Digital Metering of Electrical Power Components Using Adaptive Non-Uniform Discrete Short Time Fourier Transform
-
Soumyajit Goswami
,
Arghya Sarkar
Abstract
This paper presents an adaptive Goertzel filter bank based discrete short time Fourier transform (DSTFT) implementation algorithm, called adaptive non-uniform discrete short time Fourier transform (ANDSTFT) for online measurement of electrical power components using IEEE Standard 1459–2010. The proposed ANDSTFT algorithm utilizes effective combination of non-uniform discrete Fourier transform (NDFT) and window method to detect the spectrum of each individual finite short time segment of power signals at distinct, arbitrarily located frequencies. Compared with the well-established technique such as windowed FFT interpreted DSTFT based approaches, the proposed method offers (i) better accuracy (ii) higher degree of immunity and insensitivity to noise, and (iii) reduced computational complexity per sample interval. The simulation results have been given and its response time and accuracy have been compared with the conventional windowed FFT interpreted DSTFT based techniques. Real-time implementation of the proposed approach has also been presented.
Nomenclature
- eP
-
modulus of percent error in P
- eQ
-
modulus of percent error in QB
- eS
-
modulus of percent error in S
- f
-
fundamental frequency of power system signals
- fs
-
sampling frequency
- i (t)
-
instantaneous current of single-phase system
- i 1
-
power system frequency component of single-phase current signal
- Irms
-
rms current of single-phase system
- I 1
-
fundamental rms current of single-phase system
- iH
-
harmonic components of single-phase current signal
- IH
-
harmonic rms current of single-phase system
- Ih
-
single-phase rms current at hth harmonic
- N
-
window length
- Nint
-
nearest integer number of samples
- n
-
number of samples
- P
-
total active power
- P 1
-
fundamental active power
- PH
-
harmonic active power
- PN
-
nonactive power
- Q
-
total reactive power
- Q 1
-
fundamental reactive power
- QB
-
Budeanu’s reactive power
- S
-
total apparent power
- S 1
-
fundamental apparent power
- SN
-
nonfundamental apparent power
- t
-
time
- T
-
time period
- Vrms
-
rms voltage of single-phase system
- v(t)
-
instantaneous voltage of single-phase system
- v 1
-
power system frequency component of single-phase voltage signal
- V 1
-
fundamental rms voltage of single-phase system
- vH
-
harmonic components of single-phase voltage signal
- VH
-
harmonic rms voltage of single-phase system
- Vh
-
single-phase rms voltage at hth harmonic
- α 1
-
fundamental voltage phase angle single-phase system
- αh
-
voltage phase angle of single-phase system at hth harmonic
- β 1
-
fundamental current phase angle of single-phase system
- βh
-
current phase angle of single-phase system at hth harmonic
- ω1
-
fundamental angular frequency
- ξF[n]
-
zero mean random noise of s[n]
Appendix
Flow Chart of the ANDSTFT Implementation Algorithm
References
[1] IEEE standard definitions for the measurement of electric power quantities under sinusoidal, nonsinusoidal, balanced or unbalanced conditions. IEEE Standard, Mar 2010:1459–2010.Search in Google Scholar
[2] Pejic D, Naumovic-Vukovic D, Vujicic B, Radonjic A, Sovilj P, Vujicic V. Stochastic digital DFT processor and its application to measurement of reactive power and energy. Meas. 2018;124:494–504.10.1016/j.measurement.2018.04.004Search in Google Scholar
[3] Zhuang S, Zhao W, Wang Q, Huang S. Four harmonic analysis and energy metering algorithms based on a new cosine window function. Journal Eng. 2017;2017:2678–84.10.1049/joe.2017.0845Search in Google Scholar
