Novel Method to Solve Economic Dispatch Scheduling for Large-Scale Power System

Transcription

1 Novel Method to Solve Economc Dspatch Schedulng for Large-Scale Power System 1 Jangkung Raharjo, 2 Ad Soeprjanto and 3 Hermagasantos Zen 1 Research Scholar, Department of Electrcal Engneerng, Insttut Teknolog Sepuluh Nopember, ITS, Surabaya, Indonesa. 1 Lecturer at Faculty of Electrcal Engneerng, Unverstas Telkom, Bandung, Indonesa. 2 Professor, Department of Electrcal Engneerng, Insttut Teknolog Sepuluh Nopember, ITS, Surabaya, Indonesa. 3 Assocate Professor, Department of Energy Converson Engneerng, Bandung State Polytechnc, Polban, Bandung, Indonesa. 1 Orcd Id: Abstract The man purpose of power system operaton s to determne the optmum power generaton schedulng of generator unts n order to meet the load demand wthout volatng the prescrbed constrants. Furthermore, the computaton tme has to be as short as possble because the nterval of the schedulng s an hour. Ths paper proposes the applcaton of Mult Dmenson of Coarse to Fne Search method to solve the economc dspatch problem on large scale power system. Ths method s very smple, fast, and always convergent. Ths method runs based on the repetton of the searchng process for the best canddate of a feasble area. Some canddates are spread on a feasble area and the best canddate wll be chosen among them. After that, the smaller feasble area around the prevous best canddate wll be determned. The same process s repeated untl a very small feasble area where ts best canddate can be accepted as the pont of convergence s obtaned. As a valdaton proof, ths method has been tested wth daly load on the Large-Scale Power System, 47 generators unts, 63 buses of 500 kv Java-Bal Power System. The result ndcates that the proposed method can be appled to the power system so that the system can work fast and accurately wth accuracy level above 99.8%. Keywords: Large scale, Optmzaton, Mult-dmenson, convergent, accuracy INTRODUCTION In the power generaton system, the cost of fuel s the most domnant component. Because of that reason, the power generaton and dstrbuton process have to be done usng mnmum cost wthout gnorng ts effcency. The operaton of a power system nvolves power schedulng from each power generator n such a way so the total operaton cost can be mnmzed usng the economc dspatch (ED) calculaton. The man purpose of ED s to mnmze the operaton cost of power system. In order to satsfy the load demand, generator wth lowest cost s chosen frst to operate, then generator wth second-lowest cost s to be operated after, and so forth untl all generators operate wth every generators porton s dfferent from each other dependng on ts constrants and objectve functon. Several methods to solve the ED problem have been publshed. Some of those methods are conventonal method, such as lambda teraton method, gradent method, Newton method, lnear method, and dynamc programmng method [1 3], and the others are methods whch take the artfcal ntellgence as ts base, such as the artfcal neural network, swarm partcle optmzaton (PSO) [4 9], and genetc algorthm (GA) [10 11]. ED problem s a multdmensonal problem that depends on ts generator number and therefore to optmze the mxture of the fuel on large scale power system s a complcated problem. Complcated method wll ncrease the complexty for the whole system and leads to slower computaton tme. In order to reduce that complexty, ths research proposes a smple method to solve the ED problem on large scale power system. The method s called Mult Dmenson of Coarse to Fne Search (MDCFS) method. Ths method s a development result from the prevous CFS method that has been used n three-dmenson dgtal mage processng [12 14]. Ths method also has been successfully appled on small scale power system wth 8 generators (8 dmensons) [15]. The basc prncple of ths method s to spread some canddates nto a specfed feasble area and to determne the best canddate out of t. The next step s to determne a new, smaller feasble area around the prevous best canddate and agan to spread some canddate there. The process s to be contnued and repeated untl a very small feasble area where ts best canddate can be accepted as the pont of convergence s obtaned. In order to valdate ths method, the method tself has been tested on the Large-Scale Power System, 47 generators unts, 63 buses of 500 kv Java-Bal Power System. In other words, the prevous CFS method that has been used n threedmenson dgtal mage processng has been developed to solve the problem that occurred on 47 dmensons. The emphass of ths research s on how a smple CFS algorthm can be appled on large scale power system to solve the ED problem. As a note, n ths paper, the lnes losses have not yet been consdered. The result of ths test ndcates that ths method provde satsfyng result. Ths can be seen from the result n power generaton whch always can satsfy the load changes wth hgh accuracy level above 99.8% and fast processng tme ranged between 8 to 41 seconds. The complete test results are presented on Table IIa and Table IIb n Appendx

2 PROBLEM FORMULATION A. Objectve Functon In ths paper, the objectve functon of ED represents the fuel cost of generator unts and expressed by the followng equaton : converton process. (v). An area of x y s the smallest element n Fg. 1 and called a pxel or a pcture element. m 2 x a b P c P Mn f. (1) 1 Where f(x) s the cost of fuel-mx n IDR, m s the number of generator unts, a, b, and c are constans, and P g s the actve power of th generator n MW. B. Equalty Constrants Ths problem conssts of generator constrants, those are maxmum power P max and mnmum power P mn. P g mn max g P P, (2) g (). M M P Pg P mn 1 1 max, (3) P P 0, (4) g d where P mn s the mnmum power margn of generator, P max s the maxmum power margn of generator, P g s the amount of power generated by generator, P g s the amount of power generated by all generator, and P d s the load. RESEARCH METHOD A. The Concept of Coarse to Fne Search The concept of Coarse to Fne Search can be descrbed as follows: (). If a plane formed by two axes, P x and P y, wth dmenson [M,N], where M,N s a matrx of actve power n Megawatt, then P can be expressed as a contnuous functon P=f(x,y), whch s a functon or an analog mage plane, where both x and y are ranged from 0 to. Converton from analog to dgtal plane s done through the dgtzaton process from analog mage to dgtal mage, so that P can be expressed as : where m=dx= x and n=dy= y. P f x, y, (5) f m, n f(m,n) s a dscrete or dgtal plane, where the value of x and y are depend on the frequency used for dvdng the analog plane. (). If frequency whch s used to do the samplng from analog plane on x axs and y axs are f 1 and f 2 respectvely, then the value of x and y can be expressed as : x x y y Fgure 1 shows the llustraton of analog to dgtal mage f 1 f 2 (6) Fgure 1: The process of analog to dgtal mage processng [17] (v). In ths case, CFS plays a role of samplng from low frequency to hgh frequency, from wde area (coarse) to narrow area (fne). If the dgtal mage as a result from samplng process usng frequency f 1 and f 2 s expressed by matrx M N, then the value of P can be expressed as : P f f f m, n f 1,1 f 1,2 2,1 f 2,2 f 1, N f 2, N M,1 f M,2 f M, N (v). In the next process, sample of P s upsampled usng frequency f 1=2 f 1 and f 2=2 f 2 so that a new matrx composton can be obtaned and expressed by the followng equaton : P' f k, l f f 1,1 f 1,2 2,1 f 2,2 f f 1,2 N f 2,2N 2M,1 f 2M,2 f 2M,2N (v). The process can be stopped or contnued as optmzaton system needed. The llustraton of two-dmenson CFS s shown n Fg. 2. Whle to llustrate the N-dmenson vsually s not possble, for example N=4, then as the llustraton, two peces of 2 dmenson case are used. For N=5, one pece of 2 dmenson case and one pece of 3 dmenson case are used. For N=6, two peces of 3 dmenson case are used, and so forth. Illustraton for N=4 s shown n Fg. 3. The mechansm of best canddate search process s done smultaneously for N generators, where the teraton s done smultaneously, so that the mnmum condton s obtaned as a whole based on the overall cost functon. Ths canddate search process s done to obtan a certan pont as the best soluton nsde N-dmenson space, where those ponts are les on a poston, for example s A (P 1, P 2, P 3,, P N). (7) (8) 12501

3 Parameter ɛ s used to stop the teraton process where the value of ɛ s smaller or equal to a certan value. In the smulaton, ɛ s set to IDR 10,000. problem. Fgure 2: Two-dmenson CFS Fgure 3: N-dmenson CFS for N=4, arranged nto P 1, P 2, P 3, and P 4 [15] B. Mult Dmenson of Coarse to Fne Search Algorthm CFS s an optmzaton method that run on a feasble area a 0b 0c 0d 0 whch has been specfed as shown n Fg. 5 [15]. Some canddates are spread on a feasble area and the best canddate, whch s a canddate that has the lowest cost, wll be chosen among them. Then, a feasble area s specfed around the best canddate wth the feasble area sze s scaled. After that, a number of canddates are spread agan on new feasble area. The same process s repeated untl a very small feasble area where ts best canddate can be accepted as the pont of convergence s obtaned. Fgure 4 s a flowchart of the proposed method for solvng ED Fgure 4: Flowchart dagram Mult dmenson CFS algorthm can be descrbed as follows [16]: (). Feasble area s specfed as shown n Fg. 5. Then a number of canddates N pop are spread on t randomly. Feasble area can be n a shape of a lne for two-dmenson case, a plane for three-dmenson case, or a space for four-dmenson case, dependng on the number of generators nvolved. The structure of canddate conssts of a seres of element correspondng to the output of the generator and therefore the poston of canddate- n teraton k can be expressed by the followng equaton : k k k 1, 2 X, P P, P k. (9) Where P j k s power generated by generator-j on canddate- at teraton-k wth 1 N pop and 1 j N. N pop s the number of N 12502

4 canddates and N s the number of generators. (). The best canddate, X k B, s determned from the mnmum objectve functon. The objectve value for canddate n (9) can be expressed as : F T k N k X F P j 1 j. (10) Then, the value of the mnmum objectve functon can be expressed by the followng equaton : T k k k k X F X, F X, F X F,. (11) B mn T 1 T 2 (). N canddates are spread around the best canddate, where the length and wdth of new feasble area s half of the prevous feasble area. The best canddate s obtaned from the new feasble area. (v). Step () s to be repeated untl a very small feasble area where ts best canddate can be accepted as the pont of convergence s obtaned. Pont of convergence can be acheved f the dfference n objectve value between two best canddates from two adjacent teratons s very small. If X s the best canddate, t has to satsfy the followng equaton : T N pop Tanjungjat bus has 4 generator buses (Tanjungjat 1 4), Gresk bus has 9 generator buses (Gresk 1 9), Paton bus has 2 generator buses (Paton 1 2), and Grat bus has 9 generator buses (Grat 1 9). The test parameters are shown n Table I. Parameter ε s useful for stoppng the teraton process. Smaller ε value means the calculaton result wll be more accurate, and the computaton tme needed wll be longer. In ths paper, parameter ε s set at IDR 10,000. Table I. PARAMETER OF MD-CFS SIMULATION Parameter Value Number of canddates 100 ε IDR 10,000 Testng system Java-Bal Power System, 500 KV, 63 buses, 47 generators The data about generator and lnes s shown n Table III and Table IV. Fgure 7 shows how the power generaton satsfes the peak load and the lght load. F T k1 k X F X B T B. (12) Where F T(X B k-1 ) s the generaton cost at teraton-(k-1), F T(X B) s the egenraton cost at teraton-k, s the dfference n objectve value between two best canddates from two adjacent teratons, k s the step teraton, and ε s the prevous value specfed n whch ts value s relatve, not sgnfcant to total generaton cost. Fgure 5: Feasble area [15] SIMULATION AND ANALYSIS A. Smulaton Smulaton has been done on Large-Scale Power System, 47 generators unts, 63 buses of 500 kv Java-Bal Power System as shown n Fg. 6. Suralaya bus has 7 generator buses (Suralaya 1 7), Crata bus has 8 generator buses (Crata 1 8), Muaratawar bus has 4 bus generator (Muaratawar 1 4), Sagulng bus has 4 generator buses (Sagulng 1 4), Fgure 6: The 63 buses system 12503

5 the peak load whch s MW at 5 pm, system generated MW power wthn 8 seconds computaton tme. It has devaton value of 13 MW, or n the other words t has 99.9% accuracy level. On the other hand, to satsfy the lght load, 6238 MW at 3 am, system generated 6238 MW power wthn 36 seconds computaton tme. Ths means that the accuracy obtaned s at 99.98%. The dfference n result between generaton and load s caused by the delta cost parameter ɛ, where the value of ɛ n ths case s set at IDR 10,000. If the value of ɛ s to be set lower, then the system wll provde hgher accuracy level but wll need longer computaton tme. The executon result ndcates that the computaton tme s ranged between 8 seconds to 41 seconds, whle the accuracy level reaches above 99.8%. (a) CONCLUSION The purpose of MD-CFS method applcaton s to obtan the result quckly and accurately n order to solve the ED problem on large scale power system. Ths method has been tested on Large-Scale Power System, 47 generators unts, 63 buses of 500 kv Java-Bal Power System and provde satsfyng result. Not only the computaton tme to reach convergent condton s under 45 seconds, but also the calculaton result has hgh accuracy level whch s above 99.8%. Consderng those reasons, MD-CFS s worthy to be consdered as a method to solve ED problem on large scale power system. In the future, ths method wll also be tested on large scale power system to solve Optmal Power Flow problem. (b) Fgure 7: Optmzaton result for (a) Peak load, MW; (b) Lght load, 6238 MW Table IIa and Table IIb n the Appendx show the optmum dynamc schedule from all generator unts, computaton tme, and total fuel cost for 24 hours after the proposed method appled on the system. B. Analyss One of the success ndcators ED s accuracy whch expressed as : Pg P Accuracy 1 Pd d 100%, (13) where P g s the total power of generator, P d s the load. The proposed method works well on large scale power system. Ths can be seen from the result of program executon for peak load on the Large-Scale Power System, 47 generators unts, 63 buses of 500 kv Java-Bal Power System. In order to satsfy REFERENCES [1] Allen JW, Bruce FW. Power Generaton, Operaton, and Control. John Wley & Sons [2] Salama, M., M., Economc control for generatons n the thermal power system. Energy Converson and Management, 40, [3] IEEE Commttee Report, Present practces n the economc operaton of power systems. IEEE Trans. Power Appa. Syst., PAS-90, [4] Gang ZL. Partcle Swarm Optmzaton to Solvng the Economc Dspatch Consderng the Generator Constrants. IEEE Transacton on Power Systems. 2003; 18(3): [5] Park J.B, Lee K.S, Shn J.R, Lee K. Y. A Partcle Swarm Optmzaton for Economc Dspatch wth Nonsmooth Cost Functon. IEEE Trans. On Power Systems. 2005; 20(1): [6] Kaur G, Kumar D. Economc Load Dspatch Problem Usng Partcle Swarm Optmzaton Technuque: A Revew. An Internatonal Journal of Engneerng Scences. 2014; 3(1): [7] D. N. Jeyakumar, T. Jayabarath and T. Raghunathan, 12504

6 2006. Partcle swarm optmzaton for varous types of economc dspatch problems. Elec. Power Energy Syst, 28, [8] S. Abrol, M. Kaur, A revew on Partcle Swarm Optmzaton Technque, Internatonal Journal of Advanced Research n Scence, Engneerng and Technology, vol.3, no. 7, pp , July [9] Mng L, Wenqang D, Fuzhong N. An Adaptve Partcle Swarm Optmzaton Algorthm Based on Drected Weghted Complex Network, Mathematcal Problems n Engneerng. School of Computer and Communcaton, Lan Zhou Unversty of Technology, Chna. Report number: [10] D. C. Walters and G. B. Sheble, Genetc algorthm soluton of economc dspatch wth valvepont loadng. IEEE Trans. Power Syst., 8, [11] J. Tppayacha, W. Ongsakul and I. Ngamroo, Parallel mcro genetc algorthm for constraned economc dspatch. IEEE Trans. Power Syst., 17, [12] S. Smoncc, M. Kompolsek, P. Podrzaj, An Advance Coarse-Fne Search Approach For Dgtal Image Correlaton Applcatons, Facta Unverstes, Seres Mechancal Engneerng, vol. 14, no. 1, pp , [13] J. Lee, M-H Jeong, J. Lee, K.G. Km, and B-J. You, 3D Pose Trackng Usng Partcle Flter wth Back Projecton-Based Samplng, Internatonal Journal of Control, Automaton, and Systems, vol. 10, no. 6, pp : , [14] R. Grshck. Object Detecton wth Heurstc Coarseto-Fne Search, Ph.D Thess, Unversty of Chcago, Chcago, May [15] J. Raharjo, A. Soeprjanto, H. Zen. Mult-dmenson of Coarse to Fne Search Method Development for Solvng Economc Dspatch, Indonesan Journal of Electrcal Engneerng and Computer Scence, vol. 3, no. 1, pp. 1-9, July [16] J. Raharjo, A. Soeprjanto, H. Zen. Optmal Power Flow usng Mult Dmenson of Coarse to Fne Search Method, Internatonal Conference on Current Trends n Computer, Electrcal, Electroncs & Communcaton (ICCTCEEC), Karnataka Inda, 8-9, September [17] Rafael C. Gonzalez, Rchard E. Woods, Dgtal Image Processng Thrd Edton, Prentce Hall, 2008" Appendx Table IIa. SCHEDULE OF GENERATOR UNITS FROM 1 ST TO 12 TH HOUR No Generator/Hour Output Actve Power n MW Suralaya Suralaya Suralaya Suralaya Suralaya Suralaya Suralaya Muaratawar Muaratawar Muaratawar Muaratawar Crata Crata Crata Crata Crata Crata Crata Crata Sagulng Sagulng Sagulng Sagulng

