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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 6, DECEMBER 2009
Effect of Loop Configuration on Steam Drum Level
Control for a Multiple Drum Interconnected Loops
Pressure Tube Type Boiling Water Reactor
Avinash J. Gaikwad, P. K. Vijayan, Kannan Iyer, Sharad Bhartiya, Rajesh Kumar, H. G. Lele, A. K. Ghosh,
H. S. Kushwaha, and R. K. Sinha
Abstract—For AHWR (Advanced Heavy Water Reactor), a
pressure tube type Boiling Water Reactor (BWR) with parallel
inter-connected loops, the Steam Drum (SD) level control is closely
related to Main Heat Transport (MHT) coolant inventory and
sustained heat removal through natural circulation, hence overall
safety of the power plant. The MHT configuration with multiple
(four) interconnected loops influences the SD level control in a
manner which has not been previously addressed. The MHT
configuration has been chosen based on comprehensive overall
design requirements and certain Postulated Initiated Event (PIEs)
for Loss of Coolant Accident (LOCA), which postulates a double
ended break in the four partitioned Emergency Core Cooling
System (ECCS) header. A conventional individual three-element SD level controller can not account for the highly coupled
and interacting behaviors, of the four SD levels. An innovative
three-element SD level control scheme is proposed to overcome
this situation. The response obtained for a variety of unsymmetrical disturbances shows that the SD levels do not diverge and
quickly settle to the various new set points assigned. The proposed
scheme also leads to enhanced safety margins for most of the
PIEs considered with a little influence on the 100% full power
steady-state design conditions.
Index Terms—BWR, innovative three-element steam drum level
control, modeling simulation control of nuclear power plants, plant
transient and safety analysis, RELAP5, thermal hydraulics.
I. INTRODUCTION
T
HE research papers sited in the literature on this topic can
be mainly divided in three categories. The First Category
addresses the control system intricacies in detail [1]–[12]. The
Second type thrives on the details of the process modeling and
the process dynamics [13]–[20]. The third category makes efforts to address both the problems (process dynamic & control)
Manuscript received June 24, 2009; revised August 06, 2009 and September
14, 2009. Current version published December 09, 2009.
A. J. Gaikwad, R. Kumar, H. G. Lele, and A. K. Ghosh are with the
Reactor Safety Division, BARC, Trombay, Mumbai 400094, India (e-mail:
[email protected]).
P. K. Vijayan is with the Reactor Engineering Division, BARC, Trombay,
Mumbai 400094, India
K. Iyer and S. Bhartiya are with the Mechanical Engineering Department,
IIT, Powai, Mumbai 400094, India
H. S. Kushwaha is with the Health Safety and Environment Group, BARC,
Trombay, Mumbai 400094, India
R. K. Sinha is with the Reactor Design and Development Group, BARC,
Trombay, Mumbai 400094, India
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TNS.2009.2033682
in a balanced approach, which is difficult to meet [21]–[30]. In
this paper an attempt is made to make sufficiently detailed simulation of the process (not only single equipment but the whole
process plant) as well as the control system details to the required extent. The process dynamics simulation is done using
internationally renowned best estimate accident/safety analysis
code RELAP5/MOD3.2. This code has provisions for detailed
simulation of the control system by using various user-defined
standard mathematical equations through in-built control variables of the code, including the logical variables and trips. Many
of the papers sited in the literature also focus on the mitigation
of the swell/shrinkage problems due to presence of two-phase
mixtures in the Steam Drum (SD) either using elaborate mathematical models or by using fuzzy controllers [31]–[34]. The
other types of papers emphasize on using advanced process control techniques [35], [36] such as Predictive control [37]–[44],
Multiple Input Multiple Output (MIMO) [45] and Neural Networks [46]. Some of the literature also focuses on the accurate
prediction of the level in the SD and the process dynamics.
The current work cannot make use of all the literature support available right away as the problem at hand is not cited
or reported in the literature. Though the interacting system behavior is well known but the techniques applied for each system
are tied down to the peculiarities/specialties of that particular
system or problem at hand and the generalized methodologies
are difficult to implement, realize and may not work for all the
problems at hand. Based on the process dynamics knowledge a
new three-element SD level control problem is devised for the
given problem without disturbing the major design philosophies
and constrains. Though the solution sounds more intrusive at
the go but the detailed analysis shows that the proposed solution, not only solves the operation and control problem at hand
but also, solves many of the safety related issues and also improves the safety margins and availability of the said nuclear
power plant. All the details from the inception of the problem to
the design modification are discussed in the paper. The similar
multiple loop boiling water reactor configuration RBMK [47],
[48], Fugen ATR [49], [50], are also discussed in the next section.
To study the thermal hydraulic effects and control difficulties
of multiple connected Parallel Loops, in Boiling Channel type
Advanced Heavy Water Reactor (AHWR) has been chosen.
Such reactors have several boiling channels connected together
in multiple loops. These loops are also inter-connected in the
Main Heat Transport (MHT) system with respect to design
0018-9499/$26.00 © 2009 IEEE
GAIKWAD et al.: EFFECT OF LOOP CONFIGURATION ON STEAM DRUM LEVEL CONTROL
and safety requirements, which cause undesired effects during
normal operation (control) and also for accident situations. In
this paper the uncontrollable multiple Steam Drum (SD) level
situation created by the boiling channels and loop interaction is
analysed and the proposed solutions are described in detail.
For a natural circulation reactor low level affects the recirculation of water to the reactor core with more carry under leading
to low driving force, it also affects the core inlet subcooling control, which is required for stable natural circulation. It is also
closely related to the MHT coolant inventory for safe removal of
decay heat under normal as well as abnormal conditions. High
level reduces the surface area (required for velocity reduction
and separation) available due to horizontal cylindrical geometry
of the SD. This can lead to water and dissolved solids entering
the steam distribution system with high carryover, which can
adversely affect the turbine and axillaries.
The interface level is subject to many disturbances, change
in steam flows, change in reactor power, steam pressure etc. As
steam pressure changes due to demand, there is transient change
in level due to the effect of pressure on entrained steam bubbles below the steam interface level. As pressure drops, a rise
in level, called swell, occurs because the trapped bubbles enlarge. As pressure rises, a drop in level occurs. This is called
shrinkage. To mitigate these effects a standard three-element SD
level controller has been implemented for all the four SDs. The
Three-Element Drum Level Control uses three variables, drum
level, steam flow rate and feed water flow rate to manipulate
the feed water control valve. Before going into the details of
problem definition and its solution for multiple loops, boiling
channel type (Boiling Water Reactor) BWR, a brief introduction to this reactor is included here.
II. MAIN HEAT TRANSPORT (MHT) SYSTEM OF AHWR
AHWR which is a pressure tube type of BWR is currently
being designed uses boiling light water as the coolant in the
high-pressure (70 bar) MHT system and heavy water as the
moderator in a low-pressure system. The coolant recirculation
in the primary system is achieved by two-phase natural circulation, which depends on the density difference between the hot
and cold legs of the primary loop. This mode of core cooling is
adopted not only during normal operation but also during transients and accidental conditions.
