# Comprehensive identification of multiple harmonic sources using fuzzy logic and adjusted probabilistic neural network

- 111 Downloads

## Abstract

This paper presents a comprehensive approach based on fuzzy logic and probabilistic neural network (PNN) to identify location, relative level, and type of multiple harmonic sources in power distribution systems. The location and relative level of harmonic sources were determined in the fuzzy stage by interpreting harmonic powers together with network impedances. Then, the type of the harmonic sources was classified in the neural stage using adjusted PNN. In the proposed method, the harmonic powers were considered as classification features. Then, ReliefF feature selection method was used to reduce the redundant data and dimension of features vector. A new modified adaptive imperialist competitive algorithm (MAICA) was proposed to determine the only adjusted parameter of the PNN classifier. Furthermore, a deep belief network (DBN) was applied in the neural stage, and its results were compared with the PNN classifier. The proposed approach was evaluated on IEEE 18-bus and IEEE 69-bus test systems. Unlike the single point methods, the presented method provides information on multiple harmonic sources in the whole of the distribution system. The results show that the comprehensive approach identifies the multiple harmonic sources with high accuracy.

## Keywords

Fuzzy logic Probabilistic neural network Multiple harmonic sources Comprehensive approach Imperialist competitive algorithm## Nomenclature

*h*Index of harmonic order

*b*,*n*Indices of all busses

*r*,*i*Indices of real and imaginary parts of mathematical symbols

*H*Highest order harmonic

*B*Number of busses

- \( {\left({I}_b^h\right)}_{NLL} \)
Harmonic current of NLL at bus

*b*- \( {\left({I}_b^{h, r}\right)}_{NLL} \)
Real harmonic current of NLL at bus

*b*- \( {\left({I}_b^{h, i}\right)}_{NLL} \)
Imaginary harmonic current of NLL at bus

*b*- \( {\left({I}_b^h\right)}_{b us} \)
Injected harmonic into the system from bus

*b*- \( {V}_b^h \)
Harmonic voltage at bus

*b*- \( {y}_{b, n}^h \)
Admittance of line connecting the busses

*b*and*n*- \( {Z}_{b, b}^h \)
Diagonal element of network impedance matrix

- \( {Z}_{b, b}^{h, r} \)
Real part of harmonic impedance at bus

*b*- \( {Z}_{b, b}^{h, i} \)
Imaginary part of harmonic impedance at bus

*b*- \( {\mathrm{z}}_{\mathrm{b},0}^{\mathrm{h},\mathrm{i}} \)
Imaginary part of impedance between bus

*b*and ground- L, C
Inductance and capacitance

- \( {S}_b^h \)
Harmonic power at bus

*b*- \( {P}_b^h \)
Real harmonic power at bus

*b*- \( {Q}_b^h \)
Imaginary harmonic power at bus

*b**HLI*Harmonic localization index

- \( \overline{\overline{HLI}} \)
Maximum harmonic localization index

*col*Colony position

*imp*Imperialist position

*c*Index of all colonies

*e*Index of all imperialists

*β*Assimilation coefficients

*β*_{1},*β*_{2}Internal and external assimilation coefficients

*β*_{2b},*β*_{2w}External assimilation coefficients of the best and worst imperialist

- rand
Random number between “0” and “1”

