A Short Course on Synchronous Machines and Synchronous Condensers

Transcription

1 A Short Course on Synchronous Machnes and Synchronous Condensers G. Heydt S. Kals E. Kyrakdes Arzona State Unersty Amercan Superconductor 23 G. Heydt, S. Kals and E. Kyrakdes

2 Sesson Tme Topcs Instructor Introductons 8:3 8:4 Bradshaw Fundamentals of 8:4 9:5 Energy conerson Heydt synchronous machnes Synchronous machne constructon Energy transfer n a synchronous machne Motor and generator acton Phasor dagram for synchronous machnes osses Superconductng desgns Power factor and torque angle Example of calculatons Transents and damper wndngs Saturaton and the magnetzaton cure B R E A K 9:5 :

3 2 Synchronous condensers 3 Superconductng synchronous condensers : :3 :3 2: U N C H 2: :3 What s a synchronous condenser? Applcatons of synchronous condensers Analyss Superconductty The superconductng synchronous condenser (SSC) Performance benefts of SSC n a grd Kals Kals

4 4 Synchronous machne models 5 State estmaton appled to synchronous generators :3 2:3 Park s transformaton Transent and subtransent reactances, formulas for calculaton Machne transents 2:3 3:3 Bascs of state estmaton applcaton to synchronous generators demonstraton of software to dentfy synchronous generator parameters Heydt Kyrakdes

5 B R E A K 3:3 3:4 6 Machne nstrumentaton Queston and answer sesson 3:4 4:3 DFRs Calculaton of torque angle Usual machne nstrumentaton Heydt, Kyrakdes, and Kals 4:3 5: All partcpants

6 SESSION Fundamentals of synchronous machnes

7 Synchronous Machnes Example of a rotatng electrc machne DC feld wndng on the rotor, AC armature wndng on the stator May functon as a generator (MECHANICA EECTRICA) or a motor (EECTRICA MECHANICA) Orgn of name: syn equal, chronos tme

8 Synchronous Machnes ROTATION FIED WINDING ARMATURE WINDING

9 Synchronous Machnes The concept of ar gap flux STATOR ROTOR

10 Synchronous Machnes The nductance of the stator wndng depends on the rotor poston Energy s stored n the nductance As the rotor moes, there s a change n the energy stored Ether energy s extracted from the magnetc feld (and becomes mechancal energy that s, ts s a motor) Or energy s stored n the magnetc feld and eentually flows nto the electrcal crcut that powers the stator ths s a generator

11 Synchronous Machnes The basc relatonshps are POWER ( TORQUE ) (SPEED) ENERGY (/2) ( I 2 ) POWER d(energy) / d(time)

12 Synchronous Machnes Consder the case that the rotor (feld) s energzed by DC and the stator s energzed by AC of frequency f hertz. There wll be aerage torque produced only when the machne rotates at the same speed as the rotatng magnetc feld produced by the stator. RPM ( 2 f ) / (Poles) Example: f 6 Hz, two poles, RPM 36 re/mn

13 Synchronous Machnes d The axs of the feld wndng n the drecton of the DC feld s called the rotor drect axs or the d-axs. 9 degrees later than the d-axs s the quadrature axs (q-axs). The basc expresson for the oltage n the stator (armature) s r dλ/dt Where s the stator oltage, r s the stator resstance, and λ s the flux lnkage to the feld produced by the feld wndng ROTATION q

14 Synchronous Machnes Basc AC power flow SEND j x RECEIVE Vsend Vrecee

15 Synchronous Machnes Vnternal Vtermnal The nternal oltage, often labeled E, s produced by the feld nteractng wth the stator wndng, and ths s the open crcut oltage GENERATOR ACTION POWER FOWS FROM MACHINE TO EXTERNA CIRCUIT, E EADS Vt

16 Synchronous Machnes Vtermnal Vnternal The nternal oltage, often labeled E, s produced by the feld nteractng wth the stator wndng, and ths s the open crcut oltage MOTOR ACTION POWER FOWS FROM EXTERNA CIRCUIT INTO THE MACHINE, E AGS Vt

17 The nternal oltage, often labeled E, s produced by the feld nteractng wth the stator wndng, and ths s the open crcut oltage Synchronous Machnes Vnternal E Vtermnal Vt GENERATOR TORQUE ANGE MOTOR Vtermnal Vt TORQUE ANGE Vnternal E

