1/2) =A√L/C

sinπ

3≈ 0.866

A√L/C

. (3.11)


−2

−1

0

1

2

Out

put V

olta

ge

a)

The response of the LC circuit for active du/dt discharge

0

0.5

1

1.5

2

Stim

ulus

Timeb)

Figure 3.12. a) Response of the LC circuit. b) Charge and discharge sequences according to the activedu/dt method are succesfully applied.

As can be seen, the filter peak current is inversely proportional to the square root of the filterinductance L and proportional to the square root of the filter capacitance C. Together withthe LC constant, the peak current is an important design consideration, because the IGBTmodule must withstand the additional current stress caused by the filter current on top of theload current flowing through the output stage.

The filter output voltage and the filter charging current are presented in Figure 3.13 in anormalized form as functions of filter component values and voltage amplitude A (1 pu UDCof the applied voltage pulses.

The analysis presented in this section concerns the charge pulse, but a similar analysis canbe carried out also for the discharge pulse by adding into (3.8) the delayed step functionsdescribing the discharge pulse. The filter voltage and current waveforms are similar for boththe charge and discharge pulses, only the direction is different with respect to the zero level.

3.1.5 Different charging schemes for active du/dt filter circuit

Further, the same principle as in the presented charge consisting of a single pulse can beused to derive the filter output voltage and filter current for charge and discharge sequencesconsisting of several, narrower pulses, with the same duty cycle of 50 %. The output voltageand the filter current can be presented in a general form for a number of N charge pulses


0 0.5 1 1.5 2 2.50

0.5

1

LC Filter output voltage

Time [s] ⋅√LCa)

Vol

tage

[V] ⋅A

Filtered output

Inverter output

0 0.5 1 1.5 2 2.5−0.5

0

0.5

1LC filter current

Time [s] ⋅√LCb)

Cur

rent

[A] ⋅A

√ L

/C

Figure 3.13. Generalized filter output a) voltage and b) current waveforms during a charge pulse.

uout(t) = A2N

∑n=0

(−1)nε (t−nt1)

[1− cos

t−nt1√LC

](3.12)

if(t) =A√L/C

2N

∑n=0

(−1)nε (t−nt1)

[sin

t−nt1√LC

]. (3.13)

The pulse length, which is equal to t1, has to be solved using the same principle as above. Forexample, for a charge of N = 2 pulses, there are 2N +1 switching instants t0, t1, . . . , t4. Now,the output voltage of the filter, which is obtained from (3.12), has to be half of the DC linkvoltage amplitude A in the middle of the charge sequence, and full DC link voltage at the lastswitching instant.

For example, for a case of two charge pulses, these are now at t2 and t4. The pulse length t1can be generally solved using this method, because for a charge of N pulses, there are alwaysan odd number of switching instants (2N +1), and therefore, a switching instant in the middleof the charging sequence. For the case of two pulses, t1 can be solved

t1 =15

π√

LC. (3.14)


As the number of pulses is increased, analytical solution of (3.12) becomes more difficult,and a numerical solving method may be more feasible. As the pulse width is solved, it canbe applied to the discharge sequence because of the symmetry of the sequences.

It should also be noted that the rise time of the voltage slope is slightly increased, as morepulses are used in controlling the filter circuit. The exact value of the rise time can be solvedby combining (3.4) and (3.12). The rise time of the filter output voltage depends on the timeconstant of the LC circuit

2π

3

√LC ≤ tr = K ·

√LC < T/2 = π

√LC, (3.15)

where K depends on the number of pulses used in the charge period. For the two-pulse charge,it can be obtained from Eq. (3.14) that tr = (4π/5)

√LC ≈ 2,513 ·

√LC.

However, taking the properties of the present semiconductor power switch components intoaccount, the charging scheme consisting of only one charge pulse is the most relevant se-quence because the switching losses increase and the minimum pulse width requirement de-creases as a function of the number N of pulses used.

Another method for generating longer rise times than the base voltage slope of tr =(2π/3)

√LC is to use a pulse width different from the 50 % duty cycle in the charge and

discharge pulses. In this case, instead of charging the filter to the full amplitude A at once,each individual charge period increases the output voltage by a fraction of A/M, where M isthe number of individual charge periods. Therefore, the total output voltage slope transitiontime is increased to M times the base transition time tr by using the same LC circuit. For moreon these charging schemes, see publications (Korhonen et al., 2009; Tyster et al., 2009). Nev-ertheless, these pulse sequences are outside the scope of this work and are not studied furtherhere.

3.1.6 Measured example of active du/dt operation

Figure 3.14 illustrates typical operation in an inverter-fed drive. The cable length is 100meters, and the propagation speed of the wave in the cable is approximately half the speedof light, Reka MCMK. A steep-edged voltage pulse is reflected at the motor terminal, andoscillation occurs. In Figure 3.15, the same situation is presented when active du/dt filteringis applied. The cable resonance frequency is succesfully filtered, and the cable resonance iseliminated.

As can be seen in Figure 3.15, the LC circuit can be applied to the generation of an outputvoltage, which consists of several delayed step responses of the LC circuit in order to producea rising voltage slope. The rising and falling times of the slope depend on the time constant ofthe LC circuit. It can also be noted that if the voltage is switched off when the LC filter outputvoltage has reached half the DC link voltage, the output voltage is doubled to equal to the DC


−1 −0.5 0 0.5 1 1.5 2 2.5 3

x 10−5

−500

0

500

1000

Inverter output voltage

Time [s]a)

Vol

tage

[V]

−1 −0.5 0 0.5 1 1.5 2 2.5 3

x 10−5

−500

0

500

1000

Voltage at 100 meter open−ended cable end

Time [s]b)

Vol

tage

[V]

Figure 3.14. Measurement of a cable resonance, a) in basic inverter operation, b) for a 100 meter cable.

−1 −0.5 0 0.5 1 1.5 2 2.5 3

x 10−5

−500

0

500

1000

Active du/dt filter output voltage

Time [s]a)

Vol

tage

[V]

−1 −0.5 0 0.5 1 1.5 2 2.5 3

x 10−5

−500

0

500

1000


Time [s]b)

Vol

tage

[V]

Figure 3.15. a) Measurement of active du/dt operation. b) The cable resonance and overvoltage areeffectively eliminated.

link voltage. Since the output voltage of the LC circuit was exactly half the step voltage, thetotal time taken to the full step voltage is double the time of the voltage pulse applied. In this


case, the resonance of the LC circuit is avoided, because the switching instants are conductedexactly as described.

3.2 Active du/dt filter circuit component selection

As presented above, the active du/dt filter circuit consists of a series inductance L and aparallel capacitance C, which are provided by the filter inductors and capacitors in a realimplementation.

However, there are some considerations regarding the design and realization of the filtercircuit. First, in the filter component selection, the use of narrow, steep-edged voltage pulsesin the order of microseconds has to be taken into account. This sets special requirementsfor the inductors and capacitors. The inductors have to be designed for high-frequency use,which means that the core material has to be air or high-frequency ferrite material.

In the case of ferrite core, the saturation of the core material has to be avoided, and the filterand motor maximum currents have to considered in the design. The filter maximum currentcan be obtained from Eq. (3.11). In the filter L and C component value selection for a specifictr (LC constant) value, an increase in the inductor value decreases the filter maximum current,whereas an increase in the capacitor value increases the filter maximum current, as seen fromEq. (3.11). The filter maximum current is also an important design consideration, becausethe current handling capability and power losses of the inverter power modules set limitationson the peak charge and discharge currents. However, the inductance and capacitance valuescannot be selected arbitrarily based on the rise time and the filter peak current, because thecapacitance value has an effect on the rigidity of the active du/dt filter circuit as a voltagesource. The topic will be discussed in more detail later in the next chapter.

Furthermore, the variation in the component L and C values resulting from component tol-erances causes an error in the filter output voltage, if the manufacturing tolerances are nottaken into account in the design of the charge and discharge sequences. As can be noticedfrom Eq. (3.5), tr is proportional to the square root of the component values as follows

tr ∼√

LC. (3.16)

Variation in the component values causes a change proportional to the square root of thedesigned component value in the correct rise time tr. The amplitude of the resonance, orthe error, in the LC circuit is equal to the difference in the filter output (capacitor) and DClink voltages at the instant when the voltage pulse is switched on at the end of the charge ordischarge sequence. Therefore, faulty charge according to a wrong rise time causes the filtercapacitor to under- or overload, causing a resonating output voltage. Residual LC circuitoutput oscillations for various LC constant errors when compared with the designed value,between 80 and 120 %, are presented in Table 3.1.

However, the filter LC constant can be detected by generating a voltage step in the inverter

3.3 Selection of active du/dt rise time for various cable lengths 61

Table 3.1. Active du/dt filter output oscillation amplitude A of the target voltage UDC as a function oferror in the LC constant owing e.g. to component tolerances. %-

√LC is the actual value instead of the

designed√

LC.

%-√

LC 80 % 85 % 90 % 95 % 100 % 105 % 110 % 115 % 120 %

A/UDC 10.6 % 7.8 % 2.5 % 2.5 % 0.0 % 2.5 % 4.9 % 7.2 % 9.5 %

output stage and measuring the crossings of the DC link voltage level using a voltage mea-surement at the filter output phase. The LC constant can be calculated from the resonancefrequency of the LC circuit, and the charge and discharge sequences can be adjusted accord-ing to Eq. (3.5) in order to compensate the variations in the actual component values from thenominal values.

