Study of Power Flow Algorithm of AC/DC Distribution System including VSC-MTDC

Transcription

1 Energie 015, 8, ; oi: /en Article OEN ACCESS energie ISSN Stuy of ower Flow Algorithm of AC/DC Ditribution Sytem incluing VSC-MTDC Haifeng Liang *, Xiaoling Zhao, Xiaolei Yu, Yajing Gao an Jin Yang State Key Laboratory of Alternate Electrical ower Sytem with Renewable Energy Source (North China Electric ower Univerity), Baoing , Hebei, China; (X.Z.); (X.Y.); (Y.G.); (J.Y.) * Author to whom correponence houl be aree; hfliang@ncepu.eu.cn; Tel.: Acaemic Eitor: Hoam A. Gabbar Receive: 13 June 015 / Accepte: 3 Augut 015 / ublihe: 7 Augut 015 Abtract: In recent year, itribute generation an a large number of enitive AC an DC loa have been connecte to itribution network, which introuce a erie of challenge to itribution network operator (DNO). In aition, the avantage of DC itribution network, uch a the energy conervation an emiion reuction, mean that the voltage ource converter bae multi-terminal irect current (VSC-MTDC) for AC/DC itribution ytem emontrate a great potential, hence rawing growing reearch interet. In thi paper, coniering loe of the reactor, the filter an the converter, a mathematical moel of VSC-HVDC for the loa flow analyi i erive. An AC/DC itribution network architecture ha been built, bae on which the ifference in moifie equation of the VSC-MTDC-bae network uner ifferent control moe are analyze. In aition, correponing interface function uner five control moe are provie, an a back/forwar iterative algorithm which i applie to power flow calculation of the AC/DC itribution ytem incluing VSC-MTDC i propoe. Finally, by calculating the power flow of the moifie IEEE14 AC/DC itribution network, the efficiency an valiity of the moel an algorithm are evaluate. With variou itribute generation connecte to the network at appropriate location, power flow reult how that network loe an utilization of tranmiion network are effectively reuce.

2 Energie 015, Keywor: voltage ource converter; MTDC; itribution ytem; mathematical moel; interface function; back/forwar iterative algorithm 1. Introuction In recent year, the economic evelopment an the fat pee of the urbanization proce caue the power conumption to grow rapily. Theore, the traitional itribution ytem are facing a erie of challenge, e.g. increaing operation efficiency, enhancing ervice reliability, improving power quality an afe-interconnecting itribute generation [1 4]. The VSC-HVDC [5 8] technology bae voltage ource converter how avantage becaue of the rapily growing application of power electronic technology in the electricity itribution fiel: (1) itribute generation (DG) an energy torage (ES) evice interface to the AC itribution network require DC/AC or AC/DC converion while a complete DC network can ave lot of converter link an reuce cot an power loe but improve operational flexibility [9 11]; () AC itribution network require AC/DC converion which upplie a growing number of DC loa a DC itribution network can eliminate the link which will greatly reuce energy conervation [1,13]; (3) urbanization an the extenive ue of power-electronic evice caue voltage fluctuation, voltage ip, harmonic pollution an other power quality problem in AC itribution network [ 4]. Stuie alo how that DC itribution network have lot of other avantage: environmentally frienly, high capacity of power upply, low-cot of itribution cable an line, reuce tranmiion utilization an loe, improve power quality, an neeing no reactive power compenation [1,1,13]. Coniering the comprehenive avantage of the DC itribution network, coniering the huge invetment into evelopment of inepenent DC itribution network, the ue of a hybri AC/DC itribution cheme then graually traniting to a complete DC itribution ytem i more feaible in practice. Theore, an AC/DC power itribution ytem bae on VSC-MTDC cannot only realize inepenent control of active an reactive power, but alo improve the power quality an power upply capacity of the itribution network, facilitate the DG connection, an reuce loe an cot. The tuy of the power flow calculation metho of the AC/DC itribution ytem with VSC-MTDC will be an important bai to analyze the teay-tate an tranient characteritic, control an protection technologie of VSC-MTDC. Theore, it will be the main focu of thi paper. At preent, the reearch on the moeling an control algorithm alreay ha mae ome achievement for the AC/DC tranmiion ytem with VSC-HVDC, but the tuy of the AC/DC itribution ytem with VSC-MTDC i till in it infancy. Alternating iterative algorithm or unifie iterative algorithm are commonly applie to the problem of power flow calculation for the VSC-MTDC ytem [14 16]. Among reporte work, in [17], bae on a teay-tate moel of VSC-HVDC, a mathematical moel bae on Newton metho power flow calculation wa evelope an then a power flow algorithm wa propoe which calculate AC an DC alternately. In [18], coniering ifferent control moe of VSC, correction equation were erive. On the bai of thee correction equation, a uniform iterative power flow calculation algorithm for ytem equippe with VSC-HVDC wa propoe. In [19], uner fixe control parameter an fixe power flow control objective, repectively, a novel algorithm for power

3 Energie 015, flow calculation bae on equivalent injection power wa propoe. In [0,1], a VSC moel for VSC-MTDC power flow calculation wa erive. Accoring to the combination for control variable M (moulation egree) an δ (WM phae angle), four kin of control cheme were brought forwar; an correponing interface function for AC/DC alternant calculation are provie. In all the above reearch, converter loe are treate a equivalent to a reitance or imply ignore. To aume that the active flow through the converter i equal to the DC power flow mean that the calculation uner thi aumption i not accurate enough. In [], a generalize alternating iterative power flow algorithm for AC/DC network uitable to ifferent converter control moe i propoe. In [3], the converter loe moel i tuie in etail prior to propoing an alternating iterative power flow algorithm for AC/DC network incorporating VSC-MTDC which i compatible with other exiting commercial AC power flow calculation oftware. In thi paper, coniering the loe of reactor, the filter an the converter, a mathematical moel of VSC-HVDC i erive. After builing AC/DC itribution network architecture, the ifference in the moifie equation of the VSC-MTDC-bae network uner ifferent control pattern are analyze. In aition, correponing interface function uner five control pattern are provie, an a back/forwar iterative algorithm i propoe. Finally, by calculating the power flow of a moifie IEEE14 AC/DC itribution network, the efficiency an valiity of the moel an algorithm are evaluate. With ifferent itribute generation connecte to the network at ifferent yet appropriate location, power flow reult how that network loe an power aborption from tranmiion network are reuce.. Theoretical Conieration.1. VSC-HVDC Steay-State Moel The voltage ource converter bae high voltage irect current (VSC-HVDC) moel i hown in Figure 1., Q i i i U i, Q U ci ci ci ci I i Ztfi U fi fi Zci U i B fi I ci Figure 1. Moel of VSC-HVDC. In Figure 1, it i aume that parameter with ubcript i are thoe of the ith VSC generate from the.. DC ytem. It AC output voltage i Uci Ucici an the connecte AC ytem voltage Ui Uii with WM phae angle i ci i. The connecte filter voltage i U fi U fi an the DC voltage i fi Ui. The impeance of interface tranformer i Ztfi Rtfi jxtfi an impeance of reactor i Zci Rci jxci while the uceptance of filter i jbfi. The power injecte to AC ytem i i, Qi, an the power from the interface tranformer i ci, Qci while the DC power i i. The teay tate moel of VSC-HVDC i erive a follow [3].

4 Energie 015, i Ui Gtfi UiUfi[ Gtfi co( i fi ) Btfi in( i fi )] (1) Qi Ui Btfi UiUfi[ Gtfi in( i fi) Btfi co( i fi)] () ci Uci Gci UfiUci[ Gci co( fi ci ) Bci in( fi ci )] (3) Qci Uci Bci UfiUci[ Gci in( fi ci ) Bci co( fi ci )] (4) Coniering the converter loe of VSC loi, the relationhip between i an ci can be expree a i ci loi (5) where, with erence to [4,5], loi i mae up of contant an variable part. In thi paper, it i revie to inclue contant, linear an quaratic quare part. Among them, the circuit lo aociate with the off-tate voltage of evice i ecribe a contant an lo an witching lo aociate with the current tate relationhip a linear, while revere recovery lo an generate heat lo a quaratic quare part of the current Ici [3]. loi a bici cici (6) where, a, b, c are the lo coefficient etermine by the curve which i fitte by the tet ata of the converter loe of VSC. Moreover, the following expreion can be obtaine. where, M i the moulation egree of WM an μ i DC voltage utilization... VSC-HVDC Control Moe an arameter Contrain U ci μm i Ui (7) In VSC-HVDC, the tability of the DC voltage i irectly relate to the normal operation of the ytem an the tability of the output voltage at the AC-ie. In orer to achieve the balance of power, one of the VSC control objective i contant DC voltage control. There are four baic control moe for VSC-HVDC: Moe 1: Contant active an reactive power control; Moe : Contant active an AC voltage amplitue control; Moe 3: Contant DC voltage an reactive power control; Moe 4: Contant DC voltage an AC voltage amplitue control. In an AC/DC itribution ytem, the above control moe are alo require, but when connecte to a paive ytem, the power value cannot be etermine which can only be obtaine from the power flow calculation of the paive ytem. So, a moe 5 i propoe for connection to paive ytem where the control moe i contant AC voltage (amplitue an phae). In power flow calculation, parameter contraint are lite a follow. Umin U Umax (8) min max (9) Qmin Q Qmax (10)

5 Energie 015, Umin U Umax (11) N (1) 0 DG DG max (13) 0 M 1 (14) where, Umin, Umax, θmin, θmax, Qmin, an Qmax are repectively the low an upper limit of the AC bu voltage amplitue, phae anlge, injecte reactive flow; Umin, Umax are the limit of the U; N i the capacity of the VSC; DG i the power output of DG an DGmax i the maximum output flow..3. ower Flow Calculation of AC/DC Ditribution Sytem with VSC-MTDC.3.1. Structure of AC/DC Ditribution Sytem with VSC-MTDC The conventional raial AC itribution network commonly contain a ingle power ource, which upplie power for loa through feeer. Several AC ub-ytem will be forme when an AC itribution network tranform into an AC/DC hybri itribution ytem. In orer to analyze thi hybri ytem conveniently, the AC ytem connecte irectly with the tranmiion network i efine a the firt AC ytem, while other are branch AC ytem. AC ytem are interconnecte through VSC-MTDC ytem without irect connection, i.e., loop network i not taken into conieration. ower for the firt AC ytem i upplie by the tranmiion network, while power for other branch AC ytem i upplie by the DC ytem or itribution energy reource (DER). The AC/DC itribution ytem till tranfer electricity through the raial itribution network. The contruction of VSC-MTDC AC/DC itribution ytem i preente in Figure. AC ytem 1 connect with the tranmiion network an operate a the firt AC ytem, while AC ytem,3,, N are branch AC ytem. The firt AC ytem can connect with one or more DC ytem. DER are connecte with DC ytem or AC ytem. AC gri firt AC ytem 1 DC ytem 1 DC ytem... DC ytem n AC ytem AC ytem 3 AC ytem 4 AC ytem N DC ytem 3 Figure. Structure of AC/DC itribution network with VSC-MTDC. In the power flow calculation of AC ytem, the correponing AC noe are coniere a loa noe when the control moe of the inverter connecte with the DC ytem i contant active power a

6 Energie 015, moe 1 an or contant DC voltage a moe 3 an 4. Furthermore, the correponing AC noe are coniere a the balance noe of thi AC ytem when the control moe i contant AC voltage (amplitue an phae) a moe 5. Theore, there i only one converter to be controlle by a contant AC voltage pattern in orer to enure the uniquene of the balance noe. The noe connecte with the tranmiion network i electe a the balance noe. In the DC power flow calculation, an inverter with contant DC voltage control moe i neee to balance the power converion..3.. The Interface Equation of AC/DC ower Flow Alternate Calculation Operation with Contant Active or Reactive ower The equivalent injection power an Q of AC ytem i contant, an AC voltage U. can be obtaine by power flow calculation of AC ytem. In AC network, thoe noe are aume a Q noe. DC power, DC voltage U, phae hift angle δ an moulation epth M are unknown an neee to be calculate. Converter tation connect with AC ytem on one ie, an it equivalent power flow moel i preente in Figure 3. S Ztf Sf U f Scf Zc Sc U Q f B f U c Figure 3. Equivalent ingle phae power flow moel of a converter tation connecte to the AC gri.., Q are known, an S. + jq, Uc, c, Qc can be calculate by Equation (15) (0), an then phae hift angle δ can be obtaine. I S / U (15) * * if U U I Z (16) f tf tf S U I j B U (17) cf f tf ( f f ) I S / U (18) c cf f U U I Z (19) c f c c S U I (0) c c c Then, lo an can be calculate by Equation (6) an (5), repectively. U can be obtaine by olving the equation of DC network, an moulation epth M i calculate by Equation (7).

7 Energie 015, Operation with Contant Active ower an AC Voltage Amplitue When contant active power an AC voltage control moe i applie to the inverter, the equivalent injecte reactive power Q an AC voltage phae angle θ of AC ytem can be obtaine by olving power flow calculation. In AC network, thoe noe are aume a V noe. DC power, DC voltage U, phae hift angle δ an moulation epth M are unknown an the calculation proce i the ame a in Section Operation with Contant AC Voltage When contant AC voltage control moe i applie to the inverter, the equivalent injecte power, Q of AC ytem can be obtaine by olving power flow calculation of AC network. In AC network, thi noe i aume a the balance noe. AC voltage U i known. DC power, an DC voltage U, phae hift angle δ an moulation epth M are unknown an the calculation proce i the ame a that in Section Operation with Contant DC Voltage an Reactive ower When contant DC voltage an reactive power control moe i applie to the inverter, DC an AC voltage amplitue, equivalent injecte reactive power are known, while equivalent injecte active power, phae hift angle an moulation are unknown. In orer to obtain, the relevant DC active power b nee to be calculate by olving DC network equation firtly. Due to the known DC noe voltage Ub of the inverter operate with contant DC voltage control moe, nc 1 moifie equation exit, that i ' i i J Ui (1) n c U YU () i i ij j j1 ' J J( ib, jb) (3) where, i1,,... nc, i b, b repreent the inverter operate with contant DC voltage control moe, an nc ' tan for the number of inverter. J i the nc 1 nc 1 Jacobian matrix of moifie equation. J i the nc nc Jacobian matrix of DC network an can be calculate a per Equation (4). i i the erence value of DC active power of inverter operate with non-contant DC voltage control moe. i i the DC active power of correponing network, an Yij i the conuctance matrix element of the DC network. J ij n c YU ii i YimUm i j m1 mi YU ij i i j (4) To acquire unbalance magnitue of DC voltage, olve the moifie equation. Then, moify the DC voltage until the iteration reult atifie convergence criteria. b(i = b) can be calculate by Equation () an then can be obtaine.

8 Energie 015, In the initial calculation, the lo of inverter i unknown. The aume initial value of equivalent injecte active power i hown a Equation (5). Equivalent injecte active power from the lat iteration i applie to thi iteration. n c 0 b i i1, ib (5) 0 i i i1,,... nc, ib where, upercript 0 repreent initial value, an i i the AC active power erence value of inverter i. The lo of inverter i obtaine accoring to Equation (15) (18) an (6) an then c can be foun from Equation (6). Set c, Q a the erence value equation are hown a: c, c lo (6) Q for calculation, repectively. The unbalance moifie c c c Q Q f J F U 1 c F U f where, J i the Jacobian matrix, an F1, F are hown a: (7) F1 cf f (8) F Qcf Qf Qf (9) f Uf Gtf UU f [ Gtf co( f ) Btf in( f )] (30) Qf Uf Btf UU f [ Gtf in( f ) Btf co( f )] (31) cf Uf Gc UU c f [ Gc co( f c ) Bc in( f c )] (3) Qcf Uf Bc UU c f [ Gc in( f c ) Bc co( f c )] (33) Unbalance value can be obtaine by Equation (1) (4) an (8) (33). Moifie value can be obtaine by olving relevant equation with Jacobian matrix to calculateu c, an Qc can be obtaine by Equation (4). Then, recalculate the lo of inverter an obtain c by Equation (6) to compare with. If the iteration atifie the criteria, en the calculation; otherwie et c a the new to reolve c the moifie equation until iteration converge. Then, equivalent injecte active power, phae hift angle δ, moulation M can be obtaine Operation with Contant DC an AC Voltage When the inverter control moe operate with contant DC an AC voltage pattern, DC an AC voltage magnitue are known an equivalent injecte active an reactive power, phae hift angle an moulation are unknown. The olution i the ame a Section The initial value of Q can be et a 0.5. Q i obtaine by Equation () after olving moifie equation. Convergence of Q to Q nee to be c

9 Energie 015, evaluate: Q houl be upate for the next iteration if ivergent, otherwie, Q, δ an M can be obtaine Alternation Algorithm of AC/DC Ditribution Sytem Incorporating VSC-MTDC Alternation algorithm can be applie to the olution with the AC flow interface equation mentione above. However, the traitional alternation algorithm oe not work on the VSC-MTDC AC/DC itribution ytem. Thu, a back/forwar iterative algorithm i propoe for the power flow calculation of the AC/DC itribution ytem in thi paper by improving the traitional algorithm. Although loop exit in traitional itribution network, they are aume to be opene to be raial after the incorporation of DC itribution network, i.e., AC itribution ytem i ivie into everal AC ub-ytem. The olution for them are ifferent accoring to whether it i an active network or not. A a reult, it i unable to olve all calculation with the ame metho. Thu, a back/forwar iterative metho tarte from the en of the raial network i propoe. In one iteration, there are everal power flow alternative calculation of the AC/DC ytem. Hence, an improve back/forwar iterative algorithm i propoe. In the calculation of AC ytem, if it i an active AC network with everal ource, Newton metho i ue intea of back/forwar iterative metho. If it i a paive AC network, back/forwar iterative metho i applie. In the algorithm, b i moifie by the reult of DC power flow. In the calculation of AC network, if the reactive power of a V noe i out of limit, thi noe i converte into a Q noe. If the voltage amplitue of a Q noe i out of limit, thi noe i converte into a V noe. In the calculation of DC network, if DC voltage of any VSC i out of limit, thi voltage will be et a the new voltage limit an then the power flow calculation houl be repeate. If the error between i an the lat iteration reult i atifactorily mall, the problem i convergent. Theore, iteration convergence criterion i ( k) ( k1) max i i (34) where, upercript k repreent kth iteration. Back/forwar iterative algorithm of AC/DC itribution ytem i eparate into the following tep: Step 1: Input the ata of AC/DC network power flow calculation an characteritic, et k = 1, then forwar weep from en of the network. Step : Determine the characteritic of network. If it i a branch AC an paive network, apply back/forwar iterative algorithm to power flow calculation until convergence, an apply Newton metho if it i a branch AC an active network. When ( k ) ( ) i an Q k i of VSC are acquire, go to tep 4, otherwie continue with tep 3. ( ) Step 3: Determine the characteritic of network. If it i a DC network, calculate k i of the inverter operate with non-contant DC voltage pattern at firt, then olve DC network to obtain the DC voltage an active power of other inverter. Turn to tep 4 after obtaining ( k ) ( k) b, i an ( k ) M i, otherwie move to tep 5. Step 4: Continue to etermine the characteritic of a next network. If it i a branch AC network, return to tep. If it i a DC network, return to tep 3. If it i the firt AC network, go to tep 5. Step 5: Determine the characteritic of network. If it i the firt AC network, apply Newton metho ( k ) to obtain. Until thi tep, an iteration of thi algorithm for the AC/DC itribution ytem b

10 Energie 015, Moele Cae ha been finihe. If the reult i convergent, the calculation i complete, otherwie k k 1, an return to tep with the DC ytem ata acquire by the tep above. The moifie IEEE14 bu AC/DC itribution ytem hown in Figure 4 i ue to verify the effectivene of the propoe algorithm. The voltage bae value i 3 kv an the power bae value i 100 MVA. The IEEE14 bu AC/DC itribution ytem conit of two DC network, four AC network (one firt AC network an three branch AC network) an five VSC inverter whoe high-voltage ie are connecte with AC bu 3, 5,, 7 an 11, repectively. AC ytem I AC ytem II 5 6 AC gri 1 DC ytem 1 V III DC ytem IV 11 1 AC ytem AC ytem Figure 4. Moifie IEEE14 bu AC/DC itribution ytem bae on VSC-MTDC. The ata of voltage an power i hown in per unit (p.u.). The parameter of inverter are the ame. Impeance of converter tranformer i j0.111 p.u., uage ratio μ of converter tranformer DC voltage i 6/4, filter uceptance i j0.045 p.u., reactor impeance i j p.u. AC bu 1 i the balance bu of the firt AC network, an the AC amplitue i 1.06 p.u. AC bu 5, 7 an 11 are balance bue of branch AC network, 3, 4, an their voltage amplitue are 1.04, 1.03 an 1.0 p.u., repectively. Voltage amplitue of the ret Q bue are 1 p.u., angle are 0. Ditribute generation (DG) are connecte at ifferent bue in the IEEE14 bu AC/DC itribution ytem. Then three cheme are propoe an hown in Table 1. VSC control ata of DC network i hown in Table, control moe are mentione in 1.. Control pattern 5 i contant AC voltage moe, an control pattern 3 i contant DC voltage an reactive power moe. The power flow calculation reult of the AC ytem i hown in Table 3, while the DC ytem reult i hown in Table 4. All the cheme converge after three iteration. Aitionally, the reult meet the control requirement of each VSC. For Scheme 1 in Table 4, voltage phae angle of VSC II, VSC III lag behin the correponing AC bu voltage phae angle, o VSC aborb active power from AC network. Voltage phae angle of VSC I, VSC IV, VSC V lea ahea of the AC-ie voltage phae angle, o VSC inject active power to AC network. The reult i ame a the calculation value of. For cheme, voltage phae angle of VSC I, VSC III lag behin the correponing AC bu voltage phae angle, o VSC aborb active power from AC network. Voltage phae angle of VSC II, VSC IV, VSC V lea ahea of the AC ie voltage phae angle, o VSC inject active power to AC network. The reult i the ame a the calculation value of. For Scheme 3, voltage phae angle of VSC III lag behin AC bu voltage phae angle, o VSC aborb active power from the AC network. Other VSC voltage phae angle lea

11 Energie 015, ahea, o VSC inject active power to AC network. It i inicate that DG can upply active power to AC network through DC network, an achieve biirectional power flow. Scheme Scheme 1 Scheme Scheme 3 hotovoltaic ower Generation Table 1. Summary of Scheme. Win ower Generation Fuel Cell Ga Turbine ower Generation Bu AC 3 AC 5 AC 8 AC 1 Flow Bu AC 3 AC 8 DC II DC IV Flow Bu DC I DC II DC IV DC V Flow Bu Table. Control parameter of VSC. VSC I II III IV V Control pattern U Q Voltage Amplitue Table 3. Reult of power flow of AC ytem. Scheme 1 Scheme Scheme 3 Voltage hae Voltage Amplitue Voltage hae Voltage Amplitue Voltage hae

12 Energie 015, Table 4. Reult of power flow of DC ytem. VSC I II III IV V U I Scheme 1 / M Q U I Scheme / M Q U I Scheme 3 / M Q In Table 5, the aborption power from the AC/DC itribution ytem an network lo are not ientical accoring to the comparion of the three cheme if the DG are connecte at ifferent bue in the AC/DC itribution network. It i obviou that DC network lo i larger than AC network lo becaue the inverter lo cannot be neglecte, which valiate coniering inverter lo in thi paper. All DG are connecte with AC network in Scheme 1 while all of them are connecte with the DC network in Scheme 3. It i hown in Table 5 that the aborbe power an active power lo are minimal in Scheme 1 while maximal in Scheme 3. Thi occur becaue the potential DC/AC converion, i.e., lo of inverter when DG connect into AC network, i not taken into conieration. Table 5. Comparion of the aborbe power an loe in the AC/DC itribution network. Scheme Scheme 1 Scheme Scheme 3 S in j j j0.075 S aclo j j j0.010 convlo S tranlo j j j0.013 S reaclo j j j cllo S clo j j j Note: S in, S aclo, convlo, S tranlo, S reaclo, cllo, S clo repreent power aborbe from tranmiion network, lo of AC network, inverter lo, converter tranformer lo, reactor lo, DC line lo an lo of AC network. A hown in Table 6, the lo of network increae ignificantly ue to the growing converter lo of DG in Scheme 1 if the converter lo i taken into account. In aition, the lo of network ecreae in Scheme 3 becaue of the reuce convert lo caue by fewer converter if the DG are connecte to the

13 Energie 015, DC network irectly. It i inicate that more converter lea to higher lo if DG which generate AC power are connecte to the AC network intea of the DC network. Beie, the lo of network increae if DG which generate DC power are connecte to the AC network by converter. Hence, it i important to place the DG properly to reuce the power conumption an loe in the DC/AC itribution network. Table 6. Comparion of the abore power an loe coniering converter loe of itribution generation. Scheme Scheme 1 Scheme Scheme 3 S in j j j S aclo j j j S clo j j j0.037 Note: S clo i the DC lo of inverter in network incluing DG. The comparion of the aborbe power an loe with ifferent power generation at the ame location (ame location in Scheme 3) in the DC/AC itribution network i hown in Figure 5. With increaing output of DG, AC active power lo an the aborbe power both ecreae. It i hown that proper DG allocation can help to reuce loe an the aborbe power from tranmiion network. 0.5 active power from AC gri AC active lo 0. active power/p.u output flow of DG/p.u. Figure 5. Comparion of the aborbe power an loe with ifferent power generation. Thee cae inicate that converter lo cannot be neglecte. It i beneficial to minimize loe an aborbe power for the optimal power flow of AC/DC itribution ytem by properly allocating DG rating at the right location. 4. Concluion Bae on the VSC-HVDC teay-tate moel, thi paper introuce the interface equation uner ifferent control moe with conieration of the loe from converter tranformer, reactor, filter an

14 Energie 015, inverter. Further, a back/forwar iterative metho for the AC/DC itribution ytem incorporating VSC-MTDC i propoe. At lat, the effectivene of the back/forwar iterative metho i verifie with a moifie IEEE14 bu AC/DC itribution ytem. The algorithm achieve bi-irection power flow calculation an converge to control objection of inverter. Incorporating DG into AC/DC itribution ytem can reuce network loe an aborption of power to optimize the power flow of the AC/DC ytem. Acknowlegment The author woul like to acknowlege the financial upport from the Funamental Reearch Fun for the Central Univeritie of China (No. 1MS107). Author Contribution The author Xiaoling Zhao carrie out the main reearch tak an wrote the full manucript, an the author Haifeng Liang propoe the original iea, analyze an ouble-checke the reult an the whole manucript. The author Jin Yang an Xiaolei Yu contribute to the writing an ummarizing propoe iea, an the author Yajing Gao provie financial upport. Conflict of Interet The author eclare no conflict of interet. Reference 1. Wang, D.; Mao, C.; Lu, J. Technical analyi an eign concept of DC itribution ytem. Autom. Electr. ower Syt. 013, 37, (In Chinee). Hammertrom, D.J. AC veru DC itribution ytem i we get it right. In roceeing of the IEEE ower & Engineering Society General Meeting, Tampa, FL, USA, 4 8 June 007; pp atteron, B.T. DC, come home: DC microgri an the birth of the Enernet. IEEE ower Energ. Mag. 01, 10, Nilon, D.; Sannino, A. Efficiency analyi of low-an-meium-voltage DC itribution ytem. In roceeing of the IEEE ower & Engineering Society General Meeting, Denver, CO, USA, 10 June 004; pp Mariethoz, S.; Fuch, A.; Morari, M. A VSC-HVDC Decentralize Moel reictive Control Scheme for Fat ower Tracking. IEEE Tran. ower Delivery 014, 9, Tang, G. MTDC Technology Bae on Voltage Source Converter; China Electric ower re: Beijing, China, 009; pp (In Chinee) 7. Weimer, L. MTDC Light: A new technology for a better environment. IEEE ower Eng. Rev. 1998, 18, Hertem, V.; Ghanhari, M. Multi-terminal VSC HVDC for the European uper gri: Obtacle. Renew. Sutainable Energy Rev. 010, 14, Wang, C.; Wang, S. Stuy on problem of itribute generation energy upply ytem. Autom. Electr. ower Syt. 008, 3, 1 4. (In Chinee)

15 Energie 015, Datgeer, F.; Kalam, A. Efficiency comparion of DC an AC itribution ytem for itribute generation. In roceeing of the Autralaian Univerity ower Engineering Conference, Aelaie, SA, Autralia, 7 30 September 009; pp Zhu, K.; Jiang, D.; Hu,. Stuy on a new type of DC itribution network containing electric vehicle charge tation. ower Syt. Technol. 01, 36, (In Chinee) 1. Ma, J.; Jiang, Q.; Yu,. Survey on energy optimize control technology in DC itribution network. Autom. Electr. ower Syt. 013, 37, (In Chinee) 13. Song, Q.; Zhao, B.; Liu, W. An overview of reearch on mart DC itribution power network. roc. CSEE 013, 33, (In Chinee) 14. Mouavizaeh, S.; Haghifam, M.R. Loa flow calculation in AC/DC itribution network incluing weakly meh, itribute generation an energy torage unit. In roceeing of the Electricity Ditribution n International Conference on Electricity Ditribution, Stockholm, Sween, June 013; pp El-Marafawy, M.; Mathur, R. A new, fat technique for loa-flow olution of integrate multi-terminal DC/AC ytem. IEEE Tran. ower Appar. Syt. 1980, 99, Beerten, J.; Cole, B.R. Implementation apect of a equential AC/DC power flow computation algorithm for multi-terminal VSC HVDC ytem. In roceeing of the IET 9th International Conference on AC an DC ower Tranmiion, Lonon, UK, 19 1 October 010; pp Zheng, C.; Zhou, X.; Li, R. Stuy on the teay characteritic an algorithm of power flow for VSC-HVDC. roc. CSEE. 005, 5, 1 5. (In Chinee) 18. Zhen, C.; Sheng, C. Uniform iterative power flow algorithm for ytem equippe with VSC-HVDC. Electr. ower 007, 40, (In Chinee) 19. Li, G.; Zhou, M.; He, J. ower flow calculation of power ytem incorporating VSC-HVDC. In roceeing of the International Conference ower Sytem Technology, Singapore, 1 4 November 004; pp Chen, Q.; Tang, G.; Wang, X. AC-DC power flow algorithm for multi-terminal VSC-HVDC ytem. Autom. Electr. ower Syt. 005, 5, 1 6. (In Chinee) 1. Sun, G.; Li, Y.; Wei, Z. State etimation of power ytem with VSC-HVDC. Electr. ower Autom. Equip. 010, 30, 6 1. (In Chinee). Chai, R.; Zhang, B.; Bo, Z. Alternating Iterative ower Flower Algorithm for Hybri AC/DC Network Containing DC Gri Bae on Voltage Source Converter. Autom. Electr. ower Syt. 015, 39, (In Chinee) 3. Beerten, J.; Cole, S.; Belman, R. Generalize teay-tate VSC MTDC moel for equential AC/DC power flow algorithm. IEEE Tran. ower Syt. 01, 7, Zhang, X. Multiterminal Voltage-Source Converter-Bae HVDC Moel for ower Flow Analyi. IEEE Tran. ower Syt.004, 19, Han, B.M.; Karay, G.G.; ark, J.K. Interaction analyi moel for tranmiion tatic compenator with EMT. IEEE Tran. ower Delivery 1998, 13, by the author; licenee MDI, Bael, Switzerlan. Thi article i an open acce article itribute uner the term an conition of the Creative Common Attribution licene (