2012
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Load Model Effect Assessment on Optimal Distributed Generation Sizing and Allocation Using Improved Harmony Search Algorithm
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The operation of a distribution system in the presence of distributed generation systems has someadvantages and challenges. Optimal sizing and siting of DG systems has economic, technical, andenvironmental benefits in distribution systems. Improper selection of DG systems can reduce theseadvantages or even result in deterioration in the normal operation of the distribution system. DGallocation and capacity determination is a nonlinear optimization problem. The objective function ofthis problem is the minimization of the total loss of the distribution system. In this paper, the ImprovedHarmony Search (IHS) algorithm has been applied to the optimization problem. This algorithm has asuitable performance for this type of optimization problem. Active and reactive power demands of thedistribution system loads are dependent on bus voltage. This paper verifies the effect of voltagedependent loads on system power characteristics. The load model has an inevitable impact on DGsizing and placement. The proposed algorithm implemented and tested on 69bus distribution systemsand the impact of voltage dependent load models are demonstrated. The obtained results show that theproposed algorithm has an acceptable performance.
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حسین
نصیر اقدم
Hossein
Nasiraghdam
Iran
h.nasiraghdam@srbiau.ac.ir
مرتضی
نصیر اقدم
Morteza
Nasiraghdam
Iran
mnasiraghdam@iauahar.ac.ir
distributed generation
improved harmony search
DG sizing and sitting
load model
[[1] Zhu, D., Broadwater, R.P., Tam, KS., Seguin,##R. and Asgeirsson, H. “Impact of DG##Placement on Reliability and Efficiency with##TimeVarying Loads,” IEEE Transaction on##Power Systems, vol. 21(1), pp.41927, 2006.##[2] Celli, G., Ghiani, E., Loddo, M. and Pilo, F.##“Voltage Profile Optimization with Distributed##Generation,” IEEE Russia Power Tech, 2005.##[3] Zangiabadi, M., Feuillet, R., Lesani, H., Hadj##Said, N. and Kvaløy, J. “Assessing the##performance and benefits of customer##distributed generation developers under##uncertainties,” Energy, vol. 36, pp.170312,##[4] Porkar, S., Poure, P., AbbaspourTehranifard,##A. and Saadate, S. “A novel optimal##distribution system planning framework##implementing distributed generation in a##deregulated electricity market,” Electr. Power##Syst. Res., vol. 80, pp.828–37, 2010.##[5] Zangeneh, A., Jadid, S. and RahimiKian, A.##“A fuzzy environmentaltechnicaleconomic##model for distributed generation planning,”##Energy, vol.36, pp.343745, 2011.##[6] BayodRu´ jula, A.A. “Future development of##the electricity systems with distributed##generation,” Energy, vol. 34, pp.37783, 2009.##[7] Harrison, G.P. and Wallace, A.R. “Maximizing##distributed generation capacity in deregulated##markets,” Proceedings of the IEEE##Transmission and Distribution Conference and##Exposition, vol. 2, pp. 527–530, September,##[8] Harrison, G. P., Piccolo, A., Siano, P.and##Wallace, A. R. “Hybrid GA and OPF##evaluation of network capacity for distributed##generation connections,” Electr. Power Syst.##Res., vol. 78, pp. 392–98, 2008.##[9] Khalesi, N., Rezaei, N. and Haghifam, M. R.##“DG allocation with application of dynamic##programming for loss reduction and reliability##improvement,” Int. J. Elect. Power Energy##Syst., vol. 33(2), pp. 288–95, 2011.##[10] Wang, C. and Nehrir, MH. “Analytical##approaches for optimal placement of##distributed generation sources in power##systems,” IEEE Transaction on Power##Systems, vol. 19(4), pp. 2068–76, 2004.##[11] Acharya, N., Mahat, P., and Mithulananthan, N.##“An analytical approach for DG allocation in##primary distribution network,” Int. J. Electr.##Power Energy Syst., vol. 28, pp. 669–78, 2006.##[12] Gozel, T., and HakanHoucaoglu, M. “An##analytical method for sizing and siting of##distributed generators in radial systems,”##Electr. Power Syst. Res., vol. 79, pp. 912–8,##[13] Elnashar, M. M., ElShatshat, R. and Salama,##M. M. A. “Optimum siting and sizing of a large##distributed generator in a mesh connected##system,” Electr. Power Syst. Res., vol. 80, pp.##690–97, 2010.##[14] Parizad, A., Khazali, A. and Kalantar, M.##“Optimal Placement of Distributed Generation##with Sensitivity Factors considering Voltage##Stability and Losses Indices,” Proc. Iranian##Conference on Electrical Engineering (ICEE),##pp.8485, 2010.