Computational Solution to Economic Operation of Power Plants

Transcription

1 Electrcal and Electronc Engneerng 013, 3(6): DOI: /j.eee Computatonal Soluton to Economc Operaton of ower lants Temtope Adefarat 1,*, Ayodele Sunday Oluwole 1, Mufutau Adewolu Sanus 1 Department of Electrcal/Electronc Engneerng, Federal Unversty, Oye Ekt, 3708, gera Department of Electrcal/Electronc Engneerng, Federal ploytechnc Ede Osun State gera Abstract The producton cost of electrcty s a very mportant ndex n natonal development. Electrcty tarff depends on the fuel cost whch carres the hghest percentage of the total operaton cost n any power plant. In order to keep electrcty tarff as low as possble, fuel cost whch carres the hghest percentage of the total operatng cost has to be mnmzed. Economc operaton of the power plants can be acheved through economc load dspatch and unt commtment. Lagrange relaxaton s one of the best solutons n solvng economc load dspatch problem because t s more effcent and easer than other methods. Ths approach has been mplemented to mnmze the fuel cost of generatng electrcty whle takng nto account some techncal constrants. Keywords Economc Effcency, Economc Load Dspatch, Incremental Cost 1. Introducton The optmum economc operaton of electrc power syste m has occuped an mportant poston n the electrc power ndustry. Wth recent power deregulaton all over the world, t has become necessary for power generatng utltes to run ther power plants wth mnmum cost whle satsfyng ther customers load demand (eak and Base load). In order to acheve ths, all the generatng unts n any power plant must be loaded n such a way that optmum economc effcency can be acheved[]. The purpose of economc operaton of any power plant s to reduce the fuel cost whch carres the hghest percentage of the operatng cost whle runnng the plant[1][]. The mnmum fuel cost can only be acheved by applyng economc load dspatch and unt commtment n any nterconnected power system. Hence, Economc load dspatch s a powerful and useful tool to assess optmum operaton as well as the fnancal and electrcal performance of a power plant. economc operaton s to reduce the fuel cost of the operaton of the power system. The optmum operaton of a power plant can only be acheved by economc load schedulng of dfferent unts n the power plants or dfferent power plants n the power system. Economc load schedulng s the determnaton of the generatng output of dfferent unts n a power plant n such way to mnmze the total fuel cost and at the same tme meet the total power demand[],[7]. The economc load dvson between dfferent generatng unts can only be computed f the operatng cost expressed n terms of power output Output n MWx 1000 x100 % Effcency of generatng unt= Input n KJ per second Output n MWx 1000 x3600 x100 % = Input n KJ per hour If stands for the power output n megawatts (MW) and C be the fuel cost, then Fg.1 shows a typcal nput and output characterstc curve of a power plant.. Economc Operaton of ower Systems Economcal producton of electrcty s the most mportant factor n the power system. In any combned power plants, all the generatng unts should be loaded n such a way that optmum effcency can be acheved. The purpose of * Correspondng author: temtope.adefarat@yahoo.com (Temtope Adefarat) ublshed onlne at Copyrght 013 Scentfc & Academc ublshng. All Rghts Reserved F gure 1. Typcal nput/output Characterstc curve for a sngle unt n a power plant