*iter*Iteration

*iter*_{max}Maximum iteration

## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## References

- 1.McGranaghan MF, Dugan R, Bety HW (2012) Electrical power systems quality, 3rd edn. McGraw-Hill Professional, New YorkGoogle Scholar
- 2.Bayındır KÇ, Cuma MU, Tümay M (2006) Hierarchical neuro-fuzzy current control for a shunt active power filter. Neural Comput Appl 15(3–4):223–238Google Scholar
- 3.Li C, Xu W, Tayjasanant T (2004) A “critical impedance”-based method for identifying harmonic sources. IEEE Trans Power Deliv 19(2):671–678CrossRefGoogle Scholar
- 4.Farhoodnea M, Mohamed A, Shareef H, Zayandehroodi H (2012) An enhanced method for contribution assessment of utility and customer harmonic distortions in radial and weakly meshed distribution systems. Int J Electr Power Energy Syst 43(1):222–229CrossRefGoogle Scholar
- 5.Xu W, Liu Y (2000) A method for determining customer and utility harmonic contributions at the point of common coupling. IEEE Trans Power Deliv 15(2):804–811Google Scholar
- 6.Emanuel AE (1995) On the assessment of harmonic pollution [of power systems]. IEEE Trans Power Deliv 10(3):1693–1698CrossRefGoogle Scholar
- 7.Omran WA, El-Goharey HS, Kazerani M, Salama M (2009) Identification and measurement of harmonic pollution for radial and nonradial systems. IEEE Trans Power Deliv 24(3):1642–1650CrossRefGoogle Scholar
- 8.Barbaro PV, Cataliotti A, Cosentino V, Nuccio S (2007) A novel approach based on nonactive power for the identification of disturbing loads in power systems. IEEE Trans Power Deliv 22(3):1782–1789CrossRefGoogle Scholar
- 9.Murugan A, Kumar VS (2016) Determining true harmonic contributions of sources using neural network. Neurocomputing 173:72–80CrossRefGoogle Scholar
- 10.Srinivasan D, Ng WS, Liew AC (2006) Neural-network-based signature recognition for harmonic source identification. IEEE Trans Power Deliv 21(1):398–405CrossRefGoogle Scholar
- 11.Huang C-H, Lin C-H (2015) Multiple harmonic-source classification using a self-organization feature map network with voltage–current wavelet transformation patterns. Appl Math Model 39(19):5849–5861MathSciNetCrossRefGoogle Scholar
- 12.De Paula Silva SF, De Oliveira JC (2008) The sharing of responsibility between the supplier and the consumer for harmonic voltage distortion: a case study. Electr Power Syst Res 78(11):1959–1964CrossRefGoogle Scholar
- 13.Stevanović D, Petković P (2014) A single-point method based on distortion power for the detection of harmonic sources in a power system. Metrol Meas Syst 21(1):3–14CrossRefGoogle Scholar
- 14.D’Antona G, Muscas C, Sulis S (2009) State estimation for the localization of harmonic sources in electric distribution systems. IEEE Trans Instrum Meas 58(5):1462–1470CrossRefGoogle Scholar
- 15.Ujile A, Ding Z (2016) A dynamic approach to identification of multiple harmonic sources in power distribution systems. Int J Emerg Electr Power Syst 81:175–183CrossRefGoogle Scholar
- 16.Yu KK, Watson NR, Arrillaga J (2005) An adaptive Kalman filter for dynamic harmonic state estimation and harmonic injection tracking. IEEE Trans Power Deliv 20(2):1577–1584CrossRefGoogle Scholar
- 17.Farhoodnea M, Mohamed A, Shareef H (2010) Identification of multiple harmonic sources in power systems using independent component analysis and mutual information. Int J Eng Intell Syst Electr Eng Commun 18(1):51Google Scholar
- 18.Gursoy E, Niebur D (2009) Harmonic load identification using complex independent component analysis. IEEE Trans Power Deliv 24(1):285–292CrossRefGoogle Scholar
- 19.Saxena D, Bhaumik S, Singh S (2014) Identification of multiple harmonic sources in power system using optimally placed voltage measurement devices. IEEE Trans Ind Electron 61(5):2483–2492CrossRefGoogle Scholar
- 20.Lin W-M, Lin C-H, Tu K-P, Wu C-H (2005) Multiple harmonic source detection and equipment identification with cascade correlation network. IEEE Trans Power Deliv 20(3):2166–2173CrossRefGoogle Scholar
- 21.Mohamed A, Hussain A, Umeh KC, Mohamed R (2006) A rule based expert system for identification of harmonics originating from single phase nonlinear loads. Int J Emerg Electr Power Syst 7(2):1–14Google Scholar
- 22.Mirzaei M, Ab. Kadir MZA, Hizam H, Moazami E (2011) Comparative analysis of probabilistic neural network, radial basis function, and feed-forward neural network for fault classification in power distribution systems. Electr Power Compon Syst 39(16):1858–1871CrossRefGoogle Scholar
- 23.Hosseini S, Al Khaled A (2014) A survey on the imperialist competitive algorithm metaheuristic: implementation in engineering domain and directions for future research. Appl Soft Comput 24:1078–1094CrossRefGoogle Scholar
- 24.Hosseini S, Al Khaled A, Vadlamani S (2014) Hybrid imperialist competitive algorithm, variable neighborhood search, and simulated annealing for dynamic facility layout problem. Neural Comput Appl 25(7–8):1871–1885CrossRefGoogle Scholar
- 25.Al Khaled A, Hosseini S (2015) Fuzzy adaptive imperialist competitive algorithm for global optimization. Neural Comput Appl 26(4):813–825CrossRefGoogle Scholar
- 26.Moradi Far A, Akbari Foroud A (2016) Cost-effective optimal allocation and sizing of active power filters using a new fuzzy-MABICA method. IETE J Res 62(3):307–322CrossRefGoogle Scholar
- 27.Hosseini S, Khaled A, Jin M (2012) Solving Euclidean minimal spanning tree problem using a new meta-heuristic approach: imperialist competitive algorithm (ICA). In: Industrial Engineering and Engineering Management (IEEM), 2012 I.E. International Conference on. IEEE, pp 176–181Google Scholar
- 28.Hinton GE, Osindero S, Teh Y-W (2006) A fast learning algorithm for deep belief nets. Neural Comput 18(7):1527–1554MathSciNetCrossRefzbMATHGoogle Scholar
- 29.Jiang M, Liang Y, Feng X, Fan X, Pei Z, Xue Y, Guan R (2016) Text classification based on deep belief network and softmax regression. Neural Comput Appl:1–10Google Scholar
- 30.Yin J, Lv J, Sang Y, Guo J (2016) Classification model of restricted Boltzmann machine based on reconstruction error. Neural Comput Appl:1–16Google Scholar
- 31.Spolaôr N, Cherman EA, Monard MC, Lee HD (2012) Filter approach feature selection methods to support multi-label learning based on relieff and information gain. In: Advances in Artificial Intelligence-SBIA 2012. Springer, New York, pp 72–81Google Scholar
- 32.Robnik-Šikonja M, Kononenko I (2003) Theoretical and empirical analysis of ReliefF and RReliefF. Mach Learn 53(1–2):23–69CrossRefzbMATHGoogle Scholar
- 33.Grady WM (2012) Understanding Power System harmonics. https://web.ecs.baylor.edu/faculty/grady/Understanding_Power_System_Harmonics_Grady_April_2012.pdf. Accessed 20 March 2017
- 34.Moradifar A, Soleymanpour HR (2012) A fuzzy based solution for allocation and sizing of multiple active power filters. J Power Electron 12:830–841CrossRefGoogle Scholar
- 35.Zimmermann HJ (2013) Fuzzy set theory—and its applications. Springer Science & Business Media, New YorkGoogle Scholar
- 36.Kusy M, Zajdel R (2015) Application of reinforcement learning algorithms for the adaptive computation of the smoothing parameter for probabilistic neural network. IEEE Trans Neural Netw Learn Syst 26(9):2163–2175MathSciNetCrossRefGoogle Scholar
- 37.Hunter A (2000) Feature selection using probabilistic neural networks. Neural Comput Appl 9(2):124–132CrossRefGoogle Scholar
- 38.Fooladi M, Foroud AA (2016) Recognition and assessment of different factors which affect flicker in wind turbines. IET Renew Power Gener 10(2):250–259CrossRefGoogle Scholar
- 39.Shirazi AZ, Mohammadi Z (2016) A hybrid intelligent model combining ANN and imperialist competitive algorithm for prediction of corrosion rate in 3C steel under seawater environment. Neural Comput Appl:1–10Google Scholar
- 40.Valverde Mora GA (2012) Uncertainty and state estimation of power systems. PHD thesis, The University of Manchester, ManchesterGoogle Scholar