Cost Allocation of Losses in Autonomous Power Systems with High Penetration of RES

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1 roceedngs of the 9th WSEAS Internatonal Conference on OWER SYSTEMS Cost Allocaton of osses n Autonomous ower Systems wth Hgh enetraton of RES K.A. AADOGIAIS ACRO td Kypron Agonston 33 str, 645, Athens GREECE kp@acron.gr E.S. KARAIDAKIS Department of atural Resources and Envronment Technologcal Educatonal Insttute of Crete Romanou 3 str, 7333, Chana GREECE karapdaks@chana.tecrete.gr HATZIARGYRIOU Department of Electrcal and Computer Engneers atonal Techncal Unversty of Athens Iroon olytexneou 9 Str., 5773, Athens GREECE nh@power.ece.ntua.gr Abstract: - Cost allocaton of losses n power networks s an essental ssue especally under modern electrcty markets wth hgh penetraton of renewable energy sources (RES). Ths paper proposes the applcaton of an effcent loss allocaton method developed to evaluate the margnal loss coeffcents of dspersed generaton. The coeffcents provde the contrbuton to the actve and reactve losses of each producer/consumer n order to defne the respectve tarffs. One nnovatve feature of the proposed loss allocaton method s that, unlke other proposed approaches, t s rrespectve of the reference bus selecton and takes n consderaton the mpact of reactve flows on actve power losses. Crete's power system has been consdered as a representatve study case for the demonstraton of the presented method. Key-Words: - Dstrbuted generaton, margnal loss coeffcents, hgh renewable energy penetraton, transmsson and dstrbuton loss allocaton. Introducton Under ongong deregulated and compettve energy markets, power systems need hgher operaton standards. Consequently, modern electrc energy systems should operate under strong envronmental restrctons n parallel wth adequate servce relablty at lower possble costs. Addtonal to the current structural changes, dspersed generaton augments ts penetraton nto power dstrbuton systems, []. In [2] some of the reasons for an ncreasng share of dspersed generaton n dfferent countres has been summarzed. The presence of dspersed generaton n dstrbuton systems alters radcally the way these networks should be consdered from both techncal and economcal aspects. Dstrbuted generaton and especally dspersed generaton of renewable energy sources can provde sgnfcant benefts, such as mproved system relablty and enhanced power qualty. Addtonally, dspersed generaton could ncrease system effcency through co-generaton and local voltage support, whle under specfc condtons could even decrease network operatonal cost. Generally, the dspersed generaton changes dstrbuton networks from passve networks, wth power flows from hgher to lower voltage levels, nto actve networks wth mult-drectonal power flows. Furthermore, transmsson and dstrbuton nfrastructures requre specfc economc regulatons n order to hold access prce near the margnal cost and to provde full-powered ncentves mnmsng total costs, [3]. ISS: ISB:

2 roceedngs of the 9th WSEAS Internatonal Conference on OWER SYSTEMS On of the most mportant condtons for an essental competton development s a nondscrmnatory access to the avalable transmsson and dstrbuton networks by all the system's supplers. Ths s a network prcng ssue [4], where network cost comprses of nvestment cost, congeston cost and operatng cost, part of whch s the cost of losses. The allocaton of ths sgnfcant cost to each ndvdual generaton and/or load s n essence the allocaton of responsblty for system losses. A large number of methodologes dealng wth cost allocaton problem of transmsson servces have been descrbed [5-9] and certan maturty has been obtaned n ths area. Furthermore, snce the advent of compettve electrcty markets, several methods have been proposed for loss allocaton. More precsely, these are: the proportonal sharng loss formula, the pro rata method, the ncremental transmsson loss, and