Joural of ad Eergy Egieerig, 05, 3, 43-437 Published Olie April 05 i SciRes. http://www.scirp.org/joural/jpee http://dx.doi.org/0.436/jpee.05.34058 Study o Coal Cosumptio Curve Fittig of the Thermal Based o Geetic Algorithm Le-Le Cui, Yag-Fa Li, Pa Log State Grid MiaYag Electric Supply Compay, MiaYag, Sichua, Chia Email: lelecui5@sia.com, 378@qq.com Received Jauary 05 Abstract of the thermal power plat ca reflect the fuctio relatioship betwee the coal cosumptio of uit ad load, which plays a key role for research o uit ecoomic operatio ad load optimal dispatch. Now get coal cosumptio curve is geerally obtaied by least square method, but which are static curve ad these curves remai uchaged for a log time, ad make them are icompatible with the actual operatio situatio of the uit. Furthermore, coal cosumptio has the characteristics of typical oliear ad time varyig, sometimes the least square method does ot work for oliear complex problems. For these problems, a method of coal cosumptio curve fittig of the thermal power plat uits based o geetic algorithm is proposed. The residual aalysis method is used for data detectio; quadratic fuctio is employed to the objective fuctio; appropriate parameters such as iitial populatio size, crossover rate ad mutatio rate are set; the uit s actual coal cosumptio curves are fitted, ad comparig the proposed method with least squares method, the results idicate that fittig effect of the former is better tha the latter, ad further idicate that the proposed method to do curve fittig ca best approximate kow data i a certai sigificace, ad they ca real-timely reflect the iterdepedece betwee power ad coal cosumptio. Keywords Thermal Plat, Coal Cosumptio Curve, Uit, Least Squares Method, Geetic Algorithm, Curve Fittig, Noliear Problems. Itroductio The structure of electric power i Chia, by the ed of march 03, the total istalled power geeratig capacity of the whole coutry reached,3,000,000 kw, the thermal power istalled capacity has reached 85,000,000 kw, accoutig for 73.5% of the total istalled capacity, coal cosumptio of thermal power plats is growig, coal eergy cosumptio accouted for the total eergy cosumptio of about 67%. I order to realize eergy savig ad emissio reductio ad low carbo efficiet productio mode, it eeds to optimal load distributio How to cite this paper: Cui, L.-L., Li, Y.-F. ad Log, P. (05) Study o Coal Cosumptio Curve Fittig of the Thermal Based o Geetic Algorithm. Joural of ad Eergy Egieerig, 3, 43-437. http://dx.doi.org/0.436/jpee.05.34058
for thermal power plat uit, but realize optimal load distributio the key step is accurate fittig of the uit coal cosumptio curve. At preset, coal cosumptio curve of the thermal power plat is usually obtaied by the performace parameters which are provided by the maufacturer, or thermal test data, ad these curves remai uchaged for a log time. However, the uit i the actual operatio will be affected by the mode of operatio, coal quality, device status, the techical level of operators ad other factors, ad make these curves have a great differeces with the actual operatio situatio of the uit. Accordig to this situatio, it eeds to refit the coal cosumptio curve i actual operatio. The method of curve fittig most are usig least squares o curretly, but it is difficult to solve complex oliear problems by this method, sometimes these curves caot meet requiremets of the actual applicatios. Geetic algorithm, or GA for short []-[4], is a global optimizatio algorithm based o selectio ad atural geetic, which developed from evolutio theory ad geetic theory. Compared with the least square method, the mai characteristic of geetic algorithm is ot deped o gradiet iformatio, especially suited to be used deal with complex ad oliear problems which are difficult to be solved by traditioal search methods, it makes up for its shortcomigs of the least square method. However, the data of the thermal power plat is huge, strog oliear, this method is used to fit coal cosumptio curve of the thermal power plat i this paper, ad comparig the proposed method with least squares method.. Data Processig Sice this paper is aimed at oliear static system of the coal cosumptio curve, that is to say it eeds to the uit work o stable state, ad use the static data of the uit to model. All the tested uit data are derived from the bottom of the DCS cotrol system, ad because these date are effected by uit operatig mode ad evirometal coditios, there are errors ad oise for the collected data i DCS, if modelig directly use the data i DCS, it will cause great iterferece for coal cosumptio curve, meawhile it is meaigless if study o coal cosumptio of the uit uder the uit operatig exist fluctuatio. Therefore, it eeds to process origial data before modelig. There are two mai kids of iterferece for the data from the DCS: Oe is the radom iterferece at the time of data collectio, it ca be removed by filterig method; the other is jump poit that fluctuatio is very cospicuous. I this paper, the method of data detectio is residual aalysis. Collected data are set to x, the data after process is y,, is the limit value of data chagig, uder the same sample period, the rate of chage ca be judged by the absolute value of the differece betwee two successive samplig data. xk ( ) is the kth samplig value, to calculate xk ( ) xk ( ), if xk ( ) xk ( ) <, there is ot outlier, yk ( ) = xk ( ) ; if xk ( ) xk ( ), there may be outliers, we ca take aother poit xk+ ( ), if xk ( + ) xk ( ), ad there are same chagig tred, we thik there is disturbace. Let y( k) = ax( k ) + bx( k), where a ad b are weights, ad ab, (0,) ; if there are opposite tred, we thik xk ( ) is jump poit. Let y( k) = ax( k ) + bx( k + ) ; if xk ( + ) xk ( ), we thik there are outliers, they should be removed. 3. Coal Cosumptio Curve Fittig of the Thermal Based o Geetic Algorithm Now it eeds to fit coal cosumptio curve of the uit for a thermal power plat with 4 38.5 MW, operatio eergy cosumptio data of the each uit, as i Table below [5]. I fact, i reality project, just eed quadratic curve the it ca meet requiremets of the accuracy. Therefore, the objective fuctio set to the followig quadratic fuctio: F = x+ x P+ x3 P, where x, x, x 3 is the parameters that eeds to estimate. Program object fuctio for the # uit, ad be saved with the fileame ga_curfit.m to Matlab directory. # uit fittig results as show i Figure. The same method ca be used to fit coal cosumptio curve of the other three uits, ad the fittig results as show i Figures -4. equatios of each uit are fitted by geetic algorithm, which are: F = 0.00085796473P + 0.5954633784P + 49.746930797674 F = 0.00047686996979P + 0.7577999648337P + 43.00634087074 43
Table. -coal cosumptio table. # uit # uit 3# uit 4# uit Coal cosumptio coal cosumptio coal cosumptio coal cosumptio 89.85.00 70.00 85.00 74.00 0.6 63.70 03.00 7.59 95.00.00 93.00 9.9 07.96 9.96 08.00 0.00 96.00 05.9.00 0.83 3.0 08.5.00 40.00 04.00 0.00 07.00 0.00 4.00.96 0.00 50.00 05.00 30.00.00.9 0.00 3. 6.00 60.00.00 40.00 07.00 45.00 8.4 44.8 8.00 7.86.00 50.00 7.00 53.39 5.46 5.96.00 80.00 6.00 60.00 3.00 77.08 47.9 60.00 37.00.00 4.00 77.00 8.00.83 53.0 7.0 45.00 300.00 3.00 96.00 3.00 300.00 56.05 84.07 5.00 30.00.00 300.00 37.00 3.08 58.00 300.00 56.00 35.00 6.00 38.00 48.00 30.00 59.00 35.00 60.00 30.00.00 30.00.00 35.00 64.3 30.00 69.0 5 of uit Coal cosumptio F 0 5 05 95 85 80 00 0 40 60 80 300 30 P Figure. of uit. 0.0005089845665P + 0.845336389838P + 5.6593697733 3 3 F = 0.000844303650P 0.0599965440300P + 83.580889 4 4 4 4. Coal Cosumptio Curve Fittig of the Thermal Based o Least Square Method For compariso purposes, methods ad results of least squares fittig curve are give. 433
of uit Coal cosumptio F 0 80 60 80 00 0 40 60 80 300 30 P Figure. of uit. 70 60 of uit 3 Coal cosumptio F 0 60 80 00 0 40 60 80 300 30 340 P Figure 3. of uit 3. 70 60 of uit 4 Coal cosumptio F 0 60 80 00 0 40 60 80 300 30 P Figure 4. of uit 4. 434
Set ϕ0, ϕ,..., ϕ are the fuctios of liear idepedece o Cab [, ], ad let Φ= spa{ ϕ0, ϕ,..., ϕ }. Set f( x ) be a give discrete fuctio o m + odes which are a = x0 < x <... < xm = b, least squares method is fid * s Φ to make m m * ρ( xj)[ f( xj) s ( xj)] = mi ρ( xj)[ f( xj) s( xj)] s Φ j= 0 j= 0, where ( x) ρ is weight fuc- tio o [ ab., ] The we call s * ( x ) as the least squares solutio for f( x ) which o m + odes, also called as the least squares fittig [6]. Accordig to above priciple, the coal cosumptio curve which is used by quadratic polyomial is: F = mp + tp + k () where F coal cosumptio of the uit power supply ; P geeratio power of the uit ; mtk Eergy,, cosumptio characteristic parameters. Use least squares method to determie the biomial coefficiet mtk.,, Set there are experimets discrete data poits ( F, P ) Let i i= i J = ( mp + tp + k F ), to make the J miimum, ad the let: i i i After put i order we ca get: J = + + = () m Pi ( mpi i = tpi k Fi) 0 J = + + = (3) t Pi( mpi i= tpi k Fi) 0 J = + + = (4) k ( mpi i= tpi k Fi) 0 4 3 ( Pi ) m+ ( Pi ) t+ ( Pi ) k = ( FP i i ) i= i= i= i= (5) 3 ( Pi ) m+ ( Pi ) t+ ( Pi) k = ( FP i i) i= i= i= i= (6) ( Pi ) m + ( Pi) t + k = Fi i= i= i= (7) Coal cosumptio parameters mtk,, ca be obtaied by solve the liear equatios. Usig least square method to fit coal cosumptio curve, ad the results as show i Figures 5-8. equatios of each uit are fitted by least square method, which are: F = 0.0005804086P + 0.00488999807P + 67.88406745974 F = 0.0004337743P + 0.953379699P + 40.606863973 F = 0.000436575969P + 0.8578978488P + 47.3073009846958 3 3 3 F = 0.000873043P 0.065683946P + 84.0684067 5. Fittig Error Aalysis 4 4 4 The curve fittig is good or ot judged by SSE (sum of square error), the sum of square error are obtaied by these two algorithms as show i Table. Notes: SSE is sum of square error based o geetic algorithm ad SSE is sum of square error based o least square method i the table. From the table we ca see that the error based o geetic algorithm is sigificatly less tha least square method for uit, ad 3, ad the error of both methods are very close for uit 4. Show that fittig effect based o 435
5 of uit Coal cosumptio F 0 5 05 95 85 80 00 0 40 60 80 300 30 Figure 5. of uit. of uit Coal cosumptio F 0 80 60 80 00 0 40 60 80 300 30 Figure 6. of uit. 70 60 of uit 3 Coal cosumptio F 0 60 80 00 0 40 60 80 300 30 340 Figure 7. of uit 3. 436
70 60 of uit 4 Coal cosumptio F 0 60 80 00 0 40 60 80 300 30 Figure 8. of uit 4. Table. Error sum of square. SSE( ( t / h ) ) SSE( ( t / h ) ) # uit # uit 3# uit 4# uit 43.7 44.88 95.30 95.3 34.5 34. 83.88 83.8 geetic algorithm is sigificatly better tha based o least square method, the origial data are more fall o the curve or distributed aroud the curve, ad more truly reflect the relatioship betwee coal cosumptio ad power. 6. Coclusio The experimets show that it is practicable use geetic algorithm to fit coal cosumptio curve. From the fittig results ca be see that the fittig curve ca approximate the origial data poits, ad it ca better predict the coal cosumptio tred. But geetic algorithm also has its shortcomigs, premature covergece, o directioal geetic operator, ad every time the search results are ot fixed, these problems are expected ext step to be improved. Refereces [] Wu, J., Ma, X. ad Hou, R. (0) Optimizatio of APF LCL Output Filter Based o Geetic Algorithm. Trasactios of Chia Electrotechical Society, 6, 59-64. [] Ma, X.-F. ad Cui, H.-J. (0) A Improved Geetic Algorithm for Distributio Network Plaig With Distributed Geeratio. Trasactios of Chia Electrotechical Society, 6, 75-8. [3] Wag, X.-P. (00) Geetic Algorithms Theory, Applicatio ad Software Implemetatio. Xi a Jiaotog Uiversity Press. [4] Zhou, W.-Y., Lü, F.-P. ad Li, H. (03) Method for the Combiatio of System Operatio Mode Based o Geetic Algorithm. System Protectio ad Cotrol, 4, 5-55. [5] Zhao, L.-Q. (008) Research o the Plat s Optimal Uit Commitmet. North Chia Electric Uiversity. [6] Liu, X. (007) Research o the Plat s Optimal Load Dispatch ad Uit Commitmet of Thermal Plat Based o Geetic Algorithm. North Chia Electric Uiversity. 437