Categories
Harmonics

Commercial power quality meters

The use of a rectangular window requires that the measurement window is synchronized with the actual power system frequency, hence the use of a 10-cycle window instead of a window of exactly  200 ms. The IEC standard [1] requires that 10 cycles correspond with an integer number of samples within 0.03%. To ensure synchronism between the measurement window and the power system frequency, most power quality meters use a phase-locked loop generating a sampling frequency that is an integer multiple of the actual power system frequency. One of the commonly used in the company power quality meters is Elspec G4500 which provides full functionality regarding measurements of power quality. An exemplary connection of such measurement equipment in there phase system is presented in Figure 1 [2].

Elspec G4500 connection
Figure 1 Exemplary connection of Elspec equipment in wind turbines.

Before power quality indices are calculated by the Elspec equipment, acquired data is processed. Processing stage comprises of fundamental frequency detection, sample rate adjustment according to the detected frequency, and Fourier decomposition applied. The approach of sample rate adjustment is to adjust the finite orthogonal Hilbert basis in order to express each of frequency components in the Fourier space only by one vector from the Hilbert basis. The whole data acquisition, processing and logging process is briefly presented in Figure 2.

A synchronization (i.e. sample rate adjustment according to the fundamental frequency) error leads to cross-talk between different harmonic frequencies. The 50 hz component is by far the dominating component in most cases so that the main concern is the cross-talk from the 50 hz component to higher order components. From the other side, resampling process can affect frequency components which are not integer multiple of the fundamental frequency.

This phenomenon can be easily seen in the spectrum of pulse width modulated voltage source converters with fixed frequency ratio. Since generated output voltage of the wind turbine is a function of the fundamental frequency (fo) and the carrier frequency (fc), results obtained by the Elspec system are incorrect to some extent. The magnitudes of Fourier transform harmonic components are the more inaccurate the higher significant is the fundamental variation. Even if the result of applying the discrete Fourier transform to the basic window is a spectrum with 5-hz spacing between frequency components and the spectrum thus contains both harmonics and interharmonics, the results can be sometimes significantly inaccurate.

Power quality meter data processing
Figure 2 Data processing algorithm used by Elspec equipment.

As a good example of this is one of the most significant sideband harmonic components from the first carrier group. Exemplary results of measurements form the LV side of the wind turbine transformer can be seen in Figure 3. As it was mentioned previously the wind turbine frequency ratio is mf=49 and the analyzed sideband harmonic component is of frequency fc+2fo. Three scatter plots present the same harmonic component measured during the same period using different data acquisition devices and processing techniques.

Sideband harmonic - not resampled signal Sideband harmonic - resampled signal
(a) (b)
Sideband harmonic - Elspec G4500
(c)

Figure 3 Sideband harmonic component affected by different processing techniques: (a) sideband harmonic calculated in post-processing from resampled signal, (b) sideband harmonic calculated in post-processing from original signal, (c) sideband harmonic calculated on-line by power quality meter.

Data processing results presented in Figure 3 show how easily inappropriately applied processing techniques can provide wrong results. Results from Figure 3(a) show sideband harmonic component measured using results obtained from the measurement campaign with direct Fourier decomposition (i.e. without sample rate adjustment). From Figure 3(b) presents the same data but resampled and later discrete Fourier transform is applied, Figure 3(c) describe sideband harmonic component magnitude obtained by the Elspec measurement system.

It can be observed that results using various processing approach provide different results. Due to the fact that the frequency of sideband harmonic components generated by modulation with constant carrier frequency does not vary significantly and Fourier decomposition without earlier sample rate adjustment gives the most appropriate results. This is presented in Figure 3(a) and only small magnitude variation affected by nonlinear relation between the modulation index () and the sideband harmonic components as well as measurement and data processing (i.e. small spectral leakage) errors. Completely different and unacceptable results are seen in Figure 3(b) where analysed waveform is resampled. One can observe that due to significant spectral leakage the estimated magnitude sometimes can be even equal to zero. Therefore sometimes power quality meters can provide values significantly affected by processing errors. This behaviour is present in the scatter plot from Elspec measurements (Figure 3(c)). It is important to emphasize that the algorithm in the power quality meter applies lossy compression which also determines estimated magnitudes. Estimated harmonic components are assumed to be insignificant and not saved (i.e. set to zero) if the magnitude is lower than a certain threshold which is defined based on measured waveform distortion and maximum allowed database storage capacity per month. Such limitations provides scatter plots as in Figure 3(c) which is similar to Figure 3(b) but modified due to averaging and magnitudes below the threshold artificially set to zero.

