Cournot equilibria in twosettlement electricity markets with system contingencies. Jian Yao, Shmuel S. Oren* and Ilan Adler


 Bethany Woods
 1 years ago
 Views:
Transcription
1 142 Int. J. Crtal Infrastrutures, Vol. 3, Nos. 1/2, 2007 Cournot equlbra n twosettlement eletrty markets wth system ontngenes Jan Yao, Shmuel S. Oren* and Ilan Adler Department of Industral Engneerng and Operatons Researh Unversty of Calforna Berkeley, CA 94720, USA Emal: Emal: Emal: *Correspondng author Abstrat: We study Nash equlbrum n twosettlement ompettve eletrty markets wth horzontal market power, flow ongeston, demand unertantes and probablst system ontngenes. The equlbrum s formulated as a stohast Equlbrum Problem wth Equlbrum Constrants (EPEC) n whh eah frm solves a stohast Mathematal Programme wth Equlbrum Constrants (MPEC). We assume a noarbtrage relatonshp between the forward pres and the spot pres. We fnd that, wth two settlements, the generaton frms have nentves to ommt forward ontrats, whh nrease soal surplus and derease spot energy pres. Furthermore, these effets are amplfed when the markets beome less onentrated. Keywords: two settlements; Cournot; equlbrum problem wth equlbrum onstrants. Referene to ths paper should be made as follows: Yao, J., Oren, S.S. and Adler, I. (2007) Cournot equlbra n twosettlement eletrty markets wth system ontngenes, Int. J. Crtal Infrastrutures, Vol. 3, Nos. 1/2, pp Bographal notes: Jan Yao s a PhD anddate n the IEOR department at the Unversty of Calforna at Berkeley. He was Researh Assstant on the projet Extended Enterprse oalton for ntegrated Collaboratve Manufaturng Systems (EECOMS), funded by NIST Advane Tehnology Program (ATP), and Software Engneer for Advaned Plannng and Shedulng produts at Orale Corporaton. He reeved an MS n Computer Sene from the Unversty of North Carolna, and an MS and a BS n Mehanal Engneerng from Shangha Jao Tong Unversty. Yao s a member of the INFORMS. Dr. Shmuel S. Oren s Professor of IEOR at the Unversty of Calforna at Berkeley. He s the Berkeley Ste Dretor of PSERC (the Power System Engneerng Researh Center). He publshed numerous artles on aspets of eletrty market desgn and has been a onsultant to varous prvate and government organsatons, nludng the Brazlan regulatory ommsson, The Alberta Energy Utlty Board, the Publ Utlty Commsson, the Polsh system operator and the Publ Utlty Commsson of Texas, where he s urrently a Senor Advsor to the Market Oversght Dvson. He holds a BS and MS n Mehanal Engneerng and Materals Engneerng, respetvely, from the Tehnon n Israel, and he reeved an MS and PhD n Engneerng Eonom Systems n 1972 from Stanford. Dr. Oren s a Fellow of INFORMS and the IEEE. Copyrght 2007 Indersene Enterprses Ltd.
2 Cournot equlbra n twosettlement eletrty markets 143 Dr. Ilan Adler s Professor and Char of the IEOR department at the Unversty of Calforna at Berkeley. Hs man researh atvtes are n the area of optmsaton n general and nteror pont methods n partular. He has also been a onsultant to varous ompanes on large, omplex optmsaton problems. He holds a BA n Eonoms and Statsts from the Hebrew Unversty n Israel, an MS n Operatons Researh from the Tehnon n Israel and a PhD n Operatons Researh from Stanford. Dr. Adler s a member of INFORMS and the Mathematal Assoaton of Amera. 1 Introduton The last deade has wtnessed a fundamental transformaton of the eletr power ndustry around the world, from one domnated by regulated vertally ntegrated monopoles to an ndustry where eletrty s produed and traded as a ommodty through ompettve markets. In the USA, ths transformaton was poneered n the late 1990s by Calforna and the northeastern power pools, nludng the PennsylvanaNew JerseyMaryland (PJM) Interhange, New York and New England. A reent arrval s the Eletral Relablty Counl of Texas (ERCOT) market. Whle there are sgnfant dfferenes among the many mplemented and proposed market desgns that vary n terms of ownershp struture, level of entralsaton and authorty of the system operator, the prmary ratonale for eletrty restruturng n most markets has been to reap welfare gans by supplantng regulaton wth ompetton. Both theory and experene from other formerly regulated ndustres suggest that these gans wll nlude nreased effeny of shortrun produton, of resoure alloaton and of dynam nvestment. A potentally sgnfant obstale to these welfare gans s market power. Market power exersed by supplers typally entals the wthholdng of output and an upward dstorton n the market pre. Market power s generally assoated wth varous forms of eonom neffeny. Among the many proposed and mplemented eonom tools for mtgatng market power s a multplesettlement approah wheren forward transatons, dayahead transatons and realtme balanng transatons are settled at dfferent pres. The rss n Calforna n 2001 has drawn more attenton to the role of forward markets n mtgatng market power and n managng pre rsk n the eletrty supply han. Theoretal analyss (Allaz, 1992; Allaz and Vla, 1993; Kamat and Oren, 2004) and empral evdenes (von der Fehr and Harbord, 1993; reen, 1999; Newbery, 1998; Powell, 1993) suggest that forward ontratng and multsettlement systems redue the nentves of sellers to manpulate spot market pres, sne under a multsettlement approah, the volume of tradng that an be affeted by an nrease n spot pres s redued substantally. Thus, forward tradng s vewed as an effetve way of mtgatng market power at real tme. Allaz (1992) assumes a twoperod market and demonstrates that, f all produers have aess to a forward market, t leads to a prsoners dlemma type of game among them. Allaz and Vla (1993) show that, as the number of forward tradng perod s nreases, produers lose ther ablty to rase energy pres above ther margnal ost. Kamat and Oren (2004) analyse twosettlement markets over two or threenode networks, and extend Allaz s results to a system wth unertan transmsson apates n the spot market. It s also argued that settng pres at ommtment tme
3 144 J. Yao, S.S. Oren and I. Adler provdes nentves for aurate foreastng and provdes exante pre dsovery that faltates tradng. Aurate foreastng and advaned shedulng of generaton and load also mprove system operaton and relablty whle redung the ost of reserves to handle unexpeted devatons from shedule. Whle ntutvely the above arguments n favour of forward tradng and multsettlement systems are ompellng, these studes typally gnore network effets, flow ongeston, generator outages and other system ontngenes. When flow ongeston, system ontngenes and demand unertantes are all present n the spot market, t s not lear to what extent produers are wllng to engage n forward transatons, or how ther nentves wll be affeted. Furthermore, t s not well understood whether forward tradng may n fat help produers exerse market power n the spot market to lok n or even nrease ther olgopoly rents. If ndeed forward tradng an be used to mtgate the exerse of market power but generators have lttle nentve to engage n suh tradng, a natural publ poly queston would be whether forward ontratng should be mposed as a regulatory requrement and the market be desgned to mnmse spot transatons. As a matter of fat, the urrent market rules n Calforna and n Texas are desgned to lmt the sope of the realtme balanng markets through penaltes or added harges. In ths paper, we formulate the twosettlement ompettve eletrty markets as a twoperod game, and ts equlbrum as a subgameperfet Nash equlbrum (see Fudenberg and Trole, 1991) expressed as an Equlbrum Problem wth Equlbrum Constrants (EPEC), n whh eah frm faes a Mathematal Programme wth Equlbrum Constrants (MPEC, see Luo et al., 1996; Karush, 1939), parametr on other frms forward ommtments. We apply the model to an IEEE 24bus test network. Wth the spef data and smplfyng assumptons of the example, t s shown that n equlbrum, frms ommt ertan quanttes n forward transatons and adjust ther postons n the spot market n respondng to ontngenes and demand realsaton. Whle ths paper overs muh of the same ground and employs the same modellng framework as Yao et al. (2004), t extends the prelmnary work reported n Yao et al. (2004) n both ontent and detal. Furthermore, the prelmnary omputatonal tests reported n Yao et al. (2004) for a stylsed sxbus network have been extended to a more realst IEEE 24bus network, whh demonstrates the omputatonal feasblty of the proposed model. The rest of ths paper s organsed as follows. The next seton presents the model assumptons and the mathematal formulaton. An example and numeral results are dsussed n Seton 3. 2 The model 2.1 Modellng approah We shall desrbe now our model for alulatng the equlbrum quanttes and pres of eletrty over a gven network wth two settlements. We vew the two settlements n the eletrty market as a NashCournot game wth two perods: a forward market (Perod 1), and a spot market (Perod 2).
