Optimal Sizing and Placement of Distribution Generation Using Imperialist Competitive Algorithm

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1 Optimal Sizig ad Placemet of Distributio Geeratio Usig Imperialist Competitive Algorithm H. A. Shayafar * Electrical Eg. Departmet, Islamic Azad Uiversity, South Tehra Brach, Tehra, Ira N. Amjady Electrical Egieerig Departmet, Sema Uiversity, Sema, Ira A.Ghasemi Youg Researcher Club, Ardabil Brach, Islamic Azad Uiversity, Ardabil, Ira O. Abediia Electrical Egieerig Departmet, Sema Uiversity, Sema, Ira hashayafar@yahoo.com, _amjady@yahoo.com, ghasemi.agm@gmail.com, oveis.abediia@hotmail.com Abstract I this paper Imperialism Competitive Algorithm (ICA) is proposed to optimal placemet of Distributio Geeratio (DG) i power system. The power distributio geeratio systems are ecessary for cosumers to achieve power with less price ad best quality. I the other had, they ca help to the active power uits i power system etworks for system losses reductio, distributio lies, voltage profile improvemet. Also, ICA is a global search strategy that uses the socio-political competitio amog empires as a source of ispiratio. The effectiveess of the proposed techique is applied to mat power 30 buses ad 57 bus power system. The achieved result shows the robust reactio of the system with DG. Keywords: DG, ICA, Losses ad Prices. I. INTRODUCTION The desig ad operatio of the electricity distributio etworks always assumed power flows from higher voltage etworks to lower voltage etworks. Power ijectios ad power demads that appear at various places i the distributio systems are assumed to be distributig equally betwee the phases. This assumptio is valid for passive etworks. However, the coectio ad operatio of sigificat Distributio Geeratio (DG) (of varyig techologies) alters may etwork characteristics makig the existig assumptios of etwork desig ad operatio less applicable to distributio etworks. The power distributio geeratio systems are ecessary for cosumers to achieve power with less price ad best quality. I the other had, they ca help to the active power uits i power system etworks for system losses reductio, distributio lies, voltage profile improvemet ad etc. The mai goal for DG is determiig of optimal size ad placemet of capacitors to be istalled ad efficiet cotrol schemes i the buses of distributio systems [1-4]. The DG sources ca classified at four sets; micro DG (5KW to 1MW), small (5KW to 5MW), medium (5MW to 50MW) ad large size (50MW to 300MW). Meawhile, the source for DGs is very widespread so that they cotai fuel cells, photo voltaic, hydro turbie, combustio egies, micro turbies ad etc [5]. The optimal sizig ad placemet of DG problem is a attractive research area as publish some papers i this area such as global optimizatio techiques like geetic algorithms (GA), Harmoy Search Algorithm (HAS), Particle Swarm Optimizatio (PSO) ad Evolutioary Programmig (EP) techiques have bee applied for optimal tuig of DG based restructure schemes. These evolutioary algorithms are heuristic populatio-based search procedures that icorporate radom variatio ad selectio operators. Although, these methods seem to be good methods for the solutio of DG parameter optimizatio problem, however, whe the system has a highly epistatic objective fuctio (i.e. where parameters beig optimized are highly correlated), ad umber of parameters to be optimized is large, the they have degraded efficiecy to obtai global optimum solutio [6]. I order to overcome these drawbacks, i this paper, a stregth heuristic algorithm has bee preseted to determie the optimal sizig capacitor ad placemet, takig ito accouts fixed capacitors as well as potetial harmoic iteractios (losses, resoace ad distortio factors) i the presece of oliear loads ad DG usig ICA. Therefore, for this reasos, ICA algorithm is used to solve DG problem i order to efficietly cotrol the local search ad covergece to the global optimum ad solutio quality. This proposed method has bee tested o distorted 34-bus ad 57-bus IEEE systems. The * Correspadig Author. Address: hashayafar@yahoo.com (H. A. Shayafar)

2 objectives o this method were to miimize power loss i the distorted distributio etwork havig take the cost of capacitors ito accout [7-]. II. DG PROBLEM FORMULATION The problem is formulated with a objective fuctios, the real power loss reductio i a distributio system is required for efficiet power system operatio. The loss i the system ca be calculated, give the system operatig coditio [11]. (1) Where, S LOSS, P LOSS ad Q LOSS are power loss, active ad reactive power loss for power system etwork, respectively. The A ad B is pealty factor for INDEX objective fuctio to voltage profit improvemet ad miimize total loss. This pealty factors defie based operator for miimize loss or modified voltage profile [12]. Also, they are differet value for test systems. This problem cotais some costrais such as: (a) Power balace costrait DG G P P P P (2) DG G D L DG 1 G 1 (b) Geeratio ad voltage limits costraits DG mi max i i i P P P i 1,2,..., mi max i i i V V V i 