Educational Software for Economic Load Dispatch for Power Network of Thermal Units Considering Transmission Losses and Spinning Reserve Power

Transcription

1 Educatonal Software for Economc Load Dspatch for ower Network of Thermal Unts Consderng Transmsson Losses and Spnnng Reserve ower Mohammad T. Amel Saed Moslehpour Massoud ourhassan ower and Water Unversty Unversty of Hartford ower and Water Unversty Keywords and hrases: Economc Load Dspatch (ELD), Lagrange Method, Transmsson Losses, Spnnng Reserve ower, Operaton Abstract: ower dspatchng for generatng unts of a power network s one of the mportant consderatons of economcally optmzed power system. The provson of total consumpton load under varous specfed constrants requres determnng the share of each generatng unt n the best possble way. Mnmzaton of the total fuel cost of all unts s one of the basc objectves n large ntegrated networks. Ths s because a small percentage of savng n fuel consumpton would yeld consderable reducton n total costs and envronmental degradaton due to burnng fuels.. Ths artcle ntroduces a hghly capable software system that can be used n tranng of the generatng unts and network operators. To ths end, the exstng methods and algorthms of optmal dspatch are brefly dscussed. Ths paper consders transmsson losses and the spnnng reserve power that actually exsts n the network. Also examned are refnements of the regular calculatons for Economc Load Dspatch(ELD). By further refnement of ELD calculatons, fuel costs of the generatng plants and losses of the transmsson systems are mnmzed, thereby mprovng the optmzaton of generatng and transmsson costs. 1 - Introducton The monotoncally ncreasng global prce of fuels and the nflaton trend necesstate the frequent, f not contnuous, montorng and re-evaluaton of the optmzed dspatch n utlzaton of the power networks. Some constrants add to, and amplfy the complextes of ELD calculatons ncludng the roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

2 dversty of power plant types (steam turbne, gas turbne, hydro-electrc, solar, wnd, nuclear.). [6] Optmal dspatch requres: 1) mnmzaton of fuel costs 2) transmsson losses and envronmental degradaton, 3) due consderaton of the specfc constrants for each power plant. In fact, from a mathematcal pont of vew, the problem of ELD bols down to a large-scale, nonlnear optmzaton problem wth several constrants. Varous methods are beng used both ndvdually and n combnaton to for optmze power dspatch. These methods nclude Lagrange Method, Lambda(λ) Iteraton Method, 1 st and 2 nd -order Gradent Method, Coeffcents of Sharng, Lnear rogrammng, Neural Networks, Fuzzy Algorthms, [1] In the ard and dry countres of the mddle-east regon, hydroelectrc power plants have a neglgble share n producton of power. About 98% of the power orgnates from thermal unts lke steam turbnes, gas turbnes and combned-cycle unts. Therefore, ths artcle deals prmarly wth the thermal unts. The overall costs of the power networks can be classfed n two categores of fxed costs (for constructon of the power plants) and varable costs (for mantenance and operaton of the unts). In networks that manly consst of thermal plants, the cost of fuel s more mportant and has a great mpact on the problem of ELD and operaton. [4] 2 Selecton of the Method and Formulaton of the roblem Ths software system s based on the Lagrange Method, because t offers a precse, relable and conclusve soluton. Compared to other methods, the speed of convergence for ths software s acceptable. These make t a sutable choce for the ELD problems. 3 Objectve Functon and Constrants The objectve functon s ntroduced to mnmze the total producton costs of the generatng unts: Where F = n T F ( ) = 1 (1) roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

3 F T : Total generatng costs of all unts F : Cost of the th unt : Generatng power of the th unt n : Number of unts As shown n the followng two formulas, F s the product of heat functon H by Cost. H quantfes the generatng cost n terms of output MW, and t s a 2 nd - or 3 rd -degree functon of the generatng power of the unt that s also called "nput-output curve". In the followng formulas, "Ral" s the currency of Iran and Rals buy one USD($). H (Mbtu/ h) = A + B + C F(Ral/ h) = H (Mbtu/ h)*cost(ral/ Mbtu) 2 For mnmzaton of (1) the followng constrants should be observed: φ n = R =1 + mn max These constrants ensure that the total generatng power equals the sum of power demands and transmsson losses. Besdes, each unt should operate wthn ts own lmts: φ : Constrant Functon R : Total consumed load loss : Total system losses mn max loss = 0 : Mnmum generatng power of the th unt : Maxmum generatng power of the th unt (2) 4 Soluton by Lagrange Method The cost-mnmzaton Lagrange functon selected n ths artcle s defned as follows: L = F T + λφ (3) In other words, the Lagrange functon s defned by cost functon F plus the constrant functon φ multpled by a penalty coeffcent λ. Then to mnmze L, ts dervatve needs to be set to zero. Thereby, a system of smultaneous equatons wll be obtaned that we may call "Coordnaton Equatons", and ther soluton mnmzes the costs. roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

