Gbest Artificial Bee Colony for Non-Convex Optimal Economic Dispatch in Power Generation

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1 Indonesan Journal of Electrcal Engneerng and Computer Scence Vol.11, No.1, July 2018, pp. 187~194 ISSN: , DOI: /jeecs.v11.1.pp Gbest Artfcal Bee Colony for Non-Convex Optmal Economc Dspatch n Power Generaton M.N. Abdullah 1, A.F.A. Manan 2, J.J. Jaman 3, S.A. Jumaat 4, N.H. Radz 5 1,2,4,5 Faculty of Electrcal and Electronc Engneerng, Unverst Tun Hussen Onn Malaysa, Part Raja, Batu Pahat, Johor, Malaysa 3 Faculty of Electrcal Engneerng, Unverst Teknolog Malaysa, UTM Johor Bahru, Johor, Malaysa Artcle Info Artcle hstory: Receved Jan 9, 2018 Revsed Mar 23, 2018 Accepted Apr 13, 2018 Keywords: Artfcal Bee Colony Algorthm Power Dspatch Valve Pont Effect ABSTRACT Non-convex Optmal Economc Dspatch (OED) problem s a complex optmzaton problem n power system operaton that must be optmzed economcally to meet the power demand and system constrants. The nonconvex OED s due to the generator characterstc such as prohbted operaton zones, valve pont effects (VPE) or multple fuel optons. Ths paper proposes a Gbest Artfcal Bee Colony (GABC) algorthm based on global best partcle (gbest) guded of Partcle Swarm Optmzaton (PSO) nartfcal bee colony (ABC) algorthm for solvng non-convex OED wth VPE. In order to nvestgate the effectveness and performance of GABC algorthm, the IEEE 14-bus 5 unt generators and IEEE 30-bus 6 untgenerators test systems are consdered. The comparson of optmal soluton, convergence characterstc and robustness are also hghlghted to reveal the advantages of GABC. Moreover, the optmal results obtaned by proposed GABC are compared wth other reported results of meta-heurstc algorthms. It found that the GABC capable to obtan lowest cost as compared to others. Thus, t has great potental to be mplemented n dfferent types of power system optmzaton problem. Copyrght 2018 Insttute of Advanced Engneerng and Scence. All rghts reserved. Correspondng Author: M.N. Abdullah, Faculty of Electrcal and Electronc Engneerng, Unverst Tun Hussen Onn Malaysa, Part Raja, Batu Pahat, Johor, Malaysa. Emal: mnoor@uthm.edu.my 1. INTRODUCTION Power dspatch s one of the optmzaton problem n power system plannng and operaton. It s mportant to ensure that total cost of power generaton can be mnmze as much as possble to gan hgh proft to power company as known as optmal economc dspatch (OED) problem. Reducton of fossl fuels resources and hgh fuel prces encourage utlty to operate the system at mnmum cost as well as satsfed all the system and operatonal constrants. Commonly, the cost functon of thermal generator s modelled as quadratc functon that can be solve effcently by most of the conventonal methods such lambda teraton method [1], lnear programmng [2], quadratc programmng [3] and other methodsthat can be found n[4] [5, 6]. However, these methods shows dffculty to obtan optmal results when the non-lnear characterstc are taken nto account n cost modellng such valve pont effect (VPE), prohbted operatng zone (POZ) or multple fuels opton (MFO) [7]. In practcal, generators used mult-valve turbne that produced several rpples n heat-rate characterstc as well as cost-power characterstc that contrbutes a combnaton of snusodal and quadratc cost functon. Therefore, t challenges most optmzaton algorthms to obtaned optmal soluton n OED problem. Journal homepage:

2 188 ISSN: Due to ths problem, most of researchers use the meta-heurstcs algorthms that can search the optmal soluton wthout dependng to the convexty of the cost functon such as Genetc Algorthm, Partcle Swarm Optmzaton (PSO) [8, 9], Cuckoo Search (CS) [10], Artfcal Bee Colony (ABC) [11], Backtrackng Search Algorthm (BSA) [12] and Rooted Tree Algorthm (TRO) [13]. However, n some cases these algorthms are suffered and converged at local optmal soluton. As a results, many mprovement of orgnal algorthm have been proposed by researchers to mprove the performance of orgnal algorthm [14] [15] [7]. To have balance exploraton and explotaton capablty of orgnal ABC, the Gbest Artfcal Bee Colony (GABC) [16] has been ntroduced and successfully solve numercal functon optmzaton problem. The GABC s guded the ABC algorthm based on the global best soluton (gbest) n PSO algorthm n order to enhance the explotaton capablty of ABC. It also promses a good result for fndng optmal economcemsson consderng wnd n [17] and optmal power flow [18]. Ths paper proposes a GABC algorthm for solvng the non-convex OED problem consderng the non-lnear cost functon due VPE. Theproposed GABC has been valdatedon two dfferent test systems. The effectveness of GABC has compared wth orgnal ABC n terms of optmal cost, convergence performance and robustness after 40 trals. Moreover, the obtaned optmal results also compared wth the some reported result found n lterature. It found that, proposed GABC provded sgnfcant cost reducton for OED wth VPE. 2. PROBLEM FORMULATION: OPTIMAL ECONOMIC DISPATCH (OED) Ths secton explans the mathematcal formulaton of OED problem such as objectve functon and constrants as follows: 2.1. Objectve Functon of OED The man objectve of OED s to determne the best power output of the scheduled generator so that the power demand and system constrants can be meet n economcal way. The cost functon commonly formulated as quadratc functon. However, the practcal cost functon become non-lnear due to valve pont effect (VPE) as shown n Fgure 1. Therefore, the objectve functon of OED problem for mnmzng total cost (F c ) of th generator as follows: N c 1 2 mn sn (1) F F P ap bp c e f P P where a,b and c are quadratc cost coeffcents, e andf are non-lnear cost coeffcents due to valve pont effect, P mn andp mn are the mnmum and maxmum power output lmt of the th unt generatng, P s the power output of th unt and N s the number of the commtted generators. Fgure 1. Cost and Power Output Relatonshp wth and wthout VPE Indonesan J Elec Eng & Comp Sc, Vol. 11, No. 1, July 2018:

3 Indonesan J Elec Eng& Comp Sc ISSN: Constrants The mnmzaton of F c n (1) s subjected to the system and operatonal constrants as follows: Power Balance Constrant The total power produced by the schedulled generator must meet the total power demand (P D ) and transmsson loss (P Loss ) as follows: N P PD PLoss (2) 1 The P Loss can be calculated by Kron's loss formula as follows: N N N P P() t B P () t B P() t B (3) Loss j j j1 1 where B j, B0 and B 00 are the loss coeffcents obtaned from the power flow calculaton Power Output Lmts For stable operaton, the real power produced by each generator must be wthn allowable mnmum mn max (P ) and maxmum P ) lmts as follows: P mn P P (4) max. 3. PROPOSED GBEST ARTIFICIAL BEE COLONY (GABC) FOR OED Artfcal Bee Colony (ABC) s a populaton based algorthm nspred by behavour of honey bees colones for fndng food sources. It conssts of three man bees n order to search optmal food source (soluton) whch are employed bees, onlooker bees and scout bees. The bref workng prncple of ABC as follows[19]: Artfcal Bee Colony Algorthm Step 1 Intalzaton Determne the number of food source (SN) Calculate vector of possble soluton X =X 1, X 2 X SN ; X s represent by the locaton of food source. The ftness of each possble soluton can be calculate usng the followng formula: Ftness 1, 1 F 1 abs ( F ), f F 0 otherwse (5) Step 2 Employed Bees Employed Bees fnd the new food source poston V j usng: V j X j j * j kj X X (6) where ϕ j s a random number between [-1, 1], and k {1, 2,...N s } and j {1, 2, D} are ndex randomly chosen. D s number of problem varables. If the new poston s found better than the old poston, a new poston s memorzed and otherwse t s removed. The greedy selecton method s used to determne the best soluton... Step 3 Onlooker Bees In ths phase, onlooker bees wll search the best results accordng to the probablty (P ) as follows: Gbest Artfcal Bee Colony for Non-convex OED n Power Generaton (M.N. Abdullah)

