Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems

Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the curse of dimensionality, heuristics-based swarm intelligence can be an efficient alternative. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. This paper presents a detailed overview of the basic concepts of PSO and its variants. Also, it provides a comprehensive survey on the power system applications that have benefited from the powerful nature of PSO as an optimization technique. For each application, technical details that are required for applying PSO, such as its type, particle formulation (solution representation), and the most efficient fitness functions are also discussed.

[1]  Vladimiro Miranda,et al.  EPSO-evolutionary particle swarm optimization, a new algorithm with applications in power systems , 2002, IEEE/PES Transmission and Distribution Conference and Exhibition.

[2]  R. Romero,et al.  Optimal Capacitor Placement in Radial Distribution Networks , 2001, IEEE Power Engineering Review.

[3]  B. J. Cory,et al.  A homogeneous linear programming algorithm for the security constrained economic dispatch problem , 2000 .

[4]  K. M. Tsang,et al.  Parameter optimisation of robust power system stabilisers by probabilistic approach , 2000 .

[5]  C.E. Zoumas,et al.  Comparison of two metaheuristics with mathematical programming methods for the solution of OPF , 2005, Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems.

[6]  M.N. Vrahatis,et al.  Particle swarm optimizers for Pareto optimization with enhanced archiving techniques , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[7]  H.K.M. Youssef,et al.  Load flow solution using hybrid particle swarm optimization , 2004, International Conference on Electrical, Electronic and Computer Engineering, 2004. ICEEC '04..

[8]  Russell C. Eberhart,et al.  Particle swarm with extended memory for multiobjective optimization , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[9]  G.K. Venayagamoorthy,et al.  Optimal control parameters for a UPFC in a multimachine using PSO , 2005, Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems.

[10]  A.S. Elwer,et al.  Intelligent fuzzy controller using particle swarm optimization for control of permanent magnet synchronous motor for electric vehicle , 2003, IECON'03. 29th Annual Conference of the IEEE Industrial Electronics Society (IEEE Cat. No.03CH37468).

[11]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

[12]  E.L. da Silva,et al.  Solving the hydro unit commitment problem via dual decomposition and sequential quadratic programming , 2006, IEEE Transactions on Power Systems.

[13]  L. S. Moulin,et al.  Dynamic Security Border Identification Using Enhanced Particle Swarm Optimization , 2002, IEEE Power Engineering Review.

[14]  Babak Nadjar Araabi,et al.  Intelligent Particle Swarm Optimization Using Q-Learning , 2006 .

[15]  Hiroshi Sasaki,et al.  Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming , 2000 .

[16]  Gary B. Lamont,et al.  Visualizing particle swarm optimization - Gaussian particle swarm optimization , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[17]  T. Ray Constrained robust optimal design using a multiobjective evolutionary algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[18]  E. Miguez,et al.  Design of Large Rural Low-Voltage Networks Using Dynamic Programming Optimization , 2001, IEEE Power Engineering Review.

[19]  J.Z. Jiang,et al.  Optimal design for cogging torque reduction of transverse flux permanent motor using particle swarm optimization algorithm , 2004, The 4th International Power Electronics and Motion Control Conference, 2004. IPEMC 2004..

[20]  G. Shrestha,et al.  Medium term power planning with bilateral contracts , 2005, IEEE Transactions on Power Systems.

[21]  J. A. Domínguez-Navarro,et al.  Integral planning of primary-secondary distribution systems using mixed integer linear programming , 2005, IEEE Transactions on Power Systems.

[22]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.

[23]  R.G. Harley,et al.  Optimal STATCOM Sizing and Placement Using Particle Swarn Optimization , 2006, 2006 IEEE/PES Transmission & Distribution Conference and Exposition: Latin America.

[24]  M. M. El-Metwally,et al.  New method for transmission planning using mixed-integer programming , 1988 .

[25]  K.Y. Lee,et al.  Application of Particle Swarm Optimization to Economic Dispatch Problem: Advantages and Disadvantages , 2006, 2006 IEEE PES Power Systems Conference and Exposition.

[26]  T. Krink,et al.  Extending particle swarm optimisers with self-organized criticality , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[27]  Nidul Sinha,et al.  PSO embedded evolutionary programming technique for nonconvex economic load dispatch , 2004, IEEE PES Power Systems Conference and Exposition, 2004..

[28]  Xiaodong Li,et al.  Adaptively Choosing Neighbourhood Bests Using Species in a Particle Swarm Optimizer for Multimodal Function Optimization , 2004, GECCO.