18 Synchronous Machnes Acte power wll flow when there s a phase dfference between Vsend and Vrecee. Ths s because when there s a phase dfference, there wll be a oltage dfference across the reactance jx, and therefore there wll be a current flowng n jx. After some arthmetc Psent [ Vsend ] [ Vrecee ] sn(torque angle) / x

19 Synchronous Machnes Example A synchronous generator stator reactance s 9 ohms, and the nternal oltage (open crcut) generated s 35 kv lne to lne. The machne s connected to a three phase bus whose oltage magntude s 35 kv lne-lne. Fnd the maxmum possble output power of ths synchronous generator

20 Synchronous Machnes Example Work on a per phase bass 35 kv lne-lne 2.2 kv l-n Max P occurs when torque angle s 9 degrees P (2.2K)(2.2K)(sn(9))/9 2. MW per phase 6.3 MW three phase Vsend Vrecee

21 Synchronous Machnes Example If the phase angle s lmted to 45 degrees, fnd the generator power output Vsend TORQUE ANGE Vrecee

22 Synchronous Machnes Example P 6.3 sn(45) 4.6 MW Vsend TORQUE ANGE Vrecee

23 osses Synchronous Machnes Rotor: resstance; ron parts mong n a magnetc feld causng currents to be generated n the rotor body; resstance of connectons to the rotor (slp rngs) Stator: resstance; magnetc losses (e.g., hysteress) Mechancal: wndage; frcton at bearngs, frcton at slp rngs Stray load losses: due to nonunform current dstrbuton EFFICIENCY OUTPUT / INPUT (OSSES) / INPUT

24 Synchronous Machnes osses Generally, larger machnes hae the hgher effcences because some losses do not ncrease wth machne sze. For example, many generators n the 5 MW class and aboe hae effcences greater than 97% But 3% of 5 MW s stll 5 kw and for large unts e.g. 6 MW, 3% of 6 MW s 8 MW! Coolng Dampng

25 Power factor Power factor s the cosne between oltage and current n a snusodal AC crcut. Vsend E Vrecee V t Voltage drop n reactance GENERATOR NOTATION Current n the crcut

26 Power factor Vsend Vrecee Voltage drop n reactance Current n the crcut GENERATOR NOTATION Angle between sendng olts and current

27 Power factor Vsend E Vrecee Vt Voltage drop n reactance GENERATOR NOTATION Current n the crcut COSINE OF THIS ANGE IS THE MACHINE POWER FACTOR AT THE TERMINAS Angle between receng olts and current

28 Power factor Vrecee Vt Current n the crcut Voltage drop n reactance Vsend E Angle between receng olts and current COSINE OF THIS ANGE IS THE MACHINE POWER FACTOR AT THE TERMINAS MOTOR NOTATION

29 Power factor Note that the power factor angle s controllable by the generated oltage E and hence by the DC feld exctaton.

30 Basc expressons MOTOR V t E ji a x GENERATOR V t E - ji a x

31 Power factor Consder now a machne that:. Is operated at successely smaller and smaller torque angle 2. Greater and greater feld exctaton

32 Successely smaller and smaller torque angle The machne torque angle s made smaller and smaller by reducng the electrcal load (P) V t E ji a x Vt Current n the crcut E MOTOR NOTATION Voltage drop n reactance

33 Successely smaller and smaller torque angle The machne torque angle s made smaller and smaller by reducng the electrcal load (P) V t E ji a x Vt Current n the crcut E MOTOR NOTATION Voltage drop n reactance

34 Successely smaller and smaller torque angle The machne torque angle s made smaller and smaller by reducng the electrcal load (P) V t E ji a x Current n the crcut MOTOR NOTATION Vt E Voltage drop n reactance

35 Successely smaller and smaller torque angle The machne torque angle s made smaller and smaller by reducng the electrcal load (P) V t E ji a x Current n the crcut MOTOR NOTATION Vt E Voltage drop n reactance

36 Successely greater feld exctaton Increasng the feld exctaton causes E to ncrease V t E ji a x Current n the crcut Vt MOTOR NOTATION E Voltage drop n reactance

37 Successely greater feld exctaton Increasng the feld exctaton causes E to ncrease V t E ji a x Current n the crcut Vt MOTOR NOTATION E Voltage drop n reactance

38 Successely greater feld exctaton Increasng the feld exctaton causes E to ncrease V t E ji a x Current n the crcut Vt MOTOR NOTATION E Voltage drop n reactance

