Publicado

2018-04-01

Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation

Obtención de la fase de la impedancia eléctrica usando transformada Wavelet y transformada de Fourier de señales transitorias. Parte 2: evaluación práctica y validación

DOI:

https://doi.org/10.15446/dyna.v85n205.68458

Palabras clave:

continuous wavelet transform (CWT), frequency response, online supervision and control, power system transients and transformers (en)
transformada Wavelet continua (CWT), respuesta en frecuencia, supervisión y control en línea, transitorios del sistema eléctrico y transformadores (es)

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Autores/as

This article presents a practical assessment and validation of the new proposed approach based on the continuous wavelet transform (CWT) to obtain the electrical impedance phase from online transient signals for a real transformer. Besides the mathematical procedure presented in a previous paper, an electronic system was also designed and implemented, in order to inject superimposed controlled pulses to the power system (50/60 Hz) wave. The results show improved performance of the wavelet transform compared to that of the Fourier Transform, for transient signal analysis to be applied on a nonintrusive transformer monitoring approach. Particularly, this new approach proves useful in overcoming problems related to signal filtering and signal processing in an online frequency-response analysis of a transformer diagnosis.
Este artículo presenta la validación y evaluación práctica para la nueva propuesta presentada, basada en la Transformada Wavelet Contínua (CWT) para obtener la fase de la impedancia eléctrica de señales transitorias en línea de un transformador real. A parte del procedimiento matemático presentado en la parte 1, también se diseñó e implementó un sistema electrónico para inyectar pulsos controlados en la onda del sistema de potencia (50/60 Hz). Los resultados muestran un mejor rendimiento de la Transformada Wavelet en comparación con la transformada de Fourier, para el análisis de señales transitorias para ser aplicado en un enfoque de monitoreo de transformadores no intrusivo. En particular, este nuevo enfoque permite superar algunos problemas de filtrado y procesamiento de señales en el análisis de respuesta en frecuencia de un transformador en servicio.

Recibido: 24 de octubre de 2017; Revisión recibida: 8 de marzo de 2018; Aceptado: 9 de abril de 2018

Abstract

This article presents a practical assessment and validation of the new proposed approach based on the continuous wavelet transform (CWT) to obtain the electrical impedance phase from online transient signals for a real transformer. Besides the mathematical procedure presented in a previous paper, an electronic system was also designed and implemented, in order to inject superimposed controlled pulses to the power system (50/60 Hz) wave. The results show improved performance of the wavelet transform compared to that of the Fourier Transform, for transient signal analysis to be applied on a nonintrusive transformer monitoring approach. Particularly, this new approach proves useful in overcoming problems related to signal filtering and signal processing in an online frequency-response analysis of a transformer diagnosis.

Keywords:

continuous wavelet transform (CWT), frequency response, online supervision and control, power system transients and transformers.

Resumen

Este artículo presenta la validación y evaluación práctica para la nueva propuesta presentada, basada en la Transformada Wavelet Contínua (CWT) para obtener la fase de la impedancia eléctrica de señales transitorias en línea de un transformador real. A parte del procedimiento matemático presentado en la parte 1, también se diseñó e implementó un sistema electrónico para inyectar pulsos controlados en la onda del sistema de potencia (50/60 Hz). Los resultados muestran un mejor rendimiento de la Transformada Wavelet en comparación con la transformada de Fourier, para el análisis de señales transitorias para ser aplicado en un enfoque de monitoreo de transformadores no intrusivo. En particular, este nuevo enfoque permite superar algunos problemas de filtrado y procesamiento de señales en el análisis de respuesta en frecuencia de un transformador en servicio.

Palabras clave:

transformada Wavelet continua (CWT), respuesta en frecuencia, supervisión y control en línea, transitorios del sistema eléctrico y transformadores.

1. Introduction

A new theoretical method to obtain the frequency response from the online transient signals measurement (with the transformer in service) was presented in a previous paper [1-6].

This new method is based on the continuous wavelet transform (CWT), which enables improved performance compared to the traditional Fourier transform. The transient signals presented as examples in that paper came from simulations within the Alternative Transients Program (ATP). In recent years, there has been a growing interest in frequency-response analysis (FRA) with the transformer in service, since no transformer disconnection is required to conduct the test.

