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Comparative analysis of the measurement methods for the supraharmonic range
Electrical Power and Energy Systems 118 (2020) 105801
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Comparative analysis of the measurement methods for the supraharmonic range
T
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Thais M. Mendesa, , Carlos A. Duquea, Leandro R. Manso da Silvaa, Danton D. Ferreirab, Jan Meyerc, Paulo R. Ribeirod a
Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil Automation Department, Federal University of Lavras, Lavras, MG, Brazil c Institute of Electrical Power Systems and High Voltage Engineering Technische Universitt Dresden, Dresden, Germany d Institute of Electrical Systems and Energy, Federal University of Itajubã, Itajubã, MG, Brazil b
A R T I C LE I N FO
A B S T R A C T
Keywords: IEC 61000-4-7 standard IEC 61000-4-30 standard Measurement methods Power quality Supraharmonics
This paper provides an in-depth analysis of the methodologies proposed by the IEC 61000-4-7 and IEC 61000-430 standards for the supraharmonic frequency range. The paper presents the stat-of-the-art concerning supraharmonics and describes the existing standardized measurements for supraharmonics. The different ways of performing the measurements proposed by such standards are compared. The main contribution and novelty of the paper are the comparative analysis of the standardized measurement methods which considers both efficiency and computational complexity of them. Analyzes considering real signals, a real time signal, a timevarying synthetic signal and the influence of the noise level for the methodologies proposed by the IEC 61000-47 and IEC 61000-4-30 standards were performed. Finally, alternative ways of measuring supraharmonics are suggested. One may conclude that the method described in IEC 61000-4-30 showed to be less immune to noise and less complex (in terms of mathematical operations required during processing) than that described in the IEC 61000-4-7, but loses accuracy in estimating high-amplitude supraharmonic components.
1. Introduction Electrical networks are designed to transfer energy at 50 or 60 Hz, however, components of higher frequencies may appear in the Power System [1]. Engineers have dealt with emission problems in the range of 2–150 kHz for several decades, but the term supraharmonics is relatively recent, being first mentioned during the IEEE Power & Energy Society General Meeting in 2013 [2]. For many years the power quality (PQ) field focused on frequency distortions below 2 kHz. The limited attention given to supraharmonic frequency range in the past is justified in part due to the fact that consumer-installed equipment did not emit high-frequency component. However, new equipment connected to distribution grid is characterized by emission in the frequency range from 2 kHz up to 150 kHz. As example, one can mention more energy-efficient equipment from the consumer side, such as electric vehicle charger, LED lamps, and from the generation side PV-inverters and converters for storage process [3,4]. As a result of supraharmonic emission, some bad effect has been related in literature, such as malfunctions or impairments of household devices and reducing of the lifetime of the devices [5]. Also, as the
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frequency range used in PLC (Power Line Communication) application is in the same band as supraharmonics, interferences in communication channel is expected. Although the effects of supraharmonics (SH) are confined to neighboring devices and do not propagate over long distances, the definition of SH measurement standards is the first step in the commissioning of equipment in relation to high frequency emission. The smallest focus on the supraharmonic frequency range in the past is justified in parts by the lack of consolidated standards for this frequency range [6,7]. Recently, standards-setting organizations have been working to develop measurement methods applicable to the supraharmonic range [8]. Such methods have particularities that may hinder understanding. Due to this fact it is of great importance for the PQ field and for the supraharmonic mitigation to exploit the measurement standards for the supraharmonic frequency range. There are considerable activities within International Electrotechnical Commission (IEC), European Committee for Electrotechnical Standardization (CENELEC) and Institute of Electrical and Electronics Engineers (IEEE) with the aim of developing standards, as compatibility levels, emission and immunity limits, and adequate test methods covering this frequency range. Currently, a measurement
Corresponding author at: Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil.
https://doi.org/10.1016/j.ijepes.2019.105801 Received 18 July 2019; Received in revised form 13 December 2019; Accepted 19 December 2019 0142-0615/ © 2020 Elsevier Ltd. All rights reserved.
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method for frequencies of 2–9 kHz is presented in the informative annex of IEC 61000-4-7 [9], which may be extended to applications including higher frequencies (up to 150 kHz) [10]. The IEC 61000-4-30 Ed3 [11] standard proposes a measurement methodology for the frequency range of 9–150 kHz, and CISPR-16 (International Special Committee on Radio Interference) suggests equipment and methods for measuring disturbances and immunity to them at frequencies above 9 kHz. The measurement standards for the supraharmonic frequency range are recent in comparison with the existing standards for the frequency range below 2 kHz. The present paper exploits the measurement methodologies imposed by IEC 61000-4-7 and IEC 61000-4-30 standards because these have the most relevant information for measurements in the supraharmonic range (2–150 kHz). The main objective of this paper is to provide a review covering supraharmonic research activities, which are related to relevant measurement topics. In addition, comparisons of the measurement methods proposed by IEC 61000-4-7 and IEC 61000-4-30 standards are made. A critical analysis of the measurement method proposed by the IEC 61000-4-30 standard is carried out. A detailed analysis of the computational complexity of both methods of measurement suggested by such standards is elaborated. In the light of what has been investigated, critical conclusions and proposals for possible improvements of such standards are made. The paper is organized as follows. The next section presents a study of state-of-the-art concerning supraharmonics. Section 3 discusses about measurement methods. Analysis of measurement methods IEC 61000-4-7 and IEC 61000-4-30 are shown in Section 4 and conclusions are in Section 5.
Fig. 1. Definition of frequency range.
and the use of power factor measurement is a possible way to quantify nonlinear loads present in the network [23]. There is a considerable amount of papers discussing causes and consequences of these emissions as well as reporting measurements. Several researches refer to the supraharmonic emissions of street lamps [24–30]. Power inverters are also considered major sources of supraharmonic emissions. Results from emissions of supraharmonics referring to photovoltaic systems are shown in [31–33]. The work reported in [34] proposes the analysis by filter bank and compressive sensing of supraharmonics originated by a photovoltaic inverter and a LED lamp. Therefore, in the current scenario of modern LV electrical distribution networks that are characterized by the presence of numerous distributed PV generators and other electronic equipment [35], the injection of supraharmonics in the network is intense. However it is important to develop practical methods for the localization of main supraharmonic distortion sources in the network. The work reported in [36] proposed practical analysis of supraharmonic propagation and methods for the localization of main supraharmonic distortion sources in the network under study. The paper [37] covered the origin of supraharmonics (remnants of active switching of power electronic converters and power line communication) as well as how supraharmonics propagate between neighboring devices and through the grid. The work reported in [38] presented recent research results regarding the identification of the transfer characteristic of a distribution transformer in the frequency range between 2 kHz and 150 kHz based on measurements. In addition to these contributions highlighted above, some papers present a global view about emissions in the frequency range of 2–150 kHz. A review on measurement techniques for non-intentional emissions above 2 kHz is provided in [39]. [40] indicates the research challenges associated with the supraharmonic range, with emphasis on emission, propagation, interference, measurements, standardization, and modeling and simulation. A comprehensive and systematic classification of possible interference mechanisms and their impact on devices, considering both, intentional and non-intentional emissions is provided by [21].
2. State-of-the-art concerning supraharmonics The main characteristic of electromagnetic noise is its frequency range. The electromagnetic compatibility (EMC) standards generally cover the range from 0 Hz to 400 GHz [12]. However, not all frequency ranges are completely regulated. For decades, the lower frequency range (harmonics) was considered as PQ range [13]. Recently, the supraharmonic frequency range (2–150 kHz) has received more attention by standard-setting organizations, but there is no accepted framework as for lower frequencies [7]. The frequency range below 9 kHz is called low frequency (LF), and the range above this value is called high frequency (HF) range. This range is also called the radio-frequency or RF range. The radiated range then starts at 30 MHz. Fig. 1 shows a summary of the frequency ranges and regulated standards relationship. Smart electrical grids increase the relevance of supraharmonics emission [14,15]. These grids encourage the use of new technologies such as electric vehicles [16], smart metering [17], and demand side management [18], as well as the use of Distributed Generation (DG) [19]. Smart grids are a new electricity grid, not only dedicated to distribute energy [20]. The current trend is a convergence where all distribution lines can also carry different types of information using Power Line Communication (PLCs) [21]. It is asserted that PLC plays a significant role in emission of supraharmonics [22]. On the other hand, the effect of DG on Power Quality (PQ), related to the injection of higher frequency, is due to the presence of power electronics interfaces. Thus, the number of generating units in the system influences emissions in the frequency range studied in this paper (2–150 kHz). The analysis of higher frequency emission is very important, as it can affect the PQ of electrical system. Supraharmonic distortions can cause overheating of capacitors, can strongly affect the accuracy of energy meters, can generate audible noise due to an excitation of mechanical resonances, and malfunction of equipment. In addition, supraharmonic distortions produced by nonlinear loads increase power losses and, therefore, have a negative impact on electric utility distribution systems and components. As for harmonics, establishing the exact relationship between supraharmonics and losses is a difficult task, 2
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At the output of the filters, 32 approximately equally-spaced measurements must be performed, taking each 10/12 cycle interval (10 cycles for 50 Hz systems or 12 cycles for 60 Hz systems), as shown in Fig. 3. Each measurement should consist of 512 samples taken at a sampling rate of 1,024 kHz. The 512 samples must be processed with a FFT or equivalent. The 512 samples FFT at 1,024 kHz sampling frequency corresponds to a time window of 0.5 ms long. Then, there is an equidistant gap which amounts a total of 184 ms. Considering the sampling frequency of 1,024 kHz, the FFT calculation of 512 samples results in 2 kHz frequency resolution. The lowest 4 bins and the upper 181 bins should be discarded. The magnitudes of the remaining 71 bins contain the emissions from 8 kHz to 150 kHz The initial 4 bins represent the frequency range below 8 kHz and should be discarded. As discussed, the frequency range of 2 kHz to 9 kHz should be analyzed by the standard IEC 61000-4-7. The final 181 bins represent frequencies above 150 kHz, these should also be discarded. Therefore, the frequency range of 8–150 kHz has 71 bins that must be analyzed. Fig. 4 shows all steps of the methodology proposed in [11]. The input signal represents the time domain waveform containing supraharmonics. This signal passes through cascade High Pass and Low Pass Filters. These filters limit the signal frequency between 2 kHz and 150 kHz. At the output of these filters, for the frequency range of 9 kHz to 150 kHz, at each 10 cycles interval, 32 sets of these 71 bins are available. Each of the 32 measurement interval represents the FFT calculation of 512 signal samples. The minimum, the average, and the maximum values of the 32 r.m.s. magnitudes of each of these 71 bins should be reported. In addition, a single r.m.s. maximum value of all 71 bins should also be reported.
