Multiarea Transmission Cost Allocation in Large Power Systems Using the Nodal Pricing Control Approach

Transcription

1 Mutarea Transmsson Cost Aocaton n Lare Power Systems Usn the Noda Prcn Contro Approach Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 M. Ghayen and R. Ghaz Abstract: Ths paper proposes an aorthm for transmsson cost aocaton (TCA) n a are power system based on noda prcn approach wth mutarea scheme. The noda prcn approach s ntroduced to aocate the transmsson costs usn the noda prcn contro n a sne area network. As the number of equatons s dependent on the number of buses and enerators, ths method w be very tme consumn for are power systems. To sove ths probem, the present paper proposes a new aorthm based on mutarea approach for reuatn the noda prces, so that the smuaton tme s reaty reduced and therefore the noda prcn approach can be appcabe for are power systems. In addton, n the proposed method, the transmsson costs are aocated to the users more equtabe than the sne area method. Snce the hher transmsson costs of an area due to ts hher reabty are pad ony by users of that area n contrast wth the sne area method, n whch these costs are aocated to a users reardess of ther ocatons. The proposed method was mpemented on the IEEE 8 bus test system havn three areas. The obtaned resuts show that wth the appcaton of mutarea approach, the smuaton tme s reaty reduced and the transmsson costs are aso aocated to users wth ess varaton n new noda prces wth respect to the sne area approach. Keywords: Transmsson Cost Aocaton, Noda Prces, Lare Power Systems, Mutarea Approach. Introducton The noda prcn approach for transmsson cost aocaton s currenty deveoped wordwde. In ths approach the network revenues are equa to the transmsson rent (TR) and defned as the dfference between what the oads pay and what the enerators are pad. If the TR s cacuated by ocatona marna prces (LMPs), t w be termed as the marna TR. Marna prcn s n fact, a noda prcn whch s based on the LMPs and provdes the correct economc snas to oads, enerators and system operators towards the effcent use of the transmsson network. Here, the man concern s that the obtaned marna TR cannot recover the tota transmsson network costs (TNC). In a speca case of ossess network wth no transmsson coneston, LMPs at a buses are equa and so the marna TR becomes zero. However, even for a ossy network under transmsson coneston, there Iranan Journa of Eectrca & Eectronc Enneern, 2. Paper frst receved Au. 2 and n revsed form 8 Sept. 2. The authors are wth the Department of Eectrca Enneern, Ferdows Unversty of Mashhad, Mashhad, Iran. E-mas: mo_h82@stu-ma.um.ac.r, rhaz@um.ac.r. s no uarantee that the marna TR coud recover the TNC []. To sove ths probem, two approaches have been ntroduced. In the frst approach, the marna prcn s performed and then the uncovered costs,. e. the dfference between the TNC and marna TR, as a compementary cost, s aocated to network users n terms of ther extent of use of the network. Rubo- Oderz and Arraa have used ths approach to aocate the compementary costs usn both the partcpaton factor and the beneft factor methods [2]. Sedahat has defned the crtca capacty and then aocated the compementary costs by usn the modfed beneft factor method [3]. Guo et a. have used the power tracn method to aocate the compementary costs to network users [4]. In the second approach, LMPs can be adjusted to the new noda prces (NNPs) n such a way that the new obtaned TR coud recover the TNC. In Ref. [5] a comprehensve evauaton has carred out reardn ths approach. In ths reference the noda prces are controed to the new prces such that the TR becomes equa to the TNC and at the same tme the sum of prce devatons from marna prces s mnmzed. In ths method, the enerator and oad n each bus are ceared 238 Iranan Journa of Eectrca & Eectronc Enneern, Vo. 6, No. 4, Dec. 2