[1] "Electromagnetic compatibility (EMC) - Part 4-30: Testing and measurement techniques - Power quality measurement methods," International Electrotechnical Commission Standard IEC 61000-4-30, 2008.
[2] P. Nisenblat, A. M. Broshi, and O. Efrati, "Methods of compressing values of a monitored electrical power signal," U.S. Patent 7,415,370 B2, Aug. 19, 2008.

Categories
Harmonics Wind Farms

Harmoniske svingninger i store havmølleparker

This time Danish abstract of the PhD report entitled "Harmonics in Large Offshore Wind Farms (Harmoniske Svingninger i Store Havmølleparker)". The project was defended on the 2nd of February in 2012 at Aalborg University, Denmark.
 

Antallet af vindmøller med frekvensomformer til nominel effekt i mw-klassen, der anvendes til store havmølleparker, er stærkt stigende. De er tilsluttet et udbredt og forgrenet mellemspændingskabelnet stort set uden egetforbrug og er tilsluttet transmissionsnettet ved hjælp af lange højspændingskabler. Det stiller vindmølleindustrien og netselskaberne over for nye udfordringer i forhold til at forstå harmoniske svingningers  karakter, udbredelse og virkning. Vindmøllebranchen udvikler sig hastigt. Det stiller branchen over for nye udfordringer, hvilket har medført gennemførelse af flere og flere forskningsprojekter, der omhandler analyse af harmoniske svingninger med særligt fokus på vindenergi, og det er grunden til, at dette projekt blev påbegyndt og gennemført med et positivt resultat. Virksomhedens erfaring fra tidligere havmølleprojekter i forbindelse med forskellige harmoniske aspekter har medført et behov for at udføre omfattende undersøgelser af harmoniske svingninger.

Forskningsprojektet blev til på branchens foranledning, og blev gennemført i et  i samarbejde med institut for Energiteknik, Aalborg Universitet.  I forbindelse med planlægningen af projektforløbet blev rammerne for projektet lagt ud fra en traditionel rationalistisk tilgang for at kunne levere viden og en dybere forståelse for forskellige aspekter (f.eks. målinger, databehandling, dataanalyse, modellering, modelanvendelse) i studier af harmoniske svingninger. På baggrund af disse rammer, blev rapportens opbygning fastlagt. Læseren kan dermed følge alle projektforløbets stadier startende med målinger, databehandling og –analyse og sluttende med modellering og modelanvendelse. Forskellige aspekter af tidsdomænevalidering, frekvensdomæne og af brugen af statistiske metoder nævnes i forbindelse med specifikke problemer.

Målinger udgør en vigtig del af industriel forskning. Derfor er dette projekt unikt samtidig med, at det tilfører den akademiske verden vigtig praksis-orienteret indsigt og vice versa. Det er bevist, at analyse af systemer som store havmølleparker indebærer mange aspekter, der omhandler udvidede og mere præcise modeller, komplekse målekampagner og selvfølgelig bedre og mere anvendelige databehandlingsmodeller. Før de ovennævnte aspekter kan behandles, er det nødvendigt at have et pålideligt og robust målesystem til rådighed. Dette opnås gennem grundigt design af målesystemets hardware- og softwarelag.

I rapporten forklares det, at det er meget vigtigt at kende typen af de harmoniske svingninger, der genereres i store havmølleparker for at kunne anvende de rigtige databehandlingsteknikker. Tids-/frekvensanalyse baseret på multiresolution wavelettransformation bruges til at udføre tids-/frekvensdomæneanalyser, som kan bidrage til at definere de harmoniske svingningers oprindelse og observere korttidsvariationer. Ikke-parametrisk spektralanalyse anvendes på interpolerede signaler tilpasset de varierende elsystemfrekvenser. Forskellige databehandlingsteknikker er præsenteret og anvendt afhængig af signalet (dvs. om det er stationært eller ikke-stationært) eller typen af harmoniske svingninger (dvs. spline resampling eller direkte spektralanalyse). På baggrund af grundig analyse af målinger ses det, at visse harmoniske komponenter, der dannes på netsiden af omformeren i vindmøllen påvirkes af to faste frekvenser, dvs. af elsystemets grundfrekvens og basisbærefrekvenssignalet. Derfor er målinger af harmoniske svingninger udført primært med kommercielle spændingskvalitetsmålere i nogen grad utilstrækkelige, og den efterfølgende vurdering af resultaterne kan derfor være misvisende.

