Automatic Load Shedding calculated with Genetic Algorithms DAC-CMAG

Transcription

1 Automatc Load Sheddng calculated wth Genetc Algorthms DAC-CMAG Mchelle Guchon, Magdalena Melo, Ana Carolna Neto, Maro Vgnolo, Ncolás Yedrzejewsk Abstract-- Ths paper presents an optmzaton tool based on Genetc Algorthms, DAC-CMAG (Automatc Load Sheddng Calculated Through Genetc Algorthms), developed n Matlab and appled to the calculaton of load sheddng n Electrc Power Systems. Ths applcaton calculates the optmal load shed necessary to elmnate overloadng of any seres element of an electrcal network. It ncludes a module that runs DC load flow to calculate the power flow for each branch or transformer and verfes there are no current volatons n any equpment. The results are analyzed usng ths tool appled to the calculaton of optmum load shed requred for the worst contngences n the 500kV power system of Uruguay. - dfferences between bus angles suffcently small: cos( δ δ ) = 1 j sn( δ δ j ) = ( δ δ j ) - shunt susceptance and seres resstance not consdered - every bus n the system wth constant 1pu voltage The fnal equaton of power flow for any seres element s: N P = B n n= 1 ( δ δ ) n Index Terms DC load flow, load sheddng, Genetc Algorthm I. INTRODUCTION N electrc power systems, electrc energy demand s n Igeneral concentrated n ctes and towns. On the other hand, generaton may be far from any cty, often respondng to the type of prmary energy source used by generatng plants. The clearest example s made up of hydroelectrc power plants that use the reservor created by a rver dam, transformng the gravtatonal potental energy of water to drve a turbne and generate electrcty. Ths resource To transport energy from ponts of generaton to demand, hgh and extra hgh voltage transmsson networks are used. In Uruguay, hgh and extra hgh voltage comprses voltages up to 150 kv and 500kV respectvely. Because of the mportance of the transmsson network, the power system s n general desgned and bult to be relable and allow system operaton even n the absence of one or more consttuent elements, namely: lnes, underground cables, transformers, etc. However, there are many contngences for whch t s necessary to dsconnect part of the load to ensure the stablty of the entre system and the ntegrty of the equpment. In most cases, dsconnecton should be performed so rapdly that t s possble only automatcally, havng chosen the statons and convenently dsconnectons n advance. The project ncludes the study of the behavor of genetc algorthms (GA) to optmally calculate the least amount of load that s necessary to dsconnect from the electrcal power system after a contngency has occurred, to ensure that any equpment be loaded beyond ts load lmt n an emergency. II. DC LOAD FLOW DC load flow s mplemented consderng the common smplfcatons to load flow, namely: /12/$ IEEE Where B n s the nverse of the seres reactance of the branch between bus and bus n. III. MODELING OF THE ELECTRICAL NETWORK The electrcal system s modeled n a smplfed manner, usng only the parameters necessary for the mplementaton of DC flows. The electrcal system components ncluded are: generators, lnes and / or cables, transformers. - The generators are modeled as a typcal PV bus n any load flow, wth the actve power and voltage defned as known data. In ths case the voltage, as n the rest of buses n DC load flows s 1 pu. - In transformers, seres resstance and the magnetzng branch are neglected leavng only the seres reactance - The load buses are modeled as constant actve power regardless of the reactve power - In the lne model, seres resstance, shunt conductance and shunt susceptance are neglected leavng only the seres reactance. IV. GENETIC ALGORITHMS A. Introducton Genetc algorthms are adaptve methods generally used n search and optmzaton data problems, based on sexual reproducton and the prncple of survval of the fttest. B. Adjustment functon (ftness) The ftness n the nature of an organsm s defned as the probablty that the organsm survves to reproductve age and reproduces. The ftness functon can be thnk as a numercal measure of proft, utlty or goodness of a soluton that can be maxmze.

