Step-Voltage Regulator Model Test System

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IEEE PES GENERAL MEETING, JULY 5 Step-Voltge Regultor Model Test System Md Rejwnur Rshid Mojumdr, Pblo Arboley, Senior Member, IEEE nd Cristin González-Morán, Member, IEEE Abstrct In this pper, 4-node test feeder will be proposed s the Step-Voltge Regultor (SVR) model test system. The formultion for modelling SVR bnk consisting on three single phse Type A regultors in rise position will be stted in n extended wy. However, the procedure to extend the formultion to ny other connection will be lso explined, nd the results consider ll possible connections nd types. In the literture, there exist stndrd systems for testing, compring nd vlidte power trnsformers models, like for instnce the IEEE 4-node test feeder, but the uthors did not found ny stndrdised system for testing nd vlidte SVRs models. Thts why the uthors decided to modify the IEEE 4-node test system, embedding into it the SVR models implemented with the well known exct model equtions. Index Terms 4-node test feeder, SVR modelling, conventionl power flow results, voltge regultion.. I. INTRODUCTION MODELING of SVRs possess prticulr importnce in power flow studies of unblnced distribution networks. The IEEE test feeders of reference [] were developed, minly, to provide set of common dt to be used in testing nd vlidtion of distribution nlysis softwre. There the 4- node test feeder ws developed primrily for the purpose of testing trnsformer models []. There is no such SVR model test system vilble in literture. Hence, in this pper, the IEEE 4-node test feeder [] will be modified for SVR model test system. Kersting s voltge regultor modelings [], [4] re the mjor works in mtrix-eqution bsed SVR modeling. Those works covered the distribution system SVR modeling in bc reference frme, SVR control mechnism by clculting the compenstor R nd X settings nd other pplictions of SVRs in distribution systems. Though he did not present ll of the configurtion but he lid proper bseline for ech of them. For this pper, similr mtrix eqution bsed models were developed nd vlidted for twenty possible SVR configurtions in grounded-wye, closed-delt nd three possible open-delt connection with Type A nd Type B regultors t both rise nd lower position. These models were incorported in the complex vector bsed model of unblnced distribution system in sttionry reference frme [5] to solve for conventionl power flow results. Finlly, the benchmrk conventionl power flow result will be presented for ll these SVR configurtions, serving n unblnced lod, for both t rise nd lowering t fixed tp The uthors re with the Deprtment of Electricl Engineering, University of Oviedo, Gijón, Spin (e-mil: m.r.r.mojumdr@gmil.com; rboleypblo@uniovi.es; gonzlezmorcristin@uniovi.es). This work ws prtilly supported by the Spnish Ministry of Science nd Innovtion under Grnt ENE-4445-R (MICROHOLO Development of Holistic nd Systemticl Approch to AC Microgrids Design nd Mngement). 978--467-84-9/5/$. 