[4] Ferreira SC, Gonzatti RB, Silva CH, da Silva LE, Pereira RR, Lambert-Torres G. Adaptive real-time power measurement based on IEEE standard 1459–2010. Electr Power Compon Syst. 2015;43:1307–17.10.1080/15325008.2015.1027425Search in Google Scholar
[5] Jain NL, Priyanka R, Keerthy P, Maya P, Babu P. Empirical wavelet transform for harmonic detection under dynamic condition. In: Circuit, Power and Computing Technologies (ICCPCT), 2017 International Conference on. IEEE, Apr 2017:1–5.10.1109/ICCPCT.2017.8074357Search in Google Scholar
[6] Saleh SA. The extended Newton-phaselet method for determining the reactive power from the active power in single-phase systems. IEEE Trans Ind Appl. 2016;52:1297–307.10.1109/IAS.2015.7356946Search in Google Scholar
[7] Carugati I, Orallo CM, Donato PG, Maestri S, Strack JL, Carrica D. Three-phase harmonic and sequence components measurement method based on mSDFT and variable sampling period technique. IEEE Trans Instrum Meas. 2016;65:1761–72.10.1109/TIM.2016.2552679Search in Google Scholar
[8] Goswami S, Sarkar A, Sengupta S. Power components measurement using S-ADALINE. Int J Eng Innovations Res (IJEIR). 2017;6:120–6.Search in Google Scholar
[9] De Jesus MA, Teixeira M, Vicente L, Rodriguez Y. Nonuniform discrete short-time fourier transform a goertzel filter bank versus a FIR filtering approach. In: Circuits and Systems, 2006. MWSCAS’06. 49th IEEE International Midwest Symposium on. vol. 2. IEEE, 2006:188–92.10.1109/MWSCAS.2006.382241Search in Google Scholar
[10] Sarkar A, Sengupta S. The nonuniform discrete short time fourier transform – a new tool for electrical power components’ monitoring. In: Processing Joint International Conference on Power System Technology and IEEE Power India Conference (POWERCON 2008). New Delhi, India, Oct 2008:1–8.10.1109/ICPST.2008.4745203Search in Google Scholar
[11] Sarkar A, Sengupta S. Bandpass second-degree digital-integrator-based power system frequency estimation under nonsinusoidal conditions. Instrum Meas IEEE Trans Instrum Meas. 2011;60:846–53.10.1109/TIM.2009.2036467Search in Google Scholar
[12] Wen H, Li C, Yao W. Power system frequency estimation of sine-wave corrupted with noise by windowed three-point interpolated DFT. IEEE Trans Smart Grid. 2017;9:5163–72.10.1109/TSG.2017.2682098Search in Google Scholar
[13] Bagchi S, Mitra SK. The nonuniform discrete Fourier transform and its applications in signal processing. Springer Science & Business Media, 2012.Search in Google Scholar
[14] Jaiswal S, Ballal MS. FDST-based PQ event detection and energy metering implementation on FPGA-in-the-loop and NI-LabVIEW. IET Sci Meas Technol. 2017;11:453–63.10.1049/iet-smt.2016.0481Search in Google Scholar
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Articles in the same Issue
- Research Articles
- A Real Time Price Based Demand-Response Algorithm for Smart Grids
- Enhanced Model Predictive Current Control Based on Runge–Kutta Approximation for a Voltage Source Inverter
- A Multi-criteria Approach for Distribution Network Expansion Through Pooled MCDEA and Shannon Entropy
- Digital Metering of Electrical Power Components Using Adaptive Non-Uniform Discrete Short Time Fourier Transform
- Algorithm for Determining the State of Impregnated Paper Insulation of High-Voltage Cables
- Experimental and Estimation of Flashover Voltage of Outdoor High Voltage Insulators with Silica Filler Based on Grey Wolf Optimizer
- Investigation of the Temperature Effect on the Electrical Parameters of a Photovoltaic Module at Ouargla City
- Selection of an Efficient Linear State Estimator for Unified Real Time Dynamic State Estimation in Indian Smart Grid
- Impact of Harmonics on Power Transformer Losses and Capacity Using Open DSS
- Voltage Control Methods in the MV Grid with a Large Share of PV
- PV-Battery Hybrid System with Less AH Capacity for Standalone DC Loads
