141
IEEE Transactions on Power Systems, Vol. 10, No. 1, February 1995
Nuclear Plant Models for Medium- to Long-term Power System Stability Studies
T. Inoue
Member, IEEE
T. Ichikawa
Member, IEEE
CRIEPI
Tokyo, Japan
Abstract - CRIEPI and EPRI have jointly developed PWR and
BWR nuclear power plant models for medium- to long-term
power system dynamic simulation studies, which a r e being
implemented for EPRI’s and CRIEPI’s long-term stability
programs respectively. The models are extended versions of
CRIEPI’s previous one for short-term simulation. The models are
useful in simulating the plant dynamics taking into account
responses of the plant control and protection systems. The paper
presents functional spefification of the models, overall model
description, newly included models for medium- to long-term
studies and sample simulation results.
Key Words: Power system analysis, Medium- to long-term
stability, Computer simulation, Nuclear plant models
1. INTRODUCTION
The electricity demand has been continually increasing and is
expected to increase especially in load centers such as metropolitan
areas. To cope with the increasing demand, new large capacity nuclear
and thermal generating power plants have been constructed. However,
due to various constraints such as the site availability, the plants are
being located farther and farther from the load centers. Furthermore,
construction of new transmission lines have been lagged behind due
to various factors such as environmental considerations, costs. In
addition, interconnections between utilities have been increased for
flexible operations of the power system in reserve capacity, economic
dispatching and so on.
The background mentioned above has been making the power
system vulnerable to faults which are outside the normally supposed
contingency criteria of the system. Under a severe disturbance
condition, large imbalance between power supply and demand might
be caused, leading to large excursions in the system frequency and
voltage from the rated values. These excursions may, in turn, induce
large transient in the generating plant output, or plant trip,
compounding the severity of the situation. Unless precautionary
measures are taken, such faults may eventually lead to a black-out of
the whole system.
Therefore, it is important for those who operate power systems to
be aware of potential weak points of the system, and to provide
countermeasures for overcoming the weak points. For this purpose, it
is necessary to develop a computer program to simulate power system
dynamic behaviors with a reasonable accuracy in medium- to longterm time frame (several ten seconds to several minutes) in addition
10 short-term or transient stability studies.
9 4 WM 187-5 PWRS
A paper recommended and approved
by the IEEE Power System Engineering Committee of the
IEEE Power Engineering Society for presentation at
the IEEE/PES 1994 Winter Meeting, New York, New York,
January 30 - February 3 , 1994. Manuscript submitted
July 26, 1993; made available for printing
December 6, 1993.
P. Kundur
Fellow, IEEE
P. Hirsch
Member, IEEE
Ontario Hydro
Toronto, Canada
EPRI
Palo Alto, CA
In such a simulation program, it is especially significant to
simulate the long-term plant responses including plant trip in the
medium- to long-term period after the initial power system
disturbance. Simplified plant models traditionally used for short-term
stability analysis are inadequate for power system long-term dynamics
analysis.
The Central Research Institute of Electric Power Industry (CRIEPI)
in Japan and the Electric Power Research Institute (EPRI) in the
U.S.A. initiated a joint effort for studying power system long-term
dynamics, especially for developing nuclear and thermal plant models
applicable to long-term dynamics analysis, utilizing rich experiences
and know-how obtained in developing power system analysis tools
and in studying power system dynamics in both institutes and their
affiliates.
This paper presents the nuclear plant models that have been
developed by CRIEPI, extending its previous versions for short-term
simulation [1],[2] while the companion paper [3] presents the thermal
plant models that have been developed by Ontario Hydro, on behalf
of EPRI. All these plant models are being implemented for EPRI’s
and CRIEPI’s long-term stability programs respectively.