39 The foregong ndcates that as the machne () approaches zero power operaton the borderlne between generator and motor operaton, the acte power to/from the machne goes to zero and (2) as the machne becomes oerexcted, the power factor becomes cos(9). As the feld exctaton ncreases, E ncreases, and the machne current becomes hgher but the power factor s stll zero. And I leads Vt. In theory, there s no acte power transferred, but a hgh and controllable leel of Q. Ths mode of operaton s called a synchronous condenser

40 Synchronous condenser operaton Ia Q V t 2 I a 2 P 2 V t I a V ji a x E

41 Synchronous condenser operaton Nearly zero acte power flow, nearly zero power factor, nearly perpendcular Ia and Vt, current leads termnal oltage actng as a motor, t acts as a capactor Ia Vt ji a x Power factor correcton, reacte power support, oltage support, reacte power can be ared by aryng exctaton, low loss, no resonance problems of conentonal fxed capactors, potentally a large source of reacte power E

42 Examples A synchronous generator s rated MVA. The machne s ntended to be operated at rated power at torque angle 37 degrees. The armature resstance s.%, and the reactance s 85%. The termnal oltage s rated 34.5 kv. Fnd the machne nternal percent exctaton and termnal pf when the machne operates at MW. Estmate the armature I 2 R losses.

43 Examples P Vt E x ()( E.4 sn( δ ) sn(37.85 o )

44 Examples E.4 /37 o Vt. / o Ia..85 I a I o a ji a ϕ (.85) 9.2 φ o o o o o cos( 8.9 ) POWER FACTOR 98.8% AGGING

45 Examples A sx pole synchronous generator operates at 6 Hz. Fnd the speed of operaton

46 Examples RPM ( 2 f ) / (Poles) RPM 2*6 / 6 2

47 Examples A 4 MVAr synchronous condenser operates on a 34.5 kv bus. The synchronous reactance s 5%. Estmate the feld exctaton to obtan a 3 to 4 MVAr range of reacte power.

48 Examples ) 9 (9.5 [. (.5) f f a o o a f a f a t E E I At I E ji E x ji E V. } I a Q

49 Examples V t E E f ji a x ji a (.5) [. E f.5 I a (9 o 9 o ) At I. a E f..5. E f 2.5 Therefore the feld exctaton should be between 23% and 25 %

50 SESSION 4 Synchronous machne models

51 Saturaton and the magnetzaton cure Park s transformaton Transent and subtransent reactances, formulas for calculaton Machne transents

52 Saturaton and the magnetzaton cure SHORT CIRCUIT ARMATURE CURRENT SCC RATED Vt OCC RATED Ia c AIR GAP INE f f FIED EXCITATION OPEN CIRCUIT TERMINA VOTAGE

53 SHORT CIRCUIT ARMATURE CURRENT SCC RATED Vt OCC RATED Ia c AIR GAP INE f f FIED EXCITATION OPEN CIRCUIT TERMINA VOTAGE SHORT CIRCUIT RATRIO Of /Of SYNCHRONOUS REACTANCE SOPE OF AIR GAP INE

54 Saturaton and the magnetzaton cure Saturaton occurs because of the algnment of magnetc domans. When most of the domans algn, the materal saturates and no lttle further magnetzaton can occur Saturaton s manly a property of ron -- t does not manfest tself oer a practcal range of fluxes n ar, plastc, or other nonferrous materals The effect of saturaton s to lower the synchronous reactance (to a saturated alue )

55 Saturaton and the magnetzaton cure Saturaton may lmt the performance of machnes because of hgh ar gap lne oltage drop Saturaton s often accompaned by hysteress whch results n losses n AC machnes Saturaton s not present n superconductng machnes

56 Transents and the dq transformaton r F a F F F a r D r a aa D D D bb r b b b a r Q r n cc b Q Q Q n n r c c c r G c G G G n n

57 Transents and the dq transformaton r F a F F F a r D r a aa D D D bb r b b b a r Q r n cc b Q Q Q n n r c c c r G c G G G n n r λ

58 Transents and the dq transformaton d-axs THE BASIC IDEA IS TO WRITE THE VOTAGE EQUATION AS IF THERE WERE ONY A d- AXIS, AND AGAIN AS IF THERE WERE ONY A q-axis ROTATION q-axs r λ

59 Transents and the dq transformaton λ r Q G D F c b a Q G D F c b a Q G D F c b a Q G D F c b a λ λ λ λ λ λ λ r r r r r r r

