A three-phase power flow approach for integrated 3-wire MV and 4-wire multigrounded LV networks with rooftop Solar PV

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1 University of Wollongong Researh Online Faulty of Engineering and Information Sienes - Papers: Part A Faulty of Engineering and Information Sienes 13 A three-phase power flow approah for integrated 3-wire MV and 4-wire multigrounded LV networks with rooftop Solar PV Md J E Alam University of Wollongong, mjea98@uowmail.edu.au K M. Muttaqi University of Wollongong, kashem@uow.edu.au Darmawan Sutanto University of Wollongong, soetanto@uow.edu.au Publiation Details M. Alam, K. M. Muttaqi & D. Sutanto, "A three-phase power flow approah for integrated 3-wire MV and 4-wire multigrounded LV networks with rooftop Solar PV," IEEE ransations on Power Systems, vol. 8, () pp , 13. Researh Online is the open aess institutional repository for the University of Wollongong. For further information ontat the UOW Library: researh-pubs@uow.edu.au

2 A three-phase power flow approah for integrated 3-wire MV and 4-wire multigrounded LV networks with rooftop Solar PV Abstrat With inreasing level of rooftop solar photovoltai (PV) penetration into low voltage (LV) distribution networks, analysis with realisti network models is neessary for adequate apturing of network behavior. raditional three-phase 3-wire power flow approah laks the apability of exat analysis of 4-wire multigrounded LV networks due to the approximation of merging the neutral wire admittane into the phase wire admittanes. Suh an approximation may not be desirable when neutral wire and grounding effets need to be assessed, espeially in the presene of single-phase solar power injetion that may ause a signifiant level of network unbalane. his paper proposes a three-phase power flow approah for distribution networks while preserving the original 3-wire and 4-wire onfigurations for more aurate estimation of rooftop PV impats on different phases and neutrals. A three-phase transformer model is developed to interfae between the 3-wire medium voltage (MV) and the 4-wire LV networks. Also an integrated network model is developed for an expliit representation of different phases, neutral wires and groundings of a distribution system. A series of power flow alulations have been performed using the proposed approah to investigate the impats of single-phase variable PV generation on an Australian distribution system and results are presented. Keywords approah, flow, power, solar, phase, networks, three, pv, lv, multigrounded, 4, rooftop, mv, wire, 3, integrated Disiplines Engineering Siene and ehnology Studies Publiation Details M. Alam, K. M. Muttaqi & D. Sutanto, "A three-phase power flow approah for integrated 3-wire MV and 4-wire multigrounded LV networks with rooftop Solar PV," IEEE ransations on Power Systems, vol. 8, () pp , 13. his journal artile is available at Researh Online:

3 1 A hree-phase Power Flow Approah for Integrated 3-Wire MV and 4-Wire Multigrounded LV Networks with Rooftop Solar PV M J E Alam, Student Member, IEEE, K M Muttaqi, Senior Member, IEEE, and D Sutanto, Senior Member, IEEE Abstrat With inreasing level of rooftop solar PV penetration into LV distribution networks, analysis with realisti network models is neessary for adequate apturing of network behavior. raditional three-phase 3-wire power flow approah laks the apability of exat analysis of 4-wire multigrounded LV networks due to the approximation of merging the neutral wire admittane into the phase wire admittanes. Suh an approximation may not be desirable when neutral wire and grounding effets need to be assessed, espeially in the presene of single-phase solar power injetion that may ause a signifiant level of network unbalane. his paper proposes a three-phase power flow approah for distribution networks while preserving the original 3-wire and 4-wire onfigurations for more aurate estimation of rooftop PV impats on different phases and neutrals. A three-phase transformer model is developed to interfae between the 3-wire MV and the 4-wire LV networks. Also an integrated network model is developed for an expliit representation of different phases, neutral wires and groundings of a distribution system. A series of power flow alulations have been performed using the proposed approah to investigate the impats of single-phase variable PV generation on an Australian distribution system and results are presented. Index erms hee-phase distribution networks, 3-wire and 4-wire multigrounded systems, hree-phase power flow, Rooftop solar PV impats. I. INRODUCION Integration of solar photovoltai (PV) resoures in high penetration level may introdue a multitude of adverse impats [1], [] on distribution networks. Voltage rise [3], reverse power flow [4], voltage unbalane [] an be listed as some of the major impats. Analysis of network behavior under PV penetration is essential for understanding these impats. hree phase power flow is often deployed as a tool for the analysis of network asymmetry and load imbalane in distribution networks. With an inreasing level of single phase rooftop solar PV penetration, phase domain analysis is essential not only for inorporating the load unbalane and network asymmetries, but also to assess the impats of single-phase solar PV units installed in the three phase distribution networks. Without the diret ontrol of distribution utilities over the sizes and loations of ustomer-installed rooftop PV units, his work is supported by the Australian Researh Counil (ARC) and Essential Energy Linkage Grant, LP M J E Alam, K M Muttaqi and D Sutanto is with the Endeavour Energy Power Quality and Reliability Researh Centre, Shool of Eletrial, Computer, and eleommuniations