Juha-Pekka Ström - Doria

Juha-Pekka Ström 

ACTIVE DU/DT FILTERING FOR VARIABLE- 

SPEED AC DRIVES 

Acta Universitatis 

Lappeenrantaensis 

378 

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 University 

of Technology, Lappeenranta, Finland, on the 17 th of 

December, 2009, at noon.

Supervisor Professor Pertti Silventoinen 

Laboratory of Applied Electronics 

LUT Institute of Energy Technology (LUT Energia) 

Faculty of Technology 

Lappeenranta University of Technology 

Finland 

Reviewers Professor Heikki Tuusa 

Laboratory of Power Electronics 

Tampere University of Technology 

Finland 

Dr. Mika Sippola 

Nidecon Technologies Oy 

Finland 

Opponent Dr. Mika Sippola 

Nidecon Technologies Oy 

Finland 

ISBN 978-952-214-888-9 

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

ISSN 1456-4491 

Lappeenrannan teknillinen yliopisto 

Digipaino 2009

Abstract 

Juha-Pekka Ström 

Active du/dt Filtering for Variable-Speed AC Drives 

Acta Universitatis Lappeenrantaensis 378 

Dissertation, Lappeenranta University of Technology 

127 p. 

Lappeenranta 2009 

ISBN 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 in 

inverter-fed variable-speed drives. The problem has emerged since modern insulated gate 

bipolar transistors have become the standard choice as the power switch component in lowvoltage 

frequency converter drives. The overvoltage phenomenon is a consequence of the 

pulse shape of inverter output voltage and impedance mismatches between the inverter, motor 

cable, and motor. The overvoltages are harmful to the electric motor, and may cause, for 

instance, insulation failure in the motor. Several methods have been developed to mitigate 

the 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 a 

low-loss LC circuit and active control to eliminate the motor overvoltages is discussed. The 

main benefits of the method are the controllability of the output voltage du/dt within certain 

limits, considerably smaller inductances in the filter circuit resulting in a smaller physical 

component size, and excellent filtering performance when compared with typical traditional 

du/dt filtering solutions. Moreover, no additional components are required, since the active 

control of the filter circuit takes place in the process of the upper-level PWM modulation 

using the same power switches as the inverter output stage.

Further, the active du/dt method will benefit from the development of semiconductor power 

switch modules, as new technologies and materials emerge, because the method requires additional 

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 in 

the inverter as a result of the application of the method. Considerations on the application of 

the active du/dt filtering method in electric drives are presented together with experimental 

data in order to verify the potential of the method. 

Keywords: Electric drive, output filter, active filter 

UDC 681.527.7 : 681.532.52

Acknowledgments 

The research documented in this work was carried out at the LUT Institute of Energy Technology 

(LUT Energia) at Lappeenranta University of Technology (LUT) during the years 

2006–2009. The research was funded by the Finnish Graduate School of Electrical Engineering 

(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 the 

author 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 research 

topic is most sincerely acknowledged, as is also the valuable support by the Vacon Company 

during the research projects. Without you and Vacon Plc. this research would not have been 

possible. 

I would like to thank the preliminary examiners of this dissertation, Professor Heikki Tuusa 

and Dr. Mika Sippola for their valuable comments on the manuscript. I am very grateful for 

your contribution and help in improving the thesis. I would like to express my gratitude to my 

supervisor, Professor Pertti Silventoinen, and to Dr. Julius Luukko and Dr. Mikko Kuisma 

for 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-steady 

writing schedule. It has been a huge help in the writing. 

I express my deepest thanks to my collegues, Mr. Juho Tyster and Mr. Juhamatti Korhonen 

for their contribution, many ideas, and uncompromising attitude towards the active du/dt 

research. Your work for the development of the method, for the prototypes, and in the laboratory 

has really been worthy. I also thank for your help during the preparation of the 

manuscript. 

I would like to thank all the people I have worked with at the Deparment of Electrical Engineering 

here at LUT during these years; especially those who have been spending all those 

coffee breaks – sometimes even the longer ones – around the coffee table. All the shared 

experiences when we have hit the road – in the name of science, of course – have always 

been something worth remembering. It has been a pleasure, thank you!

The financial support for this work by Emil Aaltonen Foundation, Walter Ahlström Foundation, 

Lahja and Lauri Hotinen Fund and the Foundation of the Finnish Society of Electronics 

Engineers is most sincerely appreciated. 

Finally, I would like to express my deepest gratitude to my family; your support during all 

the rush, and your understanding for my absence during all those hours at work have been 

very important. This is for you Tiina, Pietu, and Neela; you are my all. 

Lappeenranta, December 1 st , 2009 

Juha-Pekka Ström

Contents 

Abstract 3 

Acknowledgments 5 

List of Symbols and Abbreviations 9 

1 Introduction 15 

1.1 Background and motivation of the work . . . . . . . . . . . . . . . . . . . . 16 

1.2 Objective of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

1.4 Scientific contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

2 Cable-reflection-induced terminal overvoltages in variable-speed drives 23 

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

mode inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

2.2 Overvoltages caused by switching transients . . . . . . . . . . . . . . . . . . 26 

2.2.1 Transmission line properties of the motor feeder cable in an electric 

drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 

2.2.2 Transmission line discontinuities . . . . . . . . . . . . . . . . . . . . 30 

2.2.3 Discontinuities in a typical inverter-fed electric drive . . . . . . . . . 31 

2.3 Critical cable length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 

2.4 Fundamental properties of second-order systems . . . . . . . . . . . . . . . . 33 

2.5 Typical output filtering solutions . . . . . . . . . . . . . . . . . . . . . . . . 35 

2.5.1 Output du/dt filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 

2.5.2 Output du/dt filters with a clamping diode circuit . . . . . . . . . . . 36 

2.5.3 Motor terminal cable terminators . . . . . . . . . . . . . . . . . . . . 37 

2.5.4 Summary on typical topologies . . . . . . . . . . . . . . . . . . . . 37 

2.5.5 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 41 

3.1 Active du/dt filtering method . . . . . . . . . . . . . . . . . . . . . . . . . . 43 

3.1.1 Active du/dt filter circuit . . . . . . . . . . . . . . . . . . . . . . . . 45 

3.1.2 Active control of the active du/dt LC filter circuit . . . . . . . . . . . 46 

3.1.3 Analysis of the active du/dt filtering method . . . . . . . . . . . . . . 49 

3.1.4 Active du/dt filter current analysis . . . . . . . . . . . . . . . . . . . 55

3.1.5 Different charging schemes for active du/dt filter circuit . . . . . . . 56 

3.1.6 Measured example of active du/dt operation . . . . . . . . . . . . . . 58 

3.2 Active du/dt filter circuit component selection . . . . . . . . . . . . . . . . . 60 

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

4 Applying active du/dt filtering to an electric drive 65 

4.1 Effects of an electric motor on the active du/dt filtering method . . . . . . . . 65 

4.1.1 Error caused by the induction motor current . . . . . . . . . . . . . . 66 

4.1.2 Effect caused by resistive losses in the circuit . . . . . . . . . . . . . 76 

4.2 Simulations of the error caused by the motor current . . . . . . . . . . . . . . 76 

4.3 Measurements and experimental results . . . . . . . . . . . . . . . . . . . . 84 

4.3.1 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 

4.3.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 87 

4.3.3 Additional switching losses caused by the application of the active 

du/dt method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 

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

5 Discussion and Conclusions 101 

5.1 Key results of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 

5.2 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 

fc 

fosc 

frequency bandwidth 

switching frequency 

oscillation frequency 

G conductance 

H system transfer function in Laplace plane 

Uout 

output voltage in Laplace plane 

I current wave 

i instantaneous current 

icm 

if 

IL 

common mode current 

filter current 

load current 

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

L inductance 

l cable length 

lc 

Lf 

LL 

Lm 

L ′ s 

Lrσ 

Lsσ 

critical cable length 

filter inductance 

load inductance 

magnetizing inductance of an asynchronous machine 

transient inductance of an asynchronous machine 

rotor leakage inductance of an asynchronous machine 

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 

Rr 

Rs 

equivalent loss resistance 

rotor resistance of an asynchronous machine 

stator resistance of an asynchronous machine 

s Laplace variable, s = σ + jω 

T period 

t time 

t1 

t2 

tcorr 

tf 

tp 

tr 

t 1/2 

charge sequence pulse turn-off time, same as t 1/2 

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

load current correction pulse length 

fall time 

cable propagation delay 

rise time 

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

u instantaneous voltage 

uA 

mains voltage phase A

uB 

ucm 

uC 

UDC 

uinv 

uout 

uU 

u ′ U 

uV 

u ′ V 

uW 

u ′ W 

mains voltage phase B 

common mode voltage 

mains voltage phase C 

DC link voltage 

inverter output voltage 

output voltage 

inverter output phase U voltage 

filtered inverter output phase U voltage 

inverter output phase V voltage 

filtered inverter output phase V voltage 

inverter output phase W voltage 

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 

XL 

capacitive reactance 

inductive reactance 

∆z differentially small increment in position 

z position 

Z0 

Zc 

ZL 

Zm 

Greek letters 

characteristic impedance 

cable impedance 

load impedance 

motor impedance 

α attenuation constant

β propagation constant 

ε permittivity 

εeff 

effective dielectric constant experienced by electromagnetic wave at a certain 

dielectric configuration at a certain frequency 

γ complex propagation constant 

Γi 

ΓL 

Γm 

inverter reflection coefficient 

load reflection coefficient 

motor reflection coefficient 

λ wave length 

µ permeability 

ωn 

resonance frequency 

ω angular frequency 

φL 

δs 

load reflection phase angle 

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

Chapter 1 

Introduction 

The consumption of energy has considerably increased in the European Union during the past 

years, despite the efforts of union-wide and national policies and programmes to increase energy 

efficiency. During the period of 1990–2005, the final electricity consumption in the 

EU-27 countries has increased by 29 %, at an annual growth rate of 1.8 %, and in Finland by 

37 %, at an annual growth rate of 2.3 % (Eurostat, 2007). In the future, even more pressure 

will be put on cutting electricity consumption. The European Union has agreed on an integrated 

energy and environmental policy, and one of the main objectives is to save 20 % of the 

projected energy consumption by the year 2020. 

In order to rise to the challenge, modern electronic power converters and control of electric 

power on the whole play a very important role in improving the energy efficiency of upcoming 

and present installations. A very typical and important application example of such a system 

is an electric drive, in which electrical power is converted into mechanical torque, or vice 

versa. To control the electromechanical conversion process, in many cases, an electronic 

power converter is essential in a modern electric drive. This is achieved by controlling the 

output 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, and 

compressor applications, and also in the control of the process in general, when compared 

with a noncontrolled drive. This is one of the main reasons why power-converter-controlled 

electric drives have established themselves in the industry during the past decades. This has 

taken place especially in the low-voltage segment (under one thousand volts) in both low- and 

high-power drives, because of the rapid development of low-voltage semiconductor power 

switches. 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 in 

the industry (Bertoldi and Atanasiu, 2007), for example in the above-mentioned, numerous 

electric drives. Even though frequency-converter-controlled electric drives have been applied 

especially in new electric drive installations, even more energy could be saved by installing a 

15

16 Introduction 

frequency converter to all suitable electric drives. In the industry, of all the installed electric 

drives, induction motor drives are widely used in the industry, and are generally considered 

very reliable. However, the switched-mode operation of the frequency converter may cause 

adverse effects in the drive, as will be discussed later in this chapter. Therefore, various 

filtering solutions have been introduced to be used in conjunction with converter drives in 

order to mitigate the effects. 

In this dissertation, a new output filtering method consisting of a passive LC filter circuit 

and active control is developed for induction motor drives. Compared with more traditional, 

completely passive approaches, the filtering performance is improved. Further, the size of 

the 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 cost 

of the actual filter. However, extra losses are introduced as a result of extra switching of the 

output stage. The method is verified by both a theoretical analysis and measurements for 

induction motor drives utilizing a modern frequency converter that uses fast switching IGBT 

power switches. The focus of this dissertation is on the development and feasibility study 

of the method, while the actual implementation on a real electric drive still requires further 

development. 

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 converter 

can as well be applied to generator and synchronous motor drives. The number of converter 

drives is also likely to increase in the future, because of the significant improvements in 

energy efficiency for example in the above-mentioned motor drives, and in decentralized and 

renewable energy production. 

Further, there is no reason why the method should not be applicable also to other types of 

machines suitable for converter drives, because the developed output filtering method is independent 

of the electric motor properties present in the drive. Only the output voltage is shaped 

to achieve a more motor-friendly behavior by decreasing the du/dt value of the transients. The 

filtering method does not interfere with the upper-level control of the drive, because the control 

of the filter circuit can be carried out as the lowest level of modulation. The developed 

method may even improve the control performance, since the motor terminal voltage, and 

therefore motor flux, can now be accurately predicted, because the harmful cable oscillation 

is 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) applying 

pulse width modulation (PWM) has established as the frequency converter in low-voltage 

AC drives. As a result of the remarkable advancements in the semiconductor power switch 

device generations, the switching losses have reduced significantly. This has made it possible 

for example to reduce the sizes of cooling profiles and device enclosures and to use higher 

switching 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 the 

inverter output stage and the iron losses caused by eddy current losses in the motor increase 

as a function of switching frequency (Mohan et al., 2003). 

The basic operating principle of a voltage source inverter using pulse width modulation is 

presented in Figure 1.1. 

Voltage [V] 

Voltage [V] 

500 

0 

−500 

500 

0 

−500 

0 0.005 0.01 

Time [s] 

a) 

0.015 0.02 

0 0.005 0.01 

Time [s] 

b) 

0.015 0.02 

Figure 1.1. Normal sine wave, 50 Hz, 400 V, three-phase, phase-to-phase AC voltages available from 

the standard European grid are shown in Figure 1.1a. In Figure 1.1b, the same voltages are constructed 

from rectified AC voltage applying pulse width modulation (PWM). The modulated voltage consists 

of switched voltage pulses, which are modulated according to the reference, which is in this case the 

50 Hz three-phase sine voltages. 

Figure 1.1a shows the standard 50 Hz, three-phase sine AC voltages available from the standard 

European grid. These are the voltage waveforms for which most electric motors are 

designed. However, in an electric drive using a power converter, the output voltage waveform 

is quite different from the sine wave, as shown in Figure 1.1b. Because of the requirement to 

be able to control the output frequency and voltage, the electrical power available from the 

grid has to be constructed by using an inverter to produce the desired output voltage properties. 

In the most common case, the output voltage is produced using pulse width modulation 

from rectified AC voltage, in which the width of the voltage pulse is modulated according to 

the reference voltage. Therefore, the output voltage consists of steep rising and falling edges 

of the DC voltage, instead of true sine wave behavior. This has a remarkable effect on the 

frequency content of the output voltage. The properties of the output voltage edges depend 

on the properties of the power switches used in the output stage of the inverter.


Although the IGBT has clear advantages when set against previous generations of semiconductor 

power switches, the remarkable advances in the switching times also manifest certain 

drawbacks far more clearly than the older generations of power switches: The rise and fall 

switching times of an IGBT are very short, at present in the order of tens of nanoseconds 

at best, and therefore the rate of change, namely du/dt, in the inverter output voltage pulse 

is very high. Hence, the output voltage contains a broad range of frequencies, including a 

lot of high-frequency components (Skibinski et al., 1999). In the industry, a typical length 

of the interconnecting cable is tens or hundreds of meters, which is substantial compared 

with 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 and 

electromagnetic 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 is 

typically applied to the output voltage to narrow the frequency spectrum of the motor voltage 

below the natural oscillation frequency of the motor cable. 

