### A Hybrid Water Cycle Algorithm-Least Square based Framework for Robust Estimation of

#### Abstract

*The power quality is becoming an extensively addressing aspect of power system because of sensitive operation of smart grid, awareness of power quality and modern power system equipment. This paper proposes a new hybrid framework of Water Cycle Algorithm-Least Square (WCA-LS) for estimation of harmonics present in time varying noisy power signals. Water Cycle Algorithm (WCA) is a population based algorithm which realizes the concepts of exploitation and exploration to find global optimal in search space under consideration. This algorithm exploits the concept of natural hydrologic cycle to perform heuristic optimization. In hydrologic cycle water flow in the form of streams, rivers and sea. When the rain falls from clouds and snow melts from glaciers, water flows downhill in the form of streams. When streams combine at one point they generate rivers which ultimately fall into the sea. Water from lakes is evaporated and the trees also transpire the water during photosynthesis process into atmosphere to generate clouds. These clouds release water back to the earth in the form of rains and precipitation to complete the cycle. The Proposed approach has been applied on test system from literature and results prove the effectiveness of technique in terms of precision and computational time. Results are further authenticated by estimating harmonics of real time voltage waveform of Axial Flux Parmanent Magnet Synchronous Generator (AFPMSG). The proposed WCA-LS delivers promising results compared to some of the state of art frameworks such as Genetic Algorithm (GA) and Particle Swarm Optimization with Passive Congregation based Least Square (PSOPC-LS). *

#### Full Text:

PDF#### References

S.K. Singh, N. Sinha, A.K. Goswami and N. Sinha, "Several variants of Kalman filter algorithm for power system harmonic estimation", Int. J. Electrical Power & Energy Systems, vol. 78, pp. 793-800, 2016.

T. Lobos, T. Kozina and H.-J. Koglin, "Power system harmonics estimation using linear least squares method and SVD, "Generation, Transmission and Distribution", IEE Proceedings, 2001, pp. 567-572.

S.K. Jain, P. Jain, and S.N. Singh, "A fast harmonic phasor measurement method for smart grid applications", IEEE Transactions on Smart Grid, vol. 8, pp. 493-502, 2017.

J.M. Guerrero, "Guest editorial special issue on power quality in smart grids", IEEE Transactions on Smart Grid, vol. 8, pp. 379-381, 2017.

B. Subudhi and P. Ray, "A hybrid adaline and bacterial foraging approach to power system harmonics estimation," International Conference on Industrial Electronics, Control & Robotics (IECR), pp. 236-242, 2010.

S.K. Jain and S. Singh, "Harmonics estimation in emerging power system: Key issues and challenges", Electric Power Systems Research, vol. 81, pp. 1754-1766, 2011.

E.A.A. Al-Feilat, I. El-Amin, and M. Bettayeb, "Power system harmonic estimation: a comparative study", Electric Power Systems Research, vol. 29, pp. 91-97, 1994.

M. Bettayeb and U. Qidwai, "Recursive estimation of power system harmonics", Electric Power Systems Research, vol. 47, pp. 143-152, 1998.

M. Bettayeb and U. Qidwai, "A hybrid least squares-GA-based algorithm for harmonic estimation", Power Delivery, IEEE Transactions on, vol. 18, pp. 377-382, 2003.

S. Mishra, "A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation", IEEE Transactions on Evolutionary Computation, , vol. 9, pp. 61-73, 2005.

T. Lobos, "Nonrecursive methods for real-time determination of basic waveforms of voltages and currents," in Generation, Transmission and Distribution, IEE Proceedings C, pp. 347-352, 1989.

J. Xi and J.F. Chicharo, "A new algorithm for improving the accuracy of periodic signal analysis", IEEE Transactions on Instrumentation and Measurement, vol. 45, pp. 827-831, 1996.