Schema of the proposed method for the measurement of the online FRA in transformers.

Figure 1: Schema of the proposed method for the measurement of the online FRA in transformers.

Source: [5].

Testing under these conditions allows for the monitoring of the transformer and the detection of any abnormalities before they cause catastrophic failures in power grids [2,3]. Although there have been efforts and contributions to carry out the frequency response test with the transformer in service, state of the art is not mature and there is still much research to be done [4].

This paper presents the assessment and validation of the proposed method in real transformers, using the continuous wavelet transform (CWT) [1] as a powerful tool for the filtering, denoising, and processing of transient signals. As will be shown, improvement is achieved when using this new method, including non-repeatability effects and noise content in the measurements, as well as in non-periodical waveforms processing constraints.

2. Experimental set in the pilot transformer

Fig. 2 shows the experimental set in the pilot transformer carried out in the high-voltage laboratory of the Universidad del Valle [6] and Fig. 3 shows the pilot transformer. An OFF- LINE test was performed in a transformer, with high voltage winding short circuited and low winding open to obtain the transient signals. Results of voltage and current signal measurements are shown in Fig. 4 and Fig. 5, respectively.

Experimental set in the pilot transformer.

Figure 2: Experimental set in the pilot transformer.

Source: [6].

Pilot transformer.

Figure 3: Pilot transformer.

Source: [6].

Time domain voltage signal, with a 2ms window of 20.000 samples at 10M samples/s.

Figure 4: Time domain voltage signal, with a 2ms window of 20.000 samples at 10M samples/s.

Source: The authors.

Time domain current signal, with a 2ms window of 20.000 samples at 10M samples/s.

Figure 5: Time domain current signal, with a 2ms window of 20.000 samples at 10M samples/s.

Source: The authors.

3. Practical proposed method for carrying out the online FRA test

The proposed method to obtain the frequency response with the transformer in service (online) involves the three stages presented in the block diagram shown in Fig. 1.

3.1. Stage 1. Injection and signal measurements

An electronic circuit was designed and implemented for the injection system to inject microsecond-width controlled voltage pulses on the power wave of 60 Hz [4]. The injection system enables setting the amplitude, width, and phase of the generated pulses, by means of the circuit shown in Fig. 6, with Fig. 7 showing an example of controlled pulses on the (60 Hz) voltage signal.

Actual assembly of the injection system for online IFRA.

Figure 6: Actual assembly of the injection system for online IFRA.

Source: [3].

Controlled pulses on the (60 Hz) voltage signal used for the online IFRA method.

Figure 7: Controlled pulses on the (60 Hz) voltage signal used for the online IFRA method.

Source: The authors.

Block diagram of the filtering and signal processing of S(t).

Figure 8: Block diagram of the filtering and signal processing of S(t).

Source: [3].

3.2. Stage 2. Filtering, denoising, signal acquisition, and processing

The voltage and current signals were modeled according to S(t) presented in Eq. (1), which is composed of three terms. The first one represents the nature of the transformer’s condition itself and constitutes the main information we want to extract from the measurement. It is mathematically defined as a summation of N terms, where Bk are the residues and Pk the modes or poles determining the shape of the transient signal. This main information is contaminated by the background noise n(t), and the harmonic distortion h(t) coming from the fundamental power 50/60-Hz frequency component.

Once made filtering applies the CWT, it is defined as Eq. (2) [5].

Where the asterisk represents the conjugate of the complex function, f t is the transient signal itself, 𝜓(t) is the wavelet function which defines the mother wavelet in use, in which “𝜏” conducts the translation and factor, and “𝑎” provides the dilation (or scaling) factor.

In part 1, it was demonstrated that using the mother wavelet Complex Morlet yields excellent results [1]. The complex Morlet wavelet transform is defined in Eq. (3) [5-16].

Applying the wavelet transform to the transient signals of both current and voltage [10-15] in its discrete form. Eq. (4) and Eq. (5), since a measured transient is not a continuous function but a matrix of points [16-20].