Forskellige statistiske værktøjer er anvendt til at analysere oprindelsen og karakteren af forskellige harmoniske komponenter. En omfattende sammenligning af harmoniske spændinger og strømme baseret på en vurdering af den sandsynlige fordeling samt passende statistiske beregninger (f.eks. middel, varians, sandsynlig tæthedsfunktion mv.) anvendes. En sådan tilgang giver et bedre overblik og en bedre sammenligning af harmoniske komponenters variationer og forekomst.

Flere frekvensdomænemetoder til beskrivelse af vindmølleparker bestående af flere komponenter såsom vindmøller, transformere, kabler mv. beskrives og sammenlignes. Det forklares, at store havmølleparker kan producere yderligere uønskede resonanser i lavfrekvensområdet. Dette kan have en betydelig indflydelse på systemets generelle stabilitet. Derfor er analyse og designoptimering af store havmølleparker mere komplekst end analyse og designoptimering af små landmølleparker.

I dag er vindmøller komplekse anlæg udstyret med den nyeste teknologi. Derfor er analyse af harmoniske svingninger i sådanne anlæg ikke så ligetil. På grund af vindmøllernes kompleksitet kan man ved studier af harmoniske svingninger fokusere på flere forskellige aspekter såsom reguleringsstrategi, moduleringsteknik, omformerdesign og hardwareimplementering.

Forskellige reguleringsstrategier er blevet overvejet sammen med deres indflydelse på dannelsen af harmoniske svingninger og generel systemstabilitet. Analyser er hovedsaglig udført i frekvensdomænet. En analyse går ud på at finde ud af, hvordan forskellige komponenter i reguleringskonceptet (f.eks. filtre, kontrolenheder mv.) kan påvirke styringen og dens evne til at udkompensere harmoniske svingninger. Reguleringsstrategiernes indflydelse på mølleparkens generelle stabilitet er ligeledes blevet grundigt undersøgt. Egnede stabilitetsindeks er foreslået og anvendt i flere konkrete cases.

Omhyggeligt modelerede ækvivalenter af store vindmølleparker i frekvensdomænet sammen med møllernes frekvensrespons giver et godt overblik over, hvordan store havmølleparker reagerer ved forskellige frekvenser. En sådan tilgang har vist gode resultater i forbindelse med studier af eksisterende mølleparker.

Da harmoniske svingninger i vindmøller og vindmølleparker har forskellig oprindelse og er af forskellige typer, kan det være problematisk at sammenligne dem. Derfor er selektiv validering af specifikke frekvenskomponenter til tider mere anvendelig. Det blev observeret, at sammenligning af resultater i frekvensdomænet og tidsdomænet og anvendelse af statistiske metoder er nøglen til forståelse af resultaterne.

På baggrund af de præsenterede studier kan det ses, at store havmølleparker sammenlignet med typiske landmølleparker kan generere flere uønskede resonansscenarier. Uønskede resonanser kan påvirke mølleparkens generelle stabilitet og ydelse (f.eks. kan harmonisk resonans anslåsog forstærkes). Derfor er det meget vigtigt at analysere mølleparker grundigt, især store havmølleparker, også ud fra et harmonisk perspektiv.

Denne erhvervsPhD fokuserer på at finde frem til de bedst mulige metoder til at gennemføre forskellige harmoniske studier af havmølleparker, herunder en række forhold som ikke før er blevet overvejet. Anvendelse af nye metoder og en udvidelse af rækken af modeller bidrager til at opnå den højere rådighed, der er nødvendig på havmøllerparker, hvis de skal fungere som store kraftværker i det elektriske system.

