Design of a Proportional-Integral-Derivative Controller for an Automatic Generation Control of Multi-area Power Thermal Systems Using Firefly Algorithm
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摘要
Essentially, it is significant to supply the consumer with reliable and sufficient power. Since, power quality is measured by the consistency in frequency and power flow between control areas. Thus, in a power system operation and control,automatic generation control(AGC) plays a crucial role. In this paper, multi-area(Five areas: area 1, area 2, area 3, area 4 and area 5) reheat thermal power systems are considered with proportional-integral-derivative(PID) controller as a supplementary controller. Each area in the investigated power system is equipped with appropriate governor unit, turbine with reheater unit, generator and speed regulator unit. The PID controller parameters are optimized by considering nature bio-inspired firefly algorithm(FFA). The experimental results demonstrated the comparison of the proposed system performance(FFA-PID)with optimized PID controller based genetic algorithm(GAPID) and particle swarm optimization(PSO) technique(PSOPID) for the same investigated power system. The results proved the efficiency of employing the integral time absolute error(ITAE) cost function with one percent step load perturbation(1 % SLP) in area 1. The proposed system based FFA achieved the least settling time compared to using the GA or the PSO algorithms, while, it attained good results with respect to the peak overshoot/undershoot. In addition, the FFA performance is improved with the increased number of iterations which outperformed the other optimization algorithms based controller.
Essentially, it is significant to supply the consumer with reliable and sufficient power. Since, power quality is measured by the consistency in frequency and power flow between control areas. Thus, in a power system operation and control,automatic generation control(AGC) plays a crucial role. In this paper, multi-area(Five areas: area 1, area 2, area 3, area 4 and area 5) reheat thermal power systems are considered with proportional-integral-derivative(PID) controller as a supplementary controller. Each area in the investigated power system is equipped with appropriate governor unit, turbine with reheater unit, generator and speed regulator unit. The PID controller parameters are optimized by considering nature bio-inspired firefly algorithm(FFA). The experimental results demonstrated the comparison of the proposed system performance(FFA-PID)with optimized PID controller based genetic algorithm(GAPID) and particle swarm optimization(PSO) technique(PSOPID) for the same investigated power system. The results proved the efficiency of employing the integral time absolute error(ITAE) cost function with one percent step load perturbation(1 % SLP) in area 1. The proposed system based FFA achieved the least settling time compared to using the GA or the PSO algorithms, while, it attained good results with respect to the peak overshoot/undershoot. In addition, the FFA performance is improved with the increased number of iterations which outperformed the other optimization algorithms based controller.
Essentially, it is significant to supply the consumer with reliable and sufficient power. Since, power quality is measured by the consistency in frequency and power flow between control areas. Thus, in a power system operation and control,automatic generation control(AGC) plays a crucial role. In this paper, multi-area(Five areas: area 1, area 2, area 3, area 4 and area 5) reheat thermal power systems are considered with proportional-integral-derivative(PID) controller as a supplementary controller. Each area in the investigated power system is equipped with appropriate governor unit, turbine with reheater unit, generator and speed regulator unit. The PID controller parameters are optimized by considering nature bio-inspired firefly algorithm(FFA). The experimental results demonstrated the comparison of the proposed system performance(FFA-PID)with optimized PID controller based genetic algorithm(GAPID) and particle swarm optimization(PSO) technique(PSOPID) for the same investigated power system. The results proved the efficiency of employing the integral time absolute error(ITAE) cost function with one percent step load perturbation(1 % SLP) in area 1. The proposed system based FFA achieved the least settling time compared to using the GA or the PSO algorithms, while, it attained good results with respect to the peak overshoot/undershoot. In addition, the FFA performance is improved with the increased number of iterations which outperformed the other optimization algorithms based controller.
引文
[1]A.Polycarpou,“Power quality and voltage sag indices in electrical power systems,”in Electrical Generation and Distribution Systems and Power Quality Disturbances,G.R.Rey and L.M.Muneta,Eds.Rijieka,Croatia:INTECH Open Access Publisher,2011,pp.139-160.
[2]S.Pande and R.Kansal,“Load frequency control of multi area system using integral-fuzzy controller,”Surbhi Pande Int.J.Eng.Res.Appl.,vol.5,no.6,pp.59-64,Jun.2015.