These effects have been mitigated by using many different passive filtering topologies, which 

are typically somewhat large in size and therefore expensive, but not very effective in all 

respects. The active du/dt filtering method presented in this dissertation is based on a passive 

LC filter circuit and active control of the filter using pulse width modulation: each transient 

or edge in the fundamental modulation of the inverter has to be supplemented with additional 

edge modulation to provide control for the filter circuit to produce output voltage of the 

desired shape in a controlled way. Both the guidelines of pulse width modulation and the 

behavior of a passive LC circuit are commonly known and documented, whereas combining 

these 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 out 

from a different point of view, for example EMI reduction, and the switching transition speed 

of 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 in 

this 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 in 

Chapter 3, significant switching losses would be generated, and therefore the methods are not 

beneficial 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 electric 

drives, in terms of both electrical performance and size. In this study, the goal is achieved 

by active control of the filter circuit, which is based on fast control of the circuit and fast 

switching properties of the modern semiconductor power switches. This results in better 

electrical 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 in 

terms 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 is 

the 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 more 

efficient 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 the 

components are and the less switching loss is generated, the more beneficial it will be for the 

developed output filtering method. 

1.3 Outline of the thesis 

This doctoral dissertation studies output filtering needs arising from the switching-mode operation 

of a motor driven with a frequency converter. This is mainly a result of the advancements 

in semiconductor power switch transition times between the conducting and nonconducting 

states. Existing output filtering solutions and the problems caused by the fast transitions 

are discussed, and a new output filtering method to be used in a frequency converter 

applying fast power switches is introduced. The theoretical background for the method is 

developed, and the feasibility of the method is verified by implementing it in a real induction 

motor drive, which consists of a standard industrial frequency converter with a custom-built 

control 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 in 

frequency-converter-fed electric drives as a result of the development of the power 

switch components. Common solutions to the problems presented in the literature are 

also discussed in brief. 

Chapter 3 discusses output filtering of a frequency-converter-fed electric drive and introduces 

issues to be taken into account in the design of output filtering for a certain 

electric motor drive. The developed active output filtering method is presented, and 

the theory for application of the method is provided. Design considerations for the 

implementation of the method are presented. 

Chapter 4 introduces issues related to the developed active output filtering method in an 

actual electric drive. Guidelines are given for solving these issues, when the output 

filtering method is applied to a drive. Measurements using a prototype equipment are 

presented. The objective of the measurements is to show that the theory developed is 

feasible and the narrow pulses required by the method are in fact achievable in standard 

industrial electric drive hardware. Considerations especially for the selection of 

components 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.


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 LC 

circuit and a specific control of the circuit in order to produce voltage slopes of designed 

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 filtering 

method in an electric drive. 

• Development of guidelines for the filter component value selection and the basis for the 

corresponding 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 the 

motor present in the drive. 

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

experimental measurements. 

The author has published research results related to the subjects covered in the dissertation as 

a co-author in the following publications: 

1) J.-P. Ström, J. Tyster, J. Korhonen, K. Rauma, H. Sarén and P. Silventoinen, "Active 

du/dt Filtering for Variable Speed AC drives," in 13 th European Conference on Power 

Electronics 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 of 

an Inverter Output Active du/dt Filtering Method", in The 35 th Annual Conference of 

the 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 minimum 

gate drive pulse," in 13 th European Conference on Power Electronics and Applications, 

EPE 2009, 8–10 September, Barcelona, Spain, 2009, (Tyster et al., 2009). 

4) J.-P. Ström, H. Eskelinen and P. Silventoinen, "Manufacturability and Assembly Aspects 

of an Advanced Cable Gland Design for an Electrical Motor Drive," Intl. Journal of 

Design Engineering, Vol. 1, Issue 4, 2009. 

5) J.-P. Ström, M. Koski, H. Muittari and P. Silventoinen, "Analysis and filtering of common 

mode and shaft voltages in adjustable speed AC drives," in 12 th European Conference 

on 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 PWM 

Variable Speed AC Drives - Modeling and Analysis," in Nordic Workshop on Power 

and 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 research 

for 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 first 

authors of the corresponding publications. 

Background research for publication 4 was carried out by the authors. The research on the 

manufacturability and assembly aspects in publication 4 was carried out by Dr. H. Eskelinen. 

The cable gland prototypes were constructed by the Department of Mechanical Engineering 

at 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 prototype 

construction and the measurements were carried out by J.-P. Ström and Ms. H. Muittari. For 

publication 6, J.-P. Ström was in the major role in the background research, measurements 

and writing, with the help of the co-authors. 

The author is designated as a co-inventor in the following patents or patent applications considering 

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 filed 

May 19 2008, (Sarén et al., 2008a). 

US Patent application 20080316780 "Limitation of voltage pulse". Application filed Dec 

25 2008, (Sarén et al., 2008b).

22 Introduction

Chapter 2 

Cable-reflection-induced terminal 

overvoltages in variable-speed drives 

Along with the development of new power semiconductor switching components and identification 

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 publications 

can be found considering both the phenomenon itself and various means to mitigate 

its 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 of 

variable voltage and frequency, and in a very typical case, this is implemented by using a 

switching-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 into 

a DC link capacitor by using a rectifying bridge, and the DC link capacitor acts as the lowimpedance 

voltage source for the inverter bridge. 

The AC voltage is formed from the DC link voltage by the inverter bridge as a series of 

pulses, which have a constant amplitude – neglecting the DC link fluctuations – and a varying 

width, the output of the phases being connected either to the positive or negative DC link 

rail; therefore, the phase-to-phase voltage between two phases can be either the positive or 

negative DC bus voltage. A schematic of a main circuit of a frequency converter is shown in 

Figure 2.1. Further, a possible output filter connection is shown along with a typical motor 

common-mode current path. 

In order to keep the losses produced in the switching operation of a single power semiconductor 

component in the inverter bridge to a minimum, the transition time between the on- and 

off-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 

23

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

K ) 

K * 

K + 

+ , + 1 

, + 

, + 

K 7 

7 8 9 

K 8 K 9 

 

+ 

K JF K J BEJA H 

EB = F F EA @ 

Figure 2.1. Frequency converter main circuit. Power from the grid is rectified into the DC link. The 

motor AC voltage of variable frequency and voltage is generated from the DC link voltage using the 

three-phase inverter bridge shown. A possible output du/dt filter, and a typical motor common-mode 

current path are also presented. 

of the component and a possible current flowing through the component will generate power 

loss (heat) during the transition according to the following equation 

P = 1 

 

T 

K 7 

K 8 

K 9 

uidt. (2.1) 

On this account, the transitions in the voltage pulses generated by the DC to AC converter in 

the adjustable speed drive are kept as short as possible, leading to the fact that the steepness 

of the edges of the voltage pulses is high. In an inverter power switch component generally 

applied, that is, the insulated gate bipolar transistor (IGBT), the transition time between the 

states is at fastest in the order of tens of nanoseconds, as can be seen for instance in the 

next section. In addition to the benefits presented above, the fast switching voltage transient 

and thereby the output voltage of the inverter contains a lot of high-frequency components 

as a byproduct of the switching mode operation. The frequency components beside the base 

frequency of the electric drive are by definition unnecessary and even harmful to the operation 

of the drive, but are not irrelevant for the operation of the drive. This is the key difference 

between the voltage waveforms in a traditional direct-on-line (DOL) and VSI-converter-fed 

drives. 

The switching transients occuring in the inverter are – and have to be – fast, when compared 

with the fundamental and switching frequencies. Therefore, the output voltage waveform 

contains in addition to the fundamental base frequency, switching frequency, and their harmonics, 

high-frequency components resulting from the steep voltage pulse edges extending 

up to the megahertz range (Skibinski et al., 1999). If the speed of propagation in the motor 

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, whereas 

the wavelength of a signal of 1 MHz is only 300 meters. 

K + 

 

E +

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

inverter 25 

Hence, the lengths of a typical motor cable, which are in the order of tens to a few hundred 

meters, are substantial compared with the high-frequency components present in the inverter 

output voltage. Therefore, each switching in the inverter output stage induces a traveling 

wave into the motor cable, and the transmission line theory must be applied in the analysis of 

the behavior of the traveling waves in the motor cable (Persson, 1992); see Chapter 4 for measurements 

of the propagation speed for the MCMK power cables used in the measurements 

of this dissertation. 

This also sets special requirements for the motor cabling and the insulations in the electric 

motor, because the motor and the motor cable are typically designed for low operating frequencies, 

and also the effects caused by the high frequency content in the output voltage 

must be taken into account in a converter drive, for example the overvoltages caused by wave 

reflections, as will be discussed later in this chapter. 

2.1 Frequency spectrum of the output voltage of a typical 

three-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 varying 

width, and the frequency spectrum of the signal can be approximated by means of Fourier 

analysis (Zhong et al., 1998). An example of an inverter output voltage and corresponding 

differential-mode voltage spectrum presented in (Skibinski et al., 1999) are shown in Figures 

2.2a and 2.2b. 

7 , + 

7 F D = I A 8 

J H 

7 F D = I A @ * 

 

 

6 B ? 

J I B ? B * 9 B 0 

= > 

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 and 

the switching frequency fc. According to (Zhong et al., 1998), the theoretical spectrum is 

flat 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 of 

the inverter output voltage waveform (Skibinski et al., 1999): 

fBW ≈ 1 

. (2.2) 

πtr 

When IGBT power switches with typical transition times between 50 and 400 ns (Saunders 

et al., 1996; IEC, 2007) are employed in the inverter output stage, the frequency spectrum of 

the output voltage extends up to the radio frequency region, from hundreds of kilohertz up 

to several megahertz. As an example, the rise and fall times and the calculated bandwidth 

estimate using (2.2) for some Semikron Semitrans packaged IGBT modules are presented in 

Table 2.1. These modules are selected as an example, because they fit in the Vacon NXP series 

frame size 6 industrial frequency converter, which is also used in the prototype equipment and 

tests. 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 of 

some Semikron Semitrans packaged IGBT modules, as stated by the manufacturer 

Module Typical Typical Total switching Bandwidth 

type rise time fall time energy estimate 

Semikron SKM 

tr tf @100 A Eq. (2.2) 

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 (Skibinski 

et al., 1999), in which the spectral width was found to reach up to the megahertz range. In 

the 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 of 

meters 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 is 

converter fed. In this case, the voltages and currents are not only functions of time, but have 

to be regarded also as functions of position along the motor cable. This is because the inverter 

output voltage contains frequency components that have wavelengths in the order of the motor 

cable length, as pointed out above. As a consequence, voltage and current oscillations may 

occur along the power cable. Providing that the physical length of the motor cable length l 

is less than λ/16 of a frequency component in the output voltage, the voltages and currents 

can be assumed to be constant along the transmission line, and hence no transmission line 

analysis is required, nor cable oscillations or overvoltage caused by it have to be taken into 

account. λ is the wave length of a certain frequency in the cable. Equation (2.2) can be used 

to roughly approximate the spectral bandwidth of the inverter output voltage. 

The transmission line theory, see (Heaviside, 1893, 1899), which describes the propagation 

of an electromagnetic wave along a transmission line, has been succesfully applied to the 

analysis of cable oscillations and voltage reflections, as pointed out above. In general, the 

motor cable consists of several phase conductors and a ground conductor, since the threephase 

AC system is used in most installations. Therefore, the motor cable is generally a 

multiconductor transmission line. 

However, the motor cable is typically presented as a two-wire transmission line model, because 

the analysis is simplified and the use of multiple phase transmission line models is 

avoided. In addition, since the cable oscillation phenomenon takes place at each transition of 

the 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 one 

phase can be considered at a time, and the other phases have to be assumed stationary and in 

a steady state during the analysis. 

In the two-wire transmission line model, the electromagnetic wave is assumed to propagate 

in the pure transverse electromagnetic (TEM) mode. However, in an actual motor cable, the 

mode 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 of 

the 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 electric 

drive 

The electrical length of the transmission line depends on the phase velocity (propagation velocity) 

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 fundamental 

equation: 

νp = λ f . (2.3)


The equivalent circuit of a two-wire transmission line of an infinitesimal length ∆z is presented 

in Figure 2.3, which consists of the distributed parameters inductance, capacitance, 

resistance, and conductance per unit length of the transmission line. These parameters describe 

the properties of the transmission line and depend on the geometry and the dielectrics 

used in the physical conductor. Series inductance describes the self-inductivity of the conductor, 

capacitance refers to the natural capacitance in the proximity of the conductors, resistance 

represents 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 caused 

by the polarization of dipoles in the insulating material. The inductance and capacitance represent 

delay, whereas resistance and conductance express losses (or attenuation) along the 

transmission line. A transmission line of finite length can be thought to consist of a group of 

elements, as presented in Figure 2.3, connected in series. 

E J 

4 , , 

 

 

L J / , + , L , J 

 

 

, 

E , J 

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 unit 

length. The voltages v and currents i indicated in the figure describe the voltages and currents in the 

transmission 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 vary 

not only as a function of time, but also as a function of position z, according to the telegrapher’s 

equations (Heaviside, 1899). The voltages and currents consist of a superposition of 

incident and reflected waves. Therefore, standing waves may occur on the line. The properties 

of the transmission line are defined by the complex propagation constant γ and the 

characteristic 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 the 

damping and the wavelength as a function of the length of the transmission line with the 

distributed circuit parameters resistance R, inductance L, conductance G and capacitance C 

per unit length. The characteristic impedance of a transmission line is defined as (Collin, 

1992) p. 88


Z0 = 

 

R + jωL 

. (2.5) 

G + jωC 

If the transmission line is assumed lossless or the losses are negligible, the characteristic 

impedance can be approximated with the following equation: 

Z0 = 

 

L 

. (2.6) 

C 

The characteristic impedance defines the relation between the amplitudes of the corresponding 

voltage and the current waves on the transmission line, thus 

Z0(z) = 

V (z) 

, (2.7) 

I(z) 

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 frequency 

dependent. 

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 propagation 

velocity of the wave depends only on the properties of the dielectric materials, if the currents 

propagate only along the surface of the conductor. However, because of the finite conductivity 

of the conductor, the currents flow also inside the conductive material. The current 

distribution on the cross-section of the conductor at a certain frequency is described by skin 

depth, which depends on the angular frequency ω, permeability µ, and conductivity σ as 

follows (Wheeler, 1942) 

δs = 

 

2 

. (2.9) 

ωµσ 

The skin-effect also increases the resistive losses, because the current density near the surface 

of the conductor increases, increasing the ac resistance of the conductor. In addition, the 

proximity 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 discontinuity, 

part of the incident power passes through the interface while part reflects back to the 

original 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 in 

the characteristic impedance and therefore a reflection. Typically, a change in the characteristic 

impedance is a consequence of a mismatched load impedance at the end of a transmission 

line, 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 engineering 

cause a significant change in the geometry of the propagation path and therefore in the 

characteristic impedance. 

The relationship between the incident wave and the reflected wave depends on the difference 

of the characteristic impedances at the discontinuity: the greater the difference, the more of 

the incident wave is reflected. The reflection coefficient is defined at the impedance mismatch 

as follows (Heaviside, 1899), p. 375: 

ΓL = 

V − 

V + = Z0 − ZL 

= |ΓL| · e 

Z0 + ZL 

jφL , (2.10) 

where V + is the incident wave, V − is the reflected wave at the discontinuity, Z0 is the characteristic 

impedance of the transmission line, and ZL is the loading impedance seen at the 

discontinuity in the direction of the incident wave. |ΓL| defines the magnitude of the reflected 

wave and φL defines the phase angle shift of the reflected wave with respect to the incident 

wave at the mismatch point. If the transmission line is perfectly matched, ZL = Z0, no reflection 

takes place, as can be seen from the above equation. If the transmission line is terminated 

to a short circuit (ZL = 0) or an open circuit (ZL = ∞), all the incident wave is reflected at 

a phase angle of 0 or 180 degrees, correspondingly. During the transient, the electric motor 

resembles an open circuit at the end of the motor cable, leading to an in-phase reflection and 

overvoltage 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 applying 

the reflection coefficient as follows: 

V (z) = V + 0 e jγz − 

1 +ΓLe 

j2γz 

(2.11) 

I(z) = V + 0 

e 

Z0 

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 output 

voltage pulses, the interconnecting power cable length, the motor characteristic impedance, 

and the impedance mismatch between the characteristic impedances of the cable and the 

motor. 