3.3 Selection of active du/dt rise time for various cablelengths

As stated above, the phase velocity and the cable length affect to the cable oscillation fre-quency. Therefore, the filter rise time has to be designed according to the motor cable length.According to (Persson, 1992), the overvoltage is minimized, when the rise time of a linearramp is four times the cable propagation delay. However, the frequency content of an activedu/dt ramp for a certain rise time tr is different, since the du/dt is not constant along the risetime, for rise time definition presented in Figure 3.16. The rise time is defined as the rampsequence length, from the 0 to 100 % voltage. Therefore, the maximum cable lengths forvarious linear (Figure 3.16a) and active du/dt (Figure 3.16b) ramp rise times have been de-termined in the following tables. In addition, in a practical installation, overvoltages of forexample 30 % or 50 % are allowed, and thus such values are presented also.

Figure 3.16. Definitions for the a) linear and b) active du/dt ramp lengths. The rise time is defined asthe ramp sequence length, from the 0 % to the 100 % voltage.

Linear ramp risetimes for zero overvoltage and 100 % overvoltage have been determined


using the above-mentioned Persson’s formula and definition for the critical cable length. Fur-thermore, the 30 % and 50 % allowed overvoltages for certain cable lengths have been sim-ulated on a similar basis than presented in (Ström et al., 2006) and (Tarkiainen et al., 2002).The ramp fed into a model consisting of transport delays and reflection coefficients. Thepropagation delay was assumed 0.5c, the motor reflection coefficient Γm = 1, and inverterreflection coefficient Γi = −1. Cable attenuation was neglected. The model is presented inAppendix A.

The cable lengths for various linear ramps are presented in Table 3.2.

Table 3.2. Cable lengths for various linear ramp lengths for a certain allowed overvoltage value (νp =0.5c).

0 % 30 % 50 % 100 %

0.5 µs 19 m 24 m 28 m 37.5 m

1 µs 37.5 m 48 m 56 m 75 m

2 µs 75 m 97 m 112 m 150 m

3 µs 112.5 m 146 m 168 m 225 m

5 µs 187.5 m 243 m 281 m 375 m

8 µs 300 m 390 m 450 m 600 m

The values from the table are presented in Figure 3.17.

As can be seen, the cable length for 0 % overshoot for 1 µs is 37.5 m. Therefore, the 0 %linear ramp for a certain cable length can be calculated as follows

l [m] = 37.5[ m

10−6s

]· tr [10−6s]. (3.17)

In addition, the 30 % and 50 % overvoltage lengths can be determined from Table 3.2 asfollows

l (30 %)≈ 1.3 · l(0 %), (3.18)

l (50 %)≈ 1.5 · l(0 %). (3.19)

The cable lengths for various active du/dt ramps are presented in Table 3.3.

The values from the table are presented in Figure 3.18.

3.3 Selection of active du/dt rise time for various cable lengths 63

0 1 2 3 4 5 6 7 8 90

50

100

150

200

250

300

350

400

450

500Cable lengths for linear ramp for certain overshoot

Time [us]

Cab

le le

ngth

[m

]

0 %

30 %

50 %

Figure 3.17. Cable lengths for various linear ramp lengths for a certain allowed overvoltage value(νp = 0.5c)

Table 3.3. Cable lengths for various active du/dt ramp lengths for a certain allowed overvoltage value(νp = 0.5c).

0 % 30 % 50 % 100 %

0.5 µs 11.5 m 16 m 19.5 m 37.5 m

1 µs 23 m 32 m 38 m 75 m

2 µs 46 m 64 m 77 m 150 m

3 µs 69 m 96 m 116 m 225 m

5 µs 114 m 160 m 194 m 375 m

8 µs 183 m 256 m 310 m 600 m

As can be seen, the cable length for 0 % overshoot for 1 µs is 23 m. Therefore, the 0 % activedu/dt ramp for a certain cable length for an arbitrary ramp length can be calculated as follows

l [m] = 23[ m

10−6s

]· tr [10−6s]. (3.20)


0 1 2 3 4 5 6 7 8 90

50

100

150

200

250

300

350

400

450

500Cable lengths for active du/dt ramp for certain overshoot

Time [us]

Cab

le le

ngth

[m

]

0 %30 %50 %

Figure 3.18. Cable lengths for various active du/dt ramp lengths for a certain allowed overvoltage value(νp = 0.5c)

In addition, the 30 % and 50 % overvoltage lengths can be determined from Table 3.3 asfollows

l (30 %)≈ 1.4 · l(0 %), (3.21)

l (50 %)≈ 1.7 · l(0 %), (3.22)

Furthermore, as the values were determined using ideal open end and short circuit reflectioncoefficients, overvoltage of 0 % cannot be achieved in a real application, because the ampli-tude of the cancelling wave has decayed due to cable attenuation and incomplete reflection atthe interfaces.

65

Chapter 4

Applying active du/dt filtering to anelectric drive

In the previous chapter, the basis of active du/dt control was presented, and the theory forapplication of the method and design of the filter circuit was developed. However, if themethod presented is applied in an electric drive as described above, the induction motorcurrent causes error in the active du/dt operation. Nevertheless, in the worst case, where theload current is greater than the filter current, the load current renders the filtering methodunusable, unless the error is corrected. The principles for correction of the load-current-induced error are described in this chapter. The error is dependent on the relation of the filtermaximum current and the instantaneous value of the motor current. The correction can beimplemented using a similar active control as the standard active du/dt control of the LC filtercircuit.

4.1 Effects of an electric motor on the active du/dt filteringmethod

To develop the control principles, the analysis presented in the previous chapter was basedon the ideal LC circuit model of the active du/dt filter, as shown in Figure 3.7. Therefore, nononidealities nor any external loading effects were taken into account. However, the analysisof these effects is of great importance when the method is applied to the output filtering in anactual induction motor drive.

66 Applying active du/dt filtering to an electric drive

4.1.1 Error caused by the induction motor current

The error in the operation of the active du/dt filter, caused by the load current of the inductionmotor, can be analyzed using a simplified equivalent circuit as presented in Figure 4.1.

Figure 4.1. LC filter for active du/dt control presented with the loading impedance of the inductionmotor on a per-transition basis.

The impedance ZL is used to model the loading impedance of the induction motor for theanalysis from a viewpoint of a single transient. From this viewpoint, for a pulse-width-modulated voltage waveform, the rate of change in the motor current is slow. For example,in a typical case, the period of the motor current is in the order of tens of milliseconds (tensof hertz) and the pulse width modulation at the switching frequency in the order of a hundredmicroseconds (corresponds to 10 kHz), as the edge modulation of each switching transient ofthe PWM-switched voltage is carried out in a time plane that is in the order of a microsecond.Therefore, in the analysis of the effect of load current, the instantaneous value of the slowmotor current can be approximated as a constant current, when the edge modulation of asingle voltage transient is considered.

Second, the inductance visible from the asynchronous machine for a single voltage transientis the transient inductance L′s, which is defined as (Pyrhönen et al., 2008)

L′s = Lsσ +Lrσ Lm

Lrσ +Lm≈ Lsσ +Lrσ , (4.1)

where Lsσ is the stator leakage inductance, Lrσ is the rotor leakage inductance, and Lm is themagnetizing inductance. The transient inductance is in a major role to filter the motor currentin an inverter drive, and it mainly consists of the stator and rotor flux leakages (Pyrhönenet al., 2008). For typical one-phase asynchronous machine equivalent circuit parameters andtransient inductances for various motor sizes, see Appendix C.

If the load impedance ZL is considered as the transient inductance, L′s, it can be stated for asingle transient that

4.1 Effects of an electric motor on the active du/dt filtering method 67

Lf << LL. (4.2)

Since the equivalent loading resistance of the induction machine, regardless of the loadingcondition of the machine, resides behind the transient inductance, the electric motor canthereby be regarded as a constant current source for the single transient, and thus, for a singleactive du/dt charge or discharge pulse. This is also equal to the analysis above, because thetime constant and hence the transient behavior is considerably slower in the system presentedby the higher inductance, that is, the induction motor.

The voltage and current waveforms of the active du/dt filtering, together with the correspond-ing gate control signals in basic operation as presented above for one inverter phase, areshown in Figure 4.2. As seen, dead times are not taken into account in the simplified analy-sis.

When the power switch corresponding to the voltage step transition direction is turned on,the absolute value of the current begins to increase at a rate defined by the LC constant, andthe capacitor begins to either charge or discharge depending on the slope direction. Whenthe half of the total voltage transition is reached, the power switch is turned off. At thatmoment, both the power switches are in a nonconducting state, and the current flows throughthe freewheeling diodes in the output stage. The absolute current begins to decrease at thesame rate at which it increased, and the output voltage of the filter continues to rise or falldepending on the direction of the voltage, as the transient behavior of the LC circuit presentedin Chapter 3 defines. After this, the same power switch is turned on, when the current hasreturned to the same value as it was before the transient, and the voltage has reached eitherthe negative or positive DC link rail potential. In the case of no external loading of the filter,as presented in Figure 4.2, the initial current before the transition is zero.

In the figure, there is no load at the output of the filter, but the only load to the inverter outputstage is the LC filter circuit. In Figures 4.3 and 4.4, the rising and falling voltage slopesand the corresponding filter currents are shown in two cases: for positive and negative loadcurrents IL.

As can be seen from Figures 4.3 and 4.4, the load, or the base current, at which the filtercharge or discharge is carried out, will cause an error depending directly on the idle currentinstantaneous value related to the magnitude of the filter current during the operation of thefilter. Therefore, the residual oscillation in the filter output, and also the correction method,is a function of load current.

If the load current IL is greater than zero, generation of the rising voltage slope is not af-fected, and the filter will operate normally in the freewheeling mode in the same way as inthe zero idle current situation. However, the falling voltage slope is affected, because theedge modulation pattern of the falling slope will cause crossing of the zero current. In thefreewheeling mode, the current will not return to the same value as in the beginning of theedge modulation sequence, and the current will thus remain at the zero current level. As thefilter inductor current drops to zero, the inductive load impedance will start to drain charge


Figure 4.2. Basic active du/dt operation: a) filter output voltage and b) filter current. c) The gate controlsignals of the inverter leg are also shown along with d) the inverter output voltage.


Figure 4.3. a) and c) Operation of the active du/dt method, when the load current instantaneous valueis greater than zero (towards the motor), and b) and d) less than the filter peak current. As shown, zeroend current d) will result in oscillation c).


Figure 4.4. a) and c) Operation of the active du/dt method, when the load current instantaneous value isless than zero (towards the inverter), and b) and d) less than the filter peak current. As shown, zero endcurrent d) will result in oscillation c).


from the filter capacitor, causing the filter phase output voltage to turn into negative.

The error in the current waveform is related to the instantaneous value of the load current.In order to correct this error, the filter inductor current must be returned to the initial value,which is carried out using the opposing inverter switch. Similarly as in the basic operationof active du/dt with no load, the capacitor voltage must be at the target value and the filterinductance current must be at the initial value at the end of the sequence to avoid residualfilter oscillation.

In the contrary case, if the current IL is less than zero, the falling voltage slope is not affected,but the rising voltage slope will be erroneous for the same reason: the filter inductor currentwill stay at zero current instead of returning to the initial negative current. The correction iscarried out in the same way as in the case of positive idle current, using the opposite inverterswitch in comparison with the basic active du/dt operation presented in Chapter 3. The ideaof the correction sequence is presented in Figure 4.5 for both the cases requiring the currentcorrection pulse described above.

Figure 4.5. Principle of the current correction pulse to correct the operation of the active du/dt method.a) and b) show the effect of the current correction pulse, c) and d), on the filter current.

The idea of the current correction pulse is presented in Figure 4.6. As the load current |IL|


increases as a result of the fundamental modulation, depending on the potential the phasevoltage is switched to, either the falling or rising voltage edge modulation must include acurrent correction pulse. As the absolute value of the idle current increases, the compensatingcurrent correction pulse extends from the end of the charge or discharge period toward thestart of the period. Therefore, the minimum value of the pulse length is zero, at zero loadcurrent, which also means that the correction pulse is absent. As a result of the 50 % dutycycle of the basic active du/dt voltage level transition edge modulation, the ideal maximumlength of the current correction pulse is half of the charging or dicharging period, becauseotherwise inverter leg short circuit would occur. This situation is also equal to the instant atwhich the filter current is at its maximum value and the current correction pulse will last forthe entire period.

The pulse length in the ideal case can be derived from the filter current equation (3.10) basedon the principle presented in Figure 4.6.

The length of the current correction pulse tcorr is indicated in Figures (4.6) and (4.7). Equa-tion (3.10) can be divided into parts in the same way as the voltage equation presented inFigure 3.10:

if(t) =

(1)︷︸︸︷A√L/C

sint√LC−

(2)︷︸︸︷ε (t− t1)

A√L/C

sint− t1√

LC+

(3)︷︸︸︷ε (t− t2)

A√L/C

sint− t2√

LC(4.3)

The parts of the current that have an effect on the different phases of the filter current arealso indicated in Figure 4.7. The length of the current correction pulse can be determined bysolving the equation

if(t) = |IL|, (4.4)

because of the symmetricity of the filter current waveform, only the part (1) of Eq. (4.3) hasto be taken into account in the solution. Therefore, the solution for the length of the currentcorrection pulse in the ideal case is

tcorr =√

LC sin−1

(IL

A

√LC

), (4.5)

where IL is the load current instantaneous value and A is the amplitude of the inverter DClink voltage.

The cases in which the absolute value of the load current is between zero and the filter max-imum current have been discussed above. The case in which the load current is greater thanthe filter current is shown in Figure 4.8.


Figure 4.6. Principle of the current correction pulse to correct the operation of the active du/dt method.As the load current absolute value increases, a) and b), a current correction pulse of increasing lengthmust be applied, c) and d). Inverter leg output voltages are shown, e) and f) for the the gate controlsignals, c) and d), of the individual power switches.


Figure 4.7. Principle of the derivation of the current correction pulse length. (1), (2), and (3) refer tothe parts of Eq. (4.3).

In this case, the current correction pulse must be half of the total charging or dischargingperiod, which is also the maximum length of the correction pulse. Now the absolute value ofthe load current is greater than the filter maximum current, and hence, no zero crossing takesplace in the current waveform. The actual edge modulation of the active du/dt modulationis not necessary in this case either, because the absolute value of the current will start todecrease in the freewheeling mode, when both the switches of the inverter leg are turnedoff. The filter inductance current is restored to the initial idle current value using only thecurrent correction pulse, which is half of the period. In this case, the edge modulation patternis similar to the basic active du/dt modulation pattern; the pattern itself is the same, but theinverter switch used is the opposite. In addition, the current correction, for any load current,can be carried out using the full-length current correction pulse, if ideal switches are used.However, the current correction idea based on the actual commutation instant was presentedas a basis for implementation on a real inverter.

However, implementing the current correction pulse in an actual inverter is not as straight-forward as presented here, because the properties of the inverter output stage, for examplethe losses, minimum pulse lengths, and required dead times, will all have a significant effecton the final result of the active du/dt modulation. Implementation of the current correctionmodulation in a real inverter should be based on the idea presented above, taking into accountthe limitations defined by the actual IGBT modules in the output stage, and it is outside thescope of the work presented in this dissertation.


Figure 4.8. a) and b) Principle of the current correction pulse to correct the operation of the active du/dtmethod, when the instantaneous load current is greater in amplitude than the filter peak current. c) andd) The charge and discharge pulses are eliminated by the freewheeling operation of the circuit, and onlythe current correction pulse is required to restore the current of the filter reactor to the starting value.Inverter leg output voltages, e) and f), are shown for the gate control signals of the individual powerswitches, c) and d).


4.1.2 Effect caused by resistive losses in the circuit

The error in the operation of the active du/dt filter, caused by resistive losses – which is notthe case with the effective power of the induction motor – can be analyzed using a simplifiedequivalent circuit as presented in Figure 4.9.

Figure 4.9. LC filter for active du/dt control presented with a resistive losses.

The impedance ZL and the resistance Rloss are used to model the induction motor and resistivelosses caused by the resistances in the DC link, inverter bridge, and filter circuit. The effectsof the load current IL and means to mitigate it were presented in the previous subsection.However, the resistive losses also cause an error in the output voltage in the active du/dtfilter output voltage, because the filter capacitor will be underloaded, which in turn causes aresonating filter output voltage.

The effect of the underload can be compensated by increasing the charge and discharge pulsewidths from the ideal 50 %, which is the ideal pulse width, when there are no resistive lossesat the filter circuit. In practice, this means an increase in the modulated output voltage (higherduty cycle) in order to overcome the resistive losses. Since the resistive loss in the circuit isstatic, no dynamic correction is necessary, as is the case with the load current.

4.2 Simulations of the error caused by the motor current

In order to verify the current correction method for the load-current-caused error in the activedu/dt filter output voltage, a simulation model was developed in the MATLAB SIMULINKenvironment. A block diagram of the developed model is presented in Figure 4.10. Themodulator block forms the gate drive signals for the output stage consisting of SIMULINKSimPowerSystems IGBT/Diode components. The output stage drives the active du/dt LCfilter circuit, which is connected to the SimPowerSystems asynchronous machine model.Three-phase current measurements are carried out after the output stage and after the activedu/dt filter. The motor current measurement is used to form correction pulses of the rightlength. A more detailed description of the simulation model structure is given in AppendixA.

Because the research on the development of the current correction method for a frequencyconverter was outside the scope of this dissertation, no measurement results with the current

4.2 Simulations of the error caused by the motor current 77

Figure 4.10. Block diagram of the correction pulse simulation model. The top level model and theblocks are presented in more detail in Appendix A.

correction method are presented. The simulation model applies the theory presented previ-ously in this chapter. However, the error caused by the load current is noticeable, to the extentit can be detected at the motor sizes used in the measurement, are presented later. If the filtermaximum peak current and the motor current are in the same order, the filter output voltageerror becomes more apparent. Simulations are carried out for a filter design of L = 7 µH andC = 0.33 µF, which leads to tr ≈ 3.2 µs and If(t)max ≈ 113 A.

In the simulation data, part of the start-up transient of the standard SimPowerSystems Asyn-chronous machine model is shown. The model was configured to represent an inductionmotor of approximately 37 kW. In the SimPowerSystems IGBT model, some of the losses,for example the losses in the conducting state, are taken into account. However, for examplethe dead times, which are mandatory in a real inventer, were omitted in the simulation, andtherefore, the output stage model is an idealized model of a real output stage.

In Figures 4.11–4.14, the operation of the active du/dt method is shown without the currentcorrection pulse; only the active du/dt charge and discharge pulses are used. As can be seen,the increasing instantaneous value of the motor current causes an error in the output voltageof the filter, that is, in the motor voltage, as the LC circuit resonates. The greater the loadcurrent value during the charge is, the greater is the error and the amplitude of the unwantedLC resonance. Moreover, the resonance is visible in the filter current, which is seen in theinverter output current. Time-enlarged waveforms of inverter and motor voltages are alsoshown at two different time instants.

In Figures 4.19–4.22, the operation of the active du/dt method is shown with the currentcorrection pulse applied. As can be seen, there is negligible LC oscillation, or error in thefilter output and in the motor voltage, and the current correction pulses applied is seen tocorrect the LC filter resonance in cases, where the load current is significant compared withthe filter current. Time-enlarged waveforms of inverter and motor voltages are shown at twodifferent time instants. Furthermore, the inverter current consists of the motor current and thecharge and discharge current spikes of the active du/dt LC filter.


0 0.5 1 1.5 2

x 10−3

−1000

0

1000Inverter voltage U

Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Inverter voltage V

Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Inverter voltage W

Vol

tage

[V]

Time [s]

Figure 4.11. Simulated inverter bridge output voltages. During the transients in the PWM, charge pulsesare applied according to the theory presented in Chapter 3. No correction pulse is applied.

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Motor voltage U

Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−2000

0

2000Motor voltage V

Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−2000

0

2000Motor voltage W

Vol

tage

[V]

Time [s]

Figure 4.12. Simulated filter output voltages. As can be seen, the LC resonance increases as theinstantaneous motor current value increases. No correction pulse is applied.


4.5 5 5.5

x 10−4

−1000

−500

0

500


Vol

tage

[V]

4.5 5 5.5

x 10−4

−1000

−500

0

500

1000Motor voltage U

Vol

tage

[V]

Figure 4.13. Simulated inverter bridge and motor voltages, a time-enlarged version of one time instantof Figures 4.11 and 4.12. No correction pulse is applied.

1.7 1.72 1.74 1.76 1.78 1.8

x 10−3

−1000

−500

0

500


Vol

tage

[V]

1.7 1.72 1.74 1.76 1.78 1.8

x 10−3

−1000

−500

0

500

1000Motor voltage U

Vol

tage

[V]

Figure 4.14. Simulated inverter bridge and motor voltages, a time-enlarged version of one time instantof Figures 4.11 and 4.12. No correction pulse is applied. As can be seen, the increasing load current,see Figure 4.16, causes LC filter resonance. The resonance does not originate from cable reflections,since a motor cable is not present in the model.


0 0.5 1 1.5 2

x 10−3

−500

−400

−300

−200

−100

0

100

200

300

400Inverter output currents

Time [s]

Cur

rent

[A]

Phase U

Phase V

Phase W

Figure 4.15. Simulated inverter bridge output currents. As the amplitude of the motor current increases,the resonant LC filter current is seen in the inverter output current. No correction pulse is applied.

0 0.5 1 1.5 2

x 10−3

−400

−300

−200

−100

0

100

200

300Motor currents

Time [s]

Cur

rent

[A]

Phase U

Phase V

Phase W

Figure 4.16. Simulated currents of the asynchronous machine model at the beginning of the start-uptransient. No correction pulse is applied.


0 0.5 1 1.5 2

x 10−3

−500

−400

−300

−200

−100

0

100

200

300

400Inverter output currents

Time [s]

Cur

rent

[A]

Phase U

Phase V

Phase W

Figure 4.17. Simulated inverter bridge output currents. The currents consist of the sum of the motorcurrent and the charge and discharge currents of the LC filter circuit during the transients. The correctionpulses are applied as a function of the current instantaneous value.

0 0.5 1 1.5 2

x 10−3

−400

−300

−200

−100

0

100

200

300Motor currents

Time [s]

Cur

rent

[A]

Phase U

Phase V

Phase W

Figure 4.18. Simulated currents of the asynchronous machine model at the beginning of the start-uptransient. The correction pulses are applied as a function of current instantaneous value.


0 0.5 1 1.5 2

x 10−3

−1000

0


Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Inverter voltage V

Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Inverter voltage W

Vol

tage

[V]

Time [s]

Figure 4.19. Simulated inverter bridge output voltages. During the transients in the PWM, chargepulses are applied according to the theory presented in Chapter 3. The correction pulses are applied asa function of current instantaneous value.

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Motor voltage U

Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Motor voltage V

Vol

tage

[V]

0 0.5 1 1.5 2

x 10−3

−1000

0

1000Motor voltage W

Vol

tage

[V]

Time [s]

Figure 4.20. Simulated filter output voltages. As can be seen, the LC resonance is negligible, ascorrection pulses are applied as a function of current instantaneous value.


4.5 5 5.5

x 10−4

−1000

−500

0

500


Vol

tage

[V]

4.5 5 5.5

x 10−4

−1000

−500

0

500

1000Motor voltage U

Vol

tage

[V]

Figure 4.21. Simulated inverter bridge and motor voltages, a time-enlarged version of one time instantof Figures 4.19 and 4.20. Current correction pulse is applied.

1.7 1.72 1.74 1.76 1.78 1.8

x 10−3

−1000

−500

0

500


Vol

tage

[V]

1.7 1.72 1.74 1.76 1.78 1.8

x 10−3

−1000

−500

0

500

1000Motor voltage U

Vol

tage

[V]

Figure 4.22. Simulated inverter bridge and motor voltages, a time-enlarged version of one time instantof Figures 4.19 and 4.20. Current correction pulse is applied. As can be seen, the current correc-tion pulses are applied to correct the LC filter resonance in cases where the load current is significantcompared with the filter current; cf. Figure 4.14.


4.3 Measurements and experimental results

A prototype was built to assess the potential of the active du/dt method presented. A three-phase Vacon NXP frame size 6 frequency converter unit was modified to make the edgemodulation according to the active du/dt method possible. The original IGBT modules of thepower unit were replaced with SEMIKRON SEMiTRANS series SKM 100GB123D IGBTmodules, and the original control card was replaced with a custom-designed (at LappeenrantaUniversity of Technology) control card based on a XILINX Spartan-3 field programmablegate array (FPGA).

Otherwise, the converter unit and the gate drivers were factory standard design. A control unitimplementing active du/dt pulse modulation was developed for the FPGA card by Juho Tys-ter, M.Sc. (Tech.) and Juhamatti Korhonen, M.Sc (Tech.). For more on the implementation,see (Korhonen et al., 2009).

The cable used in all the test setups was MCMK type power cable. Cables from two man-ufacturers were used. The insulation material between the phase conductors and the shieldwas different for the cables, and therefore the high-frequency properties, most importantlythe velocity of propagation, varied slightly between the cable brands. The measurements ofthe properties are presented below, in Table 4.1.

A prototype LC filter circuit was designed and built by Juho Tyster, M.Sc. (Tech.) andJuhamatti Korhonen, M.Sc (Tech.). According to Chapter 3, the overvoltage is minimized,when the rise time for a 100 meter cable with active du/dt ramp is

tr [10−6s] = 100 [m]/23[ m

10−6s

]≈ 4.4 ·10−6s. (4.6)

The phase velocity of a polyvinychloride-insulated (PVC) power cable can be assumed to bein the order of half the speed of light (≈ 0.5 · c), (Skibinski et al., 1997; Ahola, 2003).

Three custom-built inductors based on FERROXCUBE ETD49/25/16 coil former, 3C90 fer-rite core, and Litz wire were wound. The reactor in the filter circuit was specifically designedfor the purpose, using core material suitable for an application containing fast pulses. Themeasured inductance of the coils was 16 µH, and 0.33 µF plastic-insulated pulse capacitorswere chosen. This results in a rise time of approximately tr=4.8 µs, (3.5) and a filter peakcurrent of 75 A for the DC link value of 600 V, (3.11). The maximum length of the powercable for this filter is, therefore, approximately 110 meters, if no overvoltage is allowed. Thisis a fairly valid assumption for PVC-insulated power cables, such as the MCMK cable.

4.3.1 Measurement setup

The setup used for the measurements is presented in Figures 4.23 and 4.25–4.27. A schematicof the measurement setup is shown in Figure 4.23. Figure 4.25 shows the measurement setup

4.3 Measurements and experimental results 85

consisting of the frequency converter, active du/dt filter circuit, motor cables, two sizes ofinduction motors, and the measurement instrumentation. The electric motors used in themeasurements were ABB 5.5 kW and 7.5 kW induction motors, which are shown in Fig-ure 4.26. The active du/dt filter circuit is shown in more detail in Figure 4.27. The motorswere idling at 50 Hz in all the measurements, in which the motors were used.

!

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( - ( ( . /

0 + 1 ( - (

( - ( ( + . /

& -

&

2 3

4

5

& 5 6

2 3

4

%

33

3

Figure 4.23. Schematic of the measurement setup consisting of a frequency converter, an active du/dtfilter circuit, a motor cable, an induction motor, and measurement instrumentation. All the measure-ments are indicated in the figure.

The frequency converter was fed from the grid using a variable transformer. The active du/dtfilter circuit was constructed on a PCB card, which was attached to the frequency converternegative DC link rail and output phases.

The power cables were MCMK type, 3x2.5 mm2+2.5 mm2 screened 0.6/1 kV power cables.Cables from two manufacturers were used, Draka MCMK and Reka MCMK. The Drakacables were approximately 30 and 300 meters long. The insulation system of the cable con-sists of phase conductor insulations, filler around the phase conductors, a screen consistingof copper leads and foil, and an outer sheath. The Reka cable used in the measurements wasapproximately 100 meters in length. The insulation of the Reka MCMK is slightly different,consisting of phase conductor insulations, an insulating film around the phase conductors, ascreen of copper leads and foil, an insulating film around the screen, and an outer sheath. Theinsulation material used in both cables is polyvinylchloride (PVC). The dielectric configura-tion of the cables is shown in Figure 4.24.

Because of differences in the dielectric configuration, the high-frequency properties of thecables differ causing a difference in the propagation velocities. The approximate propagationvelocities determined from the cable oscillation frequencies are presented in Table 4.1. Thecalculation is based on the measurement presented in Figures 4.28, 4.29 and 4.32, based on


Figure 4.24. Dielectric configuration of the Draka and Reka MCMK 1 kV power cables.

Eqs. 2.8 and 2.15.

Table 4.1. Approximate signal propagation velocities of the MCMK power cables used in the measure-ments.

Cable Cable length fosc vp εeff

Draka MCMK 29.6±0.1 m 1.111 MHz 0.44·c ≈ 5.3

Draka MCMK 295±2 m 96.51 kHz 0.38·c ≈ 6.9

Reka MCMK 97.4±0.5 m 385.1 kHz 0.50·c ≈ 4.0

c in the table is the speed of light, and εeff is the effective dielectric constant. The results arewell in line with the literature and assumptions of the cable properties. Further, the higherpropagation speed in the Reka MCMK cable without a filler is valid, because the dielectricconfiguration in which the electric field propagates consists of a mix of air and insulationmaterial. This results in a smaller effective dielectric constant than in the Draka MCMK,where the electric field propagates in a dielectric environment consisting approximately onlyof the insulating material. The dielectric constant of air is approximately one, whereas it ishard to determine a general dielectric constant value for PVC, since the material is availablein many formulations depending on the target of application.

The measurement instrumentation consisted of an Agilent DSO6104A four-channel, 1 GHzdigital oscilloscope, a Tektronix probe power supply 1103, Tektronix high-voltage differen-tial probes P5205, and a Fluke 80i110s current probe for measuring the slow, 50 Hz motorphase currents. More details on the instrumentation can be found in Appendix B, where theequipment used in the measurements and the uncertainty of the equipment are discussed.


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1 $ 2

3 * 4

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$ #

. ( ( 3

5 6 7 # /

# 8 * + $

- ' 9 " ( : 9

* /

* #

Figure 4.25. Measurement setup consisting of a modified frequency converter, custom control circuitry,active du/dt filter circuit, various lengths of motor cables, induction motors, and measurement instru-mentation. The measurement instrumentation consisted of a four-channel Agilent digital oscilloscope,Tektronix voltage probes, a power supply, and Fluke current probes.

4.3.2 Experimental results

The measured voltage waveforms of one inverter output phase (U) and one motor phase-to-phase voltage (U-V) without filtering are shown in Figures 4.28–4.32. The peak voltagelevel caused by the cable reflection is approximately twice the DC link voltage level (1100 V,183 % UDC) without any filtering applied.

Operation of active du/dt filtering without any load is shown in Figures 4.33–4.35. In additionto the perfectly timed charge pulses, the operation of the filter circuit without any control andwith mismatched timing are also shown. Incorrect timing is not critical for the operation, butit can be seen that the control is nevertheless necessary, because of the strong LC resonanceowing to the low damping factor.

When active du/dt is applied, Figures 4.36–4.44, the peak voltage at the motor end decreasesconsiderably, and on the shorter, 30 meter and 100 meter cables, the oscillation is eliminated.However, the slight inaccuracies in the charge pulse and the loading effect of the motor cablecause some error inducing oscillation in the output voltage of the LC circuit, even if the cable


! "

# $ % &

'

$ ( $ ) * + , "

- .

Figure 4.26. ABB 5.5 kW and 7.5 kW induction motors used in the measurements. The MCMK typepower cable and the Tektronix differential voltage probe are also shown.

is left open ended. The effect of the motor current is also visible, since the current correctionmethod was not implemented. However, since the load current is smaller compared with thefilter charging current (75 A), the error is not significant. However, in designs where theload current is in the order of the filter current, correction pulses should be implemented;otherwise, LC resonance up to twice the DC link will be induced. It is also shown in the mea-surements that the 300 meter cable is too long for the designed filter, and the cable oscillationis not eliminated.


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Figure 4.27. Active du/dt filter circuit in more detail.

−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000


Time [s]a)

Vol

tage

[V]

−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000


Time [s]b)

Vol

tage

[V]

Figure 4.28. Measured voltage waveforms without active du/dt filtering applied. a) The inverter outputvoltage waveform, and b) the voltage at the open end of the 30 meter motor cable are shown. Theovervoltage and oscillation caused by the cable reflection are clearly visible. Overvoltage 506 V, 84 %.


−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000


Time [s]a)

Vol

tage

[V]

−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000


Time [s]b)

Vol

tage

[V]

Figure 4.29. Measured voltage waveforms without active du/dt filtering applied. a) The inverter outputvoltage waveform and b) the voltage at the open end of the 100 meter motor cable are shown. Theovervoltage and oscillation caused by the cable reflection are clearly visible. Overvoltage 507 V, 84 %.

−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000


Time [s]a)

Vol

tage

[V]

−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000

Voltage at 100 meter 5,5 kW motor−ended cable end

Time [s]b)

Vol

tage

[V]

Figure 4.30. Measured voltage waveforms without active du/dt filtering applied. a) The inverter outputvoltage waveform and b) the voltage at the motor end of the 100 meter cable are shown. The overvoltageand oscillation caused by the cable reflection are clearly visible. The effect of the 5.5 kW electric motoron the oscillation is minimal. Overvoltage 482 V, 80 %.


−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000


Time [s]a)

Vol

tage

[V]

−4 −3 −2 −1 0 1 2 3 4

x 10−5

−500

0

500

1000

Voltage at 100 meter 7,5 kW motor−ended cable end

Time [s]b)

Vol

tage

[V]

Figure 4.31. Measured voltage waveforms without active du/dt filtering applied. a) The inverter outputvoltage waveform and b) the voltage at the motor end of the 100 meter cable are shown. The overvoltageand oscillation caused by the cable reflection are clearly visible. The effect of the 7.5 kW electric motoron the oscillation is minimal. Overvoltage 473 V, 79 %.

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500

1000


Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500

1000


Time [s]b)

Vol

tage

[V]

Figure 4.32. Measured voltage waveforms without active du/dt filtering applied. a) The inverter outputvoltage waveform and b) the voltage at the open end of the 300 meter motor cable are shown. Theovervoltage and oscillation caused by the cable reflection are clearly visible. Overvoltage 498 V, 83 %.


−1 0 1

x 10−4

−800

−600

−400

−200

0

200

400

600

800

1000

1200

Inverter and active du/dt filter output voltage

Time [s]

Vol

tage

[V]

Inverter output voltageFiltered output voltage

Figure 4.33. Measured voltage waveforms, when active du/dt filter is attached to the output phases ofthe inverter, but no charge or discharge pulses are generated. No motor cable is connected. The filter isat full resonance, the frequency set by the filter LC constant. The low damping factor (i.e. losses) of theactive du/dt filter is seen from the output voltage waveform, as the oscillation decays slowly, making theactive du/dt filter useless without the active control. Absence of the active du/dt sequence has causedapproximately 500 V of the LC resonance overvoltage, 83 %.

−1 0 1 2 3 4 5

x 10−5

−100

0

100

200

300

400

500

600

700

800Inverter and active du/dt filter output voltage

Time [s]

Vol

tage

[V]


Figure 4.34. Measured voltage waveforms, when active du/dt filter is attached to the output phases ofthe inverter. No motor cable is connected. When active control as presented in Chapter 3 is properly im-plemented, the filter circuit functions as predicted by the theory. A rising and falling slope is generated,and the du/dt is set by the filter LC constant. No remaining oscillation of the LC circuit is visible.


−1 0 1 2 3 4 5

x 10−5

−100

0

100

200

300

400

500

600

700

800Inverter and active du/dt filter output voltage

Time [s]

Vol

tage

[V]


Figure 4.35. Measured voltage waveforms, when active du/dt filter is attached to the output phases ofthe inverter. No motor cable is connected. The effect of a faulty charge sequence is illustrated. The pulsewidth is over 50 %, causing the filter capacitor to overcharge above the DC link voltage. The transientinduces filter resonance, the amplitude of the resonance being the difference between the DC link andfilter voltages at the switching instant. An error in the active du/dt sequence has caused approximately80 V of the LC resonance overvoltage, 13 %.

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500

1000Active du/dt filter output voltage

Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500

1000Voltage at 30 meter open−ended cable end

Time [s]b)

Vol

tage

[V]

Figure 4.36. Measured voltage waveforms with active du/dt filtering applied. a) The filter outputvoltage waveform and b) the voltage at the open end of the 30 meter motor cable are shown. Theovervoltage and oscillation caused by the cable reflection are eliminated. Slight resonance is shownin the waveforms resulting from the loading caused by the power cable to the filter, because the filtercapacitor is not an ideal voltage source. Overvoltage 10 V, 1.6 %.


−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

x 10−4

−500

0

500


Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500

1000Filter output current, motor voltage, 30 m cable, 5,5 kW motor

Time [s]b)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

0

2

4

6

8

10

Cur

rent

[A]

Figure 4.37. Measured voltage waveforms and filter output current with active du/dt filtering applied.a) The filter output voltage waveform and b) the voltage at the motor end of the 30 meter power cableare shown. The motor was a 5.5 kW induction motor. The motor current (towards the motor) causesfaulty filter discharge during the falling slope. The motor current, ≈5 A, has caused approximately10 V, 1.6 % LC resonance overvoltage.

−0.03 −0.02 −0.01 0 0.01 0.02 0.03−100

0

100

200

300

400

500

600

700

Time [s]

Vol

tage

[V]

Filter output voltage and current, 30 m cable, 5,5 kW motor

−0.03 −0.02 −0.01 0 0.01 0.02 0.03−10

−8

−6

−4

−2

0

2

4

6

8

10

Cur

rent

[A]

Figure 4.38. Measured filter output voltage and current with active du/dt filtering applied. The powercable was 30 meters long, and the motor was a 5.5 kW induction motor. The load current causes faultyfilter discharge during the falling slope, and the negative motor current causes faulty filter charge duringthe rising slope. The resonance can be detected from the envelope of the filtered PWM voltage. Themotor current, peak ≈±8 A, has caused approximately 40 V, 7 % LC resonance overvoltage.


−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]b)

Vol

tage

[V]

Figure 4.39. Measured voltage waveforms with active du/dt filtering applied. a) The filter outputvoltage waveform and b) the voltage at the open end of the 100 meter motor cable are shown. Theovervoltage and oscillation caused by the cable reflection are eliminated. Slight resonance is shownin the waveforms resulting from the loading caused by the power cable to the filter, because the filtercapacitor is not an ideal voltage source. Overvoltage 6 V, 1.0 %.

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]b)

Vol

tage

[V]

Figure 4.40. Measured voltage waveforms with active du/dt filtering applied. a) The filter output voltagewaveform and b) the voltage at the open end of the 100 meter motor cable are shown. The effect of afaulty charge sequence is illustrated. Eventually, the oscillation in the filter output voltage will be visiblein the open or motor end of the cable. An error in the active du/dt sequence has caused approximately80 V, 13 % of the LC resonance overvoltage. The cable-reflection-induced overvoltage is 20 V, 2.9 %.


−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]b)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

0

2

4

6

8

10

Cur

rent

[A]

Figure 4.41. Measured voltage waveforms and filter output current with active du/dt filtering applied. a)The filter output voltage waveform and b) the voltage at the motor end of the 100 meter power cable areshown. The motor was a 7.5 kW induction motor. The motor current (towards the motor) causes faultyfilter discharge during the falling slope. The motor current, 6.5 A, has caused approximately 30 V, 5 %LC resonance overvoltage.

−0.03 −0.02 −0.01 0 0.01 0.02 0.03−100

0

100

200

300

400

500

600

700

Time [s]

Vol

tage

[V]

Filter output voltage and current, 100 m cable, 7,5 kW motor

−0.03 −0.02 −0.01 0 0.01 0.02 0.03−10

−8

−6

−4

−2

0

2

4

6

8

10

Cur

rent

[A]

Figure 4.42. Measured voltage waveforms and filter output current with active du/dt filtering applied.The power cable was 100 meters long, and the motor was a 7.5 kW induction motor. The load currentcauses faulty filter discharge during the falling slope, and the negative motor current causes faultyfilter charge during the rising slope. The resonance can be detected from the envelope of the filteredPWM voltage. The motor current, peak ≈ ±8 A, has caused approximately 35 V, 6 % LC resonanceovervoltage.


−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]b)

Vol

tage

[V]

Figure 4.43. Measured voltage waveforms with active du/dt filtering applied. a) The filter output voltagewaveform and b) the voltage at the open end of the 300 meter motor cable are shown. The overvoltageis approximately 180 V, 30 % of UDC, because the du/dt of the designed filter is too high for the longcable. Furthermore, the operation of the filter is interfered by the cable resonance; the LC resonanceovervoltage is approximately 120 V, 20 % and the cable-reflection-induced overvoltage 160 V, 23 %.

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]a)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

−500

0

500


Time [s]b)

Vol

tage

[V]

−10 −8 −6 −4 −2 0 2 4 6

x 10−5

0

2

4

6

8

10

Cur

rent

[A]

Figure 4.44. Measured waveforms with active du/dt filtering applied. a) The filter output voltagewaveform and b) the voltage at the motor end of the 300 meter power cable are shown. The motor was a5.5 kW induction motor. In addition, the current oscillation at the cable resonance frequency interferesthe filter operation. The motor current ≈5 A, the LC resonance overvoltage approximately 30 V, 13 %,and the cable-reflection-induced overvoltage 230 V, 37 %.


4.3.3 Additional switching losses caused by the application of the activedu/dt method

Estimates of the additional switching losses generated by the application of the active du/dtmethod in the prototype equipment (presented in the measurements section) were measuredusing the Norma D6100 three-phase, wide-band power analyzer. The properties of the powermeasurement equipment are presented in more detail in Appendix B.

The measurements were carried out at the interface between the grid and the frequency con-verter, the measured effective power contains all the effictive power consumed in the proto-type equipment. The measured effective powers are presented in Tables 4.2 and 4.3.

Table 4.2. Measured effective power in various conditions of the prototype equipment, without an activedu/dt LC filter connected. Phase voltage ≈ 244V

Pidle P, fc=4 kHz, f =50 Hz P, fc=4 kHz, f =1 Hz P, edge modulation on

45 W 55 W 55 W 55 W

Table 4.3. Measured effective power in various conditions of the prototype equipment, with the activedu/dt LC filter connected and edge modulation on. Phase voltage ≈ 244V

Pidle P, fc=4 kHz, f =50 Hz P, fc=4 kHz, f =1 Hz

45 W 310 W 330 W

The measurements were carried out at a switching frequency of 4 kHz, which was the switch-ing frequency in all the measurements. The 50 Hz and 1 Hz conditions were chosen to emu-late a typical drive state situation and a 50 % duty cycle in the inverter output. As can be seenfrom the tables, the additional loss caused by the active du/dt method is 255 W for 50 Hzand 275 W for the 1 Hz test. The active du/dt filter in the built prototype was designed fora 5.5 kW drive, and it is mainly limited by the Litz wire cross-sectional area. As the lossis in the inverter output stage, it scales according to the modulator switching frequency. Adrawback of active du/dt is that the losses are doubled as the switching frequency increasedto twice the original value.

As a comparison, the losses according to the datasheet for example in the Schaffner FN 510output du/dt filter are 90 W for power classes of 1.5 to 7.5 kW, and 100 to 150 W for powerclasses of 11 to 30 kW. However, the maximum cable length of the filter is limited to 80meters, and the electrical performance of the active du/dt is better compared with the FN 510.

However, one should consider these preliminary active du/dt power loss measurements withcriticism, since the measured total active powers from 50–330 W were small compared withthe total dynamic range of 30 kW of the instrument in its present configuration. Accordingto the instrument data presented in Appendix B, the voltage measurement uncertainty for


voltage measurement in one phase is ≈ ±0.3 V (for 244 V, range 470 V), and for a currentmeasurement of a total power of 50 W and 300 W ≈ ±2.5 mA and ≈ ±2.9 mA, for eachphase current, respectively.

Since the total loss power is relatively small, though, more accurate efficiency measurementswould require measurements in a calorimeter. Nevertheless, the preliminary loss power mea-surements based on increased switching losses should give indicative results on the order ofthe additional loss in this test setup.

4.3.4 Effect of active du/dt filtering method on common-mode voltages

As a product of operation, the two-level inverter produces common-mode voltages to theinverter output, since there are no inverter bridge switching combinations, which would pro-duce a zero common-mode voltage. Common-mode voltages, for example, are one of thecauses for bearing currents in motors. If the voltage transients in the single output phases aresteep, so are also the transitions in the common-mode voltage, which is detrimental for theelectric motor, especially if the number of steep transitions per time unit is high.

If the active du/dt capacitor wye point is connected to the negative DC link rail, as in Fig-ure 3.4, the active du/dt ouput filtering method smooths also the common-mode voltage wave-form, which is beneficial for the operation of the drive. However, active du/dt does functionwithout the wye point connection, but in that case the wye potential is not tied to any knownpotential, and common-mode filtering capabilities of the method are lost.

101

Chapter 5

Discussion and Conclusions

In this chapter, the main results of the study are summarized, and the results obtained arediscussed along with suggestions for further research.

In this work, motivation for the use of power converters in both electrical and electromechani-cal energy conversion is presented. The development taken place in the actual semiconductorpower switch components generally used in power electronics is discussed in brief, and theproblems evolved as the switches have become faster are described and explained, with aspecial focus on converter-driven motor drives.

The known cable reflection phenomenon resulting from pulse-width-modulated inverter out-put voltage, or more precisely, from the harmonic frequency content present in the voltage,and typical filtering solutions to the problems caused by cable reflections are presented. Thecable oscillation and the motor terminal overvoltages caused by the voltage reflection are de-scribed. The typical approach to mitigate the overvoltage and harmful stress caused by thehigh voltage peak with a high du/dt to the insulation of system is to slow down the transi-tions in the output voltage using output reactors or du/dt filters consisting of inductors andcapacitors.

Typically, the design of output filtering presented in the literature is based on the transientresponse of the filter, with an emphasis on the output du/dt value, whereas little attentionis paid to the frequency plane behavior of the filter designs. Indeed, it is very important totake the transient response into consideration to avoid undesired behavior in the time domain.As the filter circuits typically are second-order systems, and therefore resonance circuits,the transient response can contain considerable overshoot, if the damping is too low. Theovershoot is seen as overvoltage. By increasing the damping factor, in other words, the lossesof the circuit, the transient behavior of the circuit is improved, and the response is sloweddown. The oscillation frequency of an undamped second-order circuit depends on the timeconstant of the circuit, and it can be linked to the du/dt in the filter output voltage. In thisdissertation, new viewpoints were also presented for the filter design process.

102 Discussion and Conclusions

5.1 Key results of the work

The main objective was to develop a new output filtering method, with a target to reducethe size of the filter components and to increase the filter performance in electrical sense.The filter circuit is based on a conventional passive LC filter circuit, with smaller componentvalues and smaller filter losses than in a conventional approach. However, as can be predictedfrom the step response of an LC circuit with a low damping factor, the voltage pulses of theinverter induce a resonance in the circuit, at the frequency determined by the filter componentvalues of the circuit. Therefore, the behavior of the filter circuit must be controlled. Thecontrol is implemented using extra switching in the inverter output stage at right instants toproduce voltage slopes of desired length. The control method presented in the dissertationis based on the idea to use pulse width modulation in the LC circuit to produce the voltageslopes.

It is claimed that, in addition to the loss and transient response considerations in the filterdesign process, attention should be paid to the frequency plane behavior of the filter design.The whole inverter, motor cable, and electric motor system can be regarded as a system thathas a natural resonance frequency, which depends on the propagation velocity of the voltagewave on the cable, and the cable length. In order to suppress the unwanted resonance in thesystem, the resonance frequency present on the stimulus fed to the system should be removedby means of filtering in order to achieve good results in the mitigation of the problem.

However, using a passive, second-order system filtering approach, such as a damped LCcircuit, it is difficult to achieve great frequency plane performance, as there are no zerosin the frequency response to be set on the desired suppression frequencies, and to keep thetransient response and losses at a reasonable level. In this dissertation, a new filtering methodis presented, which overcomes these design problems present in traditional aproaches.

In this dissertation, a new output filtering method consisting of a passive LC circuit witha low damping factor and active control of the filter circuit is presented, the active du/dtoutput filtering. The passive components are required in the filter circuit to provide an abilityto produce the desired output voltage, since this cannot be implemented by using only theinverter output stage, at least when using the present semiconductor power switches. Theactiveness in the method refers to the fact that the filter circuit in the method is not functionalas such, but the active control of the circuit is required to obtain the desired output voltageproperties. However, no extra hardware is required, besides the filter components, but theactive control of the filter can be carried out using the same inverter components alreadypresent. Moreover, the active control can be quite easily implemented to the modulator, sinceit can be added as the lowest (fastest time plane) modulator level. Since a correctly designedactive du/dt filter produces a well-known output voltage waveform, which is very closely thesame at both ends of the motor cable, the estimated realized motor terminal voltage can befed as a feedback signal to the upper-level control, and the performance of the motor controlcan be improved.

The main benefits of the method are that the controllability of the transient response is verygood, and the desired rise time according to certain cable lengths can be reached by selection

5.2 Suggestions for future work 103

of the component values, which together constitute the time constant of the circuit. Thecomponent value selection affects the filter charging current, and the current can be decreasedby increasing the inductance or decreasing the capacitance value. Large currents introduceproblems because the current rating of the output stage must be taken into account, especiallyin low- and medium-power drives, and decreasing the capacitor too much will result in aconsiderably weaker equivalent voltage source in the output of the filter circuit. The outputvoltage rise time can also be controlled, or more precisely prolonged by the active controlof the LC filter circuit within certain limits, but the actual component values have to beselected according to the fundamental, shortest rise time needed. Another major benefit ofthe active du/dt filtering method is smaller component values compared with the traditionaloutput filtering methods, which means smaller filter losses, a smaller physical size, and costs.However, additional switching losses are generated.

When applying the active du/dt method in a real electric drive, the load current of the motorcauses charging and discharging errors in the filter circuit. The analysis of the filter circuitwas carried out with an assumption that the instantaneous load current is zero when the filter ischarged or discharged. If not, the filter current waveform is disturbed resulting in an unwantedresonance of the circuit. This is a problem related to implementation of the method into areal drive, and if the issue is not corrected, if the load current is in the order of the filter peakcurrent, the method will be rendered useless. If load current values are significantly smallerthan the filter current, the correction is not absolutely necessary, as shown by the experimentalresults of this dissertation. However, it is possible to take the produced error into account,and to correct the current waveform by using a corrective pulse. The current correction pulseacts as a current commutation that returns the current in the filter reactor to the level at whichit was before the charge or discharge.

Finally, the feasibility of the active du/dt filtering method was verified in a prototype environ-ment. The method was implemented on a custom-built control card, with a standard VaconNXP frame size 6 industrial frequency converter power unit. However, the original switchesin the power unit were changed from the standard to faster modules. The main challengesare the gate driver implementation, the operation of the IGBT components at such high-speedpulse patterns, and the filter inductor operation. A standard scalar pulse width modulator withthe active du/dt edge modulation was implemented in the control card and the operation ofthe prototype was tested. It was found that the developed method is feasible. The operationof the gate driver and the IGBT was found to be possible at the desired pulse patterns, and itwas shown that the active du/dt method operated as predicted by the developed theory.

5.2 Suggestions for future work

An active du/dt output filtering method to be used in an frequency-converter-fed electric mo-tor drive has been presented in the dissertation. The theory for the operation of the methodwas provided, the key issues were discussed, and the method was proven to be feasible bymeasurements carried out using the prototype equipment developed. However, some impor-tant questions have arisen in the course of research, and they still remain unanswered. These


questions require further investigation before the functionality of the method can finally beshown.

Investigation of the losses generated in the application of the active du/dt method. The com-ponent costs can be decreased by smaller filter components, especially if stock componentscan be used. Additional losses are generated as a result of extra switching conducted in thedc-to-ac inverter of the frequency converter. The active du/dt method outperforms passivefiltering in terms of electrical performance, but is the active du/dt method better also in termsof losses? In addition, research must be carried out on a new power semiconductor compo-nent generation manufactured of new materials, which provide lower losses, such as siliconcarbide, because the method will benefit from the development of the components. However,extra switching always introduces extra loss, and therefore, the question is at which point thetotal losses of the developed method will be congruent with an equal passive filter.

The active du/dt method involves high-frequency activity in the inverter circuit, and the cir-cuitry participating in the active filtering includes the DC link, inverter, and LC filter com-ponents. Therefore, all the components participating in the active du/dt must be capable ofoperating at the required frequencies, and must withstand the charging and discharging cur-rent impulses of the method. More consideration should be given on the filter circuit design;in particular, implementation of the filter inductor is of importance, and it is a challengingtask especially for high current ratings.

The limitations of an actual inverter output stage and the power switch components must betaken into account in order to succesfully develop the method in an electric drive. These arefor example the losses, dead times, and various delays present in a real inverter. The basicoperation of the active du/dt method can be performed with dead times, and the losses can betaken into account with sufficient accuracy by identification of the LC constant of the circuitby measuring DC link crossings in the step response of the circuit. However, the currentcorrection pulse depends on the instantaneous value of the load current and the losses anddelays present in the system, and thus realization of the correction pulse is more difficultin a real inverter than what is presented in Chapter 4 of the dissertation. The problem canbe solved iteratively by using a simulation tool, but the properties of the power switch willnevertheless affect the results, and the solution is still fixed. Furthermore, the various delayspresent for example in the logic paths, gate drivers, and in the power switches themselvesmust be compensated to produce pulses of the length required by the theory, which calls forfurther investigation.

The possibility to use various pulse patterns with the same filter circuit should be investi-gated. The applicability of the method is extended, if various lengths of voltage slopes canbe generated using the same filter circuit. However, more detailed research is required on theusage of different pulse widths in charging and discharging the filter.

5.2 Suggestions for future work 105

Suggestions for the most important topics requiring further research include the following:

• Research of the losses of the active du/dt method and comparison with traditional meth-ods.

• Research of the active du/dt filter components, especially for high current ratings.

• Research of the effect of the limitations of an actual inverter.

As shown, the feasibility of the method was proven for low-power drives in the course of thisdissertation. However, for the method to be generally applicable, additional research espe-cially on the implementation of the method itself, including the current correction method,and filter inductor implementation is still required. Since high-power drives would gain fromactive du/dt, this would be beneficial for the usability of the method. In addition, as moredata on the applicability of present power switch components in the method, availability ofadvanced chip technologies in the near future, and accurate power-loss measurements areobtained, the usability of this method can finally be verified.

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Appendices

115

Appendix A

Simulation models

The simulation model used to verify the usage of the correction pulse in Chapter 4 for themitigation of the filter output voltage error caused by the load current of the electric mo-tor is presented in this appendix. The model is implemented in the MATLAB SIMULINKenvironment. Also, the simple cable reflection simulation model is shown in this appendix.

116 Simulation models

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e du

/dt f

ilter

L W

Act

ive

du/d

t filt

er L

V

Act

ive

du/d

t filt

er L

U

Act

ive

du/d

t filt

er C

W

Act

ive

du/d

t filt

er C

V

Act

ive

du/d

t filt

er C

U

<Ele

ctro

mag

netic

torq

ue T

e (N

*m)>

<Rot

or c

urre

nt ir

_a (A

)>

<Sta

tor c

urre

nt is

_a (A

)>

<Rot

or s

peed

(wm

)>

Figure A.1. Top level of the correction pulse simulation model. The modulator block forms the gatedrive signals for the output stage consisting of SIMULINK SimPowerSystems IGBT/Diode compo-nents. The output stage drives the active du/dt LC filter circuit, which is connected to the SimPower-Systems asynchronous machine model. Three-phase voltage and current measurements are carried outafter the output stage and after the active du/dt filter. The motor current measurement is used to formcorrection pulses of the right length.

117

1

Gat

eDriv

e

Hi

Lo

Cur

rent

Hi_

out

Lo_o

ut

Pha

se_W

Hi

Lo

Cur

rent

Hi_

out

Lo_o

ut

Pha

se_V

Hi

Lo

Cur

rent

Hi_

out

Lo_o

ut

Pha

se_U

Sig

nal(s

)Pul

ses

PW

M G

ener

ator

1

Cur

rent

s

Figure A.2. Top level of the modulator block. It consists of a standard, configurable SimPowerSystemsPWM Generator and three identical active du/dt edge modulator blocks to provide the output stage withthe required gate drive signals.


2

Lo_o

ut

1

Hi_

out

Sw

itch1

Sw

itch

Hi

Lo Kill

pul

ses!

Cur

rent

Hi_

out

Lo_o

ut

Sub

mod

ulat

or

Sat

urat

ion1

Sat

urat

ion

>=

Rel

atio

nal

Ope

rato

r

Hi

Lo Cur

rent

Ful

l_th

rottl

e!

Hi_

out

Lo_o

ut

Cur

rent

Cor

rect

ion

Pul

se G

ener

ator

killm

odul

atio

n

Con

stan

t1

If_pe

ak

Con

stan

t

Add

1

Add

|u|

Abs

3

Cur

rent

2 Lo1 Hi

Figure A.3. One of the active du/dt edge modulator blocks. It consists of an active du/dt edge modulatorand a current correction pulse generator. The edge modulator forms the charge and discharge sequencesaccording to the filter LC constant, as presented by the theory in Chapter 3. The current correction pulseis formed according to the theory presented at the beginning of Chapter 4. It is also possible to disablethe active du/dt modulation and pass through the plain PWM signals.

119

2

Lo_o

ut

1

Hi_

out

Sw

itch1

Sw

itch

>=

Rel

atio

nal

Ope

rato

r1

Pro

duct

3

Pro

duct

2

Pro

duct

1

Pro

duct

AN

D

Logi

cal

Ope

rato

r2

NO

T

Logi

cal

Ope

rato

r1

AN

D

Logi

cal

Ope

rato

r

1

z+ze

ros(

t2,1

)’

Dis

cret

eT

rans

fer

Fcn

3

1

z+ze

ros(

t1,1

)’

Dis

cret

eT

rans

fer

Fcn

2

1

z+ze

ros(

t2,1

)’

Dis

cret

eT

rans

fer

Fcn

1

1

z+ze

ros(

t1,1

)’

Dis

cret

eT

rans

fer

Fcn

0

Con

stan

t1

Add

1

Add

4

Cur

rent

3

Kill

pul

ses!

2 Lo1 Hi

Figure A.4. Active du/dt charge and discharge pulses are formed according to the theory. If the loadcurrent is greater than the LC filter maximum current, only the correction pulse is used, and thereforethe charge or discharge pulse is omitted, depending on the sign of the load current.


2

Lo_o

ut

1

Hi_

out

z−i

In Del

ayO

ut

Var

iabl

eIn

tege

r D

elay

1

z−i

In Del

ayO

ut

Var

iabl

eIn

tege

r D

elay

Sw

itch1

Sw

itch

>=

Rel

atio

nal

Ope

rato

r1

Pro

duct

1

Pro

duct

1

z+ze

ros(

t2,1

)’

Dis

cret

eT

rans

fer

Fcn

2

1

z+ze

ros(

t2,1

)’

Dis

cret

eT

rans

fer

Fcn

1

0

Con

stan

t2

0

Con

stan

t1

Abs

Cur

rent

Ful

l_pu

lse

t_de

lay

Cal

cula

te d

elay

Add

1

Add

|u|

Abs

4

Ful

l_th

rottl

e!

3

Cur

rent2 Lo 1 H

i

Figure A.5. Correction pulse is formed according to the theory. Depending on the sign of the loadcurrent, either the charge or discharge sequence requires a correction pulse of a varying length. If theload current exceeds the filter maximum current, the charge or discharge pulse is omitted, depending onthe direction of the current, and only a correction pulse is used. In this case, the length of the correctionpulse is half the rise time calculated from the filter LC constant.

121

1

t_de

lay

asin

Trig

onom

etric

Fun

ctio

n

Sw

itch

Sub

trac

tro

und

Rou

ndin

gF

unct

ion

Pro

duct

3

Pro

duct

2

Pro

duct

1P

rodu

ct

sqrt

Mat

hF

unct

ion1

sqrt

Mat

hF

unct

ion

Div

ide1

Div

ide

t1

Con

stan

t6

T

Con

stan

t4

stco

ef

Con

stan

t3

Udc

link

Con

stan

t2

C

Con

stan

t1

L

Con

stan

t

2

Ful

l_pu

lse

1

Abs

Cur

rent

Figure A.6. Length of the correction pulse is calculated by using Eq. (4.5). If the full-length correctionpulse is required, a precalculated constant is used.


Ste

p_ou

t

Sou

rce

Gl

Mot

or re

flect

ion

coef

ficie

ntM

otor

Vol

tage

Zs

LTI S

yste

m

Gs

Inve

rter r

efle

ctio

n co

effic

ient

Cab

leD

elay

1

Cab

leD

elay

1

Atte

nuat

ion1

1

Atte

nuat

ion

Add

1A

dd

Figure A.7. Simple cable reflection model used in the determination of cable-reflection-induced over-voltages, as presented in (Tarkiainen et al., 2002; Ström et al., 2006).

123

Appendix B

Measurement equipment

The measurement equipment used in the measurements is presented in this appendix, alongwith the measurement instrumentation accuracy.

Agilent DSO6104A oscilloscope

• Bandwidth (-3 dB): DC to 1 GHz

• Highest sampling frequency: 4 GS/s

• Length of recorded data: 4 MS/ch.

• Calculated rise time (=0.35/bandwidth): 350 ps

• Vertical resolution: 8 bits

• DC vertical gain accuracy: ±2.0 % full scale

• DC vertical offset accuracy: ±1.5 % full scale

• Horizontal resolution: 2.5 ps

• Time scale accuracy: ≤±(15+2 · (instrumentage inyears) ppm

Instrument age was approximately 1.5 years at the moment of measurements.

Tektronix P5205 high-voltage differential probe

• Bandwidth (-3 dB): DC to 100 MHz

• DC common-mode rejection ratio: >3000:1 at 500 VDC, 20-30C, <70% RH

124 Measurement equipment

• AC common-mode rejection ratio: >300:1 above 100 kHz, >10,000:1 at 60 Hz

• Maximum operating input voltage 500X differential: ±1.3 kV (DC+peak AC)

• Maximum operating input voltage 500X common mode: ±1.0 kV RMS CAT II

• Gain accuracy: ±3% at 20-30C, <70% RH

• Rise time: 3.5 ns

• Bandwidth limit: 5 MHz

• AC noise: <300 mV RMS at 500:1 probe setting

• Input impedance: 8 MΩ, 3.5 pF between inputs

• Propagation delay: 17 ns



• Horizontal resolution: 2.5 ps

• Zero adjust: ± 5 V at 500:1 probe setting

Fluke 80i-110s AC/DC Current Probe

• Useful bandwidth (-3 dB): DC to 100 kHz

• Basic accuracy (DC to 1 kHz): 50 mA to 40 A <4% of reading + 50 mA at 100 A:1 Vprobe setting

• Extended accuracy (above 1 kHz): from 1 to 5 kHz 3 %, from 5 to 20 kHz 12 %, notdefined above 20 kHz

• Phase shift: < 1

• Rise or fall time: < 4 ms

• Output noise level: typ. 3 mV peak-to-peak

Specification valid at temperature of 3C to 23C.

125

Norma D6100 Wide Band Power Analyzer

Voltage measurement

• Maximum operating input voltage: 1000 VRMS DC–400 kHz sinusoidal


• Sampling frequency: 35–70 kHz

• Measurement accuracy (45–65 Hz): ±(0.09+0.02)% (of measured value + of range)

• Measurement accuracy (100–400 kHz): ±(3.0+0.12)% (of measured value + of range)

Current measurement


• Shunt used in measurement: 10 A Wide-band shunt

• Maximum operating input current: 10 A

• Shunt resistance approx.: 10 mΩ

• Shunt amplitude error (0–100 kHz): ±0.1 %

• Sampling frequency: 35–70 kHz

• Measurement accuracy (45–65 Hz): ±(0.09+0.05)% (for AC+DC measurement below5 A)

• Measurement accuracy (100–400 kHz): ±(3.0+0.13)% (for AC+DC measurement be-low 5 A)

Nominal temperature range 18C to 28C.

126 Measurement equipment

127

Appendix C

Asynchronous machine equivalentcircuit parameters

Figure C.1. One-phase asynchronous machine equivalent circuit for a locked rotor.

Table C.1. One-phase asynchronous machine equivalent circuit parameters for various ABB motorsizes.

P [kW] Lsσ Lrσ Lm Rs Rr L′s

1.1 43.5 mH 43.5 mH 753 mH 13100 mΩ 11300 mΩ 84.7 mH2.2 18.9 mH 18.9 mH 425 mH 5450 mΩ 3940 mΩ 36.9 mH5.5 7.18 mH 7.18 mH 209 mH 1480 mΩ 1480 mΩ 14.1 mH11 3.52 mH 3.52 mH 108 mH 447 mΩ 383 mΩ 6.93 mH45 1.18 mH 1.18 mH 31.5 mH 64.3 mΩ 52.1 mΩ 2.31 mH75 652 µH 652 µH 19.3 mH 32.4 mΩ 24.8 mΩ 1.28 mH110 491 µH 491 µH 13.7 mH 18.5 mΩ 13.3 mΩ 964 µH355 147 µH 147 µH 4.71 mH 3.67 mΩ 3.67 mΩ 289 µH710 71.7 µH 71.7 µH 2.29 mH 1.54 mΩ 1.53 mΩ 141 µH

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Juha-Pekka Ström ACTIVE DU/DT FILTERING FOR VARIABLE

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