A Static Compensator Model For Use With Electromagnetic Transients Simulation Programs
A Static Compensator Model For Use With Electromagnetic Transients Simulation Programs
A Static Compensator Model For Use With Electromagnetic Transients Simulation Programs
1398
Abstract - A static var compensator (SVC) model based on state variable techniques is presented. This model is capable of being interfaced to a parent (or host) electromagnetic transients program, and a
stable method of interfacing to the EMTDC program, in particular, is
described. The model is primarily that of a thyristor controlled reactor
(TCR) and a thyristor switched capacitor (TSC) . Capacitor switchings
within the TSC have been handled in a novel way to simplify storage
and computation time requirements. During thyristor switching, the
child SVC model is capable of using a smaller timestep than the one
used by the parent electromagnetic transients program: after the
switching, the SVC model is capable of reverting back to a (larger)
timestep compatible with the one used by the parent program. Other
features that are considered include the modeling of a phase-lockedloop based valve firing system. The paper ends with the discussion of
an application of this model in the simulation of a SVC controlling the
ac voltage at the inverter bus of a back-to-back HVdc tie.
Keywords : Static compensator model, Transient simulation, Variable
timestep, HVdc transmission.
INTRODUCTION
Some of the popular electromagnetic transients simulation programs
[1,2] utilize the modeling algorithm proposed by Dommel [l], in which
an inductor, capacitor, transmission line or other device is represented
as a parallel combination of a resistor and a current source; the values
of these depend on the past history of current and voltage in the device. This representation is used to solve for node voltages at any time
t , based on known values from the previous simulation instant (t-At),
At being the simulation timestep. This approach has the great advantage of simplicity, because an entire network can be quickly reduced
to one containing resistors and current sources, and from which the
network admittance matrix Y is readily constructed. There is no need
for the user to actually write down the differential equations associated
with the network to study its transient behaviour. There are two major
disadvantages of this approach, however.
Firstly, it requires a relatively small timestep to avoid spikes (numerical) whenever switching due to convertor/compensator models within
the network takes place. This requires a premium in terms of CPU time
for the overall simulation. It is difficult to change the timestep dynamically during the simulation run, because that would mean re-calculation of all resistor values and current sources and a re-inversion of the
network matrix. (This may be possible if these electromagnetic transients programs are re-written, and this feature introduced, but that
would entail a great deal of effort.) One approach to overcome this
limitation is that used by the 'NETOMAC' simulation program [ 5 ] . In
this approach the timestep is not changed but the history terms in the
trapezoidal algorithm are interpolated and modified so that the simulation timestep can be synchronized with the switching instant.
Secondly, since the Dommel algorithm is not state variable based, it
leads to a poorer conditioning of the network admittance matrix Y due
to its unequal treatment of inductors and capacitors within the network.
For example, the equivalent resistance associated with an inductor L is
2L/At, and for a capacitor C it is Atl2C. Thus, elements in the network
admittance matrix for L and C are affected in opposite ways when At is
reduced leading to a poorer conditioning of the V matrix. Although this
algorithm usually works, at times this drawback may cause the system
to show numerical instablity. A state variable formulation, on the other
hand, always integrates the differential equations of the system and
solves the equations for capacitor voltages and inductor currents, not
for node voltages as in the Dommel method. Thus all the variables
have the same dependance on the timestep, and the resulting matrices are better conditioned and less likely to give numerical instability.
Another advantage of the state variable approach is that the dependence of the system matrices on the value of the timestep is directly
proportional, and the timestep can be readily changed during a run.
The major disadvantage, however, of the state variable approach is
that it is difficult to write code for the automatic generation of the state
equations given the network connectivity information; the Dommel algorithm, on the other hand, handles this with ease.
For the above mentioned reasons it was decided to use a compromise
approach in modeling the static compensator and its associated external network by developing a stand-alone (child) state variable model
for the static compensator, but retaining the powerful network modeling capabilities of the parent transients program for modeling the external network. The compensator model program interfaces as a Norton
current source with the transient simulation program. The state variable based static compensator module results in a robust algorithm for
calculating the currents and voltages internal to the static compensator, and also allows for features such as the introduction of a variable
local timestep required for the switching elements to be modeled adequately. This approach is similar to that proposed by other authors
[111 who have interfaced a dc convertor model in an electromagnetics
transients program (EMTP) to a Transient Stability Program where the
two programs run with different (though not variable) timestep; interfacing between programs was achieved by using Norton and Thevenin
equivalents.
The authors' program differs from the NETOMAC approach and
merely selects a smaller timestep which is a submultiple of the parent
program's timestep. Also, unlike NETOMAC, the authors' approach
uses a state variable based formulation which has the advantages
mentioned earlier. In addition the authors' approach can be used to
develop models which can be interfaced to electromagnetic transients
simulation programs (such as EMTP or EMTDC) that do not have the
time mesh shifting capability of NETOMAC.
Many authors [ 3 , 4 ] have successfully used state variable based modeling for HVdc convertors, but in their approaches even the associated
external systems have been modeled in state variable form. These external systems cannot therefore be easily changed to a different topology (without rewriting the equations) as is possible with the Dommel
method.
The following sections of this paper deal with details of modeling the
SVC, the method of making a stable interface between the child model
and the parent EMTDC (although the same could be done with EMTP,
or any other programs based on the algorithm proposed by Dommel)
and present some sample results. The paper concentrates on the
modeling of the SVC itself because the bulk of the controls are simulated with the control system building blocks (EMTDC CSMF functions
or EMTP TACS functions) of the parent program. Some modeling details of the phase-locked-loop (PLL) firing system used here, are also
discussed because this is modeled internally in the SVC module. The
paper concludes with the simulation of a SVC regulating the ac voltage
bus at the inverter end of a back-to-back HVdc tie.
1399
The matrices in the equation are functions of the states of the thyristors, and the appropriate entries are re-calculated whenever the firing
logic requires the turning on or off of a thyristor. Also, the capacitor
voltages and the capacitance values are initialized whenever the TSC
operates.
Method of lntearation
The trapezoidal rule has been extensively used in electromagnetic transient programs [ 11. However, implementing it here would have entailed
a matrix inversion every time a switching occurred, or whenever the
timestep had to be changed. For this reason, an Adams second order
closed formula [7] was used, the numerical stability of which is identical to that of the trapezoidal rule. Equations I A , 2A - 5A in the Appendix can be written as
x=A.X(t)+B.u(t)
(la)
where X is the state variable vector, and U the vector of inputs (primary voltages). To apply the chosen method of integration, the increment in X is defined as
AX = [A.X(t -At)
+ B.u(t)]At
(1 b)
Xe,(t) = X ( t - A t ) + A X
(IC)
Equation 1b is re-evaluated with X(t - At) replaced by Xe,(t), to find a
new update X,,(t) , which is used to re-evaluate AX again, until there
is negligible change in the updated Xe,(t) . In practice, for the range
of timestep values used (25 - 50 ps), 3 iterations are found to be
sufficient. Notice also, that no matrix inversions are involved. An application of the trapezoidal rule would have involved only one evaluation
intead of 3, but would have required a matrix inversion, every time the
value of matrix A changed with a switching or change of timestep.
Figure1 : SVC Circuit Diagram.
The TCR elements are connected in c Ita, with the thyristor switches
modeled as changing resistances. The snubber circuik are modeled
as R-C elements in parallel with the thyristors.
The TSC branches are modeled as capacitors. Regardless of the number of TSC branches in operation at a given time, all of these are represented together as an equivalent single capacitor per phase. The
value of this equivalent capacitor and its initial voltage are adjusted
when the TSC switching logic indicates the turning on or off of a capacitor bank. The advantage of this approach is that only one state
variable per phase (6 phases in all) is required. With a TSC having
many stages, each extra stage would increase the number of state
variables by 6 (3 for the wye, and 3 for the delta), and the number of
state variables would rapidly become very large. This approach is exact only if the TSC branch is comprized of a pure capacitance. It was
decided not to include a series inductance (at this stage) because it
would require each arm to be modeled separately. Since the aim was
to obtain a model for relatively long duration studies (typically 100
-2000 ms), and since capacitors are switched only a few times in a
simulation run. this was a small price to pay in making the program
fast.
Saturation of the transformer is represented by flux-dependent current
sources in parallel with the transformer windings. The flux is calculated
from the integral of the voltage across the winding. A flux magnetizing
-current relationship is then consulted to determine the extra magnetizing current that must be injected for that particular flux level. At
present, there is no representation of the hysteresis loop, but there is
a provision for the representation of some core losses via a selectable
shunt resistor across each winding. The details of the equations used
are presented in Appendix. These equations are obtained by graph
theory techniques [ 6 ] .The state variables (variables to be integrated)
are the primary, secondary-delta and secondary-wye currents
(ip, is,, isy); the TSC capacitor voltages (VCA. VCY) ; the TCR inductor
currents (ii,, ii,) : and the snubber capacitor voltages (VSCA. vScy)
Each of these except VCA. vcY and iiy have three state variable components, corresponding to each individual phase. Since the capacitors
are connected in delta, the three voltages add up to zero, so that only
two capacitor voltages can be chosen as independent state variables.
Likewise, in the wye connected transformer secondary winding, the
three currents sum to zero, thus allowing for only two independant
state variables. One could have introduced a fictitious (large) resistance to ground at the neutral point to make the formulation more symmetrical, with all three currents as state variables, but such solutions
often lead to numerical problems. Instead, the algorithm is made
more robust by eliminating variables when capacitor loops or inductor
cutsets are present. Thus, the SVC model has 21 state variables in all.
Since the simulation algorithm works with discrete timesteps, the zero
crossing of a current often falls in-between two timesteps as in Figure
2a. When the turnoff of a thyristor in series with a current carrying
inductor (such as in a TCR) is being simulated, there is the distinct
possibility of a spurious voltage spike appearing in the thyristor and
inductor voltages. Figures 3a(i) and (ii) show simulated TCR current
and voltage waveforms respectively for a simple SVC system (Figure
6), with timestep A t = 50 ps.
St
1400
Figure 4 shows a block diagram of this type of PLL. The three phase
synchronising voltages derived from the commutating bus are Va. Vb
and Vc. Using a 3-phase to 2-phase transformation, the direct and
quadrature axes voltages, Valpha and Vbeta respectively, are derived
according to the following equations'
Valpha = (213)Va - ( l i 3 ) V b - (l13)Vc
12)
Vbeta = (1 /43)(Vb - Vc)
(3)
c.
si""
v coq9
osc
.~
~~~
.~
~~
(4)
where 0 is the phase output of the VCO. The Error signal is acted upon
by a PI controller with proportional gain K1 and integral gain K2. This IS
followed by a VCO to derive a control signal Theta 0 for a Sine-Cosine
Oscillator: the nominal frequency of the VCO is controlled by a reference voltage Uref; dynamic modulation of this reference voltage can
be accomplished by the input AUref. The outputs of the Sine-Cosine
Oscillator, VsinB and VcosO, are fed back to derive the Error, as indicated in equation ( 4 ) . The output of the VCO. which is limited between
0 and 180 degrees, generates the timing Sawtooth waveform 0 (derived as in eq.5). which is utilised to derive the firing pulses for the
valves of the compensatoriconvertor.
0 = [ (Kl1s + K2) (Error) + Uref + AUref ] i s
(5)
b) Variable timestep with A t = 50 ps and fit = 10 p s
Figure 3 : TCR waveforms for fixed and variable timesteps.
Twelve ramps for the 12 thyristor firings are generated from this basic
ramp, and each is compared with the firing angle order. Thus it is even
possible to modulate the firing angle order to provide controlled individ-
-7
7-
8:
oU
U-
-~
--I
0 7
0 1
1401
ual phase firing such as may be required for, say damping a given
harmonic in a system [ 9 ] . The PLL also shows improved immunity to
system harmonics and rapidly regains a lock on phase following faults
causing loss of synchronising voltage [ 131.
Figure 5, is a typical simulation of this PLL where a single phase to
ground fault on Phase a reduced Va to zero. The following results are
presented in Figure 5: (a) Va Single Phase AC voltage input signal (b)
Valpha and Vbeta signals, (c) Error signal as defined by e q . ( 4 ) , (d)
Va(fund) and VsinO signals. The fault resulted in a reduced magnitude
for Valpha to one third of its original value, and no change in Vbeta. A
second harmonic component is observed in the Error signal. These
results are consistent with theoretical predictions. The synchronization
of the fundamental component of Va, Va(fund), and VsinO signals is
rapid and achieved in less than one cycle after the fault is removed
(Figure 5d). Two-phase and three phase faults gave similar results.
The value for R, is chosen to approximate the very short term behaviour of the SVC (for example R, = 21"/At where l" is the zero
sequence inductance of the SVC transformer). The exact value chosen
is not too important because an extra current i, is injected to compensate for any errors introduced by R, . This compensation current is
estimated from the most recent (and therefore stale by one timestep)
is
voltage information available to the SVC model. If i, =V(t-At)/R,
added to Is(t) and injected into the parent program, a current. V(t)/Rc
bleeds into R, and the current entering the rest of the system is
I s ( t ) + [V(t - At) -V(t)]/R,. Note that the second term of this current
vanishes in the limit At
0, and so the current has a value very nearly
equal toI,(t), as was intended.
+
kA
2.0
1 0
0 0
- 1 .o
lo2)
ko(x
02)
0.4
0 2
0 0
-0 2
0.1
I
0.0
-0.
!nsta"ts.
0.2 I
TCR
TSC
rn
MVA
1
T
73MVA
1
-r
0.1
time
0.1
0 0
p
~
J
b toi m e
-O
l
h
_
i
_
t
r switchings
0 1
I
rv(x ,02)
0.4
0.2 -
-0.2
0.0
Voltage decay
I
-
0.1
-03!0
time
I
L
1
-
----__-_---_-Model
I
I
J
t
I
-_-__-__--_
i
I
I
I
I
i
I
i
I
I
I
i
--_J
EMTDC
1402
A rams
Comparator
pulses
7
Harmonic
Harmonic
Fillers
13. H r
Filters
1 1 . 13, HP
1
7; 6
Allocator
BSVS
Capacitor
ONiOFF
to TSC
T 6 0 H z
Inductive
Capacitive
11.
SVC
1671lrad)l
lOfl(iag1
MVA
The block diagram of the SVC controls is shown in Figure 10a [ 1 2 ] , and
a steady state control characteristic typical of SVC model is shown in
Figure 10 b. The SVC controls are identical to the compensator used at
Chateauguay. It consists of a three phase bus voltage measurement
block and a three phase current measurement block. These measurements are used to indicate the reactive power Qsvc of the compensator. The magnitude of the voltage measurement VL is used to derive
a droop. This is followed by a block that adds the droop, proportional
to the reactive current of the SVC, to the magnitude of the measured
voltage. This signal is then filtered. The error between this filtered signal and the reference bus voltage Vref is passed through a PI controller
that results in a reactive power order (BSVS) to the SVC. This order is
split by the 'allocator' into a capacitor onioff signal for the TSC and a
reactive power demand (BTCR) from the TCR. Hysteresis between capacitor stages is built into the model. A relationship representing the
non-linear dependence between BTCR and the required firing angle cy
is consulted and the required cy-order passed on to the PLL-based
firing system in the SVC model. All these control blocks are modeled
with the control system modeling facilities of the parent program
(CSMF in EMTDC). In addition there are the usual set of controls
(based on Chateauguay tie) for the dc system which are similarly modeled but not described here. The HVdc convertors and the SVC are
modeled as 12 pulse valve groups.
1403
kV(x
103)
0 2
1 0
-0
0 2
0 4
0 6
ordered
I
1 6 -
0 2
deqrees(x
0 4
CY
CY
0 2
0 4
and Invertor y
-----
0 6
1 6
I '
Rectifier
')
I
t*me(sJ
102)
loz)
0 4
-I
1 0 4
O BL0
t,me(s)
kA
0 2
0.4
0.6
With proper care, models such as the one developed here can be interfaced to commercially available transient simulation programs and
provide the benefits of a variable timestep and stable numerical performance. From the simulation example presented in the last section,
it is evident that the model can be used succesfully in very detailed
simulation studies.
time(s)
k~
Further work: The techniques presented here can also be used for
detailed representation of other switching models such as an HVdc
convertor.
ACKNOWLEDGEMENTS
1
-
-~
. fi
ttme(s)
4.0
CONCLUDING REMARKS
The state variable technique is a powerful tool for modeling power
electronic circuits, even though accomodating topological changes in
these circuits means rewriting the state equations. The Dommel algorithm (used in popular electromagnetic transients programs) has the
ability to accomodate such changes with ease, but often suffers from
the numerical problems associated with poorly conditioned matrices. In
addition, many of these modern programs do not allow the variable
timestep feaure which economises computer CPU usage when simulating power electronic circuits. A technique has been presented in this
paper which uses the advantages of both these techniques.
-1
1404
pi+
primary wye
APPENDIX
!sQ!xLd
secondary delta
= [ \ ' P I , " p i , vp31T
VP
ip =
Lip2,ip:?
~ ' P \ = [ ~ S I I ~
ip31T
Vs12, \ s \ 3 1 T
=I"\,
"srlr
vs\
"C_\
= [VC:
primary voltages,
primary currents,
secondary wye
Vr~51T-
"C2]T
= rVC4. VC51T
\ ' C s i = ['CY:.
\'CS:. v C s j l T
ii, =
i 1 2 . i131.r
i > \ = [is
. is:.
is31T
i ' s ) = Li--.
C:. C ; C i . C:. C ,
ri:. r i :
ri
i 5 , = [iCl. i,i]'
Loss resistor.
TSC capacitors,
equivalent resistors
TCR Inductor,
r ~ - - Thyristor
r t l . r1:.
C>
- Snubber Capacitor
Rs
L , ~ . --
--
- -
(3.4)
'
Snubber Resistor.
(4.4)
1405
Data for the svstem used in simulation study
AC network equivalents
Sending end 315 kV SCR 4 5 at 85 degrees damping angle
L l = 22 2 mH L2 = 95 4 mH, R = 13 1 ohms
Receiving end 120 kV SCR 2 5 at 85 degrees damping angle
L1 = 10 49 mH L2 = 21 mH, R = 10 8 ohms
where
Convertor Transformers
Sending end 315 kV 120 kV 610 MVA XL = 18
Receiving end 120 kV 120 kV. 610 MVA XL = 18 %
Saturation (both) knee 1 2 pu. slope 0 4 pu
AC Filters
Sending end:
11 th harmonic: R = 1.13 ohms, L = 27.4 mH, C = 2.12 UF
13 th harmonic: R = 0.25 ohms, L = 19.5 mH, C = 2.12 UF
C = 2.4 uF.
j+i
4.5.6
Receiving end:
1 1 th harmonic: R = 0.163 ohms, L = 4 mH. C = 14.6 uF.
13 th harmonic: R = 0.14 ohms L = 2.85 mH, C = 14.6 uF.
C = 16.58 uF.
I + [
4.5.6
svc
Transformer 120 kV 12 65 kV 200 MVA
X LD = X LY = 17 " 0 . X LDY =2 1 U.
knee level = 1 2 pu Saturation slope 0 4 pu
2=
+ Bti
with
6 = Cp
Aq
- 9;" = 9 3 - 9 30
(7)
c:,
*$ 2 ~ 0
where s o = 9:o +
There are thus two independent equations
92
9 3 - 920
18al
- s i 0 = 9 3 - 930
(8b)
BIOGRAPHIES
= 91 - 9 1 0 = 9 2
91 - 910 =
DC system
Rating 140 6 kV 506 MW. 3 6 kA
Smoothing Reactor 34 mH on each side
c: 1
"2AO
C 2 ~in phase 2.
-1
1406
Discussion
D. Povh and H. Tyll (Siemens AG, Dept. EV NP, P. 0. Box 3240, D8520 Erlangen, Germany):
A u t h o r s a r e t o be commented f o r a v e r y i n t e r e s t i n g p a p e r o n t h e m o d e l l i n g o f SVC i n t h e
electromagnetic
t r a n s i e n t s i m u l a t i o n program
p r e s e n t i n g new i d e a s t o i m p r o v e t h e EMTP and
We u n d e r s t a n d t h a t t h e m a i n
EMTDC p r o g r a m s .
i s s u e o f t h e work i s t o overcome t h e d i f f i c u l t i e s a t t h e c a l c u l a t i o n s o f SVCs a n d HVDC i n
these programs.
As m e n t i o n e d i n t h e p a p e r t h e p r o g r a m NETOMAC
has i n c o n t r a r y t o o t h e r programs t h e a b i l i t y
t o i n t e r p o l a t e t h e time step t o switch a t curr e n t zeros and t o a d j u s t t h e f i r i n g i n s t a n t o f
thyristors
exactly
according t o t h e i n s t a n t
g i v e n b y t h e f i r i n g p u l s e c o n t r o l . The m e t h o d
u s e d i n NETOMAC i s s u p e r i o r t o o t h e r m e t h o d s
and e n a b l e c a l c u l a t i o n o f S V C a n d HVDC w i t h o u t
any r i s k s o f n u m e r i c a l i n s t a b i l i t i e s . T h i s has
been a l s o v e r y i m p r e s s i v e d e m o n s t r a t e d i n t h e
r e f e r e n c e 5 o f t h e paper.
The a u t o m a t i c r e d u c t i o n o f t i m e s t e p when
a p p r o a c h i n g c u r r e n t z e r o o r when h i g h f r e q u e n c y o s c i l l a t i o n s o c c u r i n t h e c i r c u i t was f i r s t
u s e d i n o u r p r o g r a m ADIEU / l / , w h i c h was p r e d e c e s s o r o f NETDMAC and was u s e d i n o u r company
for
years. O u r experiences w i t h t i m e s t e p red u c t i o n a r e , however, s i m i l a r t o t h e a u t h o r s ' .
I t i s m o s t l y more c o n v e n i e n t t o c a l c u l a t e t h e
t r a n s i e n t s continuously w i t h t h e reduced step.
I n NETOMAC t h i s p o s s i b i l i l t y i s a l s o i n c o r p o rated.
An e x a m p l e o f u s e o f NETOMAC t o c a l c u l a t e S V C
p e r f o r m a n c e i s shown i n F i g . 1 w h i c h i s t a k e n
o u t o f r e f e r e n c e / 2 / . The SVC s i m u l a t e d c o n s i s t s o f one TCR a n d t w o T S C b r a n c h e s o f d i f f e r e n t r a t i n g s t o g e t h e r w i t h a c f i l t e r s on t h e
secondary
side of
t h e m a i n t r a n s f o r m e r . The
c o n t r o l o f t h e S V C was r e p r e s e n t e d v e r y d e t a i l e d . F i g . l shows t h e c o m p a r i s o n o f NETOMAC
calculations
and s i m u l a t o r
(TNA)
readings
u s i n g o r i g i n a l c o n t r o l c u b i c l e s . The c a s e p r e s e n t e d shows t h e l i n e a r c h a n g e o f t h e SVC a d m i t t a n c e a n d shows an e x c e l l e n t a g r e e m e n t b e t ween m e a s u r e m e n t s a n d c a l c u l a t i o n s .
To t h e a u t h o r s ' s u g g e s t i o n t o s i m u l a t e t h e S V C
we h a v e f o l l o w i n g q u e s t i o n s :
(i)
(ii)
How i s t h e SVC c o n t r o l r e p r e s e n t e d ? I s
t h e n u m e r i c a l s o l u t i o n i n t h e c h i l d model
f o r t h e c i r c u i t and f o r t h e c o n t r o l
i n t h e same s t e p ?
1$
~TCR
'TSC2
Fig 1
I t was u n d e r s t o o d t h a t t h e c h i l d m o d e l
c a n be u s e d o n l y f o r c a l c u l a t i o n o f S V C
performance
i n t h e n e t w o r k b e c a u s e on
t h e s e c o n d a r y s i d e o f t h e t r a n s f o r m e r an
e q u i v a l e n t c i r c u i t i s used f o r c a p a c i tors.
Does i t mean t h a t t h e i m p o r t a n t
studies
on s t r e s s e s a n d p e r f o r m a n c e a t
t h e i n t e r n a l f a u l t s can n o t be done? Are
t h e corresponding v a l u e s o f TSC c u r r e n t s
and secondary s i d e v o l t a g e s a l s o c a l c u lated?
/1/ D. Povh
Berechnung von
Ausgleichsvorgangen
i n
e l e k t r i s c h e n Netzwerken insbesondere z u r
E r m i t t l u n g der
Spannungsbeanspruchungen
d e r V e n t i l e e i n e r Hochspannungs - G l e i c h strom - Ubertragungs - Anlage b e i Erdkurzschlul3
D i s s e r t a t i o n d e r TH D a r m s t a d t , 1 9 7 1
/2/
D. Poch;
H.
Tyll
S t a t i c Var C o m p e n s a t o r s
f o r High-Voltage
Systems
11. Symposium o f S p e c i a l i s t s i n E l e c t r i c
O p e r a t i o n a l and Expansion P l a n n i n g
( 1 1 . SEPOPE), Sao P a u l o , A u g u s t 1 9 8 9
Manuscript r e c e i v e d February 28,
1990.
1 -
1407
references [4, A, B] find the time instant (k) at which the current
through a thyristor goes to zero between the two integration timesteps
(tAand tB) by using linear interpolation of thyristor current. All other
state-variables are interpolated to determine their values at k.This
procedure does not result in any numerical abnormalities even
when the original timestep (At) is kept around 2 electrical degrees (or
approximately 100 ps for a 60 Hz system). Once is obtained the
program can perform the catchup step. Have the authors tried
some such approach and if so, what has been the experience?
The child program is interfaced with any parent program by using
Norton and Thevenin equivalents. Does the child program receive a
Thevenins equivalent (i.e., a 3 phase voltage source and an
impedance matrix) from the parent program on every timestep? Does
the parent program wait for the child program to compute the current
sources?
It is mentioned in the text that the parent and the child programs use
one timestep old information. Is there an inherent delay between the
child and the parent program? In case of the EMTP any such
interconnection between the parent (EMTP) and the child (non-linear
or linear network elements) programs can be achieved as described in
Sections 12.1.2.1 to 12.1.2.3 of [C] to avoid any delay if it may so
exist.
It is possible to run the child program with a larger timestep than the
parent program?
What factors prompted the authors to choose a timestep of 25 ps for
the case shown in Figure 9? Did a larger timestep than 25 ps cause
numerical instability?
As a final remark, the paper reinforces the use of state-variable approach
for representing power semiconductor circuits using graph theory. Earlier,
this approach has been used to model HVDC converters [4, A] and
industrial converters [B]. The authors have made a comment in the paper
about [4] with reference to which we would like to mention that the statevariable model of the HVDC converter proposed in [4] does not warrant
representation of the associated external system (ac system or dc network)
in the state-variable form. Hence, it is not a limitation of the modeling
approach. Instead, it shows that a flexibility exists to model each subsystem
(ac system, converter system and dc network) in any desired manner and to
any desired degree of detail. Norton-Thevenin interface between power
semiconductor circuits and an external system has been presented earlier [4,
References
K. R. Padiyar and Sachchidanand, Digital simulation of multiterminal HVDC system using a novel converter model, IEEE
Transaction on PAS, Vol. 102, June 1983, pp. 1624-1632.
S. P. Yeotikar, S. R. Doradla and Sachchidanand, Digital Simulation of a three phase AC-DC PWM converter-Motor system using a
new state space converter model, Proceedings of IEEE-Industry
Applications meeting, 1986, pp. 672-679.
H. W. Dommel, ElectroMagnetic Transients Program Reference
Manual (EMTP Theory Book), prepared for Bonneville Power
Administration, Portland, OR, USA August 1986.
.-