New Optimization Technique For Nodal Price And Reliability Calculation

Transcription

1 Internatonal Journal of Engneerng and Tehnal Researh (IJETR) ISS: , Volume-2, Issue-5, May 2014 ew Optmzaton Tehnque For odal Pre And Relablty Calulaton Pushpendra Kumar Sharma, Abhshe Sangh, Devendra Mttal, Laxmhand Sharma Abstrat Power system restruturng and deregulaton has hanged the way n whh system relablty management and eletrty prng done over the deades. The man purpose of restruturng s to offer ustomers wth a hoe of supplers based on relablty and pre requrement. Load sheddng and generaton redspath mehansm used n the exstng relablty evaluaton tehnque have to be mproved to nlude these hanges. In ths paper a planned tehnque provdes an mplement to ompute the nodal relablty and nodal pres for maret partpants. The maret partpants are able to mae use of ths nformaton to mae most favorable tradng desons n maret tradng and operaton. Contngeny analyss has been done to determne the seleted ontngeny system states. An optmzaton tehnque s proposed to determne the nodal pres for eah ontngeny state obtaned from ontngeny analyss for restrutured power system wth blateral model. The obetve of the problem s to mnmze the generaton ost subeted to maret and networ onstrants. The mpat of unavalablty of generaton and transmsson system on load pont relablty and nodal pres has been shown. Instead of usng nodal pre for the normal operaton state, the expeted nodal pre and the assoated standard devaton are used to represent the volatlty of nodal pre due to random falures. The 6 bus relablty test system (RBTS) has been analyzed to llustrate the tehnque. Manusrpt reeved May 20, Pushpendra umar sharma, M.Teh. II Year (Power Systems) Student JIT Unversty Japur, Raasthan, Inda Abhshe sangh, Asst. Professor, Department of Eletral Engneerng JIT Unversty Japur, Raasthan, Inda Devendra mttal, Asst. Professor, Department of Eletral Engneerng JIT Unversty Japur, Raasthan, Inda Laxmhand sharma, M.Teh. II Year (Power Systems) Student JIT Unversty Japur, Raasthan, Inda I. ITRODUCTIO Eletr power systems are among the most omplex and large systems that exst n the world. Broadly speang, a power system s omposed of the three funtonal zones of generaton, transmsson, and dstrbuton. Over the years, eletr power ndustry s owned by large utltes whh have all the ontrol over all the funtons of eletr power system. These utltes are referred as vertally ntegrated utltes. Eah utlty has one or more ontrol enters that mantan seurty and relablty of a spef regon. The bas funton of a power system s to provde eletr power to ts ustomers as eonomally as possble and wth an aeptable degree of ontnuty and qualty [6]. Relablty s one of the most mportant fators onsdered n power system plannng and operaton n both vertally ntegrated and deregulated utlty envronments. Relablty s an nbult haraterst and a spef measure of any omponent, deve or system, whh desrbes ts ablty to perform ts ntended funton. In terms of a power system, the measures of relablty ndate how 338