4 190 ISSN: Ftness P (7) N S Ftness j j The soluton wth better ftness value has hgh probablty of beng selected by an onlooker bee n order to explot the soluton near to global optmal value. Step 4 Scout Bees After several trals, unmproved food locaton (soluton) wll explore other possble locaton n order to mprove the current soluton usng the followng equaton: mn [0,1]* max mn j j j j X X rand X X (8) The good poston replaced the unmproved soluton. Repeat Steps 2 4 untl satsfed the stoppng crtera The detals workng prncple of ACB algorthm can be found n [20] [11] Workng Prncple of GABC To mprove the explotaton capablty of ABC, the global best soluton (gbest) n PSO algorthm [21] s used to update the soluton n ABC. Therefore, Gbest Artfcal Bee Colony (GABC) modfed soluton n (6) as follows [16]: V j X j X X * ( gbest X ) j * j kj j j j (9) where j s an unform random number n [0, C], where C s a non-negatve constant and gbest j represents the jth element of the gbest vector Implementaton Procedures of GABC for Solvng OED Problem The detals mplementaton of GABC algorthm for solvng OED problem s descrbed as follows: GABC for Solvng OED Problem Step 1 Input data: Cost and system data... Step 2 Parameter settng for GABC. The number of generator s defned as problem varables. Step 3 Calculate the ftness value n (5) accordng to objectve functon n (1). Set the teraton equal to 1. Step 4 Employed beesdetermne new canddate food source based on (9)... Step 5 Apply the constrants handlng n order to satsfy the constrants n (2) (4). The detals of constrants handlng methodology can be found n [22]. Step 6 Calculate the ftness value. If the new ftness value s better than the old one, the new food source poston s remembered; otherwse, the old one s reman n the memory. Step 7 Onlooker bees determne the better soluton usng (7). Step 8 Apply greedy selecton process and store the best soluton. Step 9 Scout bee produces a new random soluton accordng to (8) for unmproved soluton after certan lmts. Step 10 Store the best soluton (food source poston) obtaned so far and ncrease teraton number by 1. Step 11 Repeat Steps 4 to 10 untl maxmum number of cycles are reached RESULTS AND ANALYSIS The proposed GABC algorthm has been tested on two Case Studes by usng Matlab 2013b software n order to valdate ts performances. The IEEE 14-bus 5unt generators and IEEE-30 bus 6 unt generators test system are consdered n ths paper. To evaluate the robustness of GABC, 40 dfferent trals are conducted and compared wth ABC algorthm. The optmal power output are also compared wth the selected publshed results. Indonesan J Elec Eng & Comp Sc, Vol. 11, No. 1, July 2018:

5 Indonesan J Elec Eng& Comp Sc ISSN: Test Case 1: IEEE 14-Bus 5 Unt Generators The GABC and ABC algorthms have been used to determne the OED for IEEE 14 bus 5-unt generator consderng VPE and transmsson losses. The total load demand (P D ) s 259 MW. The system and operatonal data are taken from [23]. The optmal power output produced by GABC and ABC are tabulated n Table 1. It shows that proposed GABC can obtaned lower cost as well as sgnfcant cost reducton compared to ABC algorthm around 3.6 $/h. Moreover, searchng behavour of GABC s also faster than ABC as shown n Fgure 2. It can be seen the GABC has capablty to fnd mnmum cost wth 100 teratons that hghlghted the effectveness of GABC algorthm. In term of consstency, t found that GABC can gve mnmum cost for every tral as presented n Fgure 3. It can be seen that GABC has capablty to obtaned lower cost wth good soluton.the results obtaned from the GABC algorthm has been compared wth those reported results by GA [23], GA_APO [23], NSOA [23], PSO [24], MSG_HP [24], PSOGSA [7] and ABC as presented n Fgure 4. It s can be seen that proposed GABC can provde lower cost as compared to other algorthms. Thus, t can gve sgnfcant cost savng for solvng OED problem. Table 1. Optmal Power Output by ABC and GABC Algorthm (Test Case 1) Generator unt ABC GABC P P P P P Total power output (MW) P Loss (MW) Fuel cost ($/h) Fuel cost($/h) ABC GABC Iteraton Fgure 2. Convergence Characterstc of ABC and GABC Algorthm for Test Case 1 Fuel cost ($/h) ABC GABC No of trals Fgure 3. Robustness of ABC and GABC Algorthm for Test Case 1 Gbest Artfcal Bee Colony for Non-convex OED n Power Generaton (M.N. Abdullah)