3. Standardized measurements As described in the previous section a considerable number of recent papers show the growing importance that the theme has been assuming. It directly reflects the need to create or adapt international standards, mainly to define methodologies for the measurement of supraharmonics. This section provides an explanation of the principles established by the standards to measure conducted emissions above 2 kHz. 3.1. IEC 61000-4-7 IEC 61000-4-7 appendix B proposes a measurement method of components in the frequency range of 2–9 kHz. Despite the fact that this standard does not cover the whole range of supraharmonics, some researchers are proposing the extension of the methodology to the whole band. This method suggests grouping the energy of the signal to be analysed into predefined frequency bands. This document refers to the CISPR 16-1, that determines the bandwidth for the grouping of these emissions should be fixed at 200 Hz. This measurement method suggests that signal sampling is performed in a time window of 200 ms, equivalent to 10 (12) fundamental cycles of 50 Hz (60 Hz) systems. Subsequently, it must be converted to the frequency domain through the Fast Fourier Transform (FFT). The r.m.s. value of the component at the frequency f is Cf , e.g., C5100 is the r.m.s. value of the component at 5100 Hz. The frequency separation between consecutive measured components Cf must be 5 Hz. The output Cb of each band is the r.m.s. value according to (1). b + 100Hz
Cb =
∑
Cf2
f = b − 95Hz
3.3. Other measurement standards applicable to supraharmonic emission
(1)
where b represents the central frequency. The output of the raw FFT is grouped in bands of 200 Hz. Therefore, b assumes values equal to 2100 Hz, 2300 Hz, 2500 Hz, and so on. The highest central frequency is 8900 Hz. This measurement standard recommends the use of a band pass filter that attenuates the fundamental frequency and components above 9 kHz with an attenuation of the fundamental component of at least 55 dB. The measurement method proposed by this standard suggests that the sampling rate of the signal is chosen according to the rules of signal analysis so that the components up to 9 kHz can be measured. Considering the Nyquist criterion the sampling rate must be greater than or equal to 18 kHz (Fs ⩾ 18 kHz). However, in order to perform data transformation using the FFT it is advisable that the number of samples processed be a power of two, so the minimum sampling frequency according to the IEC 61000-4-7 standard would be equal to 20.48 kHz. Considering the frequency resolution of 5 Hz, as suggested by the standard, a single FFT of 4,096 samples may be calculated. Finally, 5 Hz resolution FFT components are grouped into 200 Hz bands. Fig. 2 shows the methodology proposed in [9].
The standard IEC 61000-4-19 [41] refers to immunity-related attributes and test methods for electrical and electronic equipment to conduct distortions and promote signaling in the 2–150 kHz frequency range. This standard defines test waveforms, range of test levels, test equipment, test setup, test and verification procedures. The tests carried out are aimed at verifying the immunity of electrical and electronic equipment operating at a supply voltage of up to 280 V (from phase to neutral or phase to earth, if no neutral is used) and a frequency of 50 Hz or 60 Hz when subjected to conducted, differential mode disturbances such as those originating from power electronics and power line communication systems. The International Special Committee for Radio Protection (CISPR) [42] reports product emission and immunity requirements as well as defines test methods and equipment. The Part 1 (CISPR 16-1) refers to radio disturbance and immunity measuring apparatus. Part 2 (CISPR 16-2) specifies methods of measurement of disturbances and immunity. Part 3 (CISPR 16-3) describes reports and recommendations of CISPR. CISPR 16-1-1:2015 specifies the characteristics and performance of equipment for the measurement of radio disturbance in the frequency range of 9 kHz to 18 GHz. In addition, requirements are provided for specialized equipment for discontinuous disturbance measurements. CISPR 16-1-2:2014 + A1:2017 specifies the characteristics and performance of equipment for the measurement of radio disturbance voltages and currents in the frequency range of 9 kHz to 1 GHz. CISPR 16-2-1:2014 + A1:2017 is designated a basic standard, which specifies the methods of measurement of disturbance phenomena in general in the frequency range of 9 kHz to 18 GHz and especially of conducted disturbance phenomena in the frequency range of 9 kHz to 30 MHz European Committee for Electrotechnical Standardization (CENELEC) 50065 [43] applies to electrical equipment using signals in the frequency range of 3 kHz to 148,5 kHz to transmit information on low voltage electrical systems, either on the public electricity distribution network or within consumers’ premises.
3.2. IEC 61000-4-30 The 3rd edition of the IEC 61000-4-30 standard suggests a measurement method for the supraharmonic components located in the 9 kHz to 150 kHz frequency range. A reference to the IEC 61000-4-7 standard for the frequency range of 2 kHz to 9 kHz is given in Annex C of this informative. This standart suggests that the signal be sampled at a rate of 1,024 kHz. This signal must be filtered through a High Pass (HP) filter in cascade with a Low Pass (LP) filter. The High Pass filter should be included to attenuate the fundamental and the low order harmonics of the input signal. The High Pass filter should have 2 poles, with 3 dB of attenuation at 1.5 kHz or higher. The Low Pass is a 4th order filter, with the cutoff frequency at 200 kHz. 3
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Fig. 2. Illustration of the measurement method according to IEC 6100-4-7.
Table 1 Summary of the main existing standards for the supraharmonic range. Standard
Purpose/method
Frequency Range
IEC 61000–4-7
Emissions levels from equipment, in the grid/ FFT with 5 Hz resolution, 200 Hz band aggregation at 200 ms of signal Levels in grid/ FFT, 0.5 ms intervals, 2 kHz frequency resolution, aggregation into avg and max of the 32 measurement intervals per 10/12 cycles. Levels in grid and emission from equipment/ Spectrum analyzer with tunable filter and detector (peak and quasi peak). Immunity-related attributes and test methods for electrical and electronic equipment to conduct distortions and promote signaling.
2 kHz - 9 kHz
IEC 61000–4-30
Fig. 3. Measurement methodology proposed by the standard IEC 6100-4-30 Ed3. CISPR 16–2-1
The IEEE 519 [42] is proposed to be used as guidance in the design of power systems with nonlinear loads. The limits set are for steadystate operation and are recommended for worst case conditions. This standard is limited to be a collection of Recommended Practices that serve as a guide to both suppliers and consumers of electrical energy, placing a limitation on both the amount of harmonic current that a consumer can inject into a utility network and the level of harmonic voltage that a utility can supply to a consumer. The measurement methodology is mainly based on IEC 61000-4-X series, but no explicit information is given for harmonic components of order greater than 50. Table 1 summarizes existing standards for the supraharmonic frequency range.
IEC 61000–4-19
9 kHz - 150 kHz
9 kHz - 30 MHz
2 kHz - 150 kHz
61000-4-30 measurement methods is performed. To test and compare the efficiency of the IEC 61000-4-7 and IEC 61000-4-30 methodologies, four different cases were analyzed: (i) real world signals; (ii) real time signal; (iii) synthetic signals generated with different noise levels and (iv) time-varying synthetic signal. The analyzes were performed individually for each case and the appropriate conclusions were obtained. Posteriorly, the IEC 61000-4-30 method was analyzed for a specific case of synthetic signal containing supraharmonic distortions, some criticisms and suggestions were made based on this analysis. Finally, a comparative analysis of the computational complexity required by both
4. Analysis of Measurement Methods based on IEC 61000-4-7 and IEC 61000-4-30 In this section a comparative analysis of the IEC 61000-4-7 and IEC
Fig. 4. Illustration of the measurement method according to IEC 6100-4-30 Ed3. 4
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Fig. 5. Photovoltaic inverter time domain waveform containing supraharmonics.
Fig. 7. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of the current at the PV inverter.
IEC 61000-4-7 and IEC 61000-4-30 measurement methodologies was performed.
4.1. Real signals In order to compare the standards IEC 61000-4-7 and IEC 61000-430, two waveforms containing supraharmonic distortion originated by a photovoltaic inverter and an electric vehicle charger, respectively, were processed. These signals were provided by PANDA-project (equiPment hArmoNic Database), a global web-based platform for exchanging harmonic emission measurements of household equipment [44]. Time domain signals of the emissions from a PV and a EV charger are shown in Figs. 5 and 6, respectively. These signals were acquired with a sampling rate of 1,000 kHz (1 MSa/s), with fundamental frequency equal to 50 Hz. The basic measurement window of the analyzed signals have a length of 200 ms approximately (10 cycles at 50 Hz power frequency). These signals were previously filtered, delimiting its spectrum from 2 kHz to 150 kHz, as suggested by the standard IEC 61000-4-30. Figs. 7 and 8 show a comparison between the IEC 61000-4-7 and the IEC 61000-4-30 for the supraharmonic estimation. As explained in Section 3.2, the mean of 32 measurements was calculated, referencing to the calculation of 32 FFT of 512 samples in 10 cycles of the analyzed signal. Section 3.1 presents details of the standard IEC 61000-4-7 that is applied to the range below 9 kHz, however for purposes of comparison,
Fig. 8. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of the current at the EV charger.
this measurement was applied in frequency range of 2 kHz to 150 kHz. In this case the same analog filter of IEC 61000-4-30 was used. A resolution of 5 Hz was considered, and the calculation of only one FFT of 200,000 samples was performed. The output of the FFT was grouped in bands of 2 kHz. Analyzing Figs. 7 and 8, it is observed that the measurement results for both methods are similar. In Fig. 7, referring to the comparison of the standards for the PV inverter, the relative difference in terms of amplitude at 22 kHz is 18.7%, at 54 kHz is 13.9% and at 108 kHz is 45.2%. In Fig. 8, whose analyzed signal is originated by EV charger, the relative difference at 32 kHz is 13.1%, at 54 kHz is 17.5% and at 62 kHz is 25%. It is observed through this analysis that, the results are more similar for higher distortion levels, that is, for supraharmonic with higher amplitudes. According to [10] the measurement method proposed in IEC 61000-4-30 lacks accuracy at low distortion levels, that is, for measuring supraharmonic components with small amplitudes, the IEC 61000-4-7 method is more accurate than the one described in IEC 61000-4-30. To verify if this effect has relation with the frequency of the supraharmomnic, a synthetic voltage signal contaminated by five supraharmonic components located at frequencies 30, 50, 90, 70 and 110 kHz and with the same amplitude values was generated. Both approaches were applied to this signal and it was found that the relative error between the corresponding estimated spectra is around 0.2 % and remains the same for all supraharmonic frequencies.
