Modified Method of Computing Generator Participation Factors by Electricity Tracing with Consideration of Load Flow Changes

Transcription

1 WSEAS TRANSACTIONS o OWER SYSTEMS Mauscrpt receved Aug., 007; revsed Oct. 0, 007 Modfed Method of Computg Geerator artcpato Factors by Electrcty Tracg wth Cosderato of Load Flow Chages N.D.GHAWGHAWE Departmet of Electrcal Egeerg Departmet Vsvesvaraya Natoal Isttute of Techology Nagpur, (Maharashtra) INDIA Emal:g_t@redffmal.com rof.k.l.thakre Departmet of Electrcal Egeerg Departmet Vsvesvaraya Natoal Isttute of Techology Nagpur, (Maharashtra) INDIA Emal:k_thakre@yahoo.com Abstract: - Ope access s a essetal feature the deregulated power system. It permts all the geerators to trasmt power to the system. Depedg upo the trasmsso etwork parameters, geerator resposes to the varato loads dffer from each other. To kow these resposes s mportat from varous aspects such as for determato of odal prces whch wll be eeded chargg dfferetal tarffs ad also cogesto maagemet. By cosderg the load flow chages due to chage load at a bus, electrcty tracg s appled to compute the geerator partcpato factors. A ew algorthm of proportoal sharg prcple s developed. A sestvty aalyss s proposed to determe these chages power flows due to chaged load. Ths ew approach for determato of geerators partcpato could be more approprate whe compared wth the other method based o proportoal sharg prcple of electrcty tracg Key-Words: - Deregulato, Geerator artcpato Factors, Electrcty Tracg, roportoal Sharg rcple, Sestvty Aalyss Itroducto I a deregulated power system, ubudlg of the geerato, trasmsso ad dstrbuto systems has vted varous problems as regards to the plag ad operato of a trasmsso frastructure. Whle provdg the ope access to the market partcpats, the geerato compaes ca trasmt the power as per the chages load demads. Sce the geerator cost fuctos are ot same, the ssues related to dfferetal power tarffs may become more complex. Also due to free tradg, some of the les may get overloaded thereby causg etwork cogesto. The cogesto maagemet model cosderg demad elastcty s proposed []. The prcg ssues ad cogesto maagemet could have bee effectvely met f the partcpatos of every geerator sharg the chages load were kow. Although tracg the partcpato of geerators loads s ot possble, the relatoshps betwee the chage load ad geerator power chages ca be establshed. The cotrbuto of geerators to the loads ad le flow s descrbed []. A techque s proposed wth the help of whch t could be possble to trace the power produced by the geerator. I ths techque, the buses whch are reached by the power produced from each geerator are frst detfed ad the the set of buses suppled by same geerators are determed. A proportoalty prcple was assumed to determe the sharg of geerators. A systematc approach has bee proposed [3]. Usg proportoal sharg prcple, the le flows are traced ad the cotrbuto of each geerator loads s determed. Smultaeously, sharg of loads each geerator s also determed. Upstream lookg ad dowstream lookg algorthms are proposed to trace the electrcty. 33

2 WSEAS TRANSACTIONS o OWER SYSTEMS Applcato of power tracg has bee used to compute the eergy ad coecto costs []. I [5], proportoal sharg prcple of tracg power flows has bee ratoalzed. It s show that Shapley value soluto cocept satsfes the prcple of proportoal sharg. Smlar research s foud to be [6]. A ew power flow tracg ad loss allocato method based o loop aalyss s proposed [7]. I all these researches, so as to kow the partcpato of geerators or loads, the load flow soluto must be kow. The research s very much sutable to the stadstll codto of a power system. Whe the system load s chaged, the chages system losses are allocated ot oly to the chaged load but to the other loads also. Ths approach of proportoal sharg of chaged load wll ot be accurate from the pot of vew of chargg the prces for loss allocato whe the load s chaged. Sce the power system behavour s dyamc ature, a modfed approach s eeded to determe the partcpatos of geerators. I ths paper, a sestvty aalyss approach wth proportoal sharg prcple s proposed. It ca compute the chages power shared by geerators for the chages loads. Also the chages losses due to chaged load are allocated to the chagg load oly. Ma obectve of ths paper s to prove that proportoal sharg prcple as proposed by Balek [3], ca also be appled wth cosderato of oly chages le flows, especally for cotuously chagg load codtos. A smple approach of sestvty aalyss ca be appled to determe these chages. Algorthms of proportoal sharg prcple wth ormal ad chaged load flow codtos have bee developed ad mplemeted MATLAB. roportoal Sharg rcple I a meshed structure, electrcal power ca flow from source to sk through umber of optoal paths. The electrcty tracg method s very much detcal to a geeral trasportato problem. The tracg of power from dvdual geerator to dvdual load s hghly mpossble. But the physcal paths lkg the geerators ad loads ca be establshed. Two dfferet approaches are explaed [5]. These are dowstream ad upstream lookg algorthms. The study ths paper s restrcted to upstream lookg algorthm oly. Cosder the four braches are coected through ode k, as show Fg.. Let p, p, p 3 ad p be the real power flows through -k, -k, k-m ad k- respectvely. p k p p p 3 Fg.. ower Flow through Braches Whle applyg the proportoal sharg prcple, t s assumed that the ode, to whch dfferet braches are coected (here t s ode k), s a perfect mxer. The comg power s proportoally dstrbuted through the braches wth outgog powers. Obvously p + p = p 3 + p, thereby satsfyg Krchoff s curret law. p 3 s the sum of shares of p ad p. Share of p p 3 wll be p p p ad that of p wll be, p. p + p 3 p + p 3 power p 3 ca be, p p p = p + p p + p p + p Smlarly, p wll be, p p p p p = + p + p p + p m () () roportoal sharg prcple ca be exteded to etre etwork to trace the cotrbuto of comg flows the outgog flows. A upstream lookg algorthm wth the cosderato of gross powers s explaed below.. Upstream lookg algorthm wth gross power flows I ths approach odal balace of flows s cosdered. It ca compute the sharg of geeratos the loads ad the loss allocato to the loads as well. Defg the followg terms- ( gross ), - power flow through ode ad respectvely whch satsfes KCL ad whch would flow through etwork whe the etwork s fed wth actual geerato wthout ay power loss., -Gross power flows le - odes ad respectvely whch would flow uder lossless codto. It gves, = 3

3 WSEAS TRANSACTIONS o OWER SYSTEMS, - Actual power flow through ode ad respectvely, cosderg losses, - Actual power flows through le - from odes ad respectvely, cosderg losses - geerato at ode G - demad at ode L α -The set of odes supplyg drectly ode (.e. the set of odes from whch the power flows towards ) β -The set of odes supplyg drectly from ode (.e. the set of odes towards whch the power flows from ) The gross odal flow whe lookg at the flows ca be expressed as, = + (3) G α =,,3. Sce rewrtte as, = ad rearragg, (3) ca be = + G α () Sce the trasmsso le losses are small, the rato of gross power flow over the le - to the total power flow, ca be approxmated as, Thus () ca be wrtte as, = (5) G α If gross s the vector of gross odal flows, A s the upstream dstrbuto matrx of order x ad G s the vector of geeratg powers, the (5), matrx form wll be, G =A. gross (6) The elemets of A ca be obtaed as, for = [ A] = for α (7) 0 otherwse If A - exsts, gross = A -. G (8) th elemet of gross wll be, = (9) k k = A Cotrbuto of the k th geerator to th odal power s A k. Oce the gross odal flows are determed as gve by (9), gross le flows ad gross demads ca be foud usg proportoal sharg prcple. The gross flow le -l ( l β ) wll be l l = l or l l k k = A (0) Obvously, cotrbuto of the k th geerator to (l) th l elemet wll be. A. k Gross demad at ode wll be, L L k k= A () ad cotrbuto of k th geerator to load coected at th L ode wll be. A. k. Further, gross losses, allocated to load at th bus ca be obtaed as, = () loss L L To aalyze the dyamc behavour of the system, chages the geerato ad load flows are requred to be determed. After applyg proportoal sharg prcple as explaed above, partcpato of chages of geerator powers the chages at loads ca be determed. However for determato of oly chages le flows, a sestvty aalyss approach would be more sutable. 3 roportoal Sharg rcple Appled to Chages Le Flows Sestvty aalyss has bee used may of the power system applcatos. Sestvty studes are used for determg dfferet customer outage cost fuctos sub-trasmsso systems [8]. Whe load at bus s chaged, power flows over the les, chage accordg to etwork behavour. These chages ca be drectly obtaed by power flow sestvty aalyss [9]. Thus for a chage power ( k ) at a load bus, correspodg chages geerator powers ad load bus voltages ad agles ca be obtaed usg, 35

4 WSEAS TRANSACTIONS o OWER SYSTEMS g, Qg, Vl, θl = Vg, θg, l, Ql S (3), Q -Chage Actve ad Reactve power at g g geerator buses, Q - Chage Actve ad Reactve power at l l load buses V, θ -Chage Voltage ad Agle at geerator g g buses V, θ -Chage Voltage ad Agle at load l l buses S- Sestvty matrx Smlarly chages le currets ca be gve by, [ I ] = [ R ] Vg, Vl, θg, θ l () I -Chages Currets of varous les R -Curret Sestvty Matrx The correspodg chage power flow, over the le - ca be determed thereafter. Now cosder that, proportoal sharg prcple s to be appled to the chages le flows stead of le flows, These chages ca be obtaed drectly by sestvty aalyss as above. Drectly from (), chage the gross demad wll be gve as, L L d k k = A (5) -Chage actual demad at ode L, -Chage actual power flow through ode ad respectvely by cosderg losses -Chage total geerato at ode k, - Chage actual power flows through le - from odes ad respectvely by cosderg losses. The elemets of matrx A d ca be obtaed as, for = A = for d α (6) 0 otherwse Cotrbuto of chage the geerato of k th geerator to chage load coected at th ode wll be, L =. A d k (7) Further, chage gross losses, allocated to chage load at th bus ca be obtaed as, = (8) loss L L Thus sharg of chages at all the geerators for the specfc chages loads ca be obtaed by (8). For such determato chages le flows s the oly requremet whch ca be determed by sestvty aalyss as proposed secto III. Case Study 6-bus system as show Fg. s dscussed detaled to compute the geerator sharg. Buses, ad 3 are the geerator buses where as buses, 5, ad 6 are the load buses. It s desred to obta the sharg of chages loads by the geerators. Fg.. A 6- Bus System 5 Results Sharg the geerators by loads, total geerator partcpatos ad losses allocato for the chage load at a bus ca be obtaed by applyg proportoal sharg prcple wth ) Covetoal approach (takg the dfferece of load sharg before ad after applyg the chage load) ad ) Sestvty aalyss (by applyg the proportoal sharg prcple drectly to the chages le flows). 5. Sharg Obtaed by Covetoal Approach I ths approach proportoal sharg prcple s appled at two dfferet load codtos. For a specfc load codto, a load flow s obtaed by Newto-Raphso method. For ths load flow, proportoal sharg prcple s appled as explaed secto-i. The sharg of loads by geerators s metoed Table-I. Further, load at bus s chaged by a amout of 0MW. Aga the sharg s obtaed as earler. The sharg of chaged load by geerators s gve Table-II. Dffereces of the sharg gve Table-I ad Table-II, are metoed Table-III. These values represet the sharg of chages load at by the geerators. Last row of the colums G, G ad G3 of ths table represets the geerator partcpatos for the specfed chage load at bus. Last colum represets the losses allocated to the varous loads. Implemetato of algorthm s made 36

5 WSEAS TRANSACTIONS o OWER SYSTEMS MATLAB. rogram BSHARE computes the sharg of loads geerators. Table-I Sharg at Base Load Flow (Load Flow Obtaed by NR method) Sharg by G G G3 Allocato L L L Table-II Sharg at Chaged Load (Load Flow Obtaed by NR method) Sharg by G G G3 Allocato L L L Table-III Sharg at Chaged Load (Load Flow Obtaed by NR method) Sharg by G G G3 Allocato L L L Sharg Obtaed by Applyg roportoal Sharg rcple to the Chages Le Flows I ths approach, proportoal sharg prcple s appled to the chages load flow as obtaed by sestvty aalyss. For the gve system, at the tal load codto load flow s obtaed. After applyg the same amout of 0MW chage load at bus, chages le flows are determed by sestvty aalyss. roportoal sharg prcple wth modfed algorthm s appled to theses chages to determe the sharg of chages load at bus, by geerators. These values are gve Table-IV. Last row of the colums G, G ad G3 of the table represets the geerator partcpato for correspodg chage the load. Last colum represets the losses allocated to the loads. The algorthm s mplemeted MATLAB ad results are obtaed by the program SENSSHARE, developed by the authors. Table-IV Sharg of Chage Load of 0 MW at bus (roportoal Sharg rcple appled to Load Flow Chages, obtaed by Sestvty Aalyss) Sharg by G G G3 Allocato L L L The load flow values requred to obta the sharg by geerators ca also be obtaed usg ower World Smulator 8.0. They are very smlar to that of metoed tables I to IV. The partcpatos by the geerators for chage loads are cosdered as of ma mportace. They are preseted graphcally Fg. 3 to 5. These fgures show a comparso of geerator partcpatos as obtaed by sharg prcple alog wth NR Load Flow (rogram BSHARE), Sestvty Aalyss (rogram SENSSHARE) ad ower World Smulator 8.0. artcpato NR Load Flow Sestvty Aalyss WS Geerators Fg.3 Geerator artcpatos by Varous Methods (0 MW chage at bus ) artcpato NR Load Flow Sestvty Aalyss WS Geerators Fg. Geerator artcpatos by Varous Methods (0 MW chage at bus 5) 37

6 WSEAS TRANSACTIONS o OWER SYSTEMS artcpato NR Load Flow Sestvty Aalyss WS Geerators Fg. 5 Geerator artcpatos by Varous Methods (0 MW chage at bus 6) 6 Cocluso roportoal sharg wth upstream lookg algorthm ad gross power flows s appled to IEEE 6-bus system. The covetoal algorthm s modfed by cosderg oly the chages at a load. The system s smulated by both of these algorthms to determe the sharg of geerators the loads, geerator partcpatos ad allocato of losses to the loads, for the specfed chages loads. Usg the covetoal algorthm, from table III, t s see that, the chaged load s proportoally shared by the geerators. But chages losses are allocated to other loads also, although the percetage s less. roportoal sharg prcple wth modfed approach ca determe the sharg of geerators the chaged load. It s see from the table IV that chages geerator power correspod to the respectve loads oly. Smlarly the losses due to chaged load are allocated to the correspodg load bus oly. Ths modfed approach of computg geerator partcpatos s foud to be more accurate ad should be appled for cotuously chagg loads. It s see from the fgures to 6 that the total geerator partcpatos for the chages loads are almost same whe obtaed by covetoal (NR Load Flow), the modfed algorthms (Sestvty Aalyss) ad the ower World Smulator 8.0. Whle cosderg the prcg ssues, to compute the allocato of losses for the load chages, modfed algorthm s more approprate. I the deregulated evromet, the ew proposed method could be applcable to modfy the trasfer capablty by cotrollg the geerator partcpato factors. It would further assst maagg the etwork cogesto. ower Systems, Lsbo, ortugal, September -, 006, pp [] Krsche D., Ro Alla, Gora Strbac, Cotrbuto of Idvdual Geerators to ad Flows IEEE Trasactos o ower Systems, Vol. No., Feb. 997, pp [3] Balek J., Tracg the Flow of Electrcty IEE roceedgs of Geerato Trasmsso ad Dstrbuto, Vol.3 No., July 996, pp [] Malak M., Shra R., Sahkal H., New Approach for Determato of the Eergy ad Coecto Cost at the ower Grd Nodes IEEE ower Egeerg Socety Summer Meetg 00, pp [5] Balek J., Kattuma.A., roportoal Sharg Assumpto Tracg Methodology IEE roceedgs of Geerato Trasmsso ad Dstrbuto, Vol.5 No., July 00, pp [6] Balek, J.: Topologcal geerato ad load dstrbuto factors for supplemet cost allocato trasmsso ope access, IEEE Tras. ower Syst., 997,, pp [7] Valere S.C. Lm, Joh D.F. McDoald, ad Tapa K. Saha, Applcato of Loop Frame of Referece to ower Flow Tracg ad Loss Allocato Iteratoal Joural of Emergg Electrc ower Systems, Vol. 5 No., 006, pp. -7. [8] R. Gupta, L. Goel ad M. F. Erca, Sestvty Study of Well-Beg Based Relablty Worth for Dfferet Customer Outage Cost Fuctos Sub-Trasmsso Systems roceedgs of the 6th WSEAS/IASME Iteratoal Coferece o Electrc ower Systems, Hgh Voltages, Electrc Maches (ower '06), Teerfe, Caary Islads, Spa, December 6-8, 006, pp.-9. [9] Ghawghawe N.D., ad Thakre K.L., Applcatos of ower Flow Sestvty Aalyss ad TDF for Determato of ATC, roc. IEEE Iteratoal Coferece o ower Electrocs, Drves ad Eergy Systems (EDES-006) -6 Dec Refereces: [] T.S. Chug D.Z. Fag X.Y. Kog ower Market Cogesto Maagemet Icorporatg Demad Elastcty Effects roceedgs of the 6th WSEAS Iteratoal Coferece o 38