Optimal Economic Load Dispatch of the Nigerian Thermal Power Stations Using Particle Swarm Optimization (PSO)

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1 The Internatonal Journal Of Engneerng And Scence (IJES) Volume 6 Issue 1 Pages PP ISSN (e): ISSN (p): Optmal Economc Load Dspatch of the Ngeran Thermal Power Statons Usng Partcle Swarm Optmzaton (PSO) Y. S. Haruna 1, Y. A. Ysah 2, G. A. Bakare 1, M. S. Haruna 3 and S. O. Oodo 3 1 Department of Electrcal and Electroncs Engneerng, A. T. B. U Bauch-Ngera, 2 Power Equpment and Electrcal Machnery Development Insttute (PEEMADI), P.M.B. 1029, Okene, Kog State. 3 Department of Electrcal and Electroncs Engneerng, Nle Unversty of Ngera, Abuja ABSTRACT Ths paper deals wth the optmzaton of economc load dspatch (ELD) problem; ths s to fnd the optmal combnaton of generators n order to mnmze the operatng costs of the system. Ths s done by usng the partcle swarm optmzaton (PSO) algorthm. PSO s appled to search for the optmal schedule of all the generator unts that can supply the requred demand at mnmum fuel cost whle satsfyng all system constrants. The PSO algorthm has been mplemented usng MATLAB optmzaton toolbox and was appled to solve the ELD problem of the Ngera thermal power statons. The results were compared wth publshed results obtaned va mcro-ga, conventonal-ga and dfferental evoluton (DE) technques. Keywords: Economc Load Dspatch, Partcle Swarm Optmzaton and Ngera Thermal Power Statons Date of Submsson: 28 December 2016 Date of Accepted: 20 January I. INTRODUCTION The modern power system around the world has grown n complexty of nterconnecton and power demand. The focus has shfted towards the enhanced performance, ncreased customer focus, low cost, relable and clean power. In ths changed perspectve, scarcty of energy resources, ncreasng power generaton cost, envronmental concern necesstates optmal economc load dspatch (ELD). In realty power statons nether are at equal dstances from load nor have smlar fuel cost functons. Hence for provdng cheaper power, load has to be dstrbuted among the varous power statons n a way whch results n lowest cost of generaton [1]. The man am of electrc power utltes s to provde hgh-qualty, relable power supply to the consumers at the lowest possble cost whle operatng to meet the lmts and constrants mposed on the generatng unts. Ths formulates the economc load dspatch (ELD) problem for fndng the optmal combnaton of the output power of all the onlne generatng unts that mnmzes the total fuel cost, whle satsfyng an equalty constrant and a set of nequalty constrants. As the cost of power generaton s exorbtant, an optmum dspatch results n economy [2]. Tradtonal algorthms lke lambda teraton, base pont partcpaton factor, gradent method, and Newton method can solve ths ELD problems effectvely f and only f the fuel-cost curves of the generatng unts are pece-wse lnear and monotoncally ncreasng. Practcally the nput-output characterstcs of the generatng unts are hghly non-lnear, non-smooth and dscrete n nature owng to prohbted operatng zones, ramp rate lmts and mult fuel effects. Thus the resultant ELD becomes a challengng non-convex optmzaton problem, whch s dffcult to solve usng the tradtonal methods [3, 4]. Several heurstc approaches lke evolutonary programmng (EP), genetc algorthm (GA), ant colony search (ACS), tabu search (TS), artfcal neural network (ANN), bo-geography based optmzaton (BBO), dfferental evoluton (DE) and smulated annealng (SA) have been developed for solvng both lnear and non-lnear ED problems [5-8]. In ths paper, partcle swarm optmzaton (PSO) algorthm s proposed to solve the ELD problems n power systems. The vablty of the method s analyzed for ts accuracy and rate of convergence on the Ngeran power network (1999 model) and results were compared wth other heurstcs methods. 1.1 Ngeran Power System The electrcty demand n Ngera far outstrps the supply and the supply s epleptc n nature. Ths s hnderng ts development, notwthstandng the avalablty of vast natural resources n the country. Constant power supply s the hallmark of a developed economy. Any naton whose energy need s epleptc n supply prolongs her development and rsks losng potental nvestors. Relable Power producton s crtcal to the proftablty of electrcty utltes. Ths can only be realzed when the power generators are scheduled effcently to meet electrcty demand. Economc load dspatch have been appled to obtan optmal fuel cost whle satsfyng systems system constrants and generator schedulng for DOI : / Page 17