Fig. 6. Electric vehicle charger time domain waveform containing supraharmonics. 5
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Fig. 9. Real time acquisition system.
4.2. Real time experiment Fig. 11. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of a real time signal.
In order to get more realistic results, experimental tests were performed using a real time signal. The equipment used to generate this signal is illustrated in Fig. 9. It has been used a Waveform Genarator (33500B Series Waveform Generator TrueForm - Keysight) with sample rate of 1 μ Sa/s to 250 MSa/s and 16 bits resolution, and an oscilloscope (Data Recorder DL850E - Yokogawa) with sample rate of 1 MS/s, 2 channels, and 16 bits resolution, bandwidth of 300 kHz, time axis accuracy of ±0.005%, 16 channels for data recorder and power consumption of 200 VA. By means of the software MATLAB, a signal containing supraharmonics, as shown in Fig. 10, was generated and exported in text format to the function generator. Such file is saved in internal memory and each sample is read at a sampling rate of 6 MSa/s. Afterwards, the signal is acquired through 1 oscilloscope channel, at a sampling rate of 1 MSa/s, this acquisition is online with a software specific of this equipment, being possible to save the data in real time in a computer through the cable Ethernet compatible with the acquisition rate. In this system the signal acquisition is performed in real time (online) and the signal processing by the analyzed methods (IEC 61000-4-7 and IEC 61000-4-30) is offline. The generated signal, composed by fundamental component ( f0 equal to 50 Hz) and two supraharmonic components located in the frequencies fsh1 equal to 32 kHz and fsh2 equal to 64 kHz, can be represented by Eq. (2). The amplitudes are A sh1 and A sh2 , both equal to 0.5. Fig. 10 illustrates this real time signal.
x (t ) = cos (2πf0 t + θh) + A sh1 cos (2πfsh1 t )+ A sh2 cos (2πfsh2 t )
(2)
Fig. 11 shows the spectrum achieved by both standards studied. It is observed that both standards were able to estimate the supraharmonic components present in the real time signal. 4.3. Synthetic signal with noise Synthetic signals containing supraharmonic components were presented to the measurement methodologies suggested by the standards analyzed in order to test the efficiency of such methods for supraharmonic estimation in the presence of noise. The signals were generated with an additive Gaussian white noise. Signals with different levels of noise were considered. In total, eleven different cases were generated, with SNR values equal to 10 dB, 20 dB, …, and 100 dB, it was also considered a signal without noise. A total of ten events were generated for each case. The mathematical representation of such signals is given in (3). 50
x (t ) =
∑
Ah cos (2πfh t + θh) + A sh1 cos (2πfsh1 t )+
h=1
A sh2 cos (2πfsh2 t ) + n (t )
(3)
where n (t ) represents the noise component. These signals consist of 20,480 samples taken at a sampling rate of 1,024 kHz, which corresponds to one power cycle at a fundamental frequency of 50 Hz. These signals are composed by conventional harmonic and two supraharmonic components located in the frequencies fsh1 equal to 32 kHz and fsh2 equal to 96 kHz. The amplitudes are A sh1 and A sh2 , equal to 0.05 and 0.025, respectively. At these signals different noise levels were added. Fig. 12 shows the time domain waveform and frequency spectrum of a 50 dB SNR synthetic signal used for testing. As mentioned, ten signals were generated for each case analyzed, and the root-mean-square error (RMSE) [45] between the spectrum obtained by each measurement (IEC 61000-4-7 or IEC 61000-4-30) and the ideal spectrum (gold standard) was calculated. Fig. 13 shows the results for the methodologies studied in terms of RMSE mean values (considering the ten signals for each case) and standard deviations. By analyzing Fig. 13, it can be noted that both methods are able to estimate the supraharmonic components in the presence of noise, since the obtained error values (RMSE) are low. According to [46], in practice, the SNR of the voltage signal obtained from a power system varies between 50 dB and 70 dB. Then, the methodologies proposed by the standards are not affected by noise, since the achieved RMSE for this
Fig. 10. Real time signal. 6
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Fig. 12. Time domain waveform of the signal composed of fundamental and supraharmonic components in (a) and the supraharmonic components only, in (b). The frequency spectrum of the supraharmonic components is shown in (c).
Fig. 13. Results of the methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of a synthetic signal with noise.
Fig. 14. Synthetic time-varying signal used.
SNR range is similar to that achieved for the case without noise. It is noted that the IEC 61000-4-30 method is more robust to noise than the IEC 61000-4-7 method. 4.4. Time-varying synthesized signal In order to compare the performance of the methods reported in IEC 61000-4-7 and IEC 61000-4-30 for a signal containing time-varying supraharmonics, a synthetic signal represented by Eq. (4) was used 50
x (t ) =
∑ h=1
Ah cos (2πfh t ) + Ash (t ) cos (2πfsh t )
(4)
This signal consists of 20,480 samples taken at a sampling rate of 1,024 kHz (1,024,000 Sa/s), which corresponds to one power cycle at a fundamental frequency of 50 Hz ( f0 ). This signal is composed by conventional harmonic with frequency ( fh = h·f0 ) and one supraharmonic component located in the frequency fsh equal to 80 kHz. The magnitudes of the respective components are Ah and Ash (t ), where Ash (t ) is an exponential function whose amplitude decreases and then increases. Fig. 14 illustrates this synthetic signal.
Fig. 15. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for time-varying supraharmonic estimation.
7
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Fig. 17. Time domain waveform containing a periodic voltage disturbance with high frequency components.
Fig. 16. Results of the IEC 61000-4-30 method for time-varying supraharmonic estimation.
detect the disturbance in some situations such as where distortion occurs in narrow bands and is periodic, as in the case of the analyzed signal. This analysis encourages discussions about the efficiency of the measurement methodology proposed by the IEC 61000-4-30 and shows that alternative ways of performing such measurements can present better results for supraharmonic estimation.
Fig. 15 shows a comparison between the IEC 61000-4-7 and the IEC 61000-4-30 for the time-varying supraharmonic estimation. Observing this figure it is possible to note that both methods estimate the supraharmonic component. Fig. 16 represents the maximum, mean and minimum values of the 32 measurements of the signal containing time-varying supraharmonic, as suggested by the IEC 61000-4-30 standard. This figure shows the time-varying characteristic of the analyzed signal, since the maximum, average and minimum values are different. Therefore the IEC 61000-430 method is able to detect the time-varying nature of a supraharmonic component, which is not possible using the approach based on the IEC 61000-4-7.
4.6. Computational complexity of the IEC 61000-4-7 and IEC 61000-4-30 measurement methods This section presents an analysis of the computational complexity of the measurement methods studied in this paper. The number of mathematical operations performed during the execution of an algorithm may be used to define its complexity. According to the measurement method proposed in IEC 61000-4-7 standard, only one FFT must be calculated in a window of 200 ms of the signal. Then, the signal is sampled in a 200 ms rectangular time window, corresponding to approximately 10 (12) fundamental periods of 50 Hz (60 Hz) systems. From the sampling process the relation given in (5).
4.5. Spacing between measurements The standard IEC 61000-4-30 determines that measurements must be taken equally spaced time intervals such that 32 approximately equally-spaced measurements are taken each 10/12 cycle interval. If the 32 measurements are equally distributed, some parts of the signal will never be covered by a measurement interval. Therefore, if the analyzed signal presents a disturbance that occurs at periodic intervals of time and the time of disturbance occurrence coincides with the space between measurements (where there is no measurement), this disturbance will not be detected. For performance evaluation of the methodology proposed by the IEC 61000-4-30 consider the occurrence of a notch, a periodic voltage disturbance with high frequency components, as shown in Fig. 17. Fig. 18 illustrates a comparison of different ways of performing the measurement of a signal containing notch disturbance. Equally-spaced refers to the method proposed by the standard [11], as shown in Fig. 5. Non-spaced represents 32 measurements of 512 samples carried out consecutively, without spacing. In this case, the measurements are obtained in only one cycle of the signal. Randomly spaced are sequential measurements performed on 10 cycles of the signal, but not equally spaced. In this approach, the 10 cycles of the signal are divided into 32 equal intervals and the starting point of each 0.5 ms window of the signal is randomly picked. Fig. 19 illustrates the spectrum estimated by the different measurement forms. From this figure we can conclude that the disturbance may not be detected in the case where measurements are considered equally-spaced. The chances of detecting such a disturbance are increased when measurements are taken at random spacings, or when the 32 measurements are performed consecutively, without spacing. Therefore, the IEC 61000-4-30 standard measurement methodology, which proposes equally-spaced FFT measurements, may not be able to
N = 200 ms Fs
(5)
where N is the number of samples of the signal and Fs is the sampling rate. In this measurement method, the sampling frequency should be chosen in accordance with the established rules of signal analysis.In practical measurement activities, the instrumentation part uses sampling rates much higher than the Nyquist criterion. However, it was chosen to use the minimum sampling rate values (twice the maximum signal frequency) just for the analysis and comparison of the methods suggested by the standards studied. It is worth to mention that the use of higher sampling rates is not a limitation for the methods suggested by the standards studied. It is also important to clarify that this is a theoretical comparison and additional constraints appear in the real implementation. Then, considering the supraharmonic frequency range with components up to 150 kHz, the sampling rate (Fs ) required by the Nyquist criterion will be greater than 300 kHz. Assuming Fs as being an integer R greater than 300, some considerations can be made, according to Eq. (6).
