Synchronous Generator Withstand against Energization

P. Marini

Abstract --In oil and gas plants large power distribution transformer energization takes place only after the generator are often directly connected at the same voltage black-start through an emergency diesel generator or from an level to turbo-generators having almost the same rating as the external grid supply. transformer size: hence the generator can be subjected several However, a synchronous generator can be very sensitive to times to the transformer energization, both during plant black start and during normal operating conditions. the energization of a transformer having approximately the In this paper, a typical electrical distribution from an same kVA generator rating [3], [4], in terms of stator winding industrial plant is taken into consideration: the phenomenon of thermal stress, over-excitation, excessive electro-magnetic transformer energization under one gas turbine synchronous torque oscillations, and abnormal stator voltage and frequency generator is studied and particular emphasis is put on the behavior. transient behavior of the following generator magnitudes: The phenomenon of transformer energization is well known minimum and maximum stator voltage, field current/voltage, in technical literature since many years [2], [10], and a lot of stator winding current, electromagnetic torque, turbine speed/generator frequency. A simple analytical method is also work has been done with regard to the transformer modeling provided to evaluate, starting from the calculating transformer for the aim of its magnetizing inrush current calculation [7], magnetization inrush current waveform, the stator winding [8], [9]. Several recent works have shown clearly that equivalent thermal stress to be compared to the generator transformer energization transients could affect the successful capability against unbalanced and non-linear current waveform completion of a generator black-start procedure [11] or of a 2 (I 2 *t withstand) as foreseen by IEC and ANSI standards. plant emergency restoration plan [4], as well as they could Simulations are carried out by means of EMTP-ATP program: impact on the malfunction of generator differential protection main equipment (synchronous machine, generator automatic voltage regulator and exciter, transformer) is modeled using relay [6]: following these investigations, here particular parameters from relevant manufacturers. attention is focused on the generator electro-mechanical stress, Design data from generator manufacturer regarding withstand in spite of a very detailed transformer modeling, and a term of against the transformer energization are finally compared to the comparison is looked for between calculated results and some results obtained with the EMTP-ATP program, and useful prescriptions foreseen by IEC standards for rotating machines conclusions are derived in terms of choice of the best settings for [15] and ANSI standards for synchronous generators [14]. frequency and voltage protection relays in order to avoid undue The aim of this work is to analyze the possibility of one generator trip during energization. synchronous generator to energize successfully one Keywords : magnetizing inrush current, transformer distribution transformer without exceeding the electro- energization, AVR, excitation system, synchronous generator, mechanical withstand limits declared by the generator negative sequence current, voltage sags / swells. manufacturer and preventing undue trips of voltage and frequency generator protection relays. I. INTRODUCTION HE use of distributed generation (synchronous turbo- II. SYSTEM DATA AND MODELING generators with typical rating between 5 MW and 40 T A. System Data MW) within oil & gas plants has become quite widespread in latest years [3], [5]. More often each one of these generators is The electrical distribution scheme of a typical industrial coupled directly to the plant distribution network, without a plant, in which a synchronous generator, being driven by a gas dedicated step-up transformer like in classical power station turbine, is operated in parallel to an external supply grid schemes. Hence it is not more possible to energize each plant during plant normal operating conditions, is shown in Fig. 1. distribution transformer in a gradual and soft way during the Main electro-mechanical parameters, for each network start-up of the generator and the gradual build-up of its component, are reported in the Appendix. excitation voltage versus its speed increasing, but the

Paolo Marini is with the Department of Electrical Engineering, Maire Tecnimont Group, Milan, Italy (e-mail: [email protected]).