4 Cournot equlbra n twosettlement eletrty markets 145 In Perod 1, frms enter nto forward ontrats by ompetng n a Cournot fashon, antpatng one another s forward ommtments and the ommon knowledge of the expeted spot market outome n Perod 2. In the spot market, the unertan ontngenes are realsed and the generaton frms at as Cournot ompettors, hoosng ther spot produton quanttes for the generaton unts. In dong so, they take as gven the revealed forward ommtments of all other generaton frms, the onjetured spot produton desons of all other generators, and the redspath desons of the Independent System Operator (ISO) spefyng the mport/export quantty at eah node. Smultaneously wth the generators produton desons, the ISO makes ts redspath deson, determnng mports and exports at eah node so as to maxmse total soal welfare based on ts onjetured spot produton at eah node, the transmsson onstrants and the energy balane onstrant. Our model permts dfferent levels of loatonal granularty n the forward and spot markets. Spefally, we wll assume that n the forward market nodes are lustered nto zones and frms enter nto forward ontrats, whh spefy forward zonal quantty ommtments at agreedupon zonal pres. Another key assumpton underlyng our formulaton s that the forward market s suffently lqud, so that the forward pre n eah zone s unform aross all frms operatng n the zone whle the forward ommtments are publ knowledge n the spot market. All forward ontrats are settled fnanally n the spot market based on the dfferene between the forward zonal pre and the spot zonal pre, whh s a weghted average of all spot nodal pres n the zone. The weghts used n determnng the spot zonal pres are onstants that reflet hstoral load shares but are not endogenously determned based on atual load shares n the spot market. We also assume that rskneutral speulators take opposte postons to the generaton frms and explot any arbtrage opportuntes so that the forward pre n a zone equals the orrespondng expeted spot zonal pres over all possble ontngenes (no arbtrage assumpton). The avalable apates of generaton unts and transmsson lnes n the spot market are unknown n Perod 1 and are subjet to stohast varatons n Perod 2. We model the transmsson network onstrants n the spot market n terms of a lossless DC approxmaton of Krhhoff s laws. Spefally, flows on lnes an be alulated usng Power Transfer Dstrbuton Fators (PTDFs), whh spefy the proporton of flow on any partular lne resultng from an njeton of one unt at a partular node and a orrespondng wthdrawal at an arbtrary, but fxed, slak bus (Chao and Pek, 1996). Unertanty regardng the realsed network topology n the spot market s haratersed by dfferent PTDF matres wth orrespondng probabltes. In order to avod omplatons due to dsontnuous payoffs n the spot market, we follow the ommon assumpton (see Hobbs, 2001; Smeers and We, 1997; We and Smeers, 1999) that agents do not game the transmsson pres or onsder the mpat of ther produton desons on ongeston pres. Assumng that produers an game transmsson pres may yeld multple spot market equlbra or may result n no pure strategy equlbrum (see Cardell et al., 1997; Hobbs et al., 2000), whh makes the equlbrum omputaton ntratable. Moreover, when gamng the transmssonmarket, generaton frms wll typally fnd t optmal to barely ongest some lnes so as to avod ongeston rent; ths wll lead to degenerate spot market equlbrum (see Oren, 1997), f any. Empral evdene suggests that gnorng potental gamng of transmsson pres by generators s qute realst, sne t s pratally mpossble for
5 146 J. Yao, S.S. Oren and I. Adler multplegeneraton frms to oordnate ther produton so as to avod ongeston harges by barely deongestng transmsson lnes. Indeed, the ntal desgn of the Calforna market, whh attempted to ontrol ongeston by relyng on suh oordnaton n response to advsory ongeston harges, proved to be unworkable. For smplty, we further assume that there s at most one generaton falty at a node (ths assumpton an be easly relaxed by aggregatng unts owned by a sngle frm and splttng nodes wth multple frms). 2.2 Model notatons Sets: N : The set of nodes (or buses) Z : The set of zones. Moreover, z() represents the zone where node resdes L : The set of transmsson lnes whose ongeston n the spot market s under onsderaton. These lnes are alled flowgates. C : The fnte set of states n the spot market : The set of generaton frms. N g denotes the set of nodes where generaton faltes of frm g are loated Parameters: q, q : The lower and upper apaty bounds of generaton falty at node N n state C. p (): The lnear Inverse Demand Funton (IDF) at node n state : p ( q) = p bq N, C We assume that n eah state the pre nterepts of the nverse demand urves are unform aross all nodes, and that, for eah node, the nodal demand shfts nward and outward n dfferent states, but the slope remans unhanged. C (): The ost funton at node. In ths model, the ost funtons are assumed lnear. C ( q) = d q N K : The flow apaty of lne l L n state C. l D l, : The power transfer dstrbuton fator n state C on lne l L wth respet to node N. Pr(): The probablty of state C of the spot market : δ The weghts used to settle the spot zonal pres ( δ : z( ) = zδ = ) 0, 1.
