Optimum Generation Scheduling for Thermal Power Plants using Artificial Neural Network

Transcription

1 Internatonal Journal of Electrcal and Computer Engneerng (IJECE) Vol., o., ecember 0, pp. 35~39 ISS: Optmum Generaton Schedulng for Thermal ower lants usng Artfcal eural etwork M. S. agaraja epartment of Electrcal & Electroncs Bapuj Insttute of Engneerng & Technology, B o. 35, Shabhunur Road, avangere, Karanataka, Inda. h: ,ax: msndvg@gmal.com Abstract A smple method to optmze generaton schedulng for thermal power plant usng artfcal neural network s presented. The optmal generaton of generators s acheved consderng operatonal and load constrants. The B- Coeffcents are used to evaluate transmsson loss n the system. The fuel cost of each unt n a plant s computed. The effectveness of methodology s tested wth sx thermal power plants. A result of proposed method s compared wth classcal method. The artfcal neural network method s quck. Hence, artfcal neural network technque can be used n central load dspatch center. Index Terms- eural network, B-Coeffcents, uel cost, ower loss, Real power. Introducton Wth the large nterconnecton of the electrc networks, the energy crss n the world and contnuous rse n prces, t s very essental to reduce the runnng charges of the electrc energy. In developng countres lke Inda, the cost of fuel s rapdly ncreasng. The man economc factor n power system plannng, operaton and control s the cost of generatng real power. The sze of electrc power system s ncreasng rapdly to meet the energy requrements. A number of power plants are connected n parallel to supply the system load by nterconnecton of power statons. Wth the development of grd system, t becomes necessary to operate the plant unt most economcally. The economc generaton schedulng problem nvolves two separate steps namely the unt commtment and the on-lne economc dspatch. The functon of the on-lne economc dspatch s to dstrbute the load among the generatng unts actually paralleled wth the system n such a manner as to mnmze the total cost of supplyng the mnute to mnute requrements of the system and satsfyng load and operatng constrants. Thus, economc load dspatch problem s the soluton of a large number of load flow problems and choosng the one whch s optmal n the sense that t needs mnmum cost of electrc power generaton. Accountng for transmsson losses results n consderable operatng economy. urther more, ths consderaton s equally mportant n future system plannng and n partcular, wth regard to the locaton of plants and buldng of new transmsson lnes. To calculate electrc power generaton of varous unts wth dfferent load demands, the usual Classcal (Krchmayer) method s used. These are generally solved by teratng the value of untl the some of the generator outputs equals the system demand plus transmsson losses. The ncremental transmsson losses are calculated usng transmsson loss coeffcent called B co-effcent approach. As early as the md 930s economc dspatch of real power not consderng the transmsson losses was beng performed. By the md 940 s analyss technques were suffcently developed so that transmsson losses could be taken nto account. By the md 950s number of dgtal dspatch systems was avalable to the ndustry. Economc dspatch programs whch are nstalled today n the most modern control centers uses the classcal methods to solve a well known exact co-ordnaton equatons. The man dfference between dfferent technques s the method used to solve the co-ordnatons equatons. The co-ordnaton equatons are generally solved by nteractvely adjustng the load untl the sum of the generator output matches the system load, pulse system loss. The transmsson loss penalty factor have been mplemented usng one of the several loss formulas whch are calculated off-lne or on-lne at perodc nternal and on request. In recent years, AI applcatons have receved ncreasng attenton n varous areas of power systems such as operaton, plannng and control. A number of research artcles appeared recently ndcate applcablty of AI technques to power system for wder operatng condtons under uncertantes. Artfcal neural networks have attracted much attenton due to ther computatonal speed and robustness. A major advantage of the artfcal neural network approach s that the doman knowledge s dstrbuted n the neurons and nformaton processng s carred out n a parallel dstrbuted manner. Therefore, artfcal neural network reaches the desred soluton rather effcently. ew graphcal method for optmum power generaton [] wth neglectng the mutual elements of B coeffcent matrx s dscussed. The analytcal method to optmze generaton schedule [] neglectng the transmsson losses s dscussed. Smplfed approach to soluton of co-ordnaton equaton for generaton schedulng Receved Oct 8 th, 0; Revsed ov 5 th, 0; Accepted ec 9 th, 0