2 ew Optmzaton Tehnque For odal Pre And Relablty Calulaton well the system performs ts bas funton of supplyng eletral energy to ts ustomers [9]. The lelhood of ustomers beng dsonneted for any reason an be redued by nreased nvestment durng the plannng phase and/or the operatng phase. Over nvestment an lead to exessve operatng osts. On the other hand, under nvestment an lead to lower relablty. ow to trade off these two aspets s a maor hallenge to power system managers, planners, desgners, and operators. In order to resolve the problem between the eonom and relablty onstrants, desgn, plannng, and operatng rtera and tehnques have been developed and appled over many deades. These three funtonal zones an be organzed nto the three herarhal levels (L) shown n Fgure 3. Fg.1 Power System Struture under Vertally Integrated Utltes Fgure 1 shows power system struture under vertally ntegrated utltes [7]. Ths paper presents a omprehensve tehnque to determne both nodal pres and nodal relabltes of deregulated power systems. The haratersts of ustomer demand response to nodal pre are nvestgated. II. POWER SYSTEM RELIABILITY EVALUATIO Power system relablty an be dvded nto the two aspets of adequay and seurty as shown n Fgure 2. Adequay relates to the exstene of suffent faltes wthn the system to satsfy the ustomer requrements. It s assoated wth stat ondtons and long-term analyss. Seurty relates to the ablty of the system to respond to dsturbanes. It s assoated wth dynam ondtons and short-term analyss. An overall power system an be dvded nto the three bas funtonal zones of generaton, transmsson, and dstrbuton. Fg.3 Power System herarhal levels Relablty assessment at herarhal level I (LI) s normally termed as generatng apaty adequay evaluaton and s onerned wth only the generaton faltes. In an LI study, the total system generaton nludng nteronneted assstane s examned to determne ts adequay to meet the total system load demand. The transmsson networ and the dstrbuton faltes are not part of the analyss at ths level. Relablty assessment at herarhal level II (LII) nvolves the analyss of the ombned generaton and transmsson system n regard to ts ablty to serve the system load. The relablty of supply at the ndvdual load ponts n a omposte system s a funton of the apates and avalabltes of the ndvdual generaton, transmsson faltes, and the system topology. Relablty assessment at herarhal level III (LIII) nludes all of the three funtonal zones and s not easly onduted n a pratal system due to the omputatonal omplexty and the sale of the assessment. Ths thess s entered on adequay assessment at LII. Varous tehnques have been developed and appled over many deades for relablty evaluaton of power system. Most of these tehnques are determnst n nature and some of them stll used today. Determnst rtera were developed n order to aount for randomly ourrng falures. Ther essental weaness s that they do not and annot aount for the probablst or stohast nature of system behavor, of ustomer demands, or of omponent falures. Fg.2 Subdvson of System Relablty III. CALCULATIO OF ODAL RELIABILITY AD PRICES General The funton of a power system s to produe eletral energy at the generatng soures and then move ths energy to the maor load ponts. The purpose of system relablty evaluaton s to estmate the ablty of the system to perform ths funton. Assessment of system relablty s very omplex sne t must onsder the ntegrated mpats of generaton and transmsson. LII studes nlude many aspets suh as load flow analyss, ontngeny analyss, 339

3 generaton reshedulng, transmsson overload allevaton, load urtalment et. In ths paper, ontngeny enumeraton and state seleton are used to determne ontngeny state. AC optmal power flow tehnque s used to determne the nodal pres. In the ase of generaton nadequay and networ ongeston, generatons are re-dspathed and loads are shed to remove networ volatons for a ontngeny state. Calulaton Consderng a power system wth ndependent omponents, the relablty parameters for ontngeny state wth exatly b faled omponents an be determned usng the followng equatons: p D b 1 b 1 U D * A (1) b1 (2) b1 d 1/ (3) The bas problem s to evaluate the nodal relablty and nodal pres for eah system state. The bas relablty tehnque s used to determne state probablty, departure rate and duraton. For a ontngeny state, the obetve of optmzaton s to mnmze the total system ost nludng generaton ost. For a ontngeny state, the nodal pres and the generaton re-dspath an be determned by solvng the followng optmzaton problem: 2 Mn f ( a *( P ) b * P ) g gg Subeted to followng onstrants: ) Load flow Equatons: At bus, Pg PL gg 1 V Qg QL gg 1 V g g * V * Y *os( ) ) Generatng unt lmts: P g, mn Pg Q P g, mn Qg g, Q ) Voltage lmts: V V V g g Internatonal Journal of Engneerng and Tehnal Researh (IJETR) ISS: , Volume-2, Issue-5, May 2014 g (4) (5) * V * Y *sn( ) g,,mn, v) Lne flow onstrants:, (7) (8) (9) (6) S S (10) Equatons (3) (10) are a non-lnear optmzaton problem wth a non-lnear obetve funton, non-lnear equalty and non-lnear equalty onstrants. Ths problem an be solved by usng varous ewton methods wth seond order onvergene propertes. ewton Raphson optmal power flow tehnque s used to solve the optmzaton problem. The Lagrangan funton L of the above problem for state s formed. The optmal generatng unt outputs an be obtaned usng ewton Raphson OPF tehnque. The nodal pres of atve power and reatve power at bus under the optmum soluton s obtaned as follows: L p (Rs/MW) (11) P L q (Rs/MVar) (12) Q The nodal relablty ndes for a ontngeny state are the nodal load urtalment and nodal energy not suppled. These ndes an be alulated usng the followng equatons: ES d * LC (MWh) (13) p R Optmal Power Flow The above desrbed mnmzaton optmzaton problem an be solved wth ewton Raphson method. The above onstraned mnmzaton problem an be transformed nto an unonstraned one by augmentng the load flow onstrants nto obetve funton [8]. The addtonal varable s nown as Lagrange multpler funton or nremental ost funton n power system optmzaton. The Lagrange funton for the above problem s gven as L( P, V, ) g G 1 f ( P ) g 1 [ P ( V, ) P p q G1 [ Q ( V, ) Q g P ] L g Q ] (14) In above Lagrange multpler funton, the ontrol varables are P,,, V. Any small varaton n ontrol g, p q varables about ther ntal values s obtaned by formng total dfferentals whh s gve below (n matrx form): Pg Pg Pg Pg p Pg Pg q Pg Pg p V q p Pg p pp p pq * p Pg p q V q Pg q qp q qq q J Pg J = J p (15) J V J q Or, []*[hange n ontrol varables] = [J] (16) Where [] s essan matrx, [J] s Jaoban matrx. Startng from ntal data of an nteronneted power system the optmal power flow soluton an be obtaned by solvng the equaton (16) for unnown ontrol varables. In ths method there no need for separate load flow study. Ths method s faster and gves aurate soluton. Calulaton Of odal Relablty And odal Pres In a deregulated power system, the expeted values, the standard devaton of nodal pres and nodal relabltes are mportant nformaton for the rs analyss of maret tradng, plannng and operaton. The expeted nodal pre s a L 340