##[15] Moradi, M. H. and Abedini, M. A.##“combination of genetic algorithm and particle##swarm optimization for optimal DG location##and sizing in distribution systems,” Int. J.##Elect.r Power Energy Syst., vol. 34, pp.66–74,##[16] AlRashid,i M.R. and AlHajri, M.F. “Optimal##planning of multiple distributed generation##sources in distribution networks: A new##approach,” Energy Conversion and##Management, vol. 55, pp.3301–8, 2011.##[17] AbuMouti, F. S.andElHawary, M. E.##“Optimal Distributed Generation Allocation##and Sizing in Distribution Systems via##Artificial Bee Colony Algorithm,” IEEE##Transaction on Power Delivery, vol. 26(4),##pp.2090101, 2011.##[18] Rao, R. S., Narasimham, S. V. L., Raju, M. R.##and Rao, A. S. “Optimal Network ##Reconfiguration of LargeScale Distribution##System Using Harmony Search Algorithm,”##IEEE Transaction on Power System, vol. 26(3),##pp.108088, 2011.##[19] Khazali, A. H. and Kalantar, M. “Optimal##reactive power dispatch based on harmony##search algorithm,” Int. J. Electr. Power Energy##Syst., vol.33, pp.684–92, 2011.##[20] Vasebi, A., Fesanghary, M. and Bathaee, S. M.##T. “Combined heat and power economic##dispatch by harmony search algorithm,” Electr.##Power Syst. Res., vol. 29, pp.713–19, 2007.##[21] Coelho, L. S. and Mariani, V. C. “An improved##harmony search algorithm for power economic##load dispatch,” Energy Conversion and##Management, vol. 50, pp.2522–6, 2009.##[22] Khorram, E. and Jaberipour, M. “Harmony##search algorithm for solving combined heat##and power economic dispatch problems,”##Energy Conversion and Management, vol.52,##pp.1550–4, 2011.##[23] Fesanghary, M. and Ardehali, M. M. “A novel##metaheuristic optimization methodology for##solving various types of economic dispatch##problem,” Energy, vol. 34, pp.75766, 2009.##[24] Singh, D. and Misra, R. K. “Multiobjective##feeder reconfiguration in different tariff##structures,” IET Gener. Transm.Distrib.,##2010;vol. 4(8), pp.974–988, 2010.##[25] Singh, D., Misra, R. K. and Singh, D. “Effect##of load models on assessment of energy losses##in distributed generation Planning,” IEEE##Transaction on Power Systems, vol.22(4), pp.##220412, 2007.##[26] Singh, D., Singh, D. and Verma, K.S.##“Multiobjective optimization for DG planning##with load models,” IEEE Transaction on Power##Systems, vol. 24(1), pp. 42736, 2009.##[27] Eminoglu, U. and Hocaoglu, M. H. “A new##power flow method for radial distribution##systems including voltage dependent load##models,” Electr. Power Syst. Res., vol.76, pp.##106–114, 2005.##[28] Geem, Z. W., Kim, J. H. and Loganathan, G. V.##“A new heuristic optimization algorithm:##harmony search,” Simulation, vol.76(2),##pp.60–8, 2001.##[29] Lee, K. S. and Geem, Z. W. “A new metaheuristic##algorithm for continuous engineering##optimization: harmony search theory and##practice,” Appl. Mech. Eng., vol.194, pp.3902–##[30] Mahdavi, M., Fesanghary, M. and Damangir, E.##“An improved harmony searchalgorithm for##solving optimization problems,” Appl. Math.##Comput.,vol. 188(2), pp.1567–79, 2007.##[31] Baran, M. E. and Wu, F. F. “Optimum sizing of##capacitor placed on radial distribution##systems,” IEEE Transaction on Power##Delivery, vol. 4, pp.73543, 1989.##[32] IEEE Standard for Interconnecting Distributed##Resources with Electric Power systems, IEEE##Std. 15472003, 2003, 1–16.##]
A PSOBased Static Synchronous Compensator Controller for Power System Stability Enhancement
A PSOBased Static Synchronous Compensator Controller
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In this paper Power system stability enhancement through static synchronous compensator (STATCOM)based controller is investigated. The potential of the STATCOM supplementary controllers to enhance thedynamic stability is evaluated. The design problem of STATCOM based damping controller is formulatedas an optimization problem according to the eigenvalue based objective function that is solved by a particleswarm optimization (PSO) algorithm. The controllers are tuned to simultaneously shift the lightly dampedand undamped electromechanical modes of machine to a prescribed zone in the splane. The resultsanalysis reveals that the designed PSO based STATCOM damping controller has an excellent capability indamping the power system low frequency oscillations and enhance greatly the dynamic stability of thepower system.
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25


