Determination of Inrush Current to High Power Transformers using the LabVIEW Environment

Transcription

1 Journal of Mechancal Engneerng and Automaton 017, 7(): 46-5 DOI: /j.jmea Determnaton of Inrush Current to Hgh Power Transformers usng the LabVIEW Envronment Mara-Crstna Nțu, Claudu-Ionel Ncola *, Marcel Ncola, Maran Duță Research, Development Dvson for Electrc Equpment and Energy Effcency, Natonal Insttute for Research, Development and Testng n Electrcal Engneerng Icmet, Craova, Romana Abstract The values of the current whch occurs when connectng the transformer at the mans can result n electrcal and mechancal stress n transformer, whch n turn can lead to falures, jeopardzng the relablty of the power system, and mplctly of the power transformer. In order to avod major falures n the power system, we developed a mathematcal model n ths paper n order to detect the sze and tme of occurrence of the transent current from the desgn stage. The mathematcal model of the transformer was valdated through tests (smulatons, measurements) for the purpose of assessng the electrcal stress n power transformers. The transformer on whch the test was carred out s a 15 MVA, 10.5/6.3 kv transformer, the modelng of the phenomenon whch occurs when connectng the transformer at the mans was acheved usng the LabVIEW software, and the results obtaned are consstent wth the results acheved through the expermental tests carred out. Keywords Inrush current, Transformer, Transent regme, LabVIEW smulaton 1. Introducton In recent decades, the use of computers n varous felds of actvty has become a necessty. From the frst desgn stages and up to the fnal stage (constructon) of a product, the computer has replaced the classc gear. Therefore t was possble to take advantage of effectve methods. Genune vrtual prototypes can be created usng the computer, wth a vew to obtanng products whch meet the functonal requrements on the market. Hence the smulaton of the mechancal/electrcal systems s carred out untl achevng a precse modelng of both system components and of ts operatng condtons, enablng fast testng of multple constructve versons, for system optmzaton [1]. Unlke other power equpment, power transformers are complex oscllatng systems, whch can undergo falure, for certan forms of voltage, even when the man voltage does not exceed the voltage determned through szng. When connectng the transformer to the mans, very hgh currents develop n the actve parts of the transformer, whch exceed by much the maxmum ratng of the steady state current. The relablty of the power system s a matter of nterest, due to the fact that the transformer manufacturer cannot provde nformaton on ther behavor when connectng and dsconnectng them to/from the mans, therefore t s * Correspondng author: ncolaclaudu@cmet.ro (Claudu-Ionel Ncola) Publshed onlne at Copyrght 017 Scentfc & Academc Publshng. All Rghts Reserved necessary to ensure ther relablty by predetermnng the sze of the transent current. In order to lmt the consequences of excess transent current, techncal solutons are avalable for mplementaton n the power system (controlled connecton of transformer phases [-4]; fastenng the protectons at hgh levels durng connecton) and solutons relatng to the desgn, ensurng an acceptable level of transent current. Inrush current s a problem, because t nterferes wth the operaton of crcuts as they have been desgned to functon. In a dgtal world, there s zero tolerance for perods of power falure. Some effects of hgh nrush nclude nusance fuse or breaker nterruptons, as well as arcng and falure of prmary crcut components, such as swtches. Hgh nrush currents also requre overszng of fuses or breakers, whch complcates other aspects of testng approvals and may compromse protecton for other vtal components. Another sde effect of hgh nrush s the njecton of nose and dstorton back nto the mans. Local transformer engneers currently have no custom software to hghlght the electrcal and/or mechancal stress n case of transtory regme. For ths reason we consdered developng a program to enable us to predetermne the sze of the transent current occurrng when connectng the power transformer to the mans [5-7].. Theoretcal Concepts The followng s an analyss of the transent phenomena caused by connectng the transformer to the mans, leadng