As the inverter output stage is operated, switching transient injects an incident voltage wave in 

the interconnecting power cable that propagates toward the electric motor. In the inverter-fed 

electric drive, there are at least two significant impedance mismatches between the inverter 

output stage and the motor: the interfaces between the inverter and the motor cable and 

between the cable and the motor, if the cable is solid and there are no additional connections 

along the cable. Because of the geometry and the construction, the characteristic impedances 

of 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 the 

voltage reflection coefficient Γm at the motor terminal: 

Γm = Zm − Zc 

, (2.13) 

Zm + Zc 

where Zm is the motor characteristic impedance and Zc is the characteristic impedance of the 

interconnecting power cable. The maximum peak voltage at the motor terminal expressed 

using (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 drive 

output, UDC, and the motor reflection coefficient is Γm. Because the impedance of the motor 

resembles an open end compared with a typical cable impedance, the incident wave is 

reflected back in-phase from the interface of the motor and the cable. Therefore, the voltage 

reflection can cause overvoltages up to twice the bus voltage at the motor terminal. The 

overvoltage may degrade the insulation and potentially produce destructive stress on the insulation 

system of the motor. Typically, the voltage is not evenly distributed in the stator 

winding; a major part of the voltage is across the first few coil rounds before the voltage 

distribution is balanced in the winding. Furthermore, the faster the transient, the more of the 

voltage occurs across the first coil round, which adds to the stress caused to the insulation of 

the 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 the 

size of the motor increases, the reflection coeffient decreases, for example because of larger 

stray capacitances, and the theoretical maximum value of the overvoltage decreases from 

the double voltage. Typically, in the literature, the reflection coefficient is reported to vary 

between 0.65 and 0.95, which causes a theoretical overvoltage of 1.65 to 1.95 times the DC 

link voltage. Typical motor reflection coefficients for various motor sizes are presented for 

example in (Saunders et al., 1996) and (Skibinski et al., 1998). However, it has to be taken 

into account that the motor impedance, and the load reflection coefficient, similarly as other 

transmission line parameters, are frequency dependent. 

As the incident voltage wave is reflected back from the motor terminal, the reflected wave 

starts to propagate back towards the frequency converter. A new reflection takes place at 

the interface of the motor cable and the inverter, the magnitude of which depends on the 

reflection 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 cable 

can be determined by measurements as presented in (Ahola, 2003). The impedance of the 

output stage depends on the state of the switches; measurements of the inverter output stage 

impedances 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 in 

the literature, because the DC link capacitor and freewheeling diodes are assumed to act as a 

short 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 reflecting 

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 depends 

on the propagation velocity of the wave and the length of the motor cable. The oscillation 

decays mainly as a result of the high-frequency attenuation of the cable, and also if the motor 

reflection 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 in 

the cable and the cable length. Therefore, the frequency of the cable oscillation can be solved 

as follows (Skibinski et al., 1997): 

fosc = 1 

4tp 

= νp 

, (2.15) 

4l 

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

the cable. 

The cable oscillation frequency and decaying time are also important factors in the origin of 

overvoltages that are greater than the theoretical maximum of twice the voltage for a single 

transition discussed so far. If a new transient occurs before the oscillation caused by the previous 

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 link 

voltage is called polarity reversal, where two of the inverter phases are switched from opposite 

states at the same time. 

The key in reducing the overvoltage at the motor end is to slow down the rising and falling 

times 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 switching 

time can be prolonged by slowing down the switching operation of the semiconductor power 

switch, as previously mentioned, or by filtering. Slowing down the power switch generates 

excessive switching losses, and therefore it is not an optimal solution. Different filtering 

solutions will be discussed in more detail later in this chapter. Further, a conventional LC 

filter can be used to produce rising and falling slopes of desired length, if the active control is 

used, 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 current 

waves by the motor cable. The rise time of the injected voltage affects the maximum value of 

the overvoltage. If the propagation delay is smaller than half the rise time, the voltage wave 

reflected from the inverter end reduces the overvoltage at the motor end before it has reached 

its 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 key 

in mitigating the motor-end overvoltage is to increase the critical cable length by decreasing 

the du/dt in the voltage injected to the cable. The critical cable length is defined as 

lc = tr 

2 · νp, (2.16) 

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

cable. 

2.4 Fundamental properties of second-order systems 

Systems that can be described by second-order differential equations are called second-order 

systems, such as most output filtering circuits are. The differential equation of the secondorder 

system in the general form is 

A f (t) = d2 y 

dt 

2 + 2ζ ωn 

dy 

dt + ω2 n 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 the 

natural 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 the 

damping factor is, the slower the system responds to the input. A damping factor below 

the critical value provides a faster system response, but in this case there is overshoot in the 

output, the amount of which depends on how close the damping factor is to zero. If the 

damping factor is zero, the oscillation at the system output does not decay, and the amount of 

overshoot is equal to the magnitude of the input step. Hence, an undamped system resonates 

between zero and two times the input step at the natural frequency of the system. The step 

responses of second-order systems with various damping factors are presented in Figure 2.4. 

2 

1.8 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

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

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

resonance frequency ωn. 

Typically, in a passive output filter the inductance and capacitance define the resonance frequency 

of the filter. In addition to these, the damping factor is defined by the resistance of 

the circuit. In a passive filter design, and in filter design on the whole, the step response of 

the filter circuit is an important design consideration, in addition to the frequency response of 

the system. 

ζ=0 

ζ=0.2 

ζ=0.5 

ζ=1 

ζ=2 

ζ=5

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 motor 

impulse 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 of 

high du/dt are coupled to the motor as a result of the operating principle of the two-level 

inverter, see for example (Skibinski et al., 1999). These phase-to-ground common-mode 

voltages have been shown to cause a high-frequency current in the grounding system of the 

drive and are a major cause of shaft voltages, which are among the factors causing bearing 

currents (Erdman et al., 1996; von Jouanne et al., 1998). 

The overvoltages and adverse effects caused by voltage reflections in electrically long cables 

have been mitigated by applying various different filtering solutions: output reactors, output 

filters, 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 which 

the du/dt of the output voltage is decreased. A very typical du/dt filter, see Figure 2.5, consists 

of a series inductance and a parallel capacitance, and the losses in the circuit are tuned in order 

to obtain the desired transient output response for the drive (Finlayson, 1998). This kind of 

a system consisting of inductance, capacitance, and resistance is generally a second order 

system. 

+ , + 1 

, + 

, + 

K 7 

K 8 K 9 

 

+ 

+ BEJA H 

Figure 2.5. Schematic of a conventional du/dt output filter. Damping resistors or equivalent losses in 

the inductors are not illustrated in the figure. 

However, since a second order system itself is a resonance circuit, it easily becomes a source 

of overvoltage and oscillation instead of the inverter-power cable electric motor resonator, if 

not sufficiently damped. The du/dt is decreased according to the LC constant value, but in 

order to obtain a good transient response, damping is necessary, which means losses. In the 

K 7 

K 8 

K 9


design procedure of the passive du/dt, the most essential design parameters are the resonanve 

frequency ωn and the damping factor ζ . In addition to the transient response, the frequency 

plane response is important. At the cable oscillation frequencies the filter is designed for, the 

filter attenuation should be maximized. The du/dt filter design is a compromise between these 

key 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. Designs 

with resonance frequencies close to possible switching frequencies should be avoided, since 

a strong filter resonance is induced. 

Output du/dt filters based on inductors and capacitors have been introduced for example 

in (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), (von 

Jouanne and Enjeti, 1997), (von Jouanne et al., 1996b), and (Steinke, 1999), and sinewave 

filters 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 to 

the positive and negative DC link voltage, see Figure 2.6. The clamping diodes are effective 

in preventing the filter oscillation, but they provide an alternative path for the reactive motor 

current, 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 LC 

overshoot is removed by the clamping circuit. However, current spikes through the diodes are 

introduced along with losses. The current amplitude of the current spikes can be decreased by 

adding resistance between the clamping circuit and the DC link, but at the expense of losses. 

+ , + 1 

, + 

, + 

K 7 

K 8 K 9 

 

+ 

+ BEJA H = @ 

? = F E C ? EH? K EJ 

Figure 2.6. Schematic of a conventional du/dt output filter with clamping diodes. The natural LC 

overshoot 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). 

K 7 

K 8 

K 9

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; Chen 

and Xu, 1998; Moreira et al., 2005). These are based on the fact that if the transmission line 

is 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 a 

capacitive coupling interface. The actual terminating impedances are the terminator and the 

electric motor in parallel. However, the impedance of the motor is assumed to be far higher 

than the cable characteric impedance, and therefore the effect of the motor on the terminating 

impedance can be neglected (Skibinski, 1996), which is also a typical case in reality. The 

cable terminator, see Figure 2.7, is very effective in limiting the overvoltage in the motor 

terminal, but it does not limit the du/dt value, creates power loss, since resistors in the order 

of the cable characteristic impedance are used (in the order of 10 2 Ω), even if capacitive 

coupling is used. 

+ , + 1 

, + 

, + 

K 7 

K 8 K 9 

+ 

4 

4 + BEJA H 

Figure 2.7. Schematic of a cable terminator. The motor cable is matched to the characteristic impedance 

using a terminator via a capacitive coupling interface. The purpose of the interface is to reduce losses 

in the circuit. 

2.5.4 Summary on typical topologies 

Drawbacks of the typical filtering solutions are often their large physical size, resulting in difficulties 

in the integrability. As can be seen from the well-known equation for the resonance 

frequency of a second-order system, the lower is the resonance frequency, the greater the 

component values are. A more thorough summary of the commonly used filtering solutions 

in frequency-converter-fed electric drives is provided for example in (Moreira et al., 2005). 

K 7 

K 8 

K 9


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 techniques 

have been studied extensively, and the basic mechanism of the phenomenon is quite well 

known 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 has 

also been discussed in the literature, for example in (von Jouanne and Enjeti, 1997), (von 

Jouanne 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 and 

Finke, 2001). On the detrimental effects of a switching-mode inverter on the electric motor 

itself 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 overvoltages 

caused by the voltage reflection on the insulation system of the motor, and bearing currents 

caused 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 winding 

insulations, and therefore it is a common practice to use filtering between the frequency 

converter and the motor, especially when the supply voltage is higher than 400 V. This is 

because the maximum phase-to-phase voltage as a result of cable reflection is double the DC 

link voltage, and the higher is the supplying grid voltage, the higher is the maximum voltage 

at the motor terminal. As an example, the maximum motor phase-to-phase potential peak is 

approximately 1 kV for a 400 V drive, but almost 2 kV for a 690 V drive. Therefore, the 

problems 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 when 

the du/dt value of the voltage pulse increases, since the insulating properties of the insulation 

system become more vulnerable to dielectric breakdown as the rise time decreases (Saunders 

et al., 1996), (IEC, 2007). 

The output voltage rise and fall times in a frequency converter applying IGBT semiconductors 

in 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 to 

minimize the switching losses. The switching operation produces overvoltage in the motor 

terminals, and this operation can reduce the life of the motor insulation system, if the voltage 

strength 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 times 

of the voltage pulses depend on the switching properties of the semiconductor power devices 

used, but eventually on the gate driver circuit and snubber circuits. 

Further, if the pulse width matches the propagation delay between the converter and the motor, 

an overvoltage higher than twice the voltage may be generated, in addition to the double 

pulsing and polarity reversal already mentioned. Cablings consisting of several cable sections 

can also lead to overvoltage problems, because at each switching instant, the voltage reflection 

will eventually take place at each point of impedance discontinuity, and the system will 

thereby consist of a large number of incident and reflected waves oscillating in the cabling. If 

this 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 measures 

are 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 cabling 

is proposed in order to increase high-frequency loss in the cable to attenuate the cable oscillation. 

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 is 

not feasible either. The use of a multilevel converter has also been suggested, but it seldom is 

a likely solution to overvoltages in low-voltage drives. 

The oscillating voltage as a result of the wave reflections cause stress on the main insulation 

of the windings, both on the phase-to-phase and phase-to-ground insulations. Furthermore, 

voltage pulses of a fast rise time (

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

Chapter 3 

Output filtering in a 

frequency-converter-fed electric 

drive 

In this chapter, considerations for the design of output filtering in an electric drive are presented. 

Furthermore, the theoretical basis for a new active du/dt filtering method suitable 

for the output filtering of an electric drive is introduced. As discussed earlier in the previous 

chapters, the advancements in the switching times of semiconductor power switches, especially 

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 the 

output voltage pulses in some cases. 

In terms of output filtering analysis, the frequency-converter drive can be considered as a system 

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 is 

presented 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 inverter 

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 presented 

in the previous chapter. The system forms a resonating structure that has a natural resonance 

frequency depending on the velocity of propagation in the cable and the cable length. In terms 

of high frequencies, the inverter, motor cable, and the motor system form a transmission line 

resonator. 

The propagation speed in the medium depends on the dielectric properties of the motor cable. 

When a pulse-shaped stimulus is fed to the system, the system resonates at its natural 

frequency, which in this case is typically called the cable resonance or oscillation frequency. 

41

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

) 

* 

+ 

/ H E@ 

, + 

, + 

4 A ? J EBEA H , + E 

. H A G K A ? O ? L A H J A H 

9 

7 

8 

) 

B 

1 L A H J A H . EJ A H E C J H + = > A J H 

Figure 3.1. Electric drive presented as a block diagram from the viewpoint of analyzing output filtering. 

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 filter 

circuit 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 the 

impedance mismatches in the system, the resonance effect is strong. In the output filter design 

and the frequency domain analysis, the cable oscillation frequency range is an important 

design parameter. 

As presented above, the frequency content in the inverter output extends to the megahertz region, 

as typical cable oscillation frequencies are in the order of tens of kilohertz to hundreds 

of 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 oscillation 

frequency must be filtered out, but the fundamental operation of the drive and power transmission 

from the converter to the motor may not be interfered with. In addition, the cable 

oscillation frequency increases as the cable length decreases, and the filter cut-off frequency 

must 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 enough 

to increase the cable oscillation frequency to a region where the inverter output voltage contains 

little stimulus or no stimulus at all at the cable resonance frequency, the oscillation and 

overvoltage at the motor terminal can be eliminated. Moreover, limiting the frequency spectrum 

of the inverter output voltage to contain no stimulus at the cable resonance frequency 

will provide the same result. Effectively, this corresponds to lowpass filtering in the inverter 

output. Eventually, from a practical point of view, it is not feasible to replace the IGBT devices 

by older, slower power switches in a modern low-voltage AC drive. Furthermore, in an 

industrial envinronment, the motor cable length cannot be selected arbitrarily, but it is limited 

by the installation options of the electric drive. 

Hence, in order to succesfully prevent cable oscillation and motor terminal overvoltage, the 

most reasonable solution is efficient lowpass filtering, which is analogous to slowing down 

the switching operation and limiting the output voltage spectrum below the cable oscillation 

frequency. 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 be 

designed 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 is 

also preferred for the filter topology. An ideal frequency response for output filtering is illustrated 

in Figure 3.2. For example, a digital FIR filter, whose impulse response is a Gaussian 

function, has a step and frequency plane response similar to the Figure 3.2. However, as for 

other FIR filters, there is no analog representation of the filter. 

