Harmonic Distortions Analyzer for Power Rectifiers -...

The 18th National Conference on Electrical Drives “CNAE 2016”

Harmonic Distortions Analyzer for Power Rectifiers

Gheorghe-Eugen Subtirelu1 1Faculty of Electric Engineering, University of Craiova, Romania

Abstract - The paper deals with a software solution for the study of supply energy of power rectifier in terms of harmonic distortion analysis. By using a LabVIEW graphical programming environment it is creates a virtual instrument whose operation is validated in two different ways. On the one hand the input of the virtual instrument is obtained by synthesis of a periodic signal. The deformation of current signal with a set number of harmonics can be simulated for different amplitude, frequency and phase values of each harmonic number. After the synthesis of distorted signal, it can be viewed and analysed the deforming regime characteristic parameters (the value of the total harmonic distortion factor, the fundamental frequency, the components level with the amplitudes of the measured harmonics). The validation is performed by comparing the results of the virtual instrument analysis with the input values. On the other hand, virtual instrument operation is checked on a concrete case, the experimental data taken from a real physical system: a drilling equipment powered by a three-phase rectifier. In this case the validation is performed by comparing the results of the LabVIEW virtual instrument analysis with the values obtained using the Matlab analysis. This virtual instrument can be used successfully in education and training courses.

Keywords – harmonic distortion analyzer, synthesis of a periodic signal, Fast Fourier Transform (FFT), virtual instrument

1. INTRODUCTION

It is known as a pure sinusoidal voltage is conceptual quantity. This both in terms of producing it (because an ideal environment is required to generate it) and of subsequent future uses.

Once a sinusoidal voltage is obtained, only linear loads can keep the waveform uncorrupted. Today the industrial areas are full of devices that deforms the perfect waveform of the voltage: rectifiers, variable frequency drives, computerized equipment and telecommunication equipment which uses switching mode power supplies, etc. These all loads convert the perfect sinusoidal voltage and current waves in a waveform with plenty of additional waveforms in different amplitudes and frequencies superimposed upon it.

The lines voltages usually have a satisfactory waveshape but the current are sometimes badly distorted.

The distortion of a voltage or current can be traced to the harmonics it contains. A harmonic is any voltage and current whose frequencies is an integral multiple of the line frequency.

All of these different frequencies are superior harmonics and they appear as multiple frequencies of the fundamental frequency (2, 3, 4, etc.).

IEEE and specialty literature specify in terms of norms and standards the values of superior harmonics to be respected [10], [11], [12], [13].

2. THEORETICAL ASPECTS

For designing the proposed virtual instrument, author use some general elements about harmonic distortions [2], [3], [5], [7], [8], [9].

The ac voltage generated by commercial alternators is very nearly a perfect sine wave and it may be expressed by the expression:

( )θπ += ftEte m 2cos)( (1)

where: e = instantaneous voltage [V]; Em = peak value of the sinusoidal voltage [V]; f = frequency [Hz]; t = time [s]; θ = a fixed angle [rad] By adding 90° to the angle θ convert a cosine

function into a sine function:

( )°++= 90360sin)( θftEte m (2) To synthesize current signal proposed (see

Abstract) consider a set of sine waves in which the lowest frequency (called the fundamental) is f and the other frequencies (called harmonics) are integral multiple of f.

Because the sine sources are in series, the resultant is equal to the sum of the instantaneous components produced by each source. In these conditions, the sum of a fundamental voltage / current and a harmonics yields a nosinusoidal waveform whose degree of

ACTA ELECTROTECHNICA, Volume 57, Number 3-4, 2016, Special Issue, ISSN 2344-5637

The 18th National Conference on Electrical Drives “CNAE 2016” 479 distortion depends upon the magnitude of the harmonics it contains.

There are several ways of describing the distortion The total harmonic distortion are the most used

parameter of describing the degree of distortion of a current or voltage.

By definition, the total harmonic distortion (THD) of a current or voltage is equal to the effective (root mean square, rms) value of all the harmonics divided by the effective value of the fundamental.

In the case of a distorted voltage, the THD is given by:

FHV VVTHD =)( (3)

where: VH = effective value of all the harmonics [V]; VF = effective value of the fundamental [V]. The effective value VH of all the harmonics is

given by the expression:

223

22 ... nH VVVV +++= (4)

where: V2, V3, …Vn are the effective values of the 2nd,

3rd…nth harmonics. The effective (rms) value of a distorted voltage is

given by the equation:

223

22

222 ... nFHF VVVVVVV ++++=+= (5) Similar equations apply in the case of distorted

currents. A distorted wave is made up of a fundamental and

one or more harmonics. For example, Fig. 1 shows a distorted alternating signal (current) that contains only two harmonics: the first (fundamental) and fifth.