Engineering, University of Wollongong, NSW 5, Australia ( mjea98@uowmail.edu.au, kashem@uow.edu.au, soetanto@uow.edu.au) Manusript reeived. unbalaned alloation of PV resoures will produe different level of impats on different phases of a feeder, suh as unbalaned impats of voltage rise [3] and reverse power flow [4]. Unbalaned operation of networks an also affet indution motors, power eletroni onverters [5], and, may also derease network voltage stability margins [6]. Medium voltage (MV) segments of distribution networks are typially onstruted with 3-wire onfiguration whereas low voltage (LV) segments are onstruted with 4-wire onfiguration, where the fourth wire is the neutral wire whih is grounded at multiple loations along the feeder. Using the assumption of zero neutral voltage with a perfetly grounded neutral in the LV part, matrix redution tehnique is typially applied to redue the 4x4 admittane matries orresponding to LV line-segments into 3x3 matries [7]. However, in pratial LV distribution feeders, neutral grounding resistanes an vary from less than 1 ohm to several tens of ohms depending on the type and ondition of grounding system [8] [1]. Further, the unbalane in load and line impedane and the unbalaned alloation of PV resoures an produe high neutral urrent in LV feeders, sometimes even higher than the phase urrents [7], [11]. High neutral urrent an produe signifiant neutral-to-ground voltage in the presene of neutral grounding resistane. herefore, the traditional assumption that the neutral-to-ground voltage is zero and merging the neutral line admittanes into the phase line admittanes in the modeling may not be realisti. High neutral urrent may produe voltage distortion, and may overload neutral ondutor [1]. Further, the neutral-to-ground voltage an at as a ommon-mode noise in sensitive eletroni equipment [13]. Neutral-to-ground voltage beyond manufaturer speified tolerane level [13] may ause mal-operation [14] of sensitive equipment. o avoid suh issues, the aurate determination of neutral urrent and voltage is essential, espeially for planning distribution networks with PV integration. herefore, preserving the 4-wire onfiguration in the network model would be desirable and development of a power flow approah apable of retaining the original wiring onfigurations of the MV and LV network segments is neessary. Extensive researh has been performed on 3-phase power flow algorithms for distribution networks with distributed resoures [15], however, most of those are based on a 3-wire power flow approah. A forward-bakward substitution based 4-wire power flow method is developed in [11] onsidering the ground-wire impedane. A three-phase 3-wire power flow based on a urrent-mismath variant of Newton-Raphson

4 algorithm is presented in [16]. Authors in [17] have developed a urrent-mismath based 4-wire power flow approah. However, in [17], a ombined 3-wire and 4-wire power flow formulation orresponding to MV and LV networks is not expliitly presented. his paper proposes a three-phase power flow approah developed for the analysis of single phase rooftop solar PV impats on distribution networks by preserving the realisti onfigurations of MV and LV networks. With this tehnique, the PV impats on the host LV network and the upstream MV network an be performed without modifying the model of the original wiring onfigurations. LV network modeling will be performed based on the original 4x4 matrix representation of LV line segments, and MV networks will be modeled using 3x3 matries. A primitive admittane model of deltawye transformer will be developed based on the tehnique presented in [18] to satisfy the modeling requirements of the 3-wire (MV) and 4-wire (LV) systems. he integrated system of power flow equations orresponding to the 3- wire and 4-wire networks will be solved using the urrentmismath variant of Newton-Raphson algorithm. It is worth mentioning that a network model retaining the original 3- wire and 4-wire onfigurations ould be solved using other power flow solution algorithms with minor adjustments to inorporate 3- and 4-wire onfiguration where the neutral line and ground resistanes need to be inluded. o investigate the impats of single-phase variable PV generation, a series of power flow alulations will be performed over a 4-hour period. A pratial distribution system in Australia will be used to verify the appliability of the proposed approah in real-world distribution networks. hough this paper has onentrated on rooftop PV systems, the problems presented an be experiened with any type of distributed generation resoures, suh as small residential wind power units or fuel ells, installed in an unbalaned pattern in a distribution feeder. herefore, the proposed approah an be extended to other distributed generation resoures. his paper is organized into five setions. Setion I provides an introdution of the problem of using a three-phase 3-wire power flow approah to analyze 3- and 4-wire onfiguration often found in MV and LV distribution network. his is partiularly important when neutral wire and grounding effets need to be assessed. Network modeling approah with multigrounded LV feeder with rooftop solar PV is disussed in Setion II. Formulation of the power flow problem for an integrated 3-wire MV and 4-wire LV network is presented in Setion III. he appliation of the approah has been verified in Setion IV using a pratial distribution system. Setion V onludes the paper by summarizing the works performed and observations made. II. SYSEM MODELING A distribution feeder an be represented as a ombination of series elements (overhead and underground line segments, transformers et.) onneted between, and shunt elements (line suseptanes, grounding