With the information of the data we can get the ratio between the coefficients 𝐶 𝑉 y 𝐶 𝐼 as shown in Eq. (6) obtaining the coefficients 𝐶 𝑍 .

The impedance phase at the scale defined by “𝑎” can be obtained from the integration of Eq. (6) along the whole window time of the transient. Due to its complex nature, the integration is performed under a vector approach. The phase can be obtained by means of Eq. (7).

Where the operators “𝑅𝑒” and “𝐼𝑚” are the real part and imaginary part of the complex coefficients, respectively.

3.2. Stage 3. Assessment and validation approach

The transformer impedance, computed from online time-domain records was measured while the transformer was energized and compared with the corresponding sweep frequency- response analysis (SFRA) offline response, obtained by using frequency-response analysis equipment.

4. Experimental results

With a commercial instrument (MEGGER FRAX-101), the transformer SFRA was obtained and taken as reference, as shown in Fig. 9.

Transformer frequency response SFRA (reference signal).

Figure 9: Transformer frequency response SFRA (reference signal).

Source: The authors.

The result with Fourier transform was obtained as shown in Fig. 10 and with Wavelet transform as shown in Fig. 11.

FFT assessments using a 2ms time window: phase frequency response.

Figure 10: FFT assessments using a 2ms time window: phase frequency response.

Source: The authors.

WT assessments using a 2ms time window: phase frequency response.

Figure 11: WT assessments using a 2ms time window: phase frequency response.

Source: The authors.

As observed in Fig. 11, WT offers a better approximation to reference, in a frequency range 4kHz to 40kHz, compared to FFT; After this, a repeatability analysis was performed, obtaining the response for the first three pulses of the time signal for WT and FFT methods, as shown in Fig. 13 and Fig. 14, respectively.

WT assessments using a 2ms time window: phase frequency response for three pulses.

Figure 12: WT assessments using a 2ms time window: phase frequency response for three pulses.

Source: The authors.

FFT assessments using a 2ms time window: phase frequency response for three pulses.

Figure 13: FFT assessments using a 2ms time window: phase frequency response for three pulses.

Source: The authors.

FT and WT assessments using a 1,5ms window of 15.000 samples at 2.5 M samples/s.: phase frequency response.

Figure 14: FT and WT assessments using a 1,5ms window of 15.000 samples at 2.5 M samples/s.: phase frequency response.

Source: The authors.

Table 1 shows the quantitative analysis, of the results obtained when using both methods.

A qualitative analysis, using the average Relative error (TERM), was made to compare the two methods, in which best results were obtained for the CWT method [19-22].

Table 1: Quantitative analysis of the curves.

Source: The authors.

To confirm the advantage in using WT, the same experimental example was used with a time window of 1,5ms and 15.000 samples, but with a sampling frequency of 2,5M samples / s.

Unlike the FFT, the WT is not altered by the changes generated shown in the part enclosed in Fig. 14, which demonstrates that the proposed method is a suitable one.

5. Conclusions

This article proposes an improved method for processing signals from time to frequency for the impedance phase. It allows overcoming the traditional Fourier Transform performance, since no periodical signals are required at all. This feature can be much more useful for engineering design and analysis because it allows working with non-periodical transient responses.

A simple example showed that, when the measurement conditions are tightened, the proposed WT based procedure performs better than the FT.

The key points in the procedure are a suitable election of the mother wavelet (Complex Morlet, in this case) and of the proposed frequency response values calculation (frequency domain) from the wavelets coefficients (time-scale domain). Thus, a correct analysis of the phase of the impedance, leads to better results for the wavelet transform, in comparison with those of the Fourier transform under both simulated and experimental conditions, which adds to the potential of WT as a suitable for the processing of transient signals.

Acknowledgments

The authors express their heartfelt thanks to the PTI S.A. Company for its support in the elaboration of this paper. They also thank COLCIENCIAS for its support for Project 54558, 2016, an approved project to access tax benefits and The Universidad del Valle for all it provided us with.

