2001 IEEE PES WINTER MEETINGJanuary 28 - February 1, COLUMBUS

Panel Session on DATA FORMODELING SYSTEMS TRANSIENTS

Determination of Rotating MachineParameter for Transients Simulations

Juan A. MARTINEZ

Universitat Politècnica de CatalunyaBarcelona - SPAIN

BLOCK DIAGRAM

REPRESENTATION OF SYNCHRONOUS GENERATORS

GENERATORS GROUP I : 0.1 Hz ÷ 3 kHz GROUP II : 50/60 Hz ÷ 20 kHz GROUP III : 10 kHz ÷ 3 MHz GROUP IV : 100 kHz ÷ 50 MHz

Representation

Detailed representation ofelectrical and mechanicalparts, includingrepresentation of saturationand control of excitation

Transition fromsubtransient to transientand to synchronousimpedance

Very important if close tolocation of switching event

Important only for decay ofshort circuit current, otherwisenegligible

Negligible Negligible

Voltage control Very important Negligible Negligible Negligible

Speed control Important Negligible Negligible Negligible

Frequency-dependentparameters

Very important Important Negligible Negligible

Capacitance Negligible Important Very important Very important

L = inductance L" = subtransient inductance Cs = surge capacitanceR = resistance E = electromotoric force Z = impedance measured at terminalsC = capacitance f = frequency

SCOPE

!! Representation of rotating machines from terminals

!! Determination of electrical parameters

!! Group I ( 0.3 Hz - 3 kHz) transients

!! Contents

* AC machines (synchronous, induction)

* Mathematical representation - Equivalent circuits

* Off-line test procedures (time/frequency domain)

SYNCHRONOUS MACHINE

DIAGRAM OF THE ELECTRICAL PART

[v] [R][i] ddt

[ë]

[ë] [L] [i]

Electrical part equations

[v] vector of voltages[i] vector of currents[ë] vector of fluxes[R] diagonal matrix of winding resistances[L] matrix of self and mutual inductances

Transformation of electricalvariables

(Add zero-sequence circuit)

Equivalent circuits

d-axis circuit

q-axis circuit

SYNCHRONOUS MACHINE MODELS (IEEE Std. 1110)

Q-AXISD-AXIS

NO DAMPERCIRCUIT

ONE DAMPERCIRCUIT

TWO DAMPERCIRCUITS

THREE DAMPERCIRCUITS

FIELD CIRCUIT

ONLYMODEL 1.0 MODEL 1.1

FIELD CIRCUIT+ONE DAMPER

CIRCUITMODEL 2.1 MODEL 2.2 MODEL 2.3

FIELD CIRCUIT+TWO DAMPER

CIRCUITSMODEL 3.3

SM PARAMETER IDENTIFICATION PROCEDURES

!! IEEE Std. 115 : Test procedures for SMIEC 34-4

!! Time-domain off-line tests (short-circuit test)

!! Frequency-domain off-line tests (SSFR)

!! Only two circuits per rotor axis

!! For a more general procedure see I.M. Canay,"Modelling of alternating-current machines havingmultiple rotor circuits", IEEE Trans. on EnergyConversion, vol. 8, no. 2, pp. 280-296, June 1993

!! Saturation

Synchronous machine parameters

Parameters MeasurementsLd, Lq Synchronous inductancesLf, Lg Field winding inductancesLkd, Lkq Damper winding inductancesLaf, Lakd, Lfkd d-axis mutual inductancesLag, Lakq, Lgkq q-axis mutual inductancesRa Armature resistanceRf, Rg Field winding resistancesRkd, Rkq Damper winding resistancesL0 Zero sequence inductance

Ld, Lq Synchronous inductancesL’d, L’q Transient inductancesL”d, L”q Subtransient inductancesô’d, ô’q Transient sc time constantsô”d, ô”q Subtransient sc time constantsRa Armature resistanceLl Armature leakage inductanceL0 Zero sequence inductance

! If Laf = Lakd = Lfkd and Lag = Lakq = Lqkq the above measurementsare enough

! If Laf ÖÖ Lakd a new measurement, Lc (characteristic impedance), is needed

1

Ld(s)