N = 200·R
(6)
Since R is an integer greater than 300, it is concluded that the number of FFT samples N must be greater than 60,000. To obtain an ideal FFT the number of samples must be power of 2. Therefore, the number of FFT samples can be estimated as 216 , corresponding to 65,536 samples. 8
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Fig. 18. Comparison of different ways of performing the measurements.
Fs = N ·Δf
(7)
Therefore, according to Eq. (5) the new sampling rate will be equal to 102.4 kHz (Fs = 512·200 ), however this sampling rate doesn’t reach the supraharmonic frequency range (up to 150 kHz). Thus, the number of FFT samples should be increased and a sampling rate of 300 kHz should be considered. It is observed that the number of FFT samples to guarantee a window of 5 ms, 200 Hz frequency resolution and sampling rate greater than 300 kHz would be equal to 1,500 (N = 300kHz /200 ), so N must be 2,048 (211). Therefore, the number of operations required by the standard IEC 61000-4-30 to obtain a 200 Hz frequency resolution is equal to 720,896, about four times higher than the case that considers the 2 kHz frequency resolution. From the computational complexity analyses performed, one may conclude that the standard IEC 61000-4-7 is approximately 7 times greater than the number of operations required by IEC 61000-4-30. However, when a 200 Hz resolution is considered for the IEC 61000-430 standard, the number of operations performed by the IEC 61000-4-7 standard becomes only about 1.5 times greater in comparison to the number of operations required by the IEC 61000-4-30 standard. The processing time required by the methodologies to process the real signals described in Section 4.1 was measured via MATLAB code implementation. This test was performed in an Intel Core i7-4510U Notebook, 8 GB Memory, 2.6 GHz HD. The processing time of the IEC 61000-4-30 algorithm was 1.23 s considering a frequency resolution of 2 kHz and 1.27 s for the frequency resolution of 200 Hz, while the IEC 61000-4-7 algorithm with 200 Hz frequency resolution took 1.34 s to process. Table 2 summarizes the analyzes carried out. As expected, the method suggested by IEC 61000-4-30 spends less processing time than the IEC 61000-4-7 method, since it requires less mathematical operation to process the same signal.
Fig. 19. Estimated spectrum by the different measurement forms considered.
Therefore, to obtain the resolution of 5 Hz as suggested by the IEC 61000-4-7 standard, one must calculate an FFT of 65,536 samples of a signal whose sampling rate is 327,68 kHz. For a given signal x [n] with N points, the FFT can be computed with Nlog2 N operations. Then, the number of operations required by the IEC 61000-4-7 would be equal to 1,048,576. The IEC 61000-4-30 standard suggests, for every 10 cycle window, 32 measurement intervals consisting of 512 FFT samples. Each measurement should consist of 512 samples taken at a sampling rate of 1,024 kHz. The 512 samples should be processed with a DFT or equivalent. The 32 measuring set are taken from 200 ms window, and each 512 points FFT at 1,024 kHz sampling frequency corresponds to a time window of 0.5 ms duration and a frequency resolution of 2 kHz. Hence, it is estimated that the number of operations required by the method suggested by the referred standard is around 147,456. Note that the standards suggest measurements considering different frequency resolutions. The IEC 61000-4-30 standard suggests 2 kHz frequency resolution, whereas the IEC 61000-4-7 standard suggests that the frequencies should be grouped in 200 Hz bands. In order to compare this standards, a different approach to the IEC 61000-4-30 can be considered, where the frequency resolution is 200 Hz. To obtain this frequency resolution (Δf ), considering the FFT of 512 samples (N) and a window of 5 ms of the signal, the sampling rate (Fs ) must be altered according to (7).
5. Conclusion This paper presented a survey and a comparison of measurement techniques for voltage and current distortion in the frequency range of Table 2 Comparative analysis of computational complexity and execution’s time.
9
Measurement Method
Frequency Resolution
Number of Operations
Execution’s Time
IEC 61000-4-7 IEC 61000–4-30
200 Hz 200 Hz 2 kHz
1,048,57 720,896 147,456
1.34 s 1.27 s 1.23 s
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2 kHz to 150 kHz. The purpose of the material was to provide the needed information for the development of substantial research on high frequency distortions. The IEC 61000-4-7 and IEC 61000-4-30 standards were emphasized because their content is the most relevant in supraharmonic measurements. The analyzes performed with real signals showed that the methodologies proposed by the discussed standards present similar results for the estimation of supraharmonic components with high magnitudes while the method suggested by the IEC 61000-4-30 standard loses accuracy for components with low magnitudes. Then, in order to investigate the performance of the measurement methodologies of these standards, a real-time acquired signal was processed by both methods (IEC 61000-4-7 and IEC 61000-4-30), presenting similar supraharmonic estimation results. The analysis of a synthetic signal containing supraharmonic distortions showed that the IEC 61000-4-30 method presents greater robustness to noise compared to the IEC 61000-4-7 method. Posteriorly, the investigations carried out proved that, for analysis of signals containing time-varying supraharmonic, the IEC 61000-4-30 standard presented better performance in the supraharmonic estimation compared to the IEC 61000-4-7 method. The measurement methodology suggested by the IEC 61000-4-30 standard was inefficient in estimating the supraharmonic components of the analyzed periodic signal. Alternative ways of performing such measurements have been proposed and have shown the best results. Furthermore, through the comparative analysis of computational complexity, it was verified that the IEC 61000-4-30 method is more efficient computationally than that presented in the IEC 61000-4-7, presenting a number of operations up to 7 times smaller, and consequently this methodology required a shorter processing time. For future work, the authors intend to compare the methodologies analyzed with the supraharmonic measurement method proposed by the CISPR 16 standard [47].
2014 IEEE 16th international conference on, IEEE, p. 818–22. [11] IEC, 61000-4-30. Electromagnetic compatibility (EMC) - Part 4-30: testing and measurement techniques - power quality measurement methods 4; 2015. [12] Voldman SH. Electromagnetic compatibility (emc), ESD testing: from components to systems; 2016. p. 257–83. [13] Kalair A, Abas N, Kalair A, Saleem Z, Khan N. Review of harmonic analysis, modeling and mitigation techniques. Renew Sustain Energy Rev 2017;78:1152–87. [14] Larsson E, Bollen M. Emission and immunity of equipment in the frequency range 2–150 kHz. In: PowerTech, 2009 IEEE Bucharest, IEEE, p. 1–5. [15] Ronnberg SK, Gil-de Castro A, Bollen MH, Moreno-Munoz A, Romero-Cadaval E. Supraharmonics from power electronics converters. In: Compatibility and power electronics (CPE), 2015 9th international conference on, IEEE, p. 539–44. [16] Arias A, Martínez LH, Hincapie RA, Granada M, et al. 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In: 2017 IEEE Workshop on power electronics and power quality applications (PEPQA), p. 1–6. [25] Agudelo-Martínez D, Pavas A. Measurement and simulation of power quality disturbances between 2–150 khz from compact fluorescent lamps. In: Harmonics and quality of power (ICHQP), 2018 18th international conference on, IEEE, p. 1–6. [26] Gil-de Castro A, Moreno-Munoz A, Larsson A, de la Rosa J, Bollen M. Led street lighting: a power quality comparison among street light technologies. Light Res Technol 2013;45:710–28. [27] Agudelo-Martínez D, Ríos F, Pavas A. Interaction of some low power led lamps within 2–150 kHz (supraharmonics). In: Harmonics and quality of power (ICHQP), 2018 18th international conference on, IEEE, p. 1–7. [28] Singh G, Collins ER, Ronnberg SK, Larsson EOA, Bollen MHJ. Impact of high frequency conducted voltage disturbances on led driver circuits. In: 2017 IEEE Power energy society general meeting, p. 1–5. [29] Sakar S, Rönnberg S, Bollen MH. Immunity test of led lamps based on iec 61000–4 19 and unexpected consequence. In: Harmonics and quality of power (ICHQP), 2018 18th international conference on, IEEE, p. 1–6. [30] Verma P, Patel N, Nair NKC. Myths and facts of dual-frequency operation of led lamps. In: Region 10 Conference, TENCON 2017–2017 IEEE, IEEE, p. 522–7. [31] Chicco G, Russo A, Spertino F. Supraharmonics: concepts and experimental results on photovoltaic systems. In: Nonsinusoidal currents and compensation (ISNCC), 2015 international school on, IEEE, p. 1–6. [32] Klatt M, Meyer J, Schegner P, Lakenbrink C. Characterization of supraharmonic emission caused by small photovoltaic inverters. In: Mediterranean conference on power generation, transmission, distribution and energy conversion (MedPower 2016), p. 1–6. [33] Darmawardana D, Perera S, Robinson D, Ciufo P, Meyer J, Klatt M, et al. Investigation of high frequency emissions (supraharmonics) from small, grid-tied, photovoltaic inverters of different topologies. In: Harmonics and quality of power (ICHQP), 2018 18th international conference on, IEEE, p. 1–6. [34] Mendes TM, Duque CA, Silva LRM, Ferreira DD, Meyer J. Supraharmonic analysis by filter bank and compressive sensing. Electr Power Syst Res 2019;169:105–14. [35] Kalair AR, Rauf S, Kalair A, Abas N, Hasan QU, Khan N. Dsm in hybrid ac/dc rooftop pv integrated smart nano grid. In: 2019 4th International conference on smart and sustainable technologies (SpliTech), IEEE, p. 1–7. [36] Novitskiy A, Schlegel S, Westermann D. Analysis of supraharmonic propagation in a mv electrical network. In: 2018 19th International scientific conference on electric power engineering (EPE), IEEE. [37] Rönnberg S, Bollen M, Larsson A, Lundmark M. An overview of the origin and propagation of supraharmonics (2–150 kHz). 