Paper submitted to the International Conference on Power Systems Transients (IPST2015) in Cavtat, Croatia June 15-18, 2015

studied. Moreover, the transformer energization is a phenomenon essentially of reactive type: the levels of active power consumed during this transient are very low and negligible. The transformer is modeled by means of ATP saturable transformer component (STC), based on the nonlinear version of the Steinmetz model [13]: the non-linear saturation curve and air-core inductance are provided by the manufacturer on the basis of no-load test [10], while the winding resistance and from manufacturer short circuit tests are equally split on a per unit base between primary and secondary winding. This simple model cannot represent accurately the inrush current decay, due to lack of detailed representation of core hysteresis and iron losses [7], but this is deemed more conservative for the evaluation of the generator winding stress

Fig. 1. Simplified single-line diagram of the industrial electrical system during transformer energization. The residual flux is not taken into account due to the lack of a topology-correct transformer model able of accounting of magnetic fluxes outside the core B. Modeling and windings [8]: however, this does not affect the analysis, The electrical network is simplified and modeled in ATP since the first energization during black-start or during (alternative transient program) [13] as shown in Fig. 2, restoring after a long maintenance period is studied here, following the general guidelines presented in [12]. instead of a de-energization and a fast subsequent re- G vt1 energization transients. TRANSF cable it The of the transformer feeder is modeled as a time controlled , i.e. a switch that closes at a pre- determined time.

III. PRE -ANALYSIS AND STUDY CASE KE

VREF A. Validation of Transformer Model SE The transformer model, being assumed for the simulations, is first tested in case of an ideal supply network (stiff supply Vs (rms value of Vgen) Fig. 2. ATP model of the electrical system provided with infinite short circuit power), as shown in Fig. 3.

Medium voltage (11 kV) cables are modeled as constant VG VT impedances, since they are electrically short lines and: due to TRANSF StiffNet their non significant extension (less than 1 km), also the cable IT shunt capacitance can be neglected. The turbine-generator is modeled by means of ATP SM59 model for synchronous machines [13], based on d-q reactance Park’s theory [1] and with transient control system (TACS) Fig. 3. ATP model of the electrical system: ideal network supply and magnetic saturation being taken into account. The automatic voltage regulator (AVR) of the generator The circuit breaker poles are closed at the instant when the excitation system plays an important role during the voltage on phase A passes through the zero value, to get the energization since it can respond quickly soon after the stator maximum current peak value on the same phase [2]. The winding voltage undergoes dips caused by the transformer inrush current waveform shown in Fig. 4 results. inrush current, and stator voltage swells and overshoots can The peak value on phase A is around 7050 A follow the initial dips due to the interaction between AVR and (corresponding approximately to 10.7 p.u. of transformer rated inrush currents [3], [5]: the AVR and the generator exciter are current and to 8.4 p.u. of generator rated current) and its modeled with equivalent transfer functions in Laplace s- relevant r.m.s. value (4985 A) is quite in line with the domain. symmetrical r.m.s. value provided by the manufacturer In contrast to the necessity of modeling the AVR, the (5000 A). turbine governor can be neglected [4]: in fact, it does not impact on the accuracy of the overall analysis since its time constants are longer than the duration of the transients being generator rated current) current) rated generator generator rated current) current) rated generator

y hl i ec 2 m cce crepnig o the to (corresponding cycle ms 20 each in fundamentalHz). frequency 50 of hole a by f peak one of made and A phase the for asymmetrical (), hc gvs h ae udr h cret wavef current this following null.The formula results: the of half under that considering area envelope, exponential the gives which “(1)”, function the of integration the through calculated follows: constan time one as simplyrepresented be which can t b decay exponential the an resembles of 4 Fig. in envelope waveform the however, [4]: defined exactly circuit equivalent inductive-resistive transformer reflects co time a windingresistance, the resistance as well as losses transformer the and non-linear Fig. 4. Inrush current (phase A) (phase transformer Inrush with current Fig. 4. rated current) current) rated I ∫ I I (I where

It is clearly visible the typical waveform being co being waveform typical the visible clearly is It I where ioosy paig sne h tasomr inductan transformer the since speaking, Rigorously h eegtc otn (I content energetic The T t e dt is the time variable (s) (s) timetheis variable s h isatnos neoe nuh urn (p.u. current inrush envelope instantaneous the is G G s h isatnos neoe nuh urn (p.u. current inrush envelope instantaneous the is is the exponential function (neperian number) function exponential (neperian theis is the equivalent time constant of the envelope de timeequivalenttheis envelope the of constant 2 Inrush Current [A] is the peak value of the inrush current (p.u. of g of (p.u. current inrush the of value peak the is g of (p.u. current inrush the of value peak the is t) is the integral operator operator integralthe is ( I is the let-throughtheis energy inrushthe(s of current content for the inrush current current inrush the for content energy equivalent of evaluation Approximate B. I 2 = t ) I G = 1 2 ⋅ e ∞ 0 ∫ − I T 2 t dt (1) (1) = 1 2 ∞ 0 ∫ Time[s]      I G 2 ) f h irs cret is current inrush the of t) ⋅ e − T t      2 fed by an ideal supply ideal fedby an dt = T 4 I G 2 nstant for the for nstant expressed by expressed (2) (2) cannot be be cannot t decay as decay t hp is shape the core core the cay (s). cay(s). mpletely enerator enerator enerator ehavior, ehavior, ollowed ollowed ransient ) ) e is ce orm of of