7 

J H 

J 

= > 

Figure 3.2. a) Time domain step response and b) the frequency response magnitude of a filter, which 

would be ideal for output filtering. 

A frequency response illustration is provided in Figure 3.3, which shows the shape of the 

frequency content of a linear ramp as an example of a typical approximation of an inverter 

output voltage shape. For instance, the linear ramp is the response of a system, the coefficients 

of which are a discrete-time rectangular pulse, such as a moving-average filter. The frequency 

response 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 transition 

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 to 

place the zeros at the cable oscillation frequency, if it is known. If the voltage fed to the 

cable contains stimulus at the cable resonance frequency, oscillation is induced to the extent 

provided by the amplitude of the cable oscillation frequency component present in the output 

voltage. In the context of cable resonances, the first minimum response is achieved, when the 

ramp 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 controlled 

output filtering method developed. Active du/dt is a method that is capable of forming rising 

and falling voltage slopes of desired rise and fall times. This operation is achieved by 

selecting the filter component values appropriately and by active control of the filter. The 

) 

B I ? 

B


7 

J H 

J 

= > 

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 slope 

are sinusoidal. The basic idea in the active control is to succesfully charge and discharge the 

capacitor in the filter, and handle the transient response of the LC filter circuit. The capacitor 

on the filter circuit is considered to act as a voltage source towards the load during the 

transients. The function of the reactor in the filter is to limit the charging and discharging 

current of the capacitor, and eventually the peak current of the filter serial resonance circuit 

seen in the inverter output stage. Moreover, the charging and discharging sequences have 

to be accurately timed so that the natural resonance of the LC circuit at the filter resonance 

frequency is avoided. 

In a passive output filter, the reduction in the filter output du/dt and the filtering of the cable 

resonance frequency depend on the transition frequency, which has to be low enough in order 

for 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 filter 

components. One of the benefits of the active du/dt method is that the active du/dt filter component 

values are selected based on the voltage slope transition period, and also on the filter 

peak current specification, which results in far smaller inductance values than in a conventional 

passive output filtering approach. The active du/dt LC filter is not solely responsible 

for the filtering of the inverter voltage, but the filtering result is a combined effect of the LC 

circuit 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 AC 

drive improves, because the motor flux estimation accuracy is improved. The active du/dt 

voltage causes, if correctly designed, no motor overvoltage. Therefore, the motor flux can 

be estimated more accurately in the motor control of the frequency converter. Because of 

the cable oscillation, the motor terminal voltage differs considerably from the inverter output 

voltage, which affects the performance of the control. A correct filter design attenuates the 

cable resonance and very effectively removes terminal overvoltages. 

In the analysis presented in this chapter, the filter (or more specifically the capacitor in the 

filter) is assumed to be an ideal voltage source. This assumption is very close to reality, if the 

only load driven by the filter is the long motor cable without any motor connected at the end 

) 

B I ? 

B


of the cable, or there is no load at all at the filter output. This assumption enables a simplified 

analysis of the active du/dt filter, and the basic operation and design of the filter can be analyzed. 

However, in practice, when the motor is added to the drive, the load currents interfere 

the operation of the filter, depending mostly on the rated current of the motor compared with 

the filter charging current. In order to correct the errors caused by the motor current, corrective 

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 LC 

filter, which consists of an inductor in series with the main current path of the output phase 

and a capacitor in parallel with the output phase. The idea in active du/dt filtering is to slow 

down the rising and falling edges of the inverter pulses by controlling a specifically designed 

LC circuit to produce the desired voltage slope. The LC filter topology for active du/dt control 

is presented in Figure 3.4. The topology of the filter circuit in active du/dt is an LC output 

+ , + 1 

, + 

, + 

K 7 

K 8 K 9 

 

+ 

+ BEJA H 

Figure 3.4. Proposed LC filter topology for active du/dt control, consisting of a series inductance and 

capacitance at each of the inverter output phases. The capacitor is in parallel with the load (motor and 

motor cable) and acts as a voltage source in the circuit. The capacitors are wye connected, and the wye 

point is connected to the negative DC bus of the inverter, as the operation of the inverter is based on the 

negative DC bus in the context of this research. The filters designed for active du/dt do not function by 

themselves, i.e., passively; active control is required to produce the desired voltage slopes. The transient 

response of the filter circuit is not suitable for output filtering without the control because of tendency 

to oscillate. 

filter, with the capacitors wye connected to the negative DC link rail. The DC link connection 

is not necessary for the active du/dt operation, but since the negative DC link is the reference 

potential 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 than 

in passive du/dt filters because the control of the filter significantly affects the behavior of 

the active du/dt. In a typical case, the filter inductance value can be selected to be notably 

K 7 

K 8 

K 9


smaller than in conventional output filter designs, because only the LC constant of the circuit 

affects the output du/dt. The damping factor ζ is designed as to close to zero as possible by 

filter component selection and design, because the transition behavior of the filter is actively 

controlled. The operation is achieved by using extra voltage pulses. Further, the losses in the 

filter circuit can be minimized because there is no need to stabilize the transient response by 

increasing the damping factor in the circuit. 

This is a significant difference compared with passive du/dt filter design, since the control of 

both the resonance frequency and the damping factor is necessary in passive filters, because 

the inverter output voltage consists of voltage steps, and hence the step response of the filter 

is important. However, in a passive filter, damping causes losses, and the losses take place 

mainly 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 steps 

is that of the case ζ = 0 shown in Figure 2.4. Hence, using the active du/dt filter circuit 

without any control is disadvantageous, because the filter output response to voltage steps is 

an oscillation. The filter oscillates at the resonance frequency of the filter at an amplitude 

twice the fed voltage step, and decays very slowly. A measured example of such a case is 

presented later in Chapter 4. In the case of an electric drive, this is a worse scenario than no 

output filtering at all. 

In active du/dt, the filter losses are considerably smaller than in convential passive output 

filters, but the required control of the filter circuit introduces extra switching losses in the 

output stage of the inverter. Therefore, in active du/dt, the filtering losses are transferred 

from the filter circuit to the inverter output stage. However, the development of the power 

switch components also improves du/dt loss performance, which is not the case with passive 

output filters. More loss considerations are presented in Chapter 4, in the measurements 

section. 

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/dt 

control, 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 voltage 

of an amplitude A to 2A, and resonance is induced at the frequency determined by the L and 

C component values. This property of the LC circuit can be used to produce desired voltage 

slopes using pulse width modulation: to produce a voltage level, half the voltage of the target 

voltage level is fed to the LC circuit. In this case, the aimed output voltage is the DC link 

voltage. Hence, the feeding voltage is switched off at the moment t 1/2, when the output 

voltage 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 moment 

at which the target voltage is reached, which is twice the time t 1/2. Therefore, no switching 

transient occurs because the filter and supplied voltages are the same. This also equals a duty 

cycle of 50 % during the charging period.


7 8 

) 

7 8 

) 

) 

I JA F BA @ J JD A + ? EH? K EJ 

J 6 B ? 

K JF K J L J= C A B JD A + ? EH? K EJ 

Figure 3.5. Ideal step response of an LC circuit with a small damping factor. a) A step of amplitude A 

induces b) an oscillation of amplitude 2A at the LC circuit natural resonance frequency. 

= 

J I 

> 

J I


L J= C A 

) 

L J= C A 

) 

) 

C = JA ? JH 

, # 

? D = HC A 

F K I A 

J 

J 

J 

@ K JO F = HJ B JD A F K I A 

HEC E = E L A HJA H F K I A 

L J= C A BA @ J JD A + ? EH? K EJ 

K JF K J L J= C A B JD A + ? EH? K EJ 

@ EI ? D = HC A 

F K I A 

C = JA ? JH I EC = I B A E L A HJA H A C 

J 

= 

JE A 

> 

K F F A H I M EJ? D 

M A H I M EJ? D 

Figure 3.6. Operation principle of the presented control scheme for active du/dt control. a) Additional 

edge modulation is applied to the original inverter pulse, in order generate half of the voltage A using 

PWM, b) gate control signals of the inverter leg. c) Voltage A/2 is doubled to A in the LC circuit, and 

the pulse can be switched on without transient. 

JE A 

? 

JE A


The rising and falling voltage slopes of the filter are determined by the LC constant of the 

circuit. 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 the 

upper switch of the inverter leg of the corresponding phase, and the falling voltage slope is 

modulated using the lower switch of the leg, see Figure 3.4. Therefore, also the modulation 

of the original inverter pulse edges required by active du/dt control is carried out for the 

rising and falling slopes by using the corresponding inverter leg switches. The pulse edge 

is modulated only at the turn-on of the transistor, not at the turn-off, since the output stage 

operates at the freewheel mode. 

Further, the number of pulses used in the charging of the filter affects the rising and falling 

times generated by the output filter, as will be discussed later in this chapter. However, if 

more than one required extra pulse is used during a charge or discharge period, additional 

switching losses are generated. Therefore, from a practical point of view, with the present 

IGBT power switches, these charging schemes are not as useful as the single pulse charge 

presented. 

Furthermore, the filter charging current, flowing through the inductor, rises during the first 

half of the charging sequence, as charge flows to the capacitor. As the feeding voltage is 

restored to the previous potential at the moment t 1/2, at which the filter output voltage is 

A/2, the charging current will start to decrease, and the remaining energy in the inductor will 

charge the capacitor to the full voltage 2 · A/2 = A. In addition, during a discharge, a similar 

pulse pattern is required to slow down the falling voltage in order to prevent undershoot 

and oscillation of the filter circuit after the falling voltage slope. Additionally, if the current 

flowing through the inductor is not at the level preceding the sequence at the end of the 

sequence at moment 2t 1/2, overshoot and oscillation will be present in the output voltage, as 

will 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 single 

phase equivalent circuit of the three-phase filter, Figure 3.7. 

K E L 

 

+ 

K K J 

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 capacitor 

C are in series. The output voltage of the filter is the voltage of the capacitor, and both the 

load and filter current flow through the inductor. Before the theory for the control of active 

du/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 the 

s-plane transfer function H(s) of a second-order system 

ω 2 n 

H(s) = 

s2 + 2ζ ωns + ω2 , (3.1) 

n 

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

is 

H(s) = 

1 

LC 

s2 + 1 , (3.2) 

LC 

since in this case, ωn = 1/ √ LC and ζ = 0, because in this simplified analysis, resistance is 

assumed R = 0 and the circuit is at resonance at the frequency when the reactances of both 

the 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 filter 

reaches half the DC link voltage. Based on (3.2), the step response of the presented LC circuit 

for the step of an amplitude A can be transformed into the time domain. The output voltage 

of an ideal LC circuit for a step of an amplitude A is 

see Figure 3.5. 

 

 

t 

uout(t) = A · 1 − cos √ , (3.3) 

LC 

The output voltage uout(t) of the circuit is half the DC link at the instant t1 = t 1/2, that is 

uout(t1/2) = 1 

A. (3.4) 

2 

Combining (3.3) and (3.4) yields t 1/2 = t1 = π √ LC/3. Because the instant at which the 

charge, that is, the rising voltage slope, is complete and the feeding voltage is switched on 

again is t2 = 2t 1/2, the rise time tr of the charge is 

tr = t2 = 2π √ √ 

LC ≈ 2.094 · LC. (3.5) 

3


At the moment t2, uout equals the amplitude A of the output voltage pulse, which in this case 

is equal to the DC link voltage. As we can see from (3.5), the voltage slope rise time depends 

on the LC constant of the circuit. The pulse widths of the charge sequence also depend on 

the LC constant of the circuit and thereby on the target voltage transition time. It can also be 

noted that for fast voltage transition times, the inverter output stage must be able to produce 

pulses in the order of the desired transition time. For example, if the target is a 2 µs voltage 

slope, the output pulse width in the charge sequence equals 1 µs. However, as the motor 

cable length increases, the longer are the required voltage slopes, and therefore the situation 

is easier for the inverter output stage. This is also the situation at which the motor overvoltage 

problems are most evident. 

Because of the symmetricity of the charging and discharging sequences, the pulse widths are 

the same for both the sequences in an ideal case. In a real implementation, various delays 

between 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 a 

successful implementation. However, a sufficient requirement is that the pulses produced by 

the inverter output stage are of correct length and pulse width, despite the internal implementation 

of the charge and discharge pulse generation. 

Because a common two-level inverter has only two voltage levels, it is the positive and negative 

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 voltage 

can be generated in the same way as different voltage levels are normally generated using 

pulse width modulation in the inverter, as stated earlier. This introduces a new edge modulation 

in a faster time domain compared with the normal inverter PWM modulation. In addition 

to the normal phase voltage modulation at the switching frequency, at every turn-on switching 

action of the inverter output stage, the edge modulation has to be carried out for the voltage 

step 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 the 

voltage is at the half of the DC link voltage, the LC circuit will double the output voltage to 

the full DC link voltage. By solving from Eq. (3.2) and by using the stimulus described, the 

output of the LC filter circuit in the time domain can be obtained from 

 

 

 

t 

t −t1 

uout(t) = A 1 − cos √ − ε (t −t1) · 1 − cos √ , (3.6) 

LC LC 

where A equals the DC link amplitude, ε is the Heaviside step function, ε (t −t1) is the step 

function delayed by t1, and t1 is the moment, at which the output voltage of the LC circuit is 

half the DC link step applied to the circuit. The stimulus and the output voltage of the LC 

circuit are presented in Figure 3.8 for an amplitude of A = 1, which can be considered to be 

1 pu UDC. 

The behavior presented in Figure 3.8 can be explained by the fact that the voltage is cut at the 

moment when the output voltage is at the half of the voltage step, and the LC circuit doubles


Output Voltage 

Stimulus 

2 

1 

0 

−1 

−2 

2 

1.5 

1 

0.5 

0 

The response of the LC circuit for a single charge pulse 

a) 

Time 

b) 

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 so 

that the pulse is turned off at the instant when the output voltage of the LC circuit is half the DC link 

amplitude. Therefore, the output voltage of the LC circuit increases to the potential of the DC link, at a 

rise time set by the time constant of the LC circuit, as presented. b) The LC circuit impulse response is 

also shown as a comparison. 

the voltage applied. Hence, the voltage maximum is the amplitude of the DC link voltage, not 

twice 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 applied 

voltage step, as in Figure 3.5, but now the output voltage resonates around zero instead instead 

between zero and twice the DC link voltage. Further, the stimulus approximates roughly the 

Dirac delta (impulse) function, δ(t). The impulse response of the LC circuit can be solved 

from Eq. (3.2): 

which is also presented in Figure 3.8. 

uout(t) = 1 t 

√ sin √ , (3.7) 

LC LC 

It can be noted that the curves in Figure 3.8 have a similar form, but neither of the voltage 

waveforms are useful in the generation of the filter output voltage. However, we can see from 

Figure 3.8 that if the stimulus voltage to the LC circuit is switched back on exactly at the 

instant 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 sequence 

described. The stimulus consists of a sum of step functions of amplitude A, of which two are 

delayed by t1 and t2 

Uout(s) = H(s) ·Uin(s) = 

1 

LC 

s 2 + 1 

LC 

 

1 e−t1s e−t2s 

· A − + . (3.8) 

s s s 

 

charge pulse 

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

 

 

 

 

t 

t −t1 

t −t2 

uout(t) = A · 1 − cos √ − ε (t −t1) 1 − cos √ + ε (t −t2) 1 − cos √ , (3.9) 

LC LC 

LC 

where A again equals the DC link voltage and ε is the Heaviside step function. t2 is the instant 

at which the output voltage of the LC circuit has doubled to the full step voltage. Ideally, t2 is 

two 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. 


