Löpnummer: EN1318 [622275]
Löpnummer: EN1318
Examensarbete för Civilingenjörsexamen i energiteknik, 30 hp
Energy efficiency and harmonics in electric power systems
Fredrik Kühn Department of Applied Physics and Electronics
2013 – 05 -05
I
Spring 2013
ABSTRACT
The choice of power system components is traditionally assembled with great attention to the functional
performance and interaction of components. In addition, the choice of components with respect to energy efficiency today
plays an increasingly important role, this is an aspect that is generally neglected , especially when taking into mind
indust ries efforts to reduce environmental impact, the margin is, it can also improve the economy from an investment
perspective. ÅF needs a thorough study on how the situation is today on the market and just how large potential there are
available by selecting the right components. This thesis is intended to investigate this potential and to facilitate a
comparison of the energy performanc e of electric power components.
A harmonic is a wave whose frequency is an integer multiple of the frequency of some fundamental wave. When
present in an electric power system it is added to the reference wave and the resulting wave becomes a fluctuating signal
and thus the quality of the electricity i s disfigured. They are generated by modern electronic devices that include adjustable
speed drives and ac/dc converters. Devices such as CFLs, battery chargers, speed controlled motors and pump are all
devices who contribute to the generation of harmonics in power systems. The concentration of this type of equipment
increases rapidly, for example, loading of electric cars demands ac/dc converters and industries increases their usage of
speed controlled motors and pumps.
At a first look on the energy loss and economics in power systems the losses appears to be fairly static and on the
constructor of components responsibility. However, when harmonics are present in power systems, extra heat dissipation
in equipment occurs and an increase of the RMS value of current and voltage leads to higher subscription cost for energy
consumers, a method for calculating the cost of harmonics with m easurements and analysis of harmonic content in parts of
SKF’s power system is performed and solutions for mitigation presented.
Results showed large potential in improving investments and reducing enviromental impact by choosing
components not only for funcional performance but also for energy performance, interrupters is the only component in this
project that did not hold a significant potential. A method for calculating the economic impact of harmonics in industries
was developed and showed a large economic potential in mitigation of these, however, mitigation solutions was not
profitable because of high harmonic fil ter prices.
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Spring 2013
PREFACE
This master ’s thesis has been written at the Department of Applied Physics and Electronics at Umeå University of Science
and Technology in cooperation with ÅF consulting. It closes my Energy Engineering Master with Electrical Power as main
topic.
The objectives for this thesis started out quite broad with the intent of finding parts of electric power systems worth
investigating from an energy optimization perspective. This resulted in three main questions to be investigated which are
presented in the introduction cha pter.
I want to send a special thank to my supervisor s Haris Mehmedovic and Robert Josefsson at ÅF Power System Analysis
Group for giving me this opportunity and supporting me during the making. I also want to thank my University tutor,
Johan Pålsson for the great feedback on the thesis layout and written parts.
Thank you Gert Nylén , ÅF consulting for your enthusiasm and helpfulness, you contributed a lot with your expertise in
measurements of electric quality and signal analyzing.
Hans Moberg at SKF , thank you for giving me the opportunity of analyzing your system, the case study is an important
part of this work.
Finally I would like to thank my girlfriend Karoline, my mother Marie, my father Rolf and brother Daniel for your love
and for listening to my concerns and ideas about this thesis.
Fredrik Kühn
Gothenburg, the 25th of April 2013
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Spring 2013
CONTEXT
Our earth faces severe challenges; the energy consumption needs to become
totally sustainable in order for us to survive in the long -term. This is a
challenge which is partly political and partly technical. The Kyoto Protocol
which regulated the energy policies for 191 countries worldwide from 1997
to 2012 is no longer active and negotiations about a new agreement have
been staggering. The latest confe rence was held in Copenhagen 2009 and
resulted in an agreement that we cannot let the global temperature rise reach
above two degrees Celsius, although no conclusive deals were made from
the participating nations. The negotiati ons were often characterized by short
term arguments which are unfortunate for our future population. We have to
start taking a larger responsibility for the long term future and it should begin with making a few charitable decisions.
As for the technology we are in the middle of a historical change towards energy optimization and
sustainable energy production. Fossil fuels are becoming less politically accepted and many nations are starting to replace
it with green energy. This evolution leads to large chan ges in production sites, transmission grids and distribution facilities.
In many cases it leads to some production sites closure and other, ”green”, sites replacement of it. The transmission grids
have to become adapted to the changing ways of production and consumption, in some cases this means adapting to more
decentralized sites like wind power and in other cases be able to manage the increasing share of electric car -charging. In
distribution facilities such as industries, hospitals and railways the mai n focus is on energy efficiency and thus minimizing
the energy loss at specific facilities.
IVA, the Swedish Royal Engineering Academy informs in ”Energieffektivisering, möjligheter och
hinder1” that the potential for profitable ene rgy optimization in the industry sector is about 13 TWh/y and in Sweden as a
total the potential was estimated to be about 50 TWh/y. Energy optimization is one step on the road towards total
sustainability on earth.
Spring 2013 TABLE OF CONTENT
1 INTRODUCTION ………………………….. ………………………….. ………………………….. ………………………….. ……………………. 1
1.1 ENERGY LOSS ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. …… 1
1.2 ENERGY EFFICIE NCY ………………………….. ………………………….. ………………………….. ………………………….. ………………………. 2
1.3 CHOOSING COMPONENTS ………………………….. ………………………….. ………………………….. ………………………….. ……………….. 2
1.4 RECTIFICATION ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. … 2
1.5 MANAGING HARMONICS ………………………….. ………………………….. ………………………….. ………………………….. …………………. 2
1.6 QUESTIONS TO BE ANSWE RED ………………………….. ………………………….. ………………………….. ………………………….. ………….. 3
2 TRANSFORMERS ………………………….. ………………………….. ………………………….. ………………………….. ………………….. 4
2.1 LOAD LOSS ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. …….. 4
2.2 NO LOAD LOSS ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. … 4
2.3 TRANSFORMER EFFICIEN CY ………………………….. ………………………….. ………………………….. ………………………….. ………………. 5
2.4 AMORPHOUS METAL TRANSF ORMERS – REDUCING NO LOAD LOS S ………………………….. ………………………….. ………………………. 6
2.5 TRANSFORMER EFFICIENC IES IN EUROPE ………………………….. ………………………….. ………………………….. …………………………. 7
2.6 EUROPEAN EFFICIENCY STANDARD EN 50464 -1 ………………………….. ………………………….. ………………………….. ………………. 8
2.7 ON THE MARKET ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. 9
2.7.1 ABB TRANSFORMERS ………………………….. ………………………….. ………………………….. ………………………….. ………………. 10
2.7.2 SIEMENS TRANSFORMERS ………………………….. ………………………….. ………………………….. ………………………….. ………….. 14
2.7.3 ABB AMORPHOUS METAL CORE TRANSFORMER ………………………….. ………………………….. ………………………….. …………… 17
3 CABLES – A METHOD FOR COMPARI SON ………………………….. ………………………….. ………………………….. … 18
4 BREAKERS AND INTERRU PTERS ………………………….. ………………………….. ………………………….. ……………….. 19
4.1 INTERUPTER DESIGN ………………………….. ………………………….. ………………………….. ………………………….. ……………………. 19
4.2 INTERRUPTER ENERGY PERFORMANCE ………………………….. ………………………….. ………………………….. ………………………….. . 19
5 ADJUSTABLE SPEED DRI VES ………………………….. ………………………….. ………………………….. ……………………….. 20
5.1 ASD DESIGN ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. …. 20
5.2 VFD ENERGY PERFORMANCE ………………………….. ………………………….. ………………………….. ………………………….. …………. 21
Spring 2013 6 HARMONICS ………………………….. ………………………….. ………………………….. ………………………….. …………………………. 22
6.1 CAUSES ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. ……….. 23
6.1.1 RECTIFICATION ………………………….. ………………………….. ………………………….. ………………………….. ………………………. 24
6.1.2 12 PULSE RECTIFICATION ………………………….. ………………………….. ………………………….. ………………………….. …………… 25
6.2 EFFECTS ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. ………. 26
6.3 INCREASED FREQUENCY ⇾ INCREASED LOSSES – THE SKIN EFFECT ………………………….. ………………………….. ……………………… 28
6.4 ENERGY LOSS IN COMPON ENTS DUE TO HARMONIC S ………………………….. ………………………….. ………………………….. …………. 31
6.4.1 TRANSFORMERS ………………………….. ………………………….. ………………………….. ………………………….. ……………………… 31
6.4.2 CABLES ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. ……. 31
6.4.3 CAPACITORS ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. 32
7 SOLUTIONS TO ATTENUA TE HARMONICS ………………………….. ………………………….. ………………………….. . 33
7.1 BASIC SOLUTIONS ………………………….. ………………………….. ………………………….. ………………………….. ……………………….. 33
7.1.1 POSITION THE NON -LINEAR LOADS UPSTREA M IN THE SYSTEM ………………………….. ………………………….. ………………………. 33
7.1.2 GROUP THE NON -LINEAR LOADS ………………………….. ………………………….. ………………………….. ………………………….. ….. 33
7.1.3 CREATE SEPARATE SOURC ES ………………………….. ………………………….. ………………………….. ………………………….. ……….. 34
7.1.4 TRANSFORMERS WITH SPE CIAL CONNECTIONS ………………………….. ………………………….. ………………………….. …………….. 34
7.2 HARMONIC FILTERING ………………………….. ………………………….. ………………………….. ………………………….. ………………….. 35
7.2.1 PASSIVE FILTERS ………………………….. ………………………….. ………………………….. ………………………….. ……………………… 35
7.2.2 ACTIVE FILTERS ………………………….. ………………………….. ………………………….. ………………………….. ………………………. 36
7.3 INSTALLATION OF HIGHER -PULSE RECTIFIERS ………………………….. ………………………….. ………………………….. …………………… 37
8 COMPUTER MODELING AN D ANALYSIS: HARMONIC FLOW ………………………….. ……………………….. 39
8.1 FOURIER ANALYSIS ………………………….. ………………………….. ………………………….. ………………………….. ………………………. 39
8.2 HARMONIC SYSTEM STUDY ………………………….. ………………………….. ………………………….. ………………………….. ……………. 41