Categories
Harmonics Wind Farms

Harmonics in large offshore wind farms

English abstract of the PhD report entitled "Harmonics in Large Offshore Wind Farms". The project was defended on the 2nd of February in 2012 at Aalborg University, Denmark.
 

The number of wind turbines with full converters in the MW range used in large offshore wind farms is rapidly increasing. They are connected through a widespread MV cable network with practicably no consumption and connected to the transmission system by long HV cables. This represents new challenges to the industry in relation to understanding the nature, propagation and effects of harmonics. Recently, the wind power sector is rapidly developing. This creates new challenges to the industry, and therefore more and more research projects, including harmonic analyses especially focused on wind power applications, are conducted and that is why the project was initiated and successfully developed. Also experience from the past regarding offshore projects developed in the company and various harmonic aspects causes a need to carry out extensive harmonic research.

The research project was initiated by the industry and carried out in cooperation with academia. In order to organize the project development process, the research development framework was suggested based on rationalistic tradition approach in order to provide knowledge and better understanding of different aspects (e.g. measurements, data processing, data analysis, modelling, models application) in harmonic studies. Based on the framework, also the structure of the report was organized. This allows the reader to go through all of the stages in project development starting from measurements, through data processing and analysis, and finally ending up on modelling and models application. Different aspects of validation in time domain, frequency domain, and by application of statistical methods are mentioned in relation to respective problems.

Measurements constitute a core part in industry-oriented research. Due to this fact, the research project owes its uniqueness and contributes new insight to the academia. It is proven that an analysis of such systems as large offshore wind farms considers many aspects related to extended and accurate models, complex measurement campaigns and of course appropriate and more suitable data processing methods. Before any of the above aspects could be seriously taken into consideration, a reliable and robust measurement system is needed. This is achieved by carefully designing the hardware and the software layers of the measurement system.

It is explained in the report that it is of great importance to know the nature of generated harmonics in large offshore wind farms in order to apply the most suitable data processing technique. Time-frequency analysis based on multiresolution wavelet transform is used in order to perform time-frequency domain analysis helpful to distinguish harmonic origin and observe short-term variation. Non-parametric spectrum estimation is successfully applied to interpolated signals adjusted according to the varying power system frequency. Different data processing techniques are presented and applied depending on the signal (i.e. stationary or non-stationary) or harmonic nature (i.e. spline resampling or direct spectrum estimation). Based on an in-depth investigation of measurements, it is observed that certain harmonic components generated by the grid-side converter in the wind turbine are affected by two driven frequencies, i.e. the power system fundamental frequency and the carrier signal fundamental frequency. Therefore, harmonic assessment made by major part of commercial power quality meters is to some extent inappropriate, and their measurements interpretation can be misleading.

Different statistical tools were used in order to analyse the origin and nature of various harmonic components. A comprehensive comparison of harmonic voltages and currents based on probability distribution estimation and appropriate statistics calculation (mean, variance, probability density function, etc.) is applied. Such approach gives a better overview and comparison of harmonic components variation and occurrence frequency.

Several frequency domain methods of describing wind farms comprising of various components such as wind turbines, transformers, cables, etc. are shown and compared. It is explained that large offshore wind farms can introduce additional unwanted resonances within the low frequency range. This can significantly affect overall system stability. Therefore, the analysis and design optimization of large offshore wind farms are more complex than smaller onshore wind farms.

Nowadays, wind turbines are complex devices equipped with the newest technologies. Therefore, also harmonic analysis of such devices is not a straightforward task. Harmonic studies, due to the complexity of the wind turbine structure, can be focused on several parts such as control strategy, modulation technique, converter structure, and hardware implementation.

Various control strategies are taken into consideration and their impact on possible harmonic emission and overall system stability. An analysis is performed mainly in the frequency domain. One analyses how particular components in the control structure (e.g. filters, controllers, etc.) can affect the control and its harmonic rejection capability. The influence of control strategies on overall wind farm stability is also deeply investigated. Appropriate stability indices are suggested and applied in several study cases.

Carefully modelled and aggregated large wind farms in frequency domain together with the wind turbines frequency response give a good overview about large offshore wind farm behaviour for different frequencies. Such approach is successfully used in studies of real-life existing wind farms.