1

Ld

1

L d

1

Ld

s ô d

1 s ô d

1

L d

1

L d

s ô d

1 s ô d

ô d0 ô d0

Ld

L d

ô d 1Ld

L d

Ld

L d

ô d

ô d0 ô d0 ô d ô d

Ld

L d

Lc Ll

Lmd Lfkdl

Lmd Lfkdl

Direct axis basic definitions

LL L

L L

L

Lfldc dc

dc dc

md

dc

=−

'

'

2

LL L

L L

L

Lkdldc dc

dc dc

md

dc

=−

' "

' "

2

L L Lmd d l= − L L Ldc d c= − L L Ldc d c" "= −

RL

ffl

d

=ωτ 1

RL

kdkdl

d

=ωτ 2

τ τ τ τdo dod

dd

d

d

d

dd

L

L

L

L

L

L' "

''

' ""+ = + − +

1 τ τ τ τdo do d dd

d

L

L' " ' "

"=

( ) ( )τ τ τ τ τ τd d d dd

dcdo do

c

dc

L

L

L

L1 2+ = + − +' " ' " τ τ τ τd d do dodc

dc

L

L1 2 = ' ""

L LL

L

dc dcd d

do dodc

dcd

'

' ""

=−

+ − +

τ τ

τ τ τ

1 2

21( )L L L

L

Lfkdl c lmd

dc

= −

d-axis data conversion procedure

STANDSTILL FREQUENCY RESPONSE TESTING

!! Aim : Accurate identification of SM parameters from low-voltage frequency response tests at standstill

!! IEEE Std. 115 : Test procedures for SM

!! Measurable parameters

* d-axis operational impedance Zd(s)

* q-axis operational impedance Zq(s)

* standstill armature to field transfer function sG(s)

* standstill armature to field impedance Zafo(s)

I I Vd s d s= = −2

3

1

3 V Id d= =0 0 V

Iq q= =0 0 V I I Vq s q s= = −2

3

1

3 V

I0 00 0= = V I0 00 0= = V

STANDSTILL FREQUENCY RESPONSE TESTING

Operating conditions Is = Ib = - Ic ; Ia = 0 ; Vs = Vc - Vb

d-axis q-axis

Z se s

i sdd

d e fd

( )( )

( )= −

=

∆∆

∆ 0

Z s Z s R sL sd armd a d( ) ( ) ( )= = +1

2

STANDSTILL FREQUENCY RESPONSE TESTING

Measurement of Zd(s)

Z se s

i sqq

q

( )( )

( )= −

∆

∆

Z s Z s R sL sq armq a q( ) ( ) ( )= = +1

2

STANDSTILL FREQUENCY RESPONSE TESTING

Measurement of Zq(s)

sG si s

i sfd

d e fd

( )( )

( )= −

=

∆

∆∆ 0

∆

∆

∆

∆

i s

i s

i s

i sfd

d

fd

arm

( )

( )

( )

( )=

3

2

STANDSTILL FREQUENCY RESPONSE TESTING

Measurement of sG(s)

Z se s

i safofd

d i fd

( )( )

( )= −

=

∆

∆∆ 0

Z se s

i s

e s

i safofd

d

fd

arm( )

( )

( )

( )

( )= =

∆

∆

∆

∆3

2

STANDSTILL FREQUENCY RESPONSE TESTING

Measurement of Zafo(s)

STANDSTILL FREQUENCY RESPONSE TESTING

Procedure for identification of d-axis parameters

! Use the best available estimate for stator leakage inductance LR

! Ld(0) is the low-frequency limit of Ld(s) [Lad = Ld(0) - LR]

! Find the field to armature turns ratio Nfd/Na

! Calculate the field resistance

! Define an equivalent circuit structure for the direct axis

! Use a fitting technique to find values for the unknown parametersthat produce the best fit for Ld(s) and sG(s)

! Adjust Lad to its unsaturated value Ladu

! Measure the field winding resistance, convert it to the desiredoperating temperature, and refer it to the stator

! Normalize the equivalent circuit elements to per unit values

STANDSTILL FREQUENCY RESPONSE TESTING

Procedure for identification of q-axis parameters

! Use the best available estimate for stator leakage inductance LR

! Lq(0) is the low-frequency limit of Lq(s) [Laq = Lq(0) - LR]

! Define an equivalent circuit structure for the quadrature axis

! Use a fitting technique to find values for the unknown parametersthat produce the best fit for Lq(s)

