Start up Schedule optimizing system

ELSEVIER
Copyright © IFAC Power Plants and Power Systems Control,
Seoul, Korea, 2003
IFAC
PUBLICATIONS
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START-UP SCHEDULE OPTIMIZING SYSTEM OF A COMBINED CYCLE POWER PLANT
Masakazu SHIRAKAW A * and Masashi NAKAMOTO
TOSHIBA Corporation, Industrial and Power Systems & Services Company,
36-5 Tsurumichuo 4-chome, Tsurumi-ku, Yokohama-shi, Kanagawa-ken, 230-0051 Japan
* e-mail: [email protected]
Abstract: This paper presents a method to determine the optimal operational parameters
of a combined cycle power plant. The proposed method combines a dynamic simulation
with an optimization calculation based on the nonlinear programming method. The reason
for the optimization of the plant start-up scheduling is being able to reduce the start