impedane, apaitor / reator banks, et.) onneted at, different system nodes. Admittane matrix Fig. 1. MV setion Delta-Wye transformer LV setion 1 3 Neutral Grounding 4 Impedane MV setion (a) 4-bus, 3-wire and 4-wire test system Delta-Wye transformer LV setion 1 x x+1 x+ y (b) A general extended form of 3-wire and 4-wire test system hree Wire and Four Wire est System models of the series and shunt omponents assembled in the form of a total system admittane matrix are used for network analysis. A simple 4-bus distribution test feeder shown in Fig. 1(a), similar to the IEEE 4-bus test system [19] will be used in this paper to formulate the modeling approah of 3-wire and 4-wire systems; a similar approah an be followed for the general extended form of the test system shown in Fig. 1(b). he 4-bus feeder is onfigured to have a 3-wire MV setion from bus 1 to, a delta-wye step-down transformer from bus to 3, and a 4-wire LV setion from bus 3 to 4. Detailed modeling aspets of the network omponents are disussed below. A. Modeling of the MV Lines hree wire MV distribution lines an be represented using 3 3 admittane matries onsisting of the self admittanes of three phases a, b and as the diagonal elements and the mutual oupling admittanes among them as off-diagonal elements. Following this model, the MV line admittane of the 4-bus test system, Y MV 1, an be written as, Y MV 1 = y ab = y aa y ba y a y ab y bb y b y a y b y (1) where, the subsripts i and j are used for generi modeling purpose, that represents the buses 1 and, respetively, in the network given in Fig. 1(a). It is to be noted that to onstrut the total system admittane matrix with 3-wire and 4-wire lines, the MV line admittane model needs to be aommodated into the 4-wire line model. herefore, order of the admittane matrix in (1) is inreased to 4 4 using all zero elements, as given below. Y MV 1 = y aa y ba y a B. Modeling of the LV Lines y ab y bb y b y a y b y () Low voltage distribution feeders are typially onstruted with four wire line segments where the fourth wire is the

5 3 Fig.. MV Side (3-wire, Delta onneted) I 1 I 4 = I I 3 I a w1 I a w I b w1 I b w I w1 I w Delta side neutral urrent 1x1 Ph. Bank 1x1 Ph. Bank 1x1 Ph. Bank I a w3 I a w4 I b w3 I b w4 I w3 I w4 LV Side (4-wire, Wye onneted) erminal onnetion and urrents of delta-wye transformer neutral wire. Similar to the phase ondutors, the neutral ondutor has self and mutual impedane omponents with the other phase wires, and these need to be inluded in the admittane model. he LV line admittane matrix, Y LV 34 of the test system is given below using a 4 4 matrix model. Y LV 34 = y abn = y aa y ba y a y na y ab y bb y b y nb y a y b y y n y an y bn y n y nn I 5 I 6 I 7 I 8 (3) Here, i and j are used as subsripts for the generi modeling purpose, similarly as desribed for (1), whih represents buses 3, and 4, respetively. he neutral wire is expliitly modeled in this matrix model, as refleted in the 4 th row and olumn. C. Modeling of the MV/LV ransformer A primitive admittane matrix model of a delta-wye transformer is developed based on the relationship of transformer terminal urrents with the internal winding urrents, in a similar fashion disussed for wye-delta onnetion in [18]. he per unit impedane matrix model of a three phase transformer with three phase short iruit impedanes, z a, zb and z, an be desribed in a matrix form as, Z ab = z a z b (4) z he ground referened nodal admittane matrix [18], Y L, an be obtained using the inidene matrix, B, relating the short iruit urrents with the terminal urrents [18], as given below. 1 Y L Y L = B ( Z ab ) 1B and B = he winding admittane matrix Y W by using the following equation, (5) an be obtained from Y W = NY L N (6) N a where, N = N b (7) N 1 and N a = N b = N = 1 1 (8) 1 In (7), denotes a 4 matrix of zero elements, and in (8) 1 orresponds to nominal per unit turns ratio. he terminal urrents in the delta-wye transformer shown in Fig. an be related to the winding urrents by, I 1 I I 3 I 4 I 5 I 6 I 7 I 8 A {}}{ = Iw1 a Iw a Iw3 a Iw4 a Iw1 b Iw b Iw3 b Iw4 b Iw1 Iw Iw3 Iw4 (9) It is to be noted that the 4 th row of A, orresponding to the neutral urrent of delta side, is a vetor of all zero elements as there is no neutral urrent for the delta side. his row is inserted for making the 3-wire side of the admittane matrix ompatible with the 4-wire system alulation, as disussed earlier in the MV and LV line modeling. he primitive admittane matrix of the transformer, Y prim, is found as, [ ] Y prim = AY W A Y P P = Y P S (1) Y SP Y SS where, Y P P is the primary (delta) side self admittane matrix Y SS is the seondary (wye) side self admittane matrix Y P S, YSP are the mutual admittane matries between primary and seondary sides o develop the per-unit model, Y P S and Y SP, eah has to be divided by 3 and Y P P has to be divided by 3, as desribed in []. D. Admittane Matrix of the Integrated System he total system admittane matrix, Y, for a k-bus three phase power system an be onstruted as a 4k 4k matrix to aommodate both 3-wire and 4-wire admittane matries. he diagonal and off-diagonal elements of Y are obtained by, Y ii = k i=1 y abn and, Y = y abn (11) where, i and j = 1,,, k. Self admittane matries of the transformer primary and seondary are added with the self admittane matries of