2 Journal of Mechancal Engneerng and Automaton 017, 7(): to overloads. It s establshed that when the transformer runnng wthout load, the transformer prmary steady state nput current s low compared to the rated current, reachng 3-10% of the rated current [8]. In case of transent regme resultng from closng the crcut-breaker connectng the transformer to the mans, the current can reach up to fve tmes the rated current value. In order to determne the nrush current, a snusodal voltage s appled at the termnals, such as. u 1 = U 1 sn(ωt + γ) (1) - u 1 = U 1 snγ - s the voltage appled to the prmary at tme t = 0; - γ - the ntal phase angle. The peak value and the flow of the nrush current depend on the value of the voltage appled at the tme of connecton (tme characterzed by γ). The equaton for the operaton of the prmary s [8]: dφ u 1 = r 1 I 0 + w 1 1 () dt - r 1 - prmary resstance; - I 0 - nrush current; - w 1 - number of turns n the prmary; - φ 1 - the transformer no-load connecton flow (fasccular flow), for smplcty we wll consder that ths flow passes through all the seres turns of the wndng and that t s located n the ar gap. The equaton () can be wrtten as a relaton between the nrush current and the flow, wth reference to nductance: LI 0 = w 1 φ 1 (3) - L - total nductance, whch should be consdered varable wthn certan lmts, accordng to the magnetc saturaton of the ron. I. Determnaton of φ = f(i) based on the magnetzaton curve By dentfyng the coordnates of the ponts whch correspond to the magnetzaton curve of the magnetc core [9] for a transformer of 15 MVA, respectvely values whch correspond to magnetc nducton (B) on the horzontal axs and the magnetc feld strength (H) on the vertcal axs, we can determne the magnetzaton curve of the magnetc crcut, φ = f(i). a) Determnaton of the magnetc feld flux whch occurs when connectng the transformer to the mans. In order to determne the magnetc feld flux whch occurs when connectng the transformer to the mans we use the values of the magnetc nducton generated by the magnetzaton curve materal provded by the manufacturer. The magnetc feld flux values are obtaned based on the followng relatonshp (4): ϕ[w b ] = B T [m ] (4) where s the magnetc core column secton. b) Determnaton of the current whch occurs when connectng the transformer to the mans In order to determne the current whch occurs when connectng the transformer to the mans we use the values of the magnetc feld strength obtaned from the magnetzaton curve. The values of the current are obtaned based on the followng relatonshp (5): I 0 A = H A/m l med [m ] w 1 [spre ] - l med - the average length of the magnetc feld lne; - H - the magnetc feld strength; - w 1 - the number of turns n the prmary. Fgure 1. The magnetc crcut of the transformer - l j - yoke length; - l c - column length; - w 1 - the number of turns n the prmary. The average length of the feld lne s determned based on the followng relatonshp [8]: (5) l med = H(l c + 3l j ) (6) II. Determnaton of the transformer parameters - determnaton of the no-load current: I 0 = k[%]i N [A] (7) where k s the rato n percent between dle current and nomnal current. - determnaton of the lne current: I N = S N 3U 1 [A] (8) If the connecton n the prmary s YN, then the phase current s equal to the lne current, and f the connecton n the prmary s, the current through the sdes of the trangle s determned by usng the followng relatonshp (9): I Nf = I 1N [A] (9) 3 where I Nf s the current through a phase wndng. - determnaton of the value of the magnetc feld flux φ 0 for transformer no-load operaton: φ 0 = f(i 0 ) (10)

3 48 Mara-Crstna Nțu et al.: Determnaton of Inrush Current to Hgh Power Transformers usng the LabVIEW Envronment - determnaton of the leakage reactance: X σ = U k % S n 100 I [Ω] (11) Nf - determnaton of the leakage nductance: L s = X σ / 3 [H] (1) πf - determnaton of the leakage nductance: L m = μ 0 μ r - μ 0 - absolute magnetc permeablty; - μ r - relatve permeablty; l med w 1 (13) μ 0 = 4 π 10 7 [H/m] (14) μ r = B μ 0 H (15) - - cross-secton area of the magnetc core [m ]. The sze of the magnetzaton nductance vares n tme wth the varaton of the magnetc feld flux and the current through the transformer wndng. A value of the relatve permeablty t whch corresponds to tme μ r of the transent process wll result for each value of the flux φ. μ r = B μ 0 H = φ = l med μ 0 w 1 I (16) For tme t the transent value of L m s determned usng the followng relatonshp: L m = μ 0 φ l med μ 0 w 1 I l med w 1 = φ w 1 I (17) - determnaton of the core losses equvalent resstance: R Fe = P 0 B I B = P 0 φ I φ 0 (18) - determnaton of the heat losses equvalent resstance. Current I 0 n no-load s much lower than the rated current I 1N. No current passes through the secondary wndng and therefore the heat losses (copper losses) n ths wndng are neglgble. - calculaton of total resstance: - calculaton of total nductance: P k = R Cu I 1N (19) R Cuf = P k /3 I [Ω] 1N (0) - calculaton of wndng tme constant: τ = L m +L s R - calculaton of peak flux value: R = R Fe + R Cuf [Ω] (1) L = L m + L s () [s] (3) φ 1m = 3 U 1 πf w 1 [Wb] (4) If the transformer has been prevously energzed, at ntal tme t 0, when connectng the transformer to the mans, there