2 140 Temtope Adefarat et al.: Computatonal Soluton to Economc Operaton of ower lants The max s lmted by thermal consderaton and a gven power unt cannot produce more power than t s desgned for. The mn s lmted because of the stablty lmt of the machne. If the power output of any generatng unt for optmum operaton of the system s less than a specfed value mn, the unt s not put on the bus bar because t s not possble to generate that low value of power from that unt[7],[8]. Hence the generatng ower cannot be outsde the range stated by the nequalty,.e. mn max.1. Operatonal Cost n a ower lant The man economc factor n the power system operaton s the cost of generatng real power. In any power system ths cost has two components[1]. 1. The fxed cost beng determned by the captal nvestment, nterest charged on the money borrowed, tax pad, labour charge, salary gven to staff and other expenses that contnue rrespectve of the load on the power[1].. The varable cost s a functon of loadng on generatng unts, losses, daly load requrement and purchase or sale of power[1]. The economc operaton of an electrcal power can be acheved by mnmzng the varable factor only whle the personnel n charge of the plant operaton have lttle control over the fxed costs[1]... The Objectves of the Research The objectves of the research are as follows: 1. To formulate a mathematcal model to mnmze the total fuel cost of producng electrcal power n a power plant wthn a stpulated tme nterval. The cost of each generatng unt n a power plant s represented by the quadratc equaton of the second order. The objectve functon of a power plant s the algebrac sum of the quadratc fuel cost of each gener atng unt n a power plant.[6],[1]. The objectve functon of each generatng unt can be expressed as F ( ) =a +b +c, Where a, b and c are the cost coeffcents of generatng unt at bus [6][1].. To develop the best approach that wll help all the power utlty companes to solve the problem of economc load dspatch n an nterconnected power system. 3. To estmate the output power and fuel consumpton of each generatng unt n a power plant whle meetng the load demands at a mnmum fuel cost. 4. To desgn a computer applcaton program to solve the problem of economc dspatch problem n any nterconnecte d power system. 5. To deploy all the avalable resources for power generaton such as natural gas, water, desel, uranum, coal and petrol more effcently and thus handle peak and base loads more effcently and relably wth economc load dspatch..3. Economc Load Dspatch The Economc Load Dspatch s a process of allocatng demand loads to dfferent generatng unts n a power plant at a mnmum fuel cost whle meetng the techncal constrants. It s formulated as an optmzaton process of mnmzng the total fuel cost of all the commtted generatng unts n a power plant whle meetng the load demands and techncal constrants[3],[7]. F =a +b +c (1) The fuel cost functon of a generatng unt s represented by a quadratc equaton of the second order as shown n equaton.1 Where a, b and c are constants of th generatng unt..4. Incremental Cost Incremental cost can be determned by takng the dervatve of the equaton 1.0 Subject to = b + c () λ = b + c (3) λ b = c (4) mn max Sum up the entre of the power system I.e. (5) =1 to (6) D = (7) ε (8) Or D - Where ε = If condtons n equaton (5.0) are met, Then Sum up all the (s).e. (9) Error = ABS ( - D ) (10) Error = ε (11) If convergence s not acheved then modfes λ and recompute, the process s contnued untl D - F Ρ Ρ s less than a specfed accuracy or Ρ

3 Electrcal and Electronc Engneerng 013, 3(6): D = If convergence s acheved, then compute the followng, 1. F = a + b Ρ + c Ρ. for each unt.5. Computat onal Algorthms Step1. Total power demand would be gven. Step. Assgn ntal estmated value of λ (0). Step3. Let ε be equal to Step4. F For all the unts would be gven. c Step5. Dfferentate Ρ =λ) Step6. Rearrange F wth respect to ( F Ρ (so that = λ b c F Ρ ) = b + Step7. Compute the ndvdual Unts 1, n Correspondng to λ (0). Step8. Compute Step9. Check f the relatonshp (0) =D s satsfed or D - = ε Step10. If the sum s less than total power demand, then assgns a new value λ (1) repeat steps 8 and 9. Step11. If the sum s less than the demand, then assgns a new value λ () and repeat steps 8 and 9. Contnue the teraton untl when t wll converge. unt. D = or D - Step1. Calculate fuel cost and ε for each generatng 3. Modellng of olynomal Equaton for Each Generatng Unt olynomal model for the generatng unts can be acheved through the least square method Least S quare Equatons F = a + b p + c p ( ) F p = a p + b p + c p 3 () p F = a p 3 + b p + c p 4 () 3.. MAT LAB Smulaton Wth MAT LAB smulaton coeffcents a, b and c can be acheved, therefore the polynomal equaton for each generatng unt s expressed as F= a + b + c Table 1. The 1st generatng unt ower ( Mw) Fuel Cost ( $/Hr ) 3 4 xf ( Mw) ( Mw) 3 ( Mw) 4 ( $Mw/Hr) XF ( Mw) ($/Hr) ,50, E Table 1 shows the power and fuel characterstc of the frst generatng unt

4 14 Temtope Adefarat et al.: Computatonal Soluton to Economc Operaton of ower lants START Read F,a,b,c,D,ε,mn,max,ame of Generatng staton,type of generatng Staton and o of buses Intate λ as 0 SET n=1 SOLVE THE EQUATIO FOR b = λ c Check f >max Yes Set =max Check f <mn Yes set=mn Set n=n+1 o Check f all buses have been accounted Calculate = Is <= ε ( D) Yes Calculate cost of generaton for each unt, total optmum fuel cost, total fuel cost for each type of generatng staton and compute the value of ncremental cost o Reduce λ and assgn new value λ(1) o Is Σ > ε Yes End Increase λ and assgn new value of λ() Flow chart for economc load dspatch problems Fgure. Flow chart for economc load dspat ch