[29]  J. Kennedy,et al.  Neighborhood topologies in fully informed and best-of-neighborhood particle swarms , 2003, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[30]  Yoshikazu Fukuyama,et al.  A particle swarm optimization for reactive power and voltage control considering voltage security assessment , 2000 .

[31]  R.A. Gallego,et al.  Multistage and coordinated planning of the expansion of transmission systems , 2004, IEEE Transactions on Power Systems.

[32]  Suet Yee Chu Particle swarm optimization , 2009 .

[33]  M. S. Sachdev,et al.  An on-line relay coordination algorithm for adaptive protection using linear programming technique , 1996 .

[34]  G. K. Venayagamoorthy,et al.  Optimal Design of a SVC Controller Using a Small Population Based PSO , .

[35]  G.K. Venayagamoorthy,et al.  Optimal design of power system stabilizers using a small population based PSO , 2006, 2006 IEEE Power Engineering Society General Meeting.

[36]  Yaowu Wu,et al.  A PSO-based approach to optimal capacitor placement with harmonic distortion consideration , 2004 .

[37]  Chia-Feng Juang,et al.  Power system load frequency control by evolutionary fuzzy PI controller , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[38]  Renato A. Krohling,et al.  Gaussian particle swarm with jumps , 2005, 2005 IEEE Congress on Evolutionary Computation.

[39]  Jürgen Teich,et al.  Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO) , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

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

[41]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[42]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[43]  W. Kurutach,et al.  Feeder-switch relocation based upon risk analysis of trees-caused interruption and value-based distribution reliability assessment , 2004, 2004 IEEE Region 10 Conference TENCON 2004..

[44]  N. P. Padhy,et al.  Application of particle swarm optimization technique and its variants to generation expansion planning problem , 2004 .

[45]  Sukumar Mishra,et al.  A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation , 2005, IEEE Transactions on Evolutionary Computation.

[46]  Joong-Rin Shin,et al.  A particle swarm optimization for economic dispatch with nonsmooth cost functions , 2005, IEEE Transactions on Power Systems.

[47]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[48]  Mark Richards,et al.  Choosing a starting configuration for particle swarm optimization , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[49]  Ganesh K. Venayagamoorthy,et al.  Optimal Design of SVC Damping Controllers with Wide Area Measurements Using Small Population based PSO , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[50]  Chao-Ming Huang,et al.  A particle swarm optimization to identifying the ARMAX model for short-term load forecasting , 2005, IEEE Transactions on Power Systems.

[51]  S. Kannan,et al.  Application and comparison of metaheuristic techniques to generation expansion planning problem , 2005, IEEE Transactions on Power Systems.

[52]  K. Clements,et al.  An efficient interior point method for sequential quadratic programming based optimal power flow , 2000 .

[53]  R. F. Chang,et al.  Feeder reconfiguration for load factor improvement , 2002, 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309).

[54]  S. Virmani,et al.  Implementation of a Lagrangian Relaxation Based Unit Commitment Problem , 1989, IEEE Power Engineering Review.

[55]  Ivana Kockar,et al.  Phase shifter placement in large-scale systems via mixed integer linear programming , 2003 .

[56]  T.A.A. Victoire,et al.  Reserve constrained dynamic dispatch of units with valve-point effects , 2005, IEEE Transactions on Power Systems.

[57]  Jigui Sun,et al.  An Improved Discrete Particle Swarm Optimization Algorithm for TSP , 2007, 2007 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology - Workshops.

[58]  Jonathan E. Fieldsend,et al.  Using unconstrained elite archives for multiobjective optimization , 2003, IEEE Trans. Evol. Comput..

[59]  C. Lehmkoster,et al.  Security Constrained Optimal Power Flow for an Economical Operation of FACTS Devices in Liberalized Energy Markets , 2002, IEEE Power Engineering Review.

[60]  P. Scarpellini,et al.  Dynamic Security Corrective Control by UPFCs , 2001, IEEE Power Engineering Review.

[61]  X. Alabern,et al.  Optimized design of an induction motor using fuzzy logic as a calculus and decision tool , 2003, IEEE International Electric Machines and Drives Conference, 2003. IEMDC'03..

[62]  Vladimiro Miranda,et al.  NEW EVOLUTIONARY PARTICLE SWARM ALGORITHM (EPSO) APPLIED TO VOLTAGE/VAR CONTROL , 2002 .