the ncremental blateral contract path. The proportonal sharng technque [0-] provdes a computatonally effcent procedure for loss allocaton, t fals to satsfy the economc effcency objectve, as no messages are conveyed to users regardng costs they mpose on the system. In [2] the proposed method tres to overcome the prevous dffcultes, by establshng drect relatonshp between losses n each branch of the network and njected actve and reactve power n the nodes on whch path to the power supply pont the branched s placed. The pro rata loss allocaton method has been appled n the electrcty markets of manland Span [3] and England and Wales [4]. The method does not consder the relatve locaton of the generators and the loads. Ths method has a benefcal mpact to remotely located generators or loads n contrast to all others. In the ncremental technques [5] the loss allocaton depends on the choce of the reference bus and the drect applcaton of the coeffcents leads to an over-recovery of losses. A loss allocaton scheme for blateral contracts s proposed n [6] where approxmatons are poor f the electrcal dstance between the contractors s small. In the context of multlateral trades [7] a loss allocaton method based on a quadratc approxmaton of losses s proposed. In [8], the proposed loss allocaton formula, leads to sgnfcant dfferences between losses calculated from AC power flow soluton and those obtaned from the proposed method, because of the several approxmatons assumed. All these methods do not address the ssue of the choce of the reference bus and ts mpact on loss allocaton and moreover, most of these schemes gnore the mpact of reactve flows on actve power losses. In [9] the loss allocaton method based on margnal losses has been proposed, whle n [20] a method that apples the same concept as n [9], determnes the prces at dfferent nodes n the dstrbuton networks usng nodal factors. In ths paper, loss allocaton method based on the concept of margnal cost s nvestgated. The method provdes loss allocaton factors for both actve and reactve power enablng the contrbuton of actve and reactve power consumpton and generaton to system losses to be quantfed. Furthermore, the factors can be postve or negatve reflectng the user s mpact on losses, whch s essental n addressng the mpact of counter flows, preventng thus temporal and spatal cross-subsdes. A mechansm s also proposed for neutralzng the mpact of choce of reference node on the magntude and the polarty of loss allocaton factors by apportonng total losses equally between generators (ncludng the reference node) and loads. 2 roblem Formulaton Accordng to the economc theory the margnal losses reflect the Short-Term Margnal Costs (STMC) and therefore acheve short-term economc effcency [9-20]. The margnal loss coeffcents (MC s) are senstvty factors measurng the change of total actve losses when a margnal change n consumpton/generaton of actve and reactve power Q occurs at each node n the network. Then: α =, αq = Q () where α and α Q are the actve and reactve MCs, respectvely. For the voltage control nodes (V) there are no loss related charges for the reactve power they nject n the system. There are no loss related charges for the reference bus as well, such as the njected/absorbed power to keep the system n power balance after changes n njectons n other nodes. Ths s expressed by: r Q = Q r = 0, { V } = 0,r reference bus (2) (3) ISS: ISB:

3 roceedngs of the 9th WSEAS Internatonal Conference on OWER SYSTEMS The calculaton of MCs s based on a solved power flow n a partcular operatng pont of the system. The voltages and angles are used as ntermedate state varables as there s no explct relatonshp between losses and power njectons. Applyng the standard chan rule, the followng system of lnear equatons gves the MCs. θ Q α α θ θ θ = = Q α V α Q Q Q θ Q θ (4) where the frst term s the transposed Jacoban T J. matrx [ ] The approxmately quadratc relatonshp between losses and power flows s responsble for the twce amount of losses calculated applyng the MCs to the followng equaton: α + α Q Q 2 = V, = ref (5) where s the actve power njecton and the reactve power njecton at node, respectvely. A smple reconclaton method s to apply a constant multpler n the order of 50% to both MC s. Thus, the vectors of MCs, α M and α QM reconcled by the constant scalng factor κ M 0. 5: α M = κ M α and α QM = κ M α Q (6) loss allocaton related factors by constant factors and respectvely a gven generator loss contrbuton rato can be acheved, as shown n [9]. For equal overall dvson of losses between generaton and losses a value of equal to 0.5 should be used. The fnally allocaton of the total system actve power losses to ndvdual users, rrespectve of choce of reference node s gven from the followng equaton: ( α M + δ ) + ( QM + Q ) Q α δ = = V, ref Thus, the reconcled MC s are fnally gven by: MC MC (8) = α M + δ (9) Q = α QM + δq (0) eglectng the reactve MCs, the Actve Margnal Values or Actve Addtonal Values and the revenue for each generator calculated as follows: AAV REV g ( M + ) g Π = MC g Π I = α δ () ( MC ) = Π g AAV = Π g (2) where Π s the prce n /kwh and g n MW. The dfference of the revenues assessed before and after the MC s applance gves the revenue percentage change. enable the allocaton of the total system actve power losses to ndvdual users such that: RC g [ REV Π ] g g Π g = 00 (3) α M + α QM = = V, ref Q (7) Reconclaton by constant multpler factor has the tendency to weaken economc sgnals by dmnshng prce dfferentals between nodes. The assumpton that the MCs at reference node are zero, has as consequence the dependence of MCs, n terms of magntude and polarty, from the choce of reference node It s mportant for the method to be consstent by yeldng consstent values of MCs rrespectve of choce of reference node. By shftng both actve and reactve power 3 Case Study In order to nvestgate and estmate the applcablty, the accuracy and the overall effectveness of the presented method a network wth sgnfcant dspersed generaton and substantal RES penetraton s needed. Crete's power system s one of the most representatve case studes for an essental demonstraton of the Margnal oss Allocaton method. 3. ower System of Crete Grete s the largest Greek sland wth approxmately Km2 and one of the largest n Medterranean ISS: ISB:

4 roceedngs of the 9th WSEAS Internatonal Conference on OWER SYSTEMS regon. Its populaton s more than 600,000 nhabtants that trple n summer perod. Fg. depcts the tme evoluton of load demand and energy consumpton, usng offcal long-term data ( ). It s clear that there s a consderable annual ncrease of electrcty demand approachng the 7% durng the last decade, when the correspondng natonal fgure s 3.5%. As a result, the annual energy consumpton durng 2008 surpassed the 3TWh n comparson wth the modest 280 GWh of year 975. Addtonally, there are 25 wnd parks nstalled wth nomnal power of 24,85MW n specfc and approprate regons of the sland (Fg. 3). These Ws are connected to the grd through HV/MV substatons of 20kV/50kV. Fg. 3 ower plants and wnd parks locatons Fg. oad Demand and Energy Consumpton Tme Evoluton In addton, comparng the mean hourly load demand varaton all year round, there s a consderable electrcty generaton dversfcaton between months and seasons, as t s clearly shown n fgure 2. Fg. 2 Monthly varaton of mn and max load demand However, even durng the low consumpton perods, mnmum load demand s greater than current system techncal mnmum (approxmately 00 MW). Island's electrcty generaton system s based manly on three (3) ol-fred thermal power unts, located as t s shown n Fg. 3. The offcal capacty of the local power plants s MW, although the real power of the system s 693 MW for wnter and 652 MW for summer operaton. Fg. 4 One-lne dagram of Crete's power system One-lne dagram shown n Fg.4 s a realstc