8.3 THE BUS ADMITTANCE MA TRIX ………………………….. ………………………….. ………………………….. ………………………….. ……….. 41
8.4 ADMITTANCE ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. … 42
8.5 MODELLING OF POWER LINES ………………………….. ………………………….. ………………………….. ………………………….. ………… 42
9 CASE STUDY: SKF POWE R DISTRIBUTION SYSTE M ………………………….. ………………………….. ………….. 43
9.1 SYSTEM OVERVIEW ………………………….. ………………………….. ………………………….. ………………………….. ………………………. 43
9.2 SYSTEM COMPONENTS ………………………….. ………………………….. ………………………….. ………………………….. …………………. 44
9.2.1 TRANSFORMER (T5) ………………………….. ………………………….. ………………………….. ………………………….. ………………… 44
9.2.2 2 × CAPACITOR (C1, C2) ………………………….. ………………………….. ………………………….. ………………………….. ………….. 45
9.3 MEASUREMENTS OF HARMO NICS ………………………….. ………………………….. ………………………….. ………………………….. ……. 46
Spring 2013 9.3.1 INSTRUMENTS ………………………….. ………………………….. ………………………….. ………………………….. ………………………… 46
9.3.2 METHOD ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. ….. 46
9.3.3 PERIOD ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. ……. 46
SUB PERIODS ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. ………… 46
9.3.4 QUALITY OF MEA SUREMENTS ………………………….. ………………………….. ………………………….. ………………………….. ……… 46
10 RESULTS ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. .. 47
10.1 MEASUREMENTS ………………………….. ………………………….. ………………………….. ………………………….. ………………………… 47
10.2 HARMONIC FILTER INVES TMENTS ………………………….. ………………………….. ………………………….. ………………………….. …….. 48
10.2.1 NO FILTER ………………………….. ………………………….. ………………………….. ………………………….. …………………………. 48
10.2.2 PASSIVE FILTER ………………………….. ………………………….. ………………………….. ………………………….. …………………… 50
10.2.3 PASSIVE FILTER INVESTMENT ………………………….. ………………………….. ………………………….. ………………………….. ….. 52
10.2.4 ACTIVE FILTER ………………………….. ………………………….. ………………………….. ………………………….. ……………………. 53
10.2.5 ACTIVE FILTER INVESTMENT ………………………….. ………………………….. ………………………….. ………………………….. …… 55
10.3 EXTRA HEAT DISSIPATIO N DUE TO HARMONICS ………………………….. ………………………….. ………………………….. ………………… 56
10.3.1 CABLES ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. … 56
10.3.2 TRANSFORMERS ………………………….. ………………………….. ………………………….. ………………………….. ………………….. 57
10.3.3 CAPACITORS ………………………….. ………………………….. ………………………….. ………………………….. ………………………. 58
10.4 TRANSFORMER COMPARIS ON ………………………….. ………………………….. ………………………….. ………………………….. …………. 59
10.5 CABLES COMPARISON ………………………….. ………………………….. ………………………….. ………………………….. ………………….. 61
11 CONCLUSIONS ………………………….. ………………………….. ………………………….. ………………………….. …………………. 62
11.1 IS THERE A POTENTIAL FOR SAVINGS BY CHOOS ING HIGH EFFICIENCY COMPONENTS ?………………………….. ………………………….. . 62
11.2 WHAT IS THE ECONOMIC IMPACT OF HARMONICS IN POWER SYSTEMS ? ………………………….. ………………………….. ………………. 63
11.3 HOW MUCH ENERGY LOSS DOES HARMONICS CAUSE IN ELECTRIC POWER CO MPONENTS ? ………………………….. …………………….. 64
11.3.1 CABLES ………………………….. ………………………….. ………………………….. ………………………….. ………………………….. … 64
11.3.2 TRANSFORMERS ………………………….. ………………………….. ………………………….. ………………………….. ………………….. 64
11.3.3 CAPAC ITORS ………………………….. ………………………….. ………………………….. ………………………….. ………………………. 64
12 REFERENCES ………………………….. ………………………….. ………………………….. ………………………….. …………………… 65
Spring 2013 TABLE OF FIGURES
FIGURE 1:SINGLE PHASE TRANSFOR MER CONSTRUCTION ………………………….. ………………………….. ………………………….. ……………. 4
FIGURE 2. HTTP ://WWW .ENERGYRATING .GOV.AU/WP-CONTENT /UPLOADS /2011/03/200717 -MEPS -TRANSFORMERS .PDF …………………………. 5
FIGURE 3. OPERATING EFFICIENCY OF DISTRIBUTION SECT OR DISTRIBUTION TRAN SFORMERS , EU-27 AND NORWAY ………………………….. …………. 7
FIGURE 4. BREAKDOWN OF DISTRIBU TION SECTOR DISTRIBU TION TRANSFORMER LOS SES, EU-27 AND NORWAY ………………………….. ……………… 7
FIGURE 5. NO LOAD LOSS STANDARD FOR DISTRIBUTION TRA NSFORMERS IN EUROPE ………………………….. ………………………….. …………………. 8
FIGURE 6. LOAD LOSS STANDARD FO R DISTRIBUTION TRANS FORMERS IN EUROPE ………………………….. ………………………….. ……………………… 8
FIGURE 7. NO LOAD -LOSS AND LOAD LOSS F OR DIFFERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. …………………….. 10
FIGURE 8. EFFICIENCIES FOR DIFF ERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. ………………………….. ……………… 10
FIGURE 9. NO LOAD LOSS AND LOAD LOSS FOR DIFFERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. …………………….. 11
FIGURE 10. EFFICIENCIES FOR DIFF ERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. ………………………….. ……………. 11
FIGURE 11. NO LOAD LOSS AND LOAD LOSS FOR DIFFERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. …………………… 12
FIGURE 12. EFFICIENCIES FOR DIFFERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. ………………………….. ……………. 12
FIGURE 13. NO LOAD LOSS AND LOAD LOSS FOR DIFFERENT ABB POWER DISTRIBUTION TRANSFO RMERS ………………………….. …………………… 13
FIGURE 14. EFFICIENCIES FOR DIFF ERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. ………………………….. ……………. 13
FIGURE 15. NO LOAD LOSS AND LOAD LOSS FOR DIFFERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. …………………… 14
FIGURE 16. EFFICIENCIES FOR DIFF ERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. ………………………….. ……………. 14
FIGURE 17. NO LOAD LOSS AND LOAD LOSS FOR DIFFERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. …………………… 15
FIGURE 18. EFFICIENCIES FOR DIFF ERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. ………………………….. ……………. 15
FIGURE 19. NO LOAD LOSS AND LOAD LOSS FOR DIFFERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. …………………… 16
FIGURE 20. EFFICIENCIES FOR DIFF ERENT ABB POWER DISTRIBUTION TRANSFORMERS ………………………….. ………………………….. ……………. 16
FIGURE 21. PRINCIPLE CHART OVER THE METHOD OF A TOC COMPARISON ………………………….. ………………………….. ………………………….. 18
FIGURE 22. EFFICIENCIES FOR DIFF ERENT ABB SWITCH DISCONNECTORS ………………………….. ………………………….. ………………………….. …. 19
FIGURE 23HTTP ://IMAGE .GREENMANUFACTURER .NET/A/DRIVING -ENERGY -EFFICIENCY -IN-MOTORS -VFD-DIAGRAM .GIF ………………………….. …. 20
FIGURE 24 HTTP ://WWW .ELECTRICAL -INSTALLATION .ORG/ENW/IMAGES /9/9 A/FIGM12 B.JPG ………………………….. ………………………….. …. 22
FIGURE 25HTTP ://WWW .ELECTRICAL -INSTALLATION .ORG/ENW/IMAGES /2/29/F IGM05. JPG ………………………….. ………………………….. …… 23
FIGURE 26 HTTP ://EN.WIKIPEDIA .ORG/WIKI/FILE:6_PULSE _BRIDGE _WITHOUT _INDUCTANCE .PNG ………………………….. ………………………….. 24
FIGURE 27 HTTP ://EN.WIKIPEDIA .ORG/WIKI/FILE:BRIDGE _RECTIFIER _AT_ALPHA %3D0_ U%3D0. PNG ………………………….. …………………….. 24
FIGURE 28. RESULTING VOLTAGE WIT H 30 DEGREES PHASE SHIFT CREATING A SMOOTHER DC THAN A 6-PULSE RECTIFYER ………………………….. .. 25
FIGURE 29. LINE DIAGRAM OVER A 12-PULSE RECTIFYER ………………………….. ………………………….. ………………………….. …………………… 25
FIGURE 30HTTP ://WWW .ELECTRIC AL-INSTALLATION .ORG/ENW/IMAGES /1/14/F IGM08. JPG ………………………….. ………………………….. …… 26
FIGURE 31HTTP ://UPLOAD .WIKIMEDIA .ORG/WIKIPEDIA /COMMONS /THUMB /C/C7/SKINEFFECT _REASON .SVG/220 PX-SKINEFFECT _REASON .SVG.PNG
………………………….. ………………………….. ………………………….. ………………………….. ………………………….. ……………………… 28
FIGURE 32HTTP ://UPLOAD .WIKIMEDIA .ORG/WIKIPEDIA /COMMONS /THUMB /6/61/S KIN_DEPTH .SVG/325 PX-SKIN_DEPTH .SVG.PNG …………….. 28
FIGURE 33. HTTP ://WWW .ELECTRICAL -INSTALLATION .ORG/ENWIKI /BASIC_SOLUTIONS _TO_ATTENUATE _HARMONICS ………………………….. …… 33
FIGURE 34. HTTP ://WWW .ELECTRICAL -INSTALLATION .ORG/ENWIKI /BASIC_SOLUTIONS _TO_ATTENUATE _HARMONICS ………………………….. …… 33
FIGURE 35. HTTP ://WWW .ELECTRICAL -INSTALLATION .ORG/ENWIKI /BASIC_SOLUTIONS _TO_ATTENUATE _HARMONICS ………………………….. …… 34
FIGURE 36. HTTP ://WWW .ELECTRICAL -INSTALLATION .ORG/ENWIKI /BASIC_SOLUTIONS _TO_ATTENUATE _HARMONICS ………………………….. …… 34
FIGURE 37. HTTP ://WWW .MID-ISLAND .COM/DOWNLOADS /PDFS/DRIVES -BR011 B-EN-P.PDF.PDF ………………………….. ………………………….. . 35
FIGURE 38 HTTP ://WWW .MID-ISLAND .COM/DOWNLOADS /PDFS/DRIVES-BR011 B-EN-P.PDF.PDF ………………………….. ………………………….. .. 36
FIGURE 39.
HTTP ://WWW 02.ABB.COM/GLOBAL /HUABB /HUABB 008. NSF/0/45 DF9D2440 A9199 BC1257 A2C004404 D3/$ FILE/PQF+ FELHARM %C3%
B3NIKUS +SZ%C5%B1 R%C5%91 K+.PDF ………………………….. ………………………….. ………………………….. ………………………….. .. 36
FIGURE 40 FUNDAMENTAL SINE WAVE VERSUS ITS 5TH HARMONIC ADDED , PLOTTED IN MATLAB ………………………….. ………………………….. …. 40
FIGURE 41 OVERVIEW OF THE CASE STUDY -SYSTEM . ………………………….. ………………………….. ………………………….. ……………………….. 43
FIGURE 42. CURRENT HARMONICS AT L05.1 ………………………….. ………………………….. ………………………….. ………………………….. …….. 47
FIGURE 43. VOLTAGE HARMONICS AT L05.1 ………………………….. ………………………….. ………………………….. ………………………….. …….. 47
Spring 2013 FIGURE 44. NO FILTER : FUNDAMENTAL CURRENT V ERSUS DISTORTED ………………………….. ………………………….. ………………………….. ……. 48
FIGURE 45. NO FILTER : FUNDAMENTAL VOLTAGE V ERSUS DISTORTED ………………………….. ………………………….. ………………………….. …….. 48
FIGURE 46. PASSIVE FILTER ; FUNDAMENTAL VERSUS P ASSIVE FILTER CURREN T ………………………….. ………………………….. ………………………. 50
FIGURE 47. PASSIVE FILTER ; FUNDAMENTAL VERSUS P ASSIVE FILTER VOLTAG E ………………………….. ………………………….. ……………………….. 50
FIGURE 48. PAYOFF DIAGRAM FOR A PASSIVE FILTER INVESTMENT ………………………….. ………………………….. ………………………….. ………… 52
FIGURE 49. FILTERED : FUNDAMENTAL VERSUS AC TIVE FILTER CURRENT ………………………….. ………………………….. ………………………….. ….. 53
FIGURE 50. FILTERED : FUNDAMENTAL VERSUS AC TIVE FILTER VOLTAGE ………………………….. ………………………….. ………………………….. ….. 53
FIGURE 51. PAYOFF DIAGRAM FOR AN ACTIVE FILTER INVEST MENT . ………………………….. ………………………….. ………………………….. ………. 55
FIGURE 52. HEAT DISSIPATION IN C ABLES DISTRIBUTED AT EACH HARMONIC . ………………………….. ………………………….. ………………………… 56
FIGURE 53. INCREASED HEAT DISSIP ATION IN CAPACITORS C1 AND C1 CAUSED BY HARMONICS ………………………….. ………………………….. …… 58
FIGURE 54.T RANSFORMER TOC DEVELOPMENT FOR TWO ALTERNATIVES OVER 11 YEARS ………………………….. ………………………….. …………. 60
FIGURE 55. FINAL TOC FOR TWO INVESTMENTS ; REGULAR GRAIN ORIENTED VERSUS AMOURPHOUS METAL CORE TRANSFORMERS . ………………. 60
FIGURE 56. CABLE TOC DEVELOPMENT FOR TWO ALTERNATIVES OVER 30 YEARS . ………………………….. ………………………….. ………………….. 61
Spring 2013 DISPOSTION
PART 1 •Function and energy performance of power system components
PART 2 •Energy aspect of harmonics in power systems
PART 3 •Results/conclusions from PART 1 and PART 2
1
Spring 2013 1 INTRODUCTION
This chapter introduces the reader by briefly descr ibing energy loss in electrical distribution and different attenuation
methods. At first we take a look at what energy loss in electric conductors really are and what causes it . Installing the right
components in a system with load characteristics taken into account wi ll increase energy efficiency and improve the
investment. When driving m otors, adjustable speed increase efficiency but can also cause other problems such as harmonic
current injection and thus give rise to energy loss in other parts of the system , a brief review of harmonic management are
presented and questions this project has explored are listed in the end.
