Fractional-order load-frequency control of interconnected power systems using chaotic multi-objective optimization

Multi-objective optimization-based fractional-order PID controller is designed.NSGA-II algorithm is augmented with chaotic Logistic and Henon map.Load disturbance rejection and controller effort are minimized as two conflicting objectives.FOPID controller outperforms the PID controller in suppressing frequency deviation.Better trade-off is obtained for load-frequency control of power systems with FOPID. Fractional-order proportional-integral-derivative (FOPID) controllers are designed for load-frequency control (LFC) of two interconnected power systems. Conflicting time-domain design objectives are considered in a multi-objective optimization (MOO)-based design framework to design the gains and the fractional differ-integral orders of the FOPID controllers in the two areas. Here, we explore the effect of augmenting two different chaotic maps along with the uniform random number generator (RNG) in the popular MOO algorithm-the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Different measures of quality for MOO, e.g. hypervolume indicator, moment of inertia-based diversity metric, total Pareto spread, spacing metric, are adopted to select the best set of controller parameters from multiple runs of all the NSGA-II variants (i.e. nominal and chaotic versions). The chaotic versions of the NSGA-II algorithm are compared with the standard NSGA-II in terms of solution quality and computational time. In addition, the Pareto optimal fronts showing the trade-off between the two conflicting time domain design objectives are compared to show the advantage of using the FOPID controller over that with simple PID controller. The nature of fast/slow and high/low noise amplification effects of the FOPID structure or the four quadrant operation in the two inter-connected areas of the power system is also explored. A fuzzy logic-based method has been adopted next to select the best compromise solution from the best Pareto fronts corresponding to each MOO comparison criteria. The time-domain system responses are shown for the fuzzy best compromise solutions under nominal operating conditions. Comparative analysis on the merits and de-merits of each controller structure is reported then. A robustness analysis is also done for the PID and the FOPID controllers.

[1]  Ali Feliachi,et al.  Robust load frequency control using genetic algorithms and linear matrix inequalities , 2003 .

[2]  Lalit Chandra Saikia,et al.  Solution to automatic generation control problem using firefly algorithm optimized I(λ)D(µ) controller. , 2014, ISA transactions.

[3]  H. Shayeghi,et al.  Application of ANN technique based on μ-synthesis to load frequency control of interconnected power system , 2006 .

[4]  Devendra K. Chaturvedi,et al.  Load frequency control: a generalised neural network approach , 1999 .

[5]  Tarek Hassan Mohamed,et al.  Decentralized model predictive based load frequency control in an interconnected power system , 2011 .

[6]  Leandro dos Santos Coelho,et al.  Economic dispatch optimization using hybrid chaotic particle swarm optimizer , 2007, 2007 IEEE International Conference on Systems, Man and Cybernetics.

[7]  Peter J. Fleming,et al.  Evolutionary algorithms in control systems engineering: a survey , 2002 .

[8]  Mohammad Teshnehlab,et al.  Recurrent fuzzy neural network by using feedback error learning approaches for LFC in interconnected power system , 2009 .

[9]  Yasunori Mitani,et al.  Robust decentralised load-frequency control using an iterative linear matrix inequalities algorithm , 2004 .

[10]  Sanjoy Das,et al.  A Multiobjective Evolutionary-Simplex Hybrid Approach for the Optimization of Differential Equation Models of Gene Networks , 2008, IEEE Transactions on Evolutionary Computation.

[11]  Nasser Sadati,et al.  Design of a fractional order PID controller for an AVR using particle swarm optimization , 2009 .

[12]  Ibrahim Dincer,et al.  Multi-objective exergy-based optimization of a polygeneration energy system using an evolutionary algorithm , 2012 .

[13]  Zakariya Al-Hamouz,et al.  Optimal design of a sliding mode AGC controller: Application to a nonlinear interconnected model , 2011 .

[14]  Debapriya Das,et al.  Battery energy storage for load frequency control of an interconnected power system , 2001 .

[15]  Aditya,et al.  Design of Load Frequency Controllers Using Genetic Algorithm for Two Area Interconnected Hydro Power System , 2003 .

[16]  Muwaffaq I. Alomoush,et al.  Load frequency control and automatic generation control using fractional-order controllers , 2010 .

[17]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[18]  P. Kundur,et al.  Power system stability and control , 1994 .

[19]  Saptarshi Das,et al.  Intelligent Fractional Order Systems and Control - An Introduction , 2012, Studies in Computational Intelligence.

[20]  Takashi Hiyama,et al.  Intelligent Automatic Generation Control , 2011 .

[21]  Yanbin Yuan,et al.  A hybrid chaotic genetic algorithm for short-term hydro system scheduling , 2002, Math. Comput. Simul..

[22]  E. Çam,et al.  A fuzzy gain scheduling PI controller application for an interconnected electrical power system , 2005 .

[23]  Yogesh V. Hote,et al.  Fractional order PID controller for load frequency control , 2014 .

[24]  Danqing Guo,et al.  Chaotic-NSGA-II: An effective algorithm to solve multi-objective optimization problems , 2010, 2010 International Conference on Intelligent Computing and Integrated Systems.

[25]  S. Velusami,et al.  Decentralized Biased Controllers for Load — Frequency Control of Interconnected Power Systems Considering Governor Dead Band Non-Linearity , 2005, 2005 Annual IEEE India Conference - Indicon.