The MHT system consists of a Common Reactor Inlet Header
(CRIH) from which 452 inlet feeders branch out to an equal
number of fuel channels in the reactor core. The outlets from
the fuel channels are connected to tail pipes, 113 of the 452
tail pipes are connected to each of the four SD. From each SD,
four down-comer pipes are connected to the CRIH. The Fig. 1,
illustrates the schematic of the MHT system.
The level of water in the steam drum at nominal operating
conditions is 1.54 m. The steam-water separation in AHWR
steam drum is achieved naturally by gravity without the use of
mechanical separators, by reduction of 2-phase flow velocity in
the SD. At the normal operating condition, about 405 kg/s of
steam is separated in the 4 SDs, the it flows into the turbine and
an equal mass rate of feed water enters the steam drum at 130 C
through the feed water system. The primary loop circulation rate
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Fig. 1. Schematic of the MHT system of AHWR a channel type boiling water
reactor (BWR).
maintained by the density difference is approximately 2306 kg/s
at nominal operating conditions. The average core exit quality
is about 17.6% for the rated reactor operating conditions. The
coolant channel consists of a pressure tube and end fittings at
top and bottom ends. The top end fitting has a provision for
connection to outlet tail pipe. The fission energy is produced
in the vertical core consisting of 452 coolant channels. The fuel
bundle, housed in the pressure tube, is having a cluster of 54 fuel
rods and one central dysprosium rod through which Emergency
Core Cooling System (ECCS) water is injected.
The tail pipes carry steam and water mixture from the individual coolant channels to the four SDs. In all, 113 tail pipes
enter each SD from its lower end sides so as to ensure that the tail
pipe openings in the steam drum remain covered by the water
level even in the case of a sudden void collapse in the MHT
system and thus the continuity of the coolant thermo-siphoning
route and flow through the core is maintained. The Steam Drum
(SD) is a cylindrical vessel (3.75 m ID, 11 m length) closed at
both ends by hemispherical heads. Longitudinal partition plates
provided inside each steam drum prevents the mixing of the incoming steam with the subcooled feed water. The height of the
partition plates is such that it remains submerged with water
at zero power hot shut down condition. The feed water enters
the steam drum through a sparger, which runs along the length
of the steam drum and located in the space between the partition plates. Steam is taken out from each steam drum through a
single steam outlet nozzle located on the top of the steam drum.
MHT water flows from each steam drum to the CRIH through
down-comers. Four down-comers are connected to the bottom
of the steam drum shell in between the partition plates.
Common Reactor Inlet Header (CRIH) is the largest pipe of
600 mm NB Sch. 120, in the MHT system. It is of ring shape
with the ring diameter being 17.5 m. To facilitate core submergence even in case of a postulated rupture of the header,
the header is installed 2.5 m above the active core. The header
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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 6, DECEMBER 2009
Fig. 2. AHWR MHT RELAP5 Nodalization.
is connected to all the 16 down-comers through forged nozzles. Water from the down-comer enters the CRIH from the top
through the 16 nozzles. Water exits from the header through
452 nozzles. These nozzles enable the connection of feeders to
the header. Feeders supply cooling water to the coolant channel
from the header and are made from 100mm NB pipes.
III. PROCESS DYNAMICS MODELING AND SIMULATION
RELAP5/MOD3.2 code has been used worldwide for analyzing thermal hydraulic behavior of nuclear reactor systems. It
has been reported in recent literature that RELAP5/MOD3.2 is
capable of simulating natural circulation phenomena [51]–[54].
The modeling philosophies were based on Dynna540 and
Dyna220 codes which were developed in house [55]–[58].
RELAP5 has been extensively used to analyze accident scenarios and operational transients for research reactors, power
reactors like PHWR, PWRs and BWRs. It also has provision for
user defined variable and mathematical functions to simulate
various control systems, such as level, pressure and reactor
power.
The RELAP5/MOD3.2 unsteady state conservation equation
set gives a two-fluid simulation using non-equilibrium, non-
homogeneous, six-equation representation. Constitutive models
represent inter-phase drag, the various flow regimes in vertical
and horizontal flow, wall friction and inter-phase mass transfer.
The code has point kinetics model to simulate neutronics. The
field equations are coupled to the point kinetics model thus permitting simulation of feedback between the thermal hydraulics
and neutronics.
IV. SENSITIVITY STUDIES
Fig. 2 shows the nodalization used for the dynamic simulation model of the MHT. The AHWR nodalization was developed initially with single loop with very few volumes. Later on
more number of loops were added and the number of volumes
in the SD region and the reactor core heated region were also
increased. Each loop is simulated using 112 numbers lumped
average channel and a single hot channel. The CRIH was initially modeled as a single volume. The current Nodalization has
been selected after sensitivity studies with change in number
of volumes in the most important components. To observe the
inter-loop inventory transfer at the CRIH, it was divided into
four interconnected volumes with junction area based on CRIH
dimensions. The single volume CRIH is not justified based on it
GAIKWAD et al.: EFFECT OF LOOP CONFIGURATION ON STEAM DRUM LEVEL CONTROL
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Fig. 3. AHWR MHT pressure controller.
large size, such a big volume with several inlets (16) and many
outlets (452) cannot have a single pressure representing it correctly. The single volume CRIH shows a relatively more stable
response as compared to the four volumes Nodalization. The
proposed control schemes must perform for realistic Nodalization (selected one).
V. CONTROL SYSTEM MODELS
A. Steam Drum (SD) Pressure Control
Steam line volume no. 359 pressure is taken as the controlled
pressure for all the four drums Fig. 3, using a Proportional Integral action. A set point of 67bar is assigned to this controller for
a desired SD pressure of 70bar. The turbine governor, by-pass
and relief valves are actuated to control the steam drum pressure
within the operating and safety band limit.
Valve junction connected to Time Dependent Volume (TDV)
116 representing condenser represents bypass valve, while governor valve is modeled using junction 671 connected to TDV
112.
B. Steam Drum Level Control
To monitor and maintain the water level in SDs, three-element level controllers are designed and implemented. Design
basis for level control system requirement comprises of MHT
system behavior during various transients, interaction with pressure controller, core in-let subcooling control and various safety
related considerations. Major salient features of level controller
are variable set level program and three-element control to minimize un-due loading of the SD level controller. Variable level
program has the advantage of accommodating swell/shrinkage
of the MHT inventory within the system volume. Three-element
control program is based on feed forward control action, which
change the feed flow taking steam flow signal (anticipatory action) without waiting for actual to level to change. Fig. 4 shows
the conventional design of the three-element SD level controller.
The steady state (100% full power) level is already fixed on
the basis carry over consideration at 1.5 m (swell level) to have
optimum separation to avoid moisture carryover to the turbine.
To avoid the disruption of recirculation flow as the drum level
approaches the baffle height (450 mm) on the low side, a minimum value of level has been selected to be 500 mm at zero
power. The size of the SD is very big and any change from the
steady state swell level which occurs almost at the mid point
Fig. 4. Conventional three-elememt SD level controller.
of the horizontal SD will lead to reduction in steam water separation interface area. This will affect the carry-over and carry
under along with the steam water separation.