2. FUNCTIONAL SPECIFICATIONS
Some approaches for modeling of nuclear plant dynamics for
power system long-term dynamics have been proposed [4]-[6]. These
models, however, are generally simple, based on the assumption that
excursions in power system frequency and voltage caused by system
disturbances are small. Thus they are not able to be utilized to a
severe situation probable in the long-term studies such as that
excursions in the frequency and voltage cause severe transients in the
reactor of a nuclear plant and activate the protection which decreases
the reactor power or shut down the reactor.
To develop an adequate nuclear plant model which is able to
simulate the plant transients, considering reactions of the plant control
and protection systems, it is important to define functional
specifications of a nuclear plant model. They clearly specify that how
power system disturbances cause transients in the plant, and which
variables, control systems and protection systems of the plant
components must be modeled to accurately represent plant transients
including plant trip.
In this chapter, the functional specifications of models for PWR
(Pressurized Water Reactor) plant and BWR (Boiling Water Reactor)
plants are presented, which have been defined in the joint research.
2.1 Transients of lnteresi
Operation of the nuclear power plants may be adversely affected
by power system disturbances. For example, if the power system
frequency/voltage disturbances are large, the turbine control valves
may be operated quickly and/or the electrical-motor-driven pumps in
the auxiliary systems may be affected. Subsequent change in the main
steam pressure or the reactor coolant flow rate causes severe transients
in the reactor system and the reactor protection system may decrease
the reactor power immediately or even shut down the reactor. There
are two major avenues for power system disturbances to cause
transients in the reactor.
The first is the path for the frequency disturbance only (and not for
voltage disturbance) to affect the plant operation. That is the path
0885-8950/95/$04.00 0 1994 IEEE
142
from the power system to the reactor through the generator. the
turbine and the main steam lines for both B W R and the PWR plants
and additionally the steam generators (SGs) and the reactor coolant
system for the P W R plant. The direction of the path is the reverse of
the normal energy flow from the reactor to the generator. When the
system frequency increases, the turbine speed governor system reacts
by closing the turbine control valves automatically, while the turbine
bypass valves are simultaneously operated to open. Due to a limited
capacity of the bypass valves, a steam flow rate transient in the main
steam lines results. In a BWR plant this results in a reactor steam
pressure increase to which the neutron flux is very sensitive. In a
PWR plant, on the other hand, a steam flow rate transient produces
a temperature transient in the reactor coolant system.
In addition to the above, if it lasts that the bypass valves remains
opening for several minutes, subsequent drop in the enthalpy or
temperature of the feedwater occurs due to decrease in the steam flow
rate for heating the feedwater, which is extracted form the turbines.
In a B W R plant, the drop in enthalpy of the feedwater which directly
enters the reactor will increase the reactor power. If the increase rate
of the reactor power is expected to exceed a specified limit, plant
operators will decrease the reactor power using the recirculation flow,
which leads to closing of the bypass valves. In a P W R plant, the drop
will not affect the reactor since the steam generator will almost absorb
the influence of the drop.
The second is the path for both the frequency and voltage
disturbances to affect the plant operation. That is the path through the
house power system and induction motors in auxiliary systems. The
disturbances of the system frequency and voltage result in speed
change of the motors. The reactor coolant pumps in a P W R plant are
driven by induction motors directly connected to the house power
system. A coolant flow rate transient caused by a pump speed
transient results in a coolant temperature transient. Therefore, this path
is particularly important for a P W R plant. In a BWR plant, on the
other hand, although the reactor coolant recirculation pumps are also
driven by induction motors, these motors are not directly connected
by the house power system. The motors are powered by frequency
regulated power sources such as motor-generator (M-G) sets equipped
with fluid couplers, or thyristor controlled variable frequency power
supplies. Thus the second path is not as critical for a B W R plant.
2.2 Model Scopes
2.2.1 Plant Types
The following major types of the plants commercially operated in
Japan and the U.S.A were selected for modeling.
(1) PWR plant
* Turbine bypass system with bypass capacity of 40% or 70% of
rated main steam flow rate
* Turbine control system with electro-hydraulic control equipments
Steam generator feed water system with turbine-driven or
motor-driven feed water .
oumm
.
( 2 ) BWR plant
* Turbine bypass
system
with bypass
capacity
..
.
..
.
. of 25% or 100% of
rated main steam flow rate
* Turbine control system with electro-hydraulic control equipments
Reactor feed water system with turbine-driven or motor-driven
feed water pumps
-
2.2.2 Plant Variables
Figs. 1 and 2 show plant components that have been specified so
that the plant models precisely simulate the transients in the plants
along two avenues from the power system to the reactor.
( 1 ) Control systems
The following plant control systems is modeled. These systems will
respond to the plant transients caused by the power system
disturbances
Moislure separator
& rehealel
steam generator
Feed water control valve
Reactor coolant pump
Fig.1 Modeled Components in PWR Plant Model
Moisture separalor
3eanor
T"*,"e
Control YalVe
Fig. 2 Modeled Components in BWR Plant Model
---
(1.1) PWR plant
Reactor power control
* Pressurizer level control
Pressurizer pressure control
Steam generator feed water control
Steam generator relief valve control
* Bypass valve control
Turbine speed control including normal over speed control
( 1 . 2 ) BWR plan1
Recirculation flow control
Reactor pressure control
Reactor relief valve control
Reactor feed water control
Turbine speed control including normal over speed control
( 2 ) Protection system
The following reactor trip factors is included in the plant model.
These factors may be detected under the severe reactor transients
caused by the power system disturbances.
(2.1) PWR plant
* High neutron flux
High rates in neutron flux change (increase and decrease )
Over temperature
* Over power
Low house power frequency
Low house power voltage
Low SG level
Turbine trip
(2.2) BWR plant
High neutron flux
* High reactor pressure
* Low reactor coolant level
--
143
--
* Control valve quick closing actuated through power-load
Doppler reactivity
Coolant temperature reactivity
Average reactor coolant temperature
Thermal power in fuel rods
Coolant flow rate
Coolant temperature in reactor core outlet
Coolant temperature in reactor core inlet
Coolant temperature in hot-leg
* Coolant temperature in cold-leg
Coolant temperature in SG inlet
* Coolant temperature in SG outlet
Thermal power in SGs
SG steam pressure
SG water level
SG feed water flow rate
Pressurizer coolant level
Pressurizer coolant pressure
* Pressurizer heater power
(4.2) BWR plant
Average neutron flux (reactor power)
* Control rod reactivity (in case of selective rod insertion)
* Void reactivity
Doppler reactivity
* Coolant temperature reactivity
Void fraction in reactor core
* Thermal power in fuel rods
Coolant recirculation flow rate
Coolant flow rate in reactor core
Coolant enthalpy in reactor core inlet
Coolant boiling start height in core
Generated steam flow rate in reactor core
Coolant enthalpy in reactor downcomer inlet
Steam pressure in reactor core/upper plenum
Steam pressure in reactor dome
* Steam flow rate in reactor relief valves
* Coolant flow rate in reactor separator
Reactor coolant level
Reactor feed water flow rate
..
unbalance relay (for the BWR plant with partial turbine bypass
system)
Low house power frequency (if necessary)
* Turbine trip
* In addition to the above reactor trip factors, the selective control
rod insertion due to control valve quick closing is included in the
model of the BWR plant with full turbine bypass system.
(3) Main steam system and turbine system
The main steam lines, the high and low pressure turbines, the
moisture separator & reheaters, the turbine control valves, the
intercept valves, the turbine bypass valves is included in the model.
As previously described, the operation of control valves and bypass
valves resulting in the main steam pressure transients causes the
pressure and the temperature transients in the reactor system. The
operation of control valves and intercept valves also cause the change
in the turbine mechanical power to the generator. Therefore, the
behavior of the main steam system and the turbine system is principal.
The non-linear characteristics such as rate limits in the operation of
those valves and the steam flow rate versus the valve position is
included in the model. The following major plant variables is
represented in the plant model
Main steam line pressure
Main steam flow rate
Steam flow rate in bypass valves
Steam flow rate in steam generator relief valves
Steam flow rate in turbine control valves
Steam pressure in moisture separators
Steam flow rate in turbine intercept valves
Turbine power
( 4 ) Reactor system
The reactor system model of the PWR plant includes the reactor, the
reactor coolant system including the reactor coolant pumps (RCPs),
the pressurizer and the SGs. On the other hand, the reactor system
model of the BWR plant includes the reactor, the reactor recirculation
system. The simulation of the reactor system is significant since it is
related to the operation of the reactor protection system. The reactor
protection system monitors the plant variables closely related to the
integrity of the reactor such as the neutron flux, coolant pressure,
coolant temperature and coolant level. The following major plant
variables is represented in the plant model.
(4.1) PWR plant
* Average neutron flux (reactor power)
Position of D-bank control rods
* Control rod reactivity
-
-
-
--
-
--
--
3. Model Structure
Figs. 3 and 4 show the overall structure of the PWR plant and
BWR plant models respectively. Outlines and features of these models
are described below.
Temperature
-
-E:$,s
~eactivity
model
model
A
t
Thermal'
output
dynamics
model
Reactor
Steam
- cwlant
generator
- dynamics
dynamics
model
TREF
Pressure
Main steam flow
Bypa=
valve
model
+
-
model
Rod position'
Neutron flux
TAVG
system
model
TREF
Volume
TAVG. AT
::lzr Fz2:Ln
1
TAVG
system
model
1
*
Level
Flow
t
Pressure. Level
Pressurizer
dynamics
model
__
Turbine
protection
system
model
Turbine
;wr;
model
dynamics
model
Tripping signal
output torque
Generator wrrem
Generalor speed
Terminal vollage
Fig. 3 Structure of P W R Plant Model
b
144
Temperature
Flow
Tripping signal
I
Turbine tripping signal, control valve
quick closing signal
Generator speed
Generator current
Turbine system model
Reactor system model
Fig. 4 Structure of BWR Plant Model
3.1 Main Steam System and Turbine System Models for both PWR and
BWR Plan!
* The steam pressure in the main steam lines is calculated with
9
consideration to the mass, volume, and energy balance.
The bypass valves is modeled with consideration to their rapid
opening characteristics.
The turbine system is modeled in detail. Special attention is paid
to the valve position of each valve in order to simulate its
non-linear response including quick closing mechanism.
available for both frequency and voltage disturbances has been
developed. Fig. 6 shows the block diagram of the pump-motor model.
The accuracy of the model have been verified using the RETRAN
code developed by EPRI, which is one of the detailed computer codes
for transient analysis of a nuclear plant. Fig. 7 shows an example of
comparisons between transients simulated by the developed model and
the RETRAN code.
Neutron flux
High change rate of
neutron flux
3.2 Reactor System Model for PWR Plant
(1) Overview of model
The model calculates the neutron flux, the fuel temperature, the
coolant temperature, the coolant flow rate, the pressure and level in
the SG, and the pressure and level in the pressurizer.
The average neutron flux over the entire core region is calculated
by the point kinetics representation with six groups of delayed
neutrons
The average temperature over the entire fuel rods is obtained
from the first order lag.
The coolant temperature in the primary loop is calculated with
consideration to the delay due to the time needed for the coolant
to travel in the loop.
The secondary coolant in the SG is assumed to consist of two
phase saturated steam and saturated water. The SG steam
pressure is calculated with consideration to the mass, volume and
energy balance in both phases. The SG level is simulated
through the change in the saturated water volume and the steam
volume under the level.
* The pressure and level in the pressurizer is obtained in a similar
manner to the SG model.
* The model of the reactor protection system is constructed using
only those protective factors as shown in Fig. 5.
( 2 ) Simplified model for reactor coolant pump-motor
The reactor coolant flow rate is one of the key variables for the PWR
plant dynamics under the power system disturbances as already
described. In CRIEPI’s previous PWR plant model for short-term
power system analysis [l], the coolant flow rate model is not
sufficient since transients are simulated by a simple first-order-lag
model only for the system frequency disturbances.
Accordingly, a new model for reactor coolant pump-motor that is
-
I
Bus frequency
of house power
Level in steam
generator
4
1
-
Turbine tdp
signal
Turbine trip
Fig. 5 PWR Reactor Protection System Model
Pumo~motormeed
I
I I
l
r
Simplified pump
characteristicscurve
1
l
Coolant flow
I 1
Simplified coolant
system characterislics
I
I
1
Induction motor
~requenq
01 p w e r
supply
1
+
L
voltage 01 pawet
SUPPlY
Fig. 6 P W R Reactor Coolant Pump-Motor Model
145
Reactor mlant flow rate
....... Result from the developed
model
E
-Result
from RETRAN
low pressure turbines and high pressure turbine, and of the feed water
lines from the heaters to the reactor vessel. In the developed model,
the heater system is represented by one equivalent IOW pressure
heater, one equivalent high pressure. heater and one equivalent feed
water line. The block diagram of the model is shown in Fig. 9. The
validity of the model has been verified by a comparison with an
observed feed water temperature transient at a start-up testing before
commercial operation in an actual plant.
Low pressure
feedwater heater
LOW
0
-5
5
10
TIME (SEC)
-
Feedwater line
I -
in
15
Hi hpressure
fem%ater heater
Hioh
Feedwater
enthalpy
Rated enthalpy
Fig. 7 Developed Model Compared with RETRAN Code
3.3 Reactor System Model for BWR Plant
1.o
(I) Overview of model
The model mainly calculate the neutron flux (reactor power), the fuel
temperature, the generated steam flow rate and the reactor core
pressure. The neutron flux and the fuel rod temperature is calculated
in the same way as the PWR plant model.
The average void volume in the core is simulated by taking
account of the core pressure, the starting height of boiling, the
core outlet steam quality, the slip ratio of the two-phase flow and
the axial output dishbution.
The reactor core pressure is calculated separating from the steam
dome pressure.
* The core flow is calculated from the recirculation flow rate with
jet pump characteristics taken into account.
The model of the reactor protection system is constructed using
o d y those protective factors as shown in Fig. 8.
\
Fig. 9 Feed Water Enthalpy Model
4. SAMPLE SIMULATION RESULTS
The turbine-generator speed model shown in Fig. 10 was
temporarily included in the plant models. The inertia constant (M=2H)
was assumed to 10 sec.
A simple pattern of the generator power change shown in Fig. 11
was specified as a disturbance for demonstrating performance of the
PWR and BWR plant models in simulating plant transients under a
power system islanding condition.
The simulation result of the PWR plant model is shown in Fig. 12,
and that of the BWR model is shown in Fig. 13. Judging from our
knowledge which has been cultivated through rich experiences, the
simulated results are close to actual response of the plants.
P
Abnomaliy low level
01 reanor
(Opeation 01 ~ c ~ ~ b r a t relay
ion
or powerdoad unbalance relay)
Fig. 10 Turbine-generator Speed Model for Sample Simulation
house p w e r
SSIBc1IW
Control vave is
(Operalion 01 -1eration
relay
or power-bad unbalance relay)
rn"Irnl
rod
1 .o
l"Oeni0"
?
-a
n
?
Fig. 8 BWR Reactor Protection System Model
(2) Simplified model for feedwater enthalpy
In the CRIEPI's previous BWR plant model for short-term power
system dynamic simulation, a model for feedwater enthalpy is not
included since the drop in the enthalpy will not appear in a short-term
time period.
The feed water heater system mainly consists of some stages of
heater that heat the feed water mainly by extracted steam from the
0.8
0
0.6
'
1 .o
0.95
0.85
0
I
L
90
180
Time (sec)
Fig.11 Specified Pattern of Change
in Generator Power
146
:z:h
103Turbine-generator speed NG
c
to2
Turbine-generator speed NG
101 100 99 I
0
99
30
60
90
120
150
180
0
30
60
90
120
150
180
150
180
TIME [SEC]
TIME [SEC]
120
Main steam flow rale Ms
Main steam flow rale MS
80
60
0
30
€0
90
120
150
180
TIME [SEC1
.
.
8011
0
30
60
90
120
TIME [SEC]
120
l$----Neutron flux N R
Main leedwaler Row rale M m
100
80
I
0
90 1
60
30
90
120
150
0
180
30
60
90
120
150
180
150
180
150
180
150
180
TIME [SEC]
TIME [SEC]
73.0,
Main steam line pressure PSL
Vessel pressure Py
71.0
50
0
€0
30
90
120
150
180
70.0L
0
30
60
90
120
TIME [SEC]
TIME [SEC]
Cwlant now rate MC
Main leedwaler flow rate MFW
100
80
0
30
€0
90
120
150
180
0
30
60
TIME [SEC]
Average m l a n t temperature TAVG
298
90
120
TIME (SEC]
Main feedwater enmalpy H w
210.01
0
30
60
90
120
150
180
0
30
M)
90
120
TIME [SEC]
TIME [SEC]
Neutron nux N R
Fig. 13 BWR Plant Model Sample Simulation Result
5. CONCLUSION
I
80
0
30
60
90
120
TIME [SEC]
150
180
150
180
150
180
D-bank mnbol rod positionZROD
180
0
30
60
90
120
TIME [SEC]
Pressurizerpressure P ~ R Z
1531
0
30
60
90
120
TIME [SEC]
Fig.12 PWR Plant Model Sample Simulation Result
The power system long-term dynamic analysis is important in
studying measures for stable and reliable operation of the system as
well as the short-term stability analysis. It is especially significant for
the simulation and the analysis of the power plant dynamics during a
few minutes after a disturbance, since the plant responses including
various control actions and plant trip might greatly affect the dynamic
behavior in system variables such as frequency and voltage which
subsequently might cause additional plant responses. Simplified plant
models which are used in short-term stability analysis are insufficient
for power system long-term dynamics analysis.
CRIEPI and EPRI have performed the joint study to develop
nuclear and thermal plant models which are able to apply to long-term
dynamics analysis. CRIEPI has developed the models for PWR and
BWR types of nuclear power plants, while EPRI has developed
models for thermal plants. These plant models are being implemented
for EPRI's and CRIEPI's long-term stability programs respectively.
The developed plant models are more complex than conventional
simplified ones used for short-term stability study. These models are
useful in simulating the plant dynamics taking into account the
147
responses of plant control and protection systems. These plant models
are expected to make substantial contnbution in developing tools for
power system long-term dynamics analysis. However, additional effort
will undoubtedly be required to enhance their usefulness in the form
of collecting and arranging input data for the plant models in order to
validate these against specific plant responses to specific disturbance
situations.
6. ACKNOWLEDGEMENT
This joint study project has been performed for six years as one of
the joint projects under the agreement on technical exchange and
cooperation between CRIEPI and EPRI. The authors sincerely
appreciate concerned all persons in CRIEPI, EPRI and Ontario Hydro.
7. REFERENCES
[l] T. Ichikawa and T. Inoue, "Light Water Reactor Plant Modeling
for Power System Dynamic Simulation," IEEE Trans. on PS, Vol.
PS-3, May/June 1988.
[2] Y. Sekine, Y. Oura, T. Sawada, S. Muto, K. Uyeda, T. Ichikawa
and H. Taniguchi, "Development of A Precise Simulation P r o g m
for Dynamic Analysis of Bulk Power System under Faults," Proc.