5 Electrcal and Electronc Engneerng 013, 3(6): By applyng the least square equatons = 9a + 700b c () = 700a b c () = a b x10 11 c () Where a = 40, b = 4 and c= Therefore, the polynomal equaton for the frst generatng unt can be expressed as F = Table. The nd generatng unt ower Fuel Cost ( Mw) ( $/Hr ) ( Mw) 3 ( Mw) 3 4 ( Mw) 4 xf XF ( Mw) ( $Mw/Hr) ($/Hr) ,640, Table shows the power and fuel characterstc of the second generatng unt By applyng the least square method = 7a + 875b c () = 875a b c () = 16875a b c () Where a = 00, b=9 and c= Therefore, the polynomal equaton for the second generatng unt can be expressed as F = Table 3. The 3rd generatng unt ower Fuel Cost ( Mw) 3 ( Mw) 3 4 ( Mw) 4 xf ( $Mw/Hr.) XF ( Mw) ( Mw) ($/Hr) ($/Hr.) ,000, Table 3 shows the power and fuel characterstc of the thrd generatng unt

6 144 Temtope Adefarat et al.: Computatonal Soluton to Economc Operaton of ower lants By applyng the least square equatons = 7a b c () = 1430a b c () = a b c () Where a = 0,b = 5.7 and c= Therefore, the polynomal equaton for the 3rd generatng unt can be expressed as F = Table 4. The 4th generatng unt ower Fuel Cost ( Mw) 3 ( Mw) 3 4 ( Mw) 4 XF ( Mw) xf ( $Mw/Hr.) ( Mw) ( $/Hr. ) ($/Hr.) ,640, Table 4 shows the power and fuel characterstc of the fourth generatng unt By applyng the least square equatons = 5a + 500b c () = 500a b c () = 5650a b c () Where a = 00, b = 11 and c= Therefore, the polynomal equaton for the fourth generatng unt can be expressed as F = Table 5. The 5th generatng unt Fuel Cost ower 3 XF ( Mw) ( Mw) ( Mw) 3 4 ( Mw) 4 xf ( Mw) ($Mw/Hr.) ($/Hr. ) ($/Hr.) ,640, Table 5 shows the power and fuel characterstc of the ffth generatng unt

7 Electrcal and Electronc Engneerng 013, 3(6): By applyng the least square equatons = 7a + 875b c () = 875a b c () =16875a b c () Where a = 0,b = 9.8 and c= Therefore, the polynomal equaton for the ffth generatng unt can be expressed as F = ower ( Mw) Fuel Cost ( $/Hr. ) Table 6. The 6th generatng unt 3 4 xf ( Mw) ( Mw) 3 ( Mw) 4 ($Mw/Hr.) XF ( Mw) ($/Hr.) ,960, Table 6 shows the power and fuel characterstc of the sxth generatng unt By applyng the least square equatons 1085 = 5a + 875b c () = 875a b c () =16875a b c () Where a = 190, b = 13 and c= Therefore, the polynomal equaton for the sxth generatng unt can be expressed as 4. Test System Ths system has 6 unts whle the Unts Cost data and system load demand are gven respectvely n Table 7. F1= ($/Hr) F= ($/ Hr) F3= ($/Hr) F4= ($/ Hr) F5= ($/Hr) F6= ($/Hr) F = Ta ble 7. Test Syst em Data Unt mn max A B C MW MW $/Hr $/MWHr $/MW Hr Table 7 shows the quadratc fuel cost for the sx generatng unts

8 146 Temtope Adefarat et al.: Computatonal Soluton to Economc Operaton of ower lants T me (Hr) Table 8. The results of the smulaton Load (MW) Fuel Cost ($/Hr) Incremental Cos t($/mwhr) 0100HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS HRS The smulaton results are analysed n Table 8, the table shows the load emand, fuel cost and ncremental cost for the sx generatng unt Fuel Cost($/Hr) Fgure 3. shows the relatonshp between the load demand and fuel cost n a power system. There s a lnear relatonshp between fuel cost and load demand F gure 3. ower generated vs. Fuel cost Fuel Cost($/MWHr) ower (MW) Hour(Hr) Based on the smulated results, fgure 4 shows the hourly fuel cost n the power system F gure 4. Fuel Cost per hour Incremental Cost($/MWHr) ower (MW) Fgure 5 shows that the syst em ncrement al cost λ s drect ly proportonal to the demand load F gure 5. ower generated vs. Incremental Cost Table 9. The effect of unt commtment n a power plant Unt s Type of Generatng unt Output ower MW Fuel Cost $/Hr Economc Effcency $/MWHr 1 Base load generatng unt Base load generatng unt Base load generatng unt eak load generatng unt Base load generatng unt eak load generatng unt Total