The three element drum level control program consisting of
standard proportional and reset controls with drum level deviation from a desired set level and the difference between the
steam and feed water flow rates have been adopted as an anticipatory component.
This level control scheme is based on the measured values of
three process parameters viz. drum water level, feed water flow
and steam flow. The error signal comprises level and flow error.
The level error is based on the difference between the set level
and the actual drum level, where as the flow error is based on the
feed water and the steam flow rate difference. The error signal
is fed to a proportional integral controller unit. The controller
out put modulates the feed water control valves.
C. Steam Drum Level Control Program
Constant MHT inventory was taken as basis for the variable SD level control program. This program was generated
using appropriate boundary condition using a detailed RELAP5/
MOD3.2 process dynamics simulation model of the BWR. This
program follows the inherent natural response of the reactor following a change in reactor power over the full range (Fig. 5) and
it will not put any undue load of the feed controller. This program may be further simplified for simplicity of implementation. The block diagram of the three element controller is shown
in Fig. 4.
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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 6, DECEMBER 2009
Fig. 5. AHWR SD level program.
Fig. 6. CRIH Schematic.
VI. PROBLEM DEFINATION
The individual Steam Drum (SD) level control becomes difficult due to the CRIH where all the downcommers from each
SD are connected to the CRIH at inlet side. The out flow from
the CRIH redistributes and goes to all the SDs through the reactor core after passing through inlet feeders, channels and the
tail pipes.
A. SD Level Control Using Only One Common Average
Controller
Initially to control the level in all the four SDs, only a single
common three-element controller was used to make the analysis
simple. The average of the 4 SD levels and steam minus feed
flow error signals were used for this single average level controller. Same output from this single average controller is fed
to all the four SD feed control valves. For this control scheme,
the levels in each SD can be maintained at the 100% full power
set point level value, with no perturbation or without any disturbance. The reason for this stable response is the thermalhydraulics symmetry in the CRIH and MHT system, which is not
hampered in this case. The steam flow from each steam drum
and the feed flow into each steam drum are maintained at the
same value in this case by the SD pressure and level controller.
The disturbance in this case is very small i.e., due to the approximate initial mass, pressure and temperature conditions in
the various control volumes of the simulation (used for starting
the calculation), rounding off and truncation errors in the calculations. The controlled SD levels do not oscillate or diverge due
to these small sources of error.
B. CRIH Nodalization
The CRIH receives the incoming flow from all the 16 downcomers from the 4 SDs. The out flow from the CRIH caters to all
the 452 inlet feeders (113 for each loop X 4). The CRIH (Fig. 6)
is not physically partitioned, but it is modeled using four hydraulic volumes one each for one loop (one quarter core, one
SD, 113 in-let feeders, channels and tail pipes). These four control volumes are connected in a ring shape using junctions corresponding to the CRIH cross-sectional area. This Nodalization
is necessary to visualize and extract the loop cross (inter-loop)
Fig. 7. Individual SD level controller without perturbation low gain.
flows information taking place in the CRIH which is the root
cause of the level control unsatisfactory performance.
C. Level Control Using Individual Controllers for Each SD
For each of the four SDs an individual conventional three-element level controller was considered. In this case it was observed that even steady state operation without any disturbance
was marred by diverging levels and oscillations.
It indicates that the four SD levels are not independent and
are strongly coupled with each other due to the CRIH. Figs. 7, 8
& 9 show the response for an individual SD conventional threeelement level controller for steady state behavior without any
disturbance. Similar response is also observed with for all the
gain values from low, mid to high.
The main reason for this phenomenon is obvious from the
MHT configuration. The primary coolant to a particular drum
can rise into it, only through these 113 channels, which are connected to that particular SD. The incoming flow to the CRIH
from each SD through the down-comers is based on the individual SD feed and/plus recirculation flow for the loop. The outflow from the CRIH is based on the prevailing thermal hydraulic
(s.a. differential pressure) conditions as it loses the memory of
GAIKWAD et al.: EFFECT OF LOOP CONFIGURATION ON STEAM DRUM LEVEL CONTROL
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D. Studies of Other Reactors of Similar Kind RBMK, ATR
Fugen
Fig. 8. Cross flow in the four volumes of the CRIH.
Fig. 9. CRIH In-Coming & Out-Going Flows for a Loop.
all the incoming flows once inside the CRIH. As a result the out
flow from CRIH may not match the corresponding incoming
flows to the CRIH for the given loop exactly. Mixing and redistribution of the incoming (down-comer) flows takes place into
the CRIH leading to diverging level and a run away uncontrollable situation.
As a result different amount of liquid plus vapor (riser) flow
rises into the concerned/corresponding steam drum based on the
thermal hydraulic conditions. For this phenomenon to take place
only a small unsymmetrical pressure, flow distribution in the
CRIH or unequal incoming/outgoing down-comer flows or unequal feed flows is required, which is created by the SD level
controller action.
Such a situation is routinely created as the SD level controller
responds to very small numerical perturbations also. The diverging oscillating trend is triggered by a small source of error
and its cascading effect due to loss of control. These conditions
prevail and aggravate the situation due to very small pressure
drops (by design) in the down-comers and the MHT loop as it
is designed for a natural circulation system without any pump,
as the flow changes are larger for smaller changes in pressure
drops.
RBMK and Fugen ATR are the BWRs with similar configurations. F. D’Auria, etal, have studied the Thermal-hydraulic
performance of primary system of RBMK in case of accidents
[49], with Ignalina-2 and Smolensk-3 nuclear power plants. The
document includes description of key features of the primary
system for the two NPP. This reactor also has several boiling
channels in a typical multiple loop four steam drum configuration. Same reactor is also discussed in paper by A. Kaliatka, et
al. [48], which describes “Approach to accident management in
RBMK-1500 for Ignalina NPP Figs. 10, 11. The total number
of fuel channels in the RBMK-1500 reactor is 1661. All the
fuel channels are grouped to two loops of the reactor cooling
system. Both RCS loops are interconnected via the steam lines
and do not have a connection on the water part. This is different
from vessel-type reactors where all fuel elements are placed in
a single vessel.
As seen in the sketches, the two main loops are independent
as they are not connected at the group distribution header at
the reactor core inlet. The two separator drums on one side
of the reactor are connected together to the pump and group
distribution header. This inter connection may lead to cross
flows (inter-loop transfer). The forced circulation feature will
reduce the associated hazards of inter-loop redistribution due
to higher pressure loss coefficients for the loops. The water
and liquid spaces of the two separator drums are connected to
each other, this may reduce redistribution and mitigate steam
separator drum level imbalance. No more information is available in open literature. For the current problem (AHWR) at the
hand interconnecting the steam drums does not help, as there
is no forced circulation and the inter loop flows are of larger
in magnitude. To over come these large inter loop transfers, all
the four steam drum’s steam and water space needs to be connected to each of the remaining steam drum(series and cross)
with very big diameter pipes. These studies are not included
in this paper.
Hiroyasu Mochizuki, et al. [49] work deals with another
similar kind of reactor Fig. 12. The primary loop of the ATR
prototype reactor “Fugen” (165 MWe) consists of two independent loops, and each loop consists of a steam drum,
four down-comers, two recirculation pumps, a series of check
valves, a lower header, pressure tubes of 112, inlet and outlet
pipes and other components as shown in Fig. 12. As the loops
are independent no problems are anticipated for this primary
loop configuration. Sigeo Mita, et al. [52], work also deals
with similar reactor ATR. It is a heavy-water-moderated,
boiling-light-water-cooled reactor, called Advanced Thermal
Reactor (ATR). Its prototype, Fugen, has been operating satisfactorily since its operation in March 1979. A scaled-up
version of Fugen, the Demonstration ATR plant (DATR 1930
MWth/606 MWe) is being designed for construction. The primary cooling system is composed of two identical loops. Here
also the loops are independent no problems are anticipated for
this primary loop configuration.
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Fig. 10. RBMK Main Circulation Circuit flow diagram: (1) separator drum(SD), (2) down-comers, (3) suction header (SH), (4)suction piping of the MCP, (5)
MCP, (6) pressure piping of the MCP, (7) bypass between headers, (8) pressure header (PH), (9) group distribution header (GDH) with flow limiter, check valve
and mixer, (10) water bottom piping, (11) fuel channel before the core, (12) fuel channel within the core, (13) fuel channel above the core, (14) steam water pipes,
(15) steam pipelines.
VII. NEED FOR INDIVIDUAL STEAM DRUM LEVEL
CONTROLLER AND ITS RESPONSE FOR AHWR
The heat generation in the reactor core may not be uniform
due to different flux distribution in each core quadrant. The loop
thermal hydraulic conditions decide the channel exit quality and
void. These changes result in density difference (in the heated
riser core path), and change in channel flows, which may cause
deviation in levels in all the SDs. So the feed flow requirement
to the different SDs may be different at times. A single average
level controller can not cater to such diverse requirements. To
make the four loops very similar the 113 channels selected for
each of the SD are almost identical by design for all the loops.
In spite of such a symmetrical arrangement, the control rod
movement, moderator poison distribution, the coolant void and
flow distribution may cause unsymmetrical power distribution
% of quadrant power) among the four core
(
quadrants even after corrective actions through the flux tilt controller. If the thermal hydraulic conditions are different then the
reactivity feedbacks are also different resulting in more asymmetry. The layout constrains and fabrication tolerances also can
cause certain asymmetry among the loops.
This makes the use of 4 individual, three-element SD level
controllers for 4 SDs in the feed water control system almost
mandatory. For the current design when this kind of control
scheme is used even without any disturbance, it is seen from
the result that the levels in the different SDs are diverging instead of remaining within the desired limits, due to the redistribution of the flow in the CRIH. The trigger may be due to a very
small flow disturbance in the MHT hydraulic circuit causing a
small difference among the 4 feed flows, leading to asymmetry,
after the controller responds and starts correction. A small deviation in flows or/and levels calls for correction by individual
SD level controllers. All the 4 SD levels are strongly coupled
to each other due to the CRIH; this fact is not conveyed to the
controller which assumes that all the levels are independent. As
a result the corrective action from the controller only aggravates
the situation taking it to diverging levels following a very small
trigger. The results are shown in the following Figs. 7, 8 & 9.
The controller can not apprehend the flow redistribution in the
CRIH.
This response points towards substantial interdependence
among the 4 SD levels with non-ignorable retaliatory effect on
each SD level from all the other SD levels. This calls for a Multi
Input Multi Output (MIMO) approach instead of 4 Single Input
Single Output (SISO) approach. The later approach accounts for
the interdependence and cross coupling among the SD levels.
The design of these controllers is heavily depends on the simulation models embedded into the controller. The design of such
controllers can be done with identified (simplified statistical
data based) models which are not well accepted in the nuclear
industry though the data base for the statistical models are generated using detailed physics based first principle models. The
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Fig. 11. Schematic view of confinement and reactor cooling system, 1-fuel channel, 2-main circulation pumps (MCP), 3-MCP suction header, 4-MCP pressure header, 5-group distribution header, 6-ECCS header, 7-hot condensate chamber, 8-pumps and heat exchangers, 9-section of air release pipes, 10-steam pipe,
11-steam gas mixture from the reactor cavity, 12-condensing pool, 13-steam distribution header, 14-sprays, 15-water seals, 16-vacuum breakers, 17-sprays in air
venting channel, 18-air venting channel, 19-gas delay chamber tank, 20-gas delay chamber, 21-reinforced leak-tight compartments, 22-Lower water piping compartments, 23-steam discharge valves, 24-top steam reception chamber, 25-tip-up hatches, 26-knock-down hatches, 27-main steam valves, 28-drum separators,
29-steam distribution corridors, 30-reactor.
current problem becomes multi-variable control with strong
and unavoidable interaction/coupling/retaliatory effect (among
the four SD levels). Another aspect of interactions of SD level
controller with the core inlet sub-cooling control and the SD
pressure controller needs to be addressed simultaneously. The
effect of the SD pressure controller cannot be avoided due to
the restriction on the steam line layout all the lines (for 4 SDs)
cannot be exactly same. For developing multi-variable controller this simulation model will be used and the perturbation
can be given for all the independent parameters, which affect
the concerned variable over the full range even from 0 to 200%
for developing the statistical model.
VIII. CONTROL SYSTEM STUDIES
A. Open Loop Response
If a system is open loop unstable, it can be made stable by
designing an appropriate feed back controller to stabilize it. To
rule out open loop instability, transient run was taken for a step
change in the individual feed flows to the SDs (manipulated
variable). The response for the change in feed flow along with
the forcing function is shown in Fig. 13, it shows that the system
is not open loop unstable. A step change of 50% in SD4 feed
water flow was given instantaneously to generate this response
at 100% reactor power while for the other three SDs the feed
% to maintain the mass
flow was decreased by
balance and to avoid the integrating ramp response.
It is found that the four SD levels are not independent of each
other due to the CRIH which connects all the four loops. The
open loop system response is inverse but not unstable, as the
response to a perturbation in the feed flow only leads to a new
steady state with lower SD level for the SD with higher feed
flow. Closing the system with four individual SD level controllers had led to an unstable behavior as the interactions among
the four SD levels are not implemented either in the process design and/or in the controller. The SD4 level shows an inverse
response, i.e., instead of showing an increase the level reduces
and then it stabilizes to a lower value as the open loop system is
stable and it achieves a new steady state. The other three levels
the SD levels go up instead of reducing as the feed flow is reduced, but also achieve a new steady value.
It can be inferred that the SD level controller for this MHT
system with multiple connected loop boiler channel type of reactor needs to be implemented with some process design modification and appropriate changes in the controller logics. All
these modification are based on the process dynamics response.
The options presently being considered are
1) Partial in-core feed through four portioned ECCS header
with modified three-element level controller.