4 L df L = λ 1 = 0 (4) d The nequalty condtons specfed n (2) expand to the followng set of equatons: df d = λ df λ d df λ d for for for mn max = max = mn These nequaltes sgnfy the fact that any unt wth ncremental cost hgher than λ s "expensve" and should be set to operate at lowest level of producton. In ths way all equatons are solved untl all condtons are satsfed. The man pont of consderaton s analysng and lmtng the level of producton for each unt. 5 Modellng of Transmsson Losses The relaton for the losses s based on the matrx B defned as follows: T T = [B]+ B 0 B 00 (5) L + Where : A vector showng the net MW of all generatng unts [B] : A square matrx wth dmesons equal to that of the vector B0 : A vector wth length equal to that of B00 : A constant value The equaton (5) can be rewrtten as follows: L = n n n B jj + = 1 j= 1 = 1 B 0 + B 00 (6) Varous methods are proposed for solvng the matrx of losses, but they are cumbersome and presume soluton condtons that never realze n a actual network. Therefore, the matrx of losses offers an approxmate answer. Here, the losses are assumed to be located at the man dagonal cells of the matrx [B], as shownn the followng formula: L = a1 1 + a an n (7) Ths relaton gves an acceptably good result that s close to real stuaton. [6] roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

5 6 Modellng of Spnnng Reserve ower The mplemented algorthm of the software ncludes "spnnng reserve power",.e., generatng capacty avalable from unts that s not beng used but s connected and sychronzed wth the grd to serve addtonal demand. The spnnng reserve must be under automatc governor control to nstantly respond to system requrements. The spnnng power reserve s necessary for controllng the frequency wthn set lmts n case one or more unts get out of servce. The spnnng power reserve does not add to the total demand for power. [2] Modellng of the spnnng power reserve should cover two cases: Case 1: Reserve ower s less than the unused capacty of the actve unts, n whch case the total cost remans unchanged. n = 1 ( Cost ) = Cost + Cost Load Re serve (8) Cost Re serve = 0 Case 2: Reserve ower exceeds the unused capacty of the actve unts. Ths necesstates an optmal actvaton of one or more nactve unts. Ths adds to the runnng costs of the network. n = 1 ( Cost ) = Cost + Cost Load Re serve In both cases, the sum of generatng power of thermal unts s the same but n Case 1, fewer unts wth hgher generatng power energze the network, whle n Case 2, more unts at operate at a lower generatng power. Consequently, the total unused capacty s ncreased. (9) 7 The Software rogram The program accepts all nput data va nteractve wndows for user nterface. For clarty and ease of use, the vsual envroment of the famlar GUI of the MATLAB s utlzed. The program conssts of three man wndows for nputtng the varous categotes of related data, as shown n Fg.1, Fg.2, and Fg3 and descrbed n the followng: Fg. 1 Economc Load Dspatch roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

6 Economc Load Dspatch Wndow: As can be seen n Fg.1, ths wndow has fve parts: 1- Number of Unts: Up to 40 unts can be ntroduced. 2- rce of Fuels: Allows nputtng the cost of fuel for Gas, Gasol, and Mazotte n terms of Rals per MBTU. 3- Loss Factor: For nputtng the loss factor as a percentage of the load at that tme. Inputtng 0 prevents consderaton of losses. If left blank, the losses are taken nto account on the bass of afore-mentoned formul. 4- Type of rocess: Allows processng for 24 hours or less. 5- Type of lot: Allows selecton of daly load and cost curves. Unt Structure Wndow: s shown n Fg. 2 below and s used to specfy the structure of nput data for unts. Each part has the ON / OFF optons to sgnfy the status of the varables of the generatng unts. Also, space s provded for specfyng the maxmun/mnmum levels of each varable. The "A", "B", and "C" coeffcents of each unt correspond to the formulas for the objectve functon and the constrants. The coeffcent "a" of each unt that refer to the formula (7) are also enetered here. Snce many unts use varous knds of fuels, the type of fuel can be enered n ths wndow. Fg 2. Unt's Structure Wndow (for upto 40 unts) The thrd wndow, namely, Daly Load and Reserve Load accepts the daly load and power reserve load. The reserve load can be specfed as percentage of the hourly load or MW. Besdes, a constant hourly reserve can also be specfed. roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