9 Electrcal and Electronc Engneerng 013, 3(6): Incremental Cost($/MWHr) Fuel Cost($/MW) 5. Effect of Unt Commtmen Fgure 6 shows that fuel cost s drectly proportonal to the system ncremental cost λ The frst aspect of the Economc Load Dspatch s the unt commtment problem where t s requred to select optmally out of the avalable generatng sources to operate, to meet the expected load and provde a specfed margn of operatng reserve over a specfed perod of tme[10]. From the analys s as shown n Table 9, the base load generatng unts are 1,, 3 and 5 due to ther low fuel consumpton and optmum economc operaton whle peak load generatng unts are 4 and 6. Table 10. ower plant fuel Consumpton by consderng unt commtment ower Generated (MW) FCWO($/Hr) FCW($/Hr) F gure 6. Fuel cost vs. Increment al Cost Fuel Cost($/Hr) FCWO=Fuel Cost wthout consderng unt Commtment FCW=Fuel Cost by consderng unt commtment 6. Results and Dscusson The results for the system ncremental cost and operatng cost were plotted for the varous load levels. From fgure 5 and fgure 6, t shows that operatng cost and ncremental cost rse lnearly wth load values. Therefore, t can be concluded that fuel cost and the system ncremental cost λ are drectly proportonal to the demand load. They follow an approxmately lnear trend n relaton to the load demand. Table 8.0 shows that fuel cost and ncremental costs are drectly proportonal to the demand load n any ntegrated power system. Table 10 also shows the effect of unt comm tment on unts 1,, 3, 4, 5 and 6. From the table 9, the base load generatng unts are 1,, 3 and 5 due to ther effcency and optmum economc operaton whle peak load generatng unts are 4 and 6. In any power plant, the generatng unt wth the cheapest Fuel Cost, effcency and the best optmum economc operaton wll be selected to dspatch frst. As shown n Table 3.0, Generatng Unt o. 1 s the cheapest whle Generatng Unt o. 6 s the most expensve n terms of fuel cost and economc effcency /MWHr. Hence, Generatng Unt o. 1 would be dspatched frst andgenerat ng Unt o.6 last. Generatng unt 1 s the cheapest and t has the best generatng capablty of the system. 7. Conclusons It can be seen that any ncrease n load demand brngs about the same rse n the system fuel cost; a cost that would be passed on to the customers snce fuel cost carres the hghest percentage of the operatng cost of power plants. Hence, t shows that the relatonshp between fuel prces and Load demands s approxmately lnear. Wth the current po wer deregulaton n the world, t s essental to optmse the runnng cost of power plants by reducng the fuelconsumpt on for meetng a partcular load demand. Ths can only be acheved through the economc load dspatch. REFERECES [1] Abhjt Chakrabart, Sunta Halder "ower System Analyss Operaton and Control", HI Learnng rvate Lmted, Thrd Edton, pp , 010 [] Gupta J.B, "A Course on Electrcal ower", S.K.Katara and

10 148 Temtope Adefarat et al.: Computatonal Soluton to Economc Operaton of ower lants Sons, Fourteenth Edton, 08-1, 01. [3] Manjeet Sngh, Mukesh Garg, Vneet Grdher "Comparatve study of Economc Load Dspatch usng modfed Hopfeld neural network", Internatonal Journal of Computng & Busness Research, ISS (Onlne): , pp.1,01. [4]. hanthuna V. hupha. Rugthacharoencheep, and S. Lerdwanttp "Economc Load Dspatch wth Daly Load atterns and Generator Constrants By artcle Swarm Optmzaton "World Academy of Scence, Engneerng and Technology pp [5] eetu Agrawal, K.K.Swarnkar, Dr. S.Wadhwan, Dr. A. K. WadhwanEconomc Load Dspatch roblem of Thermal Generators wth Ramp Rate Lmt Usng Bogeography - Based Optmzaton Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) Volume 1, Issue 3, March 01 ISS: pp98-10 [6] Tarek Bouktr, Lnda Slman, M. Belkacem A Genetc Algorthm for Solvng the Optmal ower Flow roblem Leonardo Journal of Scences, ISS , Issue 4, pp.46, January-June,004. [7] Wadhwa C.L, "Electrcal ower Systems", ew Agenternat onal ublshers, sxth Edton, pp67-661, 010s. [8] Wood, A, Wollenberg, B "ower Generaton Operaton and Control", Wley and Sons, Thrd Edton, pp154-05, 1984 [9] Y. Tng-Fang;. Chun-Hua, Applcaton of an mproved artcle Swarm Optmzaton to economc load dspatch n power plant, n roc IEEE Int. Conf. Advanced Computer Theory and Engneerng, 010. [10] Wadhwa C. L,"Electrcal ower Systems", ew Age nternat onal ublshers, sxth Edton, pp67-661, 010s. [11] Wood, A, Wollenberg, B "ower Generaton Operaton and Control", Wley and Sons, Thrd Edton,pp154-05,1984 [1] Vjayakumar Krshnasamy Genetc Algorthm for Solvng Optmal ower Flowroblem wth UFC, Internatonal Journal of Software Engneerng and Its Applcatons Vol. 5 o. 1,pp.41 January, 011.