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Design and analysis of BFOA-optimized fuzzy PI/PID controller for AGC of multi-area traditional/restructured electrical power systems

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Abstract

In this paper, design and performance analysis of bacterial foraging optimization algorithm (BFOA)-optimized fuzzy PI/PID (FPI/FPID) controller for automatic generation control of multi-area interconnected traditional/restructured electrical power systems is presented. Firstly a traditional two-area non-reheat thermal system is considered, and gains of the fuzzy controller are tuned employing BFOA using integral of squared error objective function. The supremacy of this controller is demonstrated by juxtaposing the results with particle swarm optimization (PSO), firefly algorithm (FA), BFOA, hybrid BFOA–PSO-based PI and fuzzy PI controllers based upon pattern search (PS) and PSO algorithms for the same power system structure. The approach is then extended to a two-area reheat system, and improved results are found with the purported FPI/FPID controller in comparison with PSO and artificial bee colony optimized PI controller. Further, the approach is implemented on a traditional multi-source multi-area (MSMA) hydrothermal system and its superb performance is observed over genetic algorithm and hybrid FA–PS tuned PI controller. Additionally, to demonstrate the scalability of the designed controller to cope with restructured power system, the study is also protracted to a restructured MSMA hydrothermal power system. Finally, sensitivity analysis is performed to ascertain the robustness of the controller designed for the systems under study. It is observed that the suggested FPI/FPID controller optimized for nominal conditions is able to handle generation rate constraints and wide variations in nominal loading condition as well as system parameters.

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Correspondence to Yogendra Arya.

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Funding

This study was not funded by any organization.

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The authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by V. Loia.

Appendix: Nomenclature and system data ( Chandrakala et al. 2013; Ali and Abd-Elazim 2011; Gozde et al. 2010

Appendix: Nomenclature and system data ( Chandrakala et al. 2013; Ali and Abd-Elazim 2011; Gozde et al. 2010

i :

Subscript referring to area-i (\(i = 1,2\))

\(\hbox {ACE}_{i}\) :

Area control error

\(P_\mathrm{ri}\) :

2000 MW; rated area capacity

\(\alpha _{12}\) :

\(-1(=\!-P_{r1} /P_{r2})\); area size ratio coefficient

\(F^{0}\) :

60 Hz; nominal system frequency

\(D_{i}\) :

0.00833 puMW/Hz (\(=\!\!\partial P_\mathrm{Li}/\partial FP_\mathrm{ri}\)); system damping constant

\(R_{i}\) :

2.4 Hz/puMW, \(R_{1} = 2 \hbox { Hz/puMW}\) for TMSMA/RMSMA; governor regulation parameter

\(\beta _{i}\) :

\(D_{i} + 1/R_{i}\) puMW/Hz; area frequency response characteristic (AFRC)

\(B_{i}\) :

\(0.425 (=\!\beta _{i})\); frequency bias constant

\(H_{i}\) :

5 s; power system inertia constant

\(K_\mathrm{PSi}\) :

120 (\(=1/D_{i}\)), 100 for TMSMA/RMSMA; power system gain

\(T_\mathrm{PSi}\) :

\(20 \hbox { s} (=\!2 H_{i}/ F^{0} D_{i})\); power system time constant

\(\delta _{i}\) :

\(30^{0}\left( {\delta _{12} =\delta _1 -\delta _2 } \right) , \, 45^{0}\) for TMSMA/RMSMA; nominal phase angle of voltages

\(\hbox {Ptie}_{\mathrm{max}}\) :

\(0.1 P_{ri} \hbox { MW}\); maximum tie-line capacity

\(T_{12}\) :

0.086 puMW/rad for reheat system, 0.0707 puMW/rad for TMSMA/RMSMA; synchronizing coefficient

\(2\pi T_{12}\) :

0.545 puMW/Hz for non-reheat system; tie-line power synchronizing coefficient

\(K_\mathrm{ri}\) :

0.5; high pressure thermal turbine power fraction

\(\hbox {cpf}_{ij}\) :

Contract participation factor of jth DISCO with ith GENCO

\(T_\mathrm{ri}\) :

10 s; reheat thermal turbine time constant

\(T_\mathrm{Gi}\) :

0.08 s; speed governor time constant

\(T_\mathrm{Ti}\) :

0.3 s; thermal turbine time constant

\(T_\mathrm{Ri}\) :

5 s; hydro turbine speed governor reset time

\(T_\mathrm{RHi}\) :

48.7 s; hydro turbine speed governor transient droop time constant

\(T_\mathrm{Wi}\) :

1 s; water starting time constant

\(\Delta P_\mathrm{UCi}\) :

Incremental change in uncontracted load power demanded by DISCO

\(T_\mathrm{GHi}\) :

0.513 s; hydro turbine speed governor main servo time constant

\(\Delta P_\mathrm{Di}\) :

Incremental change in load power demand in an area

\(\Delta F_\mathrm{i}\) :

Incremental change in the area frequency

\(\Delta P_\mathrm{Ci}\) :

Incremental change in the speed changer position

\(\Delta P_\mathrm{gi}\) :

Incremental change in area power generation

\(\Delta P_\mathrm{Gi}\) :

Incremental change in GENCO output

p :

Number of parameters to be optimized

S :

Number of bacteria

\(N_{S}\) :

Swimming length after which tumbling of bacteria will be carry out in a chemotactic loop

\(N_{C}\) :

Number of iterations to be undertaken in a chemotactic loop \((N_{C} > N_{S})\)

\(N_\mathrm{re}\) :

Maximum number of reproduction to be carry out

\(N_{\mathrm{ed}}\) :

Maximum number of elimination–dispersal events

\(P_{\mathrm{ed}}\) :

Probability with which elimination–dispersal will go on

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Arya, Y., Kumar, N. Design and analysis of BFOA-optimized fuzzy PI/PID controller for AGC of multi-area traditional/restructured electrical power systems. Soft Comput 21, 6435–6452 (2017). https://doi.org/10.1007/s00500-016-2202-2

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