4 ew Optmzaton Tehnque For odal Pre And Relablty Calulaton weghted average of the pres for dfferent states. Unle many other ommodtes, eletrty annot be stored n large amounts and needs a ontnuous balane between supply and demand. The pre for a ontngeny state mght be qute dfferent from the pre expeted. Inadequate generaton and ongeston n some ontngeny states result n extreme pre volatlty or pre spes. The random nature of falures results n great pre unertanty. As ustomers and produers fae volatle pres, ther reatons wll depend on ther atttude towards aeptng rs. A rs neutral partpant wll value a ertan beneft the same as an equal amount of expeted beneft that nvolves rs, whereas a rs adverse partpant, who faed wth two solutons wth the same expeted beneft (but dfferent rss), wll aept the one wth lower rs. Therefore hedgng ontrats have beome an mportant tool dealng wth pre rss. Customers who wsh to hedge aganst pre rs and mantan a ertan relablty level an sgn spef ontrats wth produers. The produers an also use ontrats to hedge aganst proft volatlty. These requre measurng the rs of beng exposed to hgh pres. Standard devaton of nodal pres an be used to evaluate the extent of pre flutuatng around ts expeted value. Consderng all possble system states, the expeted nodal pres and nodal relablty ndes an be determned usng the followng equatons. The expeted nodal pre of real power: S * (Rs/MW) (17) p p 1 The standard devaton of : p p Fg.5 6 Bus RBTS odal Pres and odal Relablty Random falures up to seond order are onsdered n the evaluaton. odal pres and odal relablty for are presented n terms of the frst order falure and seond order falure respetvely. odal pres for the frst order falure are gven n Table 1. The odal pres for the seond order lne falures are shown n Table 2. From the Table 1-2, t an be sad that as the dstane of the load from the generaton nreases, the pre nreases. It an be seen that the seond order lne outages produes larger pre flutuatons. The load at dfferent buses has to be shed to remove networ volatons. The odal Energy ot Suppled (ES) for seond order outages are gven n Table 3. The pre flutuatons at Bus 1 due to transmsson lne falure are small as ompared to other buses. Due to falure of Lne 5 and Lne 8, both load at Bus 5 and Bus 6 are solated. Table 1 odal pres for frst order outages S ( ) 2 * p (Rs/MW) (18) p 1 p The expeted nodal energy not suppled: EES S 1 p D * p * ES (MWh/Yr) (19) IV. TEST SYSTEM STUDY The Relablty Bus Test System has been analyzed to llustrate the tehnque. The 6-Bus RBTS [5] s shown n the Fgure 5.Fgure shows the sngle lne dagram of the system.the dstrbuton system s represented as equvalent bul load pont. The nodal relablty and nodal pres of real power and nodal pres for reatve power s alulated. The system onssts of 11 generators and 9 transmsson lnes. Table 2 odal Pres for seond order outages 341

5 Internatonal Journal of Engneerng and Tehnal Researh (IJETR) ISS: , Volume-2, Issue-5, May 2014 Table 3 ES for seond order outages Table 4 Relablty and pre ndes for eah bus of RBTS Fg. 7 odal Pres at Bus 2 Fg. 8 odal Pres at Bus 3 From fgure 6 t s lear that a nodal pres he s more our at bus 1 n ase of falure of lne 2 and lne 7 sne load at bus 4 wll be suppled wll have to be suppled by generators at bus as a result demand he our at bus 1 whh result n pre he. In fgure 7 as the ase happen at bus 1 same our at bus 2 n ase of falure of lne 1 or 6, demand rses whh result n nodal pre he at bus 2. Bus 3 are load buses so nodal pre depends on demand and transmsson losses, when transmsson losses are more pre s more, as an be onluded from the fgure 8. Fgure 9-11 shows the pre spes at Bus1 to Bus 6 n seond order outages (lne) respetvely. Fgure 6-8 shows the pre spes at Bus1 to Bus 6 n frst order outages (lne) respetvely Fg. 6 odal Pres at Bus 1 Fg. 9 odal Pres at Bus