2 hourly antcpated load wthn a perod of 24 hours. The effcency of generatng unt, the transmsson looses and the operatng costs are mportant factors to be consdered for the economc operaton of the system. In recent years, the Power Holdng Company of Ngera (PHCN) has been experencng serous problem n generaton, transmsson, dstrbuton, mantenance, fnancal constrants and ncrease n power demand [9], consderng the generaton/power demand problems, several unts were on emergency/forced outages, whch led to system dsturbance such as; partal and total system collapse. These problems were attrbuted to over stressng the unts to generate outsde ther normal operatng condtons. Ths wll thus lead to generatng electrc power at loss. In vew of the above problem, t becomes necessary for one to study the cost functons of the avalable thermal unts, ther power lmts and the maxmum power demand of the whole country at a partcular tme so as to carry out the ELD problem. The am of ths research s to apply a partcle swarm optmzaton technque to solve the economc load dspatch (ELD) problem; for the purpose of optmal allocaton of the total power demand among the avalable generatng unts that mnmzes the total generaton cost subject to specfed system constrants. 1.2 Statement of the Problem Consder a system consstng of N thermal unts connected to a transmsson network as shown n Fgure1 below. F fuel cost of unt, P power delvered by unt, G PD total power demand and P total power loss. L The quadratc cost functon of unt, s gven by; Fgure 1: Interconnected Power System Network 2 F ( P ) P P (1) G G G - Constant cost coeffcent of unt, -Lnear constant cost coeffcent of unt -A quadratc constant cost coeffcent of unt. Operatng the system subject to generaton constrants, ths objectve functon can be expressed mathematcally as: F T N F F ( P ) 1,2.N (2) T G 1 s the total cost of power generaton and F ( P ) G s the generaton cost of unt. The ELD problem seeks to fnd the optmal combnaton of thermal power generatons that mnmzed the total cost whle satsfyng the total power demand and the systems constrants. The ELD problem s formulated as mnmzaton of Eqn. (2) subject to the followng constrants: Equalty constrants N P P P G D L (3) 1 Usng the B-coeffcent method, network losses are expressed as: DOI : / Page 18

3 B T (4) L G G P P B P s the B matrx coeffcent Inequalty constrants P m n G m n (5) G G G P P P s the mnmum power lmts of the unt P s the maxmum power lmts of unt. G Fnally, PSO was appled to the coordnaton of the Ngeran thermal power plants. Ths research on economc load dspatch s modeled usng the quadratc cost functon. The ssues of envronmental constrants, generaton ramp-rate lmts, valve-pont effect and pecewse lnear cost functon are out of scope of ths paper. II. LITERATURE REVIEW The ELD problem has been wdely studed and reported by dfferent authors. The technques used n the lterature ranges from the classcal optmzaton technques to the recent meta- heurstc optmzaton technques such as evolutonary algorthms (EA), genetc algorthm (GA), smulated annealng (SA) and partcle swarm optmzaton (PSO). [3] developed a Pareto fronter Dfferental Evoluton (PDE) technque to solve MOED problem. The proposed method was mplemented on the standard IEEE-30 bus system havng sx generatng unts ncludng valve pont effects to evaluate ts performance and applcablty. From the results obtaned, the proposed method demonstrated