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Declaration of Competing Interest None. Acknowledgment The authors would like to thank FAPEMIG, CNPq and CAPES for their support to this work. References [1] Ronnberg SK, Bollen MH, Amaris H, Chang GW, Gu IY, Kocewiak ŁH, et al. On waveform distortion in the frequency range of 2 kHz–150 kHz—review and research challenges. Electric Power Systems Research 2017;150:1–10. [2] McEachern A. Electric power definitions: a debate. In: IEEE power and energy society general meeting, Vancouver, Canada. [3] Streubel T, Kattmann C, Eisenmann A, Rudion K. Detection and monitoring of supraharmonic anomalies of an electric vehicle charging station. In: 2019 IEEE Milan PowerTech, IEEE, p. 1–5. [4] Ravindran V, Busatto T, Rönnberg S, Bollen M, Meyer J. Characterization of interactions between pv systems and energy efficient lighting (led); 2019. [5] Moreno-Munoz A, Gil-de Castro A, Romero-Cavadal E, Rönnberg S, Bollen M. Supraharmonics (2–150 kHz) and multi-level converters. In: Power engineering, energy and electrical drives (POWERENG), 2015 IEEE 5th international conference on, IEEE, p. 37–41. [6] Ronnberg S, Bollen M. Power quality issues in the electric power system of the future. Electr J 2016:49–61. [7] Meyer J, Bollen M, Amaris H, Blanco AM, de Castro AG, Desmet J, et al. Future work on harmonics-some expert opinions part ii-supraharmonics, standards and measurements. In: Harmonics and quality of power (ICHQP), 2014 IEEE 16th international conference on, IEEE, p. 909–13. [8] Bollen M, Olofsson M, Larsson A, Rönnberg S, Lundmark M. Standards for supraharmonics (2–150 kHz). IEEE Electromagn Compatibil Magaz 2014;3:114–9. [9] IEC, 61000-4-7, Electromagnetic compatibility (EMC) - Part 4-7: testing and measurement techniques - General guide on harmonics and interharmonics measurements and instrumentation, for power supply systems and equipment connected thereto; 2008. [10] Klatt M, Meyer J, Schegner P. Comparison of measurement methods for the frequency range of 2 khz to 150 khz. In: Harmonics and quality of power (ICHQP),
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use by electricity suppliers and distributors, BSI Standards; 2003. [44] Dresden TU. Panda - equipment harmonic database. http://www.panda.et.tudresden.de/; 2013. [45] Chai T, Draxler RR. Root mean square error (rmse) or mean absolute error (mae)?–arguments against avoiding rmse in the literature. Geoscient Model Develop 2014;7:1247–50. [46] Tomic JJ, Kusljevic MD, Vujicic VV. A new power system digital harmonic analyzer. IEEE Trans Power Deliv 2007;22:772–80. [47] CISPR I. International special committee on radio interference. Specification for radio disturbance and immunity measuring apparatus and methods - part 2-1: Methods of measurement of disturbances and immunity - conducted disturbance measurements, Technical Report, Specification for radio disturbance and immunity measuring apparatus and methods–Part, 2008.
review on measurement techniques for non-intentional emissions above 2 kHz. In: 2016 IEEE international energy conference (ENERGYCON), pp. 1–5. Ronnberg SK, Bollen MH, Amaris H, Chang GW, Gu IY, Kocewiak Lukasz H, et al. On waveform distortion in the frequency range of 2 kHz–150 kHz - review and research challenges. Electr Power Syst Res 2017;150:1–10. IEC, 61000-4-19, Electromagnetic compatibility (EMC) - Part 4-19: testing and measurement techniques - test for immunity to conducted, differential mode disturbances and signalling in the frequency range 2 kHz to 150 kHz at a.c. power ports; 2014. Langella R, Testa A, Alii E. IEEE recommended practice and requirements for harmonic control in electric power systems; 2014. Staff B. Signalling on low-voltage electrical installations in the frequency range 3 khz to 148.5 khz. immunity requirements for mains communications equipment and systems operating in the range of frequencies 3 khz to 95 khz and intended for
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Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Comparative analysis of the measurement methods for the supraharmonic range
T
⁎
Thais M. Mendesa, , Carlos A. Duquea, Leandro R. Manso da Silvaa, Danton D. Ferreirab, Jan Meyerc, Paulo R. Ribeirod a
Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil Automation Department, Federal University of Lavras, Lavras, MG, Brazil c Institute of Electrical Power Systems and High Voltage Engineering Technische Universitt Dresden, Dresden, Germany d Institute of Electrical Systems and Energy, Federal University of Itajubã, Itajubã, MG, Brazil b
A R T I C LE I N FO
A B S T R A C T
Keywords: IEC 61000-4-7 standard IEC 61000-4-30 standard Measurement methods Power quality Supraharmonics
This paper provides an in-depth analysis of the methodologies proposed by the IEC 61000-4-7 and IEC 61000-430 standards for the supraharmonic frequency range. The paper presents the stat-of-the-art concerning supraharmonics and describes the existing standardized measurements for supraharmonics. The different ways of performing the measurements proposed by such standards are compared. The main contribution and novelty of the paper are the comparative analysis of the standardized measurement methods which considers both efficiency and computational complexity of them. Analyzes considering real signals, a real time signal, a timevarying synthetic signal and the influence of the noise level for the methodologies proposed by the IEC 61000-47 and IEC 61000-4-30 standards were performed. Finally, alternative ways of measuring supraharmonics are suggested. One may conclude that the method described in IEC 61000-4-30 showed to be less immune to noise and less complex (in terms of mathematical operations required during processing) than that described in the IEC 61000-4-7, but loses accuracy in estimating high-amplitude supraharmonic components.
1. Introduction Electrical networks are designed to transfer energy at 50 or 60 Hz, however, components of higher frequencies may appear in the Power System [1]. Engineers have dealt with emission problems in the range of 2–150 kHz for several decades, but the term supraharmonics is relatively recent, being first mentioned during the IEEE Power & Energy Society General Meeting in 2013 [2]. For many years the power quality (PQ) field focused on frequency distortions below 2 kHz. The limited attention given to supraharmonic frequency range in the past is justified in part due to the fact that consumer-installed equipment did not emit high-frequency component. However, new equipment connected to distribution grid is characterized by emission in the frequency range from 2 kHz up to 150 kHz. As example, one can mention more energy-efficient equipment from the consumer side, such as electric vehicle charger, LED lamps, and from the generation side PV-inverters and converters for storage process [3,4]. As a result of supraharmonic emission, some bad effect has been related in literature, such as malfunctions or impairments of household devices and reducing of the lifetime of the devices [5]. Also, as the
⁎
frequency range used in PLC (Power Line Communication) application is in the same band as supraharmonics, interferences in communication channel is expected. Although the effects of supraharmonics (SH) are confined to neighboring devices and do not propagate over long distances, the definition of SH measurement standards is the first step in the commissioning of equipment in relation to high frequency emission. The smallest focus on the supraharmonic frequency range in the past is justified in parts by the lack of consolidated standards for this frequency range [6,7]. Recently, standards-setting organizations have been working to develop measurement methods applicable to the supraharmonic range [8]. Such methods have particularities that may hinder understanding. Due to this fact it is of great importance for the PQ field and for the supraharmonic mitigation to exploit the measurement standards for the supraharmonic frequency range. There are considerable activities within International Electrotechnical Commission (IEC), European Committee for Electrotechnical Standardization (CENELEC) and Institute of Electrical and Electronics Engineers (IEEE) with the aim of developing standards, as compatibility levels, emission and immunity limits, and adequate test methods covering this frequency range. Currently, a measurement
Corresponding author at: Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, MG, Brazil.
https://doi.org/10.1016/j.ijepes.2019.105801 Received 18 July 2019; Received in revised form 13 December 2019; Accepted 19 December 2019 0142-0615/ © 2020 Elsevier Ltd. All rights reserved.
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method for frequencies of 2–9 kHz is presented in the informative annex of IEC 61000-4-7 [9], which may be extended to applications including higher frequencies (up to 150 kHz) [10]. The IEC 61000-4-30 Ed3 [11] standard proposes a measurement methodology for the frequency range of 9–150 kHz, and CISPR-16 (International Special Committee on Radio Interference) suggests equipment and methods for measuring disturbances and immunity to them at frequencies above 9 kHz. The measurement standards for the supraharmonic frequency range are recent in comparison with the existing standards for the frequency range below 2 kHz. The present paper exploits the measurement methodologies imposed by IEC 61000-4-7 and IEC 61000-4-30 standards because these have the most relevant information for measurements in the supraharmonic range (2–150 kHz). The main objective of this paper is to provide a review covering supraharmonic research activities, which are related to relevant measurement topics. In addition, comparisons of the measurement methods proposed by IEC 61000-4-7 and IEC 61000-4-30 standards are made. A critical analysis of the measurement method proposed by the IEC 61000-4-30 standard is carried out. A detailed analysis of the computational complexity of both methods of measurement suggested by such standards is elaborated. In the light of what has been investigated, critical conclusions and proposals for possible improvements of such standards are made. The paper is organized as follows. The next section presents a study of state-of-the-art concerning supraharmonics. Section 3 discusses about measurement methods. Analysis of measurement methods IEC 61000-4-7 and IEC 61000-4-30 are shown in Section 4 and conclusions are in Section 5.