2) Design of truly a multivariable steam drum level controller,
which accounts for all the interaction, it is difficult to implement, as it has to be based on models.
3) Inter-connecting the four SDs, it requires very big pipes
to connect each SD to all other SDs in the liquid and vapor
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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 6, DECEMBER 2009
Fig. 12. Primary loop of ATR Fugen.
space; it is ruled out based on feasibility and safety requirements.
In this paper only the first option which is more promising as it
solves many of the other operation and safety related issues and
also increases safety margins for almost all the LOCAs, is discussed in details. The feed water temperature is also controlled
based on the reactor power, from the natural circulation stability
requirement. This system also has been included in the simulation. The SD level controller also influences the core in-let subcooling. The core in-let subcooling is decided by the loops recirculation flow, feed water flow (decided by SD level controller)
and the feed temperature. These core inlet subcooling issues are
not discussed here to avoid deviation from the SD level control
problem.
B. Proposed Solution: Modified Three-Element Level
Controller With In-Core Partial Feed Injection Scheme
The system boils down to an open loop stable system and a
closed loop unstable/uncontrollable system, the reason being
flow redistribution at the CRIH. This problem calls for a minor
design modification to make the conventional three-element
level controller to work effectively with knowledge of the
redistribution and its mitigation. Sending partial feed in such a
way that it does not get redistributed/(diverted to other drums
through CRIH) can solve the problem. The partial feed is targeted to the concerned SD according to its level error without
going through the CRIH. Taking the benefit of the four-partitioned ECCS header, where each partition connects to 113
channels for a loop, a small portion of feed flow is proposed
to be diverted through this path to make individual SD level
controller work effectively.
It is also anticipated that in-core injection (partial feed) will
help in improving safety margins and other operational issues,
like reduction in the Peak Clad Temperature (PCT) for all the
Loss of Coolant Accident (LOCAs). Initial startup flow can be
provided by the feed pumps as the startup natural circulation
flow may take some time to build and some of the problems related to on-line refueling and stagnation channel break can also
be partly addressed. This scheme will also avoid total voiding of
the ECCS header and flow path; it will keep the ECCS header
filled up with water. Present work deals with issue related to
the individual SD level controller, the safety issues are being
analyzed separately. Some of the other aspects of in-core partial feed related to phenomena like mixing of steam and water
during normal and abnormal condition are being further investigated. This in-core partial feed arrangement may need reassessment of the core inlet subcooling and the natural circulation stability. One of the issues also point out to the segregation of the
safety grade ECCS system and the feed water system, which is
not of the same grade. All these issues will be addressed before
the scheme is accepted and implemented.
The ECCS for this reactor consists of 4 accumulators, 4 partitioned ECCS Header, and 452 small pipes connect the ECCS
header to the perforated water rod at the center of the fuel assembly with 1.5 mm peripheral holes at 13 different elevations
for 3.5 m long vertical fuel assembly. This perforated water rod
runs through the full core length at fuel assembly center; it receives emergency coolant at the top of the fuel assembly and injects it through various holes following breakage of the rupture
disc which is a passive device. Downstream of the rupture disk,
ECCS header and the connecting pipes are always riding on the
MHT system; if no in-core feed is added then the ECCS header
is fully voided. The ECCS header is the part of the MHT system;
during normal operation it sees the same pressure and temperature as that of the MHT system. There is no physical separation
of the ECCS header from the MHT system the rupture disks only
isolate the accumulators from the four partitioned ECCS header.
As the MHT system pressure fall below 50 bar the rupture disc
GAIKWAD et al.: EFFECT OF LOOP CONFIGURATION ON STEAM DRUM LEVEL CONTROL
3721
Fig. 13. Levels of steam drum for 50% Step change (increase) in feed (cntrlvar 4) at 100% FP.
Fig. 14. Conceptual Diagram for the modified three-element level controller.
breaks and the ECCS injection begins during a LOCA and the
emergency coolant from the accumulators enters the four partitioned ECCS header, which is almost fully voided if partial
in-core feed is not injected here.
Based on PIE which postulated double ended break of the
ECCS header, it has been partitioned into four compartments to
avoid non-injection of coolant into the affected core quadrant.
For a four-partitioned ECCS header only one partition break
is postulated, and other three partitions of the ECCS header
are intact, also the three corresponding accumulators can inject the coolant into three quarters of the core, which will also
reach the affected core quarter through the CRIH (which is not
partitioned). This can not happen if the ECCS header is not
partitioned.
Fig. 14 shows the proposed modified three-element SD level
controller. If a partial feed is injected directly through this path
(from the ECCS header down stream) then it can be routed/targeted to a particular core quadrant and the corresponding SD.
Four additional feed lines along with four additional Level Control Valves (LCVs) are drawn from the feed header up to the four
partitions of the ECCS header. These lines and LCVs represent
the in-core partial feed proposed for avoiding the level control
problem. Each of the new feed lines and LCVs, can target a particular core quadrant/SD corresponding to it without disturbing
the accumulators as the rupture disc (which is upstream of ECCS
header) is intact during a normal operation of the reactor.
With this proposal the total number of feed control valves
increases from four to eight. The modified three-element level
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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 6, DECEMBER 2009
controller sends different errors to the two sets of four LCVs.
Four main feed LCVs are connected to the baffle region of each
of the SD, these are actuated based on the mass flow error between total steam and feed flows for that particular SD or loop
or the core quadrant, including the partial in-core feed. The remaining four feed valves feed into the four partitioned ECCS
header based on the corresponding SD level error.
The direct in-core feed LCVs are not allowed to close fully
under any circumstance, to keep this flow path active and to
avoid stagnation and building up of full vapor condition, to avoid
thermal shock. In this study the partial in-core feed LCVs are
programmed to close to a minimum of 1% valve opening only on
the other hand they can open fully to bring up the SD level. The
capacity for the in-core feed LCVs has to be decided based on
the amount of controllability desired on both up and down side.
The in-core feed valves are going to close if the SD level goes up
for any SD. The extent of control in this direction will depend
on maximum allowed closing of this LCV (1%) for maximum
possible control to bring down the SD level.
To test these schemes, three cases were analysed with partial
in-core feed (10%, 20% & 30% feed capacity) coming through
the 4-partitioned ECCS header path at the 100% full power
steady state. In the case of 10% partial in-core feed, only 90%
feed enters the corresponding SD baffle region through the
normal feed route at 100% full power steady state; same logic
is extended to the remaining cases.
Total 8 Level Control Valves (LCVs) are used in this scheme,
4 LCVs cater to the normal feed through the SD baffle region
for mass balance. Another 4 LCVs cater to the partial in-core
feed through the four partitioned ECCS header to manage the
level error. All these valves have the same capacity.
Fig. 15. Step Change Response for new design 10% in-core partial feed.
IX. RESULTS & DISCUSSION
To test the performance through simulation model transient
analysis a step change in the various SD level set points were
considered with 10%, 20% and 30% in-core feed separately.