The harmonic distortion is obtained by adding two sine waves: the first signal with 50Hz the fundamental frequency and 100V the effective (rms) value of the fundamental; the second signal with frequency equal by 250Hz and the 5th harmonic with effective value equal by 20V.

Fig. 1 – A fundamental (1) and fifth harmonic signal (2) that compose

the distorted wave (3)

It is important to know how a circuit respond to harmonics.

If a sinusoidal three-phase voltage is connected to a nonlinear load (e.g. a three-phase 6-pulse rectifier), on account of the nonlinearity the current will not be sinusoidal. It will contain a fundamental component and harmonic components.

Theoretically, for a three-phase 6-pulse rectifier there are harmonics of rank 5, 7, 11, 13, 17, etc.

The fundamental component is produced by the sinusoidal voltage VF, but the harmonic components are generated by the loud. The fundamental component of current can lag, lead or be in phase with the sinusoidal signal voltage.

To analyze complex waveform signal in the frequency domain it is use the Fourier sin series and the discrete Fourier transform (DFT) of the signal.

The DFT is the most important discrete transform, used to perform Fourier analysis in many practical applications. The DFT transforms the signal from the time domain to the frequency domain and determine the frequency components present in the signal.

The simply way to calculate the DFT in computers by numerical algorithms is called the Fast Fourier Transform (FFT).

3. THE VIRTUAL INSTRUMENT

The LabVIEW virtual instrument (VI) proposed in the paper allows reconstructing and decomposing periodic signals and the overall goal is to familiarize students with the harmonic distortion analyzer of the nonsinusoidal periodic signal using two different ways.

One way uses a VI to construct the distorted signal (current signal with some harmonics: fundamental, fifth, seventh, ninth, thirteenth) using a summation of sine waves of differing frequencies, phases and amplitudes. After the synthesis of distorted signal, it can be viewed and analyzed the deforming parameters (the value of the total harmonic distortion factor THD, the fundamental frequency F1, the components level with the amplitudes of the measured harmonics).

Another way uses a VI to read data with the distorted signal from a given *.txt file or Excel file. This acquisition data is the experimental waves taken from a real physical system: a drilling equipment powered by a three-phase 6-pulse rectifier. The six signals acquired (3-phase line-to-neutral voltages and 3 line currents) can be viewed (individually or all at once) and analyzed each one (calculating the Fourier transform FFT, the value of the total harmonic distortion factor THD, the fundamental frequency F1, the components level with the amplitudes of the measured harmonics).

3.1. Front Panel of the VI

Fig. 2 presents the user interface of the virtual instrument. Select one of the two pages options in the Tab Control by click the tab (in the left-up side).

1

2

3


480 The 18th National Conference on Electrical Drives “CNAE 2016”

3.1.1. Frontal Panel for synthesis

A first page (Simulate of current with 5 harmonics) is active when the tab for that page is flush with the page and the objects on the page are visible.

Signals To Select is a boolean selector to determine which signals are selected from the input five signals for viewing on the display from right side (Waveforms of Signal).

Numerical controls specifies the frequency, root mean square (RMS) and initial phase in degree of the each number of harmonic sin wave (1, 5, 7, 11, 13).

The signal compound is simulated and displayed by the Distorted Wave graphic. To take a spectral measurement on a simulated signal is used the Peak FFT.

Components level contains the array of amplitudes of the measured harmonics; the harmonic number include: 0 (DC), 1 (fundamental), 2 (second harmonic), …n (nth harmonic) up to and including the highest harmonic.

3.1.2. Frontal Panel for analyses

Fig. 3 presents the second page by user interface of the virtual instrument.

In this page is made harmonic distortion analysis for the six experimental waveforms (the 3 instantaneous line-to-neutral voltage and 3 line current). The degree of distortion of this voltages and currents is calculated with formula (3) and displayed in percent.

After reading the file with experimental data (Read from File:), choose the signal to be viewed (Signals to Display: I1) on the (Waveforms of Signals) Chart and select the signal to analysis (I1). The FFT analysis is made for the selected signal.

The results of the FFT analysis are displayed in graph or table.

Different values on the curves can be determined using cursors so: move the mouse to the cursors, press and hold the mouse button dragging the cursor to the desired position. Use the cursors readings to find the values of: Amplitude vs Time, Amplitude vs Frequency.