1,2,..., (3) The active power trasmissio loss P L ca be calculated by the etwork loss formula: P A ( P P Q Q ) B ( Q P P Q ) (4) L ij i j i j ij i j i j i 1 j 1 Where, A B ij ij R cos( ) ij i j VV i j Rij si( i j ) (5) VV Where, Pi ad Qi are et real ad reactive power ijectio i bus i respectively, Rij is the lie resistace i j betwee bus i ad j, Vi ad δi are the voltage ad agle at bus i respectively. III. IMPERIALIST COMPETITIVE ALGORITHM Imperialism is the policy of extedig the power ad rule of a govermet beyod its ow boudaries. A coutry may attempt to domiate others by direct rule or by less obvious meas such as a cotrol of markets for goods or raw materials. The latter is ofte called eocoloialism [13]. ICA is a ovel global search heuristic that uses imperialism ad imperialistic competitio process as a source of ispiratio. This algorithm starts with some iitial coutries. Some of the best coutries are selected to be the imperialist states ad all the other coutries form the coloies of these imperialists. The coloies are divided amog the metioed imperialists based o their power. After dividig all coloies amog imperialists ad creatig the iitial empires, these coloies start movig toward their relevat imperialist state. This movemet is a simple model of assimilatio policy that was pursued by some imperialist states [14]. Figure 1 shows the iitial empires. Accordigly, bigger empires have greater umber of coloies where weaker oes have less. I this figure, Imperialist 1 has formed the most powerful empire ad cosequetly has the greatest umber of coloies. Figure 1. Geeratio of iitial empires A. Movemet of Coloies toward the Imperialist It is clear that, imperialist coutries start to improve their coloies. We have modeled this fact by movig all the coloies toward the imperialist. Figure 2 shows a coloy movig toward the imperialist by uits. The directio of the movemet is show by the arrow extedig from a coloy to a imperialist [15]. I this figure x is a radom variable with uiform (or ay proper) distributio. The for x we have: x U( 0, d)

3 Figure 2. Movemet of coloies toward their relevat imperialist Where d is the distace betwee the coloy ad the imperialist state. The coditio β >1 causes the coloies to get closer to the imperialist state from both sides. After dividig all coloies amog imperialists ad creatig the iitial empires, these coloies start movig toward their relevat imperialist state which is based o assimilatio policy [16]. Fig.3 shows the movemet of a coloy towards the imperialist. I this movemet, θ ad x are radom umbers with uiform distributio as illustrated ad d is the distace betwee coloy ad the imperialist. x U( 0, d), U(, ) (6) Where, β, γ = parameters that modify the area that coloies radomly search aroud the imperialist. i the power of weaker oes. Weak empires will lose their power gradually ad ultimately they will collapse [15]. The movemet of coloies toward their relevat imperialists alog with competitio amog empires ad also collapse mechaism will hopefully cause all the coutries to coverge to a state i which there exist just oe empire i the world ad all the other coutries are its coloies. I this ideal ew world coloies have the same positio ad power as the imperialist. Fig.4 shows a big picture of the modeled imperialistic competitio. Based o their total power, i this competitio, each of the empires will have a likelihood of takig possessio of the metioed coloies. Figure 4. Imperialistic competitio: The more powerful a empire is, the more likely it will possess the weakest coloy of weakest empire Figure 3. Movemet of coloies toward their relevat imperialist i a radomly deviated directio The total power of a empire depeds o both the power of the imperialist coutry ad the power of its coloies. I this algorithm, this fact is modeled by defiig the total power of a empire by the power of imperialist state plus a percetage of the mea power of its coloies. Ay empire that is ot able to succeed i imperialist competitio ad ca ot icrease its power (or at least prevet decreasig its power) will be elimiated. The imperialistic competitio will gradually result i a icrease i the power of great empires ad a decrease IV. ICA BASED DG PROBLEM The ICA techique for solvig the optimal placemet ad capacitor sizig DG problem to miimize the loss may be costructed with the followig mai stages: Set power system: Iput lie ad bus data, ad bus voltage limits. Calculate fitess based load flow: Calculate the loss usig distributio load flow based o backward-forward sweep. Iitial populatio: Radomly geerates a iitial populatio (array) of particles with radom positios ad velocities o dimesios i the solutio space. Set the iteratio couter k = 0. I the other had, i this step, a iitial populatio based o state variable is geerated, radomly. That is formulated as: 1 2 m D [ D, D, D,..., D ] D ( d, d,..., d ) (7) i i i i Calculate fitess: For each particle if the bus voltage is withi the limits, calculate the total loss. Otherwise, that particle is ifeasible. That is formulated as: mi INDEX Updatig: update populatio with ICA explore egie.