F. Siddiq and H. Jamal, T. Muhammad and M. Iqbal, "Area efficient radix 4 2 64 point pipeline FFT architecture using modified CSD multiplier", The Nucleus, vol. 51, pp. 345-353, 2014.

M.M. Ashraf et al. / The Nucleus 55, No. 2 (2018) 47-60

T.A. George and D. Bones, "Harmonic power flow determination using the fast Fourier transform", IEEE Transactions on Power Delivery, vol. 6, pp. 530-535, 1991.

T.X. Zhu, "Exact Harmonics/Interharmonics Calculation Using Adaptive Window Width", IEEE Transactions on Power Delivery, vol. 22, pp. 2279-2288, 2007.

P. Dash, D. Swain, A. Liew and S. Rahman, "An adaptive linear combiner for on-line tracking of power system harmonics", IEEE Transactions on Power Systems, vol. 11, pp. 1730-1735, 1996.

H. Ma and A.A. Girgis, "Identification and tracking of harmonic sources in a power system using a Kalman filter", IEEE Transactions on Power Delivery, vol. 11, pp. 1659-1665, 1996.

P. Dash and A. Sharaf, "A Kalman filtering approach for estimation of power system harmonics", Proc. 3rd Int. Conf. on Harmonics Power Syst, pp. 34-40, 1988.

P.K. Ray and B. Subudhi, "Ensemble-Kalman-Filter-Based power system harmonic estimation", IEEE Transactions on Instrumentation and Measurement, vol. 61, pp. 3216-3224, 2012.

A. Pradhan, A. Routray and A. Basak, "Power system frequency estimation using least mean square technique", IEEE Transactions on Power Delivery, vol. 20, pp. 1812-1816, 2005.

R.H. Kwong and E.W. Johnston, "A variable step size LMS algorithm", IEEE Transactions on Signal Processing, vol. 40, pp. 1633-1642, 1992.

S. Soliman, A. Al-Kandari, K. El-Nagar, and M. El-Hawary, "New dynamic filter based on least absolute value algorithm for on-line tracking of power system harmonics", IEE Proceedings in Generation, Transmission and Distribution, pp. 37-44, 1995.

S.K. Singh, N. Sinha, A.K. Goswami and N. Sinha, "Variable Constraint based Least Mean Square algorithm for power system harmonic parameter estimation", International Journal of Electrical Power & Energy Systems, vol. 73, pp. 218-228, 2015.

M. Ashraf, M.O. Ullah, T. Malik, A. Waqas, M. Iqbal and F. Siddiq, "Robust extraction of harmonics using heuristic advanced gravitational search algorithm-based least square estimator", The Nucleus, vol. 54, pp. 219-231, 2017.

Z. Lu, T. Ji, W. Tang and Q. Wu, "Optimal harmonic estimation using a particle swarm optimizer", IEEE Transactions on Power Delivery, vol. 23, pp. 1166-1174, 2008.

T. Ji, M. Li, Q. Wu and L. Jiang, "Optimal estimation of harmonics in a dynamic environment using an adaptive bacterial swarming algorithm", Generation, Transmission & Distribution, IET, vol. 5, pp. 609-620, 2011.

S.K. Singh, A.K. Goswami and N. Sinha, "Harmonic parameter estimation of a power signal using FT-RLS algorithm", IEEE 16th International Conference on Harmonics and Quality of Power (ICHQP), , pp. 157-161, 2014.

S.K. Singh, N. Sinha, A.K. Goswami and N. Sinha, "Optimal estimation of power system harmonics using a hybrid firefly algorithm-based least square method", Soft Computing, vol. 21, pp. 1-14, 2015.

V.M. Saiz and J.B. Guadalupe, "Application of Kalman filtering for continuous real-time tracking of power system harmonics", Generation, Transmission and Distribution, IEE Proceedings, pp. 13-20, 1997.