Stimulus 

2 

1.5 

1 

0.5 

0 

2 

1.5 

1 

0.5 

0 

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

a) 

Time 

b) 

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

applied. 

As can be seen from Figure 3.9, the LC circuit can be employed in generation of an output 

voltage, 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 LC 

circuit. 

By definition, the LC circuit doubles the modulated voltage applied to full voltage, but in 

this case the resonance of the LC circuit is avoided, if the switching instants are conducted 

exactly 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 amplitude 

of the residual oscillation depends on the amount of inaccuracy, as will be presented later in 

this 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 3.9 

is known as the charge pulse. In addition to this, generation of the charging pulse can be 

thought to consist of several delayed steps, in this analysis unit steps (1 pu UDC). If the steps 

are correctly timed, the step responses, as in Figure 3.5, are superimposed in the LC circuit in 

a way that produces a voltage slope of desired length. This idea is illustrated in Figure 3.10. 

Step responses 

Stimulus 

Combined response 

2 

0 

−2 

2 

0 

−2 

2 

1 

0 

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

a) 

b) 

Time 

c) 

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 active 

du/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), and 

thereby on the actual L and C component values. 

As stated before, t1 and t2 correspond to π/3 and 2π/3, respectively. Therefore, the phase 

shift between the individual responses has to be π/3 for zero residual oscillation. Inaccurate 

timing 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 in 

addition 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. If 

the filter circuit is not succesfully discharged, LC circuit resonance will occur, as presented 

in Figure 3.11. An example of a successful charge and discharge sequence is presented in 

Figure 3.12. 


Stimulus 

2 

1 

0 

−1 

−2 

2 

1.5 

1 

0.5 

0 

The response of the LC circuit for a falling voltage step 

a) 

Time 

b) 

Figure 3.11. a) The response of the LC circuit. The effect of an unmodulated falling step is also 

presented. 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 be 

solved using the same principle as in solving (3.8), that is, by determining the s-plane LC 

circuit voltage equation and solving for the current in the LC filter circuit caused by the 

charging pulse. In the time domain, this analysis yields for the filter current 

if(t) = A 

 

sin 

L/C 

 

t 

t −t1 

t −t2 

√ − ε (t −t1)sin √ + ε (t −t2)sin √ 

LC LC LC 

(3.10) 

The maximum filter current during the charging period is at the moment t 1/2, as the supplying 

voltage is switched off; after that instant the charging current of the inductor L begins to 

decrease. Based on (3.5) and (3.10), the charging current maximum value can be solved 

if(t)max = i(t1/2) = A 

sin 

L/C π A 

≈ 0.866 . (3.11) 

3 L/C



Stimulus 

2 

1 

0 

−1 

−2 

2 

1.5 

1 

0.5 

0 

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

a) 

Time 

b) 

Figure 3.12. a) Response of the LC circuit. b) Charge and discharge sequences according to the active 

du/dt method are succesfully applied. 

As can be seen, the filter peak current is inversely proportional to the square root of the filter 

inductance L and proportional to the square root of the filter capacitance C. Together with 

the LC constant, the peak current is an important design consideration, because the IGBT 

module must withstand the additional current stress caused by the filter current on top of the 

load current flowing through the output stage. 

The filter output voltage and the filter charging current are presented in Figure 3.13 in a 

normalized form as functions of filter component values and voltage amplitude A (1 pu UDC 

of the applied voltage pulses. 

The analysis presented in this section concerns the charge pulse, but a similar analysis can 

be carried out also for the discharge pulse by adding into (3.8) the delayed step functions 

describing the discharge pulse. The filter voltage and current waveforms are similar for both 

the 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 be 

used to derive the filter output voltage and filter current for charge and discharge sequences 

consisting of several, narrower pulses, with the same duty cycle of 50 %. The output voltage 

and the filter current can be presented in a general form for a number of N charge pulses


Voltage [V] ⋅A 

Current [A] ⋅A√ L/C 

1 

0.5 

LC Filter output voltage 

Filtered output 

Inverter output 

0 

0 0.5 1 1.5 2 2.5 

Time [s] ⋅√LC 

a) 

LC filter current 

1 

0.5 

0 

−0.5 

0 0.5 1 1.5 2 2.5 

Time [s] ⋅√LC 

b) 

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

uout(t) = A 

2N 

∑ 

n=0 

if(t) = A 

L/C 

(−1) n 

ε (t − nt1) 1 − cos 

2N 

∑ (−1) 

n=0 

n 

ε (t − nt1) sin 

 

t − nt1 

√ 

LC 

(3.12) 

 

t − nt1 

√ . (3.13) 

LC 

The pulse length, which is equal to t1, has to be solved using the same principle as above. For 

example, 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 link 

voltage amplitude A in the middle of the charge sequence, and full DC link voltage at the last 

switching instant. 

For example, for a case of two charge pulses, these are now at t2 and t4. The pulse length t1 

can be generally solved using this method, because for a charge of N pulses, there are always 

an odd number of switching instants (2N +1), and therefore, a switching instant in the middle 

of the charging sequence. For the case of two pulses, t1 can be solved 

t1 = 1 

5 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 can 

be 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 more 

pulses are used in controlling the filter circuit. The exact value of the rise time can be solved 

by combining (3.4) and (3.12). The rise time of the filter output voltage depends on the time 

constant of the LC circuit 

2π √ 

LC ≤ tr = K · 

3 

√ 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 into 

account, the charging scheme consisting of only one charge pulse is the most relevant sequence 

because the switching losses increase and the minimum pulse width requirement decreases 

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 is 

the number of individual charge periods. Therefore, the total output voltage slope transition 

time is increased to M times the base transition time tr by using the same LC circuit. For more 

on these charging schemes, see publications (Korhonen et al., 2009; Tyster et al., 2009). Nevertheless, 

these pulse sequences are outside the scope of this work and are not studied further 

here. 

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 100 

meters, and the propagation speed of the wave in the cable is approximately half the speed 

of light, Reka MCMK. A steep-edged voltage pulse is reflected at the motor terminal, and 

oscillation occurs. In Figure 3.15, the same situation is presented when active du/dt filtering 

is applied. The cable resonance frequency is succesfully filtered, and the cable resonance is 

eliminated. 

As can be seen in Figure 3.15, the LC circuit can be applied to the generation of an output 

voltage, which consists of several delayed step responses of the LC circuit in order to produce 

a rising voltage slope. The rising and falling times of the slope depend on the time constant of 

the LC circuit. It can also be noted that if the voltage is switched off when the LC filter output 

voltage has reached half the DC link voltage, the output voltage is doubled to equal to the DC


Voltage [V] 

Voltage [V] 

1000 

500 

0 

Inverter output voltage 

−1 −0.5 0 0.5 1 1.5 2 2.5 3 

x 10 −5 

−500 

Time [s] 

a) 

Voltage at 100 meter open−ended cable end 

1000 

500 

0 

−1 −0.5 0 0.5 1 1.5 2 2.5 3 

x 10 −5 

−500 

Time [s] 

b) 

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

Voltage [V] 

Voltage [V] 

1000 

500 

0 

Active du/dt filter output voltage 

−1 −0.5 0 0.5 1 1.5 2 2.5 3 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−1 −0.5 0 0.5 1 1.5 2 2.5 3 

x 10 −5 

−500 

Time [s] 

b) 

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

effectively eliminated. 

link voltage. Since the output voltage of the LC circuit was exactly half the step voltage, the 

total 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 conducted 

exactly 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 a 

parallel capacitance C, which are provided by the filter inductors and capacitors in a real 

implementation. 

However, there are some considerations regarding the design and realization of the filter 

circuit. First, in the filter component selection, the use of narrow, steep-edged voltage pulses 

in the order of microseconds has to be taken into account. This sets special requirements 

for 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 filter 

and motor maximum currents have to considered in the design. The filter maximum current 

can be obtained from Eq. (3.11). In the filter L and C component value selection for a specific 

tr (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 from 

Eq. (3.11). The filter maximum current is also an important design consideration, because 

the current handling capability and power losses of the inverter power modules set limitations 

on the peak charge and discharge currents. However, the inductance and capacitance values 

cannot be selected arbitrarily based on the rise time and the filter peak current, because the 

capacitance value has an effect on the rigidity of the active du/dt filter circuit as a voltage 

source. 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 tolerances 

causes an error in the filter output voltage, if the manufacturing tolerances are not 

taken into account in the design of the charge and discharge sequences. As can be noticed 

from 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 the 

designed component value in the correct rise time tr. The amplitude of the resonance, or 

the error, in the LC circuit is equal to the difference in the filter output (capacitor) and DC 

link voltages at the instant when the voltage pulse is switched on at the end of the charge or 

discharge sequence. Therefore, faulty charge according to a wrong rise time causes the filter 

capacitor to under- or overload, causing a resonating output voltage. Residual LC circuit 

output 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 of 

error 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 measurement 

at the filter output phase. The LC constant can be calculated from the resonance 

frequency of the LC circuit, and the charge and discharge sequences can be adjusted according 

to Eq. (3.5) in order to compensate the variations in the actual component values from the 

nominal values. 

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

lengths 

As stated above, the phase velocity and the cable length affect to the cable oscillation frequency. 

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 linear 

ramp is four times the cable propagation delay. However, the frequency content of an active 

du/dt ramp for a certain rise time tr is different, since the du/dt is not constant along the rise 

time, for rise time definition presented in Figure 3.16. The rise time is defined as the ramp 

sequence length, from the 0 to 100 % voltage. Therefore, the maximum cable lengths for 

various linear (Figure 3.16a) and active du/dt (Figure 3.16b) ramp rise times have been determined 

in the following tables. In addition, in a practical installation, overvoltages of for 

example 30 % or 50 % are allowed, and thus such values are presented also. 

7 

J H 

= J 

> 

Figure 3.16. Definitions for the a) linear and b) active du/dt ramp lengths. The rise time is defined as 

the ramp sequence length, from the 0 % to the 100 % voltage. 

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

7 

J H 

J


using the above-mentioned Persson’s formula and definition for the critical cable length. Furthermore, 

the 30 % and 50 % allowed overvoltages for certain cable lengths have been simulated 

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. The 

propagation delay was assumed 0.5c, the motor reflection coefficient Γm = 1, and inverter 

reflection coefficient Γi = −1. Cable attenuation was neglected. The model is presented in 

Appendix 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 

10−6 

·tr [10 

s 

−6 s]. (3.17) 

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

follows 

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 

Cable length [m] 

500 

450 

400 

350 

300 

250 

200 

150 

100 

50 

Cable lengths for linear ramp for certain overshoot 

0 % 

30 % 

50 % 

0 

0 1 2 3 4 5 6 7 8 9 

Time [us] 

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 % active 

du/dt ramp for a certain cable length for an arbitrary ramp length can be calculated as follows 

l [m] = 23 

 

m 

10−6 

·tr [10 

s 

−6 s]. (3.20)


Cable length [m] 

500 

450 

400 

350 

300 

250 

200 

150 

100 

50 

Cable lengths for active du/dt ramp for certain overshoot 

0 % 

30 % 

50 % 

0 

0 1 2 3 4 5 6 7 8 9 

Time [us] 

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 as 

follows 

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 reflection 

coefficients, overvoltage of 0 % cannot be achieved in a real application, because the amplitude 

of the cancelling wave has decayed due to cable attenuation and incomplete reflection at 

the interfaces.

Chapter 4 

Applying active du/dt filtering to an 

electric drive 

In the previous chapter, the basis of active du/dt control was presented, and the theory for 

application of the method and design of the filter circuit was developed. However, if the 

method presented is applied in an electric drive as described above, the induction motor 

current causes error in the active du/dt operation. Nevertheless, in the worst case, where the 

load current is greater than the filter current, the load current renders the filtering method 

unusable, unless the error is corrected. The principles for correction of the load-currentinduced 

error are described in this chapter. The error is dependent on the relation of the filter 

maximum current and the instantaneous value of the motor current. The correction can be 

implemented using a similar active control as the standard active du/dt control of the LC filter 

circuit. 

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

method 

To develop the control principles, the analysis presented in the previous chapter was based 

on the ideal LC circuit model of the active du/dt filter, as shown in Figure 3.7. Therefore, no 

nonidealities nor any external loading effects were taken into account. However, the analysis 

of these effects is of great importance when the method is applied to the output filtering in an 

actual induction motor drive. 

65

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 induction 

motor, can be analyzed using a simplified equivalent circuit as presented in Figure 4.1. 

1 B 1 

 

K E L + K K J 

Figure 4.1. LC filter for active du/dt control presented with the loading impedance of the induction 

motor on a per-transition basis. 

The impedance ZL is used to model the loading impedance of the induction motor for the 

analysis from a viewpoint of a single transient. From this viewpoint, for a pulse-widthmodulated 

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 (tens 

of hertz) and the pulse width modulation at the switching frequency in the order of a hundred 

microseconds (corresponds to 10 kHz), as the edge modulation of each switching transient of 

the 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 slow 

motor current can be approximated as a constant current, when the edge modulation of a 

single voltage transient is considered. 

Second, the inductance visible from the asynchronous machine for a single voltage transient 

is the transient inductance L ′ s, which is defined as (Pyrhönen et al., 2008) 

L ′ s = Lsσ + Lrσ Lm 

≈ Lsσ + Lrσ , (4.1) 

Lrσ + Lm 

where Lsσ is the stator leakage inductance, Lrσ is the rotor leakage inductance, and Lm is the 

magnetizing inductance. The transient inductance is in a major role to filter the motor current 

in an inverter drive, and it mainly consists of the stator and rotor flux leakages (Pyrhönen 

et al., 2008). For typical one-phase asynchronous machine equivalent circuit parameters and 

transient 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 a 

single transient that 

1

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

Lf


L J= C A 

? K HHA J 

C = JA ? JH 

K JF K J 

K JF K J L J= C A B JD A + BEJA H 

K JF K J ? K HHA J B A F D = I A B JD A E L A HJA H 

C = JA ? JH I EC = I B A E L A HJA H A C 

E L A HJA H F D = I A K JF K J L J= C A 



Figure 4.2. Basic active du/dt operation: a) filter output voltage and b) filter current. c) The gate control 

signals of the inverter leg are also shown along with d) the inverter output voltage. 

= 

JE A 

> 

? 

@


L J= C A 

L J= C A 


JE A 

JE A 

? K HHA J 

? K HHA J 

1 

= > 

JE A 

? @ 

JE A 


Figure 4.3. a) and c) Operation of the active du/dt method, when the load current instantaneous value 

is greater than zero (towards the motor), and b) and d) less than the filter peak current. As shown, zero 

end current d) will result in oscillation c).


L J= C A 

L J= C A 


JE A 

JE A 

? K HHA J 

= > 

? K HHA J 

? @ 

1 

JE A 

JE A 


Figure 4.4. a) and c) Operation of the active du/dt method, when the load current instantaneous value is 

less than zero (towards the inverter), and b) and d) less than the filter peak current. As shown, zero end 

current 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 operation 

of active du/dt with no load, the capacitor voltage must be at the target value and the filter 

inductance current must be at the initial value at the end of the sequence to avoid residual 

filter 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 current 

will stay at zero current instead of returning to the initial negative current. The correction is 

carried out in the same way as in the case of positive idle current, using the opposite inverter 

switch in comparison with the basic active du/dt operation presented in Chapter 3. The idea 

of the correction sequence is presented in Figure 4.5 for both the cases requiring the current 

correction pulse described above. 

? K HHA J 

C = JA ? JH 

1 

? K HHA J B A F D = I A B JD A E L A HJA H 

JE A 



JE A 

? K HHA J 

C = JA ? JH 

1 

= > 


JE A 

? @ 



C = JA ? JH I EC = I B A E L A HJA H A C C = JA ? JH I EC = I B A E L A HJA H A C 

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| 

JE A


increases as a result of the fundamental modulation, depending on the potential the phase 

voltage is switched to, either the falling or rising voltage edge modulation must include a 

current correction pulse. As the absolute value of the idle current increases, the compensating 

current correction pulse extends from the end of the charge or discharge period toward the 

start of the period. Therefore, the minimum value of the pulse length is zero, at zero load 

current, which also means that the correction pulse is absent. As a result of the 50 % duty 

cycle of the basic active du/dt voltage level transition edge modulation, the ideal maximum 

length of the current correction pulse is half of the charging or dicharging period, because 

otherwise inverter leg short circuit would occur. This situation is also equal to the instant at 

which the filter current is at its maximum value and the current correction pulse will last for 

the entire period. 

The pulse length in the ideal case can be derived from the filter current equation (3.10) based 

on the principle presented in Figure 4.6. 

The length of the current correction pulse tcorr is indicated in Figures (4.6) and (4.7). Equation 

(3.10) can be divided into parts in the same way as the voltage equation presented in 

Figure 3.10: 

(1) 

(2) 

 

A t 

A t −t1 

A t −t2 

if(t) = sin √ −ε 

(t −t1) sin √ + ε (t −t2) sin √ 

L/C LC L/C LC L/C LC 

(3) 

(4.3) 

The parts of the current that have an effect on the different phases of the filter current are 

also indicated in Figure 4.7. The length of the current correction pulse can be determined by 

solving the equation 

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

because of the symmetricity of the filter current waveform, only the part (1) of Eq. (4.3) has 

to be taken into account in the solution. Therefore, the solution for the length of the current 

correction pulse in the ideal case is 

tcorr = √ LC sin −1 

 

IL 

A 

 

L 

, (4.5) 

C 

where IL is the load current instantaneous value and A is the amplitude of the inverter DC 

link voltage. 

The cases in which the absolute value of the load current is between zero and the filter maximum 

current have been discussed above. The case in which the load current is greater than 

the filter current is shown in Figure 4.8.


B 

? K HHA J 

C = JA ? JH 

K JF K J 

1 


= > 

1 

JE A 



JE A 

? K HHA J 

C = JA ? JH 

1 

1 

JE A 


? @ 




E L A HJA H F D = I A L J= C A 

K JF K J 


JE A 

A B 

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 length 

must be applied, c) and d). Inverter leg output voltages are shown, e) and f) for the the gate control 

signals, c) and d), of the individual power switches.


? K HHA J 

1 

1 

E B J 1 


! 

Figure 4.7. Principle of the derivation of the current correction pulse length. (1), (2), and (3) refer to 

the parts of Eq. (4.3). 

In this case, the current correction pulse must be half of the total charging or discharging 

period, which is also the maximum length of the correction pulse. Now the absolute value of 

the load current is greater than the filter maximum current, and hence, no zero crossing takes 

place in the current waveform. The actual edge modulation of the active du/dt modulation 

is not necessary in this case either, because the absolute value of the current will start to 

decrease in the freewheeling mode, when both the switches of the inverter leg are turned 

off. The filter inductance current is restored to the initial idle current value using only the 

current correction pulse, which is half of the period. In this case, the edge modulation pattern 

is similar to the basic active du/dt modulation pattern; the pattern itself is the same, but the 

inverter 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 presented 

as a basis for implementation on a real inverter. 

However, implementing the current correction pulse in an actual inverter is not as straightforward 

as presented here, because the properties of the inverter output stage, for example 

the losses, minimum pulse lengths, and required dead times, will all have a significant effect 

on the final result of the active du/dt modulation. Implementation of the current correction 

modulation in a real inverter should be based on the idea presented above, taking into account 

the limitations defined by the actual IGBT modules in the output stage, and it is outside the 

scope of the work presented in this dissertation. 

J ? HH 

JE A


? K HHA J 

C = JA ? JH 

K JF K J 

JE A 

1 B 




JE A 

? K HHA J 

C = JA ? JH 

1 B 


JE A 





= > 

? @ 

K JF K J 


JE A 

A B 

Figure 4.8. a) and b) Principle of the current correction pulse to correct the operation of the active du/dt 

method, when the instantaneous load current is greater in amplitude than the filter peak current. c) and 

d) The charge and discharge pulses are eliminated by the freewheeling operation of the circuit, and only 

the 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 power 

switches, 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 not 

the case with the effective power of the induction motor – can be analyzed using a simplified 

equivalent circuit as presented in Figure 4.9. 

1 B 1 

4 I I 

 

K E L + K K J 

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 resistive 

losses caused by the resistances in the DC link, inverter bridge, and filter circuit. The effects 

of 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/dt 

filter output voltage, because the filter capacitor will be underloaded, which in turn causes a 

resonating filter output voltage. 

The effect of the underload can be compensated by increasing the charge and discharge pulse 

widths from the ideal 50 %, which is the ideal pulse width, when there are no resistive losses 

at the filter circuit. In practice, this means an increase in the modulated output voltage (higher 

duty cycle) in order to overcome the resistive losses. Since the resistive loss in the circuit is 

static, 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 active 

du/dt filter output voltage, a simulation model was developed in the MATLAB SIMULINK 

environment. A block diagram of the developed model is presented in Figure 4.10. The 

modulator block forms the gate drive signals for the output stage consisting of SIMULINK 

SimPowerSystems IGBT/Diode components. The output stage drives the active du/dt LC 

filter circuit, which is connected to the SimPowerSystems asynchronous machine model. 

Three-phase current measurements are carried out after the output stage and after the active 

du/dt filter. The motor current measurement is used to form correction pulses of the right 

length. A more detailed description of the simulation model structure is given in Appendix 

A. 

Because the research on the development of the current correction method for a frequency 

converter was outside the scope of this dissertation, no measurement results with the current 

1

4.2 Simulations of the error caused by the motor current 77 

2 9 @ K = J H 

 

 

K 7 

K 8 K 9 

K 7 

+ 

 

A = I K HA A JI 

K 8 

K 9 

) 

) I O ? D H K I 

= ? D E A 

@ A 

Figure 4.10. Block diagram of the correction pulse simulation model. The top level model and the 

blocks are presented in more detail in Appendix A. 

correction method are presented. The simulation model applies the theory presented previously 

in this chapter. However, the error caused by the load current is noticeable, to the extent 

it can be detected at the motor sizes used in the measurement, are presented later. If the filter 

maximum peak current and the motor current are in the same order, the filter output voltage 

error becomes more apparent. Simulations are carried out for a filter design of L = 7 µH and 

C = 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 Asynchronous 

machine model is shown. The model was configured to represent an induction 

motor 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 example 

the dead times, which are mandatory in a real inventer, were omitted in the simulation, and 

therefore, 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 current 

correction 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 voltage 

of the filter, that is, in the motor voltage, as the LC circuit resonates. The greater the load 

current value during the charge is, the greater is the error and the amplitude of the unwanted 

LC resonance. Moreover, the resonance is visible in the filter current, which is seen in the 

inverter output current. Time-enlarged waveforms of inverter and motor voltages are also 

shown at two different time instants. 

In Figures 4.19–4.22, the operation of the active du/dt method is shown with the current 

correction pulse applied. As can be seen, there is negligible LC oscillation, or error in the 

filter output and in the motor voltage, and the current correction pulses applied is seen to 

correct the LC filter resonance in cases, where the load current is significant compared with 

the filter current. Time-enlarged waveforms of inverter and motor voltages are shown at two 

different time instants. Furthermore, the inverter current consists of the motor current and the 

charge and discharge current spikes of the active du/dt LC filter.


Voltage [V] 

Voltage [V] 

Voltage [V] 

1000 

0 

Inverter voltage U 

−1000 

0 0.5 1 1.5 2 

1000 

0 

Inverter voltage V 

x 10 −3 

−1000 

0 0.5 1 1.5 2 

1000 

0 

Inverter voltage W 

x 10 −3 

0 0.5 1 1.5 2 

x 10 −3 

−1000 

Time [s] 

Figure 4.11. Simulated inverter bridge output voltages. During the transients in the PWM, charge pulses 

are applied according to the theory presented in Chapter 3. No correction pulse is applied. 

Voltage [V] 

Voltage [V] 

Voltage [V] 

1000 

0 

Motor voltage U 

−1000 

0 0.5 1 1.5 2 

2000 

0 

Motor voltage V 

x 10 −3 

−2000 

0 0.5 1 1.5 2 

2000 

0 

Motor voltage W 

x 10 −3 

0 0.5 1 1.5 2 

x 10 −3 

−2000 

Time [s] 

Figure 4.12. Simulated filter output voltages. As can be seen, the LC resonance increases as the 

instantaneous motor current value increases. No correction pulse is applied.


Voltage [V] 

Voltage [V] 

1000 

500 

0 

−500 


−1000 

4.5 5 5.5 

1000 

500 

0 

−500 


x 10 −4 

−1000 

4.5 5 5.5 

Figure 4.13. Simulated inverter bridge and motor voltages, a time-enlarged version of one time instant 

of Figures 4.11 and 4.12. No correction pulse is applied. 

Voltage [V] 

Voltage [V] 

1000 

500 

0 

−500 


x 10 −4 

−1000 

1.7 1.72 1.74 1.76 1.78 1.8 

1000 

500 

0 

−500 


x 10 −3 

−1000 

1.7 1.72 1.74 1.76 1.78 1.8 


of 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. 

x 10 −3


Current [A] 

400 

300 

200 

100 

0 

−100 

−200 

−300 

−400 

Phase U 

Phase V 

Phase W 

Inverter output currents 

0 0.5 1 1.5 2 

x 10 −3 

−500 

Time [s] 

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. 

Current [A] 

300 

200 

100 

0 

−100 

−200 

−300 

Phase U 

Phase V 

Phase W 

Motor currents 

0 0.5 1 1.5 2 

x 10 −3 

−400 

Time [s] 

Figure 4.16. Simulated currents of the asynchronous machine model at the beginning of the start-up 

transient. No correction pulse is applied.


Current [A] 

400 

300 

200 

100 

0 

−100 

−200 

−300 

−400 

Phase U 

Phase V 

Phase W 

Inverter output currents 

0 0.5 1 1.5 2 

x 10 −3 

−500 

Time [s] 

Figure 4.17. Simulated inverter bridge output currents. The currents consist of the sum of the motor 

current and the charge and discharge currents of the LC filter circuit during the transients. The correction 

pulses are applied as a function of the current instantaneous value. 

Current [A] 

300 

200 

100 

0 

−100 

−200 

−300 

Phase U 

Phase V 

Phase W 

Motor currents 

0 0.5 1 1.5 2 

x 10 −3 

−400 

Time [s] 

Figure 4.18. Simulated currents of the asynchronous machine model at the beginning of the start-up 

transient. The correction pulses are applied as a function of current instantaneous value.


Voltage [V] 

Voltage [V] 

Voltage [V] 

1000 

0 


−1000 

0 0.5 1 1.5 2 

1000 

0 

Inverter voltage V 

x 10 −3 

−1000 

0 0.5 1 1.5 2 

1000 

0 

Inverter voltage W 

x 10 −3 

0 0.5 1 1.5 2 

x 10 −3 

−1000 

Time [s] 

Figure 4.19. Simulated inverter bridge output voltages. During the transients in the PWM, charge 

pulses are applied according to the theory presented in Chapter 3. The correction pulses are applied as 

a function of current instantaneous value. 

Voltage [V] 

Voltage [V] 

Voltage [V] 

1000 

0 


−1000 

0 0.5 1 1.5 2 

1000 

0 

Motor voltage V 

x 10 −3 

−1000 

0 0.5 1 1.5 2 

1000 

0 

Motor voltage W 

x 10 −3 

0 0.5 1 1.5 2 

x 10 −3 

−1000 

Time [s] 

Figure 4.20. Simulated filter output voltages. As can be seen, the LC resonance is negligible, as 

correction pulses are applied as a function of current instantaneous value.


Voltage [V] 

Voltage [V] 

1000 

500 

0 

−500 


−1000 

4.5 5 5.5 

1000 

500 

0 

−500 


x 10 −4 

−1000 

4.5 5 5.5 


of Figures 4.19 and 4.20. Current correction pulse is applied. 

Voltage [V] 

Voltage [V] 

1000 

500 

0 

−500 


x 10 −4 

−1000 

1.7 1.72 1.74 1.76 1.78 1.8 

1000 

500 

0 

−500 


x 10 −3 

−1000 

1.7 1.72 1.74 1.76 1.78 1.8 


of Figures 4.19 and 4.20. Current correction pulse is applied. As can be seen, the current correction 

pulses are applied to correct the LC filter resonance in cases where the load current is significant 

compared with the filter current; cf. Figure 4.14. 

x 10 −3


4.3 Measurements and experimental results 

A prototype was built to assess the potential of the active du/dt method presented. A threephase 

Vacon NXP frame size 6 frequency converter unit was modified to make the edge 

modulation according to the active du/dt method possible. The original IGBT modules of the 

power unit were replaced with SEMIKRON SEMiTRANS series SKM 100GB123D IGBT 

modules, and the original control card was replaced with a custom-designed (at Lappeenranta 

University of Technology) control card based on a XILINX Spartan-3 field programmable 

gate array (FPGA). 

Otherwise, the converter unit and the gate drivers were factory standard design. A control unit 

implementing active du/dt pulse modulation was developed for the FPGA card by Juho Tyster, 

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 manufacturers 

were used. The insulation material between the phase conductors and the shield 

was different for the cables, and therefore the high-frequency properties, most importantly 

the velocity of propagation, varied slightly between the cable brands. The measurements of 

the properties are presented below, in Table 4.1. 

A prototype LC filter circuit was designed and built by Juho Tyster, M.Sc. (Tech.) and 

Juhamatti 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 −6 s] = 100 [m]/23 

 

m 

10−6 

≈ 4.4 · 10 

s 

−6 s. (4.6) 

The phase velocity of a polyvinychloride-insulated (PVC) power cable can be assumed to be 

in 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 ferrite 

core, and Litz wire were wound. The reactor in the filter circuit was specifically designed 

for the purpose, using core material suitable for an application containing fast pulses. The 

measured inductance of the coils was 16 µH, and 0.33 µF plastic-insulated pulse capacitors 

were chosen. This results in a rise time of approximately tr=4.8 µs, (3.5) and a filter peak 

current of 75 A for the DC link value of 600 V, (3.11). The maximum length of the power 

cable for this filter is, therefore, approximately 110 meters, if no overvoltage is allowed. This 

is 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 schematic 

of 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 of 

induction motors, and the measurement instrumentation. The electric motors used in the 

measurements were ABB 5.5 kW and 7.5 kW induction motors, which are shown in Figure 

4.26. The active du/dt filter circuit is shown in more detail in Figure 4.27. The motors 

were idling at 50 Hz in all the measurements, in which the motors were used. 

+ , + 1 

, + 

, + 

K 7 

K JF K J I J= C A B JD A 

BHA G K A ? O ? L A HJA H 

 

+ 

+ BEJA H 

J H BA A @ A H ? = > A 

+ 

! N # # 5 

1 @ K ? JE J H 

K 7 ) 

K 8 K 8 

K 9 K 

9 

8 

) C EA J , 5 $ " ) I ? E I ? F A 

6 A JH EN 2 # # 

@ EBBA HA JE= F H > A 0 

. K A & E I 

? K HHA J ? = F 0 

Figure 4.23. Schematic of the measurement setup consisting of a frequency converter, an active du/dt 

filter circuit, a motor cable, an induction motor, and measurement instrumentation. All the measurements 

are indicated in the figure. 

The frequency converter was fed from the grid using a variable transformer. The active du/dt 

filter circuit was constructed on a PCB card, which was attached to the frequency converter 

negative DC link rail and output phases. 