6 4 the primary bus and the seondary bus, respetively, and the mutual admittanes are added with the mutual admittanes between primary and seondary buses. Following this method, the system admittane matrix for the 4-bus test system with integrated MV and LV networks an be written as, Y = Y MV 1 Y MV Y MV 1 Y MV Y P P Y P S Y LV 34 + Y SS Y SP Y LV 34 Y LV 34 Y LV 34 (1) Buses with grounded neutral, suh as bus 3 and 4 in Fig. 1(a), are modeled by adding the neutral grounding admittanes with the self admittanes of the neutral wire at the respetive buses. his is given in the equation below for an arbitrary bus i, where the neutral grounding admittane is y N G E. Modeling of Loads Y ii = Y ii + y N G ii ii. (13) Realisti modeling of distribution network loads is a omplex task involving omprehensive study of the types, ratings and onsumption trends of eletrial applianes. Lighting, ooking, ooling, heating, use of omputer, teleommuniation and entertainment systems are some of the ommon types of eletriity usage in residential households and all of these appliations vary throughout the day based on onsumer behavior. Pratial modeling of distribution feeder loads, espeially at LV level, would therefore require modeling of load variations of eah of the individual end-use appliations. otal load profile of the households then ould be performed by aggregation of the individual load profiles. ZIP representation of typial residential loads [1], [] will be used for modeling the loads in this paper. A ZIP load model inludes proportions of onstant power, onstant urrent, and onstant impedane loads as given below. P ZIP = P (p P + V P h N V Q ZIP = Q (q P + V P h N V pi + qi + V P h N V V P h N V ) p Z ) q Z where, p P + p I + p Z = 1 and q P + q I + q Z = 1 (14a) (14b) (14) Here, P and Q are the nominal real and reative power at nominal voltage V ; and p P, p I, p Z, and q P, q I, q Z are respetively the onstant power, onstant urrent and onstant impedane proportions of ative and reative load and termed as ZIP parameters, and V P h N is the phase-to-neutral voltage. o obtain the aggregate load model for the household, aggregate ZIP parameters for ative and reative omponents of loads, ZIP P agg and ZIP Q agg, where ZIP P { p P, p I, p Z} and ZIP Q { q P, q I, q Z}, will be determined using weighted average of individual ZIP parameters, as given below. n ( ) ZIP P Pi agg = ZIP P i (15a) i=1 P total Fig. 3. Phase a Phase b Phase I inv a I inv b Neutral Current injetion model of solar PV ZIP Q agg = n i=1 ( Qi Q total I inv ) ZIP Q i (15b) Here, i = 1,,...n, for n number of loads orresponding to different household ativities. F. Modeling of Rooftop Solar PV Solar PV systems installed in LV feeders typially ontain rooftop PV modules and assoiated single phase inverter modules. he inverter output is onneted between the phase and neutral ondutor, as shown in Fig. 3 for three single phase PV soures onneted at phases a, b ands. Current injetion of PV inverter, I inv, depends on the omplex output power of the inverter, P inv +j Sinv P inv, where, P inv is the inverter real power, S inv is the PV inverter apparent power apaity, and V P h N is the phase-to-neutral voltage. I inv = ( P inv + j S inv P inv V P h N ) (16) Here, * represents omplex onjugate. It is to be noted that S inv is not diretly related to the DC power oming out from the PV modules. he P inv is the AC power generated by the inverter for a given value of DC power generated by the PV modules, P DC, taking into aount effiieny of the inverter, η inv, mismath among multiple PV modules, η m, and dirt effets, η d, as given below [3]. P inv = η inv η m η d P DC (17) he inverter ontrols the amount of reative power output that an be generated from the inverter, and is given by S inv Pinv. For a larger reative power output required from the inverter, S inv should be made larger, for the same P inv. P DC an be obtained from the I V harateristi of the solar PV module as given by the following equation, P DC = max (V DC I DC ) (18) where, V DC is the PV module voltage, I DC is the PV module urrent and max ( ) implements the Maximum Power Point raking (MPP) funtion. he funtion max(.) given in (18), is a funtion used to selet the maximum value from a series of V DC times I DC values to obtain the maximum power point of the P V harateristi, as shown in Fig. 4. PV module voltage V DC, depends on ambient onditions and PV module eletrial parameters, whereas the PV module urrent I DC depends on the ambient onditions, the module

7 5 (a) PV Module Current [A] I-V Charateristi PV Module Voltage [V] (b) PV Module Power [W] P-V Charateristi I x V Maximum Value of I x V 1 3 PV Module Voltage [V] From (m-1) th bus I m azip I m bzip m th Bus, Phase a m th Bus, Phase b m th Bus, Phase o (m+1) th bus I m apv I m bpv Fig. 4. Implementation of MPP funtion; (a) I V harateristi (b) P V harateristi I m ZIP I m PV voltage, and the PV urrent itself [4]. Mathematially this an be desribed as, m th Bus, Neutral V DC = φ (t, p) (19) I DC = ψ (t, G, p, V DC, I DC ) () Fig. 5. Current injetion model of load and PV for power flow formulation where, t G p is the ambient temperature is the ambient sun irradiane level is a vetor of PV module eletrial parameters, suh as module resistanes, short-iruit urrent, voltage-temperature and urrent-temperature oeffiients et. is a funtion to determine the PV module voltage from ambient onditions and PV parameters is a funtion to determine the PV module urrent from ambient onditions, PV parameters, module voltage and module urrent An observation of () indiates that it is a transendental φ ψ expression and an analytial form of solution is not available [4]. herefore, numerial tehnique is applied to solve () to find the I-V harateristi of PV modules at any given ambient onditions. he I-V harateristi is then used to find out the urrent injetion from PV inverters into the network. III. PROPOSED 3-PHASE POWER FLOW FOR INEGRAED 3-WIRE AND 4-WIRE SYSEMS WIH SOLAR PV For a onverged power flow problem, the mismath between speified urrent and alulated urrent should be nearly zero. Suh mismath, denoted by I m at an arbitrary bus m of a three phase feeder an be expressed