ts effectveness by solvng the Mult Objectve economc dspatch problem consderng securty constrants. [4] proposed and developed evolutonary algorthms to solve the economc dspatch problem for the optmum performance of a nonlnear and complex systems. They consdered all the constrants of power dspatch for economc operaton of the power system. [5] presented the economc power dspatch problems usng ant colony optmzaton (ACO) technque whch s a meta-heurstc approach for solvng hard combnatoral optmzaton problems. Ths technque was tested usng the standard IEEE 26-Bus RTS and the results revealed that the proposed technque has the mert n achevng optmal soluton for addressng the problems. Comparatve studes wth artfcal mmune system (AIS) were also conducted n order to hghlght the strength of the proposed technque. In the year 2012, [6] presented an effectve and relable partcle swarm optmzaton (PSO) technque for the economc load dspatch problem usng the standard 3-generator and 6-generator systems wth and wthout consderaton of transmsson losses. The fnal results obtaned usng PSO are compared wth conventonal quadratc programmng and found to be encouragng. [7] proposed a method for solvng economc dspatch problem usng Partcle Swarm Optmzaton (PSO) Algorthm and Smulated Annealng (SA) for the three generatng unts as a case study. PSO and SA were appled to fnd out the mnmum cost for dfferent power demand. They compared ther results wth the tradtonal technque, where PSO dsplayed better result and better convergence characterstc. [8] presented an mproved exponental harmony search algorthm for mprovng the HS algorthm to solve the SELD problem consderng the valve-pont effect. The numercal results show that the proposed method has better convergence and also lower producton costs than the conventonal HS and partcle swarm optmzaton methods. [10] presented the overvew of dfferent methods for solvng economc load dspatch (ELD) problem usng MATLAB. They concluded that lambda teraton method converges rapdly but complextes ncreases as system sze ncrease. Gradent and newton methods can only be appled where cost functon s much more complex whle for the non convex nput-output curves, dynamc programmng method can be used to solve the economc load dspatch problem. [11] presented lambda teraton method to solve the ELD problem usng MATLAB for the three and sx generatng unts wth and wthout transmsson losses. [12] presented an applcaton of the GAMS method to power economc dspatch (PED) problem wth Power loss for 3 and 6 generator test case systems. The smulaton results show that the proposed GAMS Method outperforms prevous optmzaton methods. 2.1 Heurstc Optmzaton Technques As an alternatve to the conventonal mathematcal approaches, the heurstc optmzaton technques such as genetc algorthms, Tabu search, smulated annealng, and recently ntroduced partcle swarm optmzaton DOI : / Page 19

4 (PSO) are consdered as realstc and powerful soluton schemes to obtan the global optmums n power system optmzaton problems. 2.2 Partcle Swarm Optmzaton Partcle swarm optmzaton was frst ntroduced by Kennedy and Eberhart n the year It s an exctng new methodology n evolutonary computaton and a populaton-based optmzaton tool. PSO s motvated from the smulaton of the behavour of socal systems such as fsh schoolng and brds flockng. The PSO algorthm requres less computaton tme and less memory because of ts nherent smplcty [7]. The basc assumpton behnd the PSO algorthm s that brds fnd food by flockng and not ndvdually. Ths leads to the assumpton that nformaton s owned jontly n the flockng. The swarm ntally has a populaton of random solutons. Each potental soluton, called a partcle (agent), s gven a random velocty and s flown through the problem space. All the partcles have memory and each partcle keeps track of ts prevous best poston (pbest) and the correspondng ftness value. The swarm has another value called gbest, whch s the best value of all the pbest. Partcle swarm