2 2 C. Operators The smplest form of genetc algorthms nvolves three types of operatons: - Selecton: select people n the populaton for reproducton. The selecton of an ndvdual s related to ts adjustment value. The bggest adjustment has an nhabtant the more lkely s to be chosen for reproducton. The easest to create s a roulette wheel where each ndvdual n the populaton s assgned a porton of the wheel, proportonal to ts ftness value. The better ftness has an nhabtant, the greater the porton of the wheel to be assgned, ergo, the more lkely s to be chosen n the draw. - Crossover: After beng selected, ndvduals are crossed to produce offsprng that are nserted nto the next generaton. Ths operator randomly chooses a crossover pont and exchanges the subsequence before and after the crossover pont between ndvdual parents to form chldren. - Mutaton: Ths operator randomly changes one bt of the nhabtant gven by the probablty of mutaton. V. FITNESS FUNCTION It must be defne a ftness functon that qualfes each nhabtant of the populaton. After that, the populaton can be sorted by rankng. The frst thng to take nto consderaton s the load connected to the network. It s a desre to have connected load as much as possble. Therefore, the functon must reward nhabtants wth more load connected. For ths, two varables are created to quantfy the load remans connected, the frst s the amount of load remans connected (Pconectada n the software), the second s the number of buses that remans on servce (cantbarras n the software). The ftness functon s mplemented to be an ncreasng functon n these varables: ftness Pconectada cantbarras Another varable to consder s the overloaded equpments. The man target s to elmnate every current volaton. Therefore, the functon ftness must assgn smaller ftness values for the most overloaded network. In ths case, two varables are defned to represent how overloaded s the network: sob, number of overloaded branches (or transformers) and Smax, s the rato between the lne load of the most heavly loaded lne and the thermal capacty of the lne. The followng equaton for the ftness functon s proposed. ftness = 9 Pconectada cantbarras ( Smax 100) ; sob = 0 1 Pconectada cantbarras ( ); sob 1 sob 2 2 Smax 10 e Where sob, s the number of overloaded branches n the system. Ths functon accomplshes all the requrements. For further detals n the development of the functon, see [1]. VI. MAIN PROGRAM Ths secton dscusses the mplementaton of major program that calculates the optmal load sheddng for the varous contngences that may occur n the network usng tools DC power flow and genetc algorthms. Input and data procesng The network data s read from an Excel spreadsheet as explaned below. In the frst page, called Barras, s the lst of statons wth ther respectve power loads and generaton, whch expressed n MW. In some cases, dependng on user requrements, there would be convenent to leave certan fxed statons. Ths opton s ncluded on the frst page where the user must put a 1 for allow the staton of nterest to partcpate n the load sheddng and a zero n those buses not allowed to partcpate. In the second and thrd sheet there are the lne and transformer data. They contan the mpedance of each lne, expressed n pu, and up to 2 maxmum current lmts (A and B), expressed n Amper. Also expresses the voltage base. The network data s read when the fle s opened through the graphcal user nterface of the program. The functon devuelvedatos.m s who s responsble for processng them for later use n the rest of the program. Then, functons DevuelveXY.m and armamatrza.m are executed. The frst, return arrays X and Y correspondng to the seres mpedance and admttance of lnes and transformers. The second returns a matrx whth a dmenson NxB for a network wth N lnes B buses. For lne, a j =1when j s the frst bus of the lne and a j =-1 for the second bus. Matrx A completely descrbes the topology of the network and s ndependent of the partcular values of lne parameters. Once the angles of the buses are calculated (vector Ang), the power flow throw the lne from bus to j s: P j = A Ang Y Man program Intally, the program creates a certan amount of ndvduals to form the ntal populaton. Each nhabtant represents a possble combnaton of substatons to dsconnect. Each ndvdual s represented by a vector, wth length equal to the number of substatons n the network. Each vector element s assocated wth a sngle substaton and can take only two possble values, 0 or 1. The value 1 ndcates that the substaton remans n servce and s not dsconnected n that combnaton. The value 0 ndcates that the substaton s part of the load sheddng for that combnaton. Ultmately, each nhabtant represents the state of all network statons n the post-contngency stuaton. An teraton start, where n each step the program creates a new generaton dong the followng:

3 1. The program checks for fxed statons. If so, an amendment s created n the populaton by settng the value 1n postons correspondng to statons that must reman connected n every nhabtant. 2. Next, t calculates the ftness of each nhabtant of the populaton. To do ths, functon flujodchabtante.m calculates a DC power flow to fnd the angle of every bus. In a common mplementaton of a DC power flow, a prevews balance between load and generaton s mandatory so there s no need of a slack bus lke n AC power flows. However, n ths case every nhabtant has dfferent load connected so a correcton n generaton must be done before runnng a DC power flow. For ths purpose, the frst bus entered n the lst of buses wll be consdered to state the balance.. Functon elem.m calculates the node admttance matrx, Ybus. flujodepotenca.m calculates the actve power en every seres element usng matrces A and Ybus explan above. 4. Sobrecarga.m calculates the overloaded lnes and transformes. 5. ftness.m calculates the ftness of every nhabtant and place n matrx habmax the one wth best ftness for every generaton. 6. To create the next generaton, nhabtants are drawn, by sorteo.m functon whch uses ruleta.m (ruleta.m functon s based on the selecton operator of genetc algorthms explaned above). 7. Functon cruzaymuta.m cross and mutate the nhabtants drawn, creatng a new populaton. Ths process s repeated untl the total number of generatons s reached. The nhabtant of best ftness of all generatons s taken as a partal soluton. For ths nhabtant, functon ProgramaPrncpalAjuste.m mplements a fnal adjustment to the partal soluton to ensure that the combnaton selected do not dsconnect excessve and unnecessary load. The settng procedure s descrbed below: The program goes through every bt of the nhabtant changng each zero by one and re-run the DC power flow. In each test, f the new nhabtant has no overloaded elements s stored n an array. The resultng matrx contans all the changes successful. The nhabtant of the matrx wth lower dsconnected load s chosen and the rest are dscarded. Wth ths new ndvdual, the process s repeated. When every addtonal change s unsuccessful, the adjustment s termnated. The adjusted nhabtant s consdered the best soluton found. Through the user nterface, the program shows the fnal combnaton of staton to be dsconnected, the actve power assocated and the most overloaded lne or transformer expected f the soluton suggested s mplemented. VII. APPLICATIONS IN THE TRANSMISSION NETWORK OF URUGUAY Ths chapter analyzes the behavor of the tool developed n ths project to calculate the necessary load sheddng for the most severe contngences n the 500kV system of Uruguay. The rate chosen s the thermal capacty the equpment supports for an hour and no more, whch s approprate n ths regme. It consders a peak demand for the summer and wnter, It works wth a mutaton probablty of 0.1%, 70% for crossover, populaton sze of 1000 nhabtants and ntally wth 100 generatons. Ths can vary accordng to the number of lnes that may be overloaded. PAL500-MVA500 and BRU500-MVB500 double contngency for summer peak The followng table shows the lnes that are overloaded and ACO150 MVB BAY150 PAL BAY150 TRI COL150 ROS COL150 JLA

4 4 CON150 COL DUR150 FLO EFI150 SVA FBE150 MER FLO150 PRO JLA150 LIB LIB150 EFI MER150 NPA NPA150 CON PAL150 TRI PAY150 YOU PRO150 MVA ROD150 ACO ROD150 MVB SAL150 PAY SGU150 SAL SJA150 FBE TER150 BAY TER150 DUR TRI150 ROD SGU500 SGU SJA500 SJA PAL500 PAL FLO150 PRO JLA150 LIB LIB150 EFI MER150 NPA NPA150 CON PAL150 TRI PAY150 YOU PRO150 MVA ROD150 ACO ROD150 MVB SAL150 PAY SGU150 SAL SJA150 FBE TER150 BAY TER150 DUR TRI150 ROD SGU500 SGU SJA500 SJA PAL500 PAL As can be seen, the most overloaded element, PAL150- TRI150, s a percentage of %. The followng shows that t took more than 50 generatons to reach convergence of the program calculates that 858 MW to be dsconnected by sheddng the followng (all at 150kV): COL150 MEL150 MVE2 MVJ150 NPA150 PIE150 FLO150 MVA150 MVF150 MVK150 PAL150 ROC150 MAL150 MVC150 MVH150 NOR150 PES150 SOL150 ACO150 MVB BAY150 PAL BAY150 TRI COL150 ROS COL150 JLA CON150 COL DUR150 FLO EFI150 SVA FBE150 MER PAL500-MVA500 y BRU500-MVB500 double contngency for wnter peak The followng table shows the lnes that are overloaded and ACO150 MVB BAY150 PAL BAY150 TRI COL150 ROS COL150 JLA

5 5 CON150 COL DUR150 FLO EFI150 SVA FBE150 MER FLO150 PRO JLA150 LIB LIB150 EFI MER150 NPA NPA150 CON PAL150 TRI PAY150 YOU PRO150 MVA ROD150 ACO ROD150 MVB SAL150 PAY SGU150 SAL SJA150 FBE SVA150 MVC TER150 BAY TER150 DUR TRI150 ROD YOU150 TER SGU500 SGU SJA500 SJA PAL500 PAL calculates that 1057 MW to be dsconnected by sheddng the followng (all at 150kV): EFI150 SVA FBE150 MER FLO150 PRO JLA150 LIB LIB150 EFI MER150 NPA NPA150 CON PAL150 TRI PAY150 YOU PRO150 MVA ROD150 ACO ROD150 MVB SAL150 PAY SGU150 SAL SJA150 FBE SVA150 MVC TER150 BAY TER150 DUR TRI150 ROD YOU150 TER SGU500 SGU SJA500 SJA PAL500 PAL As can be seen, the most overloaded element, PAL150- TRI150, s a percentage of 99,989%. The followng fgure shows that t took more than 70 generatons to reach convergence of the program. ACO150 MAL150 MVG150 PAN150 ROD150 COL150 MVC150 MVH150 PAZ150 ROS150 CON150 MVE2 MVR1 PIE150 SOL150 LIB150 MVF150 NOR150 RIV150 TRI150 TYT150 ACO150 MVB BAY150 PAL BAY150 TRI COL150 ROS COL150 JLA CON150 COL DUR150 FLO PAL500-MVA500 y MVB500-MVA500 double contngency for wnter peak