Meisam
Mahdavi
Iran
me.mahdavi@ut.ac.ir


Ali
Nazari
Iran


Vahid
Hosseinnezhad
Iran


Amin
Safari
Iran
STATCOM
particle swarm optimization
Damping Controller
Dynamic stability
[[1] J. Machowski and J. W. Bialek, “State variable##control of shunt FACTS devices using phasor##measurements,” Electric Power Systems##Research, Vol. 78, pp. 3948, 2008.##[2] N.G. Hingorani and L. Gyugyi, Understanding##FACTS: concepts and technology of flexible AC##transmission systems, WileyIEEE Press, 1999.##[3] M.A. Abido, “Analysis and assessment of##STATCOM based damping stabilizers for power##system stability enhancement,” Electric Power##Systems Research, Vol. 73, no. 3, pp. 177185,##[4] H. F. Wang, “PhillipsHeffron model of power##systems installed with STATCOM and##applications,” IEE Proc. Generation Transmission##and Distribution, Vol. 146, pp. 521527, 1999.##[5] S. Morris, P. K. Dash and K. P. Basu, “A fuzzy##variable structure controller for STATCOM,”##Electric Power Systems Research, Vol. 65, pp. 23##[6] A. H. M. A. Rahim and M. F. Kandlawala,##“Robust STATCOM voltage controller design##using loop shaping technique,” Electric Power##Systems Research, Vol. 68, pp. 6174, 2004.##[7] J. Kennedy, “The particle swarm: social##adaptation of knowledge,” Proc. the International##Conf. Evolutionary and Computation,##Indianapolis, pp. 303308, 1997.##[8] H. Shayeghi, A. Safari and H. Shayanfar,##“Multimachine power system stabilizers design##using PSO algorithm,” International Journal of##Elect Power and Energy System Engineering, Vol. ##1, pp. 226233, 2008.##[9] J. Kennedy, R. Eberhart and Y. Shi, Swarm##intelligence, Morgan Kaufmann Publishers, San##Francisco. 2001.##[10] H. Shayeghi, H. A. Shayanfar, S. Jalilzadeh and##A. Safari, “Design of output feedback UPFC##controller for damping electromechanical##oscillations using PSO,” Energy Conversion and##Management, Vol. 50, pp. 25542561, 2009.##[11] A. T. AlAwami, Y. L. AbdelMagid and M. A.##Abido, “A particleswarmbased approach of##power system stability enhancement with unified##power flow controller,” Elect. Power and Energy##Systems, Vol. 29, pp. 251259, 2007. ##]
Using Neural Network to Control STATCOM for ImprovingTransient Stability
Using Neural Network to Control STATCOM
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FACTS technology has considerable applications in power systems, such as; improving the steady stateperformance, damping the power system oscillations, controlling the power flow, and etc. STATCOM is oneof the most important FACTS devices used in the parallel compensation, enhancing transient stability andetc. Since three phase fault is widespread in power systems, in this paper STATCOM is used to improve thetransient stability of power system when three phase fault occurred. Neural Network has been used foradjusting the gain of the supplementary controller of STATCOM. The simulation performed in MATLAB /Simulink software. Simulation results showed when STATCOM combines with proposed Neural Networkbased supplementary controller; the transient stability of power system improves.
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26
31


