1. Introduction. Keywords: Dynamic programming, Economic power dispatch, Optimization, Prohibited operating zones, Ramp-rate constraints.

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1 A Novel TANAN s Algorthm to solve Ecoomc ower Dspatch wth Geerator Costrats ad Trasmsso Losses Subramaa R 1, Thaushkod K ad Neelakata N 3 1 Assocate rofessor/eee, Akshaya College of Egeerg ad Techology, Combatore, , Ida Drector, Akshaya College of Egeerg ad Techology, Combatore, , Ida 3 Dea (Electrcal Sceces), Akshaya College of Egeerg ad Techology, Combatore, , Ida Abstract Ths paper presets a Novel TANAN s Algorthm (NTA) approach to solve the ecoomc power dspatch problem cludg trasmsso losses power systems. The trasmsso losses are augmeted wth the objectve fucto usg prce factor. The geeralzed expresso for optmal schedulg of thermal geeratg uts derved ths artcle ca be mplemeted for the soluto of the ecoomc power dspatch problem of a large-scale system. Sx-ut, fftee-ut, ad forty- ut sample systems wth o-lear characterstcs of the geerator, such as ramp-rate lmts ad prohbted operatg zoes are cosdered to llustrate the effectveess of the proposed. The proposed results have bee compared wth the results of geetc algorthm ad partcle swarm optmzato s reported the lterature. Test results show that the proposed NTA approach ca obta a hgher qualty soluto wth better performace. Keywords: Dyamc programmg, Ecoomc power dspatch, Optmzato, rohbted operatg zoes, Ramp-rate costrats. 1. Itroducto The ma objectve of the ecoomc dspatch problem s to determe the optmal combato of power outputs for commtted geeratg uts, whch mmzes the total fuel cost whle satsfyg load demad ad operatg costrats. Ths makes the ecoomc power problem a large-scale o-lear costraed optmzato problem. Tradtoal s such as Lambda-terato, the base pot ad partcpato factors s ad the gradet [1-4] are well kow for the ecoomc dspatch of geerators. I these umercal s, a essetal assumpto s that the whole of the geeratg ut operatg rage s avalable for operato. Covetoal techques offer good results but whe the search space s o-lear ad t has dscotutes they become very complcated wth a slow covergece rato ad ot always seekg the optmal soluto. I a practcal system, the geeratg uts have prohbted operatg zoes betwee ther mmum ad maxmum geerato lmts ad the operatg rage of ole uts are restrcted by ther ramp-rate lmts due to physcal operatoal lmtatos. Ut operato prohbted operatg zoes may cause amplfcato of vbratos shaft beargs, whch should be avoded practce. The prohbted operatg zoes of a ut dvde the operatg rage betwee ts mmum to maxmum geerato lmts to several dsjot covex sub-regos. Hece, covetoal s caot be drectly appled to solve the ecoomc dspatch problem wth prohbted operatg zoes. Several s have bee reported for the soluto of the ecoomc power dspatch problem wth prohbted operatg zoes. The dyamc programmg approach [5, 6] s oe of the most wdely employed s for the soluto of the ocovex ecoomc power dspatch problem. Ulke the Lambda terato approach, the dyamc programmg has o restrctos o geerator cost fucto ad performs a drect search of soluto space. However, for a practcal szed system, the fe step sze ad the large ut umber ofte cause the curse of dmesoalty problem or local optmalty the dyamc programmg soluto process. Lee et al. [7] decomposed the ocovex decso space to a small umber of subsets such that each of the assocated dspatch problems, f feasble, s solved through the covetoal Lagraga relaxato approach. Ths approach requres farly extesve computatoal tme whe a system ows more uts that have prohbted operatg zoes. Ref. [8] defed a small advatageous set of decso spaces wth respect to the system demad ad the utlzed the teratve to fd the feasble optmal soluto. Ths may ot be applcable f the problem cotas too may olear costrats for large scale ocovex systems. The stochastc search algorthms such as geetc algorthm (GA) [9], evolutoary programmg (E) [10], [11], smulated 918