6 ew Optmzaton Tehnque For odal Pre And Relablty Calulaton provded by the tehnque an be used by maret partpants to mae optmal desons n maret tradng and operaton. Fg. 10 odal Pres at Bus 5 Fg. 11 odal Pres at Bus 6 Fgure 9-11 shows that real and reatve nodal pres at many load buses are hgher than at generator buses and reatve nodal pres are smaller than real nodal pres at all the buses. These nodal pres an be used to alulate sgnfant wheelng harges of real and reatve power (margnal networ revenue) as dfferene of revenue reeved from real and reatve demand and expendture for real and reatve generaton. Reatve power nodal pre s affeted by the reatve power produton osts of generatons and the aptal nvestment ost of apators. Reatve power nodal pres an be related to the urgeny of the reatve power supply and an nentve an be gven to mprove load power fator and redue power demand. The proposed nodal transmsson prng model may forms a bass to alulate networ revenue for blateral and multlateral power transatons n deregulated power systems to wheel the power between the buses. REFERECES [1] M. Ghayen, R. Ghaz, Transmsson Cost Alloaton n Restrutured Power Systems Based on odal Prng Approah by Controllng the Margnal Pres, Iranan Journal of Eletral & Eletron Engneerng, vol.-6, no.-2, pp , June [2] Al Mansour, Al Aazam, Amn Omdan, Ehsan Mohamadan, Rahmat Aazam, Evaluaton of Power System Relablty Consderng Dret Load Control Effets, Internatonal Journal of Eletral and Computer Engneerng (IJECE) vol.-3, no.-2, pp ISS: , Aprl [3] P.Wang, Y.Dng and Y.Xao, Tehnque to evaluate nodal relablty ndes and nodal pres of restrutured power systems, IEE proeedngs Generaton, Transmsson and Dstrbuton, vol.-152, no.-3, pp , May [4] P.Wang, Y.Dng and L.Goel, Relablty assessment of restrutured power systems usng optmal load sheddng tehnque, IEE Generaton, Transmsson, Dstrbuton, vol. 3, no.-7, pp , Deember [5] R.Bllnton, S.Kumar,.Chowdhhury, K.Chu, K.Debnath, L.Goel, E.Khan, P.Kos, G. ourbahsh, J.J. Oteng Ade, A relablty test system for eduatonal purposes-bas data, IEEE Transaton on Power System, vol.-4, no.-3, pp , August [6] M. Shahdehpour and M. Alomoush, Restrutured Power System Operaton, Tradng and Volatlty, ew Yor: Marel Deer, [7] Lo Le La, Power System Struturng and Deregulaton: Tradng, Performane and Informaton Tehnology, ew Yor: Wley [8] A.Charabart and S.alder, Power System Analyss Operaton and Control, ew Delh: PI Learnng Prvate Ltd., [9] R..Allan and R.Bllnton, Power System Relablty and Its Assessment: Part 1 Baground and Generatng Capaty, Power Engneerng Journal, vol.-6, no.-4, pp , July V. COCLUSIO Basally, man obetve of power system restruturng and deregulaton s to ntrodue ompetton n the power ndustry and to allow ustomers to selet ther supplers based on pre and relablty. So, ths thess presents a omprehensve tehnque to evaluate nodal relablty and nodal pres of restruture power system. Many new problems reated by ustomer hoe regardng system operaton, prng and relablty plannng are also solved by ths tehnque. Optmzaton problem s used to alulate the nodal relablty and nodal pres. The problem s formulated usng ewton Raphson optmal power flow tehnque. The man obetve of the optmzaton problem s to mnmze the total system generaton ost. For ths purpose sx bus relablty test system (RBTS) has been analyzed to llustrate the tehnque. The analyss of results show that due to ongeston n some ontngeny states auses extreme pre volatlty or pre spes. The random nature of falure reates pre unertanty. Pres at dfferent nodes of the system an be dfferent due to transmsson loss and onstrants. odal pres and odal relablty ndes for eah state, the expeted values and the standard devatons of these ndes are very mportant nformaton for the rs analyss of maret tradng, plannng and operaton. The proposed tehnque provdes a tool to alulate all ths nformaton for maret partpants. The nformaton 343