as, I m = (I m ) spe (I m ) al (1) Here, (I m ) spe is the vetor of speified urrents and (I m ) al is the vetor of alulated urrents at the bus m. If the three phase bus m is of 3-wire onfiguration, then the length of the mismath vetor and the urrent vetors is 3, and, for a 4-wire onfiguration the length is 4, where the 4 th element orresponds to the neutral urrent. Speified urrents at bus m an be obtained from urrent ontributions from ZIP load and solar PV as given in () based on the urrent injetion model shown in Fig. 5. (I m ) spe = I ZIP m + I PV m () where, I PV m ( P where, I ZIP ZIP m + jq ZIP ) m m = V m (3) ( P and, I PV PV m = m + jq PV ) m V m (4) is the vetor of phase urrents ontributed by solar PV at phases a, b, P ZIP m + jq ZIP m is the vetor of omplex powers orresponding to loads at phases a, b, P PV m + jq PV m is the vetor of omplex powers orresponding to solar PV inverters at phases a, b, V m is the vetor of omplex voltages at phases a, b, he minus sign in () with I ZIP m represents the differene in the diretion of urrent injetions from the ZIP load and solar PV. In (4), Q PV m will be zero if unity power fator operation of PV is onsidered. It is to be noted that for 3-wire networks, V m omprises of the phase voltages, whereas, for 4-wire networks it ontains the phase-to-neutral voltages. he speified urrent through the neutral wire, ( Im) N spe an be found by adding the speified phase urrents Im, a Im b and Im, obtained from the vetor of speified phase urrents, (I m ) spe. ( I N m ) spe = ( I a m + I b m + I m) (5) he alulated urrents an be obtained using the total system admittane matrix and the vetor of system voltages using the following lassial network urrent equation. (I m ) al = k Y mn V n (6) n=1 Here, Y mn is the admittane matrix from bus m to n, where, n = 1,,..., k, and k is the total number of system buses. Mismath in the speified and alulated urrent injetion omponents in phase and neutral nodes of a three phase

8 6 feeder an be expressed in terms of their real and imaginary omponents using the following equations. I mre I mim = P mv mre + Q m V mim ( V mre + jv mim ) k (G mn V nre B mn V nim ) (7) n=1 = P mv mim Q m V mre ( V mre + jv mim ) k (G mn V nim + B mn V nre ) (8) n=1 I N m Re = ( I a m Re + I b m Re + I m Re ) k ( G N mn V nre BN mnv nim) n=1 I N m Im = ( I a m Im + I b m Im + I m Im ) k ( G N mn V + nim BN mnv nre) n=1 (9) (3) he subsripts Re and Im in (7)-(3) stand for Real and Imaginary, respetively. In (7) and (8), G mn and B mn are 3 4 matries onsisting of the orresponding real and imaginary parts of the admittane matrix from bus m to n, with respet to the phase ondutors. In (9) and (3), G N mn and B N mn are 1 4 vetors onsisting of the respetive real and imaginary parts of the admittane matrix from bus m to n orresponding to the neutral ondutor. he system of non-linear equations (7)-(3) an be solved using Newton- Raphson (N-R) iterative algorithm that needs to relate the inremental hanges in voltages with inremental hanges in urrents in terms of real and imaginary omponents, as given below. V mre V m N Re V mim V m N Im I mim = inv (J) I m N Im I mre I m N Re (31) he inremental voltage vetor in (31) refers to the updates in voltages to be used in the power flow iterations of N-R algorithm, and the inremental urrent vetor refers to the urrent mismathes. he 1 st and 3 rd row of voltage vetor ontains the real and imaginary omponents of phase voltage updates, respetively, and the nd and 4 th row ontains the updates of neutral voltage; J is the Jaobian matrix. For 3-wire segments of distribution networks, the neutral omponents are not present and therefore, the nd and 4 th rows are not inluded in the N-R equations. Following this, the N-R equation for the 4-bus test system under onsideration an written as, V ab V abn 3 V abn 4 = inv J ab J3 abn J4 abn I ab I abn 3 I abn 4 (3) where, V ab is the 6-element inremental voltage vetor onsisting of [ ] V ab Re V ab Im, orresponding to the 3-wire bus, Bus-. represents transpose. V abn 3 is the 8-element [ inremental voltage ] vetor onsisting of V abn 3 Re V abn 3 Im, orresponding to the 4-wire bus, Bus-3. he similar notations hold for the other 4-wire bus, bus 4. I ab is the 6-element urrent mismath vetor onsisting of [ ] I ab Im I ab Re, orresponding to the 3-wire bus, Bus-. I abn 3 is the 8-element urrent mismath vetor onsisting of [ ] I abn 3 Im I abn 3 Re, orresponding to the 4-wire bus, Bus-3. he similar notations hold for the other 4-wire bus, bus 4. he first element in the Jaobian matrix, J ab, is a 6x6 matrix blok orresponding to the 3 wire setion of the system, while 33, 34, 43 and 44 are 8x8 matrix bloks orresponding to the four wire setion. he remaining, 3, 4 and 3, 4 are, respetively, 6x8 and 8x6 matries, orresponding to the delta-wye transformer between the three wire and four wire network segments. It is to be noted that Bus 1, being the slak bus, has been exluded from (3). Following a similar type of notations, the N-R equation of the general form of 3-wire and 4-wire feeder in fig. 1(b) ontaining x number of 3-wire buses and (y x) number of 4-wire buses an be developed as given below. where, J = V ab.. V ab x V abn x+1. V abn y J ab J ab x..... J ab x J ab xx (x+1) y = inv (J) (x+1)x..... yx I ab.. I ab x I abn x+1. I abn y (x+1) y..... x(x+1) xy (x+1)(x+1) (x+1)y..... y(x+1) yy (33) (34) Methods of alulating Jaobian elements desribed in [16], [17] will be deployed in this paper. Updates of real and imaginary omponents of voltages are found using (33) in eah iteration of the N-R algorithm that ontinues until the urrent mismath in (1) is satisfied with an aeptable tolerane. his power flow approah using N-R algorithm works for both mesh and radial networks.