5 IEEE position of 8 with Type B configurtions nd t different tp positions with Type A configurtions, in the proposed SVR model test system. II. THE REGULATOR MODEL Bsics of SVRs modeling, equtions for single-phse Type A or Type B regultors nd possible SVR configurtions hve been described in [4]. Summrizing in the Tble I, the reltionships between the source voltge nd current to the lod voltge nd current, for both the Type A nd Type B regultors whether in rise or lower: TABLE I GENERALIZED EQUATIONS FOR SINGLE-PHASE REGULATORS [4] Type Voltge Eq Current Eq R for Rise R for Lower A V S = R V L I S = RI L R =+ N N R = B V S = RV L I S = R I L R = N N N N R =+ N N No mtter how the regultors re connected, the reltionships between the series nd shunt winding voltges nd currents for ech single-phse SVR must be stisfied. Here, N nd N re the primry nd secondry turn number of the single-phse regultors nd the vlue of effective regultor rtio is denoted s R. For n overview of configurtions, closed-delt connected Type A regultor in rise, wye connected Type B regultor in lowering nd open-delt connected (cse. ) Type B regultor in rise hs been presented in Fig., Fig. nd Fig. respectively. However, for the bsic modeling ide, the model will be presented below, only for closed-delt connected SVR with Type A regultors in rise. As shown in Fig., three single-phse Type A regultors in rise cn be connected in closed delt, to be used in three-wire delt feeders. Fig.. Closed delt-connected type A regultors in rise

IEEE PES GENERAL MEETING, JULY 5 Fig.. Open-delt connected (cse. ) Type B regultors in rise Fig.. Wye connected Type B regultors in lowering A. Voltge Equtions KVL cn be pplied round closed loop to obtin equtions for the line-to-line voltges. For exmple, for the lineto-line voltges between phses A nd B on the source side refer to the Fig. : VA B = VA + VB () But, winding voltges cn be relted in terms of turns rtios: N N.N V A = VcA = Vc N N.(N + N ) = VB = N N + N N Rc Vc Rc Vc = N Vb = Vb = Vb N + N + N Rb N Rc Vb + Vc Rb Rc VAB 4VBC VCA () (4) To determine the reltionships between the other line-toline voltges, the sme procedure cn be followed nd the three-phse voltge eqution relting source side nd lod side without considertion of drop in winding impednces for this regultor configurtion will be: Rc V A B Vb Rb Rc 4VB C 5 = 4 Rb 5 4 Vbc 5 (5) Rb Rbc Rbc V C A V c Rbc Now, in the next eqution, per phse voltge drops in the regultor impednces re relted to the phse-to-phse voltges in the primry side of the regultor [5]: () Substituting Equtions () nd () in () nd simplify: V A B = And, let s introduce the TDY mtrix [5] which is mtrix to obtin phse-phse quntities from phse-neutrl quntities. But it is singulr mtrix. This implies tht phse-to-neutrl quntities cn not be obtined from phse-to-phse voltges. This TDY mtrix s shown in Eqution (8) will be used repetedly for other configurtions lso. A TDY = @ (8) Rc However, the regultor winding impednces cn be considered s equl in ech phse so tht, in mtrix form, they cn be denoted s: ZA Zreg = @ ZB A = Z @ A (6) ZC Now, using Eqution (6), the voltge drops in the regultor impednces cn be expressed s: VAA 4VBB 5 = Zreg 4IB 5 (7) VCC IC V A B VAA VB C 5 = 4VBB V C A VCC VBB VAA VCC 5 = TDY 4VBB 5 (9) VAA VCC Combining (5), (7) nd (9) the reltionship between primry voltges, secondry voltges nd primry line currents cn be written s: VAB Rb 4VBC 5 = TDY Zreg 4IB 5 + 4 Rb Rb VCA IC Rbc Rbc Rbc Rc Vb Rc 5 4 Vbc 5 Vc Rc () B. Current Equtions Applying KCL t the lod side terminl : I = I A + I B () But s: I A = I A c + I A = N N + = ( + ) () N N So tht: I A = I = N A Rc + N () Agin s: IB = IB + IB b = N N IB + IB = ( + )IB (4) N N