[63]  A. J. Urdaneta,et al.  A Hybrid Particle Swarm Optimization for Distribution State Estimation , 2002, IEEE Power Engineering Review.

[64]  C.A. Castro,et al.  Fast computation of voltage stability security margins using nonlinear programming techniques , 2006, IEEE Transactions on Power Systems.

[65]  James Kennedy,et al.  The particle swarm: social adaptation of knowledge , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[66]  A. Feliachi,et al.  Power system stability enhancement using backstepping controller tuned by particle swarm optimization technique , 2005, IEEE Power Engineering Society General Meeting, 2005.

[67]  C. N. Lu,et al.  Feeder reconfiguration for power quality requirement and feeder service quality matching , 2002, IEEE/PES Transmission and Distribution Conference and Exhibition.

[68]  Michael N. Vrahatis,et al.  Recent approaches to global optimization problems through Particle Swarm Optimization , 2002, Natural Computing.

[69]  N. G. Boulaxis,et al.  Optimal Feeder Routing in Distribution System Planning Using Dynamic Programming Technique and GIS Facilities , 2001, IEEE Power Engineering Review.

[70]  K.S. Swarup,et al.  Particle swarm optimization for security constrained economic dispatch , 2004, International Conference on Intelligent Sensing and Information Processing, 2004. Proceedings of.

[71]  N. Grudinin Reactive power optimization using successive quadratic programming method , 1998 .

[72]  J. Kennedy,et al.  Population structure and particle swarm performance , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[73]  Ganesh K. Venayagamoorthy,et al.  Evolving Digital Circuits Using Hybrid Particle Swarm Optimization and Differential Evolution , 2006, Int. J. Neural Syst..

[74]  Yixin Ni,et al.  Applications of AI techniques to generation planning and investment , 2004, IEEE Power Engineering Society General Meeting, 2004..

[75]  Michael N. Vrahatis,et al.  Particle swarm optimization for minimax problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[76]  Vladimiro Miranda,et al.  EPSO - best-of-two-worlds meta-heuristic applied to power system problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[77]  Y.-Y. Hsu,et al.  Dispatch of capacitors on distribution system using dynamic programming , 1993 .

[78]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[79]  Ganesh K. Venayagamoorthy,et al.  Optimal PSO for collective robotic search applications , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[80]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[81]  Y.-Y. Hsu,et al.  Reactive power/voltage control in a distribution substation using dynamic programming , 1995 .

[82]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[83]  Ying Sun,et al.  Distribution network reconfiguration for load balancing using binary particle swarm optimization , 2004, 2004 International Conference on Power System Technology, 2004. PowerCon 2004..

[84]  S. A. Al-Baiyat,et al.  Economic load dispatch multiobjective optimization procedures using linear programming techniques , 1995 .

[85]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[86]  Jianming Zhang,et al.  Application of particle swarm optimization algorithm for weighted fuzzy rule-based system , 2004, 30th Annual Conference of IEEE Industrial Electronics Society, 2004. IECON 2004.

[87]  Gerry Dozier,et al.  Adapting Particle Swarm Optimizationto Dynamic Environments , 2001 .

[88]  Yutian Liu,et al.  Reactive power optimization based on PSO in a practical power system , 2004, IEEE Power Engineering Society General Meeting, 2004..

[89]  Keiichiro Yasuda,et al.  Parameter tuning of fixed structure controller for power system stability enhancement , 2002, IEEE/PES Transmission and Distribution Conference and Exhibition.

[90]  Zwe-Lee Gaing,et al.  Particle swarm optimization to solving the economic dispatch considering the generator constraints , 2003 .

[91]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[92]  D. Chattopadhyay A practical maintenance scheduling program mathematical model and case study , 1998 .

[93]  James Kennedy,et al.  Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[94]  Robert J. Marks,et al.  FPGA implementation of particle swarm optimization for inversion of large neural networks , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[95]  Russell C. Eberhart,et al.  Tracking and optimizing dynamic systems with particle swarms , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[96]  P. J. Angeline,et al.  Using selection to improve particle swarm optimization , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[97]  T. Krink,et al.  Particle swarm optimisation with spatial particle extension , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[98]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[99]  Chia-Feng Juang,et al.  Evolutionary fuzzy control of flexible AC transmission system , 2005 .

[100]  J. C. Pidre,et al.  Optimal planning of unbalanced networks using dynamic programming optimization , 2004, IEEE Transactions on Power Systems.