optmzaton has been found to be extremely effectve n solvng a wde range of engneerng problems and solves them very quckly. III. APPLICATION OF PSO IN ELD The am of ths research s to dstrbute the total power demand among the avalable thermal generatng statons to mnmzng the total fuel cost subject to both equalty and nequalty constrants as earler stated n Eqns Partcle Swarm Optmzaton was used to acheve ths desred goal. The soluton of the ELD problem usng the classcal approach presents some lmtaton n ts mplementaton. One of such lmtaton s that the Lamda-teraton method assumes the cost coeffcent to be a contnuous functon. The method breaks down when t s appled to a dscontnuous functon wth prohbted zones or larger steam turbne generatng unts [13]. Also, there s a large tendency for ths approach to converge at a local mnmum when the power system operatng status s far outsde the normal stuaton, for nstance durng and after large dsturbances. For ths purpose, the Partcle Swarm Optmzaton technque was appled n ths paper to solve an ELD problem n order to elmnate the lmtaton of the Lamda-teratons enumerated above. In a PSO system, populaton of partcles exsts n the n-dmensonal search space. Each partcle has certan amount of knowledge and wll move about the search space on the bass of ths knowledge. The partcle has some nerta attrbuted to t and hence wll contnue to have a component of moton n the drecton t s movng. The Partcle knows ts locaton n the search space and wll encounter wth the best soluton. The partcle wll then modfy ts drecton such that t has addtonal components towards ts own best poston, pbest and towards the overall best poston, gbest. The partcle updates ts velocty and poston usng the followng Eqn. (6) and (7). V k+1 = wv k + c 1 Rand 1 () pbest S k + c 2 Rand 2 () gbest S k (6) ( k 1 ) K ( k 1 ) S S V (7) k V s the velocty of ndvdual at teraton k, k s ponter of teratons, W s the weghng factor, C 1,C 2 are the acceleraton coeffcents, Rand 1 ( ), Rand 2 ( ) are the random numbers between and 1, S k s the current poston of ndvdual at teraton k, pbest s the best poston of ndvdual and gbest s the best poston of the group. The coeffcents C 1 and C 2 pull each partcle towards pbest and gbest postons. Low values of acceleraton coeffcents allow partcles to roam far from the target regons, before beng tugged back. Hence, the acceleraton coeffcents C 1 and C 2 are often set to be 2 accordng to past experences. The term C 1 Rand 1 () x (pbest -S k ) s called partcle memory nfluence or cognton part whch represents the prvate thnkng of the tself and the term C 2 Rand 2 ( ) x (gbest - S k ) s called swarm nfluence or the socal part whch represents the collaboraton among the partcles. In the procedure of the partcle swarm paradgm, the value of maxmum allowed partcle velocty V max determnes the resoluton, or ftness, wth whch regons are to be searched between the present poston and the target poston. If V max s too hgh, partcles may fly past good solutons. If V max s too small, partcles may not explore suffcently beyond local solutons. Thus, the system parameter V max has the benefcal effect of DOI : / Page 20

5 preventng exploson and scales the exploraton of the partcle search. The choce of a value for V max s often set at 10-20% of the dynamc range of the varable for each problem. Sutable selecton of nerta weght W provdes a balance between global and local exploratons, thus requrng less teraton on an average to fnd a suffcently optmal soluton. Snce W decreases lnearly from about 0.9 to 0.4 qute often durng a run, the followng weghng functon of Eqn. (8) s used n Eqn. (6): W W W W te r te r W max s the ntal weght, W mn s the fnal weght, Iter max s the maxmum teraton number, ter s the current teraton number. m n (8) Eqn. (6) s used to calculate the partcle's new velocty accordng to ts prevous velocty and the dstances of ts current poston from ts own best experence (poston) and the group's best experence. Then the partcle fles towards a new poston accordng to Eqn. (7). The performance of each partcle s measured accordng to a predefned ftness functon, whch s related to the problem to be solved. 