wll be a resdual flux ( φ 1rem ) n the ferromagnetc core, and the magnetc feld flux varaton can be determned usng the followng relatonshp [8]: The equaton of the nstantaneous flow s gven by the relaton: φ t = φ 1m e t τ cosγ cos ωt + γ + e t τ φ 1rem (5) In the case presented n ths paper we consdered that the transformer has not been prevously energzed, therefore the resdual flux wll be equal to zero. The total nductance L s the sum of the leakage nductance and the magnetzaton nductance n the frst moments of the couplng. The resstance R sums up, at the frst moment of transformer couplng, the hgh voltage wndng resstance and the resstance equvalent to ron loss. Snce the transformer has not been prevously connected to the mans, at tme t=0 there s no resdual flux n the ferromagnetc core, φ 1rem = 0. It has been establshed that the most favorable stuaton from the pont of vew of the transent regme occurs when φ 1rem = 0 and γ = π/ ; n ths case the aperodc component, does not exst, and the nstantaneous fasccular flow depends only on the connecton current (n a steady state case), and, as a consequence, the most unfavorable stuaton occurs when γ = 0 and φ 1rem = 1 φ 1m. For ths stuaton the transformer s connected when the voltage passes through zero and the resdual flux s of opposte sgn to the permanent flux. 3. Software Applcaton Interface Devloped wth LabVIEW LabVIEW (short for Laboratory Vrtual Instrument Engneerng Workbench) s a system-desgn platform and development envronment for vsual programmng language. LabVIEW programs are called vrtual nstruments, or VIs, because ther appearance and operaton often mtate physcal nstruments, such as osclloscopes and multmeters. LabVIEW contans a comprehensve set of tools for acqurng, analyzng, dsplayng, and storng data, as well as tools to help troubleshoot the code [10, 11]. The programmng language used n LabVIEW, also referred to as G, s a dataflow programmng language. Executon s determned by the structure of a graphcal block dagram on whch the programmer connects dfferent functon - nodes by drawng wres. These wres propagate varables and any node can execute as soon as all ts nput data become avalable. Snce ths mght be the case for multple nodes smultaneously, G s nherently capable of parallel executon. The nterface of the applcaton software developed n LabVIEW s presented n Fg. 1. The software applcaton nterface was based on MathScrpt RT Module ncluded n the Lab VIEW program n order to facltate data entry and n order to obtan

4 Journal of Mechancal Engneerng and Automaton 017, 7(): mmedate results. LabVIEW MathScrpt RT Module adds math-orented, textual programmng to LabVIEW. The MathScrpt Node offers ntutve means for combnng graphcal and textual code wthn LabVIEW; both are currently used n a number of scence, engneerng and technology programs and ndustres for smulaton and analyss [1-14]. We defne nputs and outputs on the MathScrpt Node border (Fg. ) to specfy the data to transfer between the graphcal LabVIEW envronment and the textual MathScrpt code. Vsual nspecton va graphng s essental n analyzng complex data sets. The sngle-plot XY graph accepts a cluster that contans an x array and a y array. The XY graph also accepts an array of ponts, where a pont s a cluster that contans an x value and a y value. The bundle functon s used to assemble ndvdual elements nto a sngle new cluster. The waveform for the nrush current on the three phases s accomplshed wth the functons block from Fg. 4. Fgure. The software applcaton nterface Fgure 4. phases XY graph of the waveform for nrush current on the three Fgure 3. Block dagram wth MathScrpt Node code One of the benefts of workng wth the MathScrpt Node s the ablty to easly nstrument your algorthms by usng powerful, bult-n LabVIEW tools for defnng custom nteractve user nterfaces. 4. Smulaton Results To smulate the transent phenomenon occurrng when connectng the transformer to the mans, a 15 MVA, 10.5/6.3 kv transformer, wth delta/delta connecton was used. The modelng of the phenomenon occurrng when connectng the transformer to the mans was acheved usng the software applcaton nterface developed wth LabVIEW software. By determnng the flux values wth eq. (4), based on the magnetzaton curve [1, 5, 6, 9, 15, 16], provded by the producer (Fg.5), we wll determne the values of the nrush current. We acheved a transposton of the magnetzaton curve, made avalable by the transformer producng company, nstead of ts representaton accordng to the magnetc feld (H) - magnetc nducton (B), we get a representaton accordng to the flow (φ) - current (I). The nrush current reaches the peak value of 3711 A, on phase A, where the phase angle s zero and the voltage when connectng the transformer to the mans passes through zero (see Fg. 6).