[3]P.I.Obi,G.C.Chidolue,and I.I.Okonkwo,“Protection and control of power system-a review,”Int.J.Advanc.Res.Technol.,vol.3,no.5,pp.158-166,2014.
[4]M.L.Kothari,P.S.Satasngi,and J.Nanda,“Sampled-data automatic generation control of interconnected reheat thermal systems considering generation rate constraints,”IEEE Trans.Power Apparatus Syst.,vol.PAS-100,no.5,pp.2334-2342,May 1981.
[5]S.C.Tripathy,T.S.Bhatti,C.S.Jha,O.P.Malik,and G.S.Hope,“Sampled data automatic generation control analysis with reheat steam turbines and governor dead-band effects,”IEEE Power Eng.Rev.,vol.PER,no.5,pp.40,May 1984.
[6]M.L.Kothari and J.Nanda,“Application of optimal control strategy to automatic generation control of a hydrothermal system,”IEE Proc.D,vol.135,no.4,pp.268-274,Jul.1988.
[7]M.L.Kothari,J.Nanda,D.P.Kothari,and D.Das,“Discrete-mode automatic generation control of a two-area reheat thermal system with new area control error,”IEEE Trans.Power Syst.,vol.4,no.2,pp.730-738,May 1989.
[8]S.Das,M.L.Kothari,D.P.Kothari,and J.Nanda,“Variable structure control strategy to automatic generation control of interconnected reheat thermal system,”IEE Proc.,vol.138,no.6,pp.579-585,Nov.1991.
[9]S.C.Tripathy,R.Balasubramaniam,and P.S.C.Nair,“Effect of superconducting magnetic energy storage on automatic generation control considering governor deadband and boiler dynamics,”IEEE Trans.Power Syst.,vol.7,no.3,pp.1266-1273,Aug.1992.
[10]R.Roy,P.Bhatt,and S.P.Ghoshal,“Evolutionary computation based three-area automatic generation control,”Expert.Syst.Appl.,vol.37,no.8,pp.5913-5924,Aug.2010.
[11]E.S.Ali and S.M.Abd-Elazim,“Bacteria foraging optimization algorithm based load frequency controller for interconnected power system,”Int.J.Electric.Power Energ.Syst.,vol.33,no.3,pp.633-638,Mar.2011.
[12]H.Gozde,M.C.Teplamacioglu,and I.Kocaarslan,“Comparative performance analysis of Artificial Bee Colony algorithm in automatic generation control for interconnected reheat thermal power system,”Int.J.Electric.Power Energ.Syst.,vol.42,no.1,pp.167-178,Nov.2012.
[13]F.Daneshfar and H.Bevrani,“Multiobjective design of load frequency control using genetic algorithms,”Int.J.Electric.Power Energ.Syst.,vol.42,no.1,pp.257-263,Nov.2012.
[14]L.C.Saikia,N.Sinha,and J.Nanda,“Maiden application of bacterial foraging based fuzzy IDD controller in AGC of a multi-area hydrothermal system,”Int.J.Electric.Power Energ.Syst.,vol.45,no.1,pp.98-109,Feb.2013.
[15]S.Debbarma,L.C.Saikia,and N.Sinha,“AGC of a multi-area thermal system under deregulated environment using a non-integer controller,”Electric Power Syst.Res.,vol.95,pp.175-183,Feb.2013.
[16]R.K.Sahu,S.Panda,and U.K.Rout,“DE optimized parallel 2-DOF PID controller for load frequency control of power system with governor dead-band nonlinearity,”Int.J.Electric.Power Energ.Syst.,vol.49,pp.19-33,Jul.2013.
[17]D.G.Padhan and S.Majhi,“A new control scheme for PID load frequency controller of single-area and multi-area power systems,”ISATrans.,vol.52,no.2,pp.242-251,Mar.2013.
[18]H.Shabani,B.Vahidi,and M.Ebrahimpour,“A robust PID controller based on imperialist competitive algorithm for load-frequency control of power systems,”ISA Trans.,vol.52,no.1,pp.88-95,Jan.2013.