3.1 Implementaton of PSO for ELD The man objectve of ELD s to obtan the amount of real power to be generated by each commtted generator, whle achevng a mnmum generaton cost wthn the constrants. The evaluaton functon for evaluatng the mnmum generaton cost of each ndvdual n the populaton s adopted as follows: Mnmze d F F ( P ) (9) T 1 The search procedure for calculatng the optmal generaton quantty of each unt s summarzed as follows: ) In the ELD problems the number of onlne generatng unts s the 'dmenson' of ths problem. The partcles are randomly generated between the maxmum and the mnmum operatng lmts of the generators and represented usng equaton (9). ) To each ndvdual of the populaton calculate the dependent unt output P du from the power balance equaton and employ the B-coeffcent loss formula to calculate the transmsson loss P L usng constrant satsfacton technque. ) Calculate the evaluaton value of each ndvdual P g n the populaton usng the evaluaton functon f, gven by equaton (10). v) Compare each ndvdual's evaluaton value wth ts pbest. The best evaluaton value among the pbest s dentfed as gbest. v) Modfy the member velocty V of each ndvdual Pg accordng to the followng equaton: t+1 t t t V d = wv d + c 1 Rand 1 () pbest d P gd +c 2 Rand 2 () gbest d P gd =1,2,. n, d =1,2,.. m (10) n s the populaton sze, m s the generator unts. v) Check the velocty constrants of the members of each ndvdual from the followng condtons: ( t 1 ) ( t 1 ) fv V, th en V V, d d d d ( t 1 ) ( t 1 ) m n fv V, th en V V, d d d d (11) m n m n w h erev 0.5 P, V 0.5 P d d d d v) Modfy the member poston of each ndvdual P g1 accordng to Eqn.(12): ( t 1) g d ( t 1) ( t ) ( t 1) P P V (12) g d gd d P must satsfy the constrants, namely the generatng lmts, descrbed by Eqn. (5). If ( t 1) constrants, then P must be modfed towards the nearest margn of the feasble soluton. g d ( t 1) P volates the v) If the evaluaton value of each ndvdual s better than prevous pbest, the current value s set to be pbest. If the best pbest s better than gbest, the best pbest s set to be gbest. x) If the number of teratons reaches the maxmum, then go to step (x). Otherwse, go to step (). x) The ndvdual that generates the latest gbest s the optmal generaton power of each unt wth the mnmum total generaton cost. g d DOI : / Page 21

6 IV. RESULTS AND DISCUSSION The procedure descrbed n chapter three for the Partcle Swarm Optmzaton based for solvng ELD problems for the thermal power plant has been mplemented usng the developed PSO software on Matlab 7.1 for wndows. The feasblty and the effectveness of the method have been tested on the Ngeran thermal power plant. Ths was executed on hp laptop computer wth the specfcaton as follows, Processor: Intel Celeron CPU 2.16GHz, nstalled Memory (RAM): 2GB, system type: 64-bt operatng system, hard dsc: 500GB and operatng system: wndows 8.1. The results of the stmulaton studes are presented. [1] used the two approaches to solve ths problem; mcro genetc algorthm (MGA) and conventonal genetc algorthm (CGA). [2] used dfferental evoluton (DE) to solve the same problem. They all used three sets of power demand P D : 340MW, 850MW and 1150MW. PSO was appled to the above system for obtanng economc load dspatch of smlar load requrements. PSO was mplemented accordng to the flow chart shown. For each sample load, under the same objectve functon and ndvdual defnton, 20 trals were performed to observe the evolutonary process and to compare ther soluton qualty and convergence characterstcs. 4.1 Smulaton Results of the Ngeran Power System The developed PSO software for ELD problem was appled to the Ngeran power system whose sngle lne dagram s shown n Fgure 2. The Ngeran power system grd s essentally a 31-bus, 330-kV network nterconnectng four thermal generatng statons and three hydro statons to the varous load ponts. The network data (Bus data, Generator data and Branch) were obtaned from [1, 2]. Table 1 presents the cost coeffcents of the four Ngeran thermal power statons and ther mnmum and maxmum loadng lmts. Fgure 2: Ngeran 330 kv, 31- Bus Grd System Table 1: Ngeran Thermal Power Plants Characterstcs [1] Staton Α Α Α P mn G (MW) P max G (MW) Sapele Delta Afam Egbn DOI : / Page 22