1.1 ENERGY LOSS
Electric energy loss are c aused by joule heating , also known as resistive heating and ohmic heating . Joule heating is the
result of the process by which the passage of an electric current through a conductor releases heat. James Prescott Joule was
the first to study this phenomenon in 1841.
Joule heating is caused by the interactions between the movin g particles that form the current and the atomic ions that make
up the body in the conductor. Charged particles in an electric circuit are accelerated by an electric field but give up some of
its kinetic energy each time they collide with an ion. This kine tic energy is then converted to vibration in the particles which
we refer to as heat.
A lot of energy that is generated to facilities goes to waste in different ways. For example w hen transformers draw power to
stay magnetized, even though they are not used for power distribution, this power then become waste. When light s, heating
and ventilation are turned on even though no one is using it, the energy is wasted and when motors and pumps is driven with
fixed speed much energy can be saved by using variab le speed.
This project has evaluated energy loss that occurs when :
– Components hold poor efficiencies, the market research in part 1 presents today’s efficiency levels on the market and
different choices are evaluated in chapter 10,”results”.
– Distribution utilities create harmonics in the load s and send these through debitation meters, the signal measures higher
power RMS than what is actually consumed , A Fourier analysis (see 8.1) solves this and gives what extra power is
debited for in the case study.
– Harmonics flow th rough components and give rise to increased energy loss (see 6.2). Harmonic m anagement methods
for attenuating this type of problems are described in the thesis and evaluated in chapter 10. A case study in SKF AB
has been performed with measurements of the harmonic content in one of the transformer stations.
2
Spring 2013 1.2 ENERGY EFFICIENCY
The ratio betw een useful output and the input of an energy conversion is called energy efficiency. Typically it is denoted the
Greek letter small Eta ( η). This ratio is used as an index of how efficient certain electric entities are. It is defined as:
Eq. 1
Where
Pout = output power [W]
Pin = input power [W]
1.3 CHOOSING COMPONENTS
In order to find out which component is optimal for some certain installation, knowledge of the load characteristics are of
utmost importance. Functional conditions such as what voltages, currents and short -circuit power are critical and nowaday s
always taken into account. But knowledge and estimations about characteristics of the load such as max, min and mean value
of the power, w hich periods that low resp. high power are expected and how much harmonics that are going to be present.
For example transformers; if the load is expected to reduce to minimum every night, no -load loss can be assumed to be a
major contributor to the total losses. Then it would be wise to choose a transformer who is constructed with extra low no -load
loss. And for cables; if harmonic levels are expected to be high, to prevent the cable from overloading an increase in the cross
area is necessary. When it come s to harmonics and preventing problems originating from them, choosing speed drives with
higher pulse numbers is an important assessment, 6 -pulse speed drives generates harmonic levels up to 30 % THD versus 24
pulse-drives who generates as low as 2.7 % THD (see section 7.3).
1.4 RECTIFICATION (AD/DC)
Installing rotating machines with adjustable speeds can cause l arge energy savings because it allows the machines to be
operated on its optimal efficiency more often. Variable speed in machines is dependent on adjustable speed drives, which are
devices that consist of three steps: rectification, filtering and pulse width modulation. The first step converts the AC power to
DC, the second smoothens the DC and the third creates AC with variable frequency which varies the rotating speed of
machines . The problem with har monics occurs in the first step, the rectification process which sends harmonics back into the
distribution system. This process is explained in section 6.1.1 . More devices that depend on rectification and thus cause
harmonics are listed in section 6.1.
1.5 MANAG ING HARMONICS
In order to prevent or fix problems with harmonics in electric power systems various measures can be taken. Basic solutions
such as designing the system in certain ways in order to protect sensitive devices, also filter solutions could sometimes prove
efficient and most ofte n, not causing the problem from start by choosing the right speed drives, low energy lamps and
rectifiers could serve as a good alternative. These solutions are presented in chapter 7 and the latter two types of attenuation
methods are evaluated and compared economically in ”Results”.
3
Spring 2013
1.6 QUESTIONS TO BE ANSWE RED
These questions are discussed in chapter 11,”Conclusions ”.
PART 1
1. Is there a potential for savings by choosing high efficiency components ?
Part 1 consists of a market research and presenting of methods with the goal of contrasting regular choices of components to
more efficient. An economic comparison between these contrasting choices is presented in the result chapter to investigate if
there are a significant potential to be earned in order to improve investments.
PART 2
2. What is the economic impact of harmonics in electric power systems?
Certain electric al devices are custom to certain frequencies e.g. 50 Hz so this can be considered as the useful frequency. The
RMS, Root -Mean -Square value of a sinusoidal is the mean value of the magnitude. When a signal also contains harmonics ,
these adds to the RM S value. When debiting electric energy , consumers do not on ly pay for the useful 50 Hz RMS but also
all other harmonic frequencies that are on the debiting signal. A Fourier analysis is used for solving what extra power that is
paid for in the case study.
3. How much energy loss does harmonics cause in electric power components ?
When harmonics travel through power components such as transformers, cables and capacitors they give rise to extra energy
loss, measurements of harmonics and calculation of losses caused by these are performed an d evaluated for the case stu dy.
PART 1
4
Spring 2013 2 TRANSFORMERS
The Transformer loss can be divided into two main components:
no-load loss and load loss. These types of losses are common to
all types of transformers, regardless of transformer application
or power rating. There are, however, two other types of losses;
extra heat dissipation created by harmonics which is described
in section 6.3 and losses which may apply particularly to larger
transformers – cooling or auxiliary losses, caused by the use of
cooling equipment like fans and pumps. Figure 1 to the right
show a single phase transformer design with its main features.
The rectangular shaped metal body is called the core and the
two coiled wires are called primary and secondary windings.
Three -phase transformers consist of three sets of primary and
secondary windings and each set is separately connected to each
phase.
2.1 LOAD LOSS
When electric current flows in a conductor, resistance generates ohmic heating . The transformers two windings are consists
of two coiled conductors and thus, the nature of the load loss is similar to the ohmic heating losses in conductors. As
illustrated in figure 2 below, thi s loss becomes dominant when the transformer is more than about 50 % loaded. Figure 2 also
shows that overloading of the transformer causes significant increase in load loss and decrease in efficiency. Load loss is also
dependent on frequency content of the load current , this is discussed in section 6.3.
2.2 NO LOAD LOSS
The core of transformers is , even when there is no load kept charged with an alternating magnetic field. As the magnetic
domains in the steel try to follow the changing orientation of the AC magnetic field they generate frictional heat in the cor e,
this loss is called hysteresis los s. These losses can be approximated as constant as long as the primary voltage is held
constant. The alternating magnetic field also induces eddy currents in the core due to the magnetic interaction. In the same
way that electrical current flow generates heat, eddy currents causes additional losses. The eddy current loss depends on the
electrical resi stance of the core material and the AC frequency. Hysteresis loss increase linearly with frequency and eddy
current l oss scales as the square of frequency.
Figure 1: Single phase transformer design
PART 1
5
Spring 2013 2.3 TRANSFORMER EFFICIEN CY
The efficiency of a transformer is expressed by the following equation:
Eq. 2
Where
Pload = Load [W]
Pload loss = Load loss [W]
Pno load loss = No Load Loss [W]
The efficiency profile is obtained from varying the load from zero -load to max -load and subtracting the energy loss . Figure 2
below illustrates the efficiency profile of an arbitrary transformer. For low load levels you can see that the efficiency are
generally poor but gets high as soon as load level passes 20%. The no load loss stays constant and load loss are exponentially
dependent on the load.
Figure 2. Efficiency profile of an arbitrary transformer2
PART 1
6
Spring 2013 2.4 AMORPHOUS METAL TRANSFORMERS – REDUCING NO LOAD LOS S
According to the project ”Strategies for development and diffusion of energy efficient distribution transformers ”, by IEE the
no-load losses account for more than 70% of total losses in Europe , as can be seen in Figure 4 below . The transformer core
designs are dominated by conv entional Regular Grain Oriented (RGO) silicon steel .
The no load loss can be reduced by choosing amorphous metal as the m aterial of the transformer -core. Amorphous metal
transformers are energy efficient transformers w ith a core consisti ng of amorphous alloy. Amorphous alloys are different
from conventional material in distribution transformer cores, RGO , in the sense that the core alloy has a structure of metal
atoms that occurs in a random pattern unlike the conventional type. RGO has an organized grain structure with much higher
resistance to magnetization cycles, which leads to higher core losses. Amorphous alloy has higher magnetic susceptibility,
lower coercivity and high electrical resistance.
The high resistance leads to decreased losses due to eddy currents when subjected to an alternating magnetic field. The
higher magnetic susceptibility makes magnetization of the core more efficient and the lower coercivity leads to easier
demagnetization and the magnetization becomes faster in response to the magn etic field. According to ABB´s ”Green
distribution transformer program ”[3] no-load losses can be reduced by up to 70 % using amorphous alloys, some of their
versions are presented in section 2.7.3.
PART 1
7
Spring 2013 2.5 TRANSFORMER EFFICIENCIES IN EUROPE
In the project ”Strategies for development and diffusion of energy efficient distribution transformers ”, IEE have conducted a
survey of losses and efficiencies in E urope where a comparison were made between already installed ”population” with
transformers available on the local market. In this project they demonstrated differences for EU -27 and Norway; this is
illustrated in Figure 3 and Figure 4. The efficiency of installed transformers compared to what’s avilable on the market
appears to differ quite variably in Europe and Scandinavia is in the top percentile of effectiveness .
Figure 3. Operating efficiency of distri bution sector distribution transformers, EU -27 and Norway
As can be seen in Figure 4 the no load losses generally dominate s as contributor to the transformer losses in Europe and UK,
DE and FR have the highest losses in commensurate to their installed power . No load losses especially can be reduced, in
some cases by as much as 70% with some of today’s transformers on the market, it is easy to see a potential for efficiency
improvements.
Figure 4. Breakdown of distribution sector distribution transformer losses, EU -27 and Norway
PART 1
8
Spring 2013 2.6 EUROPEAN EFFICIENCY STANDARD EN 50464 -1
Unlike many countries around the world, E urope has no mandatory standard on energy efficiency of distribution
transformers. The main document which desc ribes losses in transformers are the European Standard EN 50464 -1. This is a
superseded docu ment from the standard HD428 for oil cooled transformers which is still valid. The values are divided into
two types of losses: no load -loss and load -loss respectively. They are categorized by thre e efficiency levels; A, B, C for
different power -rating s, primary voltage s and short circuit impedance s. Figure 5 illustrates No Load loss standard for
distribution transformers in Europe .
Figure 5. No load loss standard for distribution transformers in Europe
Figure 6 illustrates l oad loss standard for distribution transformers in Europe .
Figure 6. Load loss standard for distribution transformers in Europe 0 0,5 1 1,5 2 2,5 3 3,5 4
50 100 160 250 400 630 1000 1600 2500 [kW] Drytype 24kV
No load loss standard
A, Noload -loss
B, Noload -loss
C, Noload -loss
[kVA]
0 5 10 15 20 25 30 35
50 100 160 250 400 630 1000 1600 2500 [kW] Drytype 24kV
load loss standard
A, Load -loss
B, Load -loss
C, Load -loss
[kVA]
PART 1
9
Spring 2013 2.7 ON THE MARKET
A market research for distribution transformers has been performed and is presented in this chapter. It should be stated
that data below are represented for full -load operation and phase angle=0°. In case s of lower load levels, the efficie ncies
decrease since the no load loss stays constant while the load loss decreases . Becaus e the no load loss stays constant the
load loss does not decrease in the same rate as the load, and thus get a larger share. The condition that the phase angle are
equal to zero means that a straight conversion between active and reactive power are possible and thus the efficiencies
can be calculated straight off with values given in both VA and W. The data are grouped by power rating [kVA] so that
comparisons in loss between transformers with the same power rating may be performed.
No load and load loss are combined to create a range of products that differs in efficiency as shown in figure 7 below. As
can be seen, products with the same power -rating differ about 0.2% in efficiency. For higher power ratings the difference
increases . Compare transformers with the same power rating.