5 50 Mara-Crstna Nțu et al.: Determnaton of Inrush Current to Hgh Power Transformers usng the LabVIEW Envronment Fgure 10. The waveform for Inrush current on phase C acheved usng LabVIEW software Fgure 5. Magnetzaton characterstc transposng Fgure 11. The waveform for Inrush current on phase C near to zero Fgure 6. The waveform for nrush current on phase A, acheved usng LabVIEW software Fgure 7. The waveform for Inrush current on phase A near to zero The nrush current on phase B reaches values of approxmately 1513 A, and γ = 4π/11 (as n Fg. 8). On phase C, the current reaches 1419 A, and γ = π/3 (see Fg. 10). 5. Expermental Results Fg. 1 shows the dagram used for testng the transformer when connectng t to the mans. The testng scheme ncludes nstrument voltage transformers, Rogowsk cols (CW), equpment for system data recordng and acquston (Dgtal recorder Geness HV 6600 TRAS HBM Geness). Fgure 8. The waveform for nrush current on phase B acheved usng LabVIEW software Fgure 9. The waveform for Inrush current on phase B near to zero Fgure 1. The transformer testng dagram for the expermental tests

6 Journal of Mechancal Engneerng and Automaton 017, 7(): Rogowsk cols are used for current montorng n precson systems. The Geness Hgh Speed Transent Recorders and Data Acquston Systems share the hghest sample rates and md to hgh channel counts. Based on modular platforms, all can be confgured accordng to the requrements of the applcaton, whether a sngle channel or thousands of channels. The Geness Hgh Speed famly has sgnal condtoners for many types of sensors. Many of the modules offer solated nputs, even for hgh voltage nputs, allowng safe measurement of phase to phase voltage sgnals. The sample rates range from 0 ks/s to 100 MS/s per channel. Systems are out-of-the-box and easy-to-use. Geness Hghspeed s a unt whch conssts of ndependent dgtal modules; sgnal condtonng modules and a data acquston system - combnng a transent data recorder wth a data acquston system; - combnng the tme-doman performance wth the frequency doman performance; - transent RAM memory at 100 Mega Samples per channel n parallel (400ms on one channel); - nsulated and non-nsulated channels; - unlmted sze and tme of recordng; - H-F sgnal condtonng; - enablng vewng and control anywhere n the computer-connected network. On-lne setup, montorng and control can be carred out from any PC, by usng Percepton dedcated software, nclusvely through fber-optc networks. Geness Hghspeed central servers nclude a communcaton module for ntranet connecton (1 GBt). The nrush current waveforms were obtaned as a result of the test carred out when connectng the transformer to the mans. Fg. 13 shows the waveforms for voltage and nrush current on phase A: the transformer was connected when the voltage passed through zero and the peak value of the nrush current equals 3717 A. It can be seen that the peak value occurs at γ = π/. The nrush current on phases B and C has a lower value compared to the nrush current value on phase A, 151 A current occurs on phase B (as n Fg.14) and 141 A current on phase C (see Fg.15). Ths appears due to a dfferent tme at the connecton. Fgure 13. The transformer testng dagram for the expermental tests Fgure 14. The transformer testng dagram for the expermental tests Fgure 15. The transformer testng dagram for the expermental tests 6. Conclusons In order to lmt the consequences of excess transent current, techncal solutons are avalable for mplementaton n the power system (controlled connecton of transformer phases, fastenng the protectons at hgh levels durng connecton) and solutons relatng to the desgn, ensurng an acceptable level of transent current. In ths paper we propose to determne the value of the nrush current for adoptng sutable protectng equpment. It can be seen that the transent regme occurrng when connectng the transformer to the mans lasts for a few seconds, after whch t s damped accordng to an exponental equaton - whch depends on the prmary resstance and on the flux varaton n tme. When couplng the transformer to the termnals of phase A at the ntal tme, the voltage s close to zero, as well as when the most mportant shock occurs. Ths was demonstrated both by smulaton of the phenomenon usng the software applcaton nterface developed wth LabVIEW software and by expermental tests. The value of the nrush current whch occurs when the transformer s connected to the mans depends on the tme of connecton of the transformer to the mans and the ntal phase angle γ. The mathematcal model proposed n ths paper can be easly extended for other types of power transformers, to predetermne the sze of the nrush current. There s always a dfference between the vrtual model adjusted to the phenomenon under study and the actual constructon of the transformer due to objectve devatons between the transformer desgn dmensons and real dmensons resultng from ts constructon. In the submtted applcaton, the dfferences notced are due to naccurate assessments of the make current dampng.