References

[1] Gómez-Luna, E., Cuartas-bermúdez, J. S. and Marlés-sáenz, E., Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 1 : Theoretical analysis DYNA vol. 84, no. 201, pp. 138-144, 2017. DOI: https://doi.org/10.15446/dyna.v84n201.58694 [Link]

[2] Krieg, T. and Napolitano, M., Techniques and experience in on-line transformer condition monitoring and fault diagnosis in ElectraNet SA. in Proc. IEEE Int. Conf. Power Syst. Technol. PowerCon Substation Maint.e Dept., 2000, vol. 2, pp. 1019-1024. DOI: 10.1109/ICPST.2000.897160[CrossRef]

[3] Mackenzie, E. A., Crossey, J., DePablo, A. and Ferguson, W., On-line monitoring and diagnostics for power transformers, in Proc. IEEE Int. Symp. Elect. Insul. Conf., 2010, pp. 1-5. DOI: 10.1109/ELINSL.2010.5549734[CrossRef]

[4] Gómez-Luna, E., Aponte, G., Gonzalez-Garcia, C. and Pleite, J., Current status and future trends in the Frequency Response Analysis (FRA) with the transformer in service, IEEE Trans. Power Del., vol. 28, no. 2, pp. 1024-1031, Apr. 2013. Research Group Gralta, Desarrollo. DOI: 10.1109/TPWRD.2012.2234141[CrossRef]

[5] Gómez-Luna, E., Silva, D., Aponte, G., Pleite, J. and Hinestroza, D., Obtaining the electrical impedance using wavelet transform from the time response, IEEE Transactions on Power Delivery, Vol. 28, No. 2, pp. 1242-1244, April 2013. DOI: 10.1109/TPWRD.2012.2234942[CrossRef]

[6] Krieg, T., and Napolitano, M., Techniques and experience in on-line transformer condition monitoring and fault diagnosis in ElectraNet SA, in Proc. IEEE Int. Conf. Power Syst. Technol. PowerCon Substation Maint.e Dept., 2000, vol. 2, pp. 1019-1024. DOI: 10.1109/ICPST.2000.897160[CrossRef]

[7] Gómez-Luna, E., Aponte, G. and Pleite, J., Application of Wavelet Transform to obtain the Frequency Response of a Transformer from Transient Signals - Part 2: Practical assessment and validation. IEEE Transactions on Power Delivery , Vol. 29, No. 5, pp. 2231 - 2238, October 2014. DOI: 10.1109/TPWRD.2013.2295377[CrossRef]

[8] Gomez-Luna, E., Obtención De La Respuesta En Frecuencia De Transformadores En Servicio a Partir De La Medida De Señales Transitorias. Tesis de Doctorado, Universidad del Valle. p. 95, 2013.

[9] Research Group Gralta, Desarrollo de una prueba piloto para obtener la respuesta en frecuencia de un transformador en servicio, Universidad del Valle, Valle, Spain, Tech. Rep. 2653, Aug. 2012.

[10] Yunhui, S. and Qiuqi, R., Continuous wavelet transforms, Proc. 7th Int. Conf. Signal Process. 2004. Proceedings. ICSP ’04. 2004., vol. 1, pp. 207-210, 2004. DOI: 10.1109/ICOSP.2004.1452618[CrossRef]

[11] Li, H., Complex Morlet Wavelet Amplitude and Phase Map Based Bearing Fault Diagnosis no. 50775219, 2010 8th World Congress on Intelligent Control and Automation, pp. 6923-6926, 2010. DOI: 10.1109/WCICA.2010.5554232[CrossRef]

[12] Nieto, N. and Orozco, D., El uso de la transformada wavelet discreta en la reconstrucción de señales senosoidales, Scientia et technica, Vol. 1, No. 38, pp. 381-386, 2008. DOI: http://dx.doi.org/10.22517/23447214.3809 [Link]

[13] Butler, K.L. and Bagriyanik., M., Characterization of transients in transformers using discrete Wavelet Transformer. IEEE Transactions on Power Systems, Vol. 18, No. 2, pp. 648-656, Mayo 2003. DOI: 10.1109/TPWRS.2003.810979[CrossRef]

[14] Mallat, S., A Wavelet Tour of Signal Processing. A Wavelet Tour Signal Process. Third Edition. pp. 20-41, 1999.