Mozhgan
Balavar
Iran
mbalavar@iauahar.ac.ir
FACTS
STATCOM
Artificial neural network (ANN)
Power Oscillation Damping
[[1] M. Karrari, “Dynamic and Control Of Power##System,” First Publishing, Tehran, Amirkabir##University Publishing Center, Winter 1382.##[2] M. Najari, A. A. Ghareveysi, M. A. Sadrniya, E.##Ebadi, “Khorasan Network Optimization By Facts##Tools,” 2005.##[3] Raviraj Vsc And Sen Pc, “Comparative Study Of##ProportionalIntegral, Sliding Mode, And Fuzzy##Logic Controllers For Power Converters,” IEEE##Transaction On Industry Applications, Pp.1824,##[4] J. Lu, M. H. Nehrir, D. A. Pierre, “A Fuzzy Logic##Based Adaptive Damping Controller For Static##VAR Compensator,” Electric Power Systems##Research 68 (2004), 113118.##[5] N. G. Hyngurany, L. Gayogi, “Introduction With##A Flexible Transmission Network Productivity##Concepts And Technologies, Facts,” First##Publishing, Advisor Engineers Of Qods, Spring##[6] S.M. Bamasak,”FactsBased Stabilizers For Power##System Stability Enhancement,” PhD Thesis, King##Fahad University Of Petroleum, 2005.##[7] N. Jamshidi, R.Rasoli, A. Abavi Mehrizi,##“Applied Learning Advanced Topics In Electrical##Engineering With Matlab,” Second Publishing,##Tehran, 1386.##]
Voltage Flicker Parameters Estimation Using Shuffled Frog Leaping Algorithm and Imperialistic Competitive Algorithm
Voltage Flicker Parameters Estimation
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Measurement of magnitude and frequency of the voltage flicker is very important for monitoring andcontrolling voltage flicker efficiently to improve the network power quality. This paper presents twonew methods for measurement of flicker signal parameters using Shuffled Frog Leaping Algorithm(SFLA) and Imperialist Competitive Algorithm (ICA). This paper estimates fundamental voltage andflicker magnitudes and frequencies with proposed methods. The goal is to minimize the error of theestimated magnitudes and frequencies via a designed fitness function. At first, we introduce voltageflicker and its measuring techniques. Then voltage flicker model is analyzed. At the next part, a reviewof SFLA and ICA is presented. These methods will be applied to a test voltage signal and the resultsare be analyzed.
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32
39


Saeid
Jalilzade
Iran
jalilzadeh@znu.ac.ir


Mehdi
Mardani
Iran
m_mardani@znu.ac.ir
Voltage flicker signal
Flicker magnitude and frequency measurement
Shuffled Frog Leaping Algorithm (SFLA)
Imperialist competitive algorithm (ICA)
The Intelligent Modeling of Human Hand Motion Using Magnetic Based Techniques
The Intelligent Modeling
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2
With increasing use of robots instead of human in industrial, medicine and military applications etc.the importance of research on designing and building of robots is increasing. In this paper variousmethods of the human hand motion simulation has been investigated and we used one of most commonmethod named Datagloves which extract data from hand and then we simulated hand motion duringseveral processing stages. At first step we designed and built circuits to digitize analog data receivedfrom sensors and we sent them to computer. Then we received extracted data in MATLAB andprocessed them to simulate bending of the wrist and fingers joints graphically. In this method wemapped data linearly to 090 and rotate points around relative Coordinate axis in the specificconditions. Results show that we can simulate hand motion in real time with low cost, lowest error andwithout complex and expensive equipments.
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47


M
Asghari
Iran
masgari@iauahar.ac.ir


M. A
Badamchizadeh
Iran


M. E
Akbari
Iran
makbari@iauahar.ac.ir
Hand motion simulation
DataGlove
Data extraction circuit
simulation in MATLAB
[[1] ChinShyurng Fahn and Herman Sun,##“Development of a Sensory Data Glove,##“Using NeuralNetworkBased##Calibration”, Taipei, Taiwan: ICAT 2000,##pages 18.##[2] Sturman, D.J.; Zeltzer, D. “A survey of##glovebased input”, IEEE Comput.##Graphics, 14, 3039, 1994, pages 106111.##[3] [Online], Available:##www.tekscan.com/flexiforce##[4] M. Bezdicek1, D. G.##aldwell2“PORTABLE ABSOLUTE ##[13] Amir Hossein Omidvar, ”EMG Feature##Extraction to Control the Prosthetic Hand##”A thesis Presented to Sharif University of##Technology, International Campus, Kish##Island, Iran, 2010pages 151158.##[14] Kostas N. Tarchanidis, Member, IEEE, and##John N. Lygouras , “Data Glove With a##Force Sensor ”IEEE TRANSACTIONS ON##INSTRUMENTATION AND##MEASUREMEN”, VOL. 52, NO. 3, JUNE##2003, pages 8895.##[15] http://www.edaboard.com/thread47834.html##[16] www.mathworks.com/help/toolbox/instrume##nt/serialreceive.html.##[17] http://www.mathkb.com. ##]
FACTS Control Parameters Identification for Enhancement of Power System Stability
FACTS Control Parameters Identification
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The aim of this paper is to investigate a novel approach for output feedback damping controller design ofSTATCOM in order to enhance the damping of power system low frequency oscillations (LFO). The design ofoutput feedback controller is considered as an optimization problem according with the time domainbasedobjective function which is solved by a honey bee mating optimization algorithm (HBMO) that has a strongability to find the most optimistic results. The effectiveness of the proposed controller are tested anddemonstrated through nonlinear timedomain simulation studies over a wide range of loading conditions. Thesimulation study shows that the designed controller by HBMO has a strong ability to damping of power systemlow frequency oscillations. Moreover, the system performance analysis under different operating conditionsshow that the φ based controller is superior to the C based controller.
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48
55


Ali
Ahmadian
Iran
ali.ahmadian1367@gmail.com


Masoud
Aliakbar Golkar
Iran
golkar@kntu.ac.ir
FACTS
STATCOM
Honey Bee Mating Optimization
Damping Controller
Low frequency oscillations
Power System
Dynamic stability
[[1] M. Anderson, and A.A. Fouad, “Power System##Control and Stability”, Ames, IA: Iowa State##Univ. Press, 1977.##[2] A.T. AlAwami, Y.L. AbdelMagid and M.A.##Abido, “A particleswarmbased approach of##power system stability enhancement with ##unified power flow controller", International##Journal of Electrical Power and Energy##System, Vol. 29, , pp. 251259, 2007.##[3] J. Machowski, and J. W. Bialek, "State##variable control of shunt FACTS devices using##phasor measurements", Electric Power Systems##Research, Vol. 78, pp. 3948, 2008.##[4] N. Mithulanathan, C.A. Canizares, J. Reeve,##G.J. Rogres, “ comparison of PSS, SVC and##STATCOM controllers for damping power##systems oscillations”, IEEE Trans. On power##syst. Vol. 18(No.2), pp.786792, 2003.##[5] S. Morris, P. K. Dash and K. P. Basu, "A fuzzy##variable structure controller for STATCOM",##Electric Power Systems Research, Vol. 65, pp.##2334, 2003.##[6] N.G. Hingorani, and L. Gyugyi,##“Understanding FACTS: concepts and##technology of flexible AC transmission##systems“, WileyIEEE Press, 1999.##[7] H. F. Wang, "PhillipsHeffron model of power##systems installed with STATCOM and##applications", IEE Proc. on Generation##Transmission and Distribution, Vol. 146, No. 5,##pp. 521527, 1999.##[8] M.A. Abido, "Analysis and assessment of##STATCOM based damping stabilizers for##power system stability enhancement", Electric##Power Systems Research, Vol. 73, pp. 177185,##[9] A. H. M. A. Rahim, and M. F. Kandlawala,##"Robust STATCOM voltage controller design##using loop shaping technique", Electric Power##Systems Research, Vol. 68, pp. 6174, , 2004.##[10] S. Lee, "Optimal Decentralized Design for##Output Feedback Power System Stabilizers",##IEE Proc. Gener. Transm. Distrib., Vol. 152,##No. 4, pp. 494502, 2005.##[11] X. R. Chen, N. C. Pahalawaththa, U.D.##Annakkage and C.S. Cumble, "Design of##Decentralized Output Feedback TCSC##Damping Controllers by Using Simulated##Annealing", IEE Proc. Gen. Transm. Dist., Vol.##145, No. 5, pp. 553558, 1998.##[12] F. Armansyah, N. Yorino and H. Sasaki,##"Robust Synchronous Voltage Sources##Designed Controller for Power System##Oscillation Damping", Electrical Power##Energy System, Vol. 24, pp. 4149, 2002.##[13] H. Shayeghi, H.A. Shayanfar, S. Jalilzadeh and##A. Safari, “Simultaneous Coordinated##Designing of UPFC and PSS Output Feedback ##Controllers using PSO”, Journal of Electrical##Engineering, Vol. 60, No. 4, pp.177 184,##]
A Novel Heuristic Optimization Methodology for Solving of Economic Dispatch Problems
A Novel Heuristic Optimization Methodology
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This paper presents a biogeographybased optimization (BBO) algorithm to solve the economic loadDispatch (ELD) problem with generator constraints in thermal plants. The applied method can solvethe ELD problem with constraints like transmission losses, ramp rate limits, and prohibited operatingzones. Biogeography is the science of the geographical distribution of biological species. The modelsof biogeography explain how a organisms arises, immigrate from an environment to another and getseliminated. The BBO has some characteristics that are shared with other population basedoptimization procedures, similar to genetic algorithms (GAs) and particle swarm optimization (PSO).The BBO algorithm mainly based on two steps: migration and mutation. The BBO has some goodfeatures in reaching to the global minimum in comparison to other evolutionary algorithms. Thisalgorithm applied on two practical test systems that have six and fifteen thermal units, results of thispaper are used to see the comparison between performances of the BBO algorithm with other existingalgorithms. The result of this investigation proves the efficiency and good performance of applyingBBO algorithm on ELD problem and show that this method can be a good substitute for otheralgorithms.
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55
65


Ali
Nazari
Iran


Amin
Safari
Iran
asafari@iauahar.ac.ir


Hossein
Shayeghi
Iran
biogeographybased optimization
economic load dispatch
prohibited operating zone
ramp rate limits
[[1] A. J. Wood and B. F. Wollenberg, Power##Generation, Operation, and Control, 2nd ed.##New York: Wiley, 1996.##[2] A. A. ElKeib, H. Ma, and J. L. Hart,##“Environmentally constrained economic##dispatch using The Lagrangian relaxation##method,” IEEE Trans. Power Syst., vol. 9, no.##4, pp. 1723–1729, Nov. 1994.##[3] C.T. Su and C.T. Lin, “New approach with a##Hopfield modeling framework to economic##Dispatch,” IEEE Trans. Power Syst., vol.##15,no. 2, p. 541, May 2000.##[4] C.T. Su and C.T. Lin, “New approach with a##Hopfield modeling framework to economic##Dispatch,” IEEE Trans. Power Syst., vol. 15,##no. 2, p. 541, May 2000.##[5] P. H. Chen and H. C. Chang, “Largescale##economic dispatch by genetic algorithm,” IEEE##Trans. Power Syst., vol. 10, no. 4, pp. 1919– ##1926, Nov. 1995. ##[6] Lin WM, Chen FS, Tsay MT. An improved##tabu search for economic dispatch with##multiple Minima. IEEE Trans Pow Syst##2002;17(1):108–12.##[7] Panigrahi B.K., Yadav S. R., Agrawal S. &##Tiwari M.K. (2007). A clonal algorithm to##solve Economic loadispatch. Electrical Power##System Research, 77: 13811389.##[8] K. P. Wong and C. C. Fung, “Simulated##annealing based economic dispatch##algorithm,” Proc. Inst. Elect. Eng. C, vol. 140,##no. 6, pp. 509–515, 1993.##[9] H. T. Yang, P. C. Yang, and C. L. Huang,##“Evolutionary programming based economic##dispatch for units with nonsmooth fuel cost##functions,” IEEE Trans. Power Syst., vol. 11,##no. 1, pp. 112–118, Feb. 1996.##[10] D. Simon, “Biogeographybased optimization,”##IEEE Trans. Evol. Comput., vol. 12, no. 6, pp.##702–713, Dec. 2008.##[11] A. Bhattacharya and P. K. Chattopadhyay##“BiogeographyBased Optimization for##Different Economic Load Dispatch Problems”##IEEE Trans. Power Syst., VOL. 25, NO. 2 , pp##1064  1077 , MAY 2010.##[12] Z.L. Gaing, “Particle swarm optimization to##solving the economic dispatch considering the##generator constraints,” IEEE Trans. Power##Syst., vol. 18, no. 3, pp. 1187–1195, Aug. 2003.##[13] I. Selvakumar and K. Thanushkodi, “A new##particle swarm optimization solution to##nonconvex economic dispatch problems,”##IEEE Trans. Power Syst., vol. 22, no. 1, pp.##42–51, Feb. 2007.##[14] K. T. Chaturvedi, M. Pandit, and L. Srivastava,##“Selforganizing hierarchical particle swarm##Optimization for nonconvex economic##dispatch,” IEEE Trans. Power Syst., vol. 23,##no. 3, p. 1079, Aug. 2008.##[15] PereiraNeto A, Unsihuay C, Saavedra OR.##Efficient evolutionary strategy optimization##Procedure to solve the non convex economic##dispatch problem with generator constraints.##IEE Proc – GenerTransm Distrib 2005;##152(5):653–660.##]