7 5 Mara-Crstna Nțu et al.: Determnaton of Inrush Current to Hgh Power Transformers usng the LabVIEW Envronment Ths devaton wll not affect the use of the vrtual model for practcal applcatons focusng on the peak current for protecton programmng. Takng nto consderaton ths requrement, the acheved vrtual model s more than acceptable. The vrtual model can also be used n the transformer desgn stage when calculatng electrodynamc forces occurrng n transformer wndngs whch are dependent on the peak current generated when connectng the transformer to the mans. The expermental results presented for predetermnaton of the power transformer nrush current valdate the theoretcal study and are consstent wth the smulaton results. There s always a dfference between the vrtual model adjusted to the the studed phenomenon and the actual desgn of the transformer due to objectve devatons between the transformer desgn dmensons and the actual dmensons resultng from ts executon. REFERENCES [1] M.C. Nțu, V. Vocu, M. Duță, P.M. Ncolae, Ensurng the Securty of the Energy System by Predetermnng the Sze of Inrush Current at Power Transformers Couplng, n: Proceedngs of 16th Internatonal Conference on Computer as a Tool- EUROCON, 015, pp [] I.S. Gheorghu, A.S. Fransua, Treat on Electrc Machnes, vol. II, A.R.S.R, Romana, [3] Y. Cu, S.G. Abdulsalam, S. Chen, W. Xu, A sequental phase energzaton technque for transformer nrush current reducton- Part I: Smulaton and expermental results, n: IEEE Transactons on Power Delvery, 005, vol.0, no., pp [4] W. Xu, S.G. Abdulsalam, Y. Cu, X. Lu, A sequental phase energzaton technque for transformer nrush current reducton- Part II- Theoretcal analyss and desgn gude, n: IEEE Transactons on Power Delvery, 005, vol.0, no., pp [5] C.E. Ln, C.L. Cheng, C.L. Huang, J.C. Yeh, Investgaton of magnetzng nrush current n transformers Part I-Numercal Smulaton, n: IEEE Transactons on Power Delvery, 1993, vol 8, no.1, pp [6] C.E. Ln, C.L. Cheng, C.L. Huang, J.C. Yeh, Investgaton of magnetzng nrush current n transformers Part II-Harmonc Analyss, IEEE Transactons on Power Delvery, 1993, vol. 8, no.1, pp [7] M.C. Nțu, M. Duță, C.I. Ncola, Predetermnng the sze of nrush current n power transformers couplng usng LabVIEW, n: Proceedngs of 016 Internatonal Conference on Hydraulcs and Pneumatcs - HERVEX, 016, pp [8] I.S. Gheorghu, A.S. Fransua, Treat on Electrc Machnes, vol. II, A.R.S.R, Romana, [9] M.G. Vant, S.L. Bertol, S.H. Cabral, A.G. Gerent, P. Kuo-Peng, Semanalytc soluton for a smple model of nrush currents n transformers, n: IEEE Transactons on Magnetcs, 008, vol. 44, no.6, pp [10] A.W. Rawool, S.V. Kulkarn, P.P. Vadya, LabVIEW based electrcal partal dscharge measurement system, n: Internatonal Journal of Electrcal and Electroncs Research, 015, vol.3, pp [11] J.A.B. Grmon, O.S. Nakao, Usng LabVIEW n a Mn Power System Model Allowng Remote Accessand New Implementatons, n: Proceedngs of Internatonal Conference on Engneerng Educaton - ICEE, 007, pp.1-5. [1] Introducton to Modern Data Acquston wth LabVIEW and MATLABhttp:// on_to_modern_data_acquston[1].pdf. [13] LabVIEW MathScrpt RT Module. ha/documents/labvew/tranng/labview%0mathscrpt/la bview%0mathscrpt.pdf. [14] R.W. Larsen, LabVIEW for Engneers, Pearson Educaton, Inc., publshng as Prentce Hall, New Jersey, USA, 010. [15] L. Mandache, D. Topan, M. Iordache, I.G. Srbu, SPICE model for effectve and accurate tme doman smulaton of power transformers, n: Proceedngs of Nonlnear Dynamcs and Synchronzaton (INDS) & 16th Internatonal Symposum on Theoretcal Electrcal Engneerng (ISTET), 011, pp [16] P. Rafajdus, P. Bracnk, V. Hrabovcova, J. Satz, L. Kankula, Current transformer analyss under transent condtons, n: Proceedngs of XIX Internatonal Conference on Electrcal Machnes (ICEM), 010, pp. 1-5.