7 Table 2: Results Comparson between MGA. CGA, DE and the Proposed PSO Technques Power Staton MGA CGA DE Proposed Method Sapele P G1(MW) Delta P G2(MW) Afam P G3(MW) Egbn P G4(MW) Kanj P G5(MW) Shroro P G6(MW) Jebba P G7(MW) Total Power Generated(MW) Total Power Demanded(MW) Total Power Loss (MW) Total Cost(N/hr) 114, , , , Fgure 3: Convergence Characterstcs of PSO V. CONCLUSION PSO method was successfully employed to solve the ELD problem. The comparson of results for the 31-bus Ngeran grd system clearly shows that the proposed PSO method was ndeed capable of obtanng hgh qualty soluton effcently for ELD problems. Fgure 3 shows the convergence characterstcs of the proposed method at the normal demand. The convergence s good snce the algorthm takes few numbers of teratons to converge hence less computaton tme. From the results obtaned, the proposed PSO technque mnmzes the total producton cost and transmsson losses better than MGA and CGA, except n some cases where the DE also performed equally good. REFERENCES [1]. Haruna, Y. S. (2004). Comparson of Economc Load Dspatch usng Genetc Algorthm and Classcal Optmzaton Method. Unpublshed M.Eng. Thess, Abubakar Tafawa Balewa Unversty, Bauch. [2]. Awodj, O.O., Bakare, G. A., Alyu, U. O. (2014). Short Term Economc Load Dspatch of Ngeran Thermal Power Plants Based on Dfferental Evoluton Approach. IJSER. Vol 5 Issue 3. [3]. Jagadeesh, G. (2011). Mult Objectve Economc Dspatch Usng Pareto Fronter Dfferental Evoluton. Internatonal Journal of Engneerng Scence and Technology (IJEST). ISSN : Vol. 3 No. 10. [4]. Faheemullah, S., Pervez, H., Shakh, M., Mran, M. and Aslam, U. (2012). Mult Crtera Optmzaton Algorthm for Economc Dspatch Complcatons for Sustanable Interconnected Power System. Internatonal Journal of Computer Applcatons ( ), Volume 50 No.4. [5]. Ismal, M., Nur, H. F. I., Mohd, R. K., Muhammad, K. I., Ttk. K. A., and Mohd, R. A. (2008). Ant Colony Optmzaton (ACO) Technque n Economc Power Dspatch Problems. Proceedngs of the Internatonal Mult Conference of Engneers and Computer Scentsts Vol II, pp [6]. Hardansyah, Junad and Yohannes, M. S. (2012). Solvng Economc Load Dspatch Problem Usng Partcle Swarm Optmzaton Technque, I.J. Intellgent Systems and Applcatons, Vol. 12, pp [7]. Senthlkumar, S. and Vjayalakshm, V. J. (2013). A New Approach to the Soluton of Economc Dspatch Usng Partcle Swarm Optmzaton wth Smulated Annealng. Internatonal Journal on Computatonal Scences & Applcatons (IJCSA) Vol.3, No.3. [8]. Damoon, R. D., Asef, G. and Seyyed, M. H. (2016). Solvng Statc Economc Load Dspatch Usng Improved Exponental Harmony Search Optmzaton. Australan Journal of Electrc and Electroncs Engneerng, Vol. 13, Issue 2. [9]. Makoju, J. (2003). Resusctatng the Ngeran Power Sector: The Resusctatng and Prvatsaton Reforms. COREN Assembly, Abuja. [10]. Rahul, D., Nkta, G. and Harsha, S. (2014). Economc Load Dspatch Problem and MATLAB Programmng of Dfferent Methods. Internatonal Conference of Advance Research and Innovaton (ICARI-2014). [11]. Susheel, K. D., Achala, J. and Huddar, A. P. (2015). IOSR Journal of Electrcal and Electroncs Engneerng (IOSR-JEEE), Vol. 10, Issue 2 Ver. III, PP [12]. Sonal, A. and Devendra, D. (2016). Power Economc Dspatch of Thermal Power Plant Usng Classcal Tradtonal Method. Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET), Vol. 4 Issue II, pp [13]. Bakare, G. A. (2001). Removal of overloads and Voltage problems n Electrc Power Systems usng Genetc Algorthm/Expert System Approaches, Shaker Verlag, Aachen Germany. DOI : / Page 23