60 Transents and the dq transformaton ) 3 2 sn( ) 3 2 sn( sn ) 3 2 cos( ) 3 2 cos( cos P π θ π θ θ π θ π θ θ PARK S TRANSFORMATION 2 π δ t ω θ R BY APPYING PARK S TRANSFORMATION, THE TIME VARYING INDUCTANCES BECOME CONSTANTS

61 Transents and the dq transformaton Q G D F q d Q G D F AD AD d AD AQ AQ q AQ n Q G D F q d r r r r ω ω r ω ω ω ω r r r ) ( ) ( 3 Q G D F q d Q AQ AQ AQ AQ G AQ AQ D AD AD AD AD F AD AD AQ AQ q AQ AD AD d AD n B ω 3

62 Machne reactances r F F r a a F r D d F D AD d D d-axs equalent crcut ωψ q

63 Machne reactances r G G r a a r Q q G Q AQ q Q q-axs equalent crcut ωψ d

64 Machne reactances These equalent crcut parameters are tradtonally obtaned by a combnaton of manufacturers desgn specfcatons and actual tests IEEE has a seres of standardzed tests for large generators that yeld seeral tme constants and equalent crcut nductances Agng and saturaton are not well accounted Change n operatng pont s not well accounted

65 Machne transent and subtransent Subtransent drect axs nductance Transent drect axs nductance Subtransent open crcut tme constant n the drect axs Transent open crcut tme constant n the drect axs Subtransent short crcut tme constant n the drect axs Transent short crcut tme constant n the drect axs reactances " D AD F AD d d 2 ' d " τ do τ ' do τ " d τ ' d 2 D d F B D F ω r D F ω r 2 2 AD F F B F " d " ' τ do d ' d τ ' do d 2 AD 2 AD 3 AD

66 E a j q x q j d x d SYNCHRONOUS GENERATOR PHASOR DIAGRAM q a r a a V t

67 E a j q x q j d x d SYNCHRONOUS GENERATOR PHASOR DIAGRAM q V t a r a POWER FACTOR ANGE a TORQUE ANGE

68 E a j q x q j d x d j a x q j q x q d x q SYNCHRONOUS GENERATOR PHASOR DIAGRAM q V t a r a POWER FACTOR ANGE a TORQUE ANGE

69 Machne transent and subtransent reactances The usual procedure s that IEEE standardzed tests are used to obtan nductances and tme constants. Then usng the formulas, crcut nductances and resstances can be soled. TESTS TIME CONSTANTS INDUCTANCES EQUIVAENT CIRCUIT PARAMETERS

70 Transent calculatons Transents n dynamc systems are calculated as solutons of dfferental equatons The usual soluton approach s a numercal soluton of (dx/dt) AX bu Most numercal solutons relate to the approxmaton of dx/dt as (delta X)/(delta t) Solutons are terate n the sense that the gen ntal condton s used to obtan X at tme t h; then X(h) s used to obtan X(2h), etc. Popular soluton methods nclude Matlab toolboxes, EMTP, ETMSP, PSpce The computer solutons could be used to compare wth actual feld measurements. And f there are dscrepances, the computer model could be updated to obtan better agreement and hence a more accurate model.

71 SESSION 5 State estmaton appled to synchronous generators

72 Sesson topcs: Bascs of state estmaton Applcaton to synchronous generators Demonstraton of software to dentfy synchronous generator parameters

73 BASICS OF STATE ESTIMATION V s V - R 5Ω R 2 5Ω V 2 V It s desred to measure the oltage across R 2 Assume we hae two oltmeters: A and B Measure the oltage across R2 wth both oltmeters V a 5. V V b 4.7 V Snce the two measurements do not agree but are close to each other, aerage the result to estmate V 2 V V a V b 2 4.9V

74 BASICS OF STATE ESTIMATION Now assume that we hae a thrd oltmeter C et the measurement from C be V c 5 V Clearly ths measurement s not relable Smple approach: dsregard V c and estmate V 2 from V a and V b Another approach: Use weghted state estmaton Ths means, assgn approprate weghts to each of the three measurements accordng to the confdence that the user has to each nstrument. For example, ge the followng weghts: f B s the best nstrument ge t a weght of 2 ge a weght of 8 to A ge a weght of to C snce t s not relable V