2 36 ISS: [3] s dscussed. Quck method [4] to optmze generaton schedulng s dscussed. It elmnates the teratve steps and offers a good savngs n computer tme and computer memory.. roblem ormulaton To determne the economc dstrbuton of load between the varous unts consstng of a turbne, generator, and stem supply, the varable operatng costs of the unt must be expressed n terms of the power output. The varaton of fuel cost of each generator wth actve power output s gven by a quadratc polynomal.,,.. a + b + c Rs / hr () Where a s a measure of losses n the system, b s the fuel cost and c s the salary and wages, nterest and deprecaton. The optmal dspatches for the thermal power plants should be such that the load demands plus lne losses, whch can be wrtten as: 0 () Where, Total number of generatng plants. Generaton of th plant. Total system transmsson loss. System load demand The transmsson losses whch occur n the lne when power s transferred from the generatng staton to the load centers ncreases n dstance between the two. The transmsson losses may vary from 5 to 3 % of the total load. If the power factor of load at each bus s assumed to reman constant the system loss can be shown to be a functon of actve power generaton at each plants.e. ( G, G, G3,.... G ) (3) One of the most mportant, smple but approxmate method of expressng transmsson loss as a functon of generator power s through B- Coeffcents as, j B j Gj (4) where,,& Gj are real power generaton at th and j th The nequalty constrants s gven by power unt. B j s loss coeffcents. GMn (5) GMax The maxmum actve power generaton GMax of source s lmted by thermal consderaton and mnmum actve power generaton GMn s lmted by the flame nstablty of a boler. 3. Methodololgy The objectve of optmum generaton schedulng for thermal power plants s to allocate the generaton to each and every unts n a plant for a gven load such that fuel cost s mnmum subjected to equal and nequalty constrants. Here, optmum generaton schedulng s acheved by two technques. The methods are presented below. 3. Artfcal eural etwork Method Artfcal neural network based method s appled to the optmum generaton schedulng problem. A multlayer feed forward neural network s selected. A neural network s constructed wth one nput layer, one hdden layer and one output layer. The nput to the neural net contans load demand. The output from the network s generaton of each generator. In the tranng process, load demand and actve power generaton whch s nputoutput patterns Tranng set) are selected from data base to determne the weghts for the neural network. The well IJECE Vol., o., ecember 0 : 35 39

3 IJECE ISS: known back propagaton algorthm and the sgmod transfer functon are used n the model. Once the network traned, the network parameters (weghts and bas terms) were kept fxed. The convergence crtera used for tranng s to have a tolerance and epochs. Once the network has been traned, the accuracy of the neural network can be evaluated by testng the neural network wth another set of nput-output data (testng set). To speed up the convergence, momentum and learnng rate are selected. Selected nput-output patterns are normalzed between 0 and to avod the convergence. Snce the varables, nput to and outputs from A have very dfferent ranges, the use of orgnal data to the network wll cause a convergence problem. The absolute percentage error (AE) of the generaton schedulng s gven below. oad Scheduled oad caluclated AE 00 (6) oad Scheduled The mean percentage error (MAE) s computed by MAE AE where umber of loads. (7) 3. Classcal Method Ths s an teratve and an accurate method to determne output of generator. An algorthm for obtanng real power generaton and fuel cost are teratvely solved on the followng steps for a partcular load demand.. Intally chose λ λ 0. Assume GI 0.0;,, 3. Solve below equaton teratvely for G s b λ a λ j j B + B j Gj 4. Calculate power loss usng j B j Gj 5. Check f power balance equaton s satsfed, ε f yes, stop. Otherwse, go to step Increase λ by λ; f 0 0 Repeat from step-3. Otherwse, decrease λ by λ ; f 4 Sample Sytem A sx plant system wth the followng cost equatons s consdered Rs/hr Optmum Generaton Schedulng for Thermal ower lants usng Artfcal eural etwork (M. S. agaraja)