[19]U.K.Rout,R.K.Sahu,and S.Panda,“Design and analysis of differential evolution algorithm based automatic generation control for interconnected power system,”Ain Shams Eng.J.,vol.4,no.3,pp.409-421,Sep.2013.
[20]S.A.Taher,M.H.Fini,and S.F.Aliabadi,“Fractional order PIDcontroller design for LFC in electric power systems using imperialist competitive algorithm,”Ain Shams Eng.J.,vol.5,no.1,pp.121-135,Mar.2014.
[21]M.N.Anwar and S.Pan,“A new PID load frequency controller design method in frequency domain through direct synthesis approach,”Int.J.Electric.Power Energ.Syst.,vol.67,pp.560-569,May 2015.
[22]Y.Sharma and L.C.Saukia,“Automatic generation control of a multiarea ST-Thermal power system using grey wolf optimizer algorithm based classical controllers,”Int.J.Electric.Power Energ.Syst.,vol.73,pp.853-862,Dec.2015.
[23]M.H.Khooban and T.Niknam,“A new intelligent online fuzzy tuning approach for multi-area load frequency control:Self Adaptive Modified Bat Algorithm,”Int.J.Electric.Power Energ.Syst.,vol.71,pp.254-261,Oct.2015.
[24]A.Y.Abdelaziz and E.S.Ali,“Cuckoo search algorithm based load frequency controller design for nonlinear interconnected power system,”Int.J.Electric.Power Energ.Syst.,vol.73,pp.632-643,Dec.2015.
[25]B.K.Sahu,S.Pati,P.K.Mohanty,and S.Panda,“Teaching-learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system,”Appl.Soft Comput.,vol.27,pp.240-249,Feb.2015.
[26]R.K.Sahu,S.Panda,and G.T.C.Sekhar,“A novel hybrid PSO-PS optimized fuzzy PI controller for AGC in multi area interconnected power systems,”Int.J.Electric.Power Energ.Syst.,vol.64,pp.880-893,Jan.2015.
[27]J.Nanda,M.Sreedhar,and A.Dasgupta,“A new technique in hydro thermal interconnected automatic generation control system by using minority charge carrier inspired algorithm,”Int.J.Electric.Power Energy Systems,vol.68,pp.259-268,Jun.2015.
[28]M.Shivaie,M.G.Kazemi,and M.T.Ameli,“A modified harmony search algorithm for solving load-frequency control of non-linear interconnected hydrothermal power systems,”Sustain.Energ.Technol.Assess.,vol.10,pp.53-62,Jun.2015.
[29]X.S.Yang,“Firefly algorithms for multimodal optimization,”in Stochastic Algorithms:Foundations and Applications,O.Watanabe and T.Zeugmann,Eds.Berlin,Heidelberg:Springer,2009,pp.169-178.
[30]M.K.Sayadia,R.Ramanziana,and N.Ghaffari-Nasaba,“A discrete firefly meta-heuristic with local search for makespan Minimisation in permutation flow shop scheduling problems,”Int.J.Industr.Eng.Comput.,vol.1,no.1,pp.1-10,Jul.2010.
[31]H.Gandomi,X.S.Yang,and A.H.Alavi,“Mixed variable structural optimization using firefly algorithm,”Comput.Struct.,vol.89,no.23-24,pp.2325-2336,Dec.2011.
[32]S.K.Azad,and S.K.Azad,“Optimum design of structures using an improved firefly algorithm,”Int.J.Optim.Civil Eng.,vol.1,no.2,pp.327-340,Jan.2011.
[33]K.Jagatheesan and B.Anand,“Dynamic performance of multi-area hydro thermal power systems with integral controller considering various performance indices methods,”in Proc.IEEE Int.Conf.Emerging Trends in Science,Engineering and Technology(INCOSET),Tiruchirappalli,Tamilnadu,India,2012,pp.474-478.
[34]X.S.Yang,“Firefly algorithm,stochastic test functions and design optimization,”Int.J.Bio-inspired Comput.,vol.2,no.2,pp.78-84,Mar.2010.
[35]X.S.Yang,Nature-Inspired Metaheuristic Algorithms,Luniver Press,2008.