4 Fiish: If the iteratio umber reaches the maximum limit, go to ext Step. Otherwise, set iteratio idex k = k + 1, ad go back to Step 4. Results: Prit out the optimal solutio to the target problem. The best positio icludes the optimal locatios ad size of DG or multi-dgs, ad the correspodig fitess value represetig the miimum total real power loss. The flowchart of the proposed ICA algorithm is shows i Fig.5. The preseted figures show the losses ad voltage of active ad reactive power i proposed case studies. Figure 5. ICADG computatioal procedure V. SIMULATION RESULTS A. 30 ad 57 bus Power System For the testig of proposed techique two case studies are cosidered as; mat power 30 ad 57 bus power system. For both of the case studies, the DGs are cosidered with 5-50 MW ad 1- Mvar. Also the proposed techique cosidered 5 source of DGs to power systems. Table. 1-2, shows the umerical results of DGs i system. I the metioed tables, the active ad reactive powers are preseted for 5 optimized buses. Fig. 6-7, shows the system respose with 5 sources ad without sources. It is clear that by icreasig the umber of DGs i power system, the stability, losses decreasig ad improvig of voltage profile will be appropriate. Figure 6. The losses ad voltage of active ad reactive power i 30- bus system.

5 TABLE I. THE RESULTS OF 30 POWER SYSTEM 30 Bus Power System SIZE DG NUMBER DG P= Q= Figure 7. The losses ad voltage of active ad reactive power i 57- bus system. TABLE II. THE RESULTS OF 57 POWER SYSTEM 57 Bus Power System SIZE DG NUMBER DG P= Q= VI. CONCLUSIONS I this paper, we ivestigated the optimal placemet ad capacitor sizig DG power problem by employig a evolutioary algorithm based o Imperialist Competitive Algorithm. The DG optimizatio problem was cosidered ad formulated as sigle-objective optimizatio problem with competig objectives of power loss ad voltage profile improvemet. The cocept of Pareto domiace was employed to provide the selectio mechaism betwee differet objectives. The proposed algorithm applied to two stadard IEEE systems to show advatages of proposed algorithm i DG problem, 34-bus IEEE test system ad 57-bus IEEE test system. The umerical results demostrate that the proposed method has better ability i fidig optimal aswers ad possibility of particle placed i local zoe. Moreover, the proposed strategy has simple structure, easy to implemet ad tue ad therefore it is recommeded to geerate good quality ad reliable electric eergy i the restructured power systems.