2 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 wth the same prce. So, at those buses n whch the NNP s ess than the LMP, oads pay ess and therefore receve a credt and at those buses the NNP s reater than the LMP, enerators are pad more and so receve credt. Ths cannot be far to a market partcpants snce some transmsson users et credt nstead of payn chare, accordny, these credts w mpose extra chare on some users eadn to more devaton of NNPs from LMPs. Furthermore, n ths reference the share of oads and enerators n TNC s tested ony for 5 percent, whe t does not work propery when the requested share s cose to zero or hundred percent. To sove these probems, the authors of present paper have ntroduced a new formuaton for TR n [6], so that the enerator and oad n each bus are ceared wth dfferent prces reardn the drecton of ther njected power. If the njected power s postve, the enerator s ceared by a new prce rather than the LMP whereas the oad w pay the prce based on the LMP. On the other hand, f the njected power s neatve, the cearn prce of oad s reuated to the new prce but the enerator s ceared by LMP. By consdern ths modfcaton, those users have a contrbuton n reducn the network fows (oads n the postve njected buses and enerators n the neatve njected buses), nstead of recevn a credt, do not pay the transmsson costs and thereby the approprate economc snas are provded. Therefore, ths coud ead to ess varaton n new prces than the method of Ref. [5]. The other advantae of ths method s ts fexbty to contro the cost spttn between oads and enerators for any pre-specfed rato from zero to hundred percent. However, the man drawback of these sne area methods [5 and 6] s that they are very tme consumn ones when dean wth are power systems as the number of constrants n optmzaton probem s reaty ncreased. The proram may take severa hours to be executed for such are power systems. Therefore, mpementaton of such methods for houry TCA n case of are power systems s not feasbe. To sove ths probem, n the present paper an aorthm s proposed n whch the mutarea framework s utzed to cacuate the noda prces, so t needs ony severa mnutes to do the job for are power systems. Consequenty, the noda prcn approach can be appcabe for are power systems as we. There are some papers dean wth varous probems usn mutarea approaches. Yu and Davd have used the senstvty factors and AC-OPF to aocate the transmsson costs n an nterconnected power system va mutarea framework [7]. G et a. have apped the equvaent batera exchane (EBE) method to aocate the transmsson costs n a mutpe nterconnected reons or countres [8]. Arraa has presented the reuatory prncpes of cross border tarffcaton n the European eectrcty transmsson network [9]. There are aso some papers assocated wth the transmsson oss aocaton usn the mutarea approaches. Sva and Costa have used the ncrementa transmsson oss concept for aocatn the eectrc osses to enerators and oads, partcpatn n mutpe nterconnected enery markets []. Baek et a. have apped the modfed tracn-based methodooy for aocatn the transmsson osses due to cross-border trades []. Kazem and Andam have used the Z-bus method to aocate the transmsson osses n mutarea networks [2]. Ths approach was further deveoped n [3] usn a new oss formua. Lma et a. have apped the EBE method to aocate the cost of transmsson osses n a mutmarket framework [4]. Wth reference to those papers tackn the TCA probem n mutarea framework t can be stated that none of them usn the noda prcn approach. In the present paper the mutarea approach s used to aocate the transmsson costs by our deveoped noda prcn method whch s fuy descrbed n [6]. Therefore, sovn the TCA probem for are power systems based on noda prcn approach n a mutarea framework s our man contrbuton. Our aorthm s not ony qute fast but t aso provdes further advantaes as foows. The proposed method aocates the transmsson costs n an equtabe manner n compare wth the sne area method. As some areas have a hher reabty, ther transmsson costs are aso hh and some others have a ower reabty so ther costs w be ess. Therefore, f the cost aocaton s made usn the sne area framework, the hher costs of the hh reabty areas are dstrbuted amon a users reardess of ther ocatons. Hence, the probem arses s that some users n ower reabty areas toerated some porton of costs correspondn to the reabty wth no apparent beneft. But n mutarea framework, the transmsson costs of each area are aocated ony to the users of that ven area so a more equtabe aocaton s provded. Furthermore, wth reard to the reabty and economc matters, most of the power systems are connected to the nehborn networks of dfferent countres throuh te nes, therefore, a are mutarea power system s created. In such cases the nternatona operator (IO) shoud aocate the transmsson costs n a mutarea framework, because the detaed nformaton of each area s not avaabe to IO own to the dfferent market autonomy. The rest of the paper s oranzed as foows: In secton 2, the fna step of formuaton of the TCA for a sne area s rewrtten from [6]. Our proposed scheme to aocate the TNC n a mutarea approach s expaned and formuated n secton 3. The presented approach s apped to IEEE 8-bus test system as numerca exampe and resuts are shown n secton 4. The concusons are ven n secton 5. 2 Sne Area Cost Aocaton In noda prcn approach the network revenues are equa to the TR whch s defned as the dfference Ghayen & Ghaz: Mutarea Transmsson Cost Aocaton n Lare Power Systems usn 239