[36]X.S.Yang,Engineering Optimization:An Introduction with Metaheuristic Applications,New Jersey:Wiley&Sons,2010.
[37]X.S.Yang,S.S.Hosseini,and A.H.Gandomi,“Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect”,Appl.Soft Comput.,vol.12,no.3,pp.1180-1186,Mar.2012.
[38]M.Shafaati and H.Mojallali,“Modified firefly optimization for IIR system identification,”J.Contr.Eng.Appl.Inform.,vol.14,no.4,pp.59-69,Dec.2012.
[39]J.Kwiecie′n and B.Filipowicz,“Firefly algorithm in optimization of queueing systems,”Bull.Polish Acad.Sci.Tech.Sci.,vol.60,no.2,pp.363-368,Oct.2012.
[40]H.M.Gomes,“A firefly metaheuristic structural size and shape optimisation with natural frequency constraints,”Int.J.Metaheur.,vol.2,no.1,pp.38-55,Jul.2012.
[41]N.Muthukumar,S.Srinivasan,K.Ramkumar,P.Kavitha,and V.E.Balas,“Supervisory GPC and evolutionary PI controller for web transport systems,”Acta Polytech.Hungar.,vol.12,no.5,pp.135-153,Oct.2015.
[42]K.Jagatheesan,B.Anand,N.Dey,A.S.Ashour,and V.E.Balas,“Proportional-Integral-Derivative(PID)controller equipped lfc of multiarea interconnected power system,”in Proc.Int.Conf.Industrial Engineering and Environmental Protection(IIZS 2015),Zrenjanin,Serbia,2005.
[43]M.Sarkar,S.Banerjee,and V.E.Balas,“Configuring trust model for cloud computing:decision exploration using fuzzy reasoning,”in Proc.19th IEEE Int.Conf.Intelligent Engineering Systems,Bratislava,Slovakia,2015.
[44]Z.Ni,H.B.He,X.N.Zhong,and D.V.Prokhorov,“Model-free dual heuristic dynamic programming,”IEEE Trans.Neural Networks Learn.Syst.,vol.26,no.8,pp.1834-1839,Aug.2015.
[45]B.Tang,H.B.He,Q.Ding,and S.Kay,“A parametric classification rule based on the exponentially embedded family,”IEEE Trans.Neural Networks Learn.Systems,vol.26,no.2,pp.367-377,Feb.2015.
[46]B.Tang and H.B.He,“ENN:extended nearest neighbor method for pattern recognition[research frontier,”IEEE Comput.Intellig.Magaz.,vol.10,no.3,pp.52-60,Aug.2015.
[47]L.Jiang,W.Yao,Q.H.Wu,J.Y.Wen,and S.J.Cheng,“Delaydependent stability for load frequency control with constant and timevarying delays,”IEEE Trans.Power Syst.,vol.27,no.2,pp.932-941,May 2012.
[48]C.K.Zhang,L.Jiang,Q.H.Wu,Y.He,and M.Wu,“Delay-dependent robust load frequency control for time delay power systems,”IEEETrans.Power Syst.,vol.28,no.3,pp.2192-2201,Aug.2013.
[49]H.Trinh,T.Fernando,H.H.C.Iu,and K.P.Wong,“Quasi-decentralized functional observers for the LFC of interconnected power systems,”IEEE Trans.Power Syst.,vol.28,no.3,pp.3513-3514,Aug.2013.
[50]S.Saxena and Y.V.Hote,“Load frequency control in power systems via internal model control scheme and model-order reduction,”IEEE Trans.Power Syst.,vol.28,no.3,pp.2749-2757,Aug.2013.
[51]H.Bevrani and P.R.Daneshmand,“Fuzzy logic-based load-frequency control concerning high penetration of wind turbines,”IEEE Syst.J.,vol.6,no.1,pp.173-180,Mar.2012.
[52]H.A.Yousef,K.AL-Kharusi,M.H.Albadi,and N.Hosseinzadeh,“Load frequency control of a multi-area power system:an adaptive fuzzy logic approach,”IEEE Trans.Power Syst.,vol.29,no.4,pp.1822-1830,Jul.2014.