PART 1
10
Spring 2013
2.7.1 ABB TRANSFORMERS
Dry-isolated transformers ABB, 12 kV
Figure 7. No load -loss and load loss for different ABB Power Distribution Transformer s
Figure 8. Efficiencies for different ABB Power Distribution Transformers
0 5 10 15 20 25 30
630
630
630
800
800
800
1000
1000
1000
1250
1250
1250
1600
1600
1600
2000
2000
2000
2500
2500
2500
3150
3150
3150 [kW] 12kV Dry -isolated transformers, ABB
Noload -loss
Load -loss
[kVA]
0,982 0,984 0,986 0,988 0,99 0,992 0,994
630
630
630
800
800
800
1000
1000
1000
1250
1250
1250
1600
1600
1600
2000
2000
2000
2500
2500
2500
3150
3150
3150 12kV Dry -isolated transformers, ABB
Efficiency
[kVA]
PART 1
11
Spring 2013 Dry isolated transformers ABB, 24 kV
Figure 9. No load loss and load loss for different ABB Power Distribution Transformers
Figure 10. Efficiencies for different ABB Power Distribution Transformers
0 5 10 15 20 25
630
630
630
800
800
800
1000
1000
1000
1250
1250
1250
1600
1600
1600
2000
2000
2000
2500
2500
2500
3150
3150
3150 [kW] 24kV Dry -isolated transformers, ABB
Noload -loss
Load -loss
[kVA]
0,983 0,984 0,985 0,986 0,987 0,988 0,989 0,99 0,991 0,992 0,993
630
630
630
800
800
800
1000
1000
1000
1250
1250
1250
1600
1600
1600
2000
2000
2000
2500
2500
2500
3150
3150
3150 24kV Dry -isolated transformers, ABB
Efficiency
[kVA]
PART 1
12
Spring 2013 Liquid filled transformers ABB, 10kV
Figure 11. No load loss and load loss for different ABB Power Distribution Transformers
Figure 12. Efficiencies for different ABB Power Distribution Transformers
0 5 10 15 20 25
50
50
100
100
160
160
200
200
250
250
400
400
400
500
630
630
630
630
800
800
1000
1000
1250
1250
1600
1600
2000 [kW] 10kV Liquid filled transformers, ABB
Noload -loss
Load -loss
[kVA]
0,96 0,965 0,97 0,975 0,98 0,985 0,99 0,995
50
50
100
100
160
160
200
200
250
250
400
400
400
500
630
630
630
630
800
800
1000
1000
1250
1250
1600
1600
2000 10kV Liquid filled transformers, ABB
Efficiency
[kVA]
PART 1
13
Spring 2013 Liquid filled transformers ABB, 20kV
Figure 13. No load loss and load loss for different ABB Power Distribution Transformers
Figure 14. Efficiencies for different ABB Power Distribution Transformers
0 5 10 15 20 25
50
50
100
100
160
160
200
200
250
250
400
400
400
500
630
630
630
630
630
800
800
1000
1000
1250
1250
1600
1600
2000 [kW] 20kV Liquid filled transformers, ABB
Noload -loss
Load -loss
[kVA]
0,96 0,965 0,97 0,975 0,98 0,985 0,99 0,995
50
50
100
100
160
160
200
200
250
250
400
400
400
500
630
630
630
630
630
800
800
1000
1000
1250
1250
1600
1600
2000 20kV Liquid filled transformers, ABB
Efficiency
[kVA]
PART 1
14
Spring 2013
2.7.2 SIEMENS TRANSFORMERS
Dry-isolated transformers, Siemens 10kV
Figure 15. No load loss and load loss for different Siemens Power Distribution Transformers
Figure 16. Efficiencies for different Siemens Power Distribution Transformers
0 5 10 15 20 25 30
100
100
160
160
250
250
315
315
400
400
500
500
630
630
800
800
1000
1000
1250
2000
2500
3150
4000
5000
6300 kW Dry-isolated transformers,
Siemens 10kV
Noload -loss
Load -loss
0,965 0,97 0,975 0,98 0,985 0,99 0,995 1
100
100
160
160
250
250
315
315
400
400
500
500
630
630
800
800
1000
1000
1250
1600
2000
2500
3150
3150
4000
5000
5000
6300
6300 Dry-isolated transformers,
Siemens 10kV
Efficiency
PART 1
15
Spring 2013 Dry-isolated transformers, Siemens 20kV
Figure 17. No load loss and load loss for different Siemens Power Distribution Transformers
Figure 18. Efficiencies for different Siemens Power Distribution Transformers
0 10 20 30 40 50 60
100
160
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
5000
6300
6300
8000
8000
10000
10000
12500
12500
16000
16000 kW Dry-isolated transformers,
Siemens 20kV
Load -loss
Noload -loss
0,965 0,97 0,975 0,98 0,985 0,99 0,995 1
100
100
160
250
315
400
400
500
630
800
1000
1000
1250
1600
2500
3150
3150
4000
4000
5000
5000
6300
6300
8000
8000
10000
10000
12500
12500
16000
16000 Dry-isolated transformers,
Siemens 20kV
Efficiency
PART 1
16
Spring 2013 Dry-isolated transformers, Siemens 30kV
Figure 19. No load loss and load loss for different Siemens Power Distribution Transformers
Figure 20. Efficiencies for different Siemens Power Distribution Transformers
0 10 20 30 40 50 60
250
315
400
500
500
630
800
1000
1250
1600
2000
2500
8000
8000
10000
10000
12500
12500
16000
16000 [kW] Dry-isolated transformers,
Siemens 30kV
Noload -loss
Load -loss
[kVA]
0,97 0,975 0,98 0,985 0,99 0,995 1
250
315
400
500
500
630
800
1000
1250
1600
2000
2500
8000
8000
10000
10000
12500
12500
16000
16000 Dry-isolated transformers,
Siemens 30kV
Efficiency
PART 1
17
Spring 2013 2.7.3 ABB AMORPHOUS METAL CORE TRANSFORM ER
Conclusions from the market research on Regular Grain Oriented (RGO) distributions transformers above is that differences
are not significant in the regular product portfolio from ABB or Siemens. They have however one type of product available
on the market and that is transfo rmers with amourphous metal cores (AMC). Table 1 below show comparisons in the no load
loss between these two types of transformers for several power ratings.
Table 1 Energy performance comparison between a RGO and an AMC for different power ratings4.
Rating
(kVA) No-Load
Losses (W) No-Load
Losses Loss
Reduction
Regular
Grain
Oriented Amorphous
Metal Core
Single Phase
15 55 20 64%
25 65 30 54%
50 105 35 67%
75 155 55 65%
100 200 75 63%
167 235 95 60%
Three Phase
300 505 200 60%
500 725 220 70%
750 1125 355 68%
1500 2170 725 67%
2500 2750 745 73%
PART 1
18
Spring 2013 3 CABLE S – A METHOD FOR COMPARI SON
This chapter concerns cables and presents a method for choosing the best cable -energy -alternative.
When comparing cable investments with energy losses related to them, the sectional area of the cable is of utmost importance.
The energy loss due to heat dissipation depends on the cross area as follows5:
Eq. 3
Where
I = current [A]
= electrical resistivity of the material [Ω ]
A = cross area [m2]
l = length [m]
As can be concluded from the equation, increased cross area leads to decreased losses. From an investment point of view the
decreased energy loss must be weightened against a higher price of investment. To compare these variables and optimize the
investment, linear graphs over the total ownership costs should be executed and compared. The best investment is the one
having the lowest TOC after a chosen period of time.
Figure 21. Principle chart over the method of a TOC comparison
To obtain a graph over the TOC , the cost due to energy loss is gradually added to the capital of investment which is where the
lines cross the y -axis. The cost of the annual losses is estimated by choosing a certain price for electricity and then
multiplying this by the energy loss from the chosen time period.
Cost Total Ownership Cost Comparision
Higher price, lower loss
Lower price, higher loss
Time
PART 1
19
Spring 2013 4 BREAKERS AND INTER RUPTERS
This chapter describes as well as the function , also based on a market research and qualitative interview discusses energy
performance of electric power interrupters .
4.1 INTERUPTER DESIGN
Interrupters have the task of breaking emerging currents. This requires interrupter designs based on mediums that can quench
the upcoming arc. The two most common types are:
– SF6 interupter s
This construction works according to the puffer principle where a compression chamber – puffer chamber – follows the
contact movement, compresses the SF6 gas and via a nozzle , length blows the channel of the arc.
– Vacuum interrupters
A competitor to SF 6 interrupters at voltage s up to 36 kV is the vacuum interrupter . It is slightly more expensive but in return
it has significantly lower audit interval. It is particularly suitable for installations where the breaking frequency is high.
Because of the close d structure, it is suitable in corrosive and explosive atmosphere. It operates at high vacuum – which
interrupts the current arc.
4.2 INTERRUPTER ENERGY PERFORMANCE
An interview with Per Johnsson, interrupter -specialist at ABB was performed on april 11, 2013 . The conclusions from that
survey were that t he biggest difference in interrupter performance is mostly a question of functionality and endurance.
Construction -differences lies in which method that is used for breaking the current ; oil-, SF6 – or vacuum -based . During
operation all interrupters hold good co nnectivity to the conductors and sometimes even lower resistance than the cables
connected to the interrupter , because of a larger
conductor cross area in the interrupter . The energy
loss in interrupters are dominated by resistivity
loss, and thus to decrease energy losses , as for all
conductors increased voltage enables a lower
current for a fix power rating. Si nce resistance
energy loss depends on R*I2 the loss is reduced by
lower current. Energy loss and efficiencies of
interrupters with different power ratings are shown
in figure 22 to the right. As can be seen, the
interrupters hold high efficiencies.
0,9997 0,99975 0,9998 0,99985 0,9999 0,99995
24000
30000
47250
60000
86250
93750 Switch -disconnectors ABB, 750 V
Efficiency
[W]
Figure 22. Efficiencies for different ABB switch disconnectors
PART 1
20
Spring 2013 5 ADJUSTABLE SPEED DRIVES
This chapter describe s function and energy performance of adjustable speed drives.
5.1 ASD DESIGN
An adjustable speed drive (ASD) is a device that controls the rotational speed of motor -driven equipment. Variable frequency
drives (VFDs), the most common type of ASD, are solid -state electronic motor controllers that efficiently meet varying
process requ irements by adjusting the frequency and voltage of power supplied to an alternating current (AC) motor to enable
it to operate over a wide speed range. External sensors monitor flow, liquid levels, or pressure and then transmit a signal t o a
controller tha t adjusts the frequency and speed of the motor to match process requirements. As illustrated in figure 23 below
variable frequency drives consists of three steps: rectification, filtering and inverting DC to AC . The first step converts the
AC power to DC, the second smoothens the DC and the third creates AC with adjustable frequency which varies the rotating
speed of machines. It is the first step, rectification which converts AC line voltage to DC voltage output by super –
imposing non-linear half-phase current
pulses thus creating harmonic current
distortion, and hence voltage
distortion, of the AC line input. More
about this in secti on 6.1.1
(Rectification) .
Figure 23. Illustration of a Variable Frequency Drive three step process.
PART 1
21
Spring 2013
5.2 VFD ENERGY PERFORMANCE
Typical efficiencies of VFDs are presented in table 2. These efficiency values may be considered representative of “typical”
PWM VFD performance. As can be seen, the VFD effic iency decreases with decreasing load and t he decline in efficiency is
more pronounced wi th drives of smaller horsepower ratings. In this thesis, the connection between VFDs and harmonic issues
has been of major concern. The rectification process is presented in section 6.1.1 and the impact of harmonics in
powersystems is discussed in chapter 6.
Table 2 Typical efficiencies of VFDs6
Variable
Frequency
Drive
Hp rating Efficiency %
Load, Percent of Drive Rated Power Output
1.6 12.5 25 42 50 75 100
5 35 80 88 91 92 94 95
10 41 83 90 93 94 95 96
20 47 86 93 94 95 96 97
30 50 88 93 95 95 96 97
50 46 86 92 95 95 96 97
60 51 87 92 95 95 96 97
75 47 86 93 95 96 97 97
100 55 89 94 95 96 97 97
200 61 81 95 96 96 97 97
PART 2
22
Spring 2013 6 HARMONICS
This chapter describes basic characteristics about harmonics in electric power systems; causes, effects and mitigation –
techniques are presented.
Harmonics are disturbances in the voltage and current of the grid, which has a frequency which is a multiple to the
fundamental frequency. (The Swedish electricity network has a fundamental frequency of 50 Hz.) Usually, harmonic
amplitude decreases with in creasing frequency and is specified as fraction of the fundamental amplitude according to the
diagram below:
Figure 24 Harmonic presentation; as a fraction of the fundamental current7.