8th PSCC, Aug. 1984
[3] P. K. Kar, A. Yan, P. Kundur, H. Taniguchi and P. Husch,
"Thermal Plant Models for Medium- to Long-term Power System
Stability Studies," Submitted to IEEE Winter Power Meeting
(1994).
[4] R. P. Schulz and A. E. Turner, "Long-term Power System
Dynamics - Phase 11," Final Report for EPRI Research Project
764-1, Report No. EL-367, Feb. 1977.
[5] M. A. Di Lascio, R. Moret and M. Poloujadoff, "Reduction of
Program Size for Long-term Power System Simulation with
Pressurized Water Reactor," IEEE Trans. on PAS, Vol. PAS-1-2,
No.3, March 1983.
[6] T. W. Kerlin and E. M. Katz, "Pressurized Water Reactor
Modeling for Long-term Power System Dynamic Simulation,"
Final Report for EPRI Research Project 764-4, Report No. EL3087, Vol. I and 2, May 1983.
8. BIOGRAPHY
Toshio Inoue was born in Tokyo, Japan on February 15, 1958. He
received M.S. degree in Electrical Engineering from Waseda
University in 1982. In 1982, he joined Central Research Institute of
Electric Power Industry (CRIEPI) as a Engineer. Between August
1988 and July 1989, he worked in Energy Systems Research Center
at the University of Texas at Arlington as a Visiting Assistant
Professor. Mr. Inoue is a Senior Research Engineer in Power System
Department at CRIEPI and a member of the IEEE.
Tatsumi Ichikawa was born in Tokyo, Japan on November 12,1945.
He received M.S. degree in Electrical Engineering from Waseda
University in 1970. In 1970, he joined Central Research Institute of
Electric Power Industry (CRIEPI) as a Engineer. Between September
1979 and September 1980, he worked in Energy Systems Research
Center at the University of Texas at Arlington as a Visiting Assistant
Professor. His major research interests are nuclear plant dynamic
simulations in power system analysis, and cooperative operations and
controls of nuclear plants with power system operations. Mr. Ichikawa
is a manager in Power System Department at CRIEPI and a member
of the IEEE.
Prabhashankar (Praba) Kundur received the M.A.Sc. and Ph.D.
degrees from the University of Toronto, Canada in 1965 and 1967
respectively. In 1969, he joined Ontario Hydro where he is currently
Manager of the Analytical Methods & Specialized Studies Department
in the Power System Planning Division. He also holds the position of
Adjunct Professor at the University of Toronto. Dr. Kundur was
elected a Fellow of the IEEE in 1985 and a member of several IEEE
working groups and task forces.
Peter Hirsch received his B.Sc., M.Sc. and Ph.D. Degrees in
Mathematics from the University of Wisconsin. From 1966 to 1992,
he was a manager for advanced systems at the IBM Scientic Centers.
He joined EPRI in 1992 and is the Manager of Power System
Engineering in Power System Planning and Operation Rogram,
Elecmcal System Division. He is responsible for formulating research
strategies for power system engineering and directing the research
contract work canying out these strategies. His current projects
include the system tools for electrical system transmission and
generation planning.
148
DISCUSSION
RICHARD P. SCHULZ, (American Electric Power Service
Corporation, Columbus, Ohio 4321 5): This is an excellent
paper about an excellent piece of useful work. It is a
necessary and reasonable development of modelling that
meets some very specialized but important needs. These
needs were identified at the time of the EPRl RP764-1 work
which was completed in 1977. That work was very lightly
funded; nine staff months were funded to make extensive
programming changes in the DIOtotVDe LOTDYS code, to
include three new models including the Boiling Water
Reactor model and to document the prototype program.
This model appears to be quite comprehensive and to meet
the objectives for long-term simulations for severe power
plant-electrical system transients.