[2]S.Pande and R.Kansal,“Load frequency control of multi area system using integral-fuzzy controller,”Surbhi Pande Int.J.Eng.Res.Appl.,vol.5,no.6,pp.59-64,Jun.2015.
[3]P.I.Obi,G.C.Chidolue,and I.I.Okonkwo,“Protection and control of power system-a review,”Int.J.Advanc.Res.Technol.,vol.3,no.5,pp.158-166,2014.
[4]M.L.Kothari,P.S.Satasngi,and J.Nanda,“Sampled-data automatic generation control of interconnected reheat thermal systems considering generation rate constraints,”IEEE Trans.Power Apparatus Syst.,vol.PAS-100,no.5,pp.2334-2342,May 1981.
[5]S.C.Tripathy,T.S.Bhatti,C.S.Jha,O.P.Malik,and G.S.Hope,“Sampled data automatic generation control analysis with reheat steam turbines and governor dead-band effects,”IEEE Power Eng.Rev.,vol.PER,no.5,pp.40,May 1984.
[6]M.L.Kothari and J.Nanda,“Application of optimal control strategy to automatic generation control of a hydrothermal system,”IEE Proc.D,vol.135,no.4,pp.268-274,Jul.1988.
[7]M.L.Kothari,J.Nanda,D.P.Kothari,and D.Das,“Discrete-mode automatic generation control of a two-area reheat thermal system with new area control error,”IEEE Trans.Power Syst.,vol.4,no.2,pp.730-738,May 1989.
[8]S.Das,M.L.Kothari,D.P.Kothari,and J.Nanda,“Variable structure control strategy to automatic generation control of interconnected reheat thermal system,”IEE Proc.,vol.138,no.6,pp.579-585,Nov.1991.
[9]S.C.Tripathy,R.Balasubramaniam,and P.S.C.Nair,“Effect of superconducting magnetic energy storage on automatic generation control considering governor deadband and boiler dynamics,”IEEE Trans.Power Syst.,vol.7,no.3,pp.1266-1273,Aug.1992.
[10]R.Roy,P.Bhatt,and S.P.Ghoshal,“Evolutionary computation based three-area automatic generation control,”Expert.Syst.Appl.,vol.37,no.8,pp.5913-5924,Aug.2010.
[11]E.S.Ali and S.M.Abd-Elazim,“Bacteria foraging optimization algorithm based load frequency controller for interconnected power system,”Int.J.Electric.Power Energ.Syst.,vol.33,no.3,pp.633-638,Mar.2011.
[12]H.Gozde,M.C.Teplamacioglu,and I.Kocaarslan,“Comparative performance analysis of Artificial Bee Colony algorithm in automatic generation control for interconnected reheat thermal power system,”Int.J.Electric.Power Energ.Syst.,vol.42,no.1,pp.167-178,Nov.2012.
[13]F.Daneshfar and H.Bevrani,“Multiobjective design of load frequency control using genetic algorithms,”Int.J.Electric.Power Energ.Syst.,vol.42,no.1,pp.257-263,Nov.2012.
[14]L.C.Saikia,N.Sinha,and J.Nanda,“Maiden application of bacterial foraging based fuzzy IDD controller in AGC of a multi-area hydrothermal system,”Int.J.Electric.Power Energ.Syst.,vol.45,no.1,pp.98-109,Feb.2013.
[15]S.Debbarma,L.C.Saikia,and N.Sinha,“AGC of a multi-area thermal system under deregulated environment using a non-integer controller,”Electric Power Syst.Res.,vol.95,pp.175-183,Feb.2013.
[16]R.K.Sahu,S.Panda,and U.K.Rout,“DE optimized parallel 2-DOF PID controller for load frequency control of power system with governor dead-band nonlinearity,”Int.J.Electric.Power Energ.Syst.,vol.49,pp.19-33,Jul.2013.
[17]D.G.Padhan and S.Majhi,“A new control scheme for PID load frequency controller of single-area and multi-area power systems,”ISATrans.,vol.52,no.2,pp.242-251,Mar.2013.
[18]H.Shabani,B.Vahidi,and M.Ebrahimpour,“A robust PID controller based on imperialist competitive algorithm for load-frequency control of power systems,”ISA Trans.,vol.52,no.1,pp.88-95,Jan.2013.