9 7 IV. APPLICAION OF HE PROPOSED 3-PHASE POWER FLOW APPROACH O ASSESS PV IMPACS A. he IEEE 4-bus est Case he IEEE 4-bus system [19] is a standard distribution test feeder to verify power flow programs with different transformer onnetions. he unbalaned loading with delta-wye step-down transformer onnetion is used in this paper. he 1.47 kv line segment is onfigured as 3-wire and the 4.16 kv segment is onfigured as 4-wire. Power flow results for the 3- wire and 4-wire segments of the test system obtained using the proposed approah are presented in able I. Neutral voltages in the order of 1 3 V are obtained for a solidly grounded neutral (1 4 ohm) and are assumed as zero, as shown in able I for the 4-wire buses, 3 and 4. On the other hand, even a low grounding resistane of.3 ohm, whih is within aeptable limit [7], produed a 74 V of neutral voltages at bus 3 and 4 in the presene of high unbalane in loads. he neutral voltages presented in able I annot be diretly obtained as a power flow result using a traditional 3-wire power flow approah. his neutral voltage alulation apability would be useful for distribution feeders with imperfet neutral grounding and ontaining unbalaned integration of solar PV. ABLE I IEEE-4 BUS ES RESULS WIH DIFFEREN GROUNDING OPIONS Grounding ype Ph Bus (V) Bus 3 (V) Bus 4 (V) Solidly Grounded Resistane Grounded B. A Pratial est Network A B C N N/A A B C N N/A he proposed power flow approah is tested on a real distribution feeder in New South Wales (NSW), Australia. It is important to note that the introdution of non-metalli underground water retiulation system in Australia is ontributing to inreased grounding impedane in the LV feeders, as many of the servie drops are bonded with previously metalli water piping system for neutral grounding purpose. Unbalaned PV alloation at a high penetration level will produe inreased neutral urrent and hene will inrease the neutral voltage in the presene of elevated neutral impedane. herefore, the proposed power flow approah ould be useful for PV impat analysis on suh a network with high neutral grounding impedanes. he test feeder is an 8 km long 11 kv rural feeder with 3 series voltage regulators, as shown in Fig. 5. he.4 kv LV feeders are onneted at different buses along the MV feeders through 11/.4 kv delta-wye transformers. Residential loads in the LV feeders are distributed in an unbalaned pattern among the phases. Load data measured on a pratial Australian feeder are used for simulation. PV resoures are integrated in a lustered form, i.e., numerous PV units are installed in a small geographial area. ransformer REG Zone REG1 65 Substation /11 kv REG Fig PV Cluster A pratial distribution feeder in NSW PV Cluster symbols are used to identify the feeders that form the PV lusters. Size of PV units at different residential households ranges from to 5 kw. PV outputs are generated using the April irradiane data given in [3] and applied to obtain the I-V harateristi of Kyoera KCG [5] PV module. Numerial values of neutral grounding resistanes in PV luster 1 have been set muh higher than the ones in PV luster for analyzing the effets of high neutral grounding resistane. Analysis is performed using both idealisti and realisti values of neutral to ground resistane in PV luster. IEEE Std [8]suggests that neutrals of LV systems are typially grounded solidly. For a solidly grounded neutral, phase-to-ground fault urrent an be equal to 1% or greater than the three-phase fault urrent [8]. Based on this riterion, and using the MV/LV substation and LV feeder data of the test system under study, an idealisti value of the neutral to ground resistane for solidly grounded neutral was determined as.5 ohm. A realisti value of.5 ohm is seleted aording to the reommended value of neutral grounding resistane in a Combined Multiple Earthed Neutral (CMEN) system for Australian distribution utilities [9], [1]. o onsider a 1- times inrease in neutral grounding resistane due to bonding with non-metalli water piping system as disussed in [6], neutral grounding resistane of 5 ohm is used in PV luster 1. C. PV Impats on LV Networks Solar PV resoures generate at their peak apaity during midday depending on the ambient sun insolation and temperature. Household load demand is omparatively lower during this time. Power generation from PV resoures, therefore, may exeed the load level at the PV onnetion point at this time, and voltage rise may be observed. Suh a senario is shown in Fig. 7 at one of the LV feeder ends seleted from both of the PV lusters in the network. he upper plot in Fig. 7(a) shows voltage from PV luster 1, whih shows signifiant rise in voltage at midday, and phase a voltage exeeds the upper limit. he lower plot in Fig. 7(b) shows the voltage rise in PV luster, whih is maintained within the limit by the ation of voltage regulator REG3 (in Fig. 6). Due to unbalaned alloation of PV units, voltage rise is different at different phases of the feeder. his unbalane in power injetion produes signifiant inrease of neutral urrent in the LV feeder at midday as shown in Fig. 8. he upper plot