3 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 between what the oads pay and what the enerators are pad. The marna TR whch s based on the LMPs cannot recover the TNC. So the noda prces must be chaned from the marna ponts to the new ponts, so that the recent TR becomes equa to the TNC. In ths secton the fna formuaton of Ref. [6] method for cacuatn the noda prces n a sne area network s presented. In ths method, the noda prces are chaned from marna prces so as the TR can recover the TNC provded that the prce varatons to be mnmzed and the cost spttn between oads and enerators reazed n a pre-specfed rato. To cacuate the NNPs, an optmzaton probem s defned n Ref. [6]. The objectve functon s to mnmze the varaton of the NNPs from LMPs expressed by (). The NNPs are controed so as the TR becomes equa to the TNC, subject to Eq. (2) as a constrant. The cost spttn between oads and enerators s controed n a pre-specfed rato. If the share of the oads n the TNC s consdered as α percent of the TNC, the NNPs must satsfy the Eq. (3) as we. The NNPs aso must satsfy the Kuhn Tucker condtons defned by the Eqs. (4)-(7). Nb Mn 2 (NNP = Subject to: N b 2 LMP ) () [(NNP Pd LMP P ) U(P P ) d + = (2) (LMP P NNP P ) U(P P )] = TNC N b = IC N b d [( NNP LMP) P d U( P d α ( TNC MTR) P d )] = ρ NNP σ L + σ U = = [( ρ δ = N N = (3) +,2,..., N (4) [( γ + NNP ) B ] + U γ L j ) H ] = j N for j =,2,..., N mn max σ (P P ) + σ (P P ) + L U = = N N (6) mn max γ (P P ) + γ (P P ) = L = = U σ, σ =, 2,..., N L U γ, γ =, 2,..., N L U where the symbos n these equatons are defned as foows: b (5) (7) LMP and NNP are the ocaton marna prce and new noda prce at bus respectvey, P and P d are the eneraton and consumpton power at bus, U(.) s the unt step functon, TNC s the tota transmsson network costs, MTR s the marna transmsson rent, N b, N and N are the number of buses, enerators and nes respectvey, ρ δ and ρ are the penaty factors for the njected power of bus and the eneraton unt respectvey, B s the network susceptance matrx and H s the matrx reatn the votae anes to nes power max mn fows, P and P are the eneraton mts of unt max mn and aso P and P are the fow mts n ne and σ L, σ, γ and γ U L U are the Larane mutpers reated to ower & upper mts for eneraton unt and transmsson ne respectvey. Ths non-near optmzaton probem s soved and the NNPs and other varabes are found. After cacuaton of NNPs, the share of each enerator and oad n transmsson costs are determned by Eqs. (8) and (9) respectvey. TCG = (LMP NNP ) P U(P P ) (8) TCL = (NNP LMP ) P U(P P ) (9) d where TCG and TCL are the share of enerator and oad at bus n TNC respectvey. It s cear that, for those buses n whch the prce s ncreased, the enerators are ceared based on LMPs and so do not pay any costs for transmsson, whe the correspondn oads pay the transmsson costs proportona to the ncrement of prce n those buses. Smary, for buses n whch the prce s decreased, the oads are ceared wth the LMPs and do not pay the transmsson costs whe the correspondn enerators pay for transmsson costs proportona to the decrement of prce n those buses. In ths method, the number of constrants s dependent on the number of buses and enerators. Therefore, n are power systems, the number of constrants s too much and the souton needs on computaton tme. To sove ths drawback, the present paper proposes the use of the mutarea framework to cacuate the noda prces whch w be expaned n the next secton. 3 The Proposed Aorthm to Reuate the Noda Prces usn the Mutarea Approach In ths secton our proposed method for reuatn the noda prces to aocate the transmsson costs s expaned n deta. By consdern the mutarea system, at frst, each te-ne s modeed by a vrtua enerator and a oad at the boundary buses to baance the power n these buses. Therefore, the areas are decouped from each other, and the sne area method s performed for each area to cacuate the area noda d d 24 Iranan Journa of Eectrca & Eectronc Enneern, Vo. 6, No. 4, Dec. 2

4 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 prces (ANPs) so as the ANPs recover ony the area transmsson network costs (ATNC). Afterwards, the nterarea transmsson costs (IATC) are determned and aocated to each area usn the equvaent network whch comprses boundary buses and te-nes. e. the a other nes connected to the boundary buses are repaced by vrtua oads and enerators. Ths aocated cost can be defned as area sharn n nterarea transmsson costs (AS-IATC). Fnay, the sne area method s used aan n each area to cacuate the fna noda prces (FNPs) to recover the sum of ATNC and AS-IATC of that area. Now at each bus, the share of each enerator and oad n transmsson costs can be cacuated based on the dfference between the LMPs and FNPs. F. shows the fowchart of our proposed method. Referrn to ths fowchart the procedure of our method comprses the foown steps. Step- Run the optma power fow for whoe system and determne the power of enerators and nes and aso the LMPs. Step2- Cacuate the ATNC n each area and aso the te-nes cost (TLC). Step3- Mode the te-nes by vrtua enerators and oads at boundary buses to baance the power n these buses. Step4- Run the sne area method for each area separatey and cacuate the ANPs to recover ony the ATNC of that area. (In ths step the TLC are not ncuded). Step5- Determne te-nes sharn n ATNC (TLS- ATNC) and then add t to TLC to determne the IATC. Step6- Make the equvaent network conssts of te-nes and boundary buses. Other nes connected to the boundary buses are modeed wth vrtua enerators and oads. Step7- Run the sne area method for equvaent network and determne the AS-IATC. Step8- Run the sne area method aan for each area to reuate the noda prces from ANPs to the FNPs to recover the sum of ATNC and AS-IATC. Step9- Cacuate the share of each enerator and oad n transmsson costs proportona to the chane of ther noda prces from LMP to the FNP. These steps are further eaborated n the rest of ths secton. 3. Optma Power Fow The transmsson cost aocaton s performed after cearance of the enery market. So, the market output ncudn the enerators and nes powers and the LMPs are the nput data for TCA probem. Therefore, t s necessary at frst to run the OPF for entre network so as to obtan these data by consdern the enerators bd and the network constrants. Then the marna transmsson rent (MTR) whch s the dfference between what the oads pay and what the enerators are pad based on the LMPs, s cacuated. Accordn to the prevous studes n ths context, the MTR recovers ony a porton of transmsson costs. Therefore, as our ntenton s to perform TCA by the noda prcn approach, the noda prces must be chaned from the marna ponts to the new ponts, so that the TR at current ponts becomes equa to the TNC. 3.2 Transmsson Costs Cacuaton The other nput data for TCA probem s the vaue of transmsson costs. The procedure of ts cacuaton s expaned n ths stae. Suppose that the entre network s composed of severa areas, connected by te-nes. F. Fowchart of the proposed method. Ghayen & Ghaz: Mutarea Transmsson Cost Aocaton n Lare Power Systems usn 24

5 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 Each area can be a country, an RTO, or a tradtona contro area. Then the transmsson network costs of each area (ATNC) and the te-nes costs (TLC) are computed. The ATNC of each area conssts of the nes cost, substatons cost and operaton cost of the network n that area. The nes cost (LC) s proportona to the capta and operaton costs whch n turn dependent on ne enth, votae eve, and ts capacty as formuated n (). The substaton s treated as a ne wth unt enth connected between hh and ow votae buses. pu LC = LC C L () pu where, LC s cost of ne havn unt enth and capacty for one hour, C and L are the capacty and enth of ne respectvey. LC s the tota cost of ne for each hour. The ATNC s cacuated by addn the area system cost (ASC) whch s reated to the operatn cost of network to the sum of nes costs usn (). ATNC N = LC + ASC = =,2,..., N A () where, N s the number of nes n area, ASC s the system cost of area. N A s the number of areas. The tenes cost (TLC) s the sum of ndvdua te ne cost: N t = t = TLC TLC t (2) where TLC s the cost of te-ne t t, and N t s the number of te-nes. 3.3 Decoupe the Areas In order to mpement the sne area method n each area, the areas must be decouped from each other. To do so the te-nes are modeed by vrtua enerators and oads at boundary buses. If the power s extracted from area (exportn te-ne) the te-ne modeed by a vrtua oad at boundary bus and f t s njected nto area (mportn te-ne) modeed by a vrtua enerator at boundary bus as shown n F. 2. F. 2 Power baance at boundary buses. Ths fure shows a te-ne connected between areas and j n whch the power s transmtted from area towards area j so, the nk s repaced by a vrtua oad at boundary bus of area and vrtua enerator at boundary bus of area j. 3.4 Area noda Prces At frst, the MTR and some other requred nformaton such as H and B matrces are determned for a areas. Then, the sne area method of secton2 s run for each area separatey to cacuate the area noda prces (ANPs) so that the resuts obtaned from these prces coud recover the ATNC and aso contro the share of oads n ths cost wth any arbtrary vaue say α percent. 3.5 Interarea Transmsson Costs It shoud be noted that some of the ATNC n each area are assocated wth the te-nes whch are modeed by vrtua oads and enerators. These costs arse from ths fact that the te-nes utze the areas network for transmttn power between areas. So the nterarea transmsson costs (IATC) have two parts, one part refectn the te-ne costs (TLC) tsef and the other part corresponds to te-nes sharn n area transmsson network costs (TLS-ATNC). The former costs are obtaned from Eq. (2) and the atter costs from Eq. (3) n whch the share of each te-ne s determned by prce varatons from LMP to ANP at boundary buses as foows. TLS ATNC from from from ( ANP ) t LMPt Pt to to to to ( LMP ANP ) P U(P ) t t = t t U(P from ) + (3) from where P t and P to t are the sendn and recevn power n te-ne t respectvey and P from and P to are the njecton power at the sendn and recevn boundary buses respectvey. The nterarea transmsson costs (IATC) s cacuated by sum ths cost for a te-nes and add t to orna te-nes costs: N t IATC = TLS ATNC t = t + TLC (4) 3.6 Te-Lnes Equvaent Network To cacuate the share of each area n IATC, the sne area equvaent network comprsn ony the tenes s needed. In [3] each area s modeed by an equvaent bus. For exampe, a three-area system s substtuted by a network havn three equvaent buses. However, n speca stuatons ths equvaent network w arse some errors. For nstance, when two areas are connected by severa te-nes n whch the power fow n every te-ne s hh but the net exchane power between two areas s ow. In such cases for obtann better resuts each area s modeed by equvaent buses 242 Iranan Journa of Eectrca & Eectronc Enneern, Vo. 6, No. 4, Dec. 2

6 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 nstead of a sne equvaent bus. The number of equvaent buses s equa to the number of boundary buses. To baance the power at these buses, every transmsson ne n each area whch s connected to boundary buses s modeed as a vrtua enerator and a oad smar to what quoted n secton Areas Sharn n IATC The matrces H and B of the above equvaent network are cacuated and then the sne area method s run to cacuate the new prces at boundary buses to recover the IATC. The share of each boundary bus n IATC s determned usn ts prce varaton. Now the area sharn n nterarea transmsson costs (AS-IATC) s determned by addn the share of a boundary buses of that area. 3.8 Fna Noda Prces Now, the ANPs whch were cacuated n secton 3-4 for recovern the ATNC, shoud be controed to the fna noda prces (FNPs) so that the transmsson rent of each area can recover the tota cost of ATNC and AS- IATC n that area. To do ths, the sne area method s run aan for each area but at ths tme the prces are chaned from ANPs to FNPs to recover the tota costs assocated wth that area. These FNPs are abe to recover a the transmsson network costs. 3.9 Share of Generators and Loads n Transmsson Costs At fna step, the share of each enerator and oad n transmsson network costs can be cacuated based on the prce varatons from LMPs to FNPs usn Eqs. (8) and (9). As was mentoned n secton2, those enerators or oads hepn reduce the network usae do not pay the transmsson cost. If the FNP of a bus s ess than ts LMP, the oad ceared wth LMP and therefore does not pay any transmsson cost and the enerator at that bus w pay the transmsson costs proportona to the rate of prce reducton. Smary, f the FNP of a bus s reater than ts LMP, the enerator s pad by LMP so does not pay any costs and the oad s chared for transmsson costs based on the prce ncreasn. 4 Smuaton Resuts Our proposed method s mpemented on a threearea IEEE 8-bus test system as shown n F. 3 [5]. Ths network comprses two votae eves, 345kV wth 2 buses and nes and 38kV wth 6 buses and 66 nes, as connected toether va 9 transformers. Ths system has aso 54 eneraton unts [6]. The bref nformaton of each area s presented n Tabe. At frst, the OPF s run for a network and the power of enerators, fow of nes, and LMP of buses are determned. The LMPs are vared between $36.54 and $4.25 where the maxmum LMP s at bus 4 and mnmum LMP s at bus 89. Then the cost of each ne F. 3 Sne ne daram of three-area IEEE 8-bus test system. Tabe Bref nformaton of 8 bus test system. Area TNC ($/h) Area Area Area Tenes Sum 262 Index No. Capacty Lnes and trans.: MVA Gen. and oad : MW Tota Mn Max 345kv Lnes kv Lnes transformer enerators oads kv Lnes kv Lnes transformer enerators oads kv Lnes 38kv Lnes transformer enerators Loads kv Lnes 38kv Lnes 9 5 s computed usn Eq. () and the ATNC of each area s cacuated by Eq. (). The ATNC n area s $3375.9/h whereas for area2 and area3 are $544.8/h and $876.2/h respectvey. Aso the te-nes cost s cacuated by Eq. (2) whch s equa to $65./h so, the TNC of entre network s $262/h. For mpementaton of our method to determne the new prces n each area, t s necessary to make the power baance at boundary buses. In ths test system, there are 3 areas connected to each other throuh 2 tenes wth 8 boundary buses. F. 4 shows the mantude (n MW) and the drecton of power fow n Ghayen & Ghaz: Mutarea Transmsson Cost Aocaton n Lare Power Systems usn 243

7 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st Area Area F. 4 Mantude of power fow (MW) n te-nes. 82 Area3 te-nes. These te-nes are modeed as vrtua oads and enerators at boundary buses. For exampe, the tene between buses 5 and 33 s modeed by a vrtua oad at bus 5 havn 8.3 MW and a vrtua enerator at bus 33 havn 8.27 MW. The dfference between these vaues arses from power osses of the ven tene. Now, the sne area method of secton 2 s run for each area separatey. So the ANPs are cacuated for each area so that the TR obtaned from these prces recovers the ATNC of that area. The cost spttn between oads and enerators can be controed n a prespecfed rato α. The resuts for α=5%,. e. the equa cost spttn between oads and enerators, are reported. The ANPs are potted for three areas n Fs Noda Prce ($/MWh) Area Noda Prce ( ANP) Locatona Marna Prce ( LMP) 96 Noda Prce ($/MWh) Area Noda Prce ( ANP) Locatona Marna Prce ( LMP) F. 7 The ANPs of area 3. Nodes number n area3 Aso, Tabe 2 shows the statstca nformaton reardn these ANPs. The maxmum ANP corresponds to bus 5 at area wth $43.58/MWh and the mnmum ANP s $35.9/MWh at bus 89 n area3. Aso the standard devaton (STD) of ANPs s ow n area3 wth amount of.4 and hh n area wth amount of.66. The te-nes whch are modeed as fcttous oads or enerators paced at boundary buses, have $243/h sharn n tota ATNC. These sharn can be shown n detas n ast coumn of Tabe 2. Now, the share of each area n IATC s computed. The IATC conssts of two parts, the TLC $65./h and the TLS-ATNC wth amount of $243/h. So the IATC s equa to $ Ths cost s aocated to areas usn the 8 bus equvaent network (boundary buses and tenes) and the resuts are presented n Tabe 3. Fnay, the sne area method s apped for consdern the tota area cost of that area as defned n Tabe 3. Therefore, the obtaned FNPs are such that the tota transmsson costs n each area are recovered. F. 8 shows the FNPs for a buses of the network. The maxmum and mnmum of FNPs are $43.695/MWh and $35.3/MWh respectvey F. 5 The ANPs of area. Nodes number n area Tabe 2 The statstca nformaton of area noda prces. Area Max ANP ($/MWh) Mn STD Area_TR ($/h) TLS-ATNC ($/h) Noda Prce ($/MWh) Area Noda Prce (ANP) Locatona Marna Prce (LMP) F. 6 The ANPs of area 2. Nodes number n area2 Area Area Area Sum Tabe 3 Contrbuton of areas n IATC. Costs Area Area 2 AS- IATC ($/h) ATNC ($/h) Sum Cost ($/h) Area Iranan Journa of Eectrca & Eectronc Enneern, Vo. 6, No. 4, Dec. 2