Fig. 1. Definition of frequency range.
and the use of power factor measurement is a possible way to quantify nonlinear loads present in the network [23]. There is a considerable amount of papers discussing causes and consequences of these emissions as well as reporting measurements. Several researches refer to the supraharmonic emissions of street lamps [24–30]. Power inverters are also considered major sources of supraharmonic emissions. Results from emissions of supraharmonics referring to photovoltaic systems are shown in [31–33]. The work reported in [34] proposes the analysis by filter bank and compressive sensing of supraharmonics originated by a photovoltaic inverter and a LED lamp. Therefore, in the current scenario of modern LV electrical distribution networks that are characterized by the presence of numerous distributed PV generators and other electronic equipment [35], the injection of supraharmonics in the network is intense. However it is important to develop practical methods for the localization of main supraharmonic distortion sources in the network. The work reported in [36] proposed practical analysis of supraharmonic propagation and methods for the localization of main supraharmonic distortion sources in the network under study. The paper [37] covered the origin of supraharmonics (remnants of active switching of power electronic converters and power line communication) as well as how supraharmonics propagate between neighboring devices and through the grid. The work reported in [38] presented recent research results regarding the identification of the transfer characteristic of a distribution transformer in the frequency range between 2 kHz and 150 kHz based on measurements. In addition to these contributions highlighted above, some papers present a global view about emissions in the frequency range of 2–150 kHz. A review on measurement techniques for non-intentional emissions above 2 kHz is provided in [39]. [40] indicates the research challenges associated with the supraharmonic range, with emphasis on emission, propagation, interference, measurements, standardization, and modeling and simulation. A comprehensive and systematic classification of possible interference mechanisms and their impact on devices, considering both, intentional and non-intentional emissions is provided by [21].
2. State-of-the-art concerning supraharmonics The main characteristic of electromagnetic noise is its frequency range. The electromagnetic compatibility (EMC) standards generally cover the range from 0 Hz to 400 GHz [12]. However, not all frequency ranges are completely regulated. For decades, the lower frequency range (harmonics) was considered as PQ range [13]. Recently, the supraharmonic frequency range (2–150 kHz) has received more attention by standard-setting organizations, but there is no accepted framework as for lower frequencies [7]. The frequency range below 9 kHz is called low frequency (LF), and the range above this value is called high frequency (HF) range. This range is also called the radio-frequency or RF range. The radiated range then starts at 30 MHz. Fig. 1 shows a summary of the frequency ranges and regulated standards relationship. Smart electrical grids increase the relevance of supraharmonics emission [14,15]. These grids encourage the use of new technologies such as electric vehicles [16], smart metering [17], and demand side management [18], as well as the use of Distributed Generation (DG) [19]. Smart grids are a new electricity grid, not only dedicated to distribute energy [20]. The current trend is a convergence where all distribution lines can also carry different types of information using Power Line Communication (PLCs) [21]. It is asserted that PLC plays a significant role in emission of supraharmonics [22]. On the other hand, the effect of DG on Power Quality (PQ), related to the injection of higher frequency, is due to the presence of power electronics interfaces. Thus, the number of generating units in the system influences emissions in the frequency range studied in this paper (2–150 kHz). The analysis of higher frequency emission is very important, as it can affect the PQ of electrical system. Supraharmonic distortions can cause overheating of capacitors, can strongly affect the accuracy of energy meters, can generate audible noise due to an excitation of mechanical resonances, and malfunction of equipment. In addition, supraharmonic distortions produced by nonlinear loads increase power losses and, therefore, have a negative impact on electric utility distribution systems and components. As for harmonics, establishing the exact relationship between supraharmonics and losses is a difficult task, 2
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At the output of the filters, 32 approximately equally-spaced measurements must be performed, taking each 10/12 cycle interval (10 cycles for 50 Hz systems or 12 cycles for 60 Hz systems), as shown in Fig. 3. Each measurement should consist of 512 samples taken at a sampling rate of 1,024 kHz. The 512 samples must be processed with a FFT or equivalent. The 512 samples FFT at 1,024 kHz sampling frequency corresponds to a time window of 0.5 ms long. Then, there is an equidistant gap which amounts a total of 184 ms. Considering the sampling frequency of 1,024 kHz, the FFT calculation of 512 samples results in 2 kHz frequency resolution. The lowest 4 bins and the upper 181 bins should be discarded. The magnitudes of the remaining 71 bins contain the emissions from 8 kHz to 150 kHz The initial 4 bins represent the frequency range below 8 kHz and should be discarded. As discussed, the frequency range of 2 kHz to 9 kHz should be analyzed by the standard IEC 61000-4-7. The final 181 bins represent frequencies above 150 kHz, these should also be discarded. Therefore, the frequency range of 8–150 kHz has 71 bins that must be analyzed. Fig. 4 shows all steps of the methodology proposed in [11]. The input signal represents the time domain waveform containing supraharmonics. This signal passes through cascade High Pass and Low Pass Filters. These filters limit the signal frequency between 2 kHz and 150 kHz. At the output of these filters, for the frequency range of 9 kHz to 150 kHz, at each 10 cycles interval, 32 sets of these 71 bins are available. Each of the 32 measurement interval represents the FFT calculation of 512 signal samples. The minimum, the average, and the maximum values of the 32 r.m.s. magnitudes of each of these 71 bins should be reported. In addition, a single r.m.s. maximum value of all 71 bins should also be reported.
3. Standardized measurements As described in the previous section a considerable number of recent papers show the growing importance that the theme has been assuming. It directly reflects the need to create or adapt international standards, mainly to define methodologies for the measurement of supraharmonics. This section provides an explanation of the principles established by the standards to measure conducted emissions above 2 kHz. 3.1. IEC 61000-4-7 IEC 61000-4-7 appendix B proposes a measurement method of components in the frequency range of 2–9 kHz. Despite the fact that this standard does not cover the whole range of supraharmonics, some researchers are proposing the extension of the methodology to the whole band. This method suggests grouping the energy of the signal to be analysed into predefined frequency bands. This document refers to the CISPR 16-1, that determines the bandwidth for the grouping of these emissions should be fixed at 200 Hz. This measurement method suggests that signal sampling is performed in a time window of 200 ms, equivalent to 10 (12) fundamental cycles of 50 Hz (60 Hz) systems. Subsequently, it must be converted to the frequency domain through the Fast Fourier Transform (FFT). The r.m.s. value of the component at the frequency f is Cf , e.g., C5100 is the r.m.s. value of the component at 5100 Hz. The frequency separation between consecutive measured components Cf must be 5 Hz. The output Cb of each band is the r.m.s. value according to (1). b + 100Hz
Cb =
∑
Cf2
f = b − 95Hz
3.3. Other measurement standards applicable to supraharmonic emission
(1)
where b represents the central frequency. The output of the raw FFT is grouped in bands of 200 Hz. Therefore, b assumes values equal to 2100 Hz, 2300 Hz, 2500 Hz, and so on. The highest central frequency is 8900 Hz. This measurement standard recommends the use of a band pass filter that attenuates the fundamental frequency and components above 9 kHz with an attenuation of the fundamental component of at least 55 dB. The measurement method proposed by this standard suggests that the sampling rate of the signal is chosen according to the rules of signal analysis so that the components up to 9 kHz can be measured. Considering the Nyquist criterion the sampling rate must be greater than or equal to 18 kHz (Fs ⩾ 18 kHz). However, in order to perform data transformation using the FFT it is advisable that the number of samples processed be a power of two, so the minimum sampling frequency according to the IEC 61000-4-7 standard would be equal to 20.48 kHz. Considering the frequency resolution of 5 Hz, as suggested by the standard, a single FFT of 4,096 samples may be calculated. Finally, 5 Hz resolution FFT components are grouped into 200 Hz bands. Fig. 2 shows the methodology proposed in [9].
The standard IEC 61000-4-19 [41] refers to immunity-related attributes and test methods for electrical and electronic equipment to conduct distortions and promote signaling in the 2–150 kHz frequency range. This standard defines test waveforms, range of test levels, test equipment, test setup, test and verification procedures. The tests carried out are aimed at verifying the immunity of electrical and electronic equipment operating at a supply voltage of up to 280 V (from phase to neutral or phase to earth, if no neutral is used) and a frequency of 50 Hz or 60 Hz when subjected to conducted, differential mode disturbances such as those originating from power electronics and power line communication systems. The International Special Committee for Radio Protection (CISPR) [42] reports product emission and immunity requirements as well as defines test methods and equipment. The Part 1 (CISPR 16-1) refers to radio disturbance and immunity measuring apparatus. Part 2 (CISPR 16-2) specifies methods of measurement of disturbances and immunity. Part 3 (CISPR 16-3) describes reports and recommendations of CISPR. CISPR 16-1-1:2015 specifies the characteristics and performance of equipment for the measurement of radio disturbance in the frequency range of 9 kHz to 18 GHz. In addition, requirements are provided for specialized equipment for discontinuous disturbance measurements. CISPR 16-1-2:2014 + A1:2017 specifies the characteristics and performance of equipment for the measurement of radio disturbance voltages and currents in the frequency range of 9 kHz to 1 GHz. CISPR 16-2-1:2014 + A1:2017 is designated a basic standard, which specifies the methods of measurement of disturbance phenomena in general in the frequency range of 9 kHz to 18 GHz and especially of conducted disturbance phenomena in the frequency range of 9 kHz to 30 MHz European Committee for Electrotechnical Standardization (CENELEC) 50065 [43] applies to electrical equipment using signals in the frequency range of 3 kHz to 148,5 kHz to transmit information on low voltage electrical systems, either on the public electricity distribution network or within consumers’ premises.
3.2. IEC 61000-4-30 The 3rd edition of the IEC 61000-4-30 standard suggests a measurement method for the supraharmonic components located in the 9 kHz to 150 kHz frequency range. A reference to the IEC 61000-4-7 standard for the frequency range of 2 kHz to 9 kHz is given in Annex C of this informative. This standart suggests that the signal be sampled at a rate of 1,024 kHz. This signal must be filtered through a High Pass (HP) filter in cascade with a Low Pass (LP) filter. The High Pass filter should be included to attenuate the fundamental and the low order harmonics of the input signal. The High Pass filter should have 2 poles, with 3 dB of attenuation at 1.5 kHz or higher. The Low Pass is a 4th order filter, with the cutoff frequency at 200 kHz. 3
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Fig. 2. Illustration of the measurement method according to IEC 6100-4-7.
Table 1 Summary of the main existing standards for the supraharmonic range. Standard
Purpose/method
Frequency Range
IEC 61000–4-7
Emissions levels from equipment, in the grid/ FFT with 5 Hz resolution, 200 Hz band aggregation at 200 ms of signal Levels in grid/ FFT, 0.5 ms intervals, 2 kHz frequency resolution, aggregation into avg and max of the 32 measurement intervals per 10/12 cycles. Levels in grid and emission from equipment/ Spectrum analyzer with tunable filter and detector (peak and quasi peak). Immunity-related attributes and test methods for electrical and electronic equipment to conduct distortions and promote signaling.
