NODAL PRICES IN THE DAY-AHEAD MARKET

Size: px

Start display at page:

Download "NODAL PRICES IN THE DAY-AHEAD MARKET"

Kerrie McKenzie
5 years ago
Views:

1 NODAL PRICES IN THE DAY-AHEAD MARET Fred Murphy Tempe Unversty AEG Meetng, Washngton, DC Sept. 7, 8 What we cover Two-stage stochastc program for contngency anayss n the day-ahead aucton. Fnd the LMPs and the expected margna vaue of eectrcty from the dua varabes. Show dfferences wth current duas Show margna vaue probem Bouffard, Gaana, and Conejo ()

2 Objectve functon: N nb N no N ns nr + u u, ν max c LL cgpg p b gs b u, ν, L Pg, L, R, S = = = = = = u= ν= Ineuaty constrants for offer/bd bocs and tota node generaton/oad bounds, respectvey: R ν,, mn, max g g g P P P no P g = P g = g mn max g g g P P P λ, mn, max L L L nb L = L L mn = L L max λ L 3 Power-baance euaty constrant and branch-fow neuaty constrants for norma operatng condtons. NG = Pg L λ NG n = NG n max max bj j bj = P SF NG P = λba 4

3 Generaton reducton and oad-sheddng neuaty constrants, oad baance euaty constrants and branch fow neuaty constrants for contngency condtons ns S u= S u, S u,,max u, + Pg = P g λ g ν, R R nr ν = R ν, + L ν,,max = L L λ NG N = = NG P P g = L λ NG λ ba n, max,max bj SF j NG Pbj = μ j Actvtes Objectve Tot oad Tot gen Net gen Sys net gn Br cap Prod w/ Dem w/ Net gen w/ Sys gen w/ Br cap w/ Bounds L c L L - Pg c g - - Pg L Pg ± ± ± ± ± ± NG NG λ g λ NG λ ba ± μ j SF j v, R ν p b L u, S u p b g Duas λ L λ g λ L λ NG λ ba ± SF j μ j 6

4 The basc step sets the prce c λ = c λ = g g L Repeatng the same anayss for the shortage varabes u g g ν b L p b λ = p λ = g L From the actvtes Pg and L = λ g +λ NG + λg = λ g = λ NG + g Smary = λ L NG L = λ =λ + λ 7 The margna vaue of consumpton s reduced by the expected margna osses ncurred due to contngences or c L λ = λ NG L = λ = λ L NG = + p = b p ν L b ν L The expected margna vaue of eectrcty s. ν EMVL = ( p ) cl p bl = = When L s not basc ν EMVL = ( p ) λl p bl = = 8

5 u P, L, R g The objectve functon wth second-stage varabes removed u P, L, R g max,, S, ν N nb N no cl L = = = = A Lagrangan wth the removed constrants ncuded and weghted by ther duas max,, S ν, λ and g λl N nb N no cl L cg Pg λ g P g λ = = = = ' ' c g P g L L are the ogca counterparts to the LMP s n the current aucton modes Comments Even though the frst-stage prces better represent the economcs of the maretpace, they st do not euate prce wth margna vaue Changng prces wth each contngency woud add greaty to the voatty of the prces of one of the most voate commodtes Gvng credts to consumers to account for the oss of surpus durng a contngency reures a tax on consumers to create a reserve to pay for osses

6 4 46 G G 63 G G G3 G6 3 G 3 7 G G G3 4 6 G 8 6 G6 G4 3 G G7 Scae on oad-oss costs... 3 Tota demand Number of postve shortage actvtes Tabe : Tota demand and number of postve shortage actvtes n the souton.

7 Node\Scae... 3 Node 7 Node Node Node Node 7 Node Node Node Tabe : Seected LMP s n oad nodes as a functon of shortage costs, measured n [$/MWh], based on the oad duas from constrant (3). These duas are the maret-cearng prces for the day-ahead aucton. 3 Node\ Scae... 3 Node Node 6 Node Node 63 Node Node Node 66 Node 67 Node Tabe 3: Seected duas at generaton nodes (LMP s), measured n [$/MWh], based on constrant (), as a functon of shortage costs. 4

8 Node\Scae... 3 Node Node Node Node Tabe 4: Dua varabes that ncorporate the effect of osses due to shortages and are the expected vaues of eectrcty at each node n [$MWh], whch are ower than the aucton prces n Tabe. Node\Scae N N.. N N N4.6 N N N Tabe : Demand eves at seected nodes n [MWh]. 6

9 Surpus\Scae... 3 Transmsson Generaton Load Tota surpus Tabe 6: Rents and Surpuses for Transmsson, Generaton, and Demand ($) 7

MARKOV CHAIN AND HIDDEN MARKOV MODEL

MARKOV CHAIN AND HIDDEN MARKOV MODEL JIAN ZHANG JIANZHAN@STAT.PURDUE.EDU Markov chan and hdden Markov mode are probaby the smpest modes whch can be used to mode sequenta data,.e. data sampes whch are not