8 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 Noda Prce ($/MWh) Locatona Marna Prces( LMP) Fna Noda Prces ( FNP) A Nodes of network F. 8 The fna noda prce n a buses of network. Contrbuton of each oad and enerator n transmsson costs s computed usn Eqs. (8) and (9) respectvey. Tabe 4 shows these contrbutons for some buses (ony the frst twenty and the ast ten are shown because space mtaton). Tabe 4 Contrbuton of oads and enerators n transmsson costs for some buses. Bus No Max Sum P d MW P MW LMP NNP TCG TCL The hhest contrbuton amon producers corresponds to enerator at bus 69 wth $936.2 and the hhest contrbuton amon consumers s $49.64 reated to bus 59. Generators at buses 3, 46, 54 and 59 do not pay any transmsson costs, snce ther productons are consumed ocay. Aso oads at buses 2, 49, 66, 7, 75, 8,, 3 and 8 are supped ocay and therefore they do not pay any transmsson costs. At fna stae, a comparson s made between our mutarea proposed method wth the sne area methods of [5], [6]. For ths purpose, the obtaned resuts from a methods are reported aon wth the statstca ndces n Tabe 5. It can be seen that, the smuaton tme n our method s consderaby reduced. The smuaton tme s 489s for Ref. [5] method and 542s for Ref. [6] method whereas for our method s about 45.7s. Aso, n our method the prce varaton s much ower than that of sne area methods. The mnmum FNP has ncreased from $33.35/MWh and $34.43/MWh to $35.3/MWh and aso the maxmum FNP decreased from $43.48/MWh and $45.44/MWh to $43.695/MWh reardn the sne area methods and the mutarea method. The dfference between Max and Mn of FNPs n [5] s $.49/MWh and $./MWh n [6], whe ths ndex has decreased to $8.57/MWh n our method, athouh the standard devaton of FNPs s shty ncreased. Statstca ndces aso show that the varaton of FNPs n our method s ess than that of sne area methods. It means that the transmsson costs are aocated to users wth smoother varatons n the noda prces. If the share of enerators or oads n transmsson costs s compared, n the presented method the maxmum share for enerators decreased from $874/h and $235.6/h to $936.24/h and for oads decreased from $252.5 and $696.7 to $49.64/h. The correspondn standard devaton s aso decreased about 3.74 & 3.7 percent for enerators and 9.55 & percent for oads respectvey. Tabe 5 Comparson of our method and Refs. [5, 6] methods. Statstca Indces Smuaton Tme (second) Max FNP ($/MWh) Mn FNP ($/MWh) Max FNP- Mn FNP STD FNP ($/MWh) Voatty% Max TCG ($/h) STD TCG ($/h) Max TCL ($/h) STD TCL ($/h) Ref [5] method Ref [6] method Proposed Method Ghayen & Ghaz: Mutarea Transmsson Cost Aocaton n Lare Power Systems usn 245

9 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 Tabe 6 Contrbuton of each area from TNC. Method Users The share of areas n TNC ($/h) Area Area2 Area3 Sum Sne area method [5] Sne area method [6] Proposed mutarea method Loads Generators Tota Loads Generators Tota Loads Generators Tota Aso, the share of a oads and enerators n each area s compared for a methods n Tabe 6. It s seen that n sne area methods athouh the cost spttn between enerators and oads for entre network has been done n accordance wth predefned rato (5/5 percent) but ths spttn rato s not observed n each area. For sne area methods, n area the oads pay 37.7 and 42.5 percent and enerators pay 62.3 and 57.5 percent of costs, n area 2 oads have 65.5 and 56.6 percent contrbuton n transmsson costs and these contrbutons are 34 and 38.2 percent n area3. However, n mutarea method ths cost spttn s controed not ony for entre system but aso for each area as shown n Tabe 6. In addton, by comparn the tota payment made by oads and enerators n each area t s found that the tota payment by users n each area n mutarea method s very cose to ATNC of that area but ths s not vad n the sne area methods. For exampe, the ATNC of area3 s $876.2 but the tota payment by oads and enerators of ths area n sne area methods are $38.2 and $ whch are far from tota costs. It means that the users of ths area are toerated some porton of transmsson costs of other areas wthout recevn any apparent beneft. So, a more equtabe aocaton s provded by our proposed mutarea method n compare wth the sne area methods. 