75 BASICS OF STATE ESTIMATION Defnton: State estmaton s the process of assgnng a alue to an unknown system state arable, usng measurements from the system under study. Knowledge of the system confguraton and of the accuracy of the measurng nstruments s used n ths process. System Measurements Estmator z H xˆ Estmated states

76 EXAMPE Assume that t s desred to estmate two states (arables) Three measurements are obtaned, whch form the followng equatons x x2 3. 2x x2.2 x 3x In matrx form: 2 x 3 x Process matrx 3x2 2 states 2x ector 3 measurements 3x ector The matrx equaton s of the form Hx z

77 2 x 3 x EXAMPE Number of measurements: n3 Number of states: m2 Snce n>m, the system s oerdetermned Hence there s no unque soluton The soluton s not unque snce n general t s not possble to satsfy all the equatons exactly for any choce of the unknowns. A soluton should be selected such that the error n satsfyng each equaton s mnmum. Ths error s called the resdual of the soluton and can be computed by, r z Hxˆ xˆ : the ector of the estmated parameters The resdual wll be calculated later

78 EXAMPE There are many ways to mnmze the resdual r One of the most popular s the least squares method, whch n effect mnmzes the length (Eucldean norm) of the resdual r. Ths method results n a smple formula to calculate the estmated parameters Gen the system s of the form Hxz,the ector of the estmated parameters s gen by, xˆ ( H T T H ) H z H z H s called the pseudonerse of H

79 x x EXAMPE H x z z H H H x T T ) ( ˆ Substtute H and z n and sole for the unknown states ˆ ˆ ˆ x x x

80 EXAMPE To see how much error we hae n the estmated parameters, we need to calculate the resdual n a least squares sense J r T r T ( z Hxˆ) ( z Hxˆ) r Hxˆ z J.3 [ ]

81 WHY ARE ESTIMATORS NEEDED? In power systems the state arables are typcally the oltage magntudes and the relate phase angles at the nodes of the system. The aalable measurements may be oltage magntudes, current, real power, or reacte power. The estmator uses these nosy, mperfect measurements to produce a best estmate for the desred states.

82 WHY ARE ESTIMATORS NEEDED? It s not economcal to hae measurement deces at eery node of the system The measurement deces are subject to errors If errors are small, these errors may go undetected If errors are large, the output would be useless There are perods when the communcaton channels do not operate. Therefore, the system operator would not hae any nformaton about some part of the network.

83 HOW DOES THE ESTIMATOR HEP? An estmator may: reduce the amount of nose n the measurements detect and smooth out small errors n readngs detect and reject measurements wth gross errors fll n mssng measurements estmate states that otherwse are dffcult to measure

84 V R EXAMPE 2 Assume we hae a network confguraton as n the fgure on the left. V 2 R 2 V 3 Assume that measurements are aalable for V R, V 2, and V 3. Fnd a 3 relatonshp for V 3 that has the followng form: V 3 av bv 2 c Aalable measurements V V 2 V Ths s clearly an estmaton problem wth three unknowns (a, b, c), and four measurements. Therefore t s an oerdetermned estmaton problem. Now, t s necessary to express the estmaton problem mathematcally

85 EXAMPE 2 Substtute the measurements obtaned n the desred model V 3 av bv 2 c V V 2 V a b c a 3.2b c.4.4a 5.b c 4. a 9.b c In matrx form, a b c H x z As n example, we can sole ths matrx equaton by takng the pseudonerse of the H matrx 7. aˆ 8.3 bˆ.4 cˆ

86 EXAMPE 3 et s work out another example: Estmate the relate phase angles at the buses of the fgure below BUS BUS 2 5 MW M 2 2 MW 4 MW 6 MW M 32 9 MW M 3 3 MW Gen: X 2.2 p.u. X 3.4 p.u. X 23. p.u. System base: MVA BUS 3

87 5 MW BUS BUS 2 M 2 M 3 2 MW 3 MW 4 MW 6 MW EXAMPE 3 SOUTION M 32 The lne flows are gen by, f ab ( ϑa ϑb ) X ab M ab 9 MW BUS 3 The aboe formula can be shown consderng a smple two bus arrangement P V V sn( δ δ2) 2 X et bus be the reference bus ϑ From the measurements: M 2 2 MW.2 p.u. M 3 3 MW.3 p.u. M 32-6 MW -.6 p.u. V δ V2 δ2 Snce V and V 2 are approxmately p.u., and the δ angle δ 2 s small, P can be obtaned as, δ δ2 P X P X