[26]  Sanghamitra Bandyopadhyay,et al.  Multiobjective GAs, quantitative indices, and pattern classification , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[27]  Youyi Wang,et al.  New robust adaptive load-frequency control with system parametric uncertainties , 1994 .

[28]  Ertuğrul Çam,et al.  Fuzzy logic controller in interconnected electrical power systems for load-frequency control , 2005 .

[29]  K. R. Sudha,et al.  Robust decentralized load frequency control of interconnected power system with Generation Rate Constraint using Type-2 fuzzy approach , 2011 .

[30]  Seyed Abbas Taher,et al.  Fractional order PID controller design for LFC in electric power systems using imperialist competitive algorithm , 2014 .

[31]  Bijay Ketan Panigrahi,et al.  Multiobjective fuzzy dominance based bacterial foraging algorithm to solve economic emission dispatc , 2010 .

[32]  Elyas Rakhshani,et al.  Intelligent Linear-Quadratic Optimal Output Feedback Regulator for a Deregulated Automatic Generation Control System , 2012 .

[33]  Goshaidas Ray,et al.  Design of decentralized robust load-frequency controller based on SVD method , 1999 .

[34]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[35]  Hassan Bevrani,et al.  Robust Power System Frequency Control , 2009 .

[36]  H. Shayeghi,et al.  Load frequency control strategies: A state-of-the-art survey for the researcher , 2009 .

[37]  I J Nagrath,et al.  Power System Engineering , 2007 .

[38]  Ibraheem,et al.  Recent philosophies of automatic generation control strategies in power systems , 2005, IEEE Transactions on Power Systems.

[39]  S. Velusami,et al.  Design of Decentralized Biased Controllers for Load-Frequency Control of Interconnected Power Systems , 2005 .

[40]  Indranil Pan,et al.  On the Mixed H 2 / H ∞ Loop Shaping Trade-offs in Fractional Order Control of the AVR System , 2022 .

[41]  Rabindra Kumar Sahu,et al.  A novel hybrid DEPS optimized fuzzy PI/PID controller for load frequency control of multi-area interconnected power systems , 2014 .

[42]  Salvatore Graziani,et al.  Stochastic Resonance: Theory and Applications , 2000 .

[43]  Lothar Thiele,et al.  Quality Assessment of Pareto Set Approximations , 2008, Multiobjective Optimization.

[44]  Xiaohui Yuan,et al.  Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II , 2014 .

[45]  Saptarshi Das,et al.  Chaotic multi-objective optimization based design of fractional order PIλDμ controller in AVR system , 2012, ArXiv.

[46]  Luigi Fortuna,et al.  Chaotic sequences to improve the performance of evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[47]  S. Das.  Functional Fractional Calculus , 2011 .

[48]  Bijay Ketan Panigrahi,et al.  Multiobjective bacteria foraging algorithm for electrical load dispatch problem , 2011 .

[49]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[50]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[51]  Marjan Mernik,et al.  Exploration and exploitation in evolutionary algorithms: A survey , 2013, CSUR.

[52]  Nand Kishor,et al.  A literature survey on load–frequency control for conventional and distribution generation power systems , 2013 .

[53]  Gilberto Reynoso-Meza,et al.  Controller tuning using evolutionary multi-objective optimisation: Current trends and applications , 2014 .

[54]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[55]  Lalit Chandra Saikia,et al.  Automatic generation control using two degree of freedom fractional order PID controller , 2014 .

[56]  Bernard Widrow,et al.  Application of neural networks to load-frequency control in power systems , 1994, Neural Networks.

[57]  Rujing Zhou,et al.  Robust decentralised load-frequency control of multi-area power systems , 1996 .

[58]  Saptarshi Das,et al.  Multi-objective optimization framework for networked predictive controller design. , 2013, ISA transactions.

[59]  Luigi Fortuna,et al.  Does chaos work better than noise , 2002 .

[60]  Lothar Thiele,et al.  The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration , 2007, EMO.

[61]  L. Coelho,et al.  A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch , 2009 .

[62]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[63]  Zakariya Al-Hamouz,et al.  A new load frequency variable structure controller using genetic algorithms , 2000 .

[64]  Mohammad Bagher Menhaj,et al.  Decentralized robust adaptive-output feedback controller for power system load frequency control , 2002 .

[65]  Lalit Chandra Saikia,et al.  AGC of a multi-area thermal system under deregulated environment using a non-integer controller , 2013 .

[66]  E. S. Ali,et al.  Bacteria foraging optimization algorithm based load frequency controller for interconnected power system , 2011 .

[67]  Saptarshi Das,et al.  Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization , 2013, ArXiv.

[68]  Saptarshi Das,et al.  On the Mixed ${{\rm H}_2}/{{\rm H}_\infty }$ Loop-Shaping Tradeoffs in Fractional-Order Control of the AVR System , 2013, IEEE Transactions on Industrial Informatics.

[69]  Jing Liu,et al.  A chaotic non-dominated sorting genetic algorithm for the multi-objective automatic test task scheduling problem , 2013, Appl. Soft Comput..

[70]  Shantanu Das,et al.  Performance Comparison of Optimal Fractional Order Hybrid Fuzzy PID Controllers for Handling Oscillatory Fractional Order Processes with Dead Time , 2013, ISA transactions.

[71]  Mohamed Zribi,et al.  Adaptive decentralized load frequency control of multi-area power systems , 2005 .