[101]  Russell C. Eberhart,et al.  Adaptive particle swarm optimization: detection and response to dynamic systems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[102]  Yutian Liu,et al.  An adaptive PSO algorithm for reactive power optimization , 2003 .

[103]  Michael N. Vrahatis,et al.  Particle swarm optimization for integer programming , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[104]  G. L. Torres,et al.  On a nonlinear multiple-centrality-corrections interior-point method for optimal power flow , 2001 .

[105]  M. R. AlRashidi,et al.  A Survey of Particle Swarm Optimization Applications in Power System Operations , 2006 .

[106]  Wenjun Zhang,et al.  Dissipative particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[107]  Y.P. Lu,et al.  Particle swarm optimization for economic dispatch of units with non-smooth input-output characteristic functions , 2005, Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems.

[108]  Emilio F. Campana,et al.  Dynamic system analysis and initial particles position in Particle Swarm Optimization , 2006 .

[109]  Konstantinos E. Parsopoulos,et al.  MULTIOBJECTIVE OPTIMIZATION USING PARALLEL VECTOR EVALUATED PARTICLE SWARM OPTIMIZATION , 2003 .

[110]  Nicola Bianchi,et al.  Design optimisation of electric motors by genetic algorithms , 1998 .

[111]  S. M. Shahidehpour,et al.  An intelligent dynamic programming for unit commitment application , 1991 .

[112]  E. Prempain,et al.  An improved particle swarm optimization for optimal power flow , 2004, 2004 International Conference on Power System Technology, 2004. PowerCon 2004..

[113]  Lehrstuhl für Elektrische,et al.  Gaussian swarm: a novel particle swarm optimization algorithm , 2004, IEEE Conference on Cybernetics and Intelligent Systems, 2004..

[114]  L. Chang,et al.  A neural network-based optimization approach for induction motor design , 1996, Proceedings of 1996 Canadian Conference on Electrical and Computer Engineering.

[115]  W. J. Hobbs,et al.  An enhanced dynamic programming approach for unit commitment , 1988 .

[116]  Yijia Cao,et al.  Dynamic economic dispatch in electricity market using particle swarm optimization algorithm , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[117]  M. N. Vrahatis,et al.  Particle swarm optimization method in multiobjective problems , 2002, SAC '02.

[118]  Carson W. Taylor,et al.  Definition and Classification of Power System Stability , 2004 .

[119]  Andres Ramos,et al.  A Nonlinear Programming Approach to Optimal Static Generation Expansion Planning , 1989, IEEE Power Engineering Review.

[120]  J. J. Kumar,et al.  Particle swarm optimization solution to emission and economic dispatch problem , 2003, TENCON 2003. Conference on Convergent Technologies for Asia-Pacific Region.

[121]  M. Batouche,et al.  Hybrid particle swarm with differential evolution for multimodal image registration , 2004, 2004 IEEE International Conference on Industrial Technology, 2004. IEEE ICIT '04..

[122]  Jonathan E. Rowe,et al.  Particle swarm optimization and fitness sharing to solve multi-objective optimization problems , 2005, 2005 IEEE Congress on Evolutionary Computation.

[123]  A. Ishigame,et al.  Neuro stabilizing control based on Lyapunov method for power system , 2002, Proceedings of the 41st SICE Annual Conference. SICE 2002..

[124]  S. M. Shahidehpour,et al.  Combination of Lagrangian-relaxation and linear-programming approaches for fuel-constrained unit-commitment problems , 1989 .

[125]  R.G. Harley,et al.  Multiple STATCOM Allocation and Sizing Using Particle Swarm Optimization , 2006, 2006 IEEE PES Power Systems Conference and Exposition.

[126]  P. Sensarma,et al.  A comprehensive method for optimal expansion planning using particle swarm optimization , 2002, 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309).

[127]  Antonio J. Conejo,et al.  Transmission expansion planning: a mixed-integer LP approach , 2003 .

[128]  Zwe-Lee Gaing A particle swarm optimization approach for optimum design of PID controller in AVR system , 2004, IEEE Transactions on Energy Conversion.

[129]  Russell C. Eberhart,et al.  Recent advances in particle swarm , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[130]  M. A. Abido Optimal des'ign of Power System Stabilizers Using Particle Swarm Opt'imization , 2002, IEEE Power Engineering Review.

[131]  W. Kurutach,et al.  Feeder-switch relocation for value-based distribution reliability assessment , 2004, 2004 IEEE International Engineering Management Conference (IEEE Cat. No.04CH37574).

[132]  A. A. El-Keib,et al.  Fast linear programming state estimation using the dual formulation , 1992 .

[133]  M. Pereira,et al.  A Mixed Integer Disjunctive Model for Transmission Network Expansion , 2001, IEEE Power Engineering Review.

[134]  Danny Pudjianto,et al.  Allocation of VAr support using LP and NLP based optimal power flows , 2002 .

[135]  Shuyuan Yang,et al.  A quantum particle swarm optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[136]  A. Semlyen,et al.  Hydrothermal Optimal Power Flow Based on a Combined Linear and Nonlinear Programming Methodology , 1989, IEEE Power Engineering Review.

[137]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[138]  R. Eberhart,et al.  Fuzzy adaptive particle swarm optimization , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[139]  J. Waight,et al.  Experiences with Mixed Integer Linear Programming-Based Approaches in Short-Term Hydro Scheduling , 2001, IEEE Power Engineering Review.

[140]  J.G. Vlachogiannis,et al.  Determining generator contributions to transmission system using parallel vector evaluated particle swarm optimization , 2005, IEEE Transactions on Power Systems.

[141]  D. E. Lidgate,et al.  Optimal operational planning for a hydro-electric generation system , 1988 .

[142]  H. M. Emara,et al.  Stator fault estimation in induction motors using particle swarm optimization , 2003, IEEE International Electric Machines and Drives Conference, 2003. IEMDC'03..

[143]  Gerald B. Sheblé,et al.  Direct load control-A profit-based load management using linear programming , 1998 .

[144]  P. Scarpellini,et al.  A static optimization approach to assess dynamic available transfer capability , 1999 .

[145]  Mark M. Millonas,et al.  Swarms, Phase Transitions, and Collective Intelligence , 1993, adap-org/9306002.

[146]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[147]  A. J. Urdaneta,et al.  A Linear Programming Methodology for the Optimization of Electric Power Generation Schemes , 2002, IEEE Power Engineering Review.

[148]  Malcolm Irving,et al.  A parallel processing algorithm for co-ordination of directional overcurrent relays in interconnected power systems , 1994 .

[149]  S.K. Halgamuge,et al.  Particle swarm optimisation for reactive power and voltage control with grid-integrated wind farms , 2004, IEEE Power Engineering Society General Meeting, 2004..

[150]  Dipti Srinivasan,et al.  Particle swarm optimization-based approach for generator maintenance scheduling , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[151]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[152]  Walter Cedeño,et al.  A comparison of particle swarms techniques for the development of quantitative structure-activity relationship models for drug design , 2005, 2005 IEEE Computational Systems Bioinformatics Conference - Workshops (CSBW'05).

[153]  Tapabrata Ray,et al.  A Swarm Metaphor for Multiobjective Design Optimization , 2002 .

[154]  W. M. Grady,et al.  Minimizing harmonic voltage distortion with multiple current-constrained active power line conditioners , 1997 .

[155]  J. Bishop Stochastic searching networks , 1989 .

[156]  Russell C. Eberhart,et al.  Multiobjective optimization using dynamic neighborhood particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[157]  Lan Zhang,et al.  Real-time economic dispatch with line flow and emission constraints using quadratic programming , 1998 .

[158]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[159]  G.K. Venayagamoorthy,et al.  Real-Time Implementation of a Dual Function Neuron based Wide Area SVC Damping Controller , 2006, Conference Record of the 2006 IEEE Industry Applications Conference Forty-First IAS Annual Meeting.

[160]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[161]  A.H. Mantawy,et al.  A new reactive power optimization algorithm , 2003, 2003 IEEE Bologna Power Tech Conference Proceedings,.

[162]  F.D. Galiana,et al.  Unit commitment with primary frequency regulation constraints , 2005, IEEE Transactions on Power Systems.

[163]  Hua Wei,et al.  An interior point nonlinear programming for optimal power flow problems with a novel data structure , 1997 .

[164]  J. Aguado,et al.  Cumulant-based stochastic nonlinear programming for variance constrained voltage stability analysis of power systems , 2006, IEEE Transactions on Power Systems.

[165]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[166]  Kevin Tomsovic,et al.  Optimized distribution protection using binary programming , 1998 .

[167]  Hiroshi Nakajima,et al.  On-line economic load dispatch based on fuel cost dynamics , 1997 .

[168]  B. Zhao,et al.  A multiagent-based particle swarm optimization approach for optimal reactive power dispatch , 2005, IEEE Transactions on Power Systems.