Since harmonics in wind turbines and wind farms are characterized by different origin and nature, comparison of them may be problematic. Therefore, sometimes selective validation of particular frequency components is more suitable. It was observed that comparison of results in frequency domain and time domain, as well as application of statistical methods, is the core part of results understanding.

Based on presented studies, we see that large offshore wind farms, in comparison to typical onshore wind farms, can affect more unwanted resonance scenarios. Unwanted resonances can cause overall wind farm stability and performance (e.g. unwanted harmonic excitation and amplification). Therefore, it is of great importance to carefully analyse wind farms, especially large offshore wind farms, also from a harmonic perspective.

This industrial PhD project is focused on investigating the best possible way to perform various harmonic studies of offshore wind farms including some conditions not taken into consideration before. Application of new methods and widening the range of models contributes to achieve the necessary higher reliability of offshore wind farms as large power generation units in electrical power systems.

Categories
Harmonics

Harmonics in power systems and power electronics

Ideally, an electrical power system in every certain point should show a perfectly sinusoidal voltage signal. However, it is difficult to preserve such desirable conditions. The deviation of the voltage and current waveforms from sinusoidal is described in terms of the waveform distortion, often expressed as harmonic distortion.

Harmonics are created when nonlinear loads draw nonsinusoidal current from a sinusoidal voltage source or are generated by purpose by active components. Harmonic distortion is caused by nonlinear devices in the power system where driven frequency is the power system fundamental component fo. A nonlinear device is one in which the current is not proportional to the applied voltage. While the applied voltage is perfectly sinusoidal, the resulting current is distorted.

According to definition commonly used in power system studies [1] characteristic harmonic exist when analyzed three-phase electrical system is considered to be balanced, the voltages and currents waveforms have identical shape and current and voltage are separated by exactly ±1/3 of the fundamental period. In such case zero sequence harmonics are for orders n=3m where m=1,2,3,... , positive sequence harmonics are for orders n=3m-2 and negative sequence harmonics are for orders n=3m-1.

The harmonic emission of power electronic components can be categorized in characteristic and non-characteristic harmonics. The characteristic harmonic emissions are determined by the converter topology and the switching pattern applied. For instance, a typical configuration is a two-level, three-phase voltage source converter with sinusoidal pulse-width modulation. The modulation frequency ratio mf is defined as the switching frequency fc divided by the power system fundamental frequency fo. In double-edge naturally sampled pulse-width modulation significant sideband harmonics in this carrier group will occur at frequencies of ωct±2ωot, ωct±4ωot. And for the second carrier group, the significant sideband harmonics will occur at 2ωct±ωot, 2ωct±5ωot, 2ωct±7ωot. All triple sideband harmonics (e.g. 2ωct±3ωot, etc.) are canceled between legs because the phase angles of these harmonics rotate by multiples of 2π for all phase legs (i.e. common mode signals). [2], [3].

where Amn and Bmn are the Fourier coefficients.

Non-characteristic harmonics are not related to the converter topology, but are determined by the operating point and control scenario of the individual converter. Therefore, these are weakly correlated or even completely uncorrelated between different wind turbine generators [4].

Typical device with another driven frequency than fundamental component in the power system is voltage source converter with pulse width modulation which can be seen in nowadays wind turbines. If such converter is a grid-connected device the frequency components generated by it are dependent on both the power system fundamental component (i.e. modulated signal) and the carrier signal fundamental component (i.e. modulating signal). In this particular case harmonic components generated by the voltage source converter can be integer multiple of grid frequency, carrier frequency or a mixture of both of them.

Therefore in power systems where there is more than one driven frequency it is not straight forward to identify harmonic components and their origin. In fact the only occurrence of integer multiple frequencies of the power system fundamental frequency is the trivial case where a single sinusoid interacts with itself or its own harmonics. This situation was popular in the past when power systems comprised only passive components and synchronously rotating generators. Nowadays broadly used in modern power systems advanced power electronics contains also its own driven frequencies (not always equal or multiple integer of the power system frequency) which can affect generation of harmonic components of frequencies constituting a mixture of different driven frequencies.