ht n rnil i i psil t dfn a oe g more a define (I to possible capability is withstand it principle in st that [14] standard ANSI s. 30 of value a machines, of t for prescribe, while [14] s, standards ANSI 20 to frequenc fundamental (at currents sequence negative teml ihtn cpblt (I capability withstand thermal a state conditions, i.e. to verify to followingthe i.e. conditions, rela state h lttruh nry (I energy let-through the firs a view at compare to of approach conservative point a deemed engineering an from [16], components tay tt oeain n nt uig rnins li transients during not and energization. operation state steady on defined are harmonics anyway,thesefundamental: th higher order with components harmonic unbalanced rated current) current) rated urn ae f eaie eune ye hwvr sin however, 2 type: prevailing sequence negative of are current amnc pcrm hs ms sgiiat components usually2the significant most whose spectrum harmonic n h floig iue. cmaio bten resu manufacturerthenis performed. data generator between comparison A figures. following the in ihtn cpblt (I capability withstand

oee, ol rqie oe osrcin aa from data whic bef construction analysismanufacturer insitu measurement and generator test more winding, require harmonic stator would detailed however, generator more the any performing of stress thermal safeexistmargin does good a that confident quite true holds “(3)” if current, energization transient develop content energetic whole the way, simplified to gas turbine and plant oil & gas process are fed fed are supplygrid. supply process external an gas by & or generator oil diesel emergency plant and turbine gas to loa auxiliary voltage low the sequence, black-start a during that, assumed is it Hence conditions. load operating is and started been has generator turbine IEC standard [15], for air indirect cooled generato cooled indirect air for [15], standard IEC I where I n eea, o al h hroi cmoet o the of components harmonic the all not general, In h tasomr nriain urn wvfr hs a has waveform current energization transformer The The results of numerical simulations are shown grap shown are simulations numerical of results The T t e ned sne () tks no con, lhuh in although account, into takes “(2)” since Indeed, The transformer energization takes place only after only place takes energization transformer The is the time variable (s) (s) timetheis variable 2 2 is the exponential function (neperian number) function exponential (neperian theis is the equivalent time constant of the envelope de timeequivalenttheis envelope the of constant 2 t is the let-throughtheis by energy“(2)” calculated t is the unbalance current withstand current byunbalance theis [14] defined I C. Study Case Case Study C. 2 t ≤ I nd nd 2 2 and the 5the and n 5 and t (3) (3) 2 th 2 th harmonics are negative sequence sequence negative are harmonics ) eie b te tnad i steady in standards the by defined t) IV. R IV. 2 orders [6]. [6]. orders 2 t), by taking into account also also account into taking by t), 2 ) cluae b “2” t the to “(2)”, by calculated t), ESULTS 2

2 t) against unbalanced unbalanced against t) tionship: he samehe type on the actual actual the on one can be be can one ds relevant relevant ds ll the plant plant the ll s. s. under no- under ed by the by ed ly during ly ates also also ates cay (s). cay(s). start-up y) equal equal y) rs, gives rs, t glance t the gas the lts and and lts e the ke hically e the ce n the an , [15]. [15]. , inrush eneral eneral y an by t is it are are ore ore the a a h,

otg ad vrvlae eeao poeto relay protection generator over-voltage and voltage w compatible are and generator, the for detrimental ex neither are terminals generator at swell voltage ca s 2 to equal constant steady assumed. the time reach equivalent to s an 10 values: about in out damp currents tr the that visible is it 6, Fig. the From current. gen the of p.u. 3.5 approximately to corresponds it Fig. 7. Generator voltage func Fig. a winding 7. as stator view – comp on currents Transformer Fig.6. inrush zoom – view currents Transformer Fig.on 5. inrush

t s lal vsbe ht h vlae a a well as sag voltage the that visible clearly is It shownis voltage stator in7. Fig. generator The A 2950 around is A phase maximum on value The peak

Stator voltage [p.u. r.m.s.] Transformer phase currents [A] Transformer phase currents [A] (f ile SM_GTG_TACS.pl4; x-v ar t) t) ar x-v SM_GTG_TACS.pl4; ile (f t) ar x-v SM_GTG_TACS.pl4; ile (f t) ar x-v SM_GTG_TACS.pl4; ile (f -3000 -2000 -1000 0.0 0.3 0.6 0.9 1.2 1.5 0-30 0 0-20 0 0-10 0 1000 2000 3000 1000 2000 3000 A. Electromechanical Magnitudes Magnitudes Electromechanical A. [A] 0 [A] 0 0 0.00 0 0.05 2 3 c:ITA -VT1A -VT1A c:ITA c:ITA -VT1A -VT1A c:ITA t: VS VS t: 0.10 4 Time[s] Time[s] Time[s] 6 c:ITB -VT1B -VT1B c:ITB c:ITB -VT1B -VT1B c:ITB 0.15 6 c:ITC -VT1C -VT1C c:ITC c:ITC -VT1C -VT1C c:ITC 9 0.20 8 tion of time tion first waveform first cycles letewaveform 12 0.25 10 ansient inrush ansient [s] [s] erator rated rated erator cessive nor nor cessive [s] ith under- ith settings 0.30 12

15 s the as state n be be n and and

corresponds to the minimumthe to Hz. energizatio corresponds frequency 49.97 of the of end the at reached rad/s, 0.40 - Fig. 9. Generator frequency as a function of time Generator Fig.9. function frequency a as fun a as Generator Fig.deviation speed8. angular h sao vlae h sed sae au i reache is value state steady s. approximately10 the voltage stator the di energi transformer the of emergency and procedure black-start the by d the supplied all for grid supply external the or generator be shall but generator g the moby fed be line cannot motors, on drive speed direct variable of made l loads, the s), direct 0.8 black-start about for p.u. 0.8 than (less small voltage initial the to Due following. the in provided affec not transient. energization practically is frequency the that visible orsodn gnrtr rqec cn e optd b followingformula: computed be can frequency generator corresponding

f f where 2 D Hence by means of “(4)”, the negative speed deviati speed negative the “(4)”, of means by Hence h gnrtr rqec pten s hw i Fg 9. Fig. in shown is pattern frequency generator The From the angular speed deviation, shown in Fig. 8, 8, Fig. in shown deviation, speed angular the From

is the generator frequency (Hz) frequency (Hz) generator theis n π is the rated generator frequency (equal to 50 Hz) Hz) 50 to frequency (equal generator rated theis is the angular speed deviation (centi rad/s) rad/s) (centi deviation angulartheisspeed

Generator frequency [Hz] Speed deviation [centi rad/s] angle(rad). center circle theis (f ile SM_GTG_TACS.pl4; x-v ar t) t) ar x-v SM_GTG_TACS.pl4; ile (f t) ar x-v SM_GTG_TACS.pl4; ile (f 10 20 30 40 50 60 -0.5 -0.4 -0.3 -0.2 -0.1 f 0.0 0 0.0 0 = f n      0.5 1 + 3 100 D 1.0 s1:VEL 1 1 s1:VEL t: FS FS t: 2 π 1.5      Time[s] Time[s] 6 (4) (4) 2.0 9 2.5 ction of time ction 3.0 12 3.5 uration of the of uration ow voltage voltage ow n transient, n [s] zation. For For zation. e b the by ted [s] generator generator as turbine turbine as tors and and tors 15 4.0 after d on of of on the y t is It esel esel the 0 . h bs fed urn i eul o 5. A an A 253.1 to equal is current A. 491 to ceilingvalue equal isrelevant field base The s. 10 withs a for current base current field rated the of 194% to equal ceiling a manufacturer generator transient the by provided capability the with compatible

infollowing.the relaysettings provided c are p oscillations generator over-frequency and under-frequency transient with the that show 11, Fig. with the maximum design limit of 15.31 p.u., corres p.u., 15.31 of maximumlimitthewith design Fig. 12. Generator field current as a function of Generator function a Fig.as 12. field current Generator Fig.11. frequency zoom – view subseq on Generator Fig.10. frequency zoom – view first on

1 Fig. in reported frequency, the on views zoom The The transient field voltage, shown in Fig. 13, is c is 13, Fig. in shown voltage, field transient The current field the that visible is it 12, Fig. From

Field current [A] Generator frequency [Hz] Generator frequency [Hz] (f ile SM_GTG_TACS.pl4; x-v ar t) t) ar x-v SM_GTG_TACS.pl4; ile (f t) ar x-v SM_GTG_TACS.pl4; ile (f t) ar SM_GTG_TACS.pl4;x-v ile (f 48 52 56 60 180 256 332 408 484 560 48.5 49.0 49.5 50.0 50.5 51.0 51.5 40 44 0.0 1.8 0 2.2 0.2 3 t: FS FS t: s1:IF s1:IF t: FS FS t: 2.6 0.4 Time[s] Time[s] Time[s] 6 3.0 0.6 9 time time 3.4 waveformcycles uent waveform uent cycles 0.8 12 3.8 duration of duration [s] [s] ponding to to ponding [s] ompatible ompatible ompatible ompatible d being nd rotection rotection rn is trend 1.0 4.2 15

and 0 the d tand tand equal voltage with field V base a 356 valuetheof e-huh nry (I energy let-though eeao hs wtsad aaiiy gis unbala against capability withstand (I currents a has generator

kNm. 82.78 valu torque rated is the than lower also value is and kNm 50 reached maximum the events: circuit short and 3-phase during withstand limi can the turbine-generator within well results transient energization relevant steady state values are reached after 10 s 10 after reached valuessteady are state relevant Fig. 13. Generator of Fig.13. field voltage function a as Fig. 14. Generator fun Fig. a 14. electromagnetic as torque el aife ad hrfr n polm os exist does problem winding. stator thermalgenerator the of stress no therefore and satisfied well be used for generator protection relays: protection generator for used be sett 59) code (ANSI over-voltage and 27) code (ANSI unde following the energization, transformer during

By applying “(2)”, with T = 2 s and I and s 2 = T with “(2)”, applying By Both field current and field voltage behaviors show behaviors voltage field and current field Both U<< (27 2 (27 U<<

n h bss f h cluae gnrtr ttr vol stator generator calculated the of basis the On U< (27 1 (27 U< ial, h eetoantc oqe eeoe durin developed torque electromagnetic the Finally, Electromagnetic torque [MNm] Field Voltage [V] (f ile SM_GTG_TACS.pl4; x-v ar t) t) ar x-v SM_GTG_TACS.pl4; ile (f (f ile SM_GTG_TACS.pl4; x-v ar t) t) ar x-v SM_GTG_TACS.pl4; ile (f -90 -75 -60 -45 -30 -15 *10 B. I B. C. Voltage and Frequency protection settings settings protection Frequency and Voltage C. -50 -28 0 16 38 60 -6 -3 0 0 2 2 2 2 t) equal to 20 s, the relationship in “(3)” is quit is “(3)” in relationship the s, 20 to equal t) st t unbalanced current withstand withstand current unbalanced t threshold) = 90% of 11 kV for 10 s 10 for kV 11 of 90% = threshold) nd threshold) = 80% of 11 kV for 3 s 3 for kV 11 of 80% = threshold) 3 1 s1:TQ GEN GEN s1:TQ s1:EFD s1:EFD 2 ) qa t 61 s eut. ic the Since results. s 6.12 to equal t) Time[s] Time[s] 6 2 9 3 time time ction of time ction G equal to 3.5 p.u., a a p.u., 3.5 to equal 12 4 . . to 23.25 V. V. 23.25 to [s] [s] ta the that t e equal to to equal e r-voltage ings can can ings that the that 2-phase 2-phase 15 o the for around around 5 the g nced nced tage e e U> (59 1st threshold) = 110% of 11 kV for 10 s generator shaft: it is therefore always important to get from the U>> (59 2nd threshold) = 120% of 11 kV for 3 s. turbine-generator manufacturer all the essential data, as shown in the Appendix, to carry out a careful analysis. On the basis of the calculated generator frequency during Under/over voltage and under/over frequency generator transformer energization, the following under-frequency protection relays are usually set according to short circuit and (ANSI code 81U) and over-frequency (ANSI code 81O) transient stability studies: in this context their settings shall settings can be used for generator protection relays: also take care of the transformer energization transient, without causing undue trips which could compromise the f< (81U) = 48.5 Hz = 97% of 50 Hz for 5 s commissioning of the turbo-generator unit and the plant black- f<< (81U) = 47.5 Hz = 95% of 50 Hz for 1 s start operation. Since the energization is mainly a reactive power phenomenon, between voltage and frequency f> (81O) = 51.5 Hz = 103% of 50 Hz for 10 s magnitudes the stator voltage results the one being most f>> (81O) = 53 Hz =106% of 50 Hz for 1 s. affected, and particularly attention must be paid to check that the relevant temporary overshoot during energization does not The above protection relay settings do not hinder the exceed the design limit foreseen by the generator energization of the distribution transformer and their validity manufacturer. has been confirmed by the turbine-generator manufacturer. VI. APPENDIX V. CONCLUSIONS A. Turbo-Generator Data In this paper a typical industrial system, provided with distributed generation, is taken into consideration and the analysis is focused on the effects of transformer energization TABLE I GENERATOR on one turbo-generator. 4-pole synchronous generator driven by a gas turbine For plant configurations in which the generator is directly all reactance and resistance p.u. (per unit) values are referred to the base connected to a distribution switchgear, it results not more power Sb = 15930 kVA possible to energize gradually through a soft voltage versus parameter value frequency ramp each distribution transformer during the start- rated power 15930 kVA up of the turbine-generator and the build-up of generator rated power factor 0.8 excitation, like it usually happens for the generator step-up rated voltage (r.m.s.) 11000 V (line to line) transformer of a power plant, but the transformer energization rated stator current 836 A rated angular speed 157.1 rad/s takes place once the generator is already on-line and operating rated no-load field current 274 A in no-load conditions. As a rule of thumb for the likelihood armature resistance Ra = 0.0027 p.u. and necessary condition for transformer energization, it is d–axis synchronous reactance Xd = 1.53 p.u. always advisable that the largest transformer to be fed has a q–axis synchronous reactance Xq = 0.67 p.u. rated power not greater than the rated power of the generator. d–axis transient reactance X’d = 0.267 p.u. During the energization transient, the stator voltage at (un-saturated value) q–axis transient reactance generator terminals undergoes initially voltage sags due to the X’q = 0.267 p.u. (un-saturated value) consumed reactive power, followed by voltage swells due to d–axis sub-transient reactance X”d = 0.162 p.u. the interaction between the fast response of the automatic (saturated value) voltage regulator (AVR) and the transformer inrush q–axis sub-transient reactance X”q = 0.243 p.u. magnetizing current: the AVR shall then always be modeled (saturated value) for this type of studies. The initial stator voltage dips caused leakage reactance Xl = 0.118 p.u. by transformer energization forbid the supply of direct on line zero sequence reactance Xo = 0.06 p.u. motors and variable speed drive motors by the generator negative sequence reactance X2 = 0.211 p.u. transient d-axis open circuit during the energization: in fact, low voltage contactors within T’do = 6.759 s time constant direct on line motor starters are prone to drop-out for sub-transient d-axis open T”do = 0.039 s minimum voltage, as well as variable speed drives are very circuit time constant susceptible to excessive under-voltages with even few hundred sub-transient q-axis open T”qo = 0.102 s milliseconds duration. circuit time constant moment of inertia of To evaluate the impact of transformer energization on the J = 4653 kg m 2 generator, it is necessary to analyze not only the stress on generator + turbine + gear 2 total inertia time constant H = 3.6 s stator winding, mainly in terms of withstand capability (I 2 t) IFIELD CEILING 194% for 10 s against unbalanced currents, but also the transient behavior of IFIELD BASE 253 A rotor field current and field voltage and the transient rated torque TN = 82.78 kNm electromagnetic torque oscillations developed on turbine- 3-ph short circuit torque T3-phase short circuit = 8.35 * T N representattypical AVR function transfer Fig.15. IEEE 421.5 AC brushless type type ACbrushless 421.5 IEEE

T A V V T K AVR actuator time constant 0.0001 s 0.0001 constant time AVR actuator RMAX D K RMIN -hsotcruttru T torque circuit short 2-ph P K G derivative time constant 0.01 s 0.01 constant derivative time model parameter K AVR proportional gain 40 40 AVRgain proportional If If D S withstand capability capability withstand A ENERATOR unbalanced current current unbalanced AVR derivative gain 6.7 6.7 AVR derivativegain S S 120 100 I If = field current at 100% terminal voltage terminal air on If100% at field current = 120 AVR integral gain 30 30 AVR integralgain AVR actuator gain 0.99 0.99 gain AVR actuator d-axis saturation saturation d-axis d-axis saturation saturation d-axis otg % time(s) (%) voltage E E saturation min. limit 0.0 p.u. p.u. 0.0 limit min. saturation saturation max. limit 10.5 p.u. p.u. 10.5 limit max. saturation parameter value value parameter S (E (E = field current at 120% terminal voltage terminal open-c on 120% at field current = voltage terminal open-c on 100% at field current = = If = 100 E FD FD E I V E = If = FDBASE FDBASE FDMAX FDMIN FDMIN 120 155 0.1 0.1 0.2 0.3 0.4 1 3 155 145 140 130 125 120 RBASE = 4.6 p.u.) p.u.) 4.6 = p.u.) 8.8 = K T E E / (1.2*If) / 100 0.229 s 0.229 1.00 1.00 O VERVOLTAGEWITHSTAND CHARACTERISTIC 253.08 A 253.08 V 15.90 If / 23.25 V 23.25 G ENERATOR G saturation curve saturation curve saturation ENERATOR TABL E TABL E TABL E E

IV III II XCITER AVR 2-phaseshortcircuit

ion ion I 15.31 p.u. p.u. 15.31 2 2 value value t = 20 s 20 = t 0 p.u. p.u. 0 1.67 1.67 0.02 0.02 0.02 1.1 1.1 gap line gap

= 9.79 *T 9.79 = ircuit ircuit ircuit

N

Fig. 17. Main transformer magnetization curve transformer magnetization Main Fig.17. IEEE Std. 421.5 AC8B excitation system model)excitation AC8B IEEE421.5 Std. represetypical function transfer Exciter 16. Fig.

h prmtr o te rnfre euvln electr equivalent transformer the of parameters The L L V1n/V2n rated voltage ratio 11 kV / 6.3 kV kV 6.3 / kV 11 voltage rated ratio V1n/V2n R 2 1 (fromsupplynetwork) ideal

Voltage [kV rms] A current) (base 656 I1current primary winding winding leakage inductance leakage inductance winding leakage inductance winding (at secondary (at voltage side) (at secondary (at voltage side) Z short circuit impedance 6% (referred 6% Sr)to impedance circuit Z short O B. Distribution Transformer and Cable Data Data Cable and Transformer Distribution B. (at primary voltage (at side) (at primary voltage (at side) (at primary voltage (at side) at rated primary voltagerated at at rated primary voltagerated at Pcc short circuit losses 0.00656 p.u. (82 kW) (82 p.u. 0.00656 losses circuit short Pcc Lo air-core inductance 1.027 H 1.027 Loair-core inductance no-loadlosses resistance 12.6 R R M 0.3 3.4 6.5 9.6 2 1 Io no-loadcurrent Pono-loadlosses Im inrush current current Iminrush winding resistance resistance winding resistance winding 0.5 AIN Sr rated power 12500 kVA power)(base 12500 power rated Sr parameter value value parameter parameter value value parameter U [kV]rms U T RANSFORMER 40.4 Current [A rms][A Current 80.2 M AIN E TABL E QUIVALENT 1 2 0. 1 TABL E T RANSFORMER I [A]rms I

160.0 VI

V 0.03 p.u. (20 A at 11 kV side) side) kV 11 A at (20 p.u. 0.03 E LECTRICAL 5000 A r.m.s. (at 11 kV) kV) 11 A(at r.m.s. 5000 ofversion (simplified ntation 0.0008 p.u. (10 kW) (10 p.u. 0.0008

0.010418 ohm ohm 0.010418 0.03176 ohm ohm 0.03176 12100 ohm ohm 12100 0.9188 mH 0.9188 0.3014 mH 0.3014

C IRCUIT ical ical circuit in Table VI are derived from manufacturer no-load and [14] IEEE Standard for Cylindrical-Rotor 50 Hz and 60 Hz Synchronous short circuit tests data reported in Table V, following the Generators Rated 10 MVA and Above, IEEE Std. C50.13, Dec. 2005. general procedure reported in [1]. [15] Rotating electrical machines, Part 1: Rating and performance, IEC Standard 60034-1, Mar. 2011. [16] G. J. Retter, Matrix and Space-phasor theory of Electrical Machines , TABLE VII Akadémiai Kiadò, 1987. CABLE equipment parameters 300 m length 240 mm 2 cross section 3-core copper conductors cable feeder from generator to 3 parallel runs main distribution transformer Rc = 0.0072 ohm resistance / phase Xc = 0.01 ohm reactance / phase

VII. ACKNOWLEDGMENT The author gratefully acknowledges the electrical department of Maire Tecnimont Group, for the consultation of the available technical literature.

VIII. REFERENCES [1] A. E. Fitzgerald, C. Kingsley, S. D. Umans, Electric Machinery , McGraw-Hill, 1990. [2] Central Station Engineers of the Westinghouse Electric Corporation, Electrical Transmission and Distribution Reference Book , Westinghouse Electric Corporation, 1964, pp. 456-464. [3] K. S. Smith, L. Ran, B. Leyman, "Analysis of transformer inrush transients in offshore electrical systems," IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 1, Jan. 1999, pp. 89-95. [4] I. Hassan, H. V. Nguyen , R. Jamison, "Analysis of energizing a large transformer from a limited capacity engine generator," IEEE PES2000, pp. 446-451. [5] K. S. Smith, L. Ran, J. Docherty, "Analysis of AVR Transients induced by Transformer Inrush Currents," in Proc. IPST 1999 – International Conference on Power Systems Transients in Budapest, Hungary . [6] P. Nunes, A. Morched, M. T. Correia de Barros, "Analysis of Generator Tripping Incidents on Energizing Nearby Transformers," in Proc. IPST 2003 – International Conference on Power Systems Transients in New Orleans, USA . [7] N. Chiesa, H. K. Hoidalen, M. Lambert, M. Martinez Duro’, "Calculation of Inrush Currents – Benchmarking of Transformer Models," in Proc. IPST 2011 – International Conference on Power Systems Transients in Delft, The Netherlands . [8] S. E. Zirka, Y. I. Moroz , C. M. Arturi, N. Chiesa, H. K. Hoidalen, "Topology-Correct Reversible Transformer Model," IEEE Transactions on Power Delivery, Vol. 27, No. 4, 0ctober 2012, pp. 2037-2045. [9] N. Chiesa, "Power Transformer – Modeling for Inrush Current Calculation," Ph.D. dissertation, Dept. Electric Power Eng., Norwegian University of Science and Technology, Trondheim, 2010. [10] CIGRE Working Group C4.307, "Transformer Energization in Power Systems: A Study Guide," Cigre’ Tech. Brochure No. 568, Feb. 2014. [11] J. Hu, B. Bisewski, "Simulations for Validation of a Black Start Restoration Plan using PSCAD," in Proc. IPST 2013 – International Conference on Power Systems Transients in Vancouver, Canada . [12] H. W. Dommel, EMTP Theory Book , Microtran Power System Analysis Corporation, Vancouver, Canada, 1992. [13] Alternative Transient Program (ATP) - Rule Book , Canadian/American EMTP User Group, 1987-92.