6 192 ISSN: Fuel cost ($/h) ,55 926,55 905,54 836,46 834,36 834,13 834,13 830,53 GA GA_APO NSOA PSO MSG_HP PSOGSA ABC GABC Algorthms Fgure 4. Comparson of Optmal Cost of GABC and Other Algorthms (Test Case 1) 4.2. Test Case 2: IEEE 30 Bus 6-Unt Generators The GABC and ABC algorthms have been tested on the IEEE 30-bus 6 unt generators wth VPEand transmsson losses. The power demand of ths system s MW. The system and operatonal data are obtaned from [23]. After 40 dfferent runs, the best results obtaned by GABC and ABC are shown n Table 2. The GABC can provde a better cost as compared to ABC wth reducton of 0.43 $/h. However, the convergence behavour of GABC algorthm s faster than ABC for fndng optmal cost wthn 100 teratons as shown n Fgure 5. The mnmum results after 40 dfferent runs are presented n Fgure 6 hghlghted the effectveness of GABC for obtanng lower cost and consstent results compared to ABC. To valdate the performance of proposed GABC for solvng OED problem, the comparson study has been made wth the reported results of GA [23], GA_APO [23], NSOA [23], PSO [24], MSG_HP [24], PSOGSA [7] and ABC as shown n Fgure 7. It clearly shows that proposed GABC obtaned better results compared to the selected algorthms. Thus, t can gve a good potental cost savng for optmal power generaton. Table 2. Optmal Power Output by ABC and GABC Algorthm (Test Case 2) Generator unt ABC GABC P P P P P P Total power output (MW) P Loss (MW) Fuel cost ($/h) Fuel cost ($/h ABC GABC Iteraton Fgure 5. Convergence Characterstc of ABC and GABC Algorthm for Test Case 2 Indonesan J Elec Eng & Comp Sc, Vol. 11, No. 1, July 2018:

7 Indonesan J Elec Eng& Comp Sc ISSN: Fuel cost ($/h) ,8 925,6 925,4 925, ,8 ABC GABC No of run Fgure 6. Robustness of ABC and GABC Algorthm for Test Case ,49 Fuel cost ($/h) ,04 984,94 925,76 925,64 925,41 925,41 924, GA GA-APO NSOA PSO MSG_HP PSOGSA ABC GABC Algorthms Fgure 7. Comparson of Optmal Cost of GABC and Other Algorthms (Test Case 2) 5. CONCLUSION The Gbest Artfcal Bee Colony (GABC) algorthm has been proposed for solvng the OED problem wth valve pont effect.the OED problem wth non-convex cost functon are dffcult to obtaned the optmal soluton by most of reported results of heurstc algorthm. Therefore, ths paper nvestgated the effectveness of proposed GABC to solve ths problem based on the two dfferent case studes whch are IEEE 14-bus 5 unt generators and IEEE 30-bus 6 unt generators consderng valve pont effect and transmsson losses. The comparson study has been conducted n terms of optmal cost, convergence characterstc and robustness. It found that GABC provded a sgnfcant cost reducton as well as good convergence behavor as compared to ABC. Moreover, the optmal OED soluton obtaned by GABC s outperformed compared to selected results reported n lterature. From ths study, t can be concluded that GABC has good potental to be mplemented n other power system optmzaton problems especally n optmal power dspatch area. ACKNOWLEDGEMENT The authors would lke to thank Unverst Tun Hussen Onn Malaysa (UTHM) for supportng the research under Short Term Grant (U639). REFERENCES [1] Wood AJ, Wollenberg BF, Power Generaton, Operaton, and Control. 2nd ed. New York: John Wley and Sons; [2] Fanshel S, Lynes ES., Economc Power Generaton Usng Lnear Programmng. Power Appar Syst IEEE Trans, 1964; 83: Gbest Artfcal Bee Colony for Non-convex OED n Power Generaton (M.N. Abdullah)

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