Download Synchronous machine/Excitation system

Synchronous machine/Excitation system
Macro file name: sm_exciter.mac
Macro name: PEAKCALC_SM_EXCITER,SSC_SM_EXCITER,VRCONT_SM_EXCITER,
SHC_SM_EXCITER, EXCITER_MACHINE,SM_EXCITER
Version number: NCS 3.1
The synchronous machine and excitation system is illustrated in Figure 1. In this system, the
voltage regulator has two parts; a control algorithm to determine the field current of the
brushless exciter, and a power converter which achieves this command. The brushless exciter
machine rotor voltage is rectified – which in turn supplies the field current to the synchronous
*
machine. Principal variables include the commanded rms line-to-line vllrms
, the brushless
exciter field voltage and current v fdbe and i fdbe , the synchronous machine field voltage and
current v fd and i fd , the synchronous machine line-to-line voltages vab and vbc , and the a- and
b- phase currents into the synchronous machine ia and ib .
Brushless
Exciter
i fdbe
as
+
*
llrms
v
i fd
Synchronous
Machine i
Voltage v
fdbe
Regulator
+
BESM
Stator Rotor
v fd
SM
ibs
vab
vbc
Stator Rotor
Feedback
Figure 1 : Synchronous machine/exciter.
The operation of the excitation system begins with the peak detector, which computes the peak
value of the fundamental component of both the voltage and current waveforms. This control
is depicted in Figure 2. Therein, and throughout this work, variables of the form x and x̂
denote measured and estimated values of x , where x is an arbitrary variable. In Figure 2, the
inputs are the measured line-to-line voltages and two of the phase currents and the two line
currents. The remaining control input is e , the position of a synchronous reference frame.
Based on these quantities, estimate values for the peak of the line-to-neutral voltage and peak
line current, vˆ pk and iˆpk are determined. The high and low pass filters shown in Figure 2 are of
the form
HPFpd ( s) 
0s
0s 1
(1)
and
LPFpd (s) 
1
 f s 1
(2)
where  0  10 s, and  f  10 ms. The transformations K ev for line-to-line voltage and K ie for line
currents to qd voltages and currents, respectively are given by
K rv 
2 cos e   cos e  2 / 3 


3  sin e   sin e  2 / 3 
(3)
K ir 
2 cos e   / 6  sin e  

,
3  sin e   / 6   cos e  
(4)
and
respectively.
vab
HPFpd (s)
LPFpd (s)
q
LPFpd (s)
d
LPFpd (s)
q
K ev
vbc
HPFpd (s)
ia
HPFpd (s)
K ie
ib
HPFpd (s)
LPFpd (s)
q2  d 2
v̂ pk
q2  d 2
iˆpk
d
e
Figure 2: Block diagram of the peak detector.
Based upon the output of the peak detector, the exciter supervisory control depicted in Figure
3 is used to determine the operating status of the voltage control. To this end, logical flags
vok and iok are created to verify that the voltage and current peaks are acceptable; these flags
are then used in accordance with the state transition diagram to determine the operating status
ovr (high to operate voltage regulator). In Figure 3, ON and OFF are logical inputs to request
turn on and turn off of the control respectively.
vllmax  620V
23
v pk
i pkmax  90.2V
i pk
+
_
vok
+
_
iok
ON  voK  iok
ovr
Initial State
vok  iok
ovr
OFF
Figure 3: Exciter supervisory control.
Based on the voltage command, peak detector, and operating status, the regulatory control
depicted in Figure 4 is used to determine a current command to the brushless exciter field
current i*fdbe .The power stage of the voltage regulator is depicted in Figure 5. The transformer
parameters are such that when rated ac voltage and frequency are applied to the transformer
primary, the rectifier (excluding the capacitor) may be represented as a voltage of 25 V in
series with a resistance of 1.4  , an inductance of 6 mH, and an ideal diode. The switching of
the power semiconductors is in accordance with a hysteresis current regulator with a band of
18 mA (center to peak).
*
vllrms
23
+

k pv
_
v pk
k pv  24.5mA/V
 vr  2000ms
i fdbe max  3A
ovr
+
ovr
1
ovr
 vr s
+
0
i fdbemax
ovr
0
i *fdbe
Anti Windup
1
ovr
Figure 4: Exciter regulation control
321mΩ
active
vdc ,befc
i fdbe
9900F
0.685V
 35m
active
v fdbe
81mΩ
active
Figure 5: Power stage of voltage regulator.
The brushless exciter itself is an 8-pole synchronous machine. Perhaps the most difficult part
of modeling this machine is the high degree of magnetic hysteresis present. Nevertheless, the
equivalent circuit shown in Figure 6 has been found to adequately portray machine dynamics.
The primary synchronous machine is a 4-pole device. It is modeled using the equivalent
circuit depicted in Figure 7. Therein, the magnetizing flux linkages are related to the
magnetizing fluxes by md  Lmd imd and mq  Lmqimq where
Lmd 
0.02397  0.036152  0.016694
1  0.993842  0.0224854
(5)
Lmd 
0.01257  0.018952  0.008754
1  1.08922  0.31234
(6)
and where
2
2
ˆ 2  mq
 md
For the test machine   1.9 .
(7)
The damper winding and field winding transfer functions may be expressed
Ydr  s  
Yqr  s  
2
(8)
1  12.54 103 s
1  629.49 106 s
'
Y fd
s 
40.093
1  0.08578 s
(10)
 r sdr
Lmq
1.8mH
rkq
40
L'lfd
'
r fd
v 'fds
rr
s
iqr
0.15
Lkq
5.74mH
i 'fds
(9)
1  5.1099  103 s  2.1913  106 s 2
 r sqr
0.036 0.83mH L
kd
3.33mH
s
v qr
rr
s
idr
0.15
Lmd
5mH
rkd
40
i pmd
1.1A
s
vdr
Figure 6: Equivalent circuit of exciter machine.
 r rds
imq
Llqs
rs
0.5mH 0.108
r
vqs
pmq
Yqr (s )
r
iqs
Lmq
i 'fd
Y fd' ( s )
L'lfd
0.8mH
v 'fd
 r rqs
imd
rs
r
ids
0.6mH 0.108
pmd
Ydr (s )
Llds
r
vds
Lmd
Figure 7: Equivalent circuit of primary generator.
SM_EXCITER : Brushless exciter model
Author: S. D. Sudhoff
Author contact: [email protected],
Date:
Macro name: SM_EXCITER
Version number: NCS 3.1
Report errors or changes to: [email protected]
Brief Description
Brushless exciter model.
List of Inputs, Outputs, Parameters, and Internal variable
Variable Name
Description
z
Concatenation variable
Units
Input Variable Name
Description
Units
i fdsm
current out of exciter into synchronous machine field
A
 rm
exciter mechanical rotational speed
rad/s
qrm
exciter mechanical angle
A
vqsm
q-axis synchronous machine terminal voltage
V
vdsm
d-axis synchronous machine terminal voltage
V
iqsm
q-axis current into synchronous machine
A
idsm
d-axis current into synchronous machine
A
*
vllrms
commanded line-to-line voltage
V
on
off
logical command to turn on converter
logical command to turn off converter
logical
logical
Output Variable Name
Description
Units
v fdsm
voltage out of exciter into SM. field
V
Te
electromagnetic torque of exciter machine
Nm
v fde
stationary dc field voltage of exciter
V
i fde
stationary dc field current of exciter
V
Parameter Name
Description
Default Value
Units
Sensors
gainVab
gain of sensor measuring vab
offsetVab
offset of sensor measuring vab
V
gainVbc
gain of sensor measuring vbc
offsetVbc
offset of sensor measuring vbc
gainia
gain of sensor measuring ia
offsetia
offset of sensor measuring ia
gainib
gain of sensor measuring ib
offsetib
offset of b-phase output current sensor
gainifde
gain of sensor measuring
offsetifde
offset of sensor measuring
V
A
A
i fde
i fde
A
Setting reference frame
Psm
number of electrical poles on synchronous
machine
qrsm0
synchronous machine position at t=0
rad
Peak detector (PEAKCALC_SM_EXCITER)
0
f
HPF time constant
sec.
LPF time constant
sec.
Supervisory Control Controller (SSC_SM_EXCITER)
vll max
maximum allowable line-to-line voltage
V (rms)
i pk max
maximum allowable peak line current
A
Voltage Regulating Controller (VRCONT_SM_EXCITER)
 vr
Integral part time constant
sec
k pv
Proportional part gain
A/V
i fde max
Maximum exciter field current command
A
Simple Hysteresis Controller (SSC_SM_EXCITER)
Hysteresis Bandwidth (from -DeltaI to +DeltaI)
I
vdcpow
dc voltage of the power supply
V
rswitch
total series resistance of switch