Fig. 3 Front panel of the VI for harmonic distortion analysis

Fig. 2 Front panel of the VI for synthesis of current with 5 harmonics


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3.2. Diagram Block of the VI

Fig. 4 shows the section of VI block diagram that synthesizes the distorted signal wave.

As shown in figure, all of diagram elements are included in a repetitive structure (type While Loop), which executed them till now at the finishing terminal (in the right – down side, the “Stop if True” state) arrives logical values True. The While Loop always executes at least once.

The sinusoidal signals generation and the distorted wave is performed using the following Express VIs: Simulate Signal and Spectral Measurements.

Simulate acquisition timing with the following parameters: sampling rate in samples per second [Hz]: 10000; number of samples in the signal: 1000.

The spectral measurement is a Peak FFT of the simulated signal.

Select Signals Express VI is used to choose the signal which will be viewed on the Waveform Chart; this accepts multiple signals as inputs and returns only the signals it select.

With Harmonic Distortion Analyzer.vi takes a signal in and performs a full harmonic analysis, including measuring a fundamental frequency and harmonics, and calculating the fundamental frequency, all harmonic amplitude levels and the total harmonic distortion (THD).

Build Table Express VI converts the distorted waveform into a table of data that lists the amplitude of each point in the signal. This data are converted in string form; the spreadsheet string is written to the desired file with the Save Data button.

Fig. 5 shows the detail of VI block diagram that process (Read from file, Select signal to display, Select signal to analysis, etc.) the real experimental data.

Spectral Measurement Express VI is used to perform FFT-based spectral measurements such as the magnitude spectrum and phase spectrum on the selected signal. This Express VI is configured to measures the magnitude spectrum and displays graphic the results in terms of root-mean-square (RMS).

Fig. 4 Section of the block diagram that synthesizes the distorted

signal wave

Fig. 5 Detail of the block diagram that process the real signals

With FFT Spectrum.vi computes FFT spectrum of

the input selected time-domain signal. This VI calculate and returns the FFT results as magnitude and phase.

The window rectangle is the time-domain window to apply to the selected time signal and the cluster view defines how the different results from the FFT Spectrum.vi are returned.

The values of magnitude (in rms) and phase (in degree) for each harmonic rank of the distorted signal are written into table (Build Table).

Value of the total harmonic distortion (THD) is obtained by mathematical calculations based definition and starting from components level of the magnitude spectrum. This value is expressed as a percent (%).

4. RESULTS AND CONCLUSIONS

To verify the correct function of proposed virtual instrument is used as input data the experimental instantaneous values taken from a drilling equipment powered by a three-phase rectifier. The drilling equipment is a dc motor fed by three-phase 6-pulse rectifier. The three-phase 6-pulse rectifier is composed of six diodes fed by a 3-phase delta-wye transformer.

These instantaneous values are found saved in a text-based measurement file (.txt) and can read out with any usual program like Microsoft Word/Excel, Notepad, etc.

In Fig. 6 is shown a capture file after input data used. As shown in this figure, they are acquired 3-phase line-to-neutral voltages and 3 line currents in the instantaneous values.

The sampling rate of data acquisition (DAQ) has been adjusted to 3200Hz (to view a minimum of 32 harmonics and to follow the Nyquist criteria).

First column in Fig. 6 is the time data for each acquisition; delta_t is 0.0003125 second (1/3200).

Fig. 7 presents the waveshapes of one complete cycle of the experimental acquired three-phase voltages (up) and currents (down).

Using graph cursors can read the exact value of a point on a current or voltage waveform. The exact cursor’s value displays in the cursor legend.

It is observed that the maximum line-to-neutral voltage for the first phase is 569V; this value is obtained in a time of 0,005 seconds (see the Fig.6 and 7).


482 The 18th National Conference on Electrical Drives “CNAE 2016”

There are 64 samples for each acquisition voltage and current parameters (v1, v2, v3 – i1, i2, i3).

It can be seen in Fig. 7 that the voltage are poor distorted (compared to the ideal shape of a sinusoid); this distortion is produced by magnetic saturation in the core of power transformer.

Note that the waveshapes of one complete cycle of the line currents i1, i2 and i3 are badly distorted. This distortion is mainly produced by a 5th harmonic having an amplitude of 137 A, 138 A respectively 150 A for each line current i1, i2 and i3.

The waveshapes depends not only on the frequency and amplitude of the harmonics but also on their angular position with respect to the fundamental harmonic.

By using the graph cursors are determined the following extreme values of each phase voltage:

-first phase: max. 569 V at 0,005 sec.; min. -567 V at 0,015 sec.;

-second phase: max. 559 V at 0,01125 sec.; min. -560 V at 0,00125 sec.;

-third phase: max. 558 V at 0,017813 sec.; min. -557 V at 0,007812 sec.