[1] N. R. Watson and J. Arrillaga, Power System Harmonics. Wiley and Sons, 2003.
[2] N. Mohan, T. M. Undeland, and W. P. Robbins, Power electronics: Converters, Applications, and Design, 3rd ed. New York: Wiley and Sons, 2003.
[3] D. G. Holmes and T. A. Lipo, Pulse Width Modulation for Power Converters: Principles and Practice. IEEE Press, 2003.
[4] J. Verboomen, R. L. Hendriks, Y. Lu, and R. Voelzk, "Summation of Non-Characteristic Harmonics in Wind Parks," in Proc. Nordic Wind Power Conference, Bornholm, 2009.

Categories
Harmonics

Short story about harmonic research

Harmonics were always of special concern in power system studies. In the past the power system was comprised of mainly passive components with relatively linear operating range as well as synchronous generators. Harmonic analysis of such systems is state-of-the art right now. Nowadays modern power systems include more and more power electronic components than in the past. The most significant power electronic components are different types of flexible alternating current transmission system (FACTS) devices such as static synchronous compensator (STATCOM) or static var compensator (SVC). Also renewable energy sources (e.g. wind turbines, photo voltaic installations, tidal steam generators) as well as high-voltage, direct current (HVDC) electric power transmission systems become more popular. Power electronic equipment in modern power systems is obviously a source of additional harmonic components not seen previously. On the other hand, the application of advanced and fast control in grid-connected power converters introduces possibility of control higher than the fundamental frequency components. Appropriately used power electronics can definitely improve the quality of power.

To show how harmonics have being been more and more important in electrical engineering and power system studies a popular electrical engineering database was investigated. Institute of Electrical and Electronics Engineers (IEEE) is considered by many as one of the biggest professional association gathering electrical and electronics engineers from many fields. The association has an extended digital library comprising more than 3 million technical and scientific documents. Unfortunately access to the documents if not open for all interested and therefore knowledge sharing is limited especially for small research units all around the world.

Analysis of such database form harmonic and wind power research perspective can give a good overview how advancement of technology in both areas has been developed in the space of the years. At the begging let us see how publications regarding harmonics have appeared.

Publications concerning harmonics
Figure 1 Total number of publications concerning harmonics.

The first paper regarding harmonics in the ieee database is from 1899 but the most significant development within the area of harmonics started in late 80's. In Figure 1 one can see that the interest of harmonics is still increasing. Up to now there are more than 55000 of publications only about harmonics. Obviously harmonic analysis can be applied in many fields of electrical engineering. Let us additionally see how in the same period the interest in wind turbines and wind farms development increased.

Publications concerning wind turbines and wind farms
Figure 2 Total number of publications about wind turbines and wind farms.

In case of research associated with harmonics the tendency is rather linear, but regarding both wind turbines and wind farms there is an exponential growth of interest directly reflected in number of publications. This tendency can be easily seen in Figure 2. This general interest in wind power can be also easily seen in increasing number of commercial projects. Therefore harmonics analysis in this particular field of electrical engineering seems to be important also from market tendencies perspective.

Wind power capacity
Figure 3 Existing world capacity of wind power.

Figure 3 shows that increasing interest of wind power technology is correlated with increasing world capacity of wind power [1]. As it can be concluded this tendency will be increasing within next few years. Therefore new research projects are required to extend knowledge and experience in the area of renewable energy sources. This also implies an increasing interest of harmonic research within this area of power industry. As it can be seen also in Figure 2 wind turbine studies are more popular than wind farm. It seems to be a natural way of research. Although it also indicates that there is much less experience with wind farm analysis as a whole system comprising many wind turbines and other components. The first observed publication in the IEEE database regarding wind turbines is from 1958 but regarding wind farms is much later (1982). Even less experience is gained in offshore wind power solutions. This field is newbie (first mention in 2000) in comparison to onshore installations. Anyway nowadays knowledge sharing capability and technology development allow deriving knowledge from other fields and continuous improvement.

Publications concerning offshore wind farms.
Figure 4 Number of publications regarding strictly offshore wind farms.

In Figure 4 one can see even clearer tendency of exponential growth of interest and research within the field of offshore wind farms. I hope that based on presented above facts one can see that there is a great interest in offshore wind power solutions which creates new challenges to the wind industry from harmonic analysis perspective.

[1] J. L. Sawin and E. Martinot, "Renewables 2011 Global Status Report," Renewable Energy Policy Network for the 21st Century, Annual Report, 2011.