The power cables were MCMK type, 3x2.5 mm 2 +2.5 mm 2 screened 0.6/1 kV power cables. 

Cables from two manufacturers were used, Draka MCMK and Reka MCMK. The Draka 

cables were approximately 30 and 300 meters long. The insulation system of the cable consists 

of phase conductor insulations, filler around the phase conductors, a screen consisting 

of copper leads and foil, and an outer sheath. The Reka cable used in the measurements was 

approximately 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, a 

screen of copper leads and foil, an insulating film around the screen, and an outer sheath. The 

insulation material used in both cables is polyvinylchloride (PVC). The dielectric configuration 

of the cables is shown in Figure 4.24. 

Because of differences in the dielectric configuration, the high-frequency properties of the 

cables differ causing a difference in the propagation velocities. The approximate propagation 

velocities determined from the cable oscillation frequencies are presented in Table 4.1. The 

calculation is based on the measurement presented in Figures 4.28, 4.29 and 4.32, based on 

8 

8


K JA H 2 8 + 

E I K = JE 

2 8 + 

BEA H 

5 ? HA A 

2 8 + E I K = JE 

2 D = I A ? @ K ? J HI 

, H= = + 4 A = + 

K JA H 2 8 + 

E I K = JE 

) EH 

1 I K = JE C 

B E 

5 ? HA A 

2 8 + E I K = JE 

2 D = I A ? @ K ? J HI 

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 measurements. 

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 are 

well in line with the literature and assumptions of the cable properties. Further, the higher 

propagation speed in the Reka MCMK cable without a filler is valid, because the dielectric 

configuration in which the electric field propagates consists of a mix of air and insulation 

material. This results in a smaller effective dielectric constant than in the Draka MCMK, 

where the electric field propagates in a dielectric environment consisting approximately only 

of the insulating material. The dielectric constant of air is approximately one, whereas it is 

hard to determine a general dielectric constant value for PVC, since the material is available 

in many formulations depending on the target of application. 

The measurement instrumentation consisted of an Agilent DSO6104A four-channel, 1 GHz 

digital oscilloscope, a Tektronix probe power supply 1103, Tektronix high-voltage differential 

probes P5205, and a Fluke 80i110s current probe for measuring the slow, 50 Hz motor 

phase currents. More details on the instrumentation can be found in Appendix B, where the 

equipment used in the measurements and the uncertainty of the equipment are discussed.


) C EA J , 5 $ " ) 

@ EC EJ= I ? E I ? F A 

" ? D = A I 

/ 0 " / 5 I 

6 A JH EN 2 5 ! 

F H > A F M A H I K F F O 

5 K F F O JH= I B H A H 

L = HE= ? 

6 A JH EN 2 # # 

@ EBBA HA JE= D EC D L J= C A F H > A 

0 

. K A & E I 

? K HHA J F H > A 

0 

+ JO F A F M A H ? = > A 

! N # # 5 

8 = ? : BH= A 

BHA G K A ? O ? L A HJA H 

5 / * ! , 1/ * 6 I 

? K I J ? JH ? = H@ = @ 

K I A H E JA HB= ? A 

) ? JEL A @ K @ J BEJA H 

$ 0 ! ! . 

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 instrumentation. 

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 phaseto-phase 

voltage (U-V) without filtering are shown in Figures 4.28–4.32. The peak voltage 

level 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 addition 

to the perfectly timed charge pulses, the operation of the filter circuit without any control and 

with mismatched timing are also shown. Incorrect timing is not critical for the operation, but 

it can be seen that the control is nevertheless necessary, because of the strong LC resonance 

owing to the low damping factor. 

When active du/dt is applied, Figures 4.36–4.44, the peak voltage at the motor end decreases 

considerably, 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 cable 

cause some error inducing oscillation in the output voltage of the LC circuit, even if the cable


) * * % # 9 

" 8 # ) 

" " HF 

) * * # # 9 

" 8 ! ) 

" ! HF 

6 A JH EN 2 # # 

@ EBBA HA JE= D EC D L J= C A F H > A 

0 

+ JO F A F M A H ? = > A 

! N # # 5 

Figure 4.26. ABB 5.5 kW and 7.5 kW induction motors used in the measurements. The MCMK type 

power 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 correction 

method was not implemented. However, since the load current is smaller compared with the 

filter charging current (75 A), the error is not significant. However, in designs where the 

load 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 measurements 

that the 300 meter cable is too long for the designed filter, and the cable oscillation 

is not eliminated.


Voltage [V] 

Voltage [V] 

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

1000 

500 

0 


−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

b) 

. EJA H ? EI $ 0 

. A HH N ? K > A - 6 , " ' # $ 

? E B H A HI 

! + ' BA HHEJA ? HA M EJD = EH C = F 

. EJA H ? = F = ? EJ HI ! ! . 

2 = I JE? E I K = JA @ 

F K I A ? = F = ? EJ HI 

Figure 4.28. Measured voltage waveforms without active du/dt filtering applied. a) The inverter output 

voltage waveform, and b) the voltage at the open end of the 30 meter motor cable are shown. The 

overvoltage and oscillation caused by the cable reflection are clearly visible. Overvoltage 506 V, 84 %.


Voltage [V] 

Voltage [V] 

1000 

500 

0 


−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

b) 


voltage waveform and b) the voltage at the open end of the 100 meter motor cable are shown. The 

overvoltage and oscillation caused by the cable reflection are clearly visible. Overvoltage 507 V, 84 %. 

Voltage [V] 

Voltage [V] 

1000 

500 

0 


−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

a) 

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

1000 

500 

0 

−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

b) 


voltage waveform and b) the voltage at the motor end of the 100 meter cable are shown. The overvoltage 

and oscillation caused by the cable reflection are clearly visible. The effect of the 5.5 kW electric motor 

on the oscillation is minimal. Overvoltage 482 V, 80 %.


Voltage [V] 

Voltage [V] 

1000 

500 

0 


−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

a) 

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

1000 

500 

0 

−4 −3 −2 −1 0 1 2 3 4 

x 10 −5 

−500 

Time [s] 

b) 


voltage waveform and b) the voltage at the motor end of the 100 meter cable are shown. The overvoltage 

and oscillation caused by the cable reflection are clearly visible. The effect of the 7.5 kW electric motor 

on the oscillation is minimal. Overvoltage 473 V, 79 %. 

Voltage [V] 

Voltage [V] 

1000 

500 

0 


−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

b) 



overvoltage and oscillation caused by the cable reflection are clearly visible. Overvoltage 498 V, 83 %.


Voltage [V] 

1200 

1000 

800 

600 

400 

200 

0 

−200 

−400 

−600 

−800 

Inverter and active du/dt filter output voltage 


Filtered output voltage 

−1 0 1 

x 10 −4 

Time [s] 

Figure 4.33. Measured voltage waveforms, when active du/dt filter is attached to the output phases of 

the inverter, but no charge or discharge pulses are generated. No motor cable is connected. The filter is 

at full resonance, the frequency set by the filter LC constant. The low damping factor (i.e. losses) of the 

active du/dt filter is seen from the output voltage waveform, as the oscillation decays slowly, making the 

active du/dt filter useless without the active control. Absence of the active du/dt sequence has caused 

approximately 500 V of the LC resonance overvoltage, 83 %. 

Voltage [V] 

800 

700 

600 

500 

400 

300 

200 

100 

0 




−1 0 1 2 3 4 5 

x 10 −5 

−100 

Time [s] 


the inverter. No motor cable is connected. When active control as presented in Chapter 3 is properly implemented, 

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.


Voltage [V] 

800 

700 

600 

500 

400 

300 

200 

100 

0 




−1 0 1 2 3 4 5 

x 10 −5 

−100 

Time [s] 


the inverter. No motor cable is connected. The effect of a faulty charge sequence is illustrated. The pulse 

width is over 50 %, causing the filter capacitor to overcharge above the DC link voltage. The transient 

induces filter resonance, the amplitude of the resonance being the difference between the DC link and 

filter voltages at the switching instant. An error in the active du/dt sequence has caused approximately 

80 V of the LC resonance overvoltage, 13 %. 

Voltage [V] 

Voltage [V] 

1000 

500 

0 


−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

b) 

Figure 4.36. Measured voltage waveforms with active du/dt filtering applied. a) The filter output 


overvoltage and oscillation caused by the cable reflection are eliminated. Slight resonance is shown 

in the waveforms resulting from the loading caused by the power cable to the filter, because the filter 

capacitor is not an ideal voltage source. Overvoltage 10 V, 1.6 %.


Voltage [V] 

Voltage [V] 

1000 

500 

0 


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

x 10 −4 

−500 

Time [s] 

a) 

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

1000 

10 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

−10 −8 −6 −4 −2 0 2 4 6 

Time [s] 

b) 

x 10 −5 

0 

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 cable 

are shown. The motor was a 5.5 kW induction motor. The motor current (towards the motor) causes 

faulty filter discharge during the falling slope. The motor current, ≈5 A, has caused approximately 

10 V, 1.6 % LC resonance overvoltage. 

Voltage [V] 

700 

600 

500 

400 

300 

200 

100 

0 

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

−100 

−0.03 −0.02 −0.01 0 

Time [s] 

0.01 0.02 0.03 −10 

Figure 4.38. Measured filter output voltage and current with active du/dt filtering applied. The power 

cable was 30 meters long, and the motor was a 5.5 kW induction motor. The load current causes faulty 

filter discharge during the falling slope, and the negative motor current causes faulty filter charge during 

the rising slope. The resonance can be detected from the envelope of the filtered PWM voltage. The 

motor current, peak ≈ ±8 A, has caused approximately 40 V, 7 % LC resonance overvoltage. 

10 

8 

6 

4 

2 

0 

8 

6 

4 

2 

−2 

−4 

−6 

−8 

Current [A] 

Current [A]


Voltage [V] 

Voltage [V] 

1000 

500 

0 


−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

b) 

Figure 4.39. Measured voltage waveforms with active du/dt filtering applied. a) The filter output 


overvoltage and oscillation caused by the cable reflection are eliminated. Slight resonance is shown 

in the waveforms resulting from the loading caused by the power cable to the filter, because the filter 

capacitor is not an ideal voltage source. Overvoltage 6 V, 1.0 %. 

Voltage [V] 

Voltage [V] 

1000 

500 

0 


−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

b) 

Figure 4.40. Measured voltage waveforms with active du/dt filtering applied. a) The filter output voltage 

waveform and b) the voltage at the open end of the 100 meter motor cable are shown. The effect of a 

faulty charge sequence is illustrated. Eventually, the oscillation in the filter output voltage will be visible 

in the open or motor end of the cable. An error in the active du/dt sequence has caused approximately 

80 V, 13 % of the LC resonance overvoltage. The cable-reflection-induced overvoltage is 20 V, 2.9 %.


Voltage [V] 

Voltage [V] 

1000 

500 

0 


−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

a) 


1000 

10 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

−10 −8 −6 −4 −2 0 2 4 6 

Time [s] 

b) 

x 10 −5 

0 

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 are 

shown. The motor was a 7.5 kW induction motor. The motor current (towards the motor) causes faulty 

filter discharge during the falling slope. The motor current, 6.5 A, has caused approximately 30 V, 5 % 

LC resonance overvoltage. 

Voltage [V] 

700 

600 

500 

400 

300 

200 

100 

0 

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

−100 

−0.03 −0.02 −0.01 0 

Time [s] 

0.01 0.02 0.03 −10 

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 current 

causes faulty filter discharge during the falling slope, and the negative motor current causes faulty 

filter charge during the rising slope. The resonance can be detected from the envelope of the filtered 

PWM voltage. The motor current, peak ≈ ±8 A, has caused approximately 35 V, 6 % LC resonance 

overvoltage. 

8 

6 

4 

2 

10 

8 

6 

4 

2 

0 

−2 

−4 

−6 

−8 

Current [A] 

Current [A]


Voltage [V] 

Voltage [V] 

1000 

500 

0 


−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

a) 


1000 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

b) 

Figure 4.43. Measured voltage waveforms with active du/dt filtering applied. a) The filter output voltage 

waveform and b) the voltage at the open end of the 300 meter motor cable are shown. The overvoltage 

is approximately 180 V, 30 % of UDC, because the du/dt of the designed filter is too high for the long 

cable. Furthermore, the operation of the filter is interfered by the cable resonance; the LC resonance 

overvoltage is approximately 120 V, 20 % and the cable-reflection-induced overvoltage 160 V, 23 %. 

Voltage [V] 

Voltage [V] 

1000 

500 

0 


−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

Time [s] 

a) 


1000 

10 

500 

0 

−10 −8 −6 −4 −2 0 2 4 6 

x 10 −5 

−500 

−10 −8 −6 −4 −2 0 2 4 6 

Time [s] 

b) 

x 10 −5 

0 

Figure 4.44. Measured waveforms with active du/dt filtering applied. a) The filter output voltage 

waveform and b) the voltage at the motor end of the 300 meter power cable are shown. The motor was a 

5.5 kW induction motor. In addition, the current oscillation at the cable resonance frequency interferes 

the filter operation. The motor current ≈5 A, the LC resonance overvoltage approximately 30 V, 13 %, 

and the cable-reflection-induced overvoltage 230 V, 37 %. 

8 

6 

4 

2 

Current [A]


4.3.3 Additional switching losses caused by the application of the active 

du/dt method 

Estimates of the additional switching losses generated by the application of the active du/dt 

method in the prototype equipment (presented in the measurements section) were measured 

using the Norma D6100 three-phase, wide-band power analyzer. The properties of the power 

measurement equipment are presented in more detail in Appendix B. 

The measurements were carried out at the interface between the grid and the frequency converter, 

the measured effective power contains all the effictive power consumed in the prototype 

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 active 

du/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 active 

du/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 switching 

frequency in all the measurements. The 50 Hz and 1 Hz conditions were chosen to emulate 

a typical drive state situation and a 50 % duty cycle in the inverter output. As can be seen 

from the tables, the additional loss caused by the active du/dt method is 255 W for 50 Hz 

and 275 W for the 1 Hz test. The active du/dt filter in the built prototype was designed for 

a 5.5 kW drive, and it is mainly limited by the Litz wire cross-sectional area. As the loss 

is in the inverter output stage, it scales according to the modulator switching frequency. A 

drawback of active du/dt is that the losses are doubled as the switching frequency increased 

to twice the original value. 

As a comparison, the losses according to the datasheet for example in the Schaffner FN 510 

output du/dt filter are 90 W for power classes of 1.5 to 7.5 kW, and 100 to 150 W for power 

classes of 11 to 30 kW. However, the maximum cable length of the filter is limited to 80 

meters, 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 with 

criticism, since the measured total active powers from 50–330 W were small compared with 

the total dynamic range of 30 kW of the instrument in its present configuration. According 

to 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 current 

measurement of a total power of 50 W and 300 W ≈ ±2.5 mA and ≈ ±2.9 mA, for each 

phase current, respectively. 

Since the total loss power is relatively small, though, more accurate efficiency measurements 

would require measurements in a calorimeter. Nevertheless, the preliminary loss power measurements 

based on increased switching losses should give indicative results on the order of 

the 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 the 

inverter output, since there are no inverter bridge switching combinations, which would produce 

a zero common-mode voltage. Common-mode voltages, for example, are one of the 

causes for bearing currents in motors. If the voltage transients in the single output phases are 

steep, so are also the transitions in the common-mode voltage, which is detrimental for the 

electric 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 Figure 

3.4, the active du/dt ouput filtering method smooths also the common-mode voltage waveform, 

which is beneficial for the operation of the drive. However, active du/dt does function 

without the wye point connection, but in that case the wye potential is not tied to any known 

potential, and common-mode filtering capabilities of the method are lost.