IEEE PES GENERAL MEETING, JULY 5 Agin so: I B = N ( + N N ) I N B = I B = Rb I B (5) + N N Rb Substituting Equtions () nd (5) into Eqution (): I = Rc I A + Rb Rb I B (6) Following sme procedure t the other two lod side terminls, for this configurtion, three-phse eqution between source nd lod line currents cn be obtined s: I 4I b 5 = 4 I c C. Generlized Equtions Rb Rc Rb Rbc Rb Rbc Rc Rc Rbc 5 4 I A I B I C 5 (7) We cn denote, A R-KVL 4 nd A R-KCL 4 mtrices for closed delt connection with Type A regultors both in rise position nd lower position s: A R-KVL 4 = 4 A R-KCL 4 = 4 Rb Rb Rb Rb Rc Rc Rc Rbc Rbc Rbc Rc Rb Rbc Rb Rbc Rc Rc Rbc 5 (8) 5 (9) In the similr structure, ll other SVR configurtions were modeled. Therefore, denoting A R-KVL mtrices for voltge equtions nd A R-KCL mtrices for current equtions of ech connections nd expressing three-phse voltge nd brnch current in short form, we cn express Equtions like () nd (7) in very compct form. Finlly, by observing ll the models, there ws only one structure of the generl current eqution for ll the configurtions which is: S IBr = A P bc R-KCL IBr () bc But there re two structures of the generl voltge eqution. For ll the wye configurtions: P Vph n bc = Z P reg IBr bc + A S R-KVL Vph n bc () For ll closed nd open delt configurtions: P ph bc = T P DY Z reg IBr bc + A S R-KVL Vph ph bc () Vph D. Incorportion nd Simultion Generlized voltge nd current equtions developed in the regultor models were incorported s liner equtions in the complex vector bsed model of unblnced distribution system in sttionry reference frme [5]. Then, other non-liner equtions were lso included in the the power flow problem. Finlly, ech power flow problem with different SVR configurtions, ws simulted using FSOLVE function of MATLAB to solve ll liner or non-liner equtions to provide the benchmrk conventionl power flow results. III. THE TEST SYSTEM The system to be used in testing SVR models is proposed nd shown in Fig. 4. A. Line Configurtion We propose, the line segment on the source side nd the line segment on the lod side of the regultor bnk will hve the configurtion 6 of proposed IEEE -node test feeder t []. Like other line configurtions in tht -node test feeder (Configurtions 6-67) with single or multiple lterls, configurtion 6 is provided in the form derived fter following modified Crson s eqution [4] nd corresponding Kron reduction [4]. Finlly, ( ) phse frme mtrice of configurtion 6 will be used. And the phse impednce of configurtion 6, Z bc in /mile is:.457 + j.79.556 + j.57.5 + j.86 Z bc = 4.556 + j.57.466 + j.49.577 + j.4475.5 + j.86.577 + j.447.46 + j.66 () B. Regultor Impednce And the regultor winding impednce, Z reg in, used for the results is:.768 + j.4 + j +j Z reg = 4 +j.768 + j.4 + 5 + j + j.768 + j.4 (4) It s importnt to note tht, for the regultor with three possible open delt connections, corresponding phsing impednce were tken out from the Z reg mentioned here. Specificlly, Z B for cse, Z C for cse b nd Z A for cse c will be zero () in the Z reg of three cses of open delt configurtions. C. Unblnced Lods nd Genertions For the benchmrk power flow results presented in the following section, the unblnced lod profile used t node 4 of Fig. 4 ws: TABLE VI UNBALANCED LOAD DATA FOR TEST RESULTS Phse- Phse- Phse- kw kvr p.f kw kvr p.f kw kvr p.f 5 6.4.95 6.59.9 7 5.76.9 Fig. 4. 4-node test feeder with regultor.