2 aealg (SA) [1], tabu search algorthm (TSA) [13], ad partcle swarm optmzato (SO) [14, 15], may prove to be effectve solvg olear ED problems wthout ay restrcto o the shape of the cost curves. Although these heurstc s do ot always guaratee dscoverg the globally optmal soluto fte tme, they ofte provde a reasoable soluto. Further, the stochastc searchg algorthms take a loger tme for covergece. Neural etwork [16, 17] models were appled to the ecoomc power dspatch problem. These s also requred tremedous amouts of tme for trag the etwork.. roblem Formulato The ecoomc power dspatch problem wth ramprate lmts ad prohbted operatg zoes ca be formulated as Where j s the umber of prohbted zoes of ut. l ad u deote the lower boud ad upper boud of the prohbted zoe of the geerator. (v) ramp-rate costrats: Max ( m, 0 DR ) M( max, 0 UR ) (5) Where s the curret output power, ad 0 s the prevous output power. UR s the up-ramp lmt of the th geerator (MW/tme-perod), ad DR s the dow-ramp-lmt of the th geerator (MW/tmeperod). The trasmsso losses are represeted by: L B j j 1 j1 1 B 0 B00 (6) The modfed form of the cost equato of the - geerator system s gve by: MmseFt F( ) a b c 1 1 $/h (1) Where deotes dex of uts; F, Fuel cost fucto of ut ; a, b, ad c are cost coeffcets of geerator ; s the umber of geerators commtted to the operatg system; s the power geerated by the th ut, subject to () the power balace costrats: d l 1 () Where D s the system load demad ad L s the trasmsso loss whch ca be foud through the use of B-matrx loss coeffcets. () Geeratg capacty costrats: F t 1 a b c g ( d e f ) $/h (7) The aalytcal ature of the above problem formulato leads to the hgh possblty of a accurate soluto for the ecoomc power dspatch problem cludg trasmsso losses. 3. Novel TANAN s Algorthm Novel TANAN s Algorthm (NTA) s specally defed for solvg ecoomc dspatch problems. The algorthm s stated as follows. The TANAN fucto s gve by T r s x t x (8) m max =1,, 3 (3) Where m ad max are the mmum ad maxmum power outputs of the th ut. () The addtoal costrats for uts wth prohbted operatg zoes are: m l, 1 u l, j 1, j j=, 3, m (4) u max, m, Wth a power balace costrat T m d l 1 m T (9) Where T - TANAN fucto r, s & t - coeffcets of TANAN fucto x - TANAN fucto varable 919

3 FUEL COST($/h) The coeffcets r, s ad t have bee assumed to be the mmum lmt of th geerator. The TANAN fucto varable x s a radom varable assumed to vary from 0 to.the value of each TANAN fucto s equvalet the power output of that partcular geerator. Sce the TANAN fucto s a parabolc fucto, whch has a extreme lowest pot that correspods to the optmum value of fuel cost. 3.1 Algorthm Step1: Assg TANAN fucto to each geerator. Step: Italze r, s ad t values. Step3: Italze the value of x Step4: Assg = T. Step5: If m the fx = m ad f max the fx = max. Step6: Verfy d ad geerator costrats, f ot adjust the value of x ad go to step 3. Step7: If satsfed, otfy the fuel cost values ad stop the process. 3. Flow chart 4. Smulato Results The NTA for ELD problems has bee mplemeted MATLAB ad t was ru o a computer wth Itel Core Duo.0 GHz processor, 3GB RAM memory ad Wdows X operatg system. Sce the performace of the proposed algorthm sometmes depeds o put parameters, they should be carefully chose. After several rus, the followg results were obtaed ad are tabulated. Table 1. Ecoomc dspatch results for 6-ut system Ut power output (MW) ID SO GA NTA Method (x=1.07) Total ower (MW) Total output Loss (MW) Total geerato cost ($/h) ID SO GA NTA ALGORITHMS Fg.Comparso chart for fuel cost Fg1.flow chart for NTA 90

4 Table. Ecoomc dspatch results for 15-ut system Ut power output (MW) ID SO GA roposed NTA Total output Loss (MW) Total geerato cost ($/h) Table 3. Ecoomc dspatch results for 40- ut system Ut Geerato (MW) ID Geerato (MW) NTA (X=0.346) Fuel cost (NTA) ($) Ut Geerato (MW) ID Geerato (MW) NTA (X=0.346) Fuel cost (NTA) ($) Total power geerato ad Total Cost

5 5. CONCLUSION The proposed NTA to solve ED problem wth the practcal costrats has bee preseted ths paper. It s clear that the NTA s a smple umercal radom search techque for solvg ELD problems. From the smulatos, t ca be see that the optmum fuel cost ca be obtaed by varyg the TANAN fucto varable from 0 to ad the proposed NTA gave the best results very less computatoal tme. REFERENCES [1] J. Wood ad B. F. Wolleberg, ower geerato, operato ad cotrol, New York: Joh Wley Ic., [] K. Krchmayer, Ecoomc operato of power systems, New York: Joh Wley & Sos, [3] L. Che ad S. C. Wag, Brach ad boud schedulg for thermal geeratg uts, IEEE Tras.Eergy Coverso, vol. 8, o., pp , Jue [4] K.Y. Lee, Fuel cost mmzato for both real ad reactve power dspatches, IEE roceedgs Geerato Trasmsso Dstrbuto, vol. 131, o. 3, pp , May [5] R. Bellma, Dyamc programmg, rceto Uversty ress, [6] Z. X. Lag ad J. D. Glover, A zoom feature for a dyamc programmg soluto to ecoomc dspatch cludg trasmsso losses, IEEE Tras. ower Systems, vol. 7, o., pp , May 199. [7] F. N. Lee ad A. M. Brephol, Reserve costraed ecoomc dspatch wth prohbted operatg zoes, IEEE Tras. ower Systems, vol. 8, o. 1, pp , Feb [8] J. Y. Fa ad J. D. McDoald, A practcal approach to real tme ecoomc dspatch cosderg ut s prohbted operatg zoes, IEEE Tras. ower Systems, vol. 9, o. 4, pp , Nov [9] C. Walters ad G. B. Sheble, Geetc algorthm soluto of ecoomc dspatch wth valve pot loadgs, IEEE Tras. ower Systems, vol. 8, o. 3, pp , Aug [10] N. Sha, R. Chakrabart ad. K. Chattopadhyay, Evolutoary programmg techques for ecoomc load dspatch, IEEE Tras. Evolutoary Computato, vol. 7, o. 1, pp , Feb [11] H. T. Yag,. C. Yag ad C. L. Huag, Evolutoary programmg based ecoomc dspatch for uts wth osmooth fuel cost fuctos, IEEE Tras. ower Systems, vol. 11, o. 1, pp , Feb [1] K.. Wog ad C. C. Fug, Smulatedaealg based ecoomc dspatch algorthm, IEE roceedgs -Geerato Trasmsso Dstrbuto, vol. 140, o. 6, pp , Nov [13] W. M. L, F. S. Cheg ad M. T. Say, A mproved tabu search for ecoomc dspatch wth multple mma, IEEE Tras. ower Systems, vol. 17, o. 1, pp , Feb. 00. [14] Z.-L. Gag, artcle swarm optmzato to solvg the ecoomc dspatch cosderg the geerator costrats, IEEE Tras. ower Systems, vol. 18, o. 3, pp , Aug [15] T. A. A. Vctore ad A. E. Jeyakumar, Dscusso of partcle swarm optmzato to solvg the ecoomc dspatch cosderg the geerator costrats, IEEE Tras. ower Systems, vol. 19, o. 4, pp , Nov [16] T. Yalcoz ad M. J. Short, Neural etworks approach for solvg ecoomc dspatch problem wth trasmsso capacty costrats, IEEE Tras. ower Systems, vol. 13, o., pp , May [17] T. Yalcoz, B. J. Cory ad M. J. Short, Hopfeld eural etwork approaches to ecoomc dspatch problems, Iteratoal Joural of Electrcal ower ad Eergy Systems, vol. 3, o. 6, pp , Aug [18] R. Balamuruga ad S. Subramaa, A Improved Dyamc rogrammg Approach to Ecoomc ower Dspatch wth Geerator Costrats ad Trasmsso Losses, Joural of Electrcal Egeerg & Techology, Vol. 3, No. 3, pp. 30~330, 008 9

6 AENDIX Table I. Geeratg ut capacty ad coeffcets for 6-ut system a b c Ut 0 UR DR rohbted zoes (MW) m max ($/MW) ($/MW) ($) (MW/h) (MW/h) [10-40][ ] [90-110][ ] [ ][10-40] [80-90][110-10] [90-110][ ] [75-85][ ] Table II. Geeratg ut data for 15-ut system Ut m max a b c UR DR Table III. rohbted zoes of geeratg uts for 15-ut system Ut rohbted zoes (MW) [185-5][ ][40-450] 5 [180-00][ ][390-40] 6 [30-55][ ][ ] 1 [30-40][55-65] 93