[169]  P. Kundur,et al.  Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions , 2004, IEEE Transactions on Power Systems.

[170]  M. El-Hawary,et al.  Particle swarm optimizer for constrained economic dispatch with prohibited operating zones , 2002, IEEE CCECE2002. Canadian Conference on Electrical and Computer Engineering. Conference Proceedings (Cat. No.02CH37373).

[171]  D.G. Robinson Reliability analysis of bulk power systems using swarm intelligence , 2005, Annual Reliability and Maintainability Symposium, 2005. Proceedings..

[172]  E. Ozcan,et al.  Particle swarm optimization: surfing the waves , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[173]  Ponnuthurai N. Suganthan,et al.  A novel concurrent particle swarm optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[174]  Zhao Hui,et al.  Optimal Design of Power System Stabilizer Using Particle Swarm Optimization , 2006 .

[175]  Turan Gonen,et al.  Electric power distribution system engineering , 1985 .

[176]  K. Passino,et al.  Biomimicry of Social Foraging Bacteria for Distributed Optimization: Models, Principles, and Emergent Behaviors , 2002 .

[177]  Peter J. Bentley,et al.  Don't push me! Collision-avoiding swarms , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[178]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[179]  Ronald G. Harley,et al.  Optimal Allocation of a STATCOM in a 45 Bus Section of the Brazilian Power System Using Particle Swarm Optimization , 2006 .

[180]  Antonio J. Conejo,et al.  Allocation of the cost of transmission losses using a radial equivalent network , 2003 .

[181]  G. Lambert-Torres,et al.  A hybrid particle swarm optimization applied to loss power minimization , 2005, IEEE Transactions on Power Systems.

[182]  D.H. Werner,et al.  Particle swarm optimization versus genetic algorithms for phased array synthesis , 2004, IEEE Transactions on Antennas and Propagation.

[183]  Kun Yuan Huang Demand subscription services-an iterative dynamic programming for the substation suffering from capacity shortage , 2003 .

[184]  Mohammad Ali Abido,et al.  AGC tuning of interconnected reheat thermal systems with particle swarm optimization , 2003, 10th IEEE International Conference on Electronics, Circuits and Systems, 2003. ICECS 2003. Proceedings of the 2003.

[185]  K.,et al.  LINEAR PROGRAMMING APPLICATIONS TO POWER SYSTEM ECONOMICS , PLANNING AND OPERATIONS , 2004 .

[186]  A. K. David,et al.  Reactive power optimisation with voltage stability consideration in power market systems , 2003 .

[187]  Daniel S. Kirschen,et al.  MW/voltage control in a linear programming based optimal power flow , 1988 .

[188]  Chia-Feng Juang,et al.  A hybrid of genetic algorithm and particle swarm optimization for recurrent network design , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[189]  Xiao-Feng Xie,et al.  DEPSO: hybrid particle swarm with differential evolution operator , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[190]  B. Mozafari,et al.  An Approach for Under Voltage Load Shedding Using Particle Swarm Optimization , 2006, 2006 IEEE International Symposium on Industrial Electronics.

[191]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[192]  D. Brandt,et al.  A linear programming model for reducing system peak through customer load control programs , 1996 .

[193]  Xiaodong Li,et al.  A Non-dominated Sorting Particle Swarm Optimizer for Multiobjective Optimization , 2003, GECCO.

[194]  S. Kannan,et al.  Generation expansion planning in the competitive environment , 2004, 2004 International Conference on Power System Technology, 2004. PowerCon 2004..

[195]  Gerald B. Sheblé,et al.  Optimal power flow emulation of interchange brokerage systems using linear programming , 1992 .

[196]  J.K. Nelson,et al.  Time optimal load shedding for distributed power systems , 2006, IEEE Transactions on Power Systems.

[197]  Ganesh K. Venayagamoorthy,et al.  Online Training of a Generalized Neuron with Particle Swarm Optimization , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[198]  A.A. Abido,et al.  Particle swarm optimization for multimachine power system stabilizer design , 2001, 2001 Power Engineering Society Summer Meeting. Conference Proceedings (Cat. No.01CH37262).

[199]  F.D. Galiana,et al.  A mixed-integer LP procedure for the analysis of electric grid security under disruptive threat , 2005, IEEE Transactions on Power Systems.

[200]  Y. Fukuyama State estimation and optimal setting of voltage regulator in distribution systems , 2001, 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194).

[201]  M. Irving,et al.  Observability analysis for state estimation using linear programming , 2001 .