5 Concuson In ths paper a mutarea approach based on contron the noda prces s proposed for TCA probem. Ths aorthm s qute fast so t can be easy apped for are power systems. The resuts show that the smuaton tme s reaty reduced when apped on a are power system. In addton, the proposed method aocates the transmsson costs more equtabe than the sne area approaches. Snce, n mutarea framework, the costs of each area are aocated to a users of that area. Therefore, f the ATNC of a ven area s hh, due to ts hher reabty ndex, ony the users of ths area w contrbute, whereas, n the sne area methods the costs of whoe system aocated to a users reardess of ther ocatons. Hence, n sne area approaches the users of a ven area wth ower reabty, experencn some excessve costs wthout beneftn from t. Resuts aso show that n the proposed approach, the varatons of noda prces for recovern the transmsson costs are smooth n compare wth the sne area methods. References [] Arraa I. J. P., Rubo F. J., Puerta J. F., Arceuz J. and Martín J., Marna prcn of transmsson servces: An anayss of cost recovery, IEEE Trans. Power Syst., Vo., No., pp , February 995. [2] Rubo-Oderz F. J. and Arraa I. J. P., Marna prcn of transmsson servces: A comparatve anayss of network cost aocaton methods, IEEE Trans. Power Syst., Vo. 5, No., pp , February 2. [3] Sedahat A., Cost of Transmsson System Usae Based on an Economc Measure, IEEE Trans. Power Syst., Vo. 2, No. 2, pp , May 26. [4] Guo J., Wu Q. H., Turner D. R., Wu Z. X. and Zhou X. X., Revenue Reconcaton for Spot Prcn: Impementaton and Impcaton, Eect. Power Compon. Syst., Vo. 32, No., pp , January 24. [5] G H. A., Gaana F. D. and da Sva E. L., Noda prce contro: A mechansm for transmsson network cost aocaton, IEEE Trans. Power Syst., Vo. 2, No., pp. 3-, February 26. [6] Ghayen M. and Ghaz R., Transmsson Cost Aocaton n Restructured Power Systems Based on Noda Prcn Approach by Contron the Marna Prces, Iranan Journa of Eectrca & Eectronc Enneern, Vo. 6, No. 2, pp. 93-2, June 2. [7] Yu C. W. and Davd A. K., Transmsson cost aocaton n mut-area power poo operaton, IEE Conf. Power Syst. Contro and manaement, pp , 996. [8] G H. A., Gaana F. D. and Conejo A. J., Mutarea transmsson network cost aocaton, IEEE Trans. Power Syst., Vo. 2, No. 3, pp , Au. 25. [9] Arraa I. J. P., Cross-border tarfcaton n the nterna eectrcty market of the European unon, Proc. 4th PSCC, pp. -9, Seva, Span, Jun. 22. [] Da Sva A. M. L. and De Carvaho Costa J. G., Transmsson oss aocaton. Part II. Mutpe nterconnected enery markets, IEEE Trans. Power Syst., Vo. 8, No. 4, pp , Nov Iranan Journa of Eectrca & Eectronc Enneern, Vo. 6, No. 4, Dec. 2

10 Downoaded from jeee.ust.ac.r at 23:42 IRST on Frday September 2st 28 [] Baek J. W., Zemanek S. and Waace R. A., Methodooy for aocatn transmsson osses due to cross-border trades, IEEE Trans. Power Syst., Vo. 9, No. 3, pp , 24. [2] Kazem A. and Andam H., Mut-area Power System Loss Aocaton Usn Z-bus Method, Frst Internatona Power and Enery Conference, Maaysa, November 28-29, 26. [3] Kazem A. and Andam H., Introducn a New Method for Mutarea Transmsson Networks Loss Aocaton, Iranan Journa of Eectrca & Eectronc Enneern, Vo. 3, No. &2, pp. 2-3, Jan. 27. [4] Lma D. A., Conejo A. J. and Contreras J., Aocaton of the cost of transmsson osses n a mutmarket framework, IEE Proc.-Gener. Transm. Dstrb., Vo. 53, No. 6, pp , Nov. 26. [5] Lu B. and Shahdehpour M., Unt Commtment Wth Fexbe Generatn Unts, IEEE Trans. Power Syst., Vo. 2, No. 2, pp , May 25. [6] Chrste R., Unversty of Washnton, Avaabe at: research/pstca/. Mohsen Ghayen was born n Mashhad, Iran n 98. He receved the B.Sc. deree n eectronc enneern and the M.Sc. deree n power enneern both from Ferdows Unversty of Mashhad, Iran, n 22 and 26 respectvey. He s currenty a Ph.D. student at the Ferdows Unversty of Mashhad. Hs research nterests are power system operaton, power market and power quaty. Reza Ghaz (M 9) was born n Semnan, Iran n 952. He receved hs B.Sc., deree (wth honors) from Tehran Unversty of Scence and Technooy, Tehran, Iran n 976. In 986 he receved hs M.Sc deree from Manchester Unversty, Insttute of Scence and Technooy (UMIST) and the Ph.D. deree n 989 from Unversty of Saford UK, a n eectrca enneern. Foown recept of the Ph.D. deree, he joned the facuty of enneern Ferdows Unversty of Mashhad, Iran as an Assstant Professor of eectrca enneern. He s currenty Professor of Eectrca Enneern n Ferdows Unversty of Mashhad, Iran. Hs man research nterests are reactve power contro, FACTS devces, appcaton of power eectronc n power systems, dstrbuted eneraton, restructured power systems contro and anayss. He has pubshed over 9 papers n these feds ncudn three books. Ghayen & Ghaz: Mutarea Transmsson Cost Aocaton n Lare Power Systems usn 247