[15] Leigh, G. M. Fast FIR Algorithms for the Continuous Wavelet Transform From Constrained Least Squares. IEEE Transactions on Signal Processing, Vol. 61, No. 1, January 1, 2013. DOI: 10.1109/TSP.2012.2222376[CrossRef]

[16] Robertson, D. C., Camps, O. I., Mayer, J. S., Gish, W. B., Wavelets and electromagnetic power system transients. IEEE Transactions on Power Delivery , Vol, 11. Abril de 1996. DOI: 10.1109/61.489367[CrossRef]

[17] Dwivedi, U. D. and Singh, S. N., Denoising techniques with change-point approach for wavelet-based power-quality monitoring. IEEE Trans. Power Deliv., vol. 24, no. 3, pp. 1719-1727, 2009. DOI: 10.1109/TPWRD.2009.2022665[CrossRef]

[18] Gomez-Luna, E., Aponte Mayor, G., Pleite Guerra, J., Silva Salcedo, D. F. and Hinestroza Gutierrez, D., Application of wavelet transform to obtain the frequency response of a transformer from transient signals-part 1: Theoretical analysis. IEEE Trans. Power Deliv. , vol. 28, no. 3, pp. 1709-1714, 2013. DOI: 10.1109/TPWRD.2013.2262058[CrossRef]

[19] Pleite, J., Olias, E., Barrado, a., Lazaro, a. and Vazquez, J., Transformer modeling for FRA techniques. IEEE/PES Transm. Distrib. Conf. Exhib., vol. 1, pp. 317-321, 2002. DOI: 10.1109/TDC.2002.1178342[CrossRef]

[20] Cortés, J. A., Cano-Garzón, H. B. and Chaves, J. A., Del análisis de Fourier a las Wavelets - Transformada continua wavelet (CWT). Sci. Tech., vol. XIII, no. 37, pp. 133-138, 2007. DOI: http://dx.doi.org/10.22517/23447214.4017 [Link]

[21] Montoya, F. G., Manzano-Agugliaro, F., López, J. G. and ALGUACIL, P. S., Técnicas De Investigación En Calidad Eléctrica: Ventajas E Inconvenientes. Dyna, vol. 79, no. 173, pp. 66-74, 2012.

[22] Gómez-Luna, E., Aponte, G. and Pleite, J., Sistema de obtención de la respuesta en frecuencia de máquinas eléctricas, Madrid España Patente ES-2534954_B1, February 09, 2016.

How to cite: Gómez-Luna, E., Cuartas-Bermúdez, J.S. and Marlés-Sáenz, E., Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation. DYNA, 85(205), pp. 105-110, June, 2018

Referencias

Gómez-Luna, E., Cuartas-bermúdez, J. S. and Marlés-sáenz, E., Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 1 : Theoretical analysis Wavelet y transformada de Fourier de señales transitorias. Parte 1: Análisis teórico DYNA vol. 84, no. 201, pp. 138–144, 2017. DOI: https://doi.org/10.15446/dyna.v84n201.58694

Krieg, T. and Napolitano, M., Techniques and experience in on-line transformer condition monitoring and fault diagnosis in ElectraNet SA. in Proc. IEEE Int. Conf. Power Syst. Technol. PowerCon Substation Maint.e Dept., 2000, vol. 2, pp. 1019–1024. DOI: 10.1109/ICPST.2000.897160

Mackenzie, E. A., Crossey, J., DePablo, A. and Ferguson, W., On-line monitoring and diagnostics for power transformers, in Proc. IEEE Int. Symp. Elect. Insul. Conf., 2010, pp. 1–5. DOI: 10.1109/ELINSL.2010.5549734

Gómez-Luna, E., Aponte, G., Gonzalez-Garcia, C. and Pleite, J., Current status and future trends in the Frequency Response Analysis (FRA) with the transformer in service, IEEE Trans. Power Del., vol. 28, no. 2, pp. 1024–1031, Apr. 2013. Research Group Gralta, Desarrollo. DOI: 10.1109/TPWRD.2012.2234141

Gómez-Luna, E., Silva, D., Aponte, G., Pleite, J. and Hinestroza, D., Obtaining the electrical impedance using wavelet transform from the time response, IEEE Transactions on Power Delivery, Vol. 28, No. 2, pp. 1242-1244, April 2013. DOI: 10.1109/TPWRD.2012.2234942

Krieg, T., and Napolitano, M., Techniques and experience in on-line transformer condition monitoring and fault diagnosis in ElectraNet SA, in Proc. IEEE Int. Conf. Power Syst. Technol. PowerCon Substation Maint.e Dept., 2000, vol. 2, pp. 1019–1024. DOI: 10.1109/ICPST.2000.897160

Gómez-Luna, E., Aponte, G. and Pleite, J., Application of Wavelet Transform to obtain the Frequency Response of a Transformer from Transient Signals – Part 2: Practical assessment and validation. IEEE Transactions on Power Delivery, Vol. 29, No. 5, pp. 2231 - 2238, October 2014. DOI: 10.1109/TPWRD.2013.2295377

Gomez-Luna, E., Obtención De La Respuesta En Frecuencia De Transformadores En Servicio a Partir De La Medida De Señales Transitorias. Tesis de Doctorado, Universidad del Valle. p. 95, 2013.

Research Group Gralta, Desarrollo de una prueba piloto para obtener la respuesta en frecuencia de un transformador en servicio, Universidad del Valle, Valle, Spain, Tech. Rep. 2653, Aug. 2012.

Yunhui, S. and Qiuqi, R., Continuous wavelet transforms, Proc. 7th Int. Conf. Signal Process. 2004. Proceedings. ICSP ’04. 2004., vol. 1, pp. 207–210, 2004. DOI: 10.1109/ICOSP.2004.1452618

Li, H., Complex Morlet Wavelet Amplitude and Phase Map Based Bearing Fault Diagnosis no. 50775219, pp. 6923–6926, 2010. DOI: 10.1109/WCICA.2010.5554232

Nieto, N. and Orozco, D., El uso de la transformada wavelet discreta en la reconstrucción de señales senosoidales, no. 38, pp. 381–386, 2008. DOI: http://dx.doi.org/10.22517/23447214.3809

Butler, K. L., Bagriyanik. M., Characterization of transients in transformers using discrete Wavelet Transformer. IEEE Transactions on Power Systems, Vol. 18, No. 2, pp. 648-656, Mayo 2003. DOI: 10.1109/TPWRS.2003.810979

Mallat, S., A Wavelet Tour of Signal Processing. A Wavelet Tour Signal Process. Third Edition. pp. 20–41, 1999.

Leigh, G. M. Fast FIR Algorithms for the Continuous Wavelet Transform From Constrained Least Squares. IEEE Transactions on Signal Processing, Vol. 61, No. 1, January 1, 2013. DOI: 10.1109/TSP.2012.2222376

Robertson, D. C., Camps, O. I., Mayer, J. S., Gish, W. B., Wavelets and electromagnetic power system transients. IEEE Transactions on Power Delivery, Vol, 11. Abril de 1996. DOI: 10.1109/61.489367

Dwivedi, U. D. and Singh, S. N., Denoising techniques with change-point approach for wavelet-based power-quality monitoring. IEEE Trans. Power Deliv., vol. 24, no. 3, pp. 1719–1727, 2009. DOI: 10.1109/TPWRD.2009.2022665

Gomez-Luna, E., Aponte Mayor, G., Pleite Guerra, J., Silva Salcedo, D. F. and Hinestroza Gutierrez, D., Application of wavelet transform to obtain the frequency response of a transformer from transient signals-part 1: Theoretical analysis. IEEE Trans. Power Deliv., vol. 28, no. 3, pp. 1709–1714, 2013. DOI: 10.1109/TPWRD.2013.2262058

Pleite, J., Olias, E., Barrado, a., Lazaro, a. and Vazquez, J., Transformer modeling for FRA techniques. IEEE/PES Transm. Distrib. Conf. Exhib., vol. 1, pp. 317–321, 2002. DOI: 10.1109/TDC.2002.1178342

