Towards accurate estimation of fast varying frequency in future electricity networks: The transition from model-free methods to model-based approach

Abstract

Accurate estimation of fast varying fundamental frequency in the presence of harmonics and noise will be required for effective frequency regulation in future electricity networks with high penetration level of renewable energy sources. Two new algorithms for network frequency tracking are proposed. The first algorithm represents a robust modification of classical zero crossing method, which is widely used in industry. The second algorithm is a multiple model algorithm based on the systems with harmonic regressor. Algorithm allows complete reconstruction of the frequency content of the signal, using information about the upper bound of the number of harmonics only. Moreover, new family of high-order algorithms together with new stepwise splitting method are proposed for parameter calculation in systems with harmonic regressor for the accuracy improvement. Statistical methods are introduced for comparison of two new algorithms to classical zero crossing algorithm. The modified algorithm provides significant improvement compared to the classical algorithm, and the algorithm with harmonic regressor provides further improvement of the statistical performance indexes with respect to the modified algorithm.

Keywords

Accurate frequency tracking in future electricity networks harmonic regressor multiple model statistical quantification methods of comparison of algorithms high-order algorithms stepwise splitting inversion of ill-conditioned matrices

Get full access to this article

View all access options for this article.

References

Friedman

A zero crossing algorithm for the estimation of the frequency of a single sinusoid in white noise. IEEE T Signal Proces 1994; 42(6): 1565–1569.

Gupta

Thakur

Murarka

An efficient approach to zero crossing detection based on opto-coupler. Int J Eng Res Appl 2013; 3(5): 834–838.

Köhler

Hennig

Orglmeister

QRS detection using zero crossing counts. Prog Biomed Res 2003; 8(3): 138–145.

Grillo

Pasquino

Angrisani

. An efficient extension of the zero-crossing technique to measure frequency of noisy signals. In: Proceedings of the IEEE international instrumentation and measurement technology conference (I2MTC), Graz, Austria, 13–16 May 2012. New York: IEEE.

Wall

. Simple methods for detecting zero crossing. In: Proceedings of the 29th annual conference of the IEEE industrial electronics society (IECON ’03), Roanoke, VA, 2–6 November 2003, pp.10–30. New York: IEEE.

Duric

Durisic

. Combined Fourier and zero crossing technique for frequency measurement in power networks in the presence of harmonics. RE&PQJ 2010; 1(3): 463–469.

Jacobsen

Kootsookos

Fast, accurate frequency estimators. IEEE Signal Proc Mag 2007; 24(3): 123–125.

Kim

Ban

. A comparative study on frequency estimation methods. J Electr Eng Technol 2013; 8(1): 70–79.

Quinn

Hannan

The estimation and tracking of frequency, part of Cambridge series in statistical and probabilistic mathematics. Cambridge: Cambridge University Press, 2013.

10.

Bobtsov

Efimov

Pyrkin

. Switched algorithm for frequency estimation with noise rejection. IEEE T Automat Contr 2012; 57(9): 2400–2404.

11.

Chen

Parisini

. Robust sinusoid identification with structured and unstructured measurement uncertainties. IEEE T Automat Contr 2014; 59(6): 1588–1593.

12.

Belleter

Galeazzi

Fossen

Experimental verification of a global exponential stable nonlinear wave encounter frequency estimator. Ocean Eng 2015; 97: 48–56.

13.

Xia

Global frequency estimation using adaptive identifiers. IEEE T Automat Contr 2002; 47(7): 1188–1193.

14.

Stotsky

Frequency determination in control applications: excitation-based approach. Proc IMechE, Part I: J Systems and Control Engineering 2012; 226(8): 1142–1148.

15.

Walker

On the estimation of a harmonic component in a time series with stationary independent residuals. Biometrika 1971; 58(1): 21–36.

16.

T-H

. A fast algorithm for efficient estimation of frequencies. In: Proceedings of the signal processing IX: theories and applications: proceedings of EUSIPCO-98 (eds Theodoridis

Pitas

Stouraiti

Kalouptsidis

), Island of Rhodes, Greece: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, 8–10 August 1998, vol. 1, pp.65–68.

17.

Stotsky

Automotive engines: control, estimation, statistical detection. Berlin, Heidelberg: Springer-Verlag, 2009.

18.

Stotsky

Combined high-order algorithms in robust least-squares estimation with harmonic regressor and strictly diagonally dominant information matrix. Proc IMechE, Part I: J Systems and Control Engineering 2015; 229(2): 184–190.

19.

Stotsky

Accuracy improvement in least-squares estimation with harmonic regressor: new preconditioning and correction methods. In: Proceedings of the IEEE 54th annual conference on decision and control, Osaka, Japan, 15–18 December 2015, pp.4035–4040. New York: IEEE.

20.

Amdahl

Validity of the single processor approach to achieving large-scale computing capabilities. AFIPS Conf P 1967; 30: 483–485.

21.

Stotsky

Forgo

Recursive spline interpolation method for real-time engine control applications. Control Eng Pract 2004; 12: 409–416.

22.

Benzi

Preconditioning techniques for large linear systems: a survey. J Comput Phys 2002; 182: 418–477.

23.

Chen

Matrix preconditioning techniques and applications. Cambridge: Cambridge University Press, 2005.

24.

Horn

Johnson

Matrix analysis. Cambridge: Cambridge University Press, 1985.

25.

Durand

Solutions numeriques des equations algebriques, vol. 2. Paris: Masson, 1972.

26.

Gustafsson

Adaptive filtering and change detection. Hoboken, NJ: John Wiley & Sons, 2000.