10 8 Phase Voltage [V] Phase Voltage [V] (a) Voltage Rise in PV Cluster 1 Ph. A Ph. B Ph. C (b) Voltage Rise in PV Cluster Ph. A Ph. B Ph. C Voltage Upper Limit: Nominal +1% Voltage Upper Limit: Nominal +1% (a) Phase and Neutral Condutor Currents at LV Substation Bus in PV Cluster 1 1 Ph. A 8 Ph. B Midday Inrease of Neutral Current 6 Ph. C in PV Cluster 1 4 Neutral Feeder Current [A] Feeder Current [A] (b) Phase and Neutral Condutor Currents at LV Substation Bus in PV Cluster 1 8 Ph. A Midday Inrease of Neutral Current Ph. B in PV Cluster 6 Ph. C 4 Neutral Fig. 7. Daily voltage profile at LV feeder end (a) PV luster 1 (b) PV luster in Fig. 8(a) shows the phase and neutral urrents at an LV substation bus in PV luster 1, and the lower plot in Fig. 8(b) shows the same for PV luster. It is observed that in PV luster 1, the neutral urrent exeeds phase b and urrents, and nearly reahing the phase a urrent at midday. he situation is less severe in PV luster with muh lower grounding resistane. he high neutral urrent produed by unbalaned PV injetion inreases the neutral voltage as shown in Fig. 9; the upper plot in Fig. 9(a) shows neutral voltage in PV luster 1 that remains nearly at 1 V during high PV generation period. his is already higher than the ommonmode noise limit of.5 V [13] for sensitive equipment. With the idealisti value of neutral resistane of.5 ohm in PV luster, the neutral voltage in luster does not exeed.15 V, as shown in Fig. 9(b). However, using the realisti value of.5 ohm in PV luster, the neutral voltage in luster slightly exeeds the ommon-mode voltage limit of.5 V. Suh neutral to ground voltages may exeed the tolerane level with further inrease in unbalaned PV alloation whih would impose potential safety hazards and may also ause damage of sensitive equipments [13], [14]. A ase study is onduted for a senario where the total PV generation in the feeder is higher than the feeder demand and results are presented in Fig. 1. In this ase, surplus power from PV resoures is injeted into the upstream MV network. his is shown in the upper plot of Fig. 1(a) with a reverse power flow at one of the LV substation buses in a PV luster. his suggests that a voltage rise is reated in the MV feeder at the immediate upstream of the PV lusters due to the reverse power flow. he reative power flow at the substation bus, however, remains nearly unhanged as shown in the lower plot of Fig. 1(b), beause the PV inverters are modeled to operate at unity power fator. It is to be noted, if the neutral grounding resistanes are approximated to zero, then the power flow results obtained by inluding the neutral wire would not be different than the results obtained using a 3-wire representation of a 4-wire LV feeder. he grounding resistanes need to be non-zero to observe the effet of inluding neutral wire in network model. D. PV Impats Propagated to MV Networks PV impat propagation into the MV network is presented in this paper using MV level voltage profiles. Fig. 11 shows the Fig. 8. Daily variation of neutral urrent (a) PV luster 1 (b) PV luster Neutral Voltage [V] Neutral Voltage [V] (a) Neutral Voltage in PV Cluster 1 Common Mode Voltage Limit 1 for Sensitive Equipment V.4. (b) Neutral Voltage in PV Cluster Common Mode Voltage Limit 1 for Sensitive Equipment V.4. Voltage with 5 ohm Resistane Voltage with.5 ohm Resistane Voltage with.5 ohm Resistane Fig. 9. Daily variation of neutral voltage (a) PV luster 1 (b) PV luster Ative Power [kw] Reative Power [kvar] 1 Ph. A -1 Ph. B Ph. C - ime [Hour] (b) Reative Power Flow at LV Substation Bus (a) Ative Power Flow at LV Substation Bus Reverse Ative Power Flow during Midday Ph. A Ph. B Ph. C ime [Hour] Fig. 1. Daily variation of ative and reative power flow at substation node (a) ative power (b) reative power voltage profiles of the MV feeder along the feeder length that ontains the two PV lusters. his voltage profile orresponds to the time of peak PV generation in the luster. Voltage rise is observed along one of the spurs of the MV feeder (through the buses 47, 66, 67 and 68 in Fig. 5) due to the absene of voltage regulator at the immediate upstream. On the other hand, voltage rise produed by the PV luster is buked down by REG3. his effet is also observed in Fig. 1 that shows the tap operations of the REG3; Fig. 1(a), (b) and () shows the tappings of phase a, b, and, respetively. he positive tap numbers indiate voltage buking operation, whereas, the negative tap numbers mean voltage boosting. It is observed that at midday, from about 11 AM to 1 PM, the tapping of phase a is positive that indiates the ation of REG3 to redue the voltage rise aused by the PV luster