IEEE PES GENERAL MEETING, JULY 5 4 TABLE II TYPE B IN RAISE REGULATORS (TAPS AT 8) Connection Gnd-Y Cld-Delt Op-Delt- Op-Delt-b Op-Delt-c Tps [8 8 8] [8 8 8] [8 8 ] [ 88] [8 8] Voltge Node- 6 6 6 6 6 V 9.6. 9.9. 89.9. 98.6. 84.5. V 99.5. 99. 9..6 9.7 9.7 4..4 V 9.7 9.5 9.8 9.5 4.5 8.9 87 7.4 9. Voltge Node- 6 6 6 6 6 V 98.9 5.6 48.8.8 96 4.9 577.7.6 44.8. V 4.8.4 4.6 9.9 4.9.6 44.. 9.5 9. V 4.6 6. 4. 8.8 6.9 48. 47.4 7.4 98. 6.5 Voltge Node-4 6 6 6 6 6 V 94.6 6.4 44.6.5 9.8 5.5 574.7.9 4.6.7 V 4.6.6 4.. 4..8 4..4 6. 9.9 V 97.6 6 48. 8.5 6.5 47.8 44.5 7 95. 6. Current I 6 6 6 6 6 I 4.4 4.6 9.4.8 4.4.7 96.4 4. 98.9.5 I b 7.9 48.4 76.5 5.5 6.8 9.4 75.6 48. 4.5 55.7 I c 6.5 9.9 5.4 9.5 7.4 4.7 6.8.6 7. 9 Current I 4 6 6 6 6 6 I.4 4.6..7 4..7 9.6 4..4.9 I b 7. 48.4 68.7 45.9 7.4 47.6 7.8 48. 7.8 55.7 I c. 9.9 98.5 95.5.5 4.7 99.4 94.8 9 TABLE III TYPE B IN LOWER REGULATORS (TAPS AT 8) Connection Gnd-Y Cld-Delt Op-Delt- Op-Delt-b Op-Delt-c Tps [8 8 8] [8 8 8] [8 8 ] [ 88] [8 8] Voltge Node- 6 6 6 6 6 V 9.6. 9.. 89.8. 98.6. 84.5. V 99.5. 4. 9.6 9.7 9.7 4..4 V 9.6 9.5 9.4 9.6 4.4 8.8 87 7.4 9. Voltge Node- 6 6 6 6 6 V 6.7 5.7 5.4 8. 58. 5 5.7.7 66.. V 7.6.4 64. 4.7 7.7.6 65.6. 7.9 9. V 6. 6. 5.6 4 8.7 48. 68.6 7.4 6. 6.5 Voltge Node-4 6 6 6 6 6 V 56 6.6 46.5 9. 5.5 5.7 59.4 4 6.5.8 V 7.4.6 6.9 4.9 7.9.8 6.5.5 4. V 58.8 5.9 48.6 5 47.7 65. 6.9 56.9 6 Current I 6 6 6 6 6 I 4.8 4.8 4. 5.6 4.8.8 96.5 4. 99.7.6 I b 7.9 48.5 7.9 46. 64 9.5 75.7 48. 4.8 55.8 I c 6.7 9.9 8. 9 7.9 4.6 7..5 7. 9.9 Current I 4 6 6 6 6 6 I 47.9 4.8 5.9 7.4 48.9.8. 4. 45.6 I b 77.6 48.5 79.4 5.7 77.9 47.7 79.5 48. 4.5 55.8 I c. 9.9 5.6 9.5.8 4.6. 9.9.7 9.9 IV. VALIDATION OF THE PORPOSED FORMULATION At [4], Kersting developed regultor models for number of configurtions t bc reference frme. In this pper the uthor proposed nd lterntive formultion bsed in reference frme. The two formultions represent exct equivlent models, so the uthors used the originl formultion to vlidte the proposed one. Once the results using the bsed formultion were obtined, they were trnsformed to bc reference nd compred with those obtined directly from the originl formultion. In ll cses, the solutions were exctly the sme s it ws expected. V. BENCHMARK POWER FLOW RESULTS FOR SVRS In tbles II nd III, the obtined results for type B regultors in rise nd lower positions re shown. In both cses, the tp position is set to 8 nd the considered configurtions were Grounded-Wye, Closed-Delt nd Open-Delt considering the three different possibilities - connection with regultors between phses AB nd CB, between BC nd AC nd finlly between CA nd BA which re denoted s cse, cse b nd cse c connection respectively. In tbles IV nd V, the results re represented for ll type A regultor connections, however, in different tp positions t different single-phse regultors. It s worth mentioning tht, for three wire delt configurtions, the voltges in results provided here re phse-phse