THD – Total Harmonic Distortion is a measurement of the general level of harmonic distor tion present and is defined as the
ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency. It is expressed
mathematically as:
Eq. 3
Were Y is a signal of the current, voltage or power. Y 1 is the amplitude of the fundamental signal and Yi is the amplitude of
each harmonic in a chosen frequency band. THD is useful to get an index over just how distorted the signal are and it is
tempting to try to use if for calculations of different entities such as energy loss , level of stress on equipment and draw
conclusions from that. But the fact is, certain harmonics affect certain entities in different ways. This will be evaluated in the
following sections.
PART 2
23
Spring 2013 6.1 CAUSES
The distortion of the current or voltage wave means that the distribution of electrical energy is disturbed and power quality is
not optimum. Harmonic currents are caused by non -linear loads connected to the distribution network. The flow of harmonic
currents causes harmonic voltages via distribution -network impedances and consequently distortion of the su pply voltage.
Examples of devi ces that cause harm onics :
– Industrial equipment (welding machines, arc furnaces, induction furnaces, rectifiers)
– Adjustable -speed drives for asynchronous or DC motors
– UPSs
– Office equipment (computers, photocopy machines, fax machines, etc.)
– Home appliances (television sets, micro -wave ovens, fluorescent lighting)
– Certain devices involving magnetic saturation (transformers)
When harmonics are generated in some parts of a power system , every other part of the system is affected. Motors experience
counter electromotive force, transformers, cables, and capacitors experience increased heat -loss.
Figure 25 show the harmonics spreading and adding up from the load branches back into the distribution -system through
the transformer.
PART 2
24
Spring 2013
Figure 25. Harmonics spreading through the distribution system 8
PART 2
25
Spring 2013 6.1.1 RECTIFICATION
The common factor for most of harmonic emitting devices is rectifiers9. This is a power electronic component that is used for
converting alternating currents (AC) to direct current (DC). The process in which it operates is called rectification.
When alternating current is connected to a tyristor, it only lets through current and voltage in one direction, c reating a
pulsating direct current. This technology can be extended to three phases and connected as a six pulse converter as illustrated
in Figure 26 below.
Figure 26 6 pulse AD/DC rectifyer10.
The resulting signal U d shown in Figure 27 drives a pulsating DC current I d forward, but also backward –Id due to V 4, V6 and
V2. This backwa rd signal – Id is in this construction pushed back into the AC -signals and becomes harmonics in the original
waveforms I LN1, ILN2 and I LN3.
Figure 27 Resulting currents and voltages11.
Rectification can be performed by any number of pulses for integers that are multiples to the number 6 , the most common are
6 as descr ibed above, 12, 18, 24 and 48 are mostly used for higher power levels because of increased ivestment cost.
PART 2
26
Spring 2013 6.1.2 TWELVE PULSE RECTIFICATION
Six pulse rectifiers produce high levels of harmonics, about 30% THD on both the DC and AC side. 12 -pulse rectifiers are
often used in installations that demands lower levels of harmonics, about 12% THD. As shown in figure 30 a 12-pulse
rectifier consists of two 6 -pulse bridge ci rcuits connected in series.
It has its AC connections fed from two supply transformer s with a 30 degree phase shift between the two bridges , this is
illustrated in figure 31 . In this way, many of the characteristic harmonics produced by the six -pulse bridges are cancelled. The
30-degree phase shift is usually achieved by a transformer with two sets of secondary windings, one with D connection and
one with Y connection.
Lower harmonics such as the 5th and 7th, which normally contributes the most to the THD are due to the phase shift
eliminated because the Y current are opposite to the D current for the specific harmonic s and this consequently enables them
to cancel out each other.
Power system converters have a practical limitation of 12 pulses because of the large expense of producing high -voltage
transformers with the appropriate phase shifts.
Figure 28. Line diagram over a 12 -pulse rectifyer Figure 29. Resulting voltage with 30 degrees phase shift
creating a smoother DC than a 6 -pulse rectifyer
PART 2
27
Spring 2013 6.2 EFFECTS
The effects of harmonics can be divided into three components: joule losses caused by additional current waveforms, joule
losses caused by the skin effect and RMS increase of the waveform due to harmonics . In addition to the joule losses certain
harmonics cause negative torque in motors and pumps.
The measured current is not the same as the useful and this means that when utilities measure their active power consumption
and the signal contains harmonics , they pay for unused energy . The measured power is a function of the fundamental
component I 1 with all the harmonics added . When the cur rent contains harmonics, the RMS value of the current I rms is greater
than the fundamental I 1. This leads to a higher level of power consumption than what would be measured if the signal
contained no harmonics. Filtering the signal lead s to lower current RMS . In the case study in this thesis such an investment is
evaluated. In the same way that the fundamental current provokes joule losses t he harmonic currents also provoke an increase
in the joule losses in all conductors in which they flow and additional t emperature rise in transformers, devices cable s, etc.
Figure 30 below shows as a function of the total harmonic distortion:
– The increase in the curre nt RMS for a conductor containing a given fundamental current
– The increase in joule losses, not taking into account the skin effect
Figure 30. Increase in current RMS and increase in joule losses as a function of THD12.
Equipment connected to the current network is designed to operate with an ideal sinusoidal 50 Hz fundamental frequency
voltage. This means that when there is multiples of the fundamental current frequency the network device cannot take up the
energy that contains in these harmonics. In other words, when the equipment is not adapted to take advantage of the harmonic
energy will lead to untapped power. Because it is unused energy but get debited anyway it is said to be a loss.
PART 2
28
Spring 2013 The increased joule heating due to harmonics leads to over dimensioned components because the heating causes temperature
rise. Harmonic currents flowing in the transformer produce an increase in the load loss due to the j oule effect and increased
no load losses due to eddy currents. The harmonic voltages are responsible for "iron" losses due to hysteresis. It is generally
considered that the losses in the windings increases as the square of the THD and the core losses increase linearly with THDu .
The utilit y distribution transformers, where distortion levels are limited, the losses increase between 10 and 15%. In
capacitors the harmonic voltages applied to capacitors provoke the flow of currents proportional to the frequency of the
harmonics. These currents cause additional losses.
The 5th and 11th harmonics are also of particular concern to industry today [13]. Although the 5th harmonic is much more
prevalent, both have a negative sequence. This means that when distorted voltage containing the 5th or 11th harmonic is
applied to a 3 -phase motor, it will attempt to drive the motor in reverse, creating a negative torque. In order to compensate
for this negative torque, the motor must draw addi tional current. This, in turn, can cause overheating and/or the tripping of
over-current protection devices. 6-Pulse adjustable speed drives are a major source of the 5th, 7th and 11th harmonics. 12-
Pulse drives are significantly more expensive, and are a source of the 11th and 13th harmonics, but through their design are
able to eliminate the 5th and 7th. The negative torque created by the 5th and 11th can be calculated as an economic loss, such
an analysis would require harmonic values at each pump and motor in a facility, due to a lack of time and resources it is lef t
out of this thesis.
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Spring 2013 6.3 INCREASED FREQUENCY ⇾ INCREASED LOSSES – THE SKIN EFFECT
Harm onics are per definition steady state waveforms with frequencies that are
integer multiples of a fundamental waveform frequency, the order of each
harmonic are the integer multiple that corresponds to each harmonics
frequency. The attribute that separates each harmonic from th e other are thus
the frequency. Higher order means higher frequency. This aspect is one of the
reasons for harmonics to cause increased losses in elec trical equipment. The
skin effect causes the current to experience higher effective resistance for
higher frequencies.
Skin effect is the tendency for an alternating electric current AC to become
distributed within a conductor such that the density is largest near the surface
of the conductor, and thus decreases with greater depths in the conductor. The
cause of the skin effect is electromagnetic induction. As shown in figure 32 a
time-varying magnetic field H around the main current I is accompanied by a
time-varying induced electric field, which in turn creates secondary time -varying
currents Iw and a secondary magnetic f ield.
These induced currents produce a magnetic flux which is opposite to the external
flux that produced the induced currents. This opposing magnetic flux is call ed
counter electromotive force . The counter EMF is strongest at the center of the
conductor, and forces the electrons to the skin of the conductor. A higher
frequency intensifies this phenomenon and causes a thinner skin depth δ.
The skin depth is defined as the depth below the surface of the conductor at
which the current density has fallen to 1/e, about 0.37 of Js. Skin depth can be
expressed as14:
Eq. 4
where
= resistivity of the conductor [ Ω ]
= frequency of the current [Hz]
= absolute magnetic permeability of the conductor [ ]
Figure 32. Current flow I in a conductor
with counter EMF illustrated, resulting in
the skin effect . Figure 31. Cross section of a conductor.
Current flows mainly outside of δ.
PART 2
30
Spring 2013 Energy loss as hea t dissipation in a conductor is dependent of effective resistance and current according
to Joules Law15:
Eq. 5
where
I = current [A]
Reff = effective resistance [Ω]
Effective resistance in a conductor can be expressed according to Pouillet’s law as:
Eq. 6
where
length [m]
= resistivity of the material [Ω ]
A = cross -area [m2]
The effective resistance R eff in a conductor due to the skin effect can be solved by approximating that the current flows
uniformly through a layer of thickness corresponding to the skin depth and thus approximate it as a cylindrical flow. This
changes the cross area and Eq. 6 derives to:
Eq. 7
where
length [m]
= resistivity of the material [Ω ]
D = diameter of the conductor [m]
= skin depth [m]
PART 2
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Spring 2013
Combin ing Eq. Eq. and Eq. derives the expression:
Eq. 8
This equation gives energy losses due to heat dissipation in a conductor for a certain frequency when taking into account the
skin effect. As can be seen in the equation, increased frequency leads to increased energy loss . These equations and especially
Eq. 8 are used when calculating the energy loss caused by harmonics in the case study.
PART 2
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Spring 2013 6.4 ENERGY LOSS IN COMPONENTS DUE TO HARMONICS
6.4.1 TRANSFORMERS
Energy loss due to harmonic s in transformers is express ed as:
Eq. 9
Where
Pn = nominal load loss [W]
Kw = iron loss coefficient = 0.04
Ih = current of harmonic order h (in p.u.)
h = harmonic order
Kh1 =
6.4.2 CABLES
Energy loss due to harmonics in cables is expressed as:
Eq. 10
Where
L = length of cable [m]
Rh = resistance of cable to harmonic order h [Ω]
Ih = current of harmonic order h (in p.u.)
PART 2
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Spring 2013 6.4.3 CAPACITORS
Energy loss due to harmonics in capacitors is expressed as:
Eq.11
Where
PNC = losses in the capacitor excluding loss caused by harmonics [W]
h = harmonic order
Vh = voltage of harmonic order h (in p.u.)
PART 2
34
Spring 2013 7 SOLUTIONS TO ATTENUAT E HARMONICS
In order to eliminate problems in facilities due to harmonics, attenuation is necessary. T his chapter describes different
solutions for managing harmonics . An economical analysis of harmonic filter solutions are presented in chapter 10.
7.1 BASIC SOLUTIONS
7.1.1 POSITION THE NON -LINEAR LOADS UPSTREA M IN THE SYSTEM
As the short -circuit power decreases the overall harmonic disturbances increase. Not taking economic considerations into
account, the preferable solution is to connect the non -linear loads as far upstream as possible. Figure 33 below illustrates a
system with the non -linear loads connected above the sensitive loads.
Figure 33. Power s ystem with the non -linear loads connected above the sensitive loads16
7.1.2 GROUP THE NON -LINEAR LOADS
Create systems with non -linear loads separated from linear loads. Figure 34 show connections that should be avoided in order
to prevent harmonic disturbances on sensitive loads.
Figure 34. Connections that should be avoided in order to prevent harmonic disturbances on sensitive loads17
PART 2
35
Spring 2013 7.1.3 CREATE SEPARATE SOURCES
One solution can be to separate non -linear loads from sensitive loads via separate transformers and the linear load –
transformer -impedance will protect the linear loads from harmonics emitted from the non -linear loads. Figure 35 show this
kind of connection. This solution is appropriate only if it the cost for the extra tr ansformer are weighed against the positive
impact on the system.