In the same way it can measure extreme values for the line currents i1, i2 and i3.

Fig. 8 shows the waveshapes of the phase voltage v1 and line current i1 represented in the same graph to highlight the phase difference between them; the phase difference is calculated knowing the time difference measured using vertical cursors.

Fig. 7 Waveshapes of the acquired three-phase voltages (up) and currents (down)

Fig. 6 Capture of a input data values


The 18th National Conference on Electrical Drives “CNAE 2016” 483

Fig.8 Capture waveshapes of the phase voltage v1 and line current i1

represented in the same graph

The waveforms of the line current i1 associated with the phase voltages v1 represented in the same graph illustrate the existence of a phase difference between current and voltage: the current i1 lags approx. 33° behind the voltage of the phase 1.

It demonstrates that the load of power rectifier has an inductive character (power dc motor).

Fig. 9 shows the comparative values of components level for all first 32 harmonics amplitude of the measured voltage v3 and current i3 waveforms.

Also is presented the total harmonic distortion (THD) for this voltage (left) and current (right).

Higher harmonics are also present but their amplitudes are small.

Fig.9 FFT results as magnitude and phase of the voltage v3 (left) and

current i3 (right) with each total harmonic distortion (THD)

Table 1 shows the comparative values of several parameters calculated with LabVIEW and MATLAB.

Table 1 – Comparison between two analyzes

LabVIEW analysis v1 v2 v3 i1 i2 i3

1st 378 382 382 503 497 522 5th 18,8 16,4 19,7 137 138 150

11th 8,4 10,3 7,4 24,5 28 25,8 THD(%) 7,26 6,07 6,49 29,7 29,4 30,6

Matlab analysis v1 v2 v3 i1 i2 i3

1st 381 381 381 499 501 518 5th 17,9 17,4 19 137 137 150

11th 8 9,7 7,6 25 27,6 24,7 THD(%) 5,99 5,77 6,03 28,5 27,5 29,2

It can be seen that the values obtained with the

proposed virtual instrument are roughly equal to those obtained with Matlab.

The virtual instrument presented in this paper is for teaching about the fundamentals of harmonic distortions analyzer quickly and efficiently.

In the future it can be developed by integrating in a complex system which can analyze the power quality of any electrical equipment.

REFERENCES

1. Brian R., Lipsman R.L., “A guide to Matlab: for beginners and experienced users”, Cambridge University Press, 2001

2. Czarnecki L.S., “Harmonics and power phenomena”, Wiley Encyclopedia of Electrical and Electronics Engineering, John Wiley, New York, 2000.

3. Jacobs J., Detjen D.O., De Doncker R.W., “An overview of methods to determine the harmonics in three-phase systems”, IEEE Young, Researchers Symposium in Electrical Power Engineering Distributed Generation, 2002.

4. Munteanu M., Logofatu B., Lincke R., Aplicaţii de instrumentaţie virtuală LabView, Editura Credis, Bucureşti, 2003

5. Popescu M., Bitoleanu A., Dobriceanu M., “On the AC-side interface filter in three-phase shunt active power filter systems”, World Academy of Science, Engineering and Technology, Issue 69, August 2010, pp. 516-521.

6. Selisteanu D., Petre E., ş.a., Aplicaţii LabVIEW pentru achiziţia şi generarea datelor, Editura Sitech, Craiova, 2004

7. Subtirelu G.E., “Electronica analogica asistata de calculator”, Editura Sitech, 2011, Craiova, pp. 8-18.

8. Sutherland P., “Harmonic measurements in industrial power systems”,IEEE Trans.Ind. Appl.,Vol.31, No.1,1995,pp.175-183.

9. ***. Detection and Filtering of Harmonics, Schneider Electric, Application note, 2008.

10. ***. Harmonics Standards for Commercial Electronic Products, dBi Corporation, 2010, http://www.dbicorporation.com/harmonic.htm.

11. ***. Guide to Harmonics with AC Drives, ABB, Technical Guide No. 6.

12. ***. Harmonics, E-Source Customer Direct, Platts – a Division of The McGraw Hill Companies Inc.

13. ***. Normes CEI 61000-3-2, Limites pour les emissions de courants harmoniques.

14. ***. LabVIEW User Guide, National Instruments, SUA, 1996

Gheorghe-Eugen Subtirelu Faculty of Electrical Engineering, University of Craiova, Decebal Blv. 107, 200440, Craiova, Romania [email protected]


http://www.dbicorporation.com/harmonic.htm

mailto:[email protected]

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