Quantitative Evaluation Method of Each Generation Margin for Power System Planning

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1 1 Quanttatve Evauaton Method of Each Generaton Margn for Poer System Pannng SU Su Department of Eectrca Engneerng, Tohoku Unversty, Japan Abstract Increasng effcency of poer pants and dstrbuton systems; and demand for dstrbuted poer generaton, especay the demand for guaranteed poer suppes, aso has changed the system Wth the advancng Poer System Dereguaton, the eectrcty s prce s gettng decreeng, by another hand, the pannng method and votage stabty ere requested by resume There s an dea that transmsson ne hch aready exsts shoud be used effcency But t causes heavy fo transmsson ne to be gettng orse and eads stabty of votage as e as synchronous stabty to be more severe Ths s the method that makes cacuaton of the agorthm for generaton renforcement for system pannng n use of DC method more qucky Wth ths method, under the restrcted condton as (n-1) rue, ths paper estmates the margn of each poer rapdy, deveoped the screenng method of votage stabty and anayed the resuts that ere smuated th the IEEE30 mode system Keyords Poer system pannng, generaton margn, (n-1) restrcton 1 Introducton Most of system pannng methods hch has aready suggested are based on the approach that ork for mnmng cost under the restrcton condton on transmsson capacty th some ne proposed transmsson route, transmsson capacty and the constructon fee as a restrcton condton on overoad fo Hoever, the poer transmsson route that can be actuay ney estabshed s often mted Therefore, the necessty that the procedure for optmng target contans the route pannng tsef s not arge What s more mportant probem n a method hch has aready proposed s that ndspensabe to ponts as foos for pannng system are not consdered (1) Restrcton condton on a assumpton accdent of a transmsson ne (2) The votage stabty or the synchronaton stabty The (1) as mentoned-above s the bass of the system stabty hch s unversay and t s commony caed as (n-1) restrcton n short KAZUYUKI Tanaka Tohoku Unversty, CRIEPI, Japan denchu@ecetohokuacjp In case of ths restrcton, estmaton of a of the transmsson nes and transformers s needed and there s a probem that nvoves computatona abors In Addton, under the (n-1) restrcton condton, e shoud consder about hat knds of phenomenon probems shoud do the cacuaton As mentoned top of ths secton, the phenomenon of overoad s one of the probems, hch can be anayed reatvey smpy Hoever, to evauate poer votage stabty and the synchronaton stabty of a system n the second tem, (2), e need numerous cacuatons even snge sequence cacuaton So, ths paper s purpose s contrbuted to satsfy the ncrease of poer demandng n poer system pannng We descrbe a cacuaton method of generaton margn for overoad and votage stabty under the (n-1) restrcton Generator margn mentoned ths paper ndcates the ho much poer ncrease s possbe hen the assumed demand rse th one generator Through cacuatng generaton margn of a generators and comparng th these, e can make quanttatve evauaton n the eak area, huge margn area and so on n the poer system So far, a ot of proposas have been done for overoad evauaton or votage stabty evauaton under the (n-1) restrcton Most of proposas use the fo senstve for overoad cacuaton, and appy votage ndex for votage stabty evauaton Hoever, there s havng not suggested such proposa, () () Fg1 IEEE 30 nodes standard system mode