11 9 Phase Voltage [kv] Fig. 11. Ph. A ap Ph. B ap Ph. C ap Ph. A Main Feeder Ph. B Main Feeder Ph. C Main Feeder Ph. A Spur (Bus 44 to 49) Ph. B Spur (Bus 44 to 49) Ph. C Spur (Bus 44 to 49) Ph. A Spur (Bus 47 to 68) Ph. B Spur (Bus 47 to 68) Ph. C Spur (Bus 47 to 68) Voltage Rise due to PV Cluster 1 Voltage Rise due to PV Cluster Regulator Ation for Voltage Control Feeder Length [km] Midday voltage profile along the 11 kv feeder (a) (b) () ap Operation at Midday due to overvoltage aused by PV Fig. 1. Daily tap operations of REG3 (a) phase a tap (b) phase b tap () phase tap downstream; phase b and however, remains mostly at the neutral state as voltage in these phases remain within the limits. In the evening, tap numbers in all the phases are negative indiating a voltage boosting operation. V. CONCLUSIONS A three-phase power flow approah apable of distribution network analysis by preserving the atual wiring onfiguration of MV and LV networks has been proposed for realisti analysis of solar PV impats. his approah would be partiularly useful for multigrounded LV networks where the neutral wire needs to be modeled expliitly due to the presene of neutral grounding impedanes. A real distribution network, onsisting of 3-wire MV and 4-wire LV feeders with multiple neutral groundings, has been used to verify the appliability of the proposed power flow approah. Unlike the the traditional 3- wire power flow, the proposed approah is able to provide the neutral urrent and voltage aused by unbalaned alloation of single-phase rooftop PV units, and hene would be able to provide information regarding possible safety issues. With the peak level of PV output during midday, the neutral urrent and voltage impats beome more signifiant, as verified through a series of power flow alulations orresponding to a 4- hour load and PV output variations. Simultaneous modeling of 3-wire and 4-wire systems using the proposed approah enables the investigation the PV impats propagated to the upstream MV level. Further researh an be arried out using the proposed approah to investigate the voltage regulation oordination and protetion issues against high neutral to ground voltage related to 3-wire MV and 4-wire multigrounded LV systems with distributed resoures. ACKNOWLEDGMEN he authors gratefully aknowledge the support and ooperation of Essential Energy personnel for providing pratial information and data on distribution networks and solar PV generation. REFERENCES [1] RA Walling, R. Saint, R.C. Dugan, J. Burke, and L.A. 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12 1 [] K.P. Shneider and J.C. Fuller, Detailed end use load modeling for distribution system analysis, in Power and Energy Soiety General Meeting, 1 IEEE, july 1, pp [3] G.M. Masters, Renewable and effiient eletri power systems, Wiley- IEEE Press, 4. [4] M.G. Villalva, J.R. Gazoli, and E.R. Filho, Comprehensive approah to modeling and simulation of photovoltai arrays, Power Eletronis, IEEE ransations on, vol. 4, no. 5, pp , may 9. [5] Kyoera, Kgt high effiieny multirystal photovoltai module, Available: [Online]. [6] J. Chan J. Werda and P. Freeman, Eletrial earthing-risk management strategies for the water industry, Available: onferene papers/8 nsw/douments/johnwerda.pdf, 8, Apr, [Online]. BIOGRAPHIES M J E Alam (Std. Member 1) reeived B.S. and M.S. Degree in Eletrial and Eletroni Engineering from Bangladesh University of Engineering and ehnology, Dhaka, Bangladesh, in 5 and 9, respetively, with fous on eletrial energy and power systems. At present he is onduting PhD researh at the University of Wollongong, New South Wales, Australia. Prior to starting PhD studies, he has been involved with the power industry in Bangladesh for 4.5 years, where he worked in the field of power generation, transmission and distribution. His researh interest inludes modeling and analysis of power systems onsidering the impats of distributed and renewable energy resoures. K M Muttaqi (M 1, SM 5) reeived the Ph.D. degree from Multimedia University, Malaysia, in 1. Currently, he is an Assoiate Professor at the Shool of Eletrial, Computer, and eleommuniations Engineering, University of Wollongong, Wollongong, Australia. He was assoiated with the University of asmania, Australia as a Researh Fellow/Leturer/Senior Leturer from to 7, and with the Queensland University of ehnology, Australia as a Researh Fellow from to. Previously, he also worked for Multimedia University as a Leturer for three years. His speial fields of interests inlude distributed generation, renewable energy, power system planning, intelligent grid, and power system reliability. D Sutanto (SM 89) obtained his BEng. (Hons) and PhD from the University of Western Australia. He is presently the Professor of Power Engineering at the University of Wollongong, Australia. His researh interests inlude power system planning, analysis and harmonis, FACS and Battery Energy Storage systems. He is a Senior Member of IEEE. He is urrently the IEEE IAS Area Chair for Region 1 (Asia Paifi).