Figure 35. Separation of non-linear loads from sensitive loads via separate transformers18
7.1.4 TRANSFORMERS WITH SPE CIAL CONNECTIONS
Elimination of certain harmonic orders can be performed by different types of transformer connections:
– A Dyd connection suppresses 5th and 7th harmonics (see Figure 36)
– A Dy connection suppresses the 3rd harmonic
– A DZ 5 connection suppresses the 5th harmonic
Figure 36. A Dyd connection which suppresses 5th and 7th19
PART 2
36
Spring 2013 7.2 HARMONIC FILTERING
7.2.1 PASSIVE FILTERS
Passive filters are LC circuits which are tuned to each harmonic order to be filtered. When installed in parallel with the non –
linear load, it provides a low impedance path for the major harmonic currents demanded by the drive. This reduces the
amount of harmonic current flowing through the distr ibution system and results in improved power factor, lower RMS
currents, lower harmonic current distortion, lower harmonic voltage distortion, and increased system capacity. Figure 37
below illustrates the setup of a passive filter and how it is connected to the system. The drive generates the harmonics and
sends it back into the system and is then absorbed by the filter due to the lower impedance for chosen frequencies. Without
the filter, these frequencies would pass through the transformer and cause increased heat dissipation and increased RMS value
of the power . This solution are good for systems with harmonic levels which is easily predicted, e.g. in a system with 6 -pulse
rectifiers (AC/DC converters) to all of its drives can be predicted to have high levels of 5th and 7th harmonics, and thus a
filter tuned for absorbing these harmonics can be connected.
Figure 37. The setup of a passive filter and how it is connected to the system .20
PART 2
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Spring 2013
7.2.2 ACTIVE FILTERS
Active filters measure each harmonic level by induction and inject the inverse harmonic signal I harm to attenuate the harmonic
distortion. Figure 38 illustrates setup of an active filter and how it is connected to the system. The drive generates the
harmonics and sends it back into the syste m and when it passes through the filter measuring point it is counteracted by the
injected current I harm. Without the filter, these frequencies would pass through the transformer and cause increased heat
dissipation and increased RMS value of the power . This is a simple solution because it does not require detailed knowledge
regarding the nature of the load, or the type of harmonics present. Although it is generally considered as a more expensive a nd
energy -consuming solution than passive filters, for highe r load levels and unpredictable waveforms it is often the preferable
solution.
Figure 38. Setup of an active filter and how it is connected to the system21
Figure 39 below describes how an active filter injects the opposite signals to the harmonics present and creates a clean
fundamental signal without significant distortion.
Figure 39. Active filter op posite signal injection22
PART 2
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Spring 2013 7.3 INSTALL ATION OF HIGHER -PULSE REC TIFIERS
The source of problems with harmonic generation is primarily the rectification (AC to DC) process in the loads which sends
harmonic back into the system. 6 -pulse converters (described i n section 6.1.1 ) are the most commonly used rectification
technique in distribution facilities today; 6-pulse rectification generates high levels of 5th, 7th, 11th and 13th harmonics due
to the low pulse number. A typical harmonic current spectrum with resulting THD fo r a 3 phase 6-pulse rectifier is presented
in Table 3.
Table 3. A typical harmonic current spectrum with resulting THD for a 3 phase 6 -pulse rectifier23
h 1 5 7 11 13 17 19 THD
Ih6p,% 100 20 14.3 9.1 7.7 5.9 5.3 28.45%
Instead of treating the symptoms, sometimes treating the sources is a more effective method of attenuating problems. One
way of doing this in electric power systems, with distorted waveforms as symptoms and rectification as the source; improving
the rectif ication process is a solution. If the pulses in the rectification process are increased in number, the waveform becomes
less distorted. A typical harmonic current spectrum with resulting THD for a 3 phase 12-pulse rectifier is presented in Table
34.
Table 4 A typical harmonic current spectrum with resulting THD for a 3 phase 12 -pulse rectifier24
h 1 5 7 11 13 17 19 23 25 29 31 35 37 THD
Ih12p,% 100 1.8 1.6 6.6 5.4 0.33 0.3 1.5 1.3 0.25 0.2 0.8 0.4 9.14%
When increasing the number of pulses per period to 24, an even better result can be achieved in decreasing the harmonic
generation. A typical harmonic current spectrum with resulting THD for a 3 phase 24-pulse rectifier is presented in Table 5.
Table 5 A typical harmonic current spectrum with resulting THD for a 3 phase 24 -pulse rectifier25
h 1 5 7 11 13 23 25 47 49 THD
Ih24p,% 100 1.88 1.23 0.36 0.22 1.09 0.87 0.22 0.22 2.7%
PART 2
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Spring 2013 In a comparison between the THD generated by the 6 -pulse versus the 12 -pulse, the THD generated by a 6 -pulse is about 3
times the THD generated by the 12 pulse. The 24 pulse rectifier is superior to the 6 and 12 with its low THD level. A
summary of the rectifiers is listed in Table 6 below.
Table 6. Summary of rectifiers with corresponding THD
Pulse number THD%
6 28.45
12 9.14
24 2.7
In the choice of new devices li ke frequency drives to pumps and motors or rectifiers to for example charging equipment it is
importan t to weighted different pulse numbers for the rectification process against pric e, the resulting harmonics affect the
system in many ways.
PART 2
40
Spring 2013 8 COMPUTER MODELING AND ANALYSIS : HARMONIC FLOW
This chapter describes the method of how to deal with harmonics in power systems. How to simulate mixing and
splitting of wavefo rms and how to model the system’ s equivalent impedances.
8.1 FOURIER ANALYSIS
The fourier transform are a transform that is often used to transfer a function from the time -domain to the frequency -domain.
The function is expressed as the sum of its sinusoidal basic functions. When applied on periodic functions the results are
referred to as fourier series.
Every continuous pe riodic function can be expressed as the sum of a number of sinusoidal functions with varying amplitudes
and frequencies that are integer multiples of a fundamental waveform frequency, i.e. the same characteristics as for
harmonics. A fourier series takes a signal and decomposes it into a sum of sines and cosines of different frequencies.
Definition is as follows26:
Eq. 12
Where is the signal in the time domain and are the amplitude of each harmonic. The integer, n, has units of
Hertz (1 Hz =1/s) and corresponds to the frequency of the wave. When analyzing harmonic content on a current or voltage the
harmonic content on the fundamental waveform are most often represented by the amplitudes in the frequency domain.
In some cases, only the percentage of total harmonic content on a wave is of interest and not the specific level fo r each
harmonic. The general level is referred to as THD – Total Harmonic Distortion and is expressed for a signal Y as follows27:
Eq. 13
Where Y1 is the amplitude of the fundamental signal and Yi is the specific amplitude for each harmonic, Yi corresponds to
the coefficient an and bn in above. The signal Y c an be voltage, current or power etc.
When modeling harmonic flow in power systems you have to start with a distorted signal. One way of doing this is to
represent the signal with a fourier series and add on sinusoids representing harmonics on a fundament al wave. This is one of
the applications where fourier series is applicable.
PART 2
41
Spring 2013 Let us take a look at a fundamental sinusoid versus the same wave with its 5th (5 times the fundamental frequency) harmonic
added on having 20% of the fundamental amplitude:
Fundamental sinusoid with its 5:th harmonic
separated Fundamental with its 5:th harmonic added
Figure 40 Fundamental sine wave v ersus its 5th harmonic added , plotted in MatLab
So, when a sinusoid with higher frequency is added to the fundamental, the result becomes a fluctuating reference wave. As
can be s een from the functions above an infinite number of harmonics can be simulated using fourier analysis just by adding
them to the fundamental sinusoid function.
The RMS – Root Mean Square of an oscillating signal represents the mean value of the magnitude. In contrast of the
amplitude which represents the maximum magnitude of the osci llation. RMS is the most usual way of referri ng to a certain
level of voltage, current or power in AC. It is calculated as:
Eq. 14
Where S is an oscillating signal, usually voltage, current or power and n equals the number of magnitude samples for the
signal. This equation is used for calculating the RMS difference between a signal with harmonics and one without harmonics
in the case study.
PART 2
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Spring 2013 8.2 HARMONIC SYSTEM STUDY
Harmonic studies are used to analyze harmonic situations. They are aimed at detecting resonance and calculating harmonic
currents, voltages , phases and distortion levels.
For simple systems with bus -number lower than a dozen, spreadsheet calculation are possible. In realistic systems which
contain a large amount of buses, the Y matrix which represents the system is large and requires a computer -based approach.
The general method for a computer program to perform such a study is as follows :
1. Build the bus admittance matrix Ybus for each harmonic
2. Get the bus impedance matrix for each harmonic,
3. Given the harmonic source current spectrum I(h), find the bus harmonic voltages as
4. Calculate the line harmonic currents as
5. Calculate the voltage and current total harmonic distortion factors (see 8.1)
8.3 THE BUS ADMITTANCE MATRIX
The admittance matrix, also known as Y Matrix or Ybus is a matrix describing a power system with n buses. It
represents the nodal admittance of the busses in a power system and is constructed as described below:
1. The system single line diagram is converted to an impedance diagram
A single line diagram is a simplified notation for representing a three -phase power system. Electric elements such as circuit
breakers, transformers, capacitors, bus bars, and conductors are shown by standardized schematic symbols. These symbols
can be replaced by impedances and hence it becomes an impedance diagram.
2. All volt age sources are converted to their equivalent current source representations
Using Ohms law I=V/Z and converting the voltage sources in the impedance diagram to current sources makes the system
more manageable .
3. The impedance diagram is converted to an admittance diagram
Invert all impedances: admittance = Y = 1/Z
4. The Y Matrix itself is created
PART 2
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Spring 2013 8.4 ADMITTANCE
The admittance (Y) is a measure of how easily a circuit or device will allow a current to flow. It is defined as the inverse of
the impedance (Z). T he SI unit of admittance is the siemens (S). Mathematically expressed as:
Eq. 1 5
Where
Y = admittance [S]
Z = impedance [ Ω]
8.5 MODELLING OF POWER LINES
When constructing the admittance matrix to represent the system , the admittance of each branch of the bus system is
calculated and grouped . To calculate a power line’s admittance, because of the skin effect ( 6.3) the impedance are specific for
each harmonic and increases with the root of the harmonic number. It is calculated according to28:
Eq. 1 6
Furthermore, a power line ’s total impedance and admittance are given by:
Eq. 1 7
Where
Z(h) = specific harmonic impedance [ Ω]
h = harmonic number, integer
R = resistance [ Ω]
X = reactance [ Ω]
L = length of cable [m]
This equation is used for calculating the specific admittances in the admittance matrix for each harmonic travelling through
the power system.
44
Spring 2013 9 CASE STUDY : SKF POWER DISTRIBUTION S YSTEM
In this chapter the case study system: SKF´s distribution system is described.
9.1 SYSTEM OVERVIEW
The case study sys tem is a part of SKF´ s power
distribution system which consists of several stations
of 11000V/420V transformers. The station this
analysis is going to be performed in consists of 5
such transformers. Figure 41 Overview of the
case study system. to the right illustrates
components connected b elow T5, one of the
transformers in the station to be examined. Four
feeding lines L51, L52, L53 and L54 supplies
equipment such as fluorescent lamps, frequency
controlled motors and pumps and other harmonic
emitting loads. L55.2 and L55.3 contains two
capacitors for phase compensating purpose. Energy
losses occur in each of these components and are
increased by the order of the harmonics.
When calculating the energy loss caused by
harmonics in power components, the levels of
harmonics have to be known at each single
component before qualified results can be delivered.
In this case, measurements at L05.1 have been used
for calculating increased RMS value of current and
voltage in the debiting meter; these values are also
used calculating T5 and C1 -2 heat loss.
Measurements on the feeding lines L51 -54 has been
used for calculation of cable heat loss.
Figure 41 Overview of the case study system.
45
Spring 2013 9.2 SYSTEM COMPONENTS
9.2.1 TRANSFORMER (T5)
Table 7 show nominal values of the transformer T5 in the case study system.
Table 7. Nominal data for transformer (T5)
Rated power kVA 1600
Rated frequency Hz 50
High voltage Un1
In1 V
A 11000
83,98
Low voltage Un2
In2 V
A 420
2199,43
No-load losses Un2
Io
Io%
Po V
A
%
W
420
6,62
0,30
1879
Load -losses Usc
In1
Psc V
A
W 614,45
83,98
12988
46
Spring 2013 9.2.2 2 × CAPACITOR (C1, C2)
Table 8 show nominal values of the capacitors C1 and C2 in the case study system.
Table 8. Nominal data for each capacitor; C1 & C2
Rated power kvar 300
Rated voltage V 400
Rated frequency Hz 50
Rated current A 482
Rated capacitance – –
Rated inductance – –
Power loss W 120
Tuning frequency Hz 141/12.6 %
Icw kA 25
Conncection D
Discharge time s 60
Temperature category 0/+40
Insulation level 3/-
Ip code IP20C
Standard EN60439 -1
Serial no F0300550
Cables : 4 x 1000A cables: L51, L52, L53 and L54
Splints : Splint “Skena A5 -0,4” collecting signals from L51, L52, L53 and L54
47
Spring 2013 9.3 MEASUREMENTS OF HARMONICS
A summary of information about the instruments involved, measurement period and method.
9.3.1 INSTRUMENTS
Type: Datalogger
Product: Dranetz PX5 Power Explorer
4 x Probes: Flex probes 0 -3000A
Software: Dran -View , analyzing measurement res ults.
9.3.2 METHOD
Harmonic levels have been measured on the feeding lines L51 -54 and also on the debiting meter L05.1 . RMS -value of
voltage, current, power, harmonics and also phases are measured with 10 minutes interval. For every interval phase angle ,
RMS average -, RMS maximum and RMS minimum is registered. All odd, mild and severe events are directly recorded for
thorough analyzes.
9.3.3 PERIOD
25.03.2013 – 22.04.2013
Total time: 29 days
SUB PERIODS
L51 & L52 was measured 25/3 – 02/4
L53 was measured 02 -11/4
L54 & L05.1 was measured 11 -22/4
9.3.4 QUALITY OF MEASUR EMENTS
Even thought the measurements were performed in sub periods, the calculations that were made based on them were
separately performed and presented. No assumptions of even load levels had to be made.
48
Spring 2013 10 RESULTS
This chapter presents the results for measurements, calculations derived from the measurements and economic analysis of
energy efficient components.
10.1 MEASUREMENT S
Harmonic levels in SKF ´s distribution facility has been measured at L05.1 . These measurements are the basis for calculation
of signal RMS increase, filter investments and extra heat dissipation in transformer T5, cables L51-54 and capacitors C1 and
C2. Measurement results of current harmonics are given in figure 42, and voltage harmonics in figure 43. Phase A is
represented by red bars, B by green and C by blue. THD for each parameter is given to the left in each figure. The
fundamental components 50Hz is left out of the presentation to enable a more detailed view of the harmonics, they are listed
in table 9.
Figure 42. Current harm onics at L05.1 .
Figure 43. Voltage harmonics at L05.1 .
49
Spring 2013 10.2 HARMONIC FILTER INVESTMENTS
This chapter show how filtering of harmonics affect the RMS value of the current , voltage and hence the active power which
are debited for in the transformer station at SKF . The signals have been represented by fourier series in Matlab.
10.2.1 NO FILTER
Figure 44 below are illustrating comparisons between the fundamental 50Hz , 3-phase current waveform and the distorted
current based on the measured harmonic levels presented in section 10.1. Figure 45 illustrates the voltage.
Figure 44. No filter: Fundamental current versus distorted .
Figure 45. No filter: Fundamental voltage versus distorted .
50
Spring 2013
Table 9 below show values for calculation of active power with harmonics. The RMS values of the fourier represented signals
has been calculated using Matlab command “rms()”.
Table 9. Distorted, nonfiltered values
Irms [A] Vrms [V] [Deg]
Phase 1 451.82 166.46 15.8
Phase 2 444.97 166.58 16.73
Phase 3 423.36 166.62 18.83
W
Table 10 below show values for calculation of active power with no harmonics.
Table 10. Fundamental values
Irms [A] Vrms [V] [Deg]
Phase 1 448.88 166.4 15.8
Phase 2 443.11 166.62 16.73
Phase 3 421.88 166.55 18.83
20918 4 W
This gives the power increase caused by the harmonics ; the difference between the active power with respectively without
harmonics :
974 W
51
Spring 2013 10.2.2 PASSIVE FILTER
The figures below are illustrating comparisons between the fundamental and filtered, 3 -phase current waveform . It simulates
a passive filter tuned to eliminate the 5th, 7th, 11th and 13th which are the dominating current harmonics .
Figure 46. Passive filter; f undamental versus passive filter current .
The voltage harmonics are created by the current harmonics, so when filtering the current , implicitly the vol tage is also
filtered. Figure 47 below illustrates a small difference between the fundamental and the distorted voltage.
Figure 47. Passive filter; f undamental versus passive filter voltage .
52
Spring 2013 Table 11 below show values for calculation of active power with less harmonics ; the 5th, 7th, and 11th and 13th are eliminated
by a passive filter . The RMS values of the fourier represented signals has been calculated using Matlab command “rms()”.
Table 11. Distorted, passive filter values
Irms [A] Vrms [V] [Deg]
Phase 1 450.20 166.40 15.8
Phase 2 443.30 166.62 16.73
Phase 3 421.70 166.64 18.83
W
The harmonic active power is the difference between the active power with a passive filter respectively without harmonics ;
122 W
53
Spring 2013 10.2.3 PASSIVE FILTER INVESTMENT
The difference between the harmonic power with respectively without a passive filter gives what savings is made by installing
the filter;
852W
Table 12. Investment conditions for the payoff analysis
Electricity price [SEK/kWh] Interest rate [%] Investment Cost [SEK]
0,8 5 103000
Earning per year: 5971 SEK/y ear
Payoff time with 5% interest then becomes: 35 year s
Figure 48. Payoff diagram for a passive filter investment .
-120000 -100000 -80000 -60000 -40000 -20000 0 20000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Passive filter payoff diagram
Cashflow
54
Spring 2013 10.2.4 ACTIVE FILTER
The figures below are illustrating comparisons between the fundamental, 3 -phase current waveform and the distorted. It
simulates an active filter that eliminates 97% of all harmonics.
Figure 49. Filtered: Fundamental versus active filter current .
The voltage harmonics are created by the current harmonics, so when filtering the current , implicitly the voltage is also
filtered. Figure 26 below illustrates a very small difference between the fundamental and the distorted voltage.
Figure 50. Filtered: Fundamental versus active filter voltage .
55
Spring 2013 Table 13 below show values for calculation of active power with 97% of all harmonics eliminated by an active filter . The
RMS values of the fourier represented signals has been calculated using Matlab command “rms()”.
Table 13. Distorted active filter values.
Rrms [A] Arms [V] [Deg]
Phase 1 449.88 166.40 15.8
Phase 2 443.11 166.62 16.73
Phase 3 421.52 166.64 18.83
W
The difference between the active powers with respectively without harmonics gives us what power the harmonic contributes:
0.1W
56
Spring 2013 10.2.5 ACTIVE FILTER INVESTMENT
The difference between the harmonic powers with respectively without a passive filter gives what savings is made by
installing the filter;
974 W
Table 14. Investment conditions for the payoff analysis
Electricity price [SEK/kWh] Interest rate [%] Investment Cost [SEK]
0,8 5 168000
Earning per year: 6833 SEK/y ear
Payoff time with interest 5% then becomes: More than 50 year s
Figure 51. Payoff diagram for an active filter investment.
As can be seen, the active filter may give an increase in the earnings per year, but this increase is not significant to the higher
investment cost. The passive filter investment is better, but none of the investments are profitable in this case .
-180000 -160000 -140000 -120000 -100000 -80000 -60000 -40000 -20000 0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 Active filter payoff diagram
Cashflow
57
Spring 2013 10.3 EXTRA HEAT DISSIPATION DUE TO HARMONICS
10.3.1 CABLES
The heat dissipation in cables L51, L52, L53 and L54 have been calculated by equation 8 and measurement values presented
in section 10.1. Table 15 show calculation input.
Table 15. Calculation input for increased heat dissipation in cables due to harmonics
Calculation input: Length
[m] Area
[mm2] Resistivity
[Ω/m] Magnetic permeability
[H/m]
200 15,35 17,5E -9 1,256E -6
Calculation results are presented in figure 52 .
Figure 52. Heat dissipation in cables distributed at each harmonic.
The 5 th harmonic is the dominating contributor to the total heat dissipation caused by harmonics in the cables. The non -linear
loads th at cause the harmonics are mainly 6 -pulse frequency drives which as you know from section 7.3 emits the 5 th
harmonic to a large extent. The total harmonic heat dissipation in cables L51 + L52 + L53 + L54 adds up to: 105 W . This is
about 3,2% of the heat dissipation caused by the fundamental 50 Hz current. 0 10 20 30 40 50 60 70 80
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Heat dissipation in cables caused by harmonics Power [W]
Harmonic
number
58
Spring 2013 10.3.2 TRANSFORMERS
When calculating the increase in heat dissipation in the transformer T5, equation 9 and measurement values presented in
section 10.1 has been used. The nominal values used in the c alculation are listed in table 16 .
Table 16. Calculation input
Calculation input: Nom inal load loss [W] Iron loss koefficient
1636 0,04
And the results in table 17 below.
Table 17. Increased heat dissipation in transformer T5 due to harmonics
Results Power loss [W] Percenage of load loss [%]
411 8,38
59
Spring 2013 10.3.3 CAPACITORS
The heat dissipation in capacitors C1 and C2 have been calculated by equation 11 with measurement values presented in
section 10.1.
Calculation input: Nominal capacitor loss
[W/capacitor]
120
Calculation results are presented in figure 52.
Figure 53. Increased heat dis sipation in capacitors C1 and C2 caused by harmonics
The 5th harmonic is the dominating contributor to the total heat dissipation caused by harmonics in the c apacitors . The non –
linear loads th at cause the harmonics are mainly 6 -pulse frequency drives which as you know from section 7.3 emits the 5th
harmonic to a large extent. The total harmonic heat dissipation in ca pacitors C1 and C2 adds up to: 14,4 W. This is about 6%
of the heat dissipation caused by the fundamental 50 Hz voltage.
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 Heat dissipation in capacitors caused by harmonics Power [W]
Harmonic
number
60
Spring 2013 10.4 TRANSFORMER COMPARISON
This section presents a comparison between a ”regular” oil cooled distribution transformer with a ”green alternative” i.e.
an amorphous metal core distribution transformer.
In the comparison between a ”regular” Regular Grain Oriented (RGO) silicon steel distribution transformer with a ”green
alternative” i.e. an amorphous metal core distribution transformer table 18 shows transformer data that has been used. Table
19 shows the investment conditions used in the analysis.
Table 18 Transformer nominal data
Transformer data : Primary voltage [V] Secondary voltage [V] Power rating [kVA] Load level [%]
11000 420 1600 60
Table 19 Investment conditions for ownership cost com parison
Investment condition s: Electricity price [kr/kWh] Life length [y] Interest rate [%]
0,8 30 5
61
Spring 2013 The development of the TOC over 11 years for an RGO and an amorphous metal core alternat ive are illustrated in figure 54 .
The TOC is equal after 5 years and after that the amorphous alternative has the lower TOC.
Figure 54.Transformer TOC development for two alternatives over 11 years
The final TOC is calculated assuming the transformer service life is 30 years and the result is presented in figure 55.
Figure 55. Final TOC for two investments; Regular Grain Oriented versus Amourphous Metal Core transformers.
As can be seen, the amorphous metal core transformer outperformed the Regular Grain Oriented (RGO) silicon steel
transformer in this case. The amorphous alternative lead s to 20 % less TOC.
0 100000 200000 300000 400000 500000 600000 700000 800000 900000
1 2 3 4 5 6 7 8 9 10 11 Accumulated ownership cost Transformer TOC plan 11 years
RGO
Amourphous
[Year] kr
1 2
TOC Savings 433
Capitalized loss cost 1914 1373
Purchase price 136 244 0 500 1000 1500 2000 2500 Total Ownership Cost Total Ownership Cost, 30 years
RGO
Amourphous kkr
62
Spring 2013 10.5 CABLE COMPARISON
In figure 56 below, a comparison has been made between two copper cables that differ in two parameters; price and cross
area, chapter 3 explains the method . Higher cross area leads to lower energy loss, but is the price of a higher cross area worth
the investment? Equation 2 has been used calculating P loss.
Table 20. Cable characteristics for the comparison between alternative 1 and 2.
Cable Data Current
[A] Length
[m] Area
[mm2] Resistivity
[Ω/m] Price
[SEK/m] Loss cost
[SEK/y]
1 374 200 185 17,5E -9 966 18564
2 374 200 240 17,5E -9 1270 14310
Figure 56. Cable TOC development for two alternatives over 30 years.
As can be seen, the best alternative is the one having the higher cross area .
0 100000 200000 300000 400000 500000 600000 700000 800000 900000
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 TOC plan of cables 200m
Higher price, lower loss Lower price, higher loss
63
Spring 2013 11 CONCLUSIONS
Based on the results and market research the “questions to be answered ” that was presented in the introduction chap ter are
discussed and answered.
11.1 IS THERE A POTENTIAL FOR SAVI NGS BY CHOOSING HIGH EFFICIENCY COMP ONENTS ?
Variable frequency drives , breakers, transformers and cables has been investigated with energy performance as main subject.
Part 1 of the thesis consists of a market research and presenting of methods with the goal of contrasting regular choices of
components to more efficient. An e conomic comparison between these contrasting choices is presented in the result s chapter
to investigate if there is a significant potential to be earned in order to improve investments.
Variable Frequency Drives
Chapter 5: Variable Frequency Drives (VFD´s) has been investigated with energy performance and especially VFD´s
connection to harmonics in electric power systems. They are the largest contributor to harmonics in industries today.
Industries increase their usage of them and this leads to highe r harmonic level and lower reactive power. The first step of
VFD´s, the rectification can be performed by a 6-pulse bridge or a 12-pulse bridge, (24 -pulse bridges is rare ly installed in
distribution facilities today ). The majority of VFD´s in industries to day use 6 -pulse bridges which causes harmonic levels of
about 30%. Instead, choosing a 12 -pulse bridge for the VFD´s will half the harmonic level to about 12%. Conclusion: In the
choice of VFD´s, always evaluate the alternative of 12 -pulse variable frequen cy drives. The economic aspect of harmonic
levels is discussed in section 11.2.
Interrupters and breakers
Chapter 4: During operation interrupters and breakers hold high efficiencies. The market research resulted in efficiencies
close to 100%. Some of these components hold higher levels than the cables connected to them because of a higher conductor
cross area. The c onclusion is that this is not a component with potential to increase efficiency in electric power systems.
Transformers
Chapter 2: According to EU´s IEE, and a large survey in the project “Strategies for development and diffusion of energy
efficient distribution transformers ” the dominating type of loss in distribution transformers today are the no load loss. Further,
the most common type of transformer has a core consisting of Regular Grain Oriented silicon steel which in comparison to
transformers with amorphous metal cores hold significantly higher no load loss. In some cases, choosing an amorphous metal
transformer leads to 70 % less no load loss. The case in the result s chapter evaluates the total ownership cost (TOC) for two
transformers: one with RGO and one with amorpho us metal core, The TOC is 21% less for the amorphous metal transformer.
The conclusion is that in the choice of transformers, always evaluate an alternative with amorphous metal core.
64
Spring 2013 Cables
A method for comparison of cables which differs in energy loss and price is presented in chapter 3 and an application of this
in the r esults section 10.4.1 . The case in the result s evaluated what the cross area of a 200m power cable meant economically
with energy loss as a opera tion cost and the price of the cable as an investment cost. A larger cross area means lower
operation cost but higher investment cost. The conclusion is that the larger cross area´s impact on a lower operation cost is
significant to the higher price of inv estment.
11.2 WHAT IS THE ECONOMIC IMPACT OF HARMONICS IN POWER SYSTEMS ?
The economic impact of harmonic presence appears different for different parties; distribution facility owners, grid owners
and electricity suppliers respectively view the problem from different perspec tives. This makes the economic impact of
harmonics a quite complex question.
For distribution facility owners, the signal which the debiting meter measures is essential. Most debiting meters installed
today measures the RMS value of the wave regardless of the form. This means that if harmonics are on the signal, these get
debited f or. This is because a fluctuating wav e has a higher RMS -value than a ideal wave of the same fundamental frequency
and amplitude. Most of Sweden´s e lectronic equipment is custom to AC with 50 Hz, which means that signals consisting of
other frequencies adde d to the fundamental 50 Hz cannot be consumed. When energy distribution companies measure the
energy that consumers use and the signal contains harmonics, the consumers pay for the useful, fundamental frequency which
in Europe is 50 Hz, but also all of t he other frequencies, the harmonics .
To calc ulate this increas e in RMS and thus the economic impact of harmonics it is appropriate to le t Fourier series (see
section 8.1) represent the signal and manage each harmonic separately comparing the resulting distorted wave to the
fundamental and calculating the RMS difference between these . In section 10.2 “Harmonic Filter investment ” this method is
used for estimating the harmoni c cost in the case study, which proves to be significant.
However, two attenuation methods; active and passive filter investments has been economically evaluated, the conclusions
are that investm ents of attenuating harmonics in the case study is not profitable (10.2) .
A larger study “The cost of harmonic losses and mitigation in distribution systems” by Mohamed Ashour, Kamelia Youssef
and Salah El Sobki made similar conclusions for 10 case studies in Alexandria in Egy pt which confirms the results of this
thesis; significant potential, expensive solutions.
65
Spring 2013 11.3 HOW MUCH ENERGY LOSS DOES HARMONICS CAUSE IN ELECTRIC PO WER COMPONENTS ?
It is important to separate the increase of heat dissipation in components to the increase in current and voltage RMS.
Increased heat dissipation in certain components does not neces sarily mean increased economic loss for distribution facilities.
As an example; assume that a load emits 100% harmonic energy. Further, assume that 20% of this energy c onverts to heat in
the network. Then 80% of the energy in the harmonics is debited for . Therefore , using the energy in heat diss ipation as a base
for economic analysis could lead to wrong conclusions.
The increased heat development in components requires component over sizing to cope with the increased stress. It also
causes a reduced service life.
11.3.1 CABLES
3,2% increased resistive loss in cables L51-54 due to harmonics . The current magnitude is more important than a higher
frequency for the harmonics when it comes to energy loss in cables. Because the main current is so much larger than the
harmonic cur rent, harmonic loss becomes a small part of the total resistive losses. This can also be observed by the
distribution of the power loss for different harmonics in figure 52; even though the skin effect makes harmonics of a higher
order more contributing to the total loss, the current magnitude is much more significant to the total contribution of resistive
loss. Equation 6 is u sed for calculating the energy loss for cables and the conclusion is verified by analyzing the relationship
between power loss, frequency and current magnitude; it depends to the square of the current but only to the square root of t he
frequency.
11.3.2 TRANSFORMERS
8,38% increased load loss in transformer T5 due to harmonics . The increase in heat dissipation due to harmonics in
transformers is calculated with the harmonic currents. The load loss depends on the current and its frequency, because of the
skin effect which creates eddy currents in the windings, increased frequency leads to higher load loss. The no load loss
depends on voltage harmonics and is negligible in this context.
11.3.3 CAPACITORS
6% increased loss in capacitor C1 and C2 due to harmonics. The increase in heat dissipation due to harmonics in capacitors is
calculated with the harmonic voltages. There is no significant current flowing into the capacitor ex cept the one that replaces
heat loss; this is neglected in the heat loss due to harmonics calculations .
66
Spring 2013 12 REFERENCES
1 . Kungliga ingenjörsvetenskapsakademien (2009) Vägval Energi.
Available at: http://www.iva.se/Documents/Publikationer/Projekt/4_ENERGIEFFEKTIVISERING_web.pdf
Accesed: May 17, 2013
2. The ministerial Council on Energy of Australia and New Zealand (2007) Equipment Energy Efficiency Program.
Available at: http://www.energyrating.gov.au/wp -content/uploads/2011/03/200717 -meps -transformers.pdf
Accesed: May 17, 2013
3. ABB (2000) ABB green distribution transforme r program.
Avaliable at:
http://www05.abb.com/global/scot/scot252.nsf/veritydispla y/47f61603dac5fb168525773e0078254f/$file/1luj460910 –
lte_partnership_in_sustainable_environement.pdf
Accesed: May 17, 2013
4. ABB (2000) ABB green distribution transformer program.
Avaliable at:
http://www05.abb.com/global/scot/scot252.nsf/veritydisplay/47f61603dac5fb168525773e0078254f/$file/1luj460910 –
lte_partnership_in_sustainable_env ironement.pdf
Acces sed: May 17, 2013
5. William Francis Magie (1911). Principles of Physics: Designed for Use as a Textbook of General Physics .
6. U.S. Department of Energy (2012) Energy Efficiency & Renewable Energy.
Available at: http://www1.eere.energy.gov/manufacturing/tech_deployment/pdfs/motor_tip_shee t11.pdf
Acces sed: May 17, 2013
7. Schneider electric (2010) Wiki – EIG
Available at: http://www.electrical -installation.org/enw/images/9/9a/FigM12b.jpg
Acces sed: May 17, 2013
8. Schneider electric (2010) Wiki – EIG
Available at: http://www.electrical -installation.org/enw/images/2/29/FigM05.jpg
Acces sed: May 17, 2013
67
Spring 2013
9. George J. Wakileh, Power System Harmonics – Fundamentals, Analysis and Filter design, page 74, ISBN: 3 -540-42238 -2
10. Wikipedia (2012)
Available at: http://en.wikipedia.org/wiki/File:6_pulse_bridge_without_inductance.png
Acce ssed: May 17, 2013
11. Wikipedia (2012)
Available at: http://en.wikipedia.org/wiki/File:Br idge_rectifier_at_alpha%3D0_u%3D0.png
Acce ssed: May 17, 2013
12. Schneider electric (2010) Wiki – EIG
Available at: http://www.electrical -installation.org/enw/images/1/14/FigM0 8.jpg
Acces sed: May 17, 2013
13. Hersehey Energy Systems (2005) The Hershey Program
Available at: http://www.hersheyenergy.com/harmonics.html
Acces sed: May 17, 2013
14. Zoya Popovic and Branko D. Popovic (2000 ). Introductory Electromagnetics, Prentice Hall
Available at: http://ecee.colorado.edu/~ecen3400/Chapter%2020%20 -%20The%20 Skin%20Effect.pdf
Acces sed: May 17, 2013
15. William Francis Magie (1911). Principles of Physics: Designed for Use as a Textbook of General Physics . New York: T he
Century Co. p. 508.
16. Schneider electric (2010) Wiki – EIG
Available at: http://www.electrical -installation.org/enwiki/Basic_solutions_to_attenuate_harmonics
Acces sed: May 17, 2013
17. Schneider electric (2010) Wiki – EIG
Available at: http://www.electrical -installation.org/enwiki/Basic_solutions_to_attenuate_harmonics
Acces sed: May 17, 2013
18. Schneider electric (2010) Wiki – EIG
Available at: http://www.electrical -installation.org/enwiki/Basic_solutions_to_attenuate_harmonics
Acces sed: May 17, 2013
19. Schneider electric (2010) Wiki – EIG
68
Spring 2013
Available at: http://www.electrical -installation.org/enwiki/Basic_solutions_to_attenuate_harmonics
Acces sed: May 17, 2013
20. Rockwell Automation (2009) Variable Frequency Drive Solutions for Low Harmonics
Available at: http://www.mid -island.com/downloads/pdfs/drives -br011b -en-p.pdf.pdf
Acces sed: May 17, 2013
21. Rockwell Automation (2009) Variable Frequency Drive Solutions for Low Harmonics
Available at: http://www.mid -island.com/downloads/pdfs/drives -br011b -en-p.pdf.pdf
Acces sed: May 17, 2013
22. ABB (2008) Power Quality filters
Available at:
http://www02.abb.com/global/ huabb/huabb008.nsf/0/45df9d2440a9199bc1257a2c004404d3/$file/PQF+felharm%C3%B3nik
us+sz%C5%B1r%C5%91k+.pdf
Acces sed: May 17, 2013
23. George J. Wakileh, Power System Harmonics – Fundamentals, Analysis and Filter design, ISBN: 3 -540-42238 -2
24. George J. Wak ileh, Power System Harmonics – Fundamentals, Analysis and Filter design, ISBN: 3 -540-42238 -2
25. George J. Wakileh, Power System Harmonics – Fundamentals, Analysis and Filter design, ISBN: 3 -540-42238 -2
26. Brian D. Storey Com puting Fourier Series and Power Spectrum with MATLAB
Available at: http://faculty.olin.edu/bstorey/Notes/Fourier.pdf
Acces sed: May 17, 2013
27. Schneider electric (2010) Wiki – EIG
Available at: http://www.electrical -installation.org/enwiki/Total_harmonic_distortion_(THD)
Acces sed: May 17, 2013
28 George J. Wakileh, Power System Harmonics – Fundamentals, Analysis and Filter design, page 74, ISBN: 3 -540-42238 -2
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