2 2 hch reatng to cacuaton of the generaton margn under the demand rse stuaton The keynote descrbed n ths paper as foong 1) Proposa of the effcenty processng under (n-1) restrcton cacuaton that need (requred) cacuaton abor 2) Proposa of effcent cacuaton method of poer generaton margn from specfc poer suppy 2 The (n-1) evauaton method of generaton margn consdered from overoad current Ths study uses the fo cacuaton of DC method, hch s e knon as the cacuaton method ony th effectve poer fo P = Y θ (1) Where P,θ and Y are the vector of effectve poer n dmenson of nodes, the vector of node face ange and the node admttance matrx, respectvey () The cacuaton method of generaton margn from specfc poer suppy, g For nstance, margn from poer suppy, g, on stabty system s easy avaabe n use of the sequence as foos No, the fo margn from sent sde and receved sde are MgnS and MgnR MgnS = CAP FB (2) MgnR = CAP + FB Where F B and C ap are fo of branch,, and transmsson capacty on stabty system, respectvey Whereas, n equaton (1), PG mgn = Mn( MgnS / CP, MgnR / CP ) (3) () Effcent (n-1) fo cacuaton by fo compensaton The generaton margn from poer source g n case of one tme accdent on a transmsson ne s aso capabe of cacuatng n the same sequence as mentoned above n case of snge ne Y matrx Hoever, t needs to repeat on a transmsson nes Therefore, e suggest effcent method hch s ndependent of Y matrx re-trange resouton The frst one s the dstncton hether the reevant transmsson ne s oop-formed or rada In case of rada, the fo change th an accdent s ony reevant branch and (n-1) cacuaton s needess Therefore, hen the snge branch accdents n the system of Fgure 1 are occurred at pont () and pont (), e have to cacuate ony the pont (), hch s member of oop, agan To confrm hether the ne s oop-formed or rada by Equaton (4) makes the cacuaton ghty [ y ( Z + Z 2Z ) 1] = y ss rr sr Lop (4) Where, Z j s the factor of Z-matrx n stabty system, Lop s the current hch fos n the tme hen poer source, E, s nserted to the reevant route When Lop s 0, the transmsson ne,, beongs to rada and the cacuaton durng accdent s not needed The second one s the cacuaton method of compensaton method for oop-formed branch accdent Fgure 2(a) shos a doube branch ne When the fo n stabty system s represented as F ke Fgure 2(b), fo F, fo of snge ne, s compensated by E, poer source, for the Y-matrx n stabty system E n = nf / y [ y ( Z + Z 2Z ) n] K ss = nf / (5) E = F / K (6) Where, E = En And, K of a branches are capabe of fndng n advance From these equatons, e can obtan the equaton as foos Lop = ( Vs Vr En ) ( y ) (7) The equvaent crcut to the crcut hch ncude E n s that poer source hose both end have I = ( 1) E0 y s nstaed aong the fo drecton Vs = I Z ss Vr = I Z sr (8) Vs = I Z sr Vr = I Z rr (9) The fo vector F( n 1) can be cacuated n case of one tme ne accdent of oop branch n use of the equaton as foos F ( n 1) = FB + E CE (10) Where, F B s fo vector on stabty system and CE s fo dstrbuton n case of 1V poer source Cacuaton hch s needed for obtanng accdent fo of branch s ony to consder toce At ast, n the cacuaton method of Z-matrx factor, Z- matrx factor hch s used at Lop and K s specfc factor mted n any cases These are cacuabe by ess abor Vs F F E n y V r (a) Fo compensaton (b) Equvaent crcut Fg2 Concepton of fo compensaton by poer source rr S sr E F R

3 3 3 Effcent cacuaton method of (n-1) generaton margn based on the votage stabty Restrcton factor of the stabe poer transmsson ncudes the mantenance thn proper votage eve and synchroned stabty n addton to overoad of the effectve poer as mentoned above In the poer system n rea, hat the atter many becomes the restrcton factor s commony Therefore, n ths secton, e descrbe the method hch cacuates the generaton margn consgnment mtaton poer PG max from specfc generaton effcenty Where, the condton as foos s precondton for the cacuaton A) Votage and reactve poer s not consdered B) Reactve poer output restrcton of generaton s not consdered; generaton node s st votage assgned (1) Fundamenta cacuaton sequence The genera cacuaton method of votage stabty s as foos and settng the generaton g e ant to evauate to the standard node makes the cacuaton effcent Step 1: We do cacuate Amount of poer generaton of the generaton g Step 2: Fo cacuaton n case of openng one ne for a branches Step 3: Back to Step1 f e can obtan the fo souton of a cases, because t means (n-1) votage stabty Fnsh cacuatng f there are any cases that the dversty occurs n ths cacuaton, because s means (n-1) votage nstabty Tabe1 shos the conceptua dagram of the procedure as mentoned above and