Further studies are also being carried out to study reactor core
quadrant power mismatches and also to accident conditions, in
this paper only the first option is described. The conventional
three-element level controller was modified to account for 8
control valves simulating the above proposed modified SD level
control scheme. From the steady state runs with approximate
initial conditions, it was observed that 100% full power steady
state could be achieved without any diverging levels, which was
not possible for the unmodified conventional three-element individual SD level controller. To test the response for perturbation
and disturbances a different set point for all the four SD levels
were considered at 100% full power with (10%, 20% & 30%
in-core feed).
A. Step Change in Set Levels With 10%, 20% & 30% In-Core
Partial Feed
Disturbance was introduced by simultaneous (Fig. 15) step
increase in SD5 set level to 1.64 m, SD6 set level to 1.74 m,
SD7 level set point was driven down in a step manner to 1.44 m,
where as SD4 level set point was not disturbed it kept at 1.54 m.
Fig. 16. LCV opening for Step Change Response to SD set levels for new design 10% partial in-core feed.
Following the simultaneous changes in the level set points
the various SD level errors are induced for the three individual
level controllers. For one drum (SD4) no set point change was
considered. Due to these disturbances the SD4 level also undergoes a change, as all the four levels are not independent of
each other they are very much coupled, due to CRIH. It is observed (Figs. 15, 16) that the calculated/controlled water level
in the SD4, SD5, and SD6 settles down to the new value corresponding to new set points in about 1500 seconds after a small
overshoot by virtue of the modified three-element individual SD
level controller. The old conventional unmodified three-element
SD level controller cannot sustain any of such disturbances.
As SD7 set point was brought down from 1.54 m to 1.44 m,
it is taking longer to reach the set point even at 2200 seconds
it comes to 1.483 m. As stated earlier the partial in-core feed
through partitioned ECCS header cater to the level error, in this
case it closes the in-core feed LCV to the maximum extent possible 1% valve opening (Fig. 16) to bring down the SD7 level.
This minimum opening constrain in the simulation has been implemented to keep the ECCS path live (avoid total voiding) with
small flow and to avoid thermal shock. As the LCV has closed
to the maximum extent possible no further closing is possible
then the level correction rate can not be increased any further.
GAIKWAD et al.: EFFECT OF LOOP CONFIGURATION ON STEAM DRUM LEVEL CONTROL
Fig. 17. SD Levels for Step Change Response to SD set levels for 20% in-core
partial partitioned ECCS header feed.
Fig. 18. LCV opening for Step Change Response to SD set levels for 20%
partial in-core feed through partitioned ECCS header.
This makes the correction comparatively slow, but the correction does not stop, it continues at slower rate.
B. Sizing of the In-Core Feed LCVs & Line
To overcome these phenomena another case is being considered with 20% in-core partial feed through the partitioned
ECCS header instead of 10% to augment the control margins.
The main feed valve (feeds at the baffle region) performs the inventory control function by taking into account both the feed
. The mass
flows
balance element in the modified three-element level controller
makes the 4 main feed valves and the other 4 partial in-core feed
valves to move in opposite direction in this transient, according
to the functions assigned to the set of the LCVs. The capacity for
in-core steady state feed is decided based on the control margin
required on both the sides of the set-point to retain adequate
controllability. To access this controllability issue a parametric
study is being carried out, for the present case 10%, 20%, 30%
steady state in-core feeds were considered. In all the cases the
3723
Fig. 19. LCV opening for Step Change Response to SD set levels for new design 30% partial in-core feed through partitioned ECCS header.
margin on the lower side is restricted to 1% open valve, on the
other side the valve could open fully. The full open capacities
of the main (baffle region) LCVs and the in-core feed LCVs is
considered as same, individually each valve can provide 150%
one SD feed when opened fully, all the 8 line sizes and valve
sizes are same.
The in-core feed valve and line sizing issues can be fully
addressed after taking into account maximum credible quadrant power imbalance or some of the safety related transient to
gain more margins. The other important aspect can be related
to the changes occurring in the steady state operation (core exit
quality), due to in-core feed magnitude. It is also observed that
most of the in-core feed enters the channel from the water rod
in the top portion only almost by-passing the core. The reason
for this behavior can be attributed to the pressure gradient in the
channel which is very steep. At the bottom i.e., at the inlet of the
core the local pressure is high which offers high resistance to the
entry of the in-core feed. On the other hand due to pressure drop
in the channel the local pressure in the upper portion of the core
is comparatively less, which offers a low resistance path to the
in-core feed. Suitable modifications can be made into the water
rod design to account for this anomaly. It can be in terms of the
change in number of holes and the hole sizes, at different elevation to make the in-core feed injection uniform, from core inlet
to out-let. In an ideal case in-core feed injection at core in-let
would be best option, but the for a break in the CRIH it may
create some problem so only the hole size and number of holes
need to be manipulated for optimum design which can satisfy
both operating and safety requirement, though it may not be as
obvious.
The response obtained for the same changes in the SD level
set points is depicted in Figs. 17 & 18 for the 20% in-core feed.
Here the response obtained for SD7 is also superior as compared for the 10% in-core feed case. This can be attributed to
the increase in the partial in-core feed, capacity from 10% to
20%. The valve can now close from higher initial opening to a
minimum of 1%. In this case also it initially closes to 1% and
then all the 8 LCVs come back to their initial positions at steady
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IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 56, NO. 6, DECEMBER 2009
state. The response for 30% in-core steady state feed is also satisfactory (Fig. 19).
X. CONCLUSION
The uncontrollable multiple Steam Drum (SD) level situation
created by the boiling channels and loop interaction is analysed
and the proposed solutions has been tested successfully. It can
be concluded that:
1) The four SD levels are not independent of each other due
to the CRIH which connects all the four loops.
2) The open loop system response is inverse but not unstable,
as the response to a perturbation in the feed flow only leads
to a new steady state.
3) Closing the system with four individual SD level controllers leads to unstable behavior as the interactions
among the four SD levels is not implemented either in the
process design or the controller.
4) Instead of using bulky and complex logics and model (s.a.
MIMO) in the controller the proposed modifications in the
process is suggested which takes into account the interactions and counters/avoids the inter loop inventory transfer
through partial in-core feed to the targeted loop, and is
not affected by CRIH. Partial in-core feed through four
portioned ECCS header with modified three-element level
controller makes the SD level controller performance acceptable.
5) Though 10%, 20% and 30% in-core feed were used for performance analysis, 10% scheme is least intrusive and does
not cause much change in steady state process parameters
and design conditions and it performance is also satisfactory.
6) Further studies are being carried out to access the performance of the proposed scheme and other options such as
APC, MPC, MIMO and other less intrusive process design
options.
REFERENCES
[1] G. Y. Qiliang, X. Jianchun, and W. Ping, “Water level control of boiler
drum using one IEC61131-3-based DCS,” in Proc. 26th Chinese Control Conf., July 26–31, 2007, pp. 252–255.
[2] Y. Nanhua, M. Wentong, and S. Ming, “Application of adaptive Grey
predictor based algorithm to boiler drum level control,” Energy Convers. Manage., vol. 47, pp. 2999–3007, 2006.