4 38 ISS: The nequalty constrants are MW ; 0MW 00,,.6 The transmsson loss coeffcent matrx B mn s as gven n Table. Table.. Transmsson loss Coeffcent Matrx E-3 E-5 5E-4 5E E-4 E-4 3E-3 -E-4 E-5 E-4 E-4 5E-4 -E-4 E-3 -E-4 E-4 8E-5 5E-5 E-5 -E-4 5E-4 6E-5 5E E-4 E-4 6E-4 5E-3 E-4-3E-4 E-4 8E-8 5E-4 E-4 E-3 The data requred for the artfcal neural network s as follows. earnng Rate : 0.5 Momentum Constant : 0.8 umber of teratons (epochs) : 0000 Tolerance : Results Generaton schedulng for each load s obtaned from three layer feed forward artfcal neural network. The sze of the artfcal neural network s / / 6. A s traned wth 4 dfferent loads. etwork s traned wth back propagaton algorthm. Once the neural net s traned, the accuracy of the neural net can be evaluated by testng the network wth another 4 dfferent loads. og- sgmod and pure lnear transfer functon s selected n the hdden and output layer respectvely. Results are obtaned by A method and classcal method. The results of fuel cost for varous load s gven n Table. rom Table, t s found that the results obtaned by the A method concde wth the accurate teratve method. The mean absolute percentage error s.577. Total fuel cost for each real power demand s presented n Table 3. The graph between fuel cost aganst real power demand s drawn and shown n g.. The percentage devaton n the operatng fuel cost for the A method wth respect to classcal method s calculated and gven n Table 4. A graph between the receved power and percentage devaton n the fuel cost for the A method s shown n g.. Table. Comparson of Results of A & Classcal Method oad MW Generaton (A) Error Table.3 Comparson of uel Cost oad (MW) uel Cost (A ) uel Cost (Classcal) IJECE Vol., o., ecember 0 : 35 39

5 IJECE ISS: Table.4 % evaton n Total uel Cost oad (MW) % evaton of uel Cost uel Cost(Rs/hr) Classcal A em and(mw) gure. uel Cost and Real ower demand %evat on eamand ( M W ) gure. ercentage evaton of uel Cost & Real ower 6 Concluson Ths paper deals wth optmal generaton schedulng n thermal power plant usng artfcal neural network. Three layer feed forward A s used to optmze generaton schedulng. A s traned and tested wth back propagaton algorthm. The equalty and nequalty constrants are consdered whle optmzng generaton schedulng. The constant B- Coeffcents are used to fnd the transmsson loss. The B- Coeffcent method s smple and less tme consumng method to fnd transmsson loss when compared to load flow technque. The method s tested wth sx thermal power plants. Results are accurate and encouragng Results of A are compared wth classcal method. Reference [] K Srkrshna et al, ew graphcal method for optmum power generaton, pp48-5, vol.6, ec 980, Journal of the Insttute of Engneers (Inda). [] K agappa et al, Analytcal method to optmze generaton schedule, pp40-4, vol.66, June 986, Journal of the Insttute of Engneers (Inda). [3] K.Srkrshna et al, Analytcal approach to soluton of co-ordnaton equaton for generatng schedulng, pp54-57, vol.67, June 987, Journal of the Insttute of Engneers (Inda). Optmum Generaton Schedulng for Thermal ower lants usng Artfcal eural etwork (M. S. agaraja)

6 40 ISS: [4] C.alanchamy et al, Quck method to Optmze Generaton Schedule, pp99-03, vol.69, ec 988, Journal of the Insttute of Engneers (Inda). [5] Krchmayer.K. Economc Operaton of ower Systems, John Wlley and Sons, ew York, 958. [6] agarath I.J. & Kothar.., Modern ower System Engneerng, TMH ublcatons, ew elh, 994. [7] W..Stevenson Jr., Elements of ower systems analyss, McGraw Hll Book Company, ourth Edton. [8] Md. Mohatram et al, Applcaton of neural network n Economc generaton schedulng of thermal power plants. Bblography of Author: r. M S agaraja, completed hs BE degree n Electrcal & Electroncs n the year 986 from Government BT college of engneerng, avangere. He dd Master of Technology n ower system n the year 99 from atonal Insttute of Engneerng, Mysore & ocotoral degree n power systems n the year 007 from atonal Insttute of Engneerng, Mysore. He has publshed 7 papers n natonal & nternatonal conference ncludng two papers n natonal journals. He has teachng experence of 5 years n under graduate college. At present s workng has professsor & Head n the department of Electrcal & Electroncs Engneerng. IJECE Vol., o., ecember 0 : 35 39