s an exampe of (n-1) fo cacuaton for seven branches, L1 to L7 The sgn ndcates the votage stabty, hch means that e obtan the souton, and the sgn ndcates the votage nstabty In ths exampe, the souton s obtaned for four tmes P g ncrease, 11 cases of cacuaton s needed Tabe1 votage stabty cacuaton Conventona methodp3s the resouton Proposa method P s the resouton (n-1) banch Smagenerator g s poer generated output (arge) P1 P2 P3 P4 P Px Py P L1 L2 L3 L4 L5 L6 L7 Necessary cacuaton= 28 Necessary cacuaton= 11 Yet, t s dffcut to set the P, the dth of ncrement, reasonaby (2) Deveopment of effcent evauaton method In ths secton, e suggest a cacuaton method to reduce the cacuaton abor to around one-ten The concept of ths method s shon at rght sde of the Tabe1 In ths method, e estmate the output P of generator g hch s the votage stabty mtaton n standard fo secton and cacuate (n-1) fo n ths fo condton As a consequence, f the case s occurred at more than one tme, the votage mtaton s ess than P Therefore, th ths P decreasng, e do (n-1) fo cacuaton repeatedy At ths tme, the P here a of (n-1) cacuatons becomes stabty s the generaton margn e ant Ths method can make the hoe fo cacuaton tme feer compared th genera method In Tabe1, hen the generaton output s P, fve branches are evauated as stabty Then accdent cacuaton from there on s not needed because votage stabty s the suppy and demand condton that s reaxed, so the reevant branch can be gnored Incdentay, n ths case, the souton P s obtaned by cacuatng fo at 11 cases The dffcut pont for ths method s to assume output P of generator g ratonay In ths paper, e suggest the equaton as foos n use of the stabty ndex, Index ( = 1,2, LL, ofoad) P = oad { PL [( / Index ) 1] d} = 1 Votage of oad Present Vaue of oad B Index =B/A Fg3 1 (10) P : The votage stabty mtaton margn assumpton vaue of the generator e pay attenton to PL : Base oad vaue of Index : Votage stabty ndex of d : Inversed of the ncrement rate of, ( d = 1) k B Votage stabty m taton assum pton vaue A A Poer of Concepton of Index

4 4 Besdes, there are any possbtes that a cases are stabty n cacuatng (n-1) fo n use of assumpton P In case of ths, e have to cacuate equaton (4) by P fo secton and evauate P nearer to the stabty mtaton 4 Case: IEEE30 system and consderaton Fgure 1 shos the case for IEEE30 mode system In ths case, e assumed the demand ncreasng rate on eght ponts as shon at Tabe 2 and estmated the maxmum generaton margn under the (n-1) restrcton n these rates Aso, n ths paper, the transmsson capacty of each ne s set to around four fos as heaver than one of stabty system (I) Resut of (n-1) generaton margn based on the overoad (1) Judgment of the oop-shaped branch Before (n-1) evauaton, e can recogne that the branch conssts of the three oops,, and shon as the arro n Fgure 1 Hence, t s suffcent ony to evauate the thrteen branches that conssts of these oop and s 40% of the tota n case of (n-1) DC cacuaton (2) Generaton margn from each poer suppy Fgure 4 shos the cacuaton resut of the maxmum poer of the generaton from each generaton n snge ne accdent of the oop ne Snge tme of the DC fo dstrbuton cacuaton n Fgure 1 on stabty system s enough for the generaton margn of each branch n case of (n-1) The generaton hch has the argest generaton margn n the generaton hch has the smaest generaton capacty s G6 and the opposte generaton s G1 Therefore, f the demand s assumed to ncrease at the rate as Tabe 2, veed n the generaton margn, e can kno that the best renforced pont s G6 (3) Consderaton Tabe 3 s a st of the resut of Fgure 4 When G1 and G6 are compared th each other, G6 can become approxmate 34 tmes stronger than G1 Tabe2 Generator Pattern of the rate of ncrease on demand ncre ment rato Faut route botteneck route ncrement rato Tabe3 Condtons of each generator durng ne faut tme generaton ma rgn (MW ) G G G G G On the other hand, n ve of Baancng of System Margn, hch s the concept that the each facty are operated for makng these endurance equay n the hoe system, consdered to be