[3] M. G. Na, “Design of a steam generator water level controller via the
estimation of the flow errors,” Ann. Nucl. Energy, vol. 22, no. 6, pp.
367–376, 1995.
[4] M. G. Na and H. C. No, “Design of model reference adaptive control
system for steam generators,” Nucl. Eng. Des., vol. 122, pp. 301–311,
1990.
[5] T.-F. Cheung and W. L. Luyben, “Liquid-level control in single tanks
and cascades of tanks with proportional-only and proportional-integral
feedback controllers,” Ind. Eng. Chem. Fundam., vol. 18, no. 1, pp.
15–21, 1979.
[6] K. H. Johansson, “The quadruple-tank process: A multivariable laboratory process with an adjustable zero,” IEEE Trans. Control Syst.
Technol., vol. 8, no. 3, pp. 456–464, May 2000.
[7] C. Furtmueller and L. del Re, “Disturbance suppression for an industrial level control system with uncertain input delay and uncertain
gain,” in Proc. IEEE Int. Conf. Control Applications, Munich, Germany, Oct. 4–6, 2006, pp. 3206–3211.
[8] N. Waurajitti, J. Ngamwiwit, and Y. Prempraneerach, “Adaptive
fuzzy sliding mode controller for two cascaded tanks level control,”
in Proc. TENCON, Sep. 24–27, 2000, vol. 2, pp. 592–597, DOI
10.1109/TENCON.2000.888806.
[9] P. Eserin, “Application of canonical variate analysis to the dynamical modeling and control of drum level in an industrial boiler,” in
Proc. American Control Conf., San Diego, CA, Jun. 1999, vol. 2, pp.
1163–1166.
[10] M. A. Rami, J.-P. F. L. El Ghaoui, P. Bendotti, and C.-M. Falinowery,
“Control of jump linear systems: Application to the steam generator
water level,” in Proc. 38th Conf. Decision andControl, Phoenix, AZ,
Dec. 1999, vol. 5, pp. 4923–4928.
[11] W. Huang, Q. Huang, Q. He, Y. Zhao®, Q. Qi, and L. Dai, “Decoupling control for steam and water system,” in Proc. 2nd Int. Symp. Systems and Control Aerospace and Astronautics, Dec. 2008, pp. 1–5, DOI
10.1109/ISSCAA.2008.4776276, 10-12.
[12] F. Sanfilippo and J. L. Deltour, “Comparison between monovariable controller and multivariable controller,” in IEEE Int.
Conf. Systems, Man, and Cybernetics, San Diego, CA, Oct.
11–14, 1998, vol. 4, pp. 3914–3919, ISBN: 0-7803-4778-1, DOI:
10.1109/ICSMC.1998.726699.
[13] M. E. Flynn and M. J. O’Malley, “A drum boiler model for long term
power system dynamic simulation,” IEEE Trans. Power Syst., vol. 14,
no. 1, pp. 209–217, Feb. 1999.
[14] F. P. de Mello, “Boiler models for system dynamic performance
studies,” IEEE Trans. Power Syst., vol. 14, no. 1, pp. 209–217, Feb.
1991, Fellow.
[15] H. Kim and S. Choi, “A model on water level dynamics in natural circulation drum-type boilers,” Int. Commun. Heat Mass Transfer, vol.
32, pp. 786–796, 2005.
[16] J. Y. Lee and H. C. No, “Dynamic scaling method for testing the performance of the water level controller of nuclear steam generators,” Nucl.
Eng. Des., vol. 122, pp. 313–327, 1990.
[17] K. J. Astrom and R. D. Bell, “Drum-boiler dynamic,” Automatica, vol.
36, pp. 363–378, 2000.
[18] J. Der Leea and C. Panb, “Nonlinear analysis for a nuclear-coupled
two-phase natural circulation loop,” Nucl. Eng. Des., vol. 235, pp.
613–626, 2005.
[19] G. Dieck-Assad, “Development of a state space boiler model for
process optimization,” Simulation, vol. 55, no. 4, pp. 201–213, 1990,
DOI: 10.1177/003754979005500402.
[20] K. K. Mehta, “A dynamic simulation of a nuclear power station for
control analysis,” Nucl. Eng. Des., vol. 33, pp. 403–421, 1975.
[21] W. Dong, J. M. Doster, and C. W. Mayo, “Steam generator control in
nuclear power plants by water mass inventory,” Nucl. Eng. Des., vol.
238, pp. 859–871, 2008.
[22] W. J. Peet and T. K. P. Leung, “Improved drum level control for load
cycling,” in Proc. IEEE 2nd Int. Conf. Advances in Power System Control, Operation and Management, Hong Kong, Dec. 7–10, 1993, vol.
1, pp. 130–134.
[23] D. Sbarbaro and R. Ortega, “Averaging level control: An approach
based on mass balance,” J. Process Control, vol. 17, pp. 621–629,
2007.
[24] M. V. Kothare, B. Mettler, M. Morari, P. Bendotti, and C.-M.
Falinower, “Level control in the steam generator of a nuclear power
plant,” IEEE Trans. Control Syst. Technol., vol. 4, pp. 4851–4856,
Dec. 1996.
[25] T.-F. ai Cheung and W. L. Luyben, “Liquid-level control in single tanks
and cascades of tanks with proportional-only and proportional-integral
feedback controllers,” Ind. Eng. Chem. Fundam., vol. 18, no. 1, pp.
15–21, 1979.
[26] J. I. Choi, J. E. Meyer, and D. D. Lanning, “Automatic controller for
steam generator water level during low power operation,” Nucl. Eng.
Des., vol. 117, pp. 263–274, 1989.
[27] M. V. K. B. M. M. Morari, “Linear parameter varying model predictive
control for steam generator level control,” Comput. Chem. Eng., vol.
21, pp. S86–S866, 1997, Suppl..
[28] E. Irving, C. Miossec, and J. Tassart, “Towards efficient full automatic
operation of the PWR steam generator with water level adaptive
control,” in Proc. Int. Conf. Boiler Dynamics and Control in Nuclear
Power Stations, British Nuclear Energy Soc.y, London, U.K., 1980,
pp. 309–329.
[29] W. Huang, Q. Huang, Q. He, Y. Zhao®, Q. Qi, and L. Dai,
“Decoupling control for steam and water systemCD,” in Proc. 2nd
Int. Symp. Systems and Control in Aerospace and Astronautics, Dec.
10–12, 2008, pp. 1–5, SBN: 978-1-4244-3908-9, DOI: 10.1109/
ISSCAA.2008.4776276.
[30] H.-M. Chen, Z.-Y. Chen, and J.-P. Su, “Design of a sliding mode controller for a water tank liquid level control system,” New Trends Adv.
Control Applicat., vol. 4, no. 12, pp. 3149–3159, Dec. 2008.
[31] E. Arriaga-de-Valle and G. Dieck-Assad, “Modeling and simulation of
a fuzzy supervisory controller for an industrial boiler,” Simulation, vol.
82, no. 12, pp. 841–850, Dec. 2006.