6 6 The followng table shows the lnes that are overloaded and MER150 NPA MVB150 MVL MVB150 MVA MVD150 MVE COL150 JLA MVB500 MVB calculates that 47 MW to be dsconnected by sheddng the followng (all at 150kV): COL150 MVG150 PES150 TRI150 MAL150 MVL150 ROC150 MVB150 MVR1 ROD150 MER150 NPA MVB150 MVL MVB150 MVA MVD150 MVE COL150 JLA MVB500 MVB As can be seen, the most overloaded element, MVB500- MVB150, s a percentage of 99,69%. The followng fgure shows that t took more than 120 generatons to reach convergence of the program. PAL500-MVA500 y MVB500-MVA500 double contngency for wnter peak The followng table shows the lnes that are overloaded and MER150 NPA MVB150 MVL MVB150 MVA MVD150 MVE MVI150 MVM MVM1 MVA PAL150 TRI SGU150 SAL SGU500 SGU MVB500 MVB calculates that 529 MW to be dsconnected by sheddng the followng (all at 150kV): ACO150 MVC150 PAN150 EFI150 MVE2 PIE150 MAL150 MVF150 STE150 MER150 NPA MVB150 MVL MVB150 MVA MVD150 MVE MVI150 MVM MVM1 MVA PAL150 TRI SGU150 SAL SGU500 SGU As can be seen, the most overloaded element, SGU500- SGU150, s a percentage of 99,981%. The followng fgure shows that t took more than 120 generatons to reach convergence of the program.

7 (Insttute of Electrcal and Electroncs Engneers) of Secton Uruguay, whch won the award for best chapter worldwde n Between 2001 and 2004 was Consultng Engneer to the Electrc Power Regulatory Unt (UREE) and the Regulatory Unt of Energy and Water Servces (URSEA) where he worked on regulatory ssues n the electrcty sector and gas. In 2006 he was Head of Energy Management Integrated Cellulose M 'Bopcuá, Uruguay ENCE Group. Ncolás Yedrzejewsk was born n Montevdeo, Uruguay, on December, He graduated n Electrcal Engneerng (2006) from Unversdad de la Repúblca, Uruguay. From 2004 to 2007 worked n CIME Ingenería related wth comprehensve protecton aganst atmospherc dscharges projects. He s wth the Insttuto de Ingenería Eléctrca snce 2006 and wth UTE snce 2007 at the Dynamcal Studes Department (Natonal Load Dspatch). 7 VIII. CONCLUSIONS In all cases the soluton leaves a network whch has no overloaded elements, and most loaded lnes are very close to 100% capacty. Whle these two features are not suffcent condtons to ensure that the soluton found corresponds to the optmal load sheddng, are strctly necessary for the soluton to be vald and were the premses of the project. The result s acheved n a relatvely short tme (dependng on the computer vares between 5 and 8 mnutes). An exhaustve search program tryng all possbltes would take months to run. Part of the program's success s attrbuted to the dedcaton to the mplementaton of the ftness functon n conjuncton wth the fnal adjustment to be made to the result found by genetc algorthms. IX. BIOGRAPHIES Mchelle Guchón was born n Montevdeo, Uruguay, on July She s a student of the last year of Electrc Power Systems at the Unversty UDELAR. She currently works n the Department of Techncal Studes Network Operatons Montevdeo n UTE. Magdalena Melo was born n Montevdeo, Uruguay, on May 1, 198. She s a student of the ffth year of the Power Electrc Systems Degree at the Unversdad de la Republca Orental del Uruguay. She currently works n the Techncal Dvson of Development, at the Natonal Admnstraton of Telecomuncatons, ANTEL Ana Carolna Neto was born n Montevdeo, Uruguay, on Aprl She s a student of 5th year of the carrer Electrc Power Systems at the Unversdad de la Repúblca Orental del Uruguay. She currently works n the Techncal Dvson of Development n the Admnstracón Naconal de Telecomuncacones, ANTEL. Maro Vgnolo s an Electrcal Engneer who graduated Facultad de Ingenería de la Unversdad de la Repúblca of Uruguay. He holds a Master of Scence n Electrcal Power Engneerng (2001), Unversty of Manchester (UMIST), UK and a Ph.D. n Electrcal Engneerng (2007) conducted n a jont venture between Unversdad de la Republca of Uruguay and the U.S. Unversty of Florda, EEUU. Addtonally, a postgraduate degree n Economc Regulaton of the Facultad de Cencas Socales de la Unversdad de la Repúblca of Uruguay. Snce 2000 he s Professor, Department of Power Engneerng School where teachng and research, havng publshed over 25 papers n conferences and journals. Between 2004 and 2006 was Charman of the IEEE Power Chapter