2 kHz - 9 kHz
IEC 61000–4-30
Fig. 3. Measurement methodology proposed by the standard IEC 6100-4-30 Ed3. CISPR 16–2-1
The IEEE 519 [42] is proposed to be used as guidance in the design of power systems with nonlinear loads. The limits set are for steadystate operation and are recommended for worst case conditions. This standard is limited to be a collection of Recommended Practices that serve as a guide to both suppliers and consumers of electrical energy, placing a limitation on both the amount of harmonic current that a consumer can inject into a utility network and the level of harmonic voltage that a utility can supply to a consumer. The measurement methodology is mainly based on IEC 61000-4-X series, but no explicit information is given for harmonic components of order greater than 50. Table 1 summarizes existing standards for the supraharmonic frequency range.
IEC 61000–4-19
9 kHz - 150 kHz
9 kHz - 30 MHz
2 kHz - 150 kHz
61000-4-30 measurement methods is performed. To test and compare the efficiency of the IEC 61000-4-7 and IEC 61000-4-30 methodologies, four different cases were analyzed: (i) real world signals; (ii) real time signal; (iii) synthetic signals generated with different noise levels and (iv) time-varying synthetic signal. The analyzes were performed individually for each case and the appropriate conclusions were obtained. Posteriorly, the IEC 61000-4-30 method was analyzed for a specific case of synthetic signal containing supraharmonic distortions, some criticisms and suggestions were made based on this analysis. Finally, a comparative analysis of the computational complexity required by both
4. Analysis of Measurement Methods based on IEC 61000-4-7 and IEC 61000-4-30 In this section a comparative analysis of the IEC 61000-4-7 and IEC
Fig. 4. Illustration of the measurement method according to IEC 6100-4-30 Ed3. 4
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Fig. 5. Photovoltaic inverter time domain waveform containing supraharmonics.
Fig. 7. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of the current at the PV inverter.
IEC 61000-4-7 and IEC 61000-4-30 measurement methodologies was performed.
4.1. Real signals In order to compare the standards IEC 61000-4-7 and IEC 61000-430, two waveforms containing supraharmonic distortion originated by a photovoltaic inverter and an electric vehicle charger, respectively, were processed. These signals were provided by PANDA-project (equiPment hArmoNic Database), a global web-based platform for exchanging harmonic emission measurements of household equipment [44]. Time domain signals of the emissions from a PV and a EV charger are shown in Figs. 5 and 6, respectively. These signals were acquired with a sampling rate of 1,000 kHz (1 MSa/s), with fundamental frequency equal to 50 Hz. The basic measurement window of the analyzed signals have a length of 200 ms approximately (10 cycles at 50 Hz power frequency). These signals were previously filtered, delimiting its spectrum from 2 kHz to 150 kHz, as suggested by the standard IEC 61000-4-30. Figs. 7 and 8 show a comparison between the IEC 61000-4-7 and the IEC 61000-4-30 for the supraharmonic estimation. As explained in Section 3.2, the mean of 32 measurements was calculated, referencing to the calculation of 32 FFT of 512 samples in 10 cycles of the analyzed signal. Section 3.1 presents details of the standard IEC 61000-4-7 that is applied to the range below 9 kHz, however for purposes of comparison,
Fig. 8. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of the current at the EV charger.
this measurement was applied in frequency range of 2 kHz to 150 kHz. In this case the same analog filter of IEC 61000-4-30 was used. A resolution of 5 Hz was considered, and the calculation of only one FFT of 200,000 samples was performed. The output of the FFT was grouped in bands of 2 kHz. Analyzing Figs. 7 and 8, it is observed that the measurement results for both methods are similar. In Fig. 7, referring to the comparison of the standards for the PV inverter, the relative difference in terms of amplitude at 22 kHz is 18.7%, at 54 kHz is 13.9% and at 108 kHz is 45.2%. In Fig. 8, whose analyzed signal is originated by EV charger, the relative difference at 32 kHz is 13.1%, at 54 kHz is 17.5% and at 62 kHz is 25%. It is observed through this analysis that, the results are more similar for higher distortion levels, that is, for supraharmonic with higher amplitudes. According to [10] the measurement method proposed in IEC 61000-4-30 lacks accuracy at low distortion levels, that is, for measuring supraharmonic components with small amplitudes, the IEC 61000-4-7 method is more accurate than the one described in IEC 61000-4-30. To verify if this effect has relation with the frequency of the supraharmomnic, a synthetic voltage signal contaminated by five supraharmonic components located at frequencies 30, 50, 90, 70 and 110 kHz and with the same amplitude values was generated. Both approaches were applied to this signal and it was found that the relative error between the corresponding estimated spectra is around 0.2 % and remains the same for all supraharmonic frequencies.
Fig. 6. Electric vehicle charger time domain waveform containing supraharmonics. 5
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Fig. 9. Real time acquisition system.
4.2. Real time experiment Fig. 11. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of a real time signal.
In order to get more realistic results, experimental tests were performed using a real time signal. The equipment used to generate this signal is illustrated in Fig. 9. It has been used a Waveform Genarator (33500B Series Waveform Generator TrueForm - Keysight) with sample rate of 1 μ Sa/s to 250 MSa/s and 16 bits resolution, and an oscilloscope (Data Recorder DL850E - Yokogawa) with sample rate of 1 MS/s, 2 channels, and 16 bits resolution, bandwidth of 300 kHz, time axis accuracy of ±0.005%, 16 channels for data recorder and power consumption of 200 VA. By means of the software MATLAB, a signal containing supraharmonics, as shown in Fig. 10, was generated and exported in text format to the function generator. Such file is saved in internal memory and each sample is read at a sampling rate of 6 MSa/s. Afterwards, the signal is acquired through 1 oscilloscope channel, at a sampling rate of 1 MSa/s, this acquisition is online with a software specific of this equipment, being possible to save the data in real time in a computer through the cable Ethernet compatible with the acquisition rate. In this system the signal acquisition is performed in real time (online) and the signal processing by the analyzed methods (IEC 61000-4-7 and IEC 61000-4-30) is offline. The generated signal, composed by fundamental component ( f0 equal to 50 Hz) and two supraharmonic components located in the frequencies fsh1 equal to 32 kHz and fsh2 equal to 64 kHz, can be represented by Eq. (2). The amplitudes are A sh1 and A sh2 , both equal to 0.5. Fig. 10 illustrates this real time signal.
x (t ) = cos (2πf0 t + θh) + A sh1 cos (2πfsh1 t )+ A sh2 cos (2πfsh2 t )
(2)
Fig. 11 shows the spectrum achieved by both standards studied. It is observed that both standards were able to estimate the supraharmonic components present in the real time signal. 4.3. Synthetic signal with noise Synthetic signals containing supraharmonic components were presented to the measurement methodologies suggested by the standards analyzed in order to test the efficiency of such methods for supraharmonic estimation in the presence of noise. The signals were generated with an additive Gaussian white noise. Signals with different levels of noise were considered. In total, eleven different cases were generated, with SNR values equal to 10 dB, 20 dB, …, and 100 dB, it was also considered a signal without noise. A total of ten events were generated for each case. The mathematical representation of such signals is given in (3). 50
x (t ) =
∑
Ah cos (2πfh t + θh) + A sh1 cos (2πfsh1 t )+
h=1
A sh2 cos (2πfsh2 t ) + n (t )
(3)
where n (t ) represents the noise component. These signals consist of 20,480 samples taken at a sampling rate of 1,024 kHz, which corresponds to one power cycle at a fundamental frequency of 50 Hz. These signals are composed by conventional harmonic and two supraharmonic components located in the frequencies fsh1 equal to 32 kHz and fsh2 equal to 96 kHz. The amplitudes are A sh1 and A sh2 , equal to 0.05 and 0.025, respectively. At these signals different noise levels were added. Fig. 12 shows the time domain waveform and frequency spectrum of a 50 dB SNR synthetic signal used for testing. As mentioned, ten signals were generated for each case analyzed, and the root-mean-square error (RMSE) [45] between the spectrum obtained by each measurement (IEC 61000-4-7 or IEC 61000-4-30) and the ideal spectrum (gold standard) was calculated. Fig. 13 shows the results for the methodologies studied in terms of RMSE mean values (considering the ten signals for each case) and standard deviations. By analyzing Fig. 13, it can be noted that both methods are able to estimate the supraharmonic components in the presence of noise, since the obtained error values (RMSE) are low. According to [46], in practice, the SNR of the voltage signal obtained from a power system varies between 50 dB and 70 dB. Then, the methodologies proposed by the standards are not affected by noise, since the achieved RMSE for this
Fig. 10. Real time signal. 6
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Fig. 12. Time domain waveform of the signal composed of fundamental and supraharmonic components in (a) and the supraharmonic components only, in (b). The frequency spectrum of the supraharmonic components is shown in (c).
Fig. 13. Results of the methods IEC 61000-4-7 and IEC 61000-4-30 for a measurement of a synthetic signal with noise.
Fig. 14. Synthetic time-varying signal used.
SNR range is similar to that achieved for the case without noise. It is noted that the IEC 61000-4-30 method is more robust to noise than the IEC 61000-4-7 method. 4.4. Time-varying synthesized signal In order to compare the performance of the methods reported in IEC 61000-4-7 and IEC 61000-4-30 for a signal containing time-varying supraharmonics, a synthetic signal represented by Eq. (4) was used 50
x (t ) =
∑ h=1
Ah cos (2πfh t ) + Ash (t ) cos (2πfsh t )
(4)
This signal consists of 20,480 samples taken at a sampling rate of 1,024 kHz (1,024,000 Sa/s), which corresponds to one power cycle at a fundamental frequency of 50 Hz ( f0 ). This signal is composed by conventional harmonic with frequency ( fh = h·f0 ) and one supraharmonic component located in the frequency fsh equal to 80 kHz. The magnitudes of the respective components are Ah and Ash (t ), where Ash (t ) is an exponential function whose amplitude decreases and then increases. Fig. 14 illustrates this synthetic signal.