S.K. Singh, N. Sinha, A.K. Goswami and N. Sinha, "Robust estimation of power system harmonics using a hybrid firefly based recursive least square algorithm", Int. J. Electrical Power & Energy Systems, vol. 80, pp. 287-296, 2016.

X.-S. Yang, "Nature-inspired metaheuristic algorithms", University of Cambridge, United Kingdom: Luniver press, 2010.

X. Yang, "An Introduction with Metaheuristic Applications", Ed. Hoboken, New Jersey, USA: John Wiley & Sons, 2010.

Z. Shuai, J. Zhang, L. Tang, Z. Teng and H. Wen, "Frequency shifting and filtering algorithm for power system harmonic estimation," IEEE Transactions on Industrial Informatics, 2018.

Y. Kabalci, S. Kockanat and E. Kabalci, "A modified ABC algorithm approach for power system harmonic estimation problems", Electric power systems research, vol. 154, pp. 160-173, 2018.

S.K. Singh, D. Kumari, N. Sinha, A.K. Goswami and N. Sinha, "Gravity search algorithm hybridized recursive least square method for power system harmonic estimation", Int. J. Engg. Sci. and Tech., vol. 20, pp. 874-884, 2017.

Y. Kabalci, S. Kockanat and E. Kabalci, "A differential search algorithm application for solving harmonic estimation problems", 9th International Conference on Electronics, Computers and Artificial Intelligence (ECAI), pp. 1-5, 2017.

H. Eskandar, A. Sadollah, A. Bahreininejad and M. Hamdi, "Water cycle algorithm–A novel metaheuristic optimization method for solving constrained engineering optimization problems", Computers & Structures, vol. 110, pp. 151-166, 2012.

J. Rice, "Mathematical statistics and data analysis", Belmont, USA: Nelson Education, 2006.

S.K. Singh, N. Sinha, A.K. Goswami and N. Sinha, "Power system harmonic estimation using biogeography hybridized recursive least square algorithm", Int. J. Electrical Power & Energy Systems, vol. 83, pp. 219-228, 2016.

P.K. Ray and B. Subudhi, "BFO optimized RLS algorithm for power system harmonics estimation", Applied Soft Computing, vol. 12, pp. 1965-1977, 2012.

S. Biswas, A. Chatterjee, and S. K. Goswami, "An artificial bee colony-least square algorithm for solving harmonic estimation problems", Applied Soft Computing, vol. 13, pp. 2343-2355, 2013.

S. He, Q. Wu, J. Wen, J. Saunders and R. Paton, "A particle swarm optimizer with passive congregation", Biosystems, vol. 78, pp. 135-147, 2004.

M.M. Ashraf, T.N. Malik and M. Iqbal, "Peak load sharing based on blade pitch control of wind turbine in the presence of utility supply", Journal of Renewable and Sustainable Energy, vol. 6, p. 013110, 2014.

M.M. Ashraf, T.N. Malik, S. Zafar and U.N. Raja, "Design and fabrication of radial flux permanent magnet generator for wind turbine applications", The Nucleus, vol. 50, pp. 173-181, 2013.

M.M. Ashraf and T.N. Malik, "A modified model of axial flux permanent magnet generator for wind turbine applications," Nucleus, vol. 51, pp. 391-395, 2014.

M.M. Ashraf, T.N. Malik and M. Iqbal, "Development of a prototype micro wind energy system with adjustable blade pitch for experimentation purposes at laboratory level", The Nucleus, vol. 51, pp. 75-86, 2014.

J.F. Gieras, R.-J. Wang and M.J. Kamper, "Axial flux permanent magnet brushless machines", Springer Science & Business Media, 2008.

M.M. Ashraf and T.N. Malik, "Design of three-phase multi-stage axial flux permanent magnet generator for wind turbine applications", Turkish Journal of Electrical Engineering and Computer Sciences, vol. 25, pp. 520-538, 2017.

### Refbacks

- There are currently no refbacks.

## Comments on this article

by mr lee234 (2019-01-15)