6 Cournot equlbra n twosettlement eletrty markets 147 Deson varables: x gz, : Forward quantty ommtted by frm g to zone z Z. q : eneraton level at node N n state C of the spot market r : Import/export quantty at node N by the ISO n state C of the spot market 2.3 The formulaton The zonal forward market, whh s onduted at zonal tradng hubs (e.g., PJMs Western hub), gnores ntrazonal transmsson ongeston (although suh ongeston s aounted for mpltly through the ratonal expetaton of the spot zonal pre, whh s based on a weghted nodal pre average). The spot market, on the other hand, s organsed at a nodal level wth all transmsson onstrants reognsed n the ISO redspathes. In eah state C, the spot nodal pre at eah node N s gven by the nodal nverse demand funton p ( q + r ) appled to the net loal onsumpton that results from the loal produton deson by the generatng frms and the redspath deson by the ISO. The spot zonal (settlement) pre u z at a zone z n eah state s defned as the weghted average of the nodal pres n that zone wth predetermned weghts δ. Mathematally, the zonal spot settlement pres are gven by: u = δ p ( r + q ), z Z. z z : ( ) = z The forward zonal pres h z are the pres at whh forward ommtments are traded n the respetve zones. The noarbtrage assumpton mples that the forward zonal pres are equal to the expeted spot zonal settlement pres: hz = Pr() uz, z Z. (1) C In eah state of the spot market, the frms hoose the produton levels. Eah frm g s revenue n eah state s the sum of ts forward ommtment settlement at the spot zonal settlement pres, and the payment for ts produton quanttes at the spot nodal pres. So ts proft s: π = p ( r + q ) q u x C ( q ) g z g, z Ng z Z Ng Eah frm g s objetve n the spot market s to maxmse ts proft π g. It solves the followng proft maxmsaton problem parametr on ts forward ommtments x gz, and the ISO s redspath quanttes r : :max π g q : Ng g subjet to: q q, N (2) g q q, N. (3) g
7 148 J. Yao, S.S. Oren and I. Adler In ths programme, onstrants (2) and (3) ensure that the produton levels q fall between the apaty bounds of the generaton faltes n eah state. The ISO determnes mport/export quanttes r at the nodes. Its objetve s to maxmse the soal surplus defned by the onsumers wllngness to pay mnus the total generaton ost. It solves a soalwelfaremaxmsaton problem: r q S :max + p ( ) ( ) 0 τ dτ q r N subjet to: r = 0 (4) N Dl, r Kl, l L (5) N Dl, r Kl, l L (6) N Here, onstrant (4) represents energy balane (assumng no losses), whereas onstrants (5) and (6) enfore the network feasblty,.e., the power flows resultng from the ISO redspath must not exeed the thermal lmts. Sne the nodal nverse demand funtons as well as the ost funtons are assumed lnear, problems g and S are both strtly onavemaxmsaton programmes, whh mples that ther frstorder neessary ondtons (ommonly referred to as the KarushKuhnTuker, or KKT ondtons; see Karush, 1939; Kuhn and Tuker, 1951) are also suffent. The spot market outomes an thus be haratersed by the KKT ondtons of the frms and the ISO s problems. Let α, λl and λ l + be the Lagrange multplers orrespondng to (4) (6), then the KKT ondtons derved from problem S are: rj = 0 (7) j N p ( q + r ) b α + ( λ D λ D ) = 0 N (8) t t, t+ t, t L 0 D r + K 0 l L (9) λl l, j l j N 0 K D r 0 l L (10) λ l + l l, j j j N Here and heneforth, we use the onventonal notaton x y to represent the T omplementarty ondton x y = 0. Smlarly, let ρ and ρ + be the Lagrange multplers orrespondng to (2) and (3), then the KKT ondtons for problem are: p 2bq br d + δ bx + ρ ρ = 0 N (11) g, z( ) + g ρ g 0 q q 0 N (12) 0 q q 0 N (13) ρ + g g
8 Cournot equlbra n twosettlement eletrty markets 149 If we restrt { xgz, } = 0,.e., no frm ommts to forward ontrats, the solutons to z Zg, KKT ondtons (7) (13) haraterse the outomes of the snglesettlement market,.e., there s no forward market, and all frms at only n the spot market. If there s no flow ongeston n some state of the spot market, the shadow pres orrespondng to the transmsson apates wll all be zero,.e.: λl = λl+ = 0, l L Ths leads ondton (8) to: Thus: p ( q + r ) b α = 0, N, α = p N N q. 1/ b That s, all the spot nodal pres are dental and equal to α. The forward market s organsed as a transparent fnanal market at zonal tradng hubs and s settled n real tme at zonal settlement pres omputed as weghted averages of nodal pres. The expeted ongeston osts due to transmsson onstrants are hene propagated to the forward market through ratonal expetatons of the zonal settlement pres. In the forward market, eah frm g onjetures the other frms forward quanttes and determnes ts own forward quanttes. In general, the frms objetves are to maxmse ther respetve expeted utlty funton over total proft from spot produtons and forward settlements. For smplty, the frms are assumed here to be rsk neutral, so ther forward objetves are to maxmse the expeted jont profts n both the forward and the spot markets, subjet to the noarbtrage ondton and the preedng KKT ondtons. Eah frm g solves the followng stohast MPEC programme n the forward market: max hx + Prπ ( ) xgz, z Z z gz, g C subjet to: π = p ( r + q ) q u x C ( q ) g z g, z Ng z Z Ng h = Pr() u, z Z z j N C r = 0, C j z p ( q + r ) b α + ( λ D λ D ) = 0, N, C t t, t+ t, t L λl l, j l j N 0 D r + K 0, l L, C
9 150 J. Yao, S.S. Oren and I. Adler λ l + l l, j j j N 0 K D r 0, l L, C p 2bq br d + δ bx + ρ ρ = 0, m, N, C m, z( ) + m ρ 0 q q 0, N, C ρ + 0 q q 0, N, C Note that the forward settlement terms n the objetve funton are anelled owng to onstrant (1), so that the MPEC programme for eah frm g s redued to: subjet to: max Pr( ) p ( r + q ) q C( q ) xgz, C Ng Ng j N r = 0, C j p ( q + r ) b α + ( λ D λ D ) = 0, N, C t t, t+ t, t L λl l, j l j N 0 D r + K 0, l L, C λ l + l l, j j j N 0 K D r 0, l L, C p 2bq br d + δ bx + ρ ρ = 0, m, N, C m, z( ) + m ρ 0 q q 0, N, C ρ + 0 q q 0, N, C The general struture of eah frm s MPEC problem (after rearrangng and relabellng the varables) s of the form: mx f ( x, x, y, w) xg, y, w g g g subjet to: g g w = a+ A x g + A xg + My 0 w y 0 In ths programme, x g represents deson varables that are the frm s forward varables and x g are the orrespondng deson varables ontrolled by all other frms, whereas w and y are the shared state varables. Lkewse, a, A g, A g, and M represent sutable vetors and matres mpled by the system s parameters. Owng to the lnearty of the demand funtons and ost funtons, the objetve funtons n these MPEC problems are quadrat and the KKT onstrants (7) (13) are redued to a Lnear Complementarty Problem (LCP, see Cottle et al., 1992). Combnng all frms MPEC programmes, the
10 Cournot equlbra n twosettlement eletrty markets 151 equlbrum problem n the forward market s an EPEC, whh nvolves smultaneous solutons of the ndvdual frms MPECs. In the followng numeral example, we have employed a spealpurpose algorthm for suh problems that explots ther speal struture. Ths MPEC algorthm treats y and w as peewse lnear funtons of x g. Thus, eah frm g s MPEC problem s redued to a programme wth respet only to x g. The algorthm parttons the spae of x g nto a set of polyhedra aordng to the feasble omplementary bases of the LCP onstrant. Suh parttonng allows the MPEC algorthm to searh for a statonary pont of the MPEC problem va parametr LCP pvotng and fntely many quadrat programmes. A detaled desrpton of the algorthm s out of the sope of ths paper and wll be reported elsewhere. 3 The 24bus system In ths seton, we apply our model to the IEEE 24bus test network wth dfferent, fttous generatorownershp strutures, and observe the eonom results of two settlements. The 24bus network s omposed of 24 nodes and 38 lnes (see Fgure 1). There are ten generators n ths system, eah loated at one node. The resoure ownershps, zonal strutures, demand funtons and ontngeny states are hypothetal. (When applyng ths model to a real system, one an generate the demand funtons and ontngeny states by samplng hstoral data.) Table 1 lsts the nodal nformaton, nludng nverse demand funton slopes, margnal generaton osts and full apates of generaton plants. We assume two zones n the system wth node 1 through 13 n zone 1 and the rest of the nodes n zone 2. As to the thermal lmts, we gnore the ntrazonal flows and fous only on flowgates 3 24, 11 14, and We assume seven states n the spot market (see Table 2). In the frst state, the demands are at peak, all generaton plants operate at ther full apates and all transmsson lnes are rated at ther full thermal lmts. The seond state s the same as the frst state exept that t has shoulder demands. States 3 through 6 also have shoulder demands, but represent the ontngenes of unavalablty of the four flowgates, respetvely. Offpeak state 7 dffers from states 1 and 2 n havng very low demand levels. Table 2 also llustrates the pre nterepts of IDFs as well as the probabltes of the states. We run tests on the systems wth sngle settlement and two settlements, and observe the lkelhood of ongeston, generator output hanges, soal welfare hanges and the behavours of the spot nodal and zonal pres due to forward ontratng. For the ase of two settlements, we test dfferent generator ownershp strutures wth two, three, four or fve frms. The detals of the ownershps are lsted n Table 3. We observe that wth two settlements, the frms have strateg nentves for ommttng to forward ontrats. Furthermore, the nentves for forward ontratng are strengthened by dereased market onentraton. Fgure 2 ompares the total forward ontratng quanttes wth dfferent numbers of frms. It shows that the total forward ontrat quantty nreases from 60 MW wth two frms to 640 MW wth fve frms.
11 152 J. Yao, S.S. Oren and I. Adler Fgure 1 The 24bus network Table 1 Nodal nformaton Margnal ost ($/MWh) Capaty Margnal ost ($/MWh) Node IDF slope (MW) Node IDF slope Capaty (MW)
12 Cournot equlbra n twosettlement eletrty markets 153 Table 2 States of the spot market State Prob. IDF nterept ($/MWh) Desrpton Onpeak state: The demands are on the peak Shoulder state: The demands are at shoulder Shoulder demands wth lne breakdown: Lne 3 24 goes down Shoulder demands wth lne breakdown: Lne goes down Shoulder demands wth lne breakdown: Lne goes down Shoulder demands wth lne breakdown: Lne goes down Offpeak state: The demands are off peak. Table 3 enerator ownershp struture Number of frms Node Two Three Four Fve 1 #1 #1 #1 #1 4 #1 #2 #2 #2 7 #1 #2 #3 #3 11 #2 #3 #4 #4 13 #2 #3 #4 #5 15 #2 #1 #1 #1 17 #2 #2 #2 #2 21 #2 #2 #3 #3 22 #2 #3 #3 #4 23 #1 #3 #4 #5 In all states of the spot market, the aggregated spot outputs nrease under two settlements; moreover, the more frms n the markets, the greater s ths effet (see Fgure 3). Despte ths phenomenon, some generators stll derease the outputs n some states. Ths s beause, when fang ntensve ompetton, some frms have to redue produton of the generators loated n the nodes wth lower spot pres, so as to sustan ther profts by nreasng ther outputs from other plants. For example, when there are fve frms n the markets, generators at nodes 15 and 21 nrease ther produton levels only n the peak state, but redue them n the other sx states (see Table 4). Consequently, the expeted spot outputs from these generators mght be lower under two settlements than those under a sngle settlement. The expeted generaton quanttes are shown n Fgure 4, wth the dark bars denotng the outputs for a sngle settlement and the grey and whte bars for two settlements wth two frms and fve frms respetvely. It s shown that, under two settlements wth fve frms, the generators n both nodes 15 and 21 operate at expeted levels that are lower than those under a sngle settlement.
13 154 J. Yao, S.S. Oren and I. Adler Fgure 2 Total forward ontratng Fgure 3 Total spot generaton
14 Cournot equlbra n twosettlement eletrty markets 155 Table 4 Output level hanges (MW) Node State Fgure 4 Expeted spot nodal generaton Spot nodal and zonal pres under two settlements derease n all states. Ths follows dretly from the fat that the aggregate output s nreased n the spot market under two settlements. Fgure 5 ompares the expeted spot nodal pres under a sngle settlement to those orrespondng to two settlements for ether two and for fve frms. The pres under a sngle settlement are drawn dark, whle the pres under two settlements wth two frms are grey, and wth fve frms, whte. In Table 5, we report the spot zonal pres under a sngle settlement n olumns 2 and 3, and the spot zonal pres under two settlements n olumns 4 through 7. The last row of ths table lsts the forward zonal pres. It s also shown n Fgure 5 and Table 5 that as more frms ompete n the twosettlement system, the lower are the spot nodal and zonal pres.
15 156 J. Yao, S.S. Oren and I. Adler Fgure 5 Expeted spot nodal pres Table 5 Zonal pres Two settlements Sngle settlement Two frms Fve frms Market Zone 1 Zone 2 Zone 1 Zone 2 Zone 1 Zone 2 Spot: state Spot: state Spot: state Spot: state Spot: state Spot: state Spot: state Forward Soal surplus nreases under two settlements. Moreover, the soal welfare of the twosettlement system nreases as the number of frms nreases. The expeted soal welfare of a sngle settlement s $7796/h, whh, under two settlements, s nreased to $8133/h wth two frms and $9383/h wth fve frms. Fgure 6 shows that the same trend apples to the onsumer surplus. These results are qualtatvely onsstent wth those of Allaz and Vla (1993). Lnes not ongested n the snglesettlement system mght be ongested n the spot market of the twosettlement system, or ve versa. Ths follows from the fat that the frms adjust ther outputs, whh alters the flows on the transmsson lnes. For example, n state 3, the snglesettlement market has only lne ongested; however, the only ongested lne under two settlements wth fve frms s lne (see Table 6).
16 Cournot equlbra n twosettlement eletrty markets 157 Fgure 6 Soal surplus Table 6 Lne Flow ongeston State Sngle settlement Two settlements Lne State Sngle settlement Two settlements 1 Congested Congested Congested Congested 2 Unongested Unongested 2 Unongested Unongested 3 Breakdown Breakdown 3 Unongested Congested 4 Unongested Unongested 4 Unongested Unongested 5 Unongested Unongested 5 Breakdown Breakdown 6 Unongested Unongested 6 Congested Congested 7 Unongested Unongested 7 Unongested Unongested 1 Congested Congested Unongested Unongested 2 Unongested Unongested 2 Unongested Unongested 3 Congested Unongested 3 Unongested Unongested 4 Breakdown Breakdown 4 Congested Unongested 5 Unongested Unongested 5 Congested Congested 6 Unongested Unongested 6 Breakdown Breakdown 7 Unongested Congested 7 Unongested Unongested Fnally, Fgure 7 llustrates generator outputs for the seven states under two settlements wth two frms. We note that the generators produe at levels between 40 MW and 70 MW n the peak state, and that only three generators operate n the offpeak state. Compared to ther forward ontrats, the frms are n fat net buyers n the offpeak state, and net supplers n the peak state.
17 158 J. Yao, S.S. Oren and I. Adler Fgure 7 Statewse spot generatons 4 Conludng remarks In ths paper, we model the twosettlement eletrty system as a twoperod game wth multple states of the world n the seond perod. The Cournot equlbrum s a subgameperfet Nash equlbrum represented n the format of an EPEC. We assume lnear demand funtons and onstant margnal generaton osts, so the spot market equlbrum an be omputed as a lnear omplementarty problem. In the forward market, frms solve MPECs subjet to the noarbtrage relatonshp between the forward pres and the expeted spot zonal pres, and the spot market equlbrum ondtons. We apply our model to the 24bus network, and observe from t the strateg nentves of the frms for forward ontratng, the lkelhood of ongeston, nreased generaton quanttes, nreased soal surplus and dereased spot pres wth the ntroduton of a forward market. We also fnd that these effets are amplfed when there are more frms n the network. Fnally, t should be ponted out that our numeral tests are lmted, and that our goal s not to reah onlusve eonom results, whh requre far more extensve smulatons, but to valdate our modellng methodology. Moreover, one should expet quanttatvely dssmlar results f the model s appled to a dfferent settng of resoure ownershp strutures, demand funton dstrbutons or ontngeny states, or to dfferent networks. We plan to relax the noarbtrage assumpton between the forward and spot pres wth a marketlearng ondton that sets the forward pres based on the expeted demands n the spot market. Suh an analyss wll attempt to apture how lak of lqudty (or hghrsk averson) on the buyers sde mght be refleted n a hghrsk premum embedded n the forward pres. We expet that suh a ondton enhanes frms market power and enables them to rase forward pres above the expeted spot pres whle nreasng ther profts.
18 Cournot equlbra n twosettlement eletrty markets 159 Aknowledgements Ths researh s supported by the Natonal Sene Foundaton rant ECS , by the Power System Engneerng Researh Center (PSERC), by the Unversty of Calforna Energy Insttute (UCEI) and by the Department of Energy through the Consortum for Eletr Relablty Tehnology Solutons (CERTS). Referenes Allaz, B. (1992) Olgopoly, unertanty and strateg forward transatons, Internal Journal of Industral Organzaton, Vol. 10, pp Allaz, B. and Vla, JL. (1993) Cournot ompetton, forward markets and effeny, Journal of Eonom Theory, Vol. 59, pp Cardell, J., Htt, C. and Hogan, W.W. (1997) Market power and strateg nteraton n eletrty networks, Resoure and Energy Eonoms, Vol. 19, pp Chao, HP. and Pek, S.C. (1996) A market mehansm for eletr power transmsson, Journal of Regulatory Eonoms, Vol. 10, No. 1, pp Cottle, R.W., Pang, J.S. and Stone, R.E. (1992) The Lnear Complementarty Problem, Boston, MA: Aadem Press. Fudenberg, D. and Trole, J. (1991) ame Theory, Cambrdge, MA: The MIT Press. reen, R.J. (1999) The eletrty ontrat market n England and Wales, Journal of Industral Eonoms, Vol. 47, No. 1, pp Hobbs, B.F., Metzler, C.B. and Pang, J.S. (2000) Strateg gamng analyss for eletr power systems: an MPEC approah, IEEE Transatons on Power Systems, Vol. 15, No. 2, pp Hobbs, B.F. (2001) Lnear omplementarty models of NashCournot ompetton n blateral and POOLCO power markets, IEEE Transatons on Power Systems, Vol. 16, No. 2, pp Kamat, R. and Oren, S.S. (2004) Multsettlement systems for eletrty markets: zonal aggregaton under network unertanty and market power, Journal of Regulatory Eonoms, Vol. 25, No. 1, pp Karush, W. (1939) Mnma of funtons of several varables wth nequaltes as sde onstrants, MS Thess, Department of Mathemats, Unversty of Chago, Chago, IL. Kuhn, H.W. and Tuker, A.W. (1951) Nonlnear programmng, J. Neyman (Ed.) Proeedngs of the Seond Berkeley Symposum, Berkeley, CA: Unversty of Calforna Press. Luo, Z.Q., Pang, J.S. and Ralph, D. (1996) Mathematal Programmes wth Equlbrum Constrants, Cambrdge: Cambrdge Unversty Press. Newbery, D.M. (1998) Competton, ontrats, and entry n the eletrty spot market, Rand Journal of Eonoms, Vol. 29, No. 4, pp Oren, S.S. (1997) Eonom neffeny of passve transmsson rghts n ongested eletrty systems wth ompettve generaton, The Energy Journal, Vol. 18, pp Powell, A. (1993) Tradng forward n an mperfet market: the ase of eletrty n Brtan, The Eonom Journal, Vol. 103, pp Smeers, Y. and We, JY. (1997) Spatal Olgopolst Eletrty Models wth Cournot Frms and Opportunty Cost Transmsson Pres, Center for Operatons Researh and Eonometrs, Unverste Catholque de Louvan, Louvanlanewve, Belgum. von der Fehr, NH.M. and Harbord, D. (1993) Longterm ontrats and mperfetly ompettve spot markets: a study of UK eletrty ndustry, Memorandum No. 14, Department of Eonoms, Unversty of Oslo, Oslo, Sweden.
19 160 J. Yao, S.S. Oren and I. Adler We, JY. and Smeers, Y. (1999) Spatal olgopolst eletrty models wth Cournot frms and regulated transmsson pres, Operatons Researh, Vol. 47, No. 1, pp Yao, J., Oren, S.S. and Adler, I. (2004) Computng Cournot equlbra n twosettlement eletrty markets wth transmsson onstrants, Proeedng of the 37th Hawa Internatonal Conferene on Systems Senes (HICCS 37), Bg Island, Hawa, 5 8 January.
Multisettlement Systems for Electricity Markets: Zonal Aggregation under Network Uncertainty and Market Power 1
Proeedngs of the 35th Hawa Internatonal Conferene on System Senes  2002 Multsettlement Systems for Eletrty Markets: Zonal Aggregaton under Network Unertanty and Market Power 1 Ransh Kamat and Shmuel
More information24. Impact of Piracy on Innovation at Software Firms and Implications for Piracy Policy
4. mpat of Pray on nnovaton at Software Frms and mplatons for Pray Poly Jeevan Jasngh Department of nformaton & Systems Management, HKUST Clear Water Bay, Kowloon Hong Kong jeevan@ust.h Abstrat A Busness
More informationDECOMPOSITION ALGORITHM FOR OPTIMAL SECURITYCONSTRAINED POWER SCHEDULING
DECOMPOSITION ALGORITHM FOR OPTIMAL SECURITYCONSTRAINED POWER SCHEDULING Jorge MartínezCrespo Julo Usaola José L. Fernández Unversdad Carlos III de Madrd Unversdad Carlos III de Madrd Red Elétra de Espana
More informationUse of Multiattribute Utility Functions in Evaluating Security Systems
LLNLTR405048 Use of Multattrbute Utlty Funtons n Evaluatng Seurty Systems C. Meyers, A. Lamont, A. Sherman June 30, 2008 Ths doument was prepared as an aount of work sponsored by an ageny of the Unted
More informationData Analysis with Fuzzy Measure on Intuitionistic Fuzzy Sets
Proeedngs of the Internatonal MultConferene of Engneers and Computer Sentsts 2016 Vol II Marh 1618 2016 Hong Kong Data nalyss wth Fuzzy Measure on Intutonst Fuzzy Sets Sanghyuk Lee * Ka Lok Man Eng Gee
More informationPartner Choice and the Marital College Premium: Analyzing Marital Patterns Over Several Decades
Partner Choe and the Martal College Premum: Analyzng Martal Patterns Over Several Deades PerreAndré Chappor Bernard Salané Yoram Wess January 31, 2015 Abstrat We onstrut a strutural model of household
More informationWhen can bundling help adoption of network technologies or services?
When an bundlng help adopton of network tehnologes or serves? Steven Weber Dept. of ECE, Drexel U. sweber@oe.drexel.edu Roh Guérn Dept. of CSE, WUSTL guern@wustl.edu Jaudele C. de Olvera Dept. of ECE,
More informationOptimal Health Insurance for Multiple Goods and Time Periods
04 R.P. Ells, S. Jang, and W.G. Mannng Optmal Health Insurane for Multple Goods and Tme Perods Randall P. Ells a,, Sheny Jang b, Wllard G. Mannng a Department of Eonoms, Boston Unversty, 70 Bay State Road,
More informationModern Problem Solving Techniques in Engineering with POLYMATH, Excel and MATLAB. Introduction
Modern Problem Solvng Tehnques n Engneerng wth POLYMATH, Exel and MATLAB. Introduton Engneers are fundamentally problem solvers, seekng to aheve some objetve or desgn among tehnal, soal eonom, regulatory
More informationFigure 1. Inventory Level vs. Time  EOQ Problem
IEOR 54 Sprng, 009 rof Leahman otes on Eonom Lot Shedulng and Eonom Rotaton Cyles he Eonom Order Quantty (EOQ) Consder an nventory tem n solaton wth demand rate, holdng ost h per unt per unt tme, and replenshment
More informationPricing System Security in Electricity Markets. latter might lead to high prices as a result of unrealistic
1 Pro. Bulk Power Systems Dynams and Control{V, Onomh, Japan, August 2001. Prng System Seurty n Eletrty Markets Claudo A. Ca~nzares Hong Chen Wllam Rosehart UnverstyofWaterloo Unversty of Calgary Dept.
More informationCournot Equilibrium in Pricecapped TwoSettlement Electricity Markets
1 Cournot Equilibrium in Prieapped TwoSettlement Eletriity Markets Jian Yao 1, Bert Willems 2, Shmuel S. Oren 1, Ilan Adler 1 1 Department of Industrial Engineering and Operations Researh 2 Unversity
More informationForschung zur Entwicklungsökonomie und politik Research in Development Economics and Policy
Dsusson Paper No. 01/2004 Comparatve advantage of Vetnam s re setor under dfferent lberalsaton senaros A Poly Analyss Matrx (PAM) study Nguyen Manh Ha and Franz Hedhues Department of Agrultural Development
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationNew Optimization Technique For Nodal Price And Reliability Calculation
Internatonal Journal of Engneerng and Tehnal Researh (IJETR) ISS: 23210869, Volume2, Issue5, May 2014 ew Optmzaton Tehnque For odal Pre And Relablty Calulaton Pushpendra Kumar Sharma, Abhshe Sangh,
More informationEnergyEfficient Design in Wireless OFDMA
Ths full text paper was peer revewed at the dreton of IEEE Communatons Soety subjet matter experts for publaton n the ICC 2008 proeedngs. EnergyEffent Desgn n Wreless OFDMA Guowang Mao, Nageen Hmayat,
More informationLognormal random eld approxmatons to LIBOR market models O. Kurbanmuradov K. Sabelfeld y J. Shoenmakers z Mathemats Subet Classaton: 60H10,65C05,90A09 Keywords: LIBOR nterest rate models, random eld smulaton,
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationBehavior Coordination in Ecommerce Supply Chains
Assoaton for Informaton ystems AI Eletron Lbrary AIeL) WHICEB 25 Proeedngs Wuhan Internatonal Conferene on ebusness ummer 6925 Behavor Coordnaton n Eommere upply Chans Yanhong Zhang Insttute of system
More informationNorthSouth TradeRelated Technology Diffusion: Virtuous Growth Cycles in Latin America
DISCUSSION PAPER SERIES IZA DP No. 4943 NorthSouth TradeRelated Tehnology Dffuson: Vrtuous Growth Cyles n Latn Amera Maure Shff Yanlng Wang May 2010 Forshungsnsttut zur Zukunft der Arbet Insttute for
More informationCONSIDER a connected network of n nodes that all wish
36 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 60, NO. 2, FEBRUARY 204 Coded Cooperatve Data Exhange n Multhop Networks Thomas A. Courtade, Member, IEEE, and Rhard D. Wesel, Senor Member, IEEE Abstrat
More informationPeertopeer systems have attracted considerable attention
Reputaton Aggregaton n PeertoPeer etwork Usng Dfferental Gossp Algorthm Ruhr Gupta, Yatndra ath Sngh, Senor Member, IEEE, arxv:20.430v4 [s.i] 28 Jan 204 Abstrat Reputaton aggregaton n peer to peer networks
More informationCartelisation of Oligopoly
Internatonal Conferene on Apple Eonoms ICOAE 29 551 Cartelsaton of Olgopoly Jaek Prokop 224 Abstrat Ths paper onsers possbltes of artelsaton n the olgopolst nustres. We stngush between two mportant ssues.
More informationRevenue Management Games
Revenue Management Games Sergue Netessne and Robert A. Shumsky 2 Unversty of Rohester W. E. Smon Graduate Shool of Busness Admnstraton Rohester, NY 4627 Otober, 2000 netessnse@smon.rohester.edu 2 shumsky@smon.rohester.edu
More informationPowerofTwo Policies for Single Warehouse MultiRetailer Inventory Systems with Order Frequency Discounts
Powerofwo Polces for Sngle Warehouse MultRetaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationVulnerability Assessment of Cybersecurity for SCADA Systems Using Attack Trees
Vulnerablty Assessment of Cyberseurty for SCADA Systems Usng Attak Trees CheeWoo Ten, Student Member, IEEE, ChenChng Lu, Fellow, IEEE, Manmaran ovndarasu, Member, IEEE Abstrat By penetratng the SCADA
More informationEconomybased Content Replication for Peering Content Delivery Networks
Eonomybased Content Replaton for Peerng Content Delvery Networs AlMuaddm Khan Pathan 1 and Raumar Buyya Grd Computng and Dstrbuted Systems (GRIDS) Laboratory Department of Computer Sene and Software
More informationOptimal Adaptive Voice Smoother with Lagrangian Multiplier Method for VoIP Service
Optmal Adaptve Voe Smoother wth Lagrangan Multpler Method for VoIP Serve ShyhFang HUANG, Er Hsaouang WU and PaoCh CHANG Dept of Eletral Engneerng, Computer Sene and Informaton Engneerng and Communaton
More informationSeries Solutions of ODEs 2 the Frobenius method. The basic idea of the Frobenius method is to look for solutions of the form 3
Royal Holloway Unversty of London Department of Physs Seres Solutons of ODEs the Frobenus method Introduton to the Methodology The smple seres expanson method works for dfferental equatons whose solutons
More informationEvaluation of Delay Performance in Valiant Loadbalancing Network
Evaluaton of Delay Performane n Valant Loadbalanng Network Yngd Yu a, Yaohu Jn a, Hong Cheng a, Yu Gao a, Weqang Sun a, We Guo a, Wesheng Hu a a State Key Laboratory on FberOt Loal Area Networks and
More informationErrorPropagation.nb 1. Error Propagation
ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then
More informationIndustrySpecific Exchange Rates for the United States
Lnda S. Goldberg IndustrySpef Exhange Rates for the Unted States The effet of exhange rate movements on U.S. produers and U.S. eonom atvty has drawn renewed nterest lately followng the large delnes n
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationChapter 6. Demand Relationships Among Goods
Chapter 6 Demand Relatonshps Among Goods Up to ths pont, we have held the pre of other goods onstant. Now we onsder how hanges n p affet n a twogood world. I p I p I p I p p p ( ) ( ) then I p then (
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationCyberSecurity Via Computing With Words
CyberSeurty Va Computng Wth Words John. Rkard Dstrbuted Infnty, In. 4637 Shoshone Drve Larkspur, CO 808 Emal: trkard@dstrbutednfnty.om ABSRAC Cyberseurty systems must deal wth a hgh rate of observable
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationRecap. Duopoly models. ! Last class (January 13, 2004) ! Today (January 15, 2004) ! Two competing firms, selling a homogeneous good
Reap! Last lass (January 13, 24)! Domnant and domnated atons! Best response! ash eulbrum! Mxed strateges! Pareto domnane! Today (January 15, 24)! Examples of games wth ontnuous aton sets! Duopoly models:
More informationA Comparison of Ex Ante versus Ex Post Vertical Market Power: Evidence from the Electricity Supply Industry *
A Comparson of Ex Ante versus Ex Post Vertcal Market Power: Evdence from the Electrcty Supply Industry * by Joshua S. Gans Frank A. Wolak Melbourne Busness School Department of Economcs 200 Lecester Street
More informationCredit Limit Optimization (CLO) for Credit Cards
Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More informationThe Application of Qubit Neural Networks for Time Series Forecasting with Automatic Phase Adjustment Mechanism
The Applaton of Qubt Neural Networks for Tme Seres Foreastng wth Automat Phase Adjustment Mehansm arlos R. B. Azevedo 1 and Tago. A. E. Ferrera 1 1 entro de ênas e Tenologa Unversdade atóla de Pernambuo
More informationAddendum to: Importing SkillBiased Technology
Addendum to: Importng SkllBased Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationSimulating the dynamics in twosettlement electricity markets via an agentbased approach
ISSN 1 7467233, England, UK International Journal of Management Science and Engineering Management Vol. 1 (2006) No. 2, pp. 8397 Simulating the dynamics in twosettlement electricity markets via an agentbased
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationApplications of the Offset in PropertyCasualty Predictive Modeling
Applatons of the Offset n PropertyCasualty Predtve Modelng Jun Yan, Ph.D. James Guszza, FCAS, MAAA, Ph.D. Matthew Flynn, Ph.D. ChengSheng Peter Wu, FCAS, ASA, MAAA Abstrat: Generalzed Lnear Model [GLM]
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationA STUDY OF SOFTBALL PLAYER SWING SPEED *
A STUDY OF SOFTBALL PLAYER SWING SPEED * LLOYD SMITH Shool of Mehanal and Materals Engneerng Washngton State Unversty Emal: lvsmth@wsu.edu JEFF BROKER Department of Bology Unversty of Colorado, Colorado
More informationVasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio
Vascek s Model of Dstrbuton of Losses n a Large, Homogeneous Portfolo Stephen M Schaefer London Busness School Credt Rsk Electve Summer 2012 Vascek s Model Important method for calculatng dstrbuton of
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationSupply chains with or without upstream competition?
Supply han wth or wthout uptream ompetton? Chryovalantou Mllou * Unverdad Carlo III de Madrd, Department of onom, Getafe Madrd 890, Span Feruary 00 Atrat We nvetgate a fnal good produer' nentve to engage
More informationMulticlass kernel logistic regression: a fixedsize implementation
Multlass kernel logst regresson: a fxedsze mplementaton Peter Karsmakers,2, Krstaan Pelkmans 2, Johan AK Suykens 2 Abstrat Ths researh studes a pratal teratve algorthm for multlass kernel logst regresson
More informationEntry Games in Exogenous Sunk Costs Industries (Sutton, Chapter 2)
Entry Games n Exogenous Sunk Costs Industres (Sutton, Chapter 2) StructureConducterformance aradgm: Models oneway chan of causaton Concentraton to erformance, treatng Conduct as a Black Box ew Industral
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationInternalization, Clearing and Settlement, and Stock Market Liquidity 1
Internalzaton, Clearng and Settlement, and Stock Market Lqudty 1 Hans Degryse, Mark Van Achter 3, and Gunther Wuyts 4 May 010 1 We would lke to thank partcpants at semnars n Louvan, Mannhem, and Tlburg
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationChapter 7: Answers to Questions and Problems
19. Based on the nformaton contaned n Table 73 of the text, the food and apparel ndustres are most compettve and therefore probably represent the best match for the expertse of these managers. Chapter
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationPiecewise affine approximation of nonlinear systems a case study of a benchmark nonlinear boiler
Proeedngs of the 8th WSEAS Internatonal Conferene on SYSTEM SCIENCE and SIMULATION n ENGINEERING Peewse affne approxmaton of nonlnear sstems a ase std of a benhmark nonlnear boler RADEK HORÁLEK* AND JAROSLAV
More informationDiscriminatory versus UniformPrice Electricity Auctions with Supply Function Equilibrium
Dscrmnatory versus UnformPrce Electrcty Auctons wth Supply Functon Equlbrum Talat S. Genc a December, 007 Abstract. A goal of ths paper s to compare results for dscrmnatory auctons to results for unformprce
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):18841889 Research Artcle ISSN : 09757384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationBond futures. Bond futures contracts are futures contracts that allow investor to buy in the
Bond futures INRODUCION Bond futures contracts are futures contracts that allow nvestor to buy n the future a theoretcal government notonal bond at a gven prce at a specfc date n a gven quantty. Compared
More informationLeonardo Raffo López **
77 The sugar market n Colomba an ts nteratons wth the usa market Leonaro Raffo López Resumen En este artíulo se propone un moelo e equlbro paral para entener el omportamento el merao el azúar en Colomba
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationFace Recognition in the Scrambled Domain via SalienceAware Ensembles of Many Kernels
Fae Reognton n the Srambled Doman va SaleneAware Ensembles of Many Kernels Jang, R., AlMaadeed, S., Bourdane, A., Crooes, D., & Celeb, M. E. (2016). Fae Reognton n the Srambled Doman va SaleneAware
More informationMarket Coupling and the Organization of CounterTrading: Separating Energy and Transmission Again?
Market Couplng and the Organzaton of CounterTradng: Separatng Energy and Transmsson Agan? Gorga Oggon Unverstà degl Stud d Bresca Bresca, Italy oggon@eco.unbs.t Yves Smeers CORE, Unversté catholque de
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationRisk Model of LongTerm Production Scheduling in Open Pit Gold Mining
Rsk Model of LongTerm Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,
More informationreduce competition increase market power cost savings economies of scale and scope cost savings Oliver Williamson: the efficiency defense
Mergers Why merge? reduce competton ncrease market power cost savngs economes of scale and scope Why allow mergers? cost savngs Olver Wllamson: the effcency defense Merger wthout cost savngs Before merger:
More informationDefining Contractor Performance Levels
Defnng Contrator Performane Leels Khaled Nassar, Ph.D., AIA Assoate Professor, Ameran Unersty n Caro In many ountres, state and prate owners often ategorze ontrators nto arous groups based on ther apates
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationA Probabilistic Theory of Coherence
A Probablstc Theory of Coherence BRANDEN FITELSON. The Coherence Measure C Let E be a set of n propostons E,..., E n. We seek a probablstc measure C(E) of the degree of coherence of E. Intutvely, we want
More informationThe Choice of Direct Dealing or Electronic Brokerage in Foreign Exchange Trading
The Choce of Drect Dealng or Electronc Brokerage n Foregn Exchange Tradng Mchael Melvn Arzona State Unversty & Ln Wen Unversty of Redlands MARKET PARTICIPANTS: Customers Endusers Multnatonal frms Central
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationCOLOR WAVELET BASED UNIVERSAL BLIND STEGANALYSIS
COLOR WAVELET BASED UNIVERSAL BLIND STEGANALYSIS Sos Agaan and Hong Ca, College of Engneerng, Department of Eletral Engneerng, Unversty of Texas at San Antono, San Antono, Texas, USA sagaan@utsa.edu; hong@lonestar.utsa.edu
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More informationSemisupervised Hierarchical Clustering Analysis for High Dimensional Data
Yuntao Qan, Xaoxu Du, and Q Wang Semsupervsed Herarhal Clusterng Analyss for Hgh Dmensonal Data Semsupervsed Herarhal Clusterng Analyss for Hgh Dmensonal Data Yuntao Qan, Xaoxu Du, and Q Wang College
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationTuition Fee Loan application notes
Tuton Fee Loan applcaton notes for new parttme EU students 2012/13 About these notes These notes should be read along wth your Tuton Fee Loan applcaton form. The notes are splt nto three parts: Part 1
More informationAllocating Time and Resources in Project Management Under Uncertainty
Proceedngs of the 36th Hawa Internatonal Conference on System Scences  23 Allocatng Tme and Resources n Project Management Under Uncertanty Mark A. Turnqust School of Cvl and Envronmental Eng. Cornell
More informationThe Shortterm and Longterm Market
A Presentaton on Market Effcences to Northfeld Informaton Servces Annual Conference he Shortterm and Longterm Market Effcences en Post Offce Square Boston, MA 0209 www.acadanasset.com Charles H. Wang,
More informationComputer Administering of the Psychological Investigations: SetRelational Representation
Open Journal of Appled Senes 2012 2 110114 do:10.4236/ojapps.2012.22015 Publshed Onlne June 2012 (http://www.srp.org/journal/ojapps) Coputer Adnsterng of the Psyhologal Investgatons: SetRelatonal Representaton
More informationA DATA MINING APPLICATION IN A STUDENT DATABASE
JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 005 VOLUME NUMBER (5357) A DATA MINING APPLICATION IN A STUDENT DATABASE Şenol Zafer ERDOĞAN Maltepe Ünversty Faculty of Engneerng BüyükbakkalköyIstanbul
More informationAllocating Collaborative Profit in LessthanTruckload Carrier Alliance
J. Servce Scence & Management, 2010, 3: 143149 do:10.4236/jssm.2010.31018 Publshed Onlne March 2010 (http://www.scrp.org/journal/jssm) 143 Allocatng Collaboratve Proft n LessthanTruckload Carrer Allance
More informationSpeech Quality Measurement Methods with Applying PLC Algorithms on Realtime Transmission Control Scheme for VoIP Service
46 JOURNAL OF MULTIMEDIA, VOL. 1, NO. 6, SEPTEMBER 2006 Seeh Qualty Measurement Methods wth Alyng PLC Algorthms on Realtme Transmsson Control Sheme for VoIP Serve Jnsul Km Dgtal Meda Laboratory, Informaton
More informationUnconstrained EOQ Analysis of a Furniture Mall  A Case Study of Bellwether Furniture
Internatonal Journal of Scentfc Research n omputer Scence and Engneerng Research Paper Volume, Issue5 ISSN: 307639 Unconstraned EOQ Analyss of a Furnture Mall  A ase Study of Bellwether Furnture Manmnder
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationThe Current Employment Statistics (CES) survey,
Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probabltybased sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,
More informationEE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN
EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson  3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson  6 Hrs.) Voltage
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationiavenue iavenue i i i iavenue iavenue iavenue
Saratoga Systems' enterprsewde Avenue CRM system s a comprehensve webenabled software soluton. Ths next generaton system enables you to effectvely manage and enhance your customer relatonshps n both
More informationNMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582
NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582 7. Root Dynamcs 7.2 Intro to Root Dynamcs We now look at the forces requred to cause moton of the root.e. dynamcs!!
More informationOnLine Fault Detection in Wind Turbine Transmission System using Adaptive Filter and Robust Statistical Features
OnLne Fault Detecton n Wnd Turbne Transmsson System usng Adaptve Flter and Robust Statstcal Features Ruoyu L Remote Dagnostcs Center SKF USA Inc. 3443 N. Sam Houston Pkwy., Houston TX 77086 Emal: ruoyu.l@skf.com
More information