Hybrid Three-Phase Load Flow Method for Ungrounded Distribution Systems

Transcription

1 MTSUBSH ELECTRC RESERCH LBORTORES htt:// Hybrid Three-Phae Load Flow Method for Ungrounded Ditribution Syte Sun, H.; Nikovki, D.; Ohno, T.; Takano, T.; Kojia, Y. TR October 2012 btract Thi aer rooe a hybrid three-hae load flow ethod for ungrounded ditribution yte. Baed on toology connectivity analyi, the yte i artitioned into a ainline yte and ultile ta yte. Newton ethod with contant adittance atri i ued to olve the ainline yte, uch that zero iedance branche are erged into adjacent iedance branche to be conidered, and contant active-ower and voltage-agnitude (P) bue with three-hae balanced voltage are tranfored into ingle- hae P bue to be odeled. backward/forward wee with loo coenation i ued to olve the ta yte, uch that a tranforer and a voltage regulator i odeled uing line-to-line voltage, a ditribution line i ilified a a erie branch, and loo coenation current i initialized baed on loo downtrea load and the iedance of loo ath. Tet reult of ale yte are given to deontrate the effectivene of the rooed ethod EEE PES nnovative Sart Grid Technologie Conference - Euroe (SGT Euroe) Thi work ay not be coied or reroduced in whole or in art for any coercial uroe. Periion to coy in whole or in art without ayent of fee i granted for nonrofit educational and reearch uroe rovided that all uch whole or artial coie include the following: a notice that uch coying i by eriion of Mitubihi Electric Reearch Laboratorie, nc.; an acknowledgent of the author and individual contribution to the work; and all alicable ortion of the coyright notice. Coying, reroduction, or reublihing for any other uroe hall require a licene with ayent of fee to Mitubihi Electric Reearch Laboratorie, nc. ll right reerved. Coyright c Mitubihi Electric Reearch Laboratorie, nc., Broadway, Cabridge, Maachuett 02139

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3 1 Hybrid Three-Phae Load Flow Method for Ungrounded Ditribution Syte Hongbo Sun, Senior Meber, EEE, Daniel Nikovki, Meber, EEE, Tetufui Ohno, Toihiro Takano, and Yauhiro Kojia, Meber, EEE btract-- Thi aer rooe a hybrid three-hae load flow ethod for ungrounded ditribution yte. Baed on toology connectivity analyi, the yte i artitioned into a ainline yte and ultile ta yte. Newton ethod with contant adittance atri i ued to olve the ainline yte, uch that zero iedance branche are erged into adjacent iedance branche to be conidered, and contant active-ower and voltage-agnitude (P) bue with three-hae balanced voltage are tranfored into ingle-hae P bue to be odeled. backward/forward wee with loo coenation i ued to olve the ta yte, uch that a tranforer and a voltage regulator i odeled uing line-to-line voltage, a ditribution line i ilified a a erie branch, and loo coenation current i initialized baed on loo downtrea load and the iedance of loo ath. Tet reult of ale yte are given to deontrate the effectivene of the rooed ethod. nde Ter-- Ditribution yte; Three-hae; Load Flow; Ungrounded; Real-tie.. NTRODUCTON WTH the increaing deloyent of art grid technologie uch a renewable energie, deand reone, luggable electric vehicle and advanced network controller, the oeration of ditribution yte becoe uch ore colicated and challenging than before. Coutational tool uitable for realtie onitoring of large-cale ditribution yte are highly deired by the electric utilitie for aiting their oerator to enure the afety, ecurity and efficiency of the oeration of ditribution yte under fluctuating and le-redictable ituation introduced by art grid alication. a fundaental tool of real-tie onitoring, three-hae realtie load flow i laying an iortant role by analyzing the teady-tate erforance of ditribution yte in a tiely anner. ariou ethod for olving three-hae ower flow roble are known. Mot of thee ethod are ainly deigned for grounded ditribution yte, and ight not be Hongbo Sun and Daniel Nikovki are with the Mitubihi Electric Reearch Laboratorie, Cabridge, M US (e-ail: [email protected]; [email protected]). Tetufui Ohno, Toihiro Takano, and Yauhiro Kojia are with the Mitubihi Electric Cororation, Hyogo Jaan (e-ail: [email protected]; Takano.Toihiro@df. MitubihiElectric.co.j; [email protected]). alied to the ungrounded yte directly. Thee ethod differ in both the for of the equation decribing the yte and in the nuerical technique ued. Uually, either toology- or atri-baed ethod are eloyed. Toologybaed ethod are uitable for radial yte, and include the Backward/Forward wee ethod[1] and Ladder ethod[2]. Coenation chee[1], [3]-[4] ut be ued when loo or P bue are reent in the yte, and the eiting chee are le efficient when dealing with P bue. The adittance-atri baed ethod include the licit Z-bu ethod [5]-[6], the Newton-Rahon ethod [7]-[8], the Fat Decouled ethod [9], and the Sequence Decouling ethod [10]-[11]. ll of thee ethod have their own liitation when alied to large yte, either in ter of odeling caabilitie, or in ter of coutational efficiency. Thi aer rooe a new hybrid three-hae load flow ethod that i uitable for real-tie alication in large-cale ungrounded ditribution yte. Baed on toology connectivity analyi, the ditribution yte i artitioned into a ainline yte and ultile ta yte to be olved by ean of a Newton ethod with contant Jacobian atri, and a backward/forward wee ethod with loo coenation, reectively. The iact of zero-iedance branche uch a voltage regulator have been odeled by erging thoe branche with adjacent iedance branche, uch that the inaccuracy or divergence roble introduced by adding all iedance into thoe branche, that i coonly ued by conventional ethod, can been avoided. Unlike the coon ractice to et active ower for each hae arbitrarily, the rooed ethod odel the control requireent for contant active-ower and voltage-agnitude (P) bue with three-hae balanced voltage reciely, that i, by aintaining the u of three-hae active ower contant, and by aintaining three-hae voltage balanced and with contant agnitude. ntead of initializing the bu voltage with the etting of the wing bu, and loo coenation current a zero, the ethod et the initial bu voltage baed on the wing-bu voltage and the alifier factor of tranforer and regulator along ath connecting each bu with the wing bu, and initialize the loo coenation current baed on the connected loo load and an allocation factor atri defined olely by the loo ath iedance. The ethod ued a cloed-for forula to uniquely convert line-to-line voltage into hae-to-ground

4 2 voltage for ungrounded bue. By uing the forula, ungrounded tranforer in ta yte are olved by uing adittance odel baed on line-to-line voltage in order to avoid the reulting atri ingularity when uing odel baed on hae-to-ground voltage. The forula alo enable the contruction of the nodal adittance atri of the ainline yte, baed on alifying factor of zeroiedance branche written in line-to-line voltage. The olution roce for a ta yte i further ilified by integrating line charging into connected bue, and only erie line current are ued during iteration.. THE PROPOSED METHOD. Syte Partitioning Baed on the toology analyi, the rooed ethod ha artitioned the ditribution yte into a ainline yte and a et of ta yte. The ainline yte i fored by ainline bue connecting a wing bu to a et of P bue, and the ta yte i fored by one or ore ta bue, uch that the root bu of each ta yte correond to a ainline bu. Fig. 1 Ditribution yte artitioning Fig. 1 how an eale of the artitioning of a ditribution yte into a correonding ainline yte and two ta yte 1 and 2. n the eale, the ainline yte include five bue, including one wing bu 1, one P bu 2, and two root bue, t1 and t2 for two ta yte, 1 and 2. The ainline yte i a radial yte. Ta yte 1 tart fro a ainline bu t1, which i it root bu, and include all bue and device downtrea to the bu t1. can be een, ta yte 1 for a loo. Ta yte 2 tart fro a correonding root bu t2 of the ainline yte, and include all bue and device downtrea to bu t2. Ta yte 2 ha no loo and i a radial yte. Baed on the nuber of device connected between the tudy bu and the root, the ta yte can be divided into layer. For eale, in Fig. 1, ta yte 1 i divided into four layer, where the firt layer contain one bu, and the lat layer contant three bue. Siilarly, ta yte 2 i divided into three layer. The ower flow of ditribution yte i olving through iterative olving of the ainline yte and ta yte, and a final olution i obtained when the required accuracy for the bu voltage or ower iatch i atified. B. The ainline yte The ainline yte i fored by ainline bue that reide on the ath between the wing bu and P bue. The ainline yte ay be radial, or ehed. The odeled bu and hae in the ainline yte are converted to node to contruct the ower flow equation. The nuber of node for each bu i equal to the nuber of odeled or available hae at the bu. The ower flow equation are forulated in olar coordinate and olved by Newton' ethod with a contant Jacobian atri. The iact of zero-iedance branche and voltage balance requireent of three-hae P bue are ebedded into the nodal adittance atri of the ainline yte. 1) Zero-iedance Branche Many branche in a ditribution yte can be regarded a zero-iedance branche, uch a te voltage regulator, witche, juer and very hort line. Uually, the iedance of thoe branche are very all and can be ignored. However, the conequence i that oe entrie in the reultant nodal adittance atri becoe infinite, and thu the adittance atri baed aroache are inalicable. n order to ue adittance atri baed aroache, conventional ethod have arbitrarily aigned all non-zero iedance to thoe branche. However, aigning uch all iedance ake the analyi ill-conditioned, and load flow analyi i difficult to converge. n the rooed ethod, a different ethod i ued that erge thoe zero-iedance branche with adjacent iedance branche into new non-zero iedance branche. Fig. 2 give an eale of a generalized three-hae zeroiedance branch between bu and bu. One of the bue, for eale the bu, i aigned to be a ater bu, and the other bu i aigned to be a lave bu. The bue are connected by an ideal tranforer. The lave bu i connected with a load current. Fig. 2 Zero-iedance branch odel The hae-to-ground voltage of it two terinal bue, and two directional hae current on the branch are related to each other with the voltage alifying factor atrice,

5 3 and a:, and current alifying factor atrice, and = (1) = (2) = (3) = (4) where and are the vector of hae current flowing fro bu to bu, and bu to bu reectively, and are the vector of hae-to-ground voltage of bu and bu. Thee alifying factor atrice are deterined according to the winding connection and ta oition for a tranforer or a voltage regulator, and the hae connection for a witch, a hort line or a juer. hown in Fig.2, the zero-iedance branch i erged into adjacent iedance branche, uch that the lave bu i not conidered in the analyi of the odel. n the eale, the zero-iedance branch i connected to two branche by the lave bu, and to another two branche by the ater bu. Taking one adjacent branch between lave bu and bu a an eale, the relationhi between the branch current and the terinal bu voltage can be decribed a: Y Y = (5) Y Y and are the vector of hae branch current where, flowing fro bu to, and bu to, i the vector of hae-to-ground voltage at bu, Y and Y are the elf adittance atrice of bu and, Y and Y are the utual adittance between and, and and reectively. n the equivalent odel, the zero-iedance branch and the lave bu are reoved. There are no change for the branche connected to the ater bu. The branche connected to the lave bu are reconnected to bu, and the branch adittance atrice and the current injection at the ater bu are odified accordingly. The load current at bu i odeled a an equivalent current at bu, a. The branch between bu and bu i relaced with a new branch directly between bu and bu, and the branch current, and, and the nodal voltage, and, are related a: Y Y = (6) Y Y f the alifying atrice are ereed with line-to-line voltage, (6) i relaced by the following equation: Y = YC C C LP LP C Y Y (7) where, and are the voltage alifying factor atrice for the branch between bu to bu written in ter of line-to-line voltage, and line-to-line voltage at bu, and bu, and are related a: = (8) = (9) LP where, C i a converion factor atri to be ued to convert voltage fro hae-to-ground for into line-to-line one. Taken bu a eale, we have The atri C LP C i defined a: LP = C (10) 1 = 0 LP C (11) i a converion factor atri to be ued to convert voltage in the for of line-to-line into hae-to-ground. For bu, we have: = C (12) The converion fro line-to-line voltage into hae-toground voltage i not trivial. Due to unknown neutral-toground voltage, ultile reult ay be obtained baed on the ae line-to-line voltage. converion equation defined below i ued to uniquely convert the line-to-line voltage to the hae-to-ground voltage: 1 3 = / / 3 C (13) The converion i accurate when the voltage only include oitive and negative equence coonent, and i a good aroiation if the zero-equence coonent are all enough. 2) Three-hae P bue with balanced voltage P bu in the ainline yte can be odeled a three P node, if the ower and voltage agnitude of each hae i regulated indeendently. However, if the bu i connected to a balanced voltage generation ource, and the generator i regulated a contant voltage agnitude and contant total active ower of three hae, accordingly, the three-hae of uch bu have to be cobined together to be odeled in the adittance atri baed ower flow equation. ued bu i a P bu with three-hae balanced voltage, it three hae a, b, and c can be cobined into an equivalent ingle-hae e to be odeled. The equivalent hae e can be any hae, and taken hae a a eale, we can have: e a = (14) e T = R (15)

6 4 e a where, and are the hae-to-ground voltage at equivalent hae e, and hae a of bu reectively, and e i the equivalent hae current flowing on the branch fro bu to bu, R i a rotation vector to rotate all hae to the T elected equivalence hae e, R i the tranoe of vector R. ued the equivalent hae i hae a, the rotation vector i defined a: 1 j R = e j e 120 o 120 o (16) Fig. 3 how an eale of deterining an equivalent odel for a ditribution yte with three-hae ganged regulated P bue. n Fig. 3, the three hae P bu i connected to two branche. n the equivalent odel, the three hae of P bue with balanced voltage are cobined into one ingle hae, and taking one branch between bu and bu a an eale, the new branch odel can be decribed a: e T * T e R YR R Y = (17) * YR Y * where R i the conjugate of rotation vector R. Fig. 3 Three-hae Balanced-oltage P Bu Model 3) nitial Bu oltage The Jacobian atri i deterined fro the initial voltage etting. The initial voltage are et to the value at the wing bu ultilied with the aggregated voltage alifying factor atri introduced by the tranforer or voltage regulator along the hortet ath between the wing bu and the bu: (0) = t t wing (18) (0) where, i the vector of initial voltage of bu, wing i the voltage of the wing bu, t i the voltage alifying factor atri of a voltage regulator or tranforer between two bue, bu and bu t reiding on the hortet ath fro the wing bu to the bu under conideration. 4) Solving ower flow of the ainline yte The ower flow of the ainline yte i olved through iteratively olving the following ower iatch equation: ΔP = ΔQ ΔP and ΔQ Δθ Δ [ J ] (19) where are vector of nodal ower iatche between the cheduled value and calculated value, Δθ and Δ are the vector of node hae angle and voltage agnitude change, and J are the Jacobian atrice of node active and reactive ower with reect to node hae angle and node voltage agnitude. The Jacobian atri i deterined fro the initial voltage etting, and factorized by uing are LU decooition or are Choleky decooition technique, deendent on whether the atri i yetrical. ny bu in the ainline yte, which i not a P, or wing bu, i treated a a PQ bu. t equivalent hae ower are deterined by the connected load, caacitor, adjacent line charging, and downtrea branche, if it i a root bu for a ta yte. The equivalent ower S for bu at hae i deterined according to: * S = + ) { a, b, c} (20) ( Ta where, i the equivalent hae current of bu at hae, i the equivalent hae current flowing through bu toward bu at hae, Ta i the et of bue that connect with bu and reide in the ta yte fed by the bu. C. The ta yte ta yte i fored by a et of ta bue and the root bu of each ta yte correond to a ainline bu. backward/forward wee chee baed on current uation with loo breakoint coenation i alied. 1) Loo Breakoint Coenation The loo in a ta yte are broken into radial ath to be conidered, and the downtrea load current fed by the loo i allocated aroriately between two breakoint, in order to aintain their voltage identical. Fig. 4 how an eale contruction of an equivalent odel for a ta yte having a loo fored between an utrea bu u and a downtrea interection bu dn. There are two ath available fro the bu u to the bu dn. By relacing the downtrea interection bu with two breakoint, i.e., one i the original bu dn, and the other i a new coenation bu co, the loo i broken into two radial ath. Coenation current co i added a a load to the coenation bu co, and a a negative load to the original bu dn. n the rooed ethod, the coenation current co i initially deterined according to: = (21) co co dn

7 5 where, co i the allocation factor atri to be ued to allocate downtrea current between two arallel loo ath. The allocation factor atri i calculated baed on the erie iedance atrice of two ath according to: where, Zu dn ( Z co = Zu dn u dn + Zu co ) (22) i the iedance atrice for the ath fro the Z utrea bu u to the downtrea bu dn, and u co i the iedance atrice for the ath fro the utrea bu u to the coenation bu co. Fig. 4 Ta Loo Model Uing above equation, the load at a downtrea bu i initially allocated into two arallel ath. The current along the two ath have to be adjuted, if the voltage at the two breakoint are not identical. The increental coenation current, Δ i deterined according to co Δ = Z co Δ co co (23) where, Δ co i the vector of the voltage difference between the coenation bu and the loo downtrea interection bu, and it can be calculated according to: Δ = ( ) dn (24) where, co co co and dn are the hae-to-ground voltage at the bu co, and the bu dn, reectively. Z co i a loo iedance atri, which for an indeendent loo can be deterined a the u of two ath iedance atrice according to: Z co = ( Z Z ) co u dn + u (25) f oe of the loo hare coon ath between different loo, above equation can till be ued to calculate the increental coenation current, but the vector Δ and co Δ co include the correonding coenation current and voltage change for each loo, and the loo iedance atrice Z co are fored baed on the ath iedance atri for each loo, and coon ath iedance between loo. 2) Three-hae tranforer branche For a three-hae tranforer, the backward/forward wee te need to calculate the invere of it adittance atrice, and unfortunately for ungrounded connection, oe of thoe atrice are ingular. So, the line-to-line voltage, and hae current are ued to ere the tranforer odel in ta yte. Becaue the riary and econdary bue are ungrounded, the u of the three hae current are zero, o only two hae current are needed. nd, only two of the three line-to-line voltage are needed a well. an eale, if we take current at hae a and b a current variable, and line-to-line voltage between hae a to hae b, and hae b to hae c a voltage variable, the adittance odel for a tranforer between bu and bu are calculated according to: ' n n ' Y = Y C, n {, } (26) where, C i a converion atri that ued to calculate the hae-to-ground voltage for three hae baed on line-to-line voltage between hae a to b, and b to c. The atri i defined a: ' 2 /3 = /3 /3 1/ 3 1/ 3 2/ 3 C (27) 3) Three-hae line branche n order to ilify the calculation for three-hae line, the conventional π-odel of ditribution line i relaced with a erie iedance branch by erging the line charging of hunt adittance into terinal bue a hown in Fig. 5. Fig. 5 Ta Line Branch Model Fig. 5 how a odel of ditribution line connect bu and bu. n the odel, there i one erie branch with e iedance atri, Z and two hunt branche and each with h half of hunt adittance atri Y. ntead of olving the actual branch current ' ' and directly, the rooed ethod ha ued the internal current, and, that flow through the erie iedance a the variable of the odel to be olved. The actual branch current can be deterined by adding the line-charging current to the internal current, after the converged ower flow olution are obtained. By doing o, the coutation effort required for both backward wee and forward wee are ignificantly reduced. For eale, for a backward wee, the current entering the line through the ending ide, can be directly et a negative of current

8 6 entering through the receiving ide, i.e. =. 4) Solving ower flow of the ta yte The ower flow of a ta yte i olved by uing the backward/forward wee chee. The chee include two integrated te. The firt i the backward wee te, or current uation te, which calculate the branch current, tarting fro the branche at the lat layer and oving toward the branche connected to the root bu. The econd i the forward wee te, or voltage udate te, which udate the branch terinal voltage, tarting fro the branche in the firt layer toward thoe in the lat, and for each branch between a ending bu and a receiving bu, the voltage at the receiving bu i calculated uing the udated voltage at the ending bu. n a backward wee, for any branch between ending bu and receiving bu, the branch current entering the receiving bu i deterined according to: = { a, b, c} (28) t t DN where, i the equivalent current for bu at hae ; DN i a et of downtrea bue connected to the bu, and t i the hae current entering fro bu to a branch between bu and bu t. The equivalent hae current for a bu take contribution fro the connected load, caacitor, the line charging fro connected line, and the loo coenation current, if it i a loo breakoint. The load and caacitor are Delta connected in an ungrounded yte. The load include contant ower load, contant current load, and contant iedance load. The equivalent hae current at bu, can be deterined according to: 1 h = C ( Y) + 2 co (29) The firt coonent of the right-hand ide of (29) i the contribution fro connected load and caacitor which are calculated a line-to-line current, and then converted to C hae current uing the current converion factor atri defined a: 1 0 C = 1 0 (30) 0 1 The econd coonent of the right-hand ide of (29) i the contribution of line charging for all line that connect to bu, h and Y i the hunt adittance of the line between bu and. The third coonent, co, i the contribution of loo coenation current that can be deterined uing (21) and (23) if bu i one of loo breakoint, and i a oitive value for the breakoint correonding to the coenation bu, and negative value for another breakoint of the loo that correond to the original bu. The line-to-line current at bu between hae and y i deterined a follow: * y * y 2 Z 2 y 2 * S S jc SS y = y* y { ab, bc, ca} (31) y R where, S y R S, S y R and S Z are the rated cole ower at bu and between hae to hae y of contant ower load, contant current load and contant iedance load y R reectively; C i the rated reactive ower generated at R bu and hae to y by connected caacitor; and i the rated voltage at bu and between hae to y. n a forward wee, the line-to-line voltage are ued for calculation of tranforer and voltage regulator, and then converted into hae-to-ground voltage by uing the voltage converion atrice. The hae-to-ground voltage are ued for calculation of line, and then converted into line-to-line voltage if the connected device i a tranforer or voltage regulator.. NUMERCL EXMES The rooed ethod wa teted againt everal ungrounded ditribution yte including the EEE 37 node tet feeder, and a 2000-node ale yte. The teting wa erfored on a dekto couter with an ntel Core i7-960 roceor. The aiu allowed ower iatch i et to be 5 10 er unit.. Tet reult for the EEE 37 node tet feeder Table lit the tet cenario that are generated baed on the EEE 37 node tet feeder in which cenario i a ure radial yte, cenario i a looed yte, cenario i a radial yte, but with additional ditribution generation that i regulated a a P bu, and cenario i a looed yte with additional P regulated generation. TBLE TEST CSES BSED ON EEE 37 NODE TEST FEEDER Tet Scenario Configuration Characteritic of yte Sae a EEE 37 node tet feeder Radial yte dd two new branche to cenario Syte with, one between node 718 and 725, and one between node 729 and 732 two loo dd one new node 788 with threehae P regulation, and one branch between 711 and 788 to cenario dd one new P bu 788, and three new branche, between 788 and 711, 729 and 732, and 718 and 725 to cenario y Radial yte with 1 P bu Syte with 2 loo and 1 P bu The coutational erforance of the rooed algorith on thoe tet cenario i reented in Table. The coutational rocedure include two tage, the firt tage involve the contruction of connected iland baed on the current or tudy-ode witch tatu through toology analyi, and the econd tage involve the calculation of load flow for

9 7 each iland that wa contructed during the firt tage. For real-tie alication, the firt tage only need to be reeecuted when there are witching oeration taking lace in the yte. TBLE COMPUTTONL PERFORMNCES OF TEST CSES Tet CPU Tie() Scenario Toology nalyi Load Flow Calculation hown in Table and, the rooed algorith i caable of analyzing three-hae load flow for ungrounded ditribution yte with variou configuration. Table and lit the coutational reult for tet cenario with different P bu odel, including threehae indeendent regulating odel, and three-hae ganged regulating odel. The generation outut of ditributed generation and the wing bu are heavily deendent on the P bu odel to be ued, and different odel reult in different generation diatch reult. t i obviou that if a three-hae ganged regulated P bu were odeled a a three-hae indeendent regulated bu, the reultant ower flow reult ight be wrong or at leat not very inaccurate. P Model Three-hae ndeendent Regulated Three-hae Ganged Regulated TBLE P BUS MODELS OF SCENRO Regulation ctive Power Magnitude of Phae-toground oltage Generation The outut of each 1.0.u for each hae hae i 100 kw The total outut of three hae i 300 kw 1.0.u. for each hae, and hae a lead 120 degree to hae b, and lag 120 degree to hae c TBLE RESULTS FOR SCENRO WTH DFFERENT P MODELS P Bu Swing Bu P Model Line-to-line oltage Generation Outut Generation Outut Mag. (.u) ngle (Deg.) kw kar kw kar Three-hae ndeendent Regulated Three-hae Ganged Regulated B. Tet reult for the 2000-node ale yte The rooed ethod wa alo teted againt a ale ungrounded ditribution yte with 2000 three-hae node. The ale yte i a radial yte, and ha one ubtation and i feeder. Siilarly, four different tet cenario were generated baed on the configuration of the 2000-node yte. Scenario i a ure radial yte which ue the original configuration of the 2000-node yte. Scenario i a looed yte which created by adding 12 loo to Scenario. Scenario i a radial yte, but with additional contant voltage ource by adding 3 P bue into Scenario. Scenario i a looed yte with P bue which created by adding 12 loo and 3 P bue into Scenario. The P bue are located at the tail of aociated feeder. The teting reult on the ale yte and coutation erforance coared with other eiting ethod are rovided in Table. Three different algorith have been coared, including the rooed ethod, the Gau-Seidel ethod, and the Newton-Rahon ethod. TBLE COMPUTTONL PERFORMNCE OF 2000 NODE TEST CSES Tet CPU Tie() Method Scenario Toology Load Flow nalyi Calculation The rooed ethod Gau- Seidel ethod Newton- Rahon ethod Fro thee tet reult, we can ee that the rooed ethod i uch ore efficient than the Gau-Seidel and Newton-Rahon algorith when dealing with yte in radial configuration, or with liited nuber of loo and contant voltage ource. Taking Cae a an eale, it took 1637 for the rooed algorith to find the final olution with the required reciion. n coarion, it took 8951 for the Gau-Seidel algorith, and for the Newton-Rahon algorith to find the olution with the ae reciion. Siilar reult can be found for the other three cae. The tet on the 2000 node yte with radial toology howed that the rooed algorith could find a olution within 7, after the connectivity of the yte wa analyzed at the initial hae within 8. n addition, the algorith could alo erfor well for yte with arbitrary toology, including loo, at a lower eed. When 12 loo were added to the ae 2000-node ditribution yte, calculation tie wa only lightly longer, 9. Even with wort cae that generation ource are located far aart, one at feeder head, and the other at feeder tail a in the lat two cenario of table, calculation tie wa coniderably lower, but till within 2 econd. Conidering the ize of tet yte, and the latfor that wa ued for teting, the calculation tie i quite reaonable. Baed on the reliinary reult, it i afe to ay that the rooed algorith i uitable of real-tie load flow analyi of large-cale ungrounded ditribution yte.. CONCLUSON new hybrid ethod for three-hae ower flow analyi of ungrounded ditribution yte wa rooed, in which the toology of the ditribution yte i artitioned into a

10 8 ainline yte and a et of ta yte, where the ainline yte i fored by ainline bue connecting a wing bu and a et of contant voltage ource bue, and the ta yte i fored by one or any ta bue, uch that a root bu of each ta yte correond to a ainline bu. The ainline yte i olved by ean of a Newton ethod with contant Jacobian atri, in which the zeroiedance branche are erged into adjacent iedance branche, and the three hae of balanced-voltage P bue are erged into one ingle hae of P bue. The ta yte are olved by a backward/forward wee chee with loo coenation, in which line-to-line voltage baed voltage regulator and tranforer araeter are ued, and both line odel and the calculation of initial loo coenation current are ilified to eed u the olution rocedure. The nuerical eale on ale yte have deontrated the effectivene of the rooed ethod and the uitablene of real tie alication.. REFERENCES [1] D. Shirohaadi, H. W. Hong,. Selyen, and G. X. Luo, Coenation-baed Power Flow Method for Weakly Mehed Ditribution and Traniion Network, EEE Tranaction on Power Syte, vol. 3, no.2, , May [2] W. H. Kerting: ethod to Teach the deign and oeration of a ditribution yte, EEE Tranaction on Power aratu and Syte, vol. PS-103, no.7, , Jul [3] G.X. Luo and. Selyen, Efficient Load Flow for Large Weakly Mehed Network," EEE Tranaction on Power Syte, vol. 5, no. 4, , Nov [4] W.C. Wu, and B.M. Zhang, three-hae ower flow algorith for ditribution yte ower flow baed on loo-analyi ethod, Electrical Power and Energy Syte, vol. 30,. 8 15, Jun [5] T.-H. Chen, M.-S. Chen, K.-J. Hwang, P. Kota, and E.. Chebli, "Ditribution yte ower flow analyi-a rigid aroach," EEE Tranaction on Power Delivery, vol.6, no.3, , Jul [6] J. H. Teng, " Modified Gau-Seidel algorith of three hae ower flow analyi in ditribution network," Electrical Power and Energy Syte, vol. 24, no. 2, , Feb [7].M. da Cota, N. Martin, and J.L.R. Pereira, "Develoent in the Newton Rahon ower flow forulation baed on current injection," EEE Tranaction on Power Syte, vol.14, no.4, , Nov [8] P..N. Garcia, J.L.R. Pereira, S. Carneiro Jr.;.M. da Cota, and N. Martin, "Three-hae ower flow calculation uing the current injection ethod," EEE Tranaction on Power Syte, vol.15, no.2, , May [9] Whei-Min Lin, Jen-Hao Teng; Three-hae ditribution network fatdecouled ower flow olution, nternational Journal of Electrical Power & Energy Syte, vol. 22, no. 5, , Jun [10] M. bdel-kher, K.M. Nor, and.h.. Rahid, "roved Three- Phae Power-Flow Method Uing Sequence Coonent," EEE Tranaction on Power Syte, vol.20, no.3, , ug [11] M. bdel-kher, K.M. Nor, and.-h. bdul-rahid, "Develoent of unbalanced three-hae ditribution ower flow analyi uing equence and hae coonent," in Proc. 12th nternational Middle-Eat Power Syte Conference(MEPCON), , Mar reearch interet include ower yte lanning and analyi, ower oeration and control, and art grid alication. Daniel Nikovki wa born in Plovdiv, Bulgaria, in He received the Ph.D. degree in Robotic fro Carnegie Mellon Univerity, US, in He i currently working at Mitubihi Electric Reearch Laboratorie in Cabridge, Maachuett, US. Hi reearch interet include achine learning, otiization and control, and nuerical ethod for analyi of cole indutrial yte. Tetufui Ohno wa born in Hyogo, Jaan in He received the M.S degree in huan inforation engineering fro Oaka Univerity, Jaan in He i a eber of EEJ. He i currently working at the dvanced Technology R&D Center, Mitubihi Electric Cor. Hi reearch interet include ditribution yte analyi and control. Toihiro Takano wa born in Oaka, Jaan, in He received the M.S degree in reciion engineering fro Kyoto Univerity, Jaan in He i a enior eber of EEJ, and a eber of SCE, CGRE. He i currently working at the dvanced Technology R&D Center, Mitubihi Electric Cor. Hi reearch interet include oeration, control and rotection for ower yte, ditribution reource, and icro-grid. Yauhiro Kojia wa born in Gifu, Jaan in He received the Ph.D. degree in Electrical Engineering fro Oaka Univerity, Jaan in He i a enior eber of EEJ, and a eber of EEE. He i currently working at the dvanced Technology R&D Center, Mitubihi Electric Cor. Hi reearch interet include art inforation technology alication for ocial infratructure like ower yte.. BOGRPHES Hongbo Sun wa born in Liaoning, China in He received the Ph.D. degree in Electrical Engineering fro Chongqing Univerity, China in He i a enior eber of EEE, and a regitered rofeional engineer. He i currently working at Mitubihi Electric Reearch Laboratorie in Cabridge, Maachuett, US. Hi