7 Fg. 3 Daly Load and Spnnng Reserve ower Fg. 4 shows the "Fle" and "Wndow" menus. Fg. 4 Fle and Wndow menus The "Fle" menu allows savng of the data and calculatons, for subsequent comparson wth further calculatons. The comparson of results from successve calculatons s useful for studyng the role and effect of each parameter on fnal results, thereby ncreasng the knowledge and nsght of the operators of the unts and the network. The "Wndow" menu s desgned to open, access and close varous wndows for nputtng and edtng data. When an ncorrect or ncomplete data s entered, an approprate message wll be dsplayed. In each wndow, the "OK" and "Cancel" buttons are used savng or dscardng the nput data. When all data s nput, pressng the "Done" button starts the calculatons and the followng results wll be shown n the "Command" wndow. roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

8 Date and Tme of calculatons Computed power produced neach unt The total fgures for unts' hourly producton, load, and the costs. Fg. 5 shows a sample of output. 8 - Solvng a Typcal Example and Comparson of Results To study and test the program, the followng problem s solved: For purposes of ths research, the daly operaton of a power staton wth 40 unts s consdered. The nomnal nstalled power s 1270 MW, usng the natural gas and gasol fuels. Snce ths problems lmted to a sngle power staton, no transmsson losses are entered. The daly load s obtaned from one day's operaton of thspower staton. After nputtng the data and calculatons, the output results ndcate that the economcal dspatch calculatons of ths program reduce the cost of fuel consumpton by 970,219 Rals per day or 400,000,000 Rals per year. 9- Concluson Ths artcle studed the subject of economc load dspatch for power statons and thermal unts of a network, wth the objectve of mnmzng the fuel costs. The fast, relable method of Lagrange method was used that converges to a conculsve result. roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

9 The software program under consderaton can be effectvely used for educatonal purpses and operator tranng. Ths s done along wth the varous methods and algorthms of Economc Load Dspatch, and optonal ncluson of the transmsson losses and spnnng reserve power that mpose modfcatons on calculaton formulas. A comprehensve and complete programme for operator tranng empowers them to: objectvely and precsely calculate the problem of Economc Load Dspatch, mnmze fuel costs, mnmze transmsson losses consder spnnng reserve power obtan a clear vson and nsght of the problem and s a step toward mprovement and optmzaton of the power system montorng and management. Some factors complcate the problem ncludng coordnaton of varous generatng unts and power statons, envronmental ssues, upkeeng the system relablty. However, a proper operator tranng and educatonal programme wth scentfc and theoretcal substantaton can greatly help the management of operatons and dramatcally reduce the non-recoverable costs References 1. Javd, M.H.; Rastegar, H.; Shamloo, S.; A New Approach to Optmal Load Dspatch n Thermal Unts va the Gradent and λ- Iteraton Methods. 15 th Intl. Conf. of Elect. ower 2. Makhdoom, M. "Economcal Sequencng of Unts' Entry and Ext for Network". An M.Sc. Thess, Unv. of Tehran, Nosrat Frooz Salar, A. "Economc Load Dspatch n Rey ower Staton", A B.Sc. Thess, Unv. of Water and ower, Tehran, Mehrab Aghdam, M. "Computer Asssted Load Dstrbuton", A B.Sc. Thess, Unv. of Water and ower, Tehran, Vol 29, "System Operaton, Experence of Advanced ower Statons" Elm-o-Sanat Unv. Tehran, Wolenberg, V., "roducton, Operaton and Control n ower Systems" roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton

10 Translated by Dr. Sef 7. Lttlefeld B. and Hanselmann, D. "Complete Reference of MATLAB" ublcatons of Jhad-Daneshgah, Mashhad, 1380 roceedngs of the 2011 ASEE Northeast Secton Annual Conference Unversty of Hartford Copyrght 2011, Amercan Socety for Engneerng Educaton