88 EXAMPE 3 Hence,.6 ) (. ) ( ) (.4 ) (.2 5 ) (.2 ) ( ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ X f X f X f In matrx form, ϑ ϑ Ths s agan of the form Hx z, and s soled as n example : ˆ ϑ rad ˆ ˆ 3 2 ϑ ϑ

89 APPICATION OF STATE ESTIMATION TO SYNCHRONOUS GENERATORS Need to know the operatng parameters of generators to perform studes study behaor of the system at arous operatng leels perform postmortem analyss Meet requrements for machne testng (e.g. NERC) To reestablsh machne parameters after a repar Fault dentfcaton / sgnature analyss Incpent eent dentfcaton

90 APPICATION OF STATE ESTIMATION TO SYNCHRONOUS GENERATORS Problems: Generator parameters change wth operatng pont, agng Cannot measure parameters whle generator s commtted Cannot afford to decommt unt n order to measure ts parameters Soluton: Use aalable termnal measurements, knowledge of the model of the generator, and state estmaton, to approxmate the requred parameters To do that, t s necessary to deelop a model for the synchronous generator

91 SYNCHRONOUS GENERATOR REPRESENTATION a axs d axs ϑ q axs drecton of rotaton b Q G c D a F a F G D Q b axs c b c axs

92 SYNCHRONOUS GENERATOR MODE r F a F F F a r D r a D D D aa bb r b b b a r Q r n cc b Q Q r G Q n n r c c c G G G c n n Schematc dagram of a synchronous generator

93 DEVEOPMENT OF SYNCHRONOUS GENERATOR MODE n λ r n Q G D F c b a Q G D F c b a Q G D F c b a Q G D F c b a λ λ λ λ λ λ λ r r r r r r r Q G D F q d Q Y Q Y G G D X D X F F Q G q D F d Q G D F q d M km M km M km M km km km km km λ λ λ λ λ λ λ Q G D F c b a QQ QG QD QF Qc Qb Qa GQ GG GD GF Gc Gb Ga DQ DG DD DF Dc Db Da FQ FG FD FF Fc Fb Fa cq cg cd cf cc cb ca bq bg bd bf bc bb ba aq ag ad af ac ab aa Q G D F c b a λ λ λ λ λ λ λ

94 ) 3 2 sn( ) 3 2 sn( sn ) 3 2 cos( ) 3 2 cos( cos π ϑ π ϑ ϑ π ϑ π ϑ ϑ P dq P abc abc dq P dq λ abc λ P DEVEOPMENT OF SYNCHRONOUS GENERATOR MODE [ ] [ ] x FDGQ x dq x x FDGQ x dq x x FDGQ x dq R Resultng model:

95 SYNCHRONOUS GENERATOR MODE Q G D F q d Q AQ AQ AQ AQ G AQ AQ D AD AD AD AD F AD AD AQ AQ q AQ AD AD d AD n B Q G D F q d Q G D F AD AD d AD AQ AQ q AQ n Q G D F q d ω r r r r ω ω r ω ω ω ω r r r 3 ) ( ) ( 3

96 MODE DISCUSSION After the deelopment of the model t s necessary to carefully examne the aalable nformaton about the system, fnd out what s known n the model, what s unknown and needs to be calculated or assumed, and what s desred to be estmated. For the synchronous generator case, Measured/Known lne-to-lne termnal oltages lne currents feld oltage (for an excter wth brushes) feld current (for an excter wth brushes) Unknown damper currents current derates Fnally, some of the parameters need to be estmated through state estmaton, whle the other parameters need to be calculated from manufacturer s data

97 STATE ESTIMATOR CONFIGURATION EXAMPE Estmate AD, AQ, and r F t t t t t ) ( ) ( ) ( Q G D F q d Q G D F q d F q d n B Q G D F q d d q n F AQ AD F D F d B Q G q B D F d Q G q D F d B V V V V V V V ω r ω ω r r r r ω ω ω ω ω 3 3 ) ( ) ( ) ( ) ( ) ( Calculate current derates by usng Rearrange system n the form z Hx

98 DEMONSTRATION OF PROTOTYPE APPICATION FOR PARAMETER ESTIMATION Prototype applcaton deeloped n Vsual C Portable, ndependent applcaton Runs under Wndows Purpose: Read measurements from DFR and use manufacturer s data to estmate generator parameters