Cortés, J. A., Cano-Garzón, H. B. and Chaves, J. A., Del análisis de Fourier a las Wavelets - Transformada continua wavelet (CWT). Sci. Tech., vol. XIII, no. 37, pp. 133–138, 2007. DOI: http://dx.doi.org/10.22517/23447214.4017

Montoya, F. G., Manzano-Agugliaro, F., López, J. G. and ALGUACIL, P. S., Técnicas De Investigación En Calidad Eléctrica: Ventajas E Inconvenientes. Dyna, vol. 79, no. 173, pp. 66–74, 2012.

Gómez-Luna, E., Aponte, G. and Pleite, J., Sistema de obtención de la respuesta en frecuencia de máquinas eléctricas, Madrid España Patente ES-2534954_B1, February 09, 2016.

Cómo citar

IEEE

[1]
E. Gómez-Luna, J. S. Cuartas-Bermúdez, y E. Marlés-Sáenz, «Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation», DYNA, vol. 85, n.º 205, pp. 105–110, abr. 2018.

ACM

[1]
Gómez-Luna, E., Cuartas-Bermúdez, J.S. y Marlés-Sáenz, E. 2018. Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation. DYNA. 85, 205 (abr. 2018), 105–110. DOI:https://doi.org/10.15446/dyna.v85n205.68458.

ACS

(1)
Gómez-Luna, E.; Cuartas-Bermúdez, J. S.; Marlés-Sáenz, E. Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation. DYNA 2018, 85, 105-110.

APA

Gómez-Luna, E., Cuartas-Bermúdez, J. S. y Marlés-Sáenz, E. (2018). Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation. DYNA, 85(205), 105–110. https://doi.org/10.15446/dyna.v85n205.68458

ABNT

GÓMEZ-LUNA, E.; CUARTAS-BERMÚDEZ, J. S.; MARLÉS-SÁENZ, E. Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation. DYNA, [S. l.], v. 85, n. 205, p. 105–110, 2018. DOI: 10.15446/dyna.v85n205.68458. Disponível em: https://revistas.unal.edu.co/index.php/dyna/article/view/68458. Acesso em: 17 mar. 2025.

Chicago

Gómez-Luna, Eduardo, Juan Sebastián Cuartas-Bermúdez, y Eduardo Marlés-Sáenz. 2018. «Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation». DYNA 85 (205):105-10. https://doi.org/10.15446/dyna.v85n205.68458.

Harvard

Gómez-Luna, E., Cuartas-Bermúdez, J. S. y Marlés-Sáenz, E. (2018) «Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation», DYNA, 85(205), pp. 105–110. doi: 10.15446/dyna.v85n205.68458.

MLA

Gómez-Luna, E., J. S. Cuartas-Bermúdez, y E. Marlés-Sáenz. «Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation». DYNA, vol. 85, n.º 205, abril de 2018, pp. 105-10, doi:10.15446/dyna.v85n205.68458.

Turabian

Gómez-Luna, Eduardo, Juan Sebastián Cuartas-Bermúdez, y Eduardo Marlés-Sáenz. «Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation». DYNA 85, no. 205 (abril 1, 2018): 105–110. Accedido marzo 17, 2025. https://revistas.unal.edu.co/index.php/dyna/article/view/68458.

Vancouver

1.
Gómez-Luna E, Cuartas-Bermúdez JS, Marlés-Sáenz E. Obtaining the electrical impedance phase using Wavelet transform and Fourier transform from transient signals. Part 2: practical assessment and validation. DYNA [Internet]. 1 de abril de 2018 [citado 17 de marzo de 2025];85(205):105-10. Disponible en: https://revistas.unal.edu.co/index.php/dyna/article/view/68458

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1. Jie Jin, Zhou Su, Yuehua Wei, Shi Lin. (2020). Online Estimation of Membrane Water Content in Vehicular PEMFC by Complex Morlet Wavelet Transformations. SAE International Journal of Advances and Current Practices in Mobility, 3(1), p.598. https://doi.org/10.4271/2020-01-2255.

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