From the fact that a point kinetics model is used for
presenting the nuclear core, with six groups of delayed
neutrons, it would appear that a fairly short time step is
required for adequate simulation; the estimate might be of
the order of 0.1 seconds. What is the maximum time step
that is allowable for use within this model? Are these
models intended to use the unified transienthid-term/longterm program method devised by EPRl under RP1208? [AI
If so, what provisions have been made for handling the
prompt dynamics when the basic time step is increased to
1 .O second?
The models clearly are not simple; this is reasonable to
meet the goals. Could the authors please give us
indications of the order of the models and of the number of
data entries that are required? Is there an appropriate EPRl
report which would have further details? It may be best to
use these detailed models in studies of relatively small
power system areas that are expected to undergo a
significant event rather than using this model in large scale
studies in the expectation of a large disturbance over the
wider region, based upon principles of computing
parsimony. Would the authors please comment on their
intended applications both within Japan and the United
States/EPRI area?
[AI Frowd, R.J., Giri, J.C., Podmore, R., "Transient
Stability and Long-Term Dynamics Unified", IEEE
Transactions, Vol. PAS-101, No. 10, October 1982,
pp. 3841-3850. Based on EPRl RP1208-7; Discussion
by R. P. Schulz.
Manuscripi received March 10, 1994
T. Inoue, T. ichikawa, P. Kundur and P. Hirsch:
We would like to thank Mr. Schulz for his interest in our
paper and for his valuable comments. The following are our
responses to the specific questions he has raised.
If an explicit numerical integration method such as
Runge-Kutta is used, the maximum time step is in the order
of 0.1 seconds. To increase the maximum step size, an
implicit method such as the trapezoidal rule has to be used.
The nuclear plant models, which were developed under
a joint effort [E], have been implemented in both CRIEPl's
and EPRl's long-term stability programs. The CRlEPl
program uses implicit numerical integration method with
variable time step. EPRl's Long Term Stability Program
(LTSP) was developed based on the existing Extended
TransienVMidterm Stability Program (ETMSP) [C] which has
provision for using either an explicit method or an implicit
method of numerical integration. Different step sizes are
used for solving different equations associated with the
nuclear plants and those associated with other dynamic
devices. Typically the step size for plant dynamics is 10
times the step size for other dynamic devices.
The order of the nuclear plant model for PWR is about 70,
and the number of data entries is about 200. As for the
model for BWR, the order is about 50 and the number of
data entries is about 150. Technical details of the nuclear
plant models are described in reference E.
Power systems are becoming larger and more complex
due to increased interconnections between electric utilities
and due to the need for operating closer to stability limits.
Severe faults that are not covered by normal design criteria
may cause large transients in the interconnected system. In
an extreme case, the system may split into islands. In
islanded systems, the frequency and voltage deviation
could be large which may lead to shutdown of nuclear
generating units by unit protective systems normally not
modeled in transient stability simulation. The nuclear plant
models are developed mainly to simulate this type of
situation and aid in the design and coordination of
protection and controls.
Modelling requirements for study of long-term power
system dynamics are well described in reference D.
[E] EPRl TR-101765, Research Project 3144-01, CRlEPl
T989102-SL, Final Report, "Long-Term Dynamic
Simulation : Nuclear and Thermal Power Plant Models
(Joint EPRliCRlEPl Study)," Prepared by Ontario Hydro
and Central Research Institute of Electric Power
Industry, December 1992 (Licensable Material).
[C] EPRl TR-103632, Vol.1, Research Project 3144-01,
"Addition of Nuclear and Thermal Power Plant Models
to Long Term Stability Program," Final Report,
Prepared by Ontario Hydro, October 1993.
[D] EPRl EL-6627, Research Project 2473-22, "Long-term
Dynamic Simulation: Modeling Requirements," Final
Report, Prepared by Ontario Hydro, December 1989.
Manuscript received April 15, 1994.