99 SESSION 6 Machne nstrumentaton

100 Sesson topcs: Dgtal Fault Recorders (DFRs) Calculaton of torque angle

101 DIGITA FAUT RECORDERS (DFRs) A DFR s effectely a data acquston system that s used to montor the performance of generaton and transmsson equpment. It s predomnantly utlzed to montor system performance durng stressed condtons. For example, f a lghtnng strkes a transmsson lne, the fault recognton by protecte relays and the fault clearance by crcut breakers takes only about 5 to 83 ms. Ths process s too fast for human nterenton. Therefore, the DFR saes a record of the desred sgnals (e.g. power and current), and transmts ths record to the central offces oer a modem, where a utlty engneer can perform posteent analyss to determne f the relays, crcut breakers and other equpment functoned properly.

102 DIGITA FAUT RECORDERS (DFRs) The DFR sends the measured sgnals to a central pc staton through a modem

103 DIGITA FAUT RECORDERS (DFRs) Typcal graphcs wndow showng a snapshot of the measured sgnals

104 TYPICA DFR SPECIFICATIONS Data fles are stored n COMTRADE IEEE format The DFR can be confgured to create transent records and contnuous records Can be used durng dsturbances, abnormal condtons, and normal condtons Typcal specfcatons: Analog channels: 8, 6, 24, or 32 Dgtal channels: 6, 32, 48, or 64 Sample rate: samples/mn Operatng oltage: 48VDC, 25VDC, 25VDC, 2VAC

105 CACUATION OF TORQUE ANGE The torque angle δ s defned as the angle between the machne emf E and the termnal oltage V as shown n the phasor dagram E φ δ V ri a jx q I a I a

106 CACUATION OF TORQUE ANGE The torque angle can be calculated n dfferent ways dependng on what nformaton s aalable Two ways to calculate the torque angle wll be shown:. Usng lne to lne oltages and lne currents (stator frame of reference) 2. Usng oltages and currents n the rotor frame of reference (dq quanttes)

107 CACUATION OF TORQUE ANGE IN THE STATOR REFERENCE FRAME Known quanttes: ne to lne oltages ( ab, bc, ca ) ne currents ( a, b, c ) Procedure:. Calculate phase oltages a b c ( ab 3 ( 3 ( 3 ab bc ca ) bc ca 3. Calculate the power factor Q φ tan P ) ) 2. Calculate three phase acte and reacte power P Q ab ab a c bc ( b ) bc c a ca 3

108 CACUATION OF TORQUE ANGE IN THE STATOR REFERENCE FRAME 4. Calculate the oltage angle for each phase For a balanced 3-phase system, a b c m m m cosθ cos( θ 2) cos( θ 2) For phase a, use phases b and c b c m m cosθ cos2 cosθ cos2 m m sn θ sn2 2 sn θ sn2 2 m m cosθ cosθ m m sn θ sn θ It can be obsered that, b b c c m 3 cosθ m sn θ b b c c tan θ 3 3 b b cot θ c c

109 CACUATION OF TORQUE ANGE IN THE STATOR REFERENCE FRAME 5. Fnd the angle of a Usng the aboe procedure, The angles for the other phases can be calculated n a smlar fashon. The angles for all phases are gen by, ) ) ( ) ( 3 ( tan ) ) ( ) ( 3 ( tan ) ) ( ) ( 3 ( tan b a b a a c a c c b c b θ θ θ c b a ) ) ( ) ( 3 ( tan c b c b θ a

110 CACUATION OF TORQUE ANGE IN THE STATOR REFERENCE FRAME 6. Calculate the nstantaneous lne to neutral rms oltage for phase a V t rms 2 bc ca 3 cosθ a 7. Calculate the machne generated emf E t V ( r jx ) I t δ s the torque angle q a E t δ

111 CACUATION OF TORQUE ANGE IN THE ROTOR REFERENCE FRAME Known quanttes: dq oltages (, d, q ) dq currents (, d, q ) Procedure:. Calculate the acte and reacte power P Q d q d d q d q q 2. Calculate the termnal oltage E t V d jv q E t γ

112 CACUATION OF TORQUE ANGE IN THE ROTOR REFERENCE FRAME 3. Calculate the termnal current I t P 2 E t Q 2 4. Calculate the power factor angle φ cos P ( E t It 5. Calculate the torque angle ( cos sn ) tan xqit φ rit φ δ ( E ri cos φ x I sn φ) t ) t q t

113 SESSION 7 Queston and answer sesson