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


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.

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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


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


Random number between “0” and “1”

iter :


iter max :

Maximum iteration


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Correspondence to Asghar Akbari Foroud.

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Appendix 1

Appendix 1

Table 9 Data of the IEEE 18-bus test system

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Moradifar, A., Akbari Foroud, A. & Gorgani Firouzjah, K. Comprehensive identification of multiple harmonic sources using fuzzy logic and adjusted probabilistic neural network. Neural Comput & Applic 31 (Suppl 1), 543–556 (2019).

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