kept the hoe system ebaance even f addtona facty are bud from optona generaton, the pannng on mprovng mnmay s aso thnkabe In Fgure 3, e can recogne that the east generaton s G1 When the G1 s consdered to be sent sde, the transmsson ne hch becomes the botteneck of the transmsson margn s 26 Whereas, the transmsson ne hch s the botteneck of transmsson margn of generaton, G6, hch s the best addtona pont, s aso 26 Hence, e can see that ne renforcement for ne 26 s advsabe because e can operate the hoe system staby n case of ncreasng the demand accdentay under the (n-1) restrcton (II) Resut of (n-1) generaton margn based on the votage stabty We descrbe the checkng resut of (n-1) votage stabty margn for IEEE30 mode system shon at Fgure1 Here, t s requred that the system at 69(pu) for tota demand s (n-1) votage stabty Tota demand as assumed to be ncreased n proporton to the oad of each oad Moreover, the thng hch a generator correspondence to demand ncrement s set to the generator of Node10 ocated at the rght end of the system Tabe4 hch s an exampe that (n-1) votage stabty th demand ncrement of 10 nterva s evauated shos the resut hch s conducted by genera method In a genera method, the tota demand hch s soved at the one prevous cacuaton s the souton hen the dvergence s occurred durng 32 tmes cacuaton th the tota demand ncreased 10(pu) a cacuaton ke 69+10=79 We got the souton of ths exampe as 1618(pu), the generaton margn from generator10 for the demand ncrement s evauated as 928(pu), The of cases of fo cacuaton requred by gettng ths souton s 297 steps, 339 No, e sha descrbe the resut of the method e suggest Maxmum generaton capacty (MW) Fauted transmsson ne Fg 3 Poer generaton s possbe capacty on each generator

5 5 Tabe4 Resut of (n-1) generaton margn based on the votage stabty 183 tmes of 69 pu 135 tmes of 1267 pu In the present condton of tota demand, a stabty margn assumpton vaue as 1263(pu), hch s shon at Tabe Then, as a resut of the (n-1) votage cacuaton th ths demand condton, a transmsson nes are stabe4 So, e cacuated Equaton agan th 1263(pu) and the resut s 1718(pu), hch means the to branches are votage nstabe From ths resut, e understand that ths souton s ess than 1668(pu) So, e set the nterva of a decrease n demand to 05(pu) and contnue to cacuate n ony to branches As a resut, a s stabty at 1618(pu) on the eghth fo cacuaton Amount of case of fo cacuaton that s requred for sovng s 71 tmes To sum up, the mprovement for sovng th the method e proposed s 024, 71/297, hch s four tmes effcent than genera method 4 Future Work In ths paper, e suggested the effectve method of generaton renforced cacuaton method for pannng system n use of DC method Practca (n-1) restrcton ncudes the votage restrcton and the stabty restrcton n addton to the effectve poer one, hch s mentoned n ths paper Therefore, e consder the (n-1) effectve cacuaton method based on the energy functon method and the votage stabty ndex Hoever, by cacuatng generaton of a generators and comparng th these, e can make quanttatve evauaton n the eak area, huge margn area and so on n the poer system References 1)RRomero and AMontce, A herarchca decomposton approach for transmsson netork expanson pannng,ieee Trans Poer Syst,Vo9,No1,pp ,Feb1994 (2)YYorno, Trend n Votage Stabty Probem and ts Anayss Methods n Poer Systems,IEEJ Trans PE,Vo123,No7,pp ,(2003-7) (n Japanese) (3)SKtagaa et a A Fast Contngency Anayss by Dstrbuted Parae Processng,The Paper of Jont Technca Meetng on Poer Engneerng and Poer Systems Engneerng,IEEJ,PE ,PSE (1999)(n Japanese) (4)GHamoud, Assessment of Avaabe Tranfer Capabty of Transmsson Systems, IEEE Trans Poer Syst,Vo15,No1,pp27-32,Feb2000 (5)NERC, Avaabe Transfer Capabty Defntons and Determnaton June,1996 (6)KTakahash et a Formaton of Sparse Bus Impedance Matrx and Its Appcaton to Short Crcut Study, Proc PICA Conference, June (1973) (7)MNagata et a Deveopment of ATC Assessment Method,Technca Report,CRIEPI,T01020(2002-4)(n Japanese)

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