Fig. 15. Results in 2 kHz bands for methods IEC 61000-4-7 and IEC 61000-4-30 for time-varying supraharmonic estimation.
7
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Fig. 17. Time domain waveform containing a periodic voltage disturbance with high frequency components.
Fig. 16. Results of the IEC 61000-4-30 method for time-varying supraharmonic estimation.
detect the disturbance in some situations such as where distortion occurs in narrow bands and is periodic, as in the case of the analyzed signal. This analysis encourages discussions about the efficiency of the measurement methodology proposed by the IEC 61000-4-30 and shows that alternative ways of performing such measurements can present better results for supraharmonic estimation.
Fig. 15 shows a comparison between the IEC 61000-4-7 and the IEC 61000-4-30 for the time-varying supraharmonic estimation. Observing this figure it is possible to note that both methods estimate the supraharmonic component. Fig. 16 represents the maximum, mean and minimum values of the 32 measurements of the signal containing time-varying supraharmonic, as suggested by the IEC 61000-4-30 standard. This figure shows the time-varying characteristic of the analyzed signal, since the maximum, average and minimum values are different. Therefore the IEC 61000-430 method is able to detect the time-varying nature of a supraharmonic component, which is not possible using the approach based on the IEC 61000-4-7.
4.6. Computational complexity of the IEC 61000-4-7 and IEC 61000-4-30 measurement methods This section presents an analysis of the computational complexity of the measurement methods studied in this paper. The number of mathematical operations performed during the execution of an algorithm may be used to define its complexity. According to the measurement method proposed in IEC 61000-4-7 standard, only one FFT must be calculated in a window of 200 ms of the signal. Then, the signal is sampled in a 200 ms rectangular time window, corresponding to approximately 10 (12) fundamental periods of 50 Hz (60 Hz) systems. From the sampling process the relation given in (5).
4.5. Spacing between measurements The standard IEC 61000-4-30 determines that measurements must be taken equally spaced time intervals such that 32 approximately equally-spaced measurements are taken each 10/12 cycle interval. If the 32 measurements are equally distributed, some parts of the signal will never be covered by a measurement interval. Therefore, if the analyzed signal presents a disturbance that occurs at periodic intervals of time and the time of disturbance occurrence coincides with the space between measurements (where there is no measurement), this disturbance will not be detected. For performance evaluation of the methodology proposed by the IEC 61000-4-30 consider the occurrence of a notch, a periodic voltage disturbance with high frequency components, as shown in Fig. 17. Fig. 18 illustrates a comparison of different ways of performing the measurement of a signal containing notch disturbance. Equally-spaced refers to the method proposed by the standard [11], as shown in Fig. 5. Non-spaced represents 32 measurements of 512 samples carried out consecutively, without spacing. In this case, the measurements are obtained in only one cycle of the signal. Randomly spaced are sequential measurements performed on 10 cycles of the signal, but not equally spaced. In this approach, the 10 cycles of the signal are divided into 32 equal intervals and the starting point of each 0.5 ms window of the signal is randomly picked. Fig. 19 illustrates the spectrum estimated by the different measurement forms. From this figure we can conclude that the disturbance may not be detected in the case where measurements are considered equally-spaced. The chances of detecting such a disturbance are increased when measurements are taken at random spacings, or when the 32 measurements are performed consecutively, without spacing. Therefore, the IEC 61000-4-30 standard measurement methodology, which proposes equally-spaced FFT measurements, may not be able to
N = 200 ms Fs
(5)
where N is the number of samples of the signal and Fs is the sampling rate. In this measurement method, the sampling frequency should be chosen in accordance with the established rules of signal analysis.In practical measurement activities, the instrumentation part uses sampling rates much higher than the Nyquist criterion. However, it was chosen to use the minimum sampling rate values (twice the maximum signal frequency) just for the analysis and comparison of the methods suggested by the standards studied. It is worth to mention that the use of higher sampling rates is not a limitation for the methods suggested by the standards studied. It is also important to clarify that this is a theoretical comparison and additional constraints appear in the real implementation. Then, considering the supraharmonic frequency range with components up to 150 kHz, the sampling rate (Fs ) required by the Nyquist criterion will be greater than 300 kHz. Assuming Fs as being an integer R greater than 300, some considerations can be made, according to Eq. (6).
N = 200·R
(6)
Since R is an integer greater than 300, it is concluded that the number of FFT samples N must be greater than 60,000. To obtain an ideal FFT the number of samples must be power of 2. Therefore, the number of FFT samples can be estimated as 216 , corresponding to 65,536 samples. 8
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Fig. 18. Comparison of different ways of performing the measurements.
Fs = N ·Δf
(7)
Therefore, according to Eq. (5) the new sampling rate will be equal to 102.4 kHz (Fs = 512·200 ), however this sampling rate doesn’t reach the supraharmonic frequency range (up to 150 kHz). Thus, the number of FFT samples should be increased and a sampling rate of 300 kHz should be considered. It is observed that the number of FFT samples to guarantee a window of 5 ms, 200 Hz frequency resolution and sampling rate greater than 300 kHz would be equal to 1,500 (N = 300kHz /200 ), so N must be 2,048 (211). Therefore, the number of operations required by the standard IEC 61000-4-30 to obtain a 200 Hz frequency resolution is equal to 720,896, about four times higher than the case that considers the 2 kHz frequency resolution. From the computational complexity analyses performed, one may conclude that the standard IEC 61000-4-7 is approximately 7 times greater than the number of operations required by IEC 61000-4-30. However, when a 200 Hz resolution is considered for the IEC 61000-430 standard, the number of operations performed by the IEC 61000-4-7 standard becomes only about 1.5 times greater in comparison to the number of operations required by the IEC 61000-4-30 standard. The processing time required by the methodologies to process the real signals described in Section 4.1 was measured via MATLAB code implementation. This test was performed in an Intel Core i7-4510U Notebook, 8 GB Memory, 2.6 GHz HD. The processing time of the IEC 61000-4-30 algorithm was 1.23 s considering a frequency resolution of 2 kHz and 1.27 s for the frequency resolution of 200 Hz, while the IEC 61000-4-7 algorithm with 200 Hz frequency resolution took 1.34 s to process. Table 2 summarizes the analyzes carried out. As expected, the method suggested by IEC 61000-4-30 spends less processing time than the IEC 61000-4-7 method, since it requires less mathematical operation to process the same signal.
Fig. 19. Estimated spectrum by the different measurement forms considered.
Therefore, to obtain the resolution of 5 Hz as suggested by the IEC 61000-4-7 standard, one must calculate an FFT of 65,536 samples of a signal whose sampling rate is 327,68 kHz. For a given signal x [n] with N points, the FFT can be computed with Nlog2 N operations. Then, the number of operations required by the IEC 61000-4-7 would be equal to 1,048,576. The IEC 61000-4-30 standard suggests, for every 10 cycle window, 32 measurement intervals consisting of 512 FFT samples. Each measurement should consist of 512 samples taken at a sampling rate of 1,024 kHz. The 512 samples should be processed with a DFT or equivalent. The 32 measuring set are taken from 200 ms window, and each 512 points FFT at 1,024 kHz sampling frequency corresponds to a time window of 0.5 ms duration and a frequency resolution of 2 kHz. Hence, it is estimated that the number of operations required by the method suggested by the referred standard is around 147,456. Note that the standards suggest measurements considering different frequency resolutions. The IEC 61000-4-30 standard suggests 2 kHz frequency resolution, whereas the IEC 61000-4-7 standard suggests that the frequencies should be grouped in 200 Hz bands. In order to compare this standards, a different approach to the IEC 61000-4-30 can be considered, where the frequency resolution is 200 Hz. To obtain this frequency resolution (Δf ), considering the FFT of 512 samples (N) and a window of 5 ms of the signal, the sampling rate (Fs ) must be altered according to (7).
5. Conclusion This paper presented a survey and a comparison of measurement techniques for voltage and current distortion in the frequency range of Table 2 Comparative analysis of computational complexity and execution’s time.
9
Measurement Method
Frequency Resolution
Number of Operations
Execution’s Time
IEC 61000-4-7 IEC 61000–4-30
200 Hz 200 Hz 2 kHz
1,048,57 720,896 147,456
1.34 s 1.27 s 1.23 s
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2 kHz to 150 kHz. The purpose of the material was to provide the needed information for the development of substantial research on high frequency distortions. The IEC 61000-4-7 and IEC 61000-4-30 standards were emphasized because their content is the most relevant in supraharmonic measurements. The analyzes performed with real signals showed that the methodologies proposed by the discussed standards present similar results for the estimation of supraharmonic components with high magnitudes while the method suggested by the IEC 61000-4-30 standard loses accuracy for components with low magnitudes. Then, in order to investigate the performance of the measurement methodologies of these standards, a real-time acquired signal was processed by both methods (IEC 61000-4-7 and IEC 61000-4-30), presenting similar supraharmonic estimation results. The analysis of a synthetic signal containing supraharmonic distortions showed that the IEC 61000-4-30 method presents greater robustness to noise compared to the IEC 61000-4-7 method. Posteriorly, the investigations carried out proved that, for analysis of signals containing time-varying supraharmonic, the IEC 61000-4-30 standard presented better performance in the supraharmonic estimation compared to the IEC 61000-4-7 method. The measurement methodology suggested by the IEC 61000-4-30 standard was inefficient in estimating the supraharmonic components of the analyzed periodic signal. Alternative ways of performing such measurements have been proposed and have shown the best results. Furthermore, through the comparative analysis of computational complexity, it was verified that the IEC 61000-4-30 method is more efficient computationally than that presented in the IEC 61000-4-7, presenting a number of operations up to 7 times smaller, and consequently this methodology required a shorter processing time. For future work, the authors intend to compare the methodologies analyzed with the supraharmonic measurement method proposed by the CISPR 16 standard [47].
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