7 24 Tanjungjat Tanjungjat Tanjungjat Tanjungjat Gresk Gresk Gresk Gresk Gresk Gresk Gresk Gresk Gresk Paton Paton Grat Grat Grat Grat Grat Grat Grat Grat Grat Total Power n MW Load n MW Devaton n MW Accuracy n % Total Cost n IDR Mllon Computaton Tme n seconds Table IIb. SCHEDULE OF GENERATOR UNITS FROM 13 TH TO 24 TH HOUR No Generator/Hour Output Actve Power n MW Suralaya Suralaya Suralaya Suralaya Suralaya Suralaya Suralaya Muaratawar Muaratawar Muaratawar Muaratawar Crata Crata Crata Crata Crata Crata Crata Crata Sagulng

8 21 Sagulng Sagulng Sagulng Tanjungjat Tanjungjat Tanjungjat Tanjungjat Gresk Gresk Gresk Gresk Gresk Gresk Gresk Gresk Gresk Paton Paton Grat Grat Grat Grat Grat Grat Grat Grat Grat Total Power n MW Load n MW Devaton n MW Accuracy n % Total Cost n IDR Mllon Computaton Tme n seconds Table III. DATA OF GENERATOR UNITS No g a b c Pmn Pmax Qmn Qmax Sstator 1 Slaya Slaya Slaya Slaya Slaya Slaya Slaya Sglng Sglng Sglng Sglng Grsk Grsk Grsk Grsk Grsk Grsk Grsk Grsk Grsk Crata

9 22 Crata Crata Crata Crata Crata Crata Crata Tjjt Tjjt Tjjt Tjjt Grat Grat Grat Grat Grat Grat Grat Grat Grat Mtwar Mtwar Mtwar Mtwar Patn Patn Table IV. LINE DATA IN PER UNIT No From To R X Y/2 Sm 1 Slaya1 Slaya Slaya2 Slaya Slaya3 Slaya Slaya4 Slaya Slaya5 Slaya Slaya6 Slaya Slaya7 Slaya Slaya Braja Slaya Clgon Cwang Bkas Cwang Mtwar Bkas Cbng Sglng1 Sglng Sglng2 Sglng Sglng3 Sglng Sglng4 Sglng Sglng Bdsln Sglng Cbng Sglng Depok Bdsln Mdrcn Grsk1 GRSIK Grsk2 GRSIK Grsk3 GRSIK Grsk4 GRSIK Grsk5 GRSIK Grsk6 Grsk Grsk7 Grsk Grsk8 Grsk Grsk9 Grsk

10 30 Grsk Srbrt Srbrt Uagrn Srbrt Grat Braja Gndul Clgon Cbng Cbng Depok Cbng Mtwar Depok Gndul Depok Task Crata1 Crata Crata2 Crata Crata3 Crata Crata4 Crata Crata5 Crata Crata6 Crata Crata7 Crata Crata8 Crata Crata Cbatu Mdrcn Uagrn Uagrn Tjjt Uagrn Pedan TJjt1 Tjjt TJjt2 Tjjt TJjt3 Tjjt TJjt4 Tjjt Grat1 Grat Grat2 Grat Grat3 Grat Grat4 Grat Grat5 Grat Grat6 Grat Grat7 Grat Grat8 Grat Grat9 Grat Grat Paton Kmbgn Gndul Mtwar1 Mtwar Mtwar2 Mtwar Mtwar3 Mtwar Mtwar4 Mtwar Mtwar Cbatu Task Pedan Pedan Kdr Kdr Paton Paton Paton Paton Paton