GAIKWAD et al.: EFFECT OF LOOP CONFIGURATION ON STEAM DRUM LEVEL CONTROL
[32] M. G. Na, “Design of a genetic fuzzy controller for the nuclear steam
generator water level control,” IEEE Trans. Nucl. Sci., vol. 45, no. 4,
pp. 2261–2271, Aug. 1998.
[33] X. Liu and T. Chai, “A weighted algorithm of fuzzy logic strategy on
water level control of steam generator,” in Proc. 76th Conf. Decision
andControl, San Diego, CA, Dec. 1997, pp. 3357–3362.
[34] T. Iijima, Y. Nakajima a, and Y. Nishiwaki, “Application of fuzzy logic
control system for reactor feedwater control,” Fuzzy Sets Syst., vol. 74,
pp. 61–72, 1995.
[35] Y. Huang’1, N. Li2, Y. Shil, and Y. Yil, “Genetic adaptive control for
drum level of a power plant boiler,” in Proc. IMACS Multiconf. Computational Engineering in Systems Applications, Oct. 4–6, 2006, vol.
2, pp. 1965–1968.
[36] D. G. Andone, J. I. Fagarasan, and M. R. Dobrescu, “Advanced control
of a steam generator,” in Proc. 3rd Int. IEEE Conf. Intelligent Systems,
Sep. 2006, pp. 338–343.
[37] M. Mercangöz and F. J. Doyle, “Distributed model predictive control
of an experimental four-tank system,” J. Process Control, vol. 17, pp.
297–308, 2007.
[38] P. J. Campo and M. Morari, “Model predictive optimal averaging level
control,” AIChE J., vol. 35, no. 4, pp. 579–591, Apr. 1989.
[39] E. P. Gatzke, E. S. Meadows, C. Wang, and F. J. Doyle, “Model based
control of a four-tank system,” Comput. Chem. Eng., vol. 24, pp.
1503–1509, 2000.
[40] M. Xua, S. Lia, and W. Caib, “Cascade generalized predictive control
strategy for boiler drum level,” ISA Trans., ISA-Instrum. Syst. Automation Soc., vol. 44, pp. 399–411, 2005.
[41] J. B. Froisy, “Model predictive control—Building a bridge between
theory and practice,” Comput. Chem. Eng., vol. 30, pp. 1426–1435,
2006.
[42] R. Di Marco, D. Semino, and A. Brambilla, “From linear to nonlinear
model predictive control: Comparison of different algorithms,” Ind.
Eng. Chem. Res., vol. 36, pp. 1708–1716, 1997.
[43] S. J. Qina and T. A. Badgwellb, “A survey of industrial model predictive control technology,” Control Eng. Practice, vol. 11, pp. 733–764,
2003.
[44] Li, “A novel predictive control and its application on water level
system of ship boiler,” in Proc. 1st Int. Conf. Innovative Computing,
Information and Control, 2006, pp. 344–347.
[45] J. Balaram, C. N. Shen, and R. T. Lahey, Jr., “Muliltivariable stability
margins for boiling water nuclear reactors,” in Proc. 21st IEEE Conf.
Decision and Control, Dec. 1982, vol. 21, pp. 1036–1041.
[46] D. H. Kim, “Nuclear steam generator level control by a neural networktuning 2-DOF PID controller,” in Proc. Int. Symp. Computational Intelligence far Measurements and Applications, Boston, MA, Jul. 14–16,
2004, pp. 168–173.
3725
[47] F. D’Auria, B. Gabaraev, V. Radkevitch, A. Moskalev, E. Uspuras, A.
Kaliatka, C. Parisi, M. Cherubini, and F. Pierro, “Thermal-hydraulic
performance of primary system of RBMK in case of accidents,” Nucl.
Eng. Des., vol. 238, pp. 904–924, 2008.
[48] A. Kaliatka, E. Urbonavicius, and E. Uspuras, “Approach to accident
management in RBMK-1500,” Nucl. Eng. Des., vol. 238, pp. 241–249,
2008.
[49] H. Mochizuki, M. H. Koike, and T. Sakai, “Core coolability of an ATR
by heavy water moderator in situations beyond design basis accidents,”
Nucl. Eng. Des., vol. 144, pp. 293–303, 1993.
[50] S. Mitaa, M. Akebib, O. Sawamuraa, and T. Kondo, “Development of
the advanced thermal reactor in Japan,” Nucl. Eng. Des., vol. 144, pp.
283–292, 1993.
[51] M. Misale, M. Frogheri, F. D’Auria, E. Fontani, and A. Garcia, “Analysis of single-phase natural circulation experiments by system codes,”
Int. J. Thermal Sci., vol. 38, no. 11, pp. 977–983, 1999.
[52] S. K. Mousavian, M. Misale, F. D’Auria, and M. A. Salehi, “Transient
and stability analysis in single-phase natural circulation,” Ann. Nucl.
Energy, vol. 31, no. 10, pp. 1177–1198, 2004.
[53] M. R. Gartia, D. S. Pilkhwal, P. K. Vijayan, and D. Saha, “Analysis of
metastable regimes in a parallel channel single phase natural circulation
system with RELAP5/MOD3.2,” Int. J. Thermal Sci., vol. 46, no. 10,
pp. 1064–1074, 2007.
[54] T.-J. Liu, C.-H. Lee, and Y.-S. Way, “IIST and LSTF counterpart test
on PWR station blackout transient,” Nucl. Eng. Des., vol. 167, no. 3,
pp. 357–373, 1997.
[55] A. J. Gaikwad, R. Kumar, S. F. Vhora, G. Chakraborty, and V. Venkat
Raj, “Transient analysis following tripping of a primary circulating
pump for 500 MWe PHWR power plant,” IEEE Trans. Nucl Sci. vol.
50, no. 2, pp. 288–293, Apr. 2003.
[56] R. Kumar, A. J. Gaikwad, S. F. Vhora, G. Chakraborty, and V.
Venkat Raj, “Logic modification to avoid ECCS lineup in the PHT
system during thermal shrinkage transients of 220 MWe PHWR
nuclear power plant,” IEEE Trans. Nucl Sci. vol. 50, no. 4, pp.
1229–1237, Aug. 2003.
[57] A. J. Gaikwad, R. Kumar, S. F. Vhora, G. Chakraborty, and V. Venkat
Raj, “Selection of a steam generator pressure control program for a
500 MWe PHWR pressurized heavy water reactor power plant through
transient analysis,” Inst. Mechan. Eng., Part A: J. Power Energy vol.
217, no. A6, pp. 631–642, 2003, ISSN 0957-6509.
[58] A. J. Gaikwad, P. K. Vijayan, S. Bhartya, K. Iyer, R. Kumar, A. D.
Contractor, H. G. Lele, S. F. Vhora, A. K. Maurya, A. K. Ghosh, and
H. S. Kushwaha, “Effect of coolant inventories and parallel loop interconnections on the natural circulation in various heat transport systems
of a nuclear power plant during station blackout,” Sci. Technol. Nucl.
Install. p. 11, 2008, Article ID 458316.