6 REFERENCES [1] J Ae - Marrie & Ja F.Kreider, "Distributed Geeratio The Ae - Marrie & Ja F.Kreider, "Distributed Geeratio The Power Paradigm for the New Milleium",CRC Press LLC, Pub [2] Thomas Ackerma, Groas Aderso, Leart Soder, "Distributed Geeratio: a defiitio", Electric Power System Research (57), pp , Jue [3] W.El-Khattam, M.M.A.Salama, "Distributed geeratio techologies,defiitios ad beefits", Electric Power System Research (57), pp ,14 jauary [4] H. Lee Willis & Walter G.scott, "Distributed Power Geeratio: Plaig ad Evaluatio",Marcel Dekker, Ic., Pub [5] A.Keyhai, "Distributed Geeratio Systems, Power System Workshop, Amirkabir Uiversity, May [6] Brow, R.E. Jiupig Pa, Xiaorig Feg, Koutlev, k., "Sitig Distributed Geeratio todefer T&D expasio", Trasmissio ad Distributio Coferece ad Expositio, 2001 IEEE/PES. [7] P.P.Barker, R.W.de Mello, "Determiig the Impact of Distributed Geeratio o PowerSystem: Part1-Radial Distributio System, Proc. Of IEEE PES Meetig, Seattle, July2000. [8] N.Hadisaid, J.F.Caard, F.Dumas: "Dispersed Geeratio Impact o Distributio Networks", IEEE Computer Applicatios i Power, Vol.12, No.2, April [9] M.A.Kashem, G. Ledwich, "Impact of Distributed Geeratio o Protectio of Sigle Wire earth Retur Lies", Electric Power System Research, [] Scietific - Techical Mothly Magazie of Electrical Power Idustry, No.1 Oct [11] Adly Girgis, Sukumar Brahma, "Effect of Distributed Geeratio o Protective DeviceCoordiatio i Distributio System", IEEE [12] G.Pepermas, J.driese, D.haeseldockx, Rr.belmas, W.dhaeseleer, "Distributed Geeratio Beefits ad Issues", Eergy Policy 33, pp , [13] The Hutchiso Dictioary of World History, Oxford: Helico Publishig, [14] Atashpaz-Gargari, E. ad C. Lucas, (2007) a. Imperialist Competitive Algorithm: A algorithm for optimizatio ispired by imperialistic competitio. I: the proceedig of IEEE Cogress o Evolutioary Computatio. Pp [15] Atashpaz-Gargari E. ad Lucas C., Imperialist Competitive Algorithm: A algorithm for optimizatio ispired by imperialistic competitio, IEEE Cogress o Evolutioary Computatio, Sigapore,2008. [16] I.Tsoulos, D.Gavrilis, E.Glavas, Neural etwork costructio ad traiig usig grammatical evolutio, Sciece Direct Neurocomputig Joural, Vol.72, Issues 1-3, December 2008, pp BIOGRAPHIES Heidarali Shayafar received the B.S. ad M.S.E. degrees i Electrical Egieerig i 1973 ad 1979, respectively. He received his Ph. D. degree i Electrical Egieerig from Michiga State Uiversity, U.S.A., i Curretly, he is a Full Professor i Electrical Egieerig Departmet of Ira Uiversity of Sciece ad Techology, Tehra, Ira. His research iterests are i the Applicatio of Artificial Itelligece to Power System Cotrol Desig, Dyamic Load Modelig, Power System Observability Studies, Voltage Collapse, Cogestio Maagemet i a Restructured Power System, Reliability Improvemet i Distributio Systems ad Reactive Pricig i Deregulated Power Systems. He has published more tha 405 techical papers i the Iteratioal Jourals ad Cofereces proceedigs. He is a member of Iraia Associatio of Electrical ad Electroic Egieers ad IEEE. Nima Amjady (SM ) was bor i Tehra, Ira, o February 24, He received the B.Sc., M.Sc., ad Ph.D. degrees i electrical egieerig from Sharif Uiversity of Techology, Tehra, Ira, i 1992, 1994, ad 1997, respectively. At preset, he is a Professor with the Electrical Egieerig Departmet, Sema Uiversity, Sema, Ira. He is also a Cosultat with the Natioal Dispatchig Departmet of Ira. His research iterests iclude security assessmet of power systems, reliability of power etworks, load ad price forecastig, ad artificial itelligece ad its applicatios to the problems of power systems. Ali Ghasemi received the B.Sc. ad M.Sc. (Hoors with first class) degree i Electrical Egieerig from Isfaha Uiversity of Techology (IUT), Esfaha, Ira i 2009 ad Techical Eg. Departmet of the Uiversity of Mohaghegh Ardabili (UMA), Ardabil, Ira i His Areas of iterest i Research are power system cotrol ad operatio, adaptive ad robust cotrol of power systems, operatio ad Plaig ad Power System Restructurig ad applicatios of heuristic techiques i power systems. Oveis Abediia received the B.S. ad M.Sc. degrees i Electrical Egieerig from Azad Uiversity, Ardabil ad Sciece ad Techology Research Brach, Tehra, Ira i 2005 ad 2009, respectively. Curretly, he is a Ph. D. studet i Electrical Eg. Departmet, Sema Uiversity, Sema, Ira. His areas of iterest i research are Applicatio of Artificial Itelligece to Power System ad Cotrol Desig, Load ad Price Forecastig, Distributio Geeratio, Restructurig i Power Systems, Cogestio Maagemet, Optimizatio.