vswitch
total series voltage drop of switch
V
rdiode
total series resistance of diode

vdiode
total series voltage drop diode
V
rseries
resistance in series with power supply

Lseries
inductance in series with power supply
H
Cdc
dc capacitance of power supply
F
Exciter Machine
P
Number of poles on exciter machine
 pm
permanent magnet flux linkage
Vs
L fd
field leakage inductance (ref. to rotor)
H
r fd
field winding resistance (ohm, ref. to rotor)

rr
Lmd
rotor winding resistance

d-axis magnetizing inductance
H
Ldd
d-axis damper winding inductance
H
rdd
d-axis damper winding resistance

Lmq
q-axis magnetizing inductance
H
Ldq
q-axis damper winding inductance
H
rdq
q-axis damper winding resistance

N
qr 0
Equivalent turns ratio
Nr/Nf
initial electrical rotor angle
rad
rlo
rectifier resistance in on state

rhi
rectifier resistance in on off state

3-Phase Rectifier
Internal Variable Name
Description
Units
vasm
synchronous machine a-phase voltage
V
vbsm
synchronous machine b-phase voltage
V
vcsm
synchronous machine c-phase voltage
V
iasm
synchronous machine a-phase voltage
A
ibsm
synchronous machine b-phase voltage
A
icsm
synchronous machine c-phase voltage
A
vabsmmeas
measured voltage between phases ab of the SM
V
vbcsmmeas
measured voltage between phases bc of the SM
V
iasmmeas
measured input current of phase a of the SM
A
ibsmmeas
measured input current of phase b of the SM
A
i fdemeas
measured exciter stationary current
A
qe
electric position of generator synch. ref frame
A
vln pk
peak value of line-to-neutral voltage
V
i pk
peak value of line current
A
op
operating status of exciter
logical
i*fde
commanded exciter field current
A
iar
a-phase exciter machine current
A
ibr
b-phase exciter machine current
A
icr
c-phase exciter machine current
A
valr
a-phase voltage to lower rail out of rectifier
V
vblr
b-phase voltage to lower rail out of rectifier
V
vclr
c-phase voltage to lower rail out of rectifier
V
var
a-phase exciter machine voltage
V
vbr
b-phase exciter machine voltage
V
vcr
c-phase exciter machine voltage
V
Macro format
MACRO SM_EXCITER(z, ifdsm,wrm,qrm,vqsm,vdsm,iqsm,idsm,vllrmsstar,on,off, &
vfdsm,te,vfde,ifde, &
par_gainvab,par_offsetvab, &
par_gainvbc,par_offsetvbc, &
par_gainia,par_offsetia, &
par_gainib,par_offsetib, &
par_gainifde,par_offsetifde, &
par_Psm,par_qrsm0, &
par_tauzero,par_tauf, &
par_vllmax,par_ipkmax, &
par_tauvr,par_kpv,par_ifdemax, &
par_DeltaI,par_vdcpow, &
par_rswitch,par_vswitch, &
par_rdiode,par_vdiode, &
par_rseries,par_Lseries,par_Cdc, &
par_P,par_lampm, &
par_Llfd,par_rfd,par_rr, &
par_Lmd,par_Ldd,par_rdd, &
par_Lmq,par_Ldq,par_rdq, &
par_N,par_qr0, &
par_rlo,par_rhi)
Validation
These models have been validated via hardware experimentations.