! Adjust Laq to its unsaturated value Laqu

! Normalize the equivalent circuit elements to per unit values

STANDSTILL FREQUENCY RESPONSE TESTING

!! SSFR testing limitations* effect of eddy current losses on Ra

* standstill measurements made at low currents* resistance in the contact points of damper windings

!! Fitting techniques* Maximum-likehood estimation* Noniterative parameter identification* Network synthesis technique* Vector fitting

!! Several procedures have been proposed to solve somelimitations, see for instance* I.M. Canay, IEEE Trans. on EC, 1993* A. Keyhani & H. Tsai, IEEE Trans. on EC, 1994* D.Y. Park et al., IEEE Trans. on EC, 1998

!! Differences between round rotor and salient polemachines (IEEE PES WM 1997 Panel & IEEE Trans. onEC, 1999)

ON-LINE TESTING

!! Limitations of off-line testing

!! Time-domain and frequency-domain methods

!! On-line tests

* on-line frequency response test

* load rejection test

* large disturbance in the excitation voltage

* small disturbance

INDUCTION MACHINE

!! Equivalent circuit* eddy currents in rotor bars* leakage inductance saturation

!! IEEE Std 112 : Standard Test Procedure for PolyphaseInduction Motors and Generators

!! Parameter estimation tests* on/off line tests* standstill time-domain test* standstill frequency response

!! Procedure based on standard specification data* G.J. Rogers & D. Shirmohamadi, IEEE Trans. on EC, 1987* EMTP Universal Machine Module

INDUCTION MACHINE EQUIVALENT CIRCUIT

!! IM performance dominated by the stator and rotor totalleakage reactances and the rotor resistance

!! These quantities are not constant but vary with slip* rotor resistance variation is caused by eddy currents* leakage inductance variation is caused by eddy currents and by magnetic saturation of the leakage flux path

Equivalent circuit - Deep bar or doublecage rotor winding

EQUIVALENT CIRCUIT

SIMPLIFIED EQUIVALENT CIRCUIT

MODIFIED EQUIVALENT CIRCUIT

Standard Specification Data Equivalent circuit parameters

Rated voltage, Vred

Full load specification* Efficiency, ç* Power factor, cosÖ* Slip, sStarting specification* Current, Ist

* Torque, Tst

Maximum torque, Tmax

Design ratio, m

Stator resistance, Rs

Stator leakage reactance, Xs

Magnetizing reactance, Xm

Rotor leakage reactance, Xr

Rotor primary resistance, R1

Rotor secundary resistance, R2

Rotor secondary leakage reactance, X2

DATA CONVERSION PROCEDURE

( )T r I

TT

T

T s

s

mr r

x

DF I I

DF I I

I

I

x x DF x

st st st

ratst st s

sat

sat

sat

tl to ts

=

= =−

⋅

=+

= <

= +

>

=

= + ⋅

−

2

1 2

2

1

1

1

2 2

2

ωφ

πα

α

α

( )

cos

sin( )

sin

Full load specifications

rs

rs

s

xs

s r

m

=−−

=−

=−

cos( ) cos

( ) sin

' '

'

φη η

φ

ηφ

1

1 1

1

Starting specifications Basic relationships

r r TI

I s

r r m r m rr r

r r

xr r

m

xV

Ir r V pu

xV

Ir r

xx x

DF DFx

x DF x DF

DF

st r rats

st

st rr

r

tlss

sts st s

tlred

reds st

tstl tls

sto

tls tl s

=

= + − =−

=+

=

− + =

=

− +

=−−

=⋅ − ⋅

2 2

12 2

21

1

21 2

22

2

22

2

2

2 2

1

1

cos

( )

( )

( )

φ

2

1

222 1

2

−

= = −+

= =

DF

xx

x x rr

r

m

m

x xx

s

soto

ro so r

ss rsts

CONCLUSIONS

!! A significant activity has been made during the last 20years to deduce rotating machine parameters fromtest measurements

!! Only machine models for low frequency and switchingtransients have been analyzed, in all cases consideringa terminal machine model

!! EMTP users can take advantage of different conversionprocedures to obtain the machine parameters for themost adequate model

!! However, very few data conversion procedures are currently implemented in transients tools