model of the power system of Crete. The model conssts of 64 bus-bars, 20 generator (V) buses, 25 wnd power generator buses and 33 load (Q) buses. The conventonal generaton system conssts of three (3) thermal power plants havng four groups of generatng unts. More precsely, power system conventonal generaton s based on sx (6) relatvely outmoded steam turbnes of total capacty amountng at.25 MW, one combned cycle power unt of 35 MW and four (4) nternal combuston engnes (desel unts) of 49 MW. The techncal mnma of all these unts are approxmately 00 MW, excludng the annual servce perods. The annual peak load demand occurs on a wnter day and overnght loads can be assumed to be approxmately equal to 25% of the correspondng daly peak loads. The steam and desel unts manly supply the base-load. The Gas turbnes normally supply the daly peak load or the load that cannot be suppled by the other unts n outage condtons. These unts have a hgh runnng cost that ncreases sgnfcantly the average cost of the electrcty beng suppled. ISS: ISB:

5 roceedngs of the 9th WSEAS Internatonal Conference on OWER SYSTEMS Fg. 5 Wnd power penetraton n power system of Crete Fg. 7 Revenue percentage change (RC) for the st day In Fg.5 the wnd power producton n parallel wth the overall producton n a specfc day wthn 2008 s presented. In ths case the porton of the correspondng wnd generaton vares between 22% and 32% of the total power supply that s consdered as a sgnfcant hgh penetraton for an autonomous system such as Crete's network. 4 Results MCs calculatons are based on actual loads and generatons tme seres n the perod Aprl-June In ths secton the results obtaned, for three days wth smlar load profle, of the month Aprl and for 24hours are presented. The W/ nodes consdered s node 58 Xerolmn as the most remote bus of the network and node 47 Moula, the only centrally located. Fg. 6, 0, and 4 llustrated the load and the generaton profles of each day. It has to be mentoned that n Fg. 4 the wnd power generaton should be dvded by 00 (as shown n fgure capton). Fg. 7,, and 5 llustrate the revenue change that can be acheved for each day, applyng the loss allocaton method. The related to actve and reactve njectons MC s tme seres are llustrated n Fgs. 8, 9, 2, 3, 6, and 7. Fg. 8 MCfs related to actve njectons and AAVfs at bus Moula for the st day Fg. 9 MCfs related to actve njectons and AAVfs at bus Xerolmn for the st day Fg. 0 System load profle and actve power generaton from Wnd arks for the 2nd day Fg. 6 System load profle and actve power generaton from Wnd arks for the st day ISS: ISB:

6 roceedngs of the 9th WSEAS Internatonal Conference on OWER SYSTEMS Fg. 5 Revenue percentage change (RC) for the 3rd day Fg. Revenue percentage change (RC) for the 2nd day Fg. 6 MCfs related to actve njectons and AAVfs at bus Moula for the 3rd day Fg. 2 MCfs related to actve njectons and AAVfs at bus Moula for the 2nd day Fg. 7 MCfs related to actve njectons and AAVfs at bus Xerolmn for the 3rd day Fg. 3 MCfs related to actve njectons and AAVfs at bus Xerolmn for the 2nd day Fg. 4 System load profle and actve power generaton from Wnd arks for the 3rd day It can be seen from the load profle and the revenue percentage change for each day that the actve power njectons at low load tme perods decrease the revenue percentage change for the Wnd arks. In some cases as llustrated n Fgs. 8 and 4 and for the low load early hours the remote node 58 Xerolmn wll be penalzed. On the contrary, actve power njectons at hgh load ncrease revenues. It s very nterestng to notce that for the 3rd day when penetraton s very low both nodes as llustrated n Fg. 3 should be rewarded. These conclusons concern only the three studed days and they are not general conclusons for the MCs. In long term, the ncrease of revenues due to loss allocaton can be qute consderable. The average revenue ncrease for a Wnd ark typcal day s approxmately equal % to 2%. In hgher load or extreme operatng condtons a 5% ore more ISS: ISB:

7 roceedngs of the 9th WSEAS Internatonal Conference on OWER SYSTEMS 5 Concluson Cost allocaton of losses n power systems' network n case of dspersed generaton and hgh penetraton of renewable energy resources s a complex problem whose mportance may ncrease as competton n power generaton ntensfes. Ths paper through comprehensve and comparatve studes for cost allocaton of losses presents the applcablty and the effectveness of a loss allocaton method, based on the concept of margnal cost. The method provdes approprate sgnals to the network users n order to take economcally effcent operatng decsons. The choce of reference node has no mpact on the magntude and the polarty of loss allocaton factors. The method s effcent and easy to mplemented, whle tests results on a representatve power network such as power system of Crete sland demonstrate the effectveness of the method are lookng forward to seeng you at the Conference. References: [] G. Strbac, Impact of dspersed generaton on dstrbuton systems: a European perspectve, ower Engneerng Socety Wnter Meetng, vol., 2002, pp [2] CIGRE Study Commttee, Impact of Increasng Contrbuton of Dspersed Generaton on the ower System, Fnal Report WG 37-23,.37, 998. [3] S. Stoft, ower System Economcs, scataway J: IEEE Wley Interscence ublcaton, [4] Fnal rogress Report, Electrcty Tarffs for Embedded Renewable Generaton, JOUE III roject JOR3-CT98-020, [5] F. Schweppe, M. Caramans, R. Tabors, and R. Bohn, Spot rcng of Electrcty. orwell, MA: Kluwer, 988. [6] H. H. Happ, Cost of wheelng methodologes, IEEE Trans. ower Systems, vol.9, no., 994, pp [7] H. Rudnck, R. alma, and J. Fernandez, Margnal prcng and supplement cost allocaton n transmsson open access, IEEE Trans. ower Systems, vol.0, 995, pp [8] F. J. Rubo and I. érez-arraga, Margnal prcng of transmsson servces: A comparatve analyss of network cost allocaton methods, IEEE Trans. ower Syst., vol. 5, 2000, pp [9].M.De Olvera-De Jesus and M.T. once de eao, ong Term Cost Allocaton Methodology for Dstrbuted etworks wth Dstrbuted Generaton, 5th SCC, ege, August, [0] J. Balek, Tracng the flow of electrcty, IEE roceedngs, Generaton, Transmsson and Dstrbuton, vol.43, no.4, 996, pp [] D. Krschen, R. Allan, and Strbac, Contrbutons of ndvdual generators to loads and flows, IEEE Trans. on ower Systems, vol. 2, no. 2, 997, pp [2] Metodja B. Atanasovsk and Vesna. Borozan, ew Method for Allocaton of osses n Dstrbuton Systems wth Dspersed Generaton, Sofa, Bulgara, 29 June July 2006, pp [3] J. J. Gonzales and. Basagot, Spansh power market and nformaton system. Desgn concepts, and operatng experence, n roceedngs of the 999 IEEE ower Industry Computer Applcatons Conference, Santa Clara, USA, 999, pp [4] J. W. Balek, S. Zemanek, and. Ab-Samra, Trackng-based loss allocaton and economc dspatch, n roceedngs of 3th ower Systems Computaton Conference, Trondhem, orway, 999, pp [5] F. Schweppe, M. Caramans, R. Tabors and R. Bohn, Spot rcng of Electrcty, Boston: Kluwer Academc ublshers, 988. [6] A. Zoban and M. Ilc, Unbundlng of transmsson and ancllary servces. art I: Techncal ssues, IEEE Trans. on ower Systems, vol.2, no.2, May 997, pp [7] F. Wu and. Varaya, Coordnated multlateral trades for electrc power networks: Theory and mplementaton, Unversty of Calforna Energy Insttute ower Report W- 03, 995. [8] G. Gross and S. Tao, A loss Allocaton Mechansm for ower System Transactons, presented at Bulk ower System Dynamcs and Controls IV Restructurng, Santorn, Greece, 998. [9] Mutale, J., Strbac, G., Curcc, S., Jenkns,., Allocaton of losses n dstrbuton systems wth embedded generaton, IEE roceedngs, Generaton, Transmsson and Dstrbuton, vol.47 no., Jan. 2000, pp [20] J. Maro Vgnolo and aul M. Sotkewcz, Allocaton of oss Costs n Dstrbuton etworks: The odal Factor rcng Method, Internatonal Journal of ower Systems, Vol. 0, o. 0, ISS: ISB: