Simulation of Wound Rotor Synchronou Machine under oltage Sag D. Aguilar, G. azquez, Student Member, IEEE, A. Rolan, Student Member, IEEE, J. Rocabert, Student Member, IEEE, F. Córcole, Member, IEEE, and P. Rodríguez, Member, IEEE. Electrical Deartment of Engineering Technical Univerity of Catalonia Colom - 8-Terraa, Sain Contact Author: aguilar.eer@gmail.com Abtract- Thi aer reent a tudy of the Wound Rotor Synchronou Machine (SM) tability under voltage ag (di). Machine behavior ha been analyzed by conidering different magnitude (or deth) and duration of the ag. oltage ag caue eed variation on SM (with oible lot of ynchronim), current and torque eak and hence may caue triing and equiment damage, which lead to financial loe. Three machine of different nominal ower have been modeled and imulated with MATLAB in order to tudy it behavior under voltage ag. Thee SM have been analyzed oerating a generator, a motor, and in both cae, working under-excited and overexcited. SM and tudy it tability under a wide variety of ymmetrical and unymmetrical voltage ag, conidering it erformance a generator, a motor and in both cae, oerating underexcited and overexcited. Section II reent the voltage ag claification and characterization. Section III how the wound rotor SM model. Finally, baed on the imulation uing MATLAB, voltage ag effect on SM tability are reented in ection I. Tye B Tye C Tye D I. INTRODUCTION Nowaday, electrical ower ytem are contituted by many generation ource. Neverthele, the vat majority of the electrical ower generation ytem conit of ynchronou generator couled to the electrical grid through a tranformer. Thi i due to it caability of generating electricity in large cale ower lant []. Large (in the MA range) and mall (in the ka range) ynchronou generator are art of electrical ytem and hence it behaviour i a very imortant iue. Moreover, during the lat year, the ower quality ha gained a great imortance in both indutry and reearch, due to technical and ituational factor, uch a the equiment enibility (which are alo the caue of erturbation), ditributed generation, new grid code requirement for ecific ower uly, by mentioned jut a few. The grid may reent many tye of diturbance, being the voltage ag the mot common one. The rincial caue of voltage ag are fault, large tranformer energizing and the tarting of large motor. The interet in tudying thi kind of diturbance i mainly due to the roblem that they caue in electrical equiment []. oltage ag may caue large torque eak on SM, and it can damage the haft or the equiment connected to the haft []. In addition, voltage ag may caue triing, which lead to financial loe. On the other hand, the imulation of the SM behaviour under voltage ag ermit defining different criteria for rotecting and reventing otential damage in uch machine, a well a the effect on the ower uly interrution [4]. Hence, a valid model for SM i eential in order to obtain a reliable analyi of tability and dynamical erformance. In [] it ha been reented the tranient behaviour of SM under ag according to their duration, deth, and initial ointon-wave. The aim of thi aer i to imulate the wound rotor Tye A Tye E Tye F Tye G Fig.. oltage ag tye: Symmetrical (tye A) and unymmetrical (tye B - G). All ag have a deth of %. [] TABLE I POSITIE, NEGATIE AND ZERO SEQUENCE EXPRESSIONS FOR OLTAGE SAGS [] Tye Poitive Negative Zero A B C D E F G A B C D h A h h B h B h h C C h h D D h E E h F F h G G h h E h F h G A 978--444-69-//$6. IEEE 66
II. OLTAGE SAGS (DIPS) A voltage ag i a hort-duration (from half cycle to minute) dro between % and 9% in the magnitude of the rm voltage. When the voltage ag i caued by hort-circuit, the triing time mut limit the fault between and cycle. Neverthele, voltage ag duration due to large motor can be of ome econd [] [6]. oltage ag can be either ymmetrical or unymmetrical, deending on the caue. If the individual hae voltage are equal and the hae relationhi i o, the ag i ymmetrical. Otherwie, the ag i unymmetrical. According to [], voltage ag can be groued into even tye denoted a A, B, C, D, E, F and G (of which C and D cover the majority of ag). Thi claification i baed on the fault tye and connection: if the fault i three-hae the ag tye i A (both tar and delta connection). When the fault i ingle-hae the ag tye are B (tar connection) and C (delta connection). The ag tye are alo C (tar connection) and D (delta connection) if the fault i hae-to-hae. Finally, in two-hae-to-ground fault the ag tye are E (tar connection) and F (delta connection). Sag tye E and G only differ in the zero-equence voltage. Table I and II how their exreion (where h i the ag deth), both in oitive-negative-zero variable and in erhae variable, reectively. The firt table make evident the difference between ag tye E and G mentioned above and alo that ymmetrical one are the mot evere voltage ag tye. Fig. how their haor diagram. In order to imulate the behaviour of SM, in thi aer it ha been conidered that the ag hae i rectangular, no hae jum occur and the ag tye doe not change when the fault i cleared. The deth (or magnitude) and duration are the main characteritic of the voltage ag, but do not comletely characterize the ag. Hence, the voltage ag will be defined by their deth h (. h.9), their duration Δt, and their initial oint-on-wave ψ i [7]. III. WOUND ROTOR SYNCHRONOUS MACHINE MODEL In thi aer a SM eight-order model i ued in order to evaluate it behaviour under voltage ag (damer winding exit in both d and q axi). The dynamic equation in the dq reference frame of SM i given by [8]. The dynamic exreion in form of tate equation can be written a: d dt d ( i ) M { v Ri ωm i } () ω m { Γ() t Γre () t } dt J () dθ ωm () dt Where i i the vector which contain the Park tator and rotor current, v i the vector that include the tranformed tator and rotor voltage, R i the winding reitance matrix and M i the tranformed inductance matrix. The mechanical equation are given in () and (). a h TABLE II SAG TYPES IN EQUATION FORM (OBTAINED FROM []) Tye A Tye B b h j h c h j h a h Tye C b j h c j h a Tye E b h j h c h j h Tye G ( h) a h b j c j a h Tye D b h j c h j a h Tye F b h j ( h) c h j ( h) a Where: h..9 ag deth b ( h) j h 6 UL / hae-to-ground ac voltage c ( h) j h 6 Saturation i not conidered. An equivalent circuit i hown in Fig.. The intantaneou electromagnetic torque Г(t) and the load angle δ(t) (meaured in teady-tate from haor E to haor U ) are exreed a: ( M dif M did ) id ( M qiq )... ( Ld Lq ) id iq Γ( t ) i q... (4) ( ω t ϕ ) ( θ ( ) ) δ ( t) t π () When the SM ha round-rotor (L d L q ), the intantaneou electromagnetic torque i reduced to: q ( M i M i ) i ( M i ) Γ ( t) i (6) d F d D d d Q Moreover, the matrix of magnetic flux ϕ i exreed a: φ M i (7) 67
Three SM have been imulated: a high-eed team turbine generator (8MA), a low-eed hydro turbine generator (MA), both obtained from [8], and a mall generator. Rated arameter of thee machine are included in Aendix. v d r L M φ q ω df M df m ( L q i q M q i Q ) ω m M FD M df LF M df rf v F LD M df r D v D v a v b v c i a i b i c -..... -..... r L M df q - LQ M df -..... v q M df r Q φ d ω m ( L d i d M df i F M df i D ) ω m Fig.. Synchronou machine equivalent circuit. v Q T m - -..... Time [ec] I. OLTAGE SAGS EFFECTS ON WOUND ROTOR SYNCHRONOUS MACHINE In [] it ha been demontrated the effect on SM uing recurive imulation for each ag characteritic: deth, duration and initial oint-on-wave. The deth influence on the torque eak i linear and the duration influence on torque eak i eriodical, for all ag tye. In addition, different initial ointon-wave can roduce eak with different amlitude for unymmetrical ag. The mot relevant voltage ag effect on the SM behaviour are eed variation, with oible lo of ynchronim, current and torque eak, a well a triing rotection. The machine behaviour i different when ymmetrical and unymmetrical ag are roduced in the grid. Fig. how the tranient effect caued by ymmetrical ag on the ka SM, whoe duration and deth are milliecond and er cent of rm voltage, reectively. When ymmetrical ag i alied on thi machine, the mot evere eak occur at the beginning and at the end of the ag, becaue ymmetrical ag do not have negative equence voltage, thu the waveform i not ocillatory. Fig. 4 how the SM behaviour againt an unymmetrical voltage ag tye C on the ka SM with the ame characteritic. In thi cae, the intantaneou active and reactive ower ha a higher ditortion, but their eak value are maller when the ag tart a well a when the ag end. It i due to the fact that the oitive equence voltage alied to the machine i higher for the unymmetrical ag than for the ymmetrical ag [7]. A can be deduced from Table I, the minimum oitive equence voltage available (when h ) in Fig.. ka Synchronou Machine behaviour for a ymmetrical voltage ag: tye A, h., Δt m, ψ i º v a v b v c i a i b i c q T m -..... -..... - -..... - -..... Time [ec] Fig. 4. ka Synchronou Machine behaviour for a unymmetrical voltage ag: tye C, h., Δt m, ψ i º 68
the all unymmetrical ag are.66 (tye B),. (tye C and D) and. (tye E, F and G). Moreover, due to fact that the machine loe are mall and the machine eed i nearly contant, torque and active ower have the ame waveform. The reactive ower (hown in dotted line in Fig. 4) ha an ocillatory behaviour for all the unymmetrical ag becaue of their negative equence voltage. According to the imulation that ha been carried out on three machine, an increae in the ag duration lead to an increae in the current eak when the ag end. On the whole, the tranient wave hae caued by voltage ag deend on different factor uch a it deth, duration, initial oint-onwave and machine arameter. On the other hand, when voltage ag occur on the SM oerating a generator, for examle due to a three-hae hort circuit at ome oint common couling (PCC) near to the machine, the rotor eed increae teadily. Thi fact occur becaue the terminal voltage (which decreae due to ag) i roortional to the electrical torque, thu it alo decreae; in conequence, the rotor eed increae in order to comenate the electrical torque reduction. Since a determined oint of view, the rotor eed could increae unlimitedly and caue an over-eed on the machine, which could lead to collae the ytem. At thi oint, of coure, the generator hould be diconnected by the rotection ytem and returning to a new teady tate. Fig. confirm the above mentioned. During the voltage ag, the SM accelerate if it i working a a generator (or reduce it eed if it i oerating a a motor), o that it may become untable due to lo of ynchronim. In thi cae, rotor eed behaviour of both hydro and team machine have been imulated when a ymmetrical ag occur at terminal voltage. oltage ag, which deth i % of rm voltage, beginning at milliecond and it finih at milliecond. ω mec [rad/ec]....99 ω hydro - Gen ω team - Gen ω hydro - Motor ω team - Motor.99....4..6.7.8.9 time [ec] Fig.. Rotor eed (ω m) tranient hae of both hydro turbine and team turbine ynchronou machine. (Sag tye A, h %, Δt m, ψ i º). In both cae, the machine are oerating a a generator a a motor. Due to the fact that ynchronou machine may loe ynchronim for the mot evere voltage ag (large duration and deth), one imortant iue i to determinate the tranient tability limit and the critical clearing time for each ecific cae. Conequently, in order to analyze the tability machine i neceary to conider variou method to ermit to define thee tability limit of the machine. Thi i treated below. deth [%] deth [%] 4 4.4.......4..6.7.8.9 (a).....6.....4..6.7.8.9 (b) Fig. 6. Symmetrical voltage ag duration and deth influence on the rotor eed (ω m) of a hydro turbine (a) and a team turbine (b) SM. (Sag tye A, h % - %, Δt - econd, ψ i º)...6..4. Fig. 6(a) how imulation reult of everal ymmetrical ag alied on a hydro turbine ynchronou generator. Thi figure i the reult of recurive imulation with deth h % to % and duration Δt to econd. In thi cae, the initial oint-on-wave i ket at º for all imulation. Thu, thi figure indicate the rotor eed eak in abolute value and er unit (.u.). In addition, real and aroximated tability machine limit have been rereented. The thick dotted line (identified with number one) in Fig. 6(a) indicate the real tability machine limit (when the ynchronou generator i unable to return to it teady tate value), obtained by uing the dynamic equation of the SM. Regarding to the thin dotted line (identified with number two) in the ame figure, it indicate the aroximated limit of the machine tability, obtained by uing the equalarea criterion decribed in [8], not only to hort circuit, but alo extended to voltage ag in order to determine the critical clearing time. Thi method conider the aroximated tranient torqueangle curve, which along with the equal-area criterion i often ued to redict the large excurion dynamic behaviour of a ynchronou machine during a ytem fault (Fig. 7). Aume that the inut torque T in i contant and the machine i oerating teadily, delivering ower to the ytem with a rotor angle δ (oint O). When the voltage ag occur at the terminal, the ower out (and the aroximate torque) dro lineally roortional to ag deth, and then the machine.7.7 69
. accelerate. The fault i cleared at δ, and in thi cae the torque immediately become the value of the aroximate tranient torque (oint D). In Fig. 7, the area OABCO i the energy tored in the rotor during the acceleration. After the clearing of the fault the rotor decelerate back to ynchronou eed at δ. The energy given u by the rotor during thi time i rereented by area CDEFC. Therefore, in order to maintain ynchronim in the machine after voltage ag, the follow mathematic exreion mut be accomlihed. δ [ Γload ( δ ) Γag ( δ )] dδ [ Γarox ( δ ) Γload ( δ )] dδ δ δ δ (8) deth [%] 7 6 9 4 8 7 6..4..6.7.8.9 (a) 4 6 7 8 9 6 4 T arox T T ag T load 4 6 8 4 6 8 deth [%] 4 4.e 6 e 8 6..4..6.7.8.9 (b) Fig. 8. Symmetrical voltage ag duration and deth influence on the load angle (δ) of a hydro turbine (a) and a team turbine (b) SM. (Sag tye A, h % - %, Δt - econd, ψ i º) 6 8 Fig. 7. Equal-area criterion extended to voltage ag: Torque v. load angle curve (Symmetrical ag on hydro turbine ynchronou generator) Fig. 6(b) how the rotor eed eak on the team turbine ynchronou generator, which ha a imilar behaviour with reect to the above one, but the ynchronim i lot for horter ag duration. The voltage ag characteritic in thi cae are the ame one. In both machine, all imulation were made conidering ymmetrical voltage ag becaue they are the caue of wort eak. Another method for determining the lo of ynchronim in the machine i to take into account the load angle. The ability to kee the ynchronim may be defined a the cae when the load angle i below 8º for all the time during and after the voltage ag [4]. Thi can be een clearly in Fig. 8, where everal ymmetrical ag have been imulated on both hydro turbine and team turbine SM. Thi figure how the load angle eak and ha been obtained through recurive imulation with deth h % to % and duration Δt to econd and the initial ointon-wave i ket at º for all imulation. In thi figure the dotted line indicate the tability machine limit. The SM behaviour when it i overexcited i different from the behaviour when it i underexcited (conidering either motor or generator mode of oeration). deth [%] deth [%] 8 6 4 8 6 4...4...6....4..6.7.8.9 (a) Overexcited......4..6.7.8.9 (b) Underexcited Fig. 9. Symmetrical voltage ag duration and deth influence on the rotor eed (ω N) of a ka SM (Sag tye A, h % - %, Δt - econd, ψ i º)..4...6.7.7..8 6
An overexcited SM i more table than an underexcited one [9]. Thi ituation can be confirmed from Fig. 9, where everal ymmetrical ag have been imulated by conidering a ka SM working a a generator. In all the imulation the following arameter have been conidered: deth h % to %, duration Δt to econd and the initial oint-on-wave i et in º. A it i hown in Fig. 9(a), the rotor eed of the overexcited generator i more table (with deeer voltage ag and when the ag duration i larger) than the ame generator when it i underexcited (Fig. 9(b)). Uing the load angle lead to the ame concluion.. CONCLUSIONS Synchronou machine tability under voltage ag ha been analyzed on three different three-hae SM. oltage ag effect on equiment deend on different element uch a ag characteritic (deth, duration, oint-on-wave and tye of ag), equiment and grid. The deth and duration influence on the torque eak are linear and eriodical, reectively, for all ag tye. The mot relevant voltage ag effect on SM are current and torque eak and oible lo of ynchronim. The ynchronou generator will be unable to return to it teady tate value if the load angle i not below 8 º for all the time during and after the voltage ag. It hould be noted that there have been no ignificant difference in the imulation of the SM in a motor or generator oeration mode, but an overexcited SM i more table than an underexcited one. ACKNOWLEDGMENT Thi reearch work wa uorted by the roject ENE8-688-C4-/ALT from the Sanih Minitry of Education and Science. REFERENCES [] P. Kundur, Power Sytem and Stability Control, Mc. Graw Hill, New York, 994. [] M. H.J. Bollen, Undertanding Power Quality Problem, IEEE Pre, New York, 999 [] L. Guach, Effect of oltage Sag on Induction Machine and Tranformer, Univerity Polytechnic of Catalonia.. 6-6, Jan. 6. [4] F. Carlon, J. Engtrom and C. Sadarangani: Before and during voltage ag, IEEE Indutry Alication Magazine, ol no,. 9-46. [] D. Aguilar, A. Luna, A. Rolan, G. azquez, G. Acevedo, Modelling and Simulation of Synchronou Machine and it behaviour againt oltage Sag, IEEE International Symoium on Indutrial Electronic, Jun 9 [6] IEEE Recommended Practice for Monitoring Electric Power Quality, IEEE Standard 9-9, June 6, 9. [7] L. Guach, F. Córcole and J. Pedra, Effect of Symmetrical and Unymmetrical oltage Sag on Induction Machine, IEEE, Tran. Power Delivery, vol. 9, No.,. 774-78. Aril 4. [8] P. C. Kraue, Analyi of Electric Machinery, McGraw-Hill, New York, 986. [9] J. C. Da, Effect of Momentary oltage Di on the Oeration of Induction and Synchronou Motor, IEEE, Tran. Indutry Alication, ol 6, No. 4, July/Augut 99. SN: fn: ωn: UN: H: Pole: co ϕn: J: APPENDIX RATED DATA OF STEAM TURBINE SYNCHRONOUS GENERATOR 8MA 6Hz 6 r/min 6k.6 ole air.8 6.8 x J r: rf: L: Ld: Lq: Lf: MdF: Mq:.4Ω.7Ω.4796mH.8648mH.8648mH.766mH.4684mH.4684mH SN: fn: ωn: UN: H: Pole: co ϕn: J: RATED DATA OF HYDRO TURBINE SYNCHRONOUS GENERATOR MA 6Hz. r/min k 7. ole air.8. x 6 J r: rf: L: Ld: Lq: Lf: MdF: Mq:.4Ω.Ω.9mH,7764mH.6794mH.6mH.844mH.79mH SN: fn: ωn: UN: H: Pole: co ϕn: J: RATED DATA OF KA SYNCHRONOUS MACHINE ka 6Hz 6 r/min 47. ole air.8(i).498 Kg m r: rf: L: Ld: Lq: Lf: MdF: Mq: 4.97Ω.Ω 4.97mH.4mH 6.9mH.8mH 6.48mH 6.4mH 6