IEEE PES GENERAL MEETING, JULY 5 5 TABLE IV CASE C TEST RESULTS: TYPE A IN RAISE REGULATORS (TAPS AT DIFFERENT POSITIONS) Connection Gnd-Y Cld-Delt Op-Delt- Op-Delt-b Op-Delt-c Optimum Tps [9 4 8] [6 7] [ 4 ] [ 76] [7 9] Voltge Node- 6 6 6 6 6 V 9.6. 9.5. 9. 98.6. 84.. V 99.5. 99.. 9.4.6 9.7 9.7 4..4 V 9.7 9.5 9. 9.5 4.5 8.9 86.9 7.4 9. Voltge Node- 6 6 6 6 6 V 4. 5.6 4. 7.7 99.8 4.9 57..9 4.. V 4.4 4 4.5 4..6 4.7. 8. 9.7 V 4.6 6. 4.4 5.5 67.9 46.9 4.4 7.4 99.5 6.6 Voltge Node-4 6 6 6 6 6 V 96 6.4 97 8.4 95.7 5.5 567 4. 96.9.7 V 4.7.6 4.6 4.6 98.4.8 98.8.4 4.8.4 V 96.6 6 97.5 5. 64.6 46.4 98.4 7 96.6 6. Current I 6 6 6 6 6 I 4.4 4.6 9.9 5.6 4..6 96. 4.4..9 I b 7.9 48.4 75.4 49.5 7. 4. 75.6 48. 4. 56. I c 6.5 9.9 5. 95.. 7..4 7. 9. Current I 4 6 6 6 6 6 I.9 4.6.6 6.6.6 9.8 4.4.6.9 I b 7. 48.4 7. 5.5 7.5 47.6 7.4 48. 8.5 56. I c.4 9.9. 9....9 94.4 9. TABLE V CASE C TEST RESULTS: TYPE A IN LOWER REGULATORS (TAPS AT DIFFERENT POSITIONS) Connection Gnd-Y Cld-Delt Op-Delt- Op-Delt-b Op-Delt-c Optimum Tps [ 6 ] [ 7 ] [ 7 ] [ ] [ 5] Voltge Node- 6 6 6 6 6 V 9.6. 9.5. 9. 98.6. 84.. V 99.5. 99.. 9..6 9.7 9.7 4..4 V 9.7 9.5 9. 9.5 4.5 8.9 86.9 7.4 9. Voltge Node- 6 6 6 6 6 V 76.5 5.6 69.6 5.4 7.8 4.9 54.7 4 74.5. V 76.6.4 69.5.5 7..6 8.5..8 V 76.7 6. 7.8 8.4 4.8 46.8 8. 7.4 75.8 6.6 Voltge Node-4 6 6 6 6 6 V 7.9 6.5 64.9 6. 69.4 5.5 59.4 4. 7.8 V 76..6 69..7 7.4.8 79.5.4..8 V 7.5 6 66.6 8 4. 46. 78.9 7 7.7 6. Current I 6 6 6 6 6 I 4.6 4.7 4.5 4.9 4.6.7 96. 4.5.6. I b 7.9 48.5 74.7 5.8 7.9 4.6 75.6 48. 4 56.7 I c 6.6 9.9 4.5 94.6. 7.6. 7. 9 Current I 4 6 6 6 6 6 I 4.5 4.7 44. 4.5 4.5.7 97.6 4.5 4. I b 76.8 48.5 78. 47.6 77.8 47.7 76. 48. 7.5 56.7 I c 8 9.9 9.7 95 8.. 6. 9.9 7.9 9 nd for four wire wye configurtions, they re phse-neutrl. VI. CONCLUSIONS The IEEE 4-node test feeder hs been modified nd dpted to test Step-Voltge Regultors (SVR). As n exmple, the extended formultion ws presented for closed-delt connected SVR with Type A regultors in rise. Due to the lck of spce the formultion ws not extended for other types of SVR. However, the guidelines for obtining other types of SVR with different connections were lso presented. In the benchmrk section the results for different SVR types with different connections were presented. In further works, the proposed formultion will be used for nlyse lrge low voltge distribution networks. REFERENCES [] Distribution Test Feeders: http://ewh.ieee.org/soc/pes/dscom/testfeeders/, IEEE PES Distribution System Anlysis Subcommittee s. Distribution Test Feeder Working Group Std. [] W. H. Kersting, Trnsformer model test system, in Trnsmission nd Distribution Conference nd Exposition, IEEE PES, vol.. IEEE,, pp. 6. [] W. Kersting, The modeling nd ppliction of step voltge regultors, in Power Systems Conference nd Exposition, 9. PSCE 9. IEEE/PES. IEEE, 9, pp. 8. [4] W. H. Kersting, Distribution system modeling nd nlysis. CRC press,. [5] P. Arboley, C. Gonzlez-Morn, nd M. Coto, Unblnced power flow in distribution systems with embedded trnsformers using the complex theory in sttionry reference frme, Power Systems, IEEE Trnsctions on, vol. 9, no., pp., My 4.

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