100 Applying active du/dt filtering to an electric drive

Chapter 5 

Discussion and Conclusions 

In this chapter, the main results of the study are summarized, and the results obtained are 

discussed along with suggestions for further research. 

101 

In this work, motivation for the use of power converters in both electrical and electromechanical 

energy conversion is presented. The development taken place in the actual semiconductor 

power switch components generally used in power electronics is discussed in brief, and the 

problems evolved as the switches have become faster are described and explained, with a 

special focus on converter-driven motor drives. 

The known cable reflection phenomenon resulting from pulse-width-modulated inverter output 

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. The 

cable oscillation and the motor terminal overvoltages caused by the voltage reflection are described. 

The typical approach to mitigate the overvoltage and harmful stress caused by the 

high voltage peak with a high du/dt to the insulation of system is to slow down the transitions 

in the output voltage using output reactors or du/dt filters consisting of inductors and 

capacitors. 

Typically, the design of output filtering presented in the literature is based on the transient 

response of the filter, with an emphasis on the output du/dt value, whereas little attention 

is paid to the frequency plane behavior of the filter designs. Indeed, it is very important to 

take 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. The 

overshoot is seen as overvoltage. By increasing the damping factor, in other words, the losses 

of the circuit, the transient behavior of the circuit is improved, and the response is slowed 

down. The oscillation frequency of an undamped second-order circuit depends on the time 

constant of the circuit, and it can be linked to the du/dt in the filter output voltage. In this 

dissertation, 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 reduce 

the 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 component 

values and smaller filter losses than in a conventional approach. However, as can be predicted 

from the step response of an LC circuit with a low damping factor, the voltage pulses of the 

inverter induce a resonance in the circuit, at the frequency determined by the filter component 

values of the circuit. Therefore, the behavior of the filter circuit must be controlled. The 

control is implemented using extra switching in the inverter output stage at right instants to 

produce voltage slopes of desired length. The control method presented in the dissertation 

is based on the idea to use pulse width modulation in the LC circuit to produce the voltage 

slopes. 

It is claimed that, in addition to the loss and transient response considerations in the filter 

design 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 that 

has a natural resonance frequency, which depends on the propagation velocity of the voltage 

wave on the cable, and the cable length. In order to suppress the unwanted resonance in the 

system, the resonance frequency present on the stimulus fed to the system should be removed 

by 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 LC 

circuit, it is difficult to achieve great frequency plane performance, as there are no zeros 

in the frequency response to be set on the desired suppression frequencies, and to keep the 

transient response and losses at a reasonable level. In this dissertation, a new filtering method 

is presented, which overcomes these design problems present in traditional aproaches. 

In this dissertation, a new output filtering method consisting of a passive LC circuit with 

a low damping factor and active control of the filter circuit is presented, the active du/dt 

output filtering. The passive components are required in the filter circuit to provide an ability 

to produce the desired output voltage, since this cannot be implemented by using only the 

inverter output stage, at least when using the present semiconductor power switches. The 

activeness in the method refers to the fact that the filter circuit in the method is not functional 

as such, but the active control of the circuit is required to obtain the desired output voltage 

properties. However, no extra hardware is required, besides the filter components, but the 

active control of the filter can be carried out using the same inverter components already 

present. Moreover, the active control can be quite easily implemented to the modulator, since 

it can be added as the lowest (fastest time plane) modulator level. Since a correctly designed 

active du/dt filter produces a well-known output voltage waveform, which is very closely the 

same at both ends of the motor cable, the estimated realized motor terminal voltage can be 

fed as a feedback signal to the upper-level control, and the performance of the motor control 

can be improved. 

The main benefits of the method are that the controllability of the transient response is very 

good, 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. The 

component value selection affects the filter charging current, and the current can be decreased 

by increasing the inductance or decreasing the capacitance value. Large currents introduce 

problems because the current rating of the output stage must be taken into account, especially 

in low- and medium-power drives, and decreasing the capacitor too much will result in a 

considerably weaker equivalent voltage source in the output of the filter circuit. The output 

voltage rise time can also be controlled, or more precisely prolonged by the active control 

of the LC filter circuit within certain limits, but the actual component values have to be 

selected according to the fundamental, shortest rise time needed. Another major benefit of 

the active du/dt filtering method is smaller component values compared with the traditional 

output 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 motor 

causes charging and discharging errors in the filter circuit. The analysis of the filter circuit 

was carried out with an assumption that the instantaneous load current is zero when the filter is 

charged or discharged. If not, the filter current waveform is disturbed resulting in an unwanted 

resonance of the circuit. This is a problem related to implementation of the method into a 

real drive, and if the issue is not corrected, if the load current is in the order of the filter peak 

current, the method will be rendered useless. If load current values are significantly smaller 

than the filter current, the correction is not absolutely necessary, as shown by the experimental 

results 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 pulse 

acts as a current commutation that returns the current in the filter reactor to the level at which 

it was before the charge or discharge. 

Finally, the feasibility of the active du/dt filtering method was verified in a prototype environment. 

The method was implemented on a custom-built control card, with a standard Vacon 

NXP frame size 6 industrial frequency converter power unit. However, the original switches 

in the power unit were changed from the standard to faster modules. The main challenges 

are the gate driver implementation, the operation of the IGBT components at such high-speed 

pulse patterns, and the filter inductor operation. A standard scalar pulse width modulator with 

the active du/dt edge modulation was implemented in the control card and the operation of 

the prototype was tested. It was found that the developed method is feasible. The operation 

of the gate driver and the IGBT was found to be possible at the desired pulse patterns, and it 

was 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 motor 

drive has been presented in the dissertation. The theory for the operation of the method 

was provided, the key issues were discussed, and the method was proven to be feasible by 

measurements carried out using the prototype equipment developed. However, some important 

questions have arisen in the course of research, and they still remain unanswered. These

104 Discussion and Conclusions 

questions require further investigation before the functionality of the method can finally be 

shown. 

Investigation of the losses generated in the application of the active du/dt method. The component 

costs can be decreased by smaller filter components, especially if stock components 

can be used. Additional losses are generated as a result of extra switching conducted in the 

dc-to-ac inverter of the frequency converter. The active du/dt method outperforms passive 

filtering in terms of electrical performance, but is the active du/dt method better also in terms 

of losses? In addition, research must be carried out on a new power semiconductor component 

generation manufactured of new materials, which provide lower losses, such as silicon 

carbide, 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 the 

total 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 circuitry 

participating in the active filtering includes the DC link, inverter, and LC filter components. 

Therefore, all the components participating in the active du/dt must be capable of 

operating at the required frequencies, and must withstand the charging and discharging current 

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 challenging 

task especially for high current ratings. 

The limitations of an actual inverter output stage and the power switch components must be 

taken into account in order to succesfully develop the method in an electric drive. These are 

for example the losses, dead times, and various delays present in a real inverter. The basic 

operation of the active du/dt method can be performed with dead times, and the losses can be 

taken into account with sufficient accuracy by identification of the LC constant of the circuit 

by measuring DC link crossings in the step response of the circuit. However, the current 

correction pulse depends on the instantaneous value of the load current and the losses and 

delays present in the system, and thus realization of the correction pulse is more difficult 

in a real inverter than what is presented in Chapter 4 of the dissertation. The problem can 

be solved iteratively by using a simulation tool, but the properties of the power switch will 

nevertheless affect the results, and the solution is still fixed. Furthermore, the various delays 

present for example in the logic paths, gate drivers, and in the power switches themselves 

must be compensated to produce pulses of the length required by the theory, which calls for 

further investigation. 

The possibility to use various pulse patterns with the same filter circuit should be investigated. 

The applicability of the method is extended, if various lengths of voltage slopes can 

be generated using the same filter circuit. However, more detailed research is required on the 

usage 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 methods. 

• 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 this 

dissertation. However, for the method to be generally applicable, additional research especially 

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 from 

active du/dt, this would be beneficial for the usability of the method. In addition, as more 

data on the applicability of present power switch components in the method, availability of 

advanced chip technologies in the near future, and accurate power-loss measurements are 

obtained, the usability of this method can finally be verified.

106 Discussion and Conclusions

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Appendices

Appendix A 

Simulation models 

115 

The simulation model used to verify the usage of the correction pulse in Chapter 4 for the 

mitigation of the filter output voltage error caused by the load current of the electric motor 

is presented in this appendix. The model is implemented in the MATLAB SIMULINK 

environment. Also, the simple cable reflection simulation model is shown in this appendix.

116 Simulation models 

Discrete, 

Ts = 1e-008 s 

powergui 

Modulator 

Currents 

GateDrive 

Memory 

Scope2 

Scope 

C 

g 

C 

g 

C 

g 

Scope3 

IGBT/Diode2 

IGBT/Diode1 

IGBT/Diode 

Scope1 

E 

m 

E 

m 

E 

m 

Saturation 

Ramp 

ir,is (A) 

Tm 

m 

A 

B 

C 

-Krpm 

Vabc 

A 

Iabc 

B a 

b 

C 

c 

Three-Phase 

V-I Measurement 

Vabc 

A 

Iabc 

B a 

b 

C 

c 

Three-Phase 

V-I Measurement1 

Figure A.1. Top level of the correction pulse simulation model. The modulator block forms the gate 

drive signals for the output stage consisting of SIMULINK SimPowerSystems IGBT/Diode components. 

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 out 

after the output stage and after the active du/dt filter. The motor current measurement is used to form 

correction pulses of the right length. 

 

Active du/dt filter L U 

 

 

Active du/dt filter L V 

DC Voltage Source 

N (rpm) 

Asynchronous Machine 

SI Units 

 

Active du/dt filter L W 

Te (N.m) 

C 

g 

Active du/dt filter C U 

C 

g 

C 

g 

IGBT/Diode5 

IGBT/Diode4 

IGBT/Diode3 

Active du/dt filter C V 

E 

m 

E 

m 

E 

m 

Active du/dt filter C W

Hi 

Hi_out 

Lo 

Lo_out 

Current 

Phase_U 

Hi 

Hi_out 

1 

GateDrive 

Signal(s)Pulses 

Lo 

PWM Generator 

Lo_out 

Current 

Phase_V 

Hi 

Hi_out 

Lo 

Lo_out 

Current 

Phase_W 

1 

Currents 

117 

Figure A.2. Top level of the modulator block. It consists of a standard, configurable SimPowerSystems 

PWM Generator and three identical active du/dt edge modulator blocks to provide the output stage with 

the required gate drive signals.


1 

Hi_out 

Switch 

Saturation 

Add 

Hi 

1 

Hi 

Hi_out 

Lo 

Kill pulses! 

killmodulation 

Lo_out 

Current 

2 

Lo 

Constant1 

Submodulator 

2 

Lo_out 

Switch1 

Saturation1 

Hi 

Hi_out 

Lo 

Current 

Lo_out 

Full_throttle! 

Current Correction Pulse Generator 

Figure A.3. One of the active du/dt edge modulator blocks. It consists of an active du/dt edge modulator 

and a current correction pulse generator. The edge modulator forms the charge and discharge sequences 

according to the filter LC constant, as presented by the theory in Chapter 3. The current correction pulse 

is formed according to the theory presented at the beginning of Chapter 4. It is also possible to disable 

the active du/dt modulation and pass through the plain PWM signals. 

3 

Current 

Add1 

|u| 

>= 

Abs 

Relational 

Operator 

If_peak 

Constant

1 

Hi_out 

1 

Hi 

Switch 

Product 

Add 

1 

z+zeros(t1,1)’ 

Discrete 

Transfer Fcn 

Product2 

1 


Discrete 

Transfer Fcn1 

2 

Lo_out 

Switch1 

Product1 

Add1 

1 


Discrete 

Transfer Fcn2 

Product3 

1 


Discrete 

Transfer Fcn3 

2 

Lo 

AND 

3 

Kill pulses! 

Logical 

Operator 

NOT 

Logical 

Operator1 

AND 

>= 

4 

Current 

Logical 

Operator2 

Relational 

Operator1 

0 

Constant1 

119 

Figure A.4. Active du/dt charge and discharge pulses are formed according to the theory. If the load 

current is greater than the LC filter maximum current, only the correction pulse is used, and therefore 

the charge or discharge pulse is omitted, depending on the sign of the load current.


1 

Hi_out 

Out 

z −i 

In 

Delay 

2 

Lo 

Switch 

Product 

Add 

Variable 

Integer Delay 

1 


Discrete 

Transfer Fcn1 

2 

Lo_out 

z −i 

In 

Out 

Delay 

Variable 

Integer Delay1 

Switch1 

1 

Hi 

Product1 

Add1 

1 


Discrete 

Transfer Fcn2 

Figure A.5. Correction pulse is formed according to the theory. Depending on the sign of the load 

current, either the charge or discharge sequence requires a correction pulse of a varying length. If the 

load current exceeds the filter maximum current, the charge or discharge pulse is omitted, depending on 

the direction of the current, and only a correction pulse is used. In this case, the length of the correction 

pulse is half the rise time calculated from the filter LC constant. 

0 

Constant2 

AbsCurrent 

|u| 

t_delay 

3 

Current 

Full_pulse 

Calculate delay 

Abs 

>= 

0 

Relational 

Operator1 

Constant1 

4 

Full_throttle!

t1 

Constant6 

1 

t_delay 

2 

Full_pulse 

Switch 

T 

Constant4 

sqrt 

L 

round 

Subtract 

Product 

Rounding 

Function 

Product3 

Product1 

Math 

Function 

Constant 

Figure A.6. Length of the correction pulse is calculated by using Eq. (4.5). If the full-length correction 

pulse is required, a precalculated constant is used. 

C 

stcoef 

sqrt 

Divide 

asin 

Constant1 

Constant3 

Trigonometric 

Function 

Product2 

Math 

Function1 

1 

AbsCurrent 

Divide1 

Udclink 

Constant2 

121


Zs 

Step_out 

LTI System 

Source 

Gl 

1 

Gs 

Motor Voltage 

Add 

Motor reflection coefficient 

Attenuation 

Cable 

Delay 

Add1 

Figure A.7. Simple cable reflection model used in the determination of cable-reflection-induced overvoltages, 

as presented in (Tarkiainen et al., 2002; Ström et al., 2006). 

Inverter reflection coefficient 

1 

Cable 

Delay1 

Attenuation1

Appendix B 

Measurement equipment 

The measurement equipment used in the measurements is presented in this appendix, along 

with 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 · (instrumentageinyears) 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, 20-30 ◦ C,

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 20-30 ◦ C,

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 below 

5 A) 

• Measurement accuracy (100–400 kHz): ±(3.0+0.13)% (for AC+DC measurement below 

5 A) 

Nominal temperature range 18 ◦ C to 28 ◦ C. 

125

126 Measurement equipment

Appendix C 

Asynchronous machine equivalent 

circuit parameters 

4 I 

I I 

 

HI 

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 motor 

sizes. 

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 mH 

2.2 18.9 mH 18.9 mH 425 mH 5450 mΩ 3940 mΩ 36.9 mH 

5.5 7.18 mH 7.18 mH 209 mH 1480 mΩ 1480 mΩ 14.1 mH 

11 3.52 mH 3.52 mH 108 mH 447 mΩ 383 mΩ 6.93 mH 

45 1.18 mH 1.18 mH 31.5 mH 64.3 mΩ 52.1 mΩ 2.31 mH 

75 652 µH 652 µH 19.3 mH 32.4 mΩ 24.8 mΩ 1.28 mH 

110 491 µH 491 µH 13.7 mH 18.5 mΩ 13.3 mΩ 964 µH 

355 147 µH 147 µH 4.71 mH 3.67 mΩ 3.67 mΩ 289 µH 

710 71.7 µH 71.7 µH 2.29 mH 1.54 mΩ 1.53 mΩ 141 µH 

4 H 

127

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