[19]U.K.Rout,R.K.Sahu,and S.Panda,“Design and analysis of differential evolution algorithm based automatic generation control for interconnected power system,”Ain Shams Eng.J.,vol.4,no.3,pp.409-421,Sep.2013.
[20]S.A.Taher,M.H.Fini,and S.F.Aliabadi,“Fractional order PIDcontroller design for LFC in electric power systems using imperialist competitive algorithm,”Ain Shams Eng.J.,vol.5,no.1,pp.121-135,Mar.2014.
[21]M.N.Anwar and S.Pan,“A new PID load frequency controller design method in frequency domain through direct synthesis approach,”Int.J.Electric.Power Energ.Syst.,vol.67,pp.560-569,May 2015.
[22]Y.Sharma and L.C.Saukia,“Automatic generation control of a multiarea ST-Thermal power system using grey wolf optimizer algorithm based classical controllers,”Int.J.Electric.Power Energ.Syst.,vol.73,pp.853-862,Dec.2015.
[23]M.H.Khooban and T.Niknam,“A new intelligent online fuzzy tuning approach for multi-area load frequency control:Self Adaptive Modified Bat Algorithm,”Int.J.Electric.Power Energ.Syst.,vol.71,pp.254-261,Oct.2015.
[24]A.Y.Abdelaziz and E.S.Ali,“Cuckoo search algorithm based load frequency controller design for nonlinear interconnected power system,”Int.J.Electric.Power Energ.Syst.,vol.73,pp.632-643,Dec.2015.
[25]B.K.Sahu,S.Pati,P.K.Mohanty,and S.Panda,“Teaching-learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system,”Appl.Soft Comput.,vol.27,pp.240-249,Feb.2015.
[26]R.K.Sahu,S.Panda,and G.T.C.Sekhar,“A novel hybrid PSO-PS optimized fuzzy PI controller for AGC in multi area interconnected power systems,”Int.J.Electric.Power Energ.Syst.,vol.64,pp.880-893,Jan.2015.
[27]J.Nanda,M.Sreedhar,and A.Dasgupta,“A new technique in hydro thermal interconnected automatic generation control system by using minority charge carrier inspired algorithm,”Int.J.Electric.Power Energy Systems,vol.68,pp.259-268,Jun.2015.
[28]M.Shivaie,M.G.Kazemi,and M.T.Ameli,“A modified harmony search algorithm for solving load-frequency control of non-linear interconnected hydrothermal power systems,”Sustain.Energ.Technol.Assess.,vol.10,pp.53-62,Jun.2015.
[29]X.S.Yang,“Firefly algorithms for multimodal optimization,”in Stochastic Algorithms:Foundations and Applications,O.Watanabe and T.Zeugmann,Eds.Berlin,Heidelberg:Springer,2009,pp.169-178.
[30]M.K.Sayadia,R.Ramanziana,and N.Ghaffari-Nasaba,“A discrete firefly meta-heuristic with local search for makespan Minimisation in permutation flow shop scheduling problems,”Int.J.Industr.Eng.Comput.,vol.1,no.1,pp.1-10,Jul.2010.
[31]H.Gandomi,X.S.Yang,and A.H.Alavi,“Mixed variable structural optimization using firefly algorithm,”Comput.Struct.,vol.89,no.23-24,pp.2325-2336,Dec.2011.
[32]S.K.Azad,and S.K.Azad,“Optimum design of structures using an improved firefly algorithm,”Int.J.Optim.Civil Eng.,vol.1,no.2,pp.327-340,Jan.2011.
[33]K.Jagatheesan and B.Anand,“Dynamic performance of multi-area hydro thermal power systems with integral controller considering various performance indices methods,”in Proc.IEEE Int.Conf.Emerging Trends in Science,Engineering and Technology(INCOSET),Tiruchirappalli,Tamilnadu,India,2012,pp.474-478.
[34]X.S.Yang,“Firefly algorithm,stochastic test functions and design optimization,”Int.J.Bio-inspired Comput.,vol.2,no.2,pp.78-84,Mar.2010.
[35]X.S.Yang,Nature-Inspired Metaheuristic Algorithms,Luniver Press,2008.
[36]X.S.Yang,Engineering Optimization:An Introduction with Metaheuristic Applications,New Jersey:Wiley&Sons,2010.
[37]X.S.Yang,S.S.Hosseini,and A.H.Gandomi,“Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect”,Appl.Soft Comput.,vol.12,no.3,pp.1180-1186,Mar.2012.
[38]M.Shafaati and H.Mojallali,“Modified firefly optimization for IIR system identification,”J.Contr.Eng.Appl.Inform.,vol.14,no.4,pp.59-69,Dec.2012.
[39]J.Kwiecie′n and B.Filipowicz,“Firefly algorithm in optimization of queueing systems,”Bull.Polish Acad.Sci.Tech.Sci.,vol.60,no.2,pp.363-368,Oct.2012.
[40]H.M.Gomes,“A firefly metaheuristic structural size and shape optimisation with natural frequency constraints,”Int.J.Metaheur.,vol.2,no.1,pp.38-55,Jul.2012.
[41]N.Muthukumar,S.Srinivasan,K.Ramkumar,P.Kavitha,and V.E.Balas,“Supervisory GPC and evolutionary PI controller for web transport systems,”Acta Polytech.Hungar.,vol.12,no.5,pp.135-153,Oct.2015.
[42]K.Jagatheesan,B.Anand,N.Dey,A.S.Ashour,and V.E.Balas,“Proportional-Integral-Derivative(PID)controller equipped lfc of multiarea interconnected power system,”in Proc.Int.Conf.Industrial Engineering and Environmental Protection(IIZS 2015),Zrenjanin,Serbia,2005.
[43]M.Sarkar,S.Banerjee,and V.E.Balas,“Configuring trust model for cloud computing:decision exploration using fuzzy reasoning,”in Proc.19th IEEE Int.Conf.Intelligent Engineering Systems,Bratislava,Slovakia,2015.
[44]Z.Ni,H.B.He,X.N.Zhong,and D.V.Prokhorov,“Model-free dual heuristic dynamic programming,”IEEE Trans.Neural Networks Learn.Syst.,vol.26,no.8,pp.1834-1839,Aug.2015.
[45]B.Tang,H.B.He,Q.Ding,and S.Kay,“A parametric classification rule based on the exponentially embedded family,”IEEE Trans.Neural Networks Learn.Systems,vol.26,no.2,pp.367-377,Feb.2015.
[46]B.Tang and H.B.He,“ENN:extended nearest neighbor method for pattern recognition[research frontier,”IEEE Comput.Intellig.Magaz.,vol.10,no.3,pp.52-60,Aug.2015.
[47]L.Jiang,W.Yao,Q.H.Wu,J.Y.Wen,and S.J.Cheng,“Delaydependent stability for load frequency control with constant and timevarying delays,”IEEE Trans.Power Syst.,vol.27,no.2,pp.932-941,May 2012.
[48]C.K.Zhang,L.Jiang,Q.H.Wu,Y.He,and M.Wu,“Delay-dependent robust load frequency control for time delay power systems,”IEEETrans.Power Syst.,vol.28,no.3,pp.2192-2201,Aug.2013.
[49]H.Trinh,T.Fernando,H.H.C.Iu,and K.P.Wong,“Quasi-decentralized functional observers for the LFC of interconnected power systems,”IEEE Trans.Power Syst.,vol.28,no.3,pp.3513-3514,Aug.2013.
[50]S.Saxena and Y.V.Hote,“Load frequency control in power systems via internal model control scheme and model-order reduction,”IEEE Trans.Power Syst.,vol.28,no.3,pp.2749-2757,Aug.2013.
[51]H.Bevrani and P.R.Daneshmand,“Fuzzy logic-based load-frequency control concerning high penetration of wind turbines,”IEEE Syst.J.,vol.6,no.1,pp.173-180,Mar.2012.
[52]H.A.Yousef,K.AL-Kharusi,M.H.Albadi,and N.Hosseinzadeh,“Load frequency control of a multi-area power system:an adaptive fuzzy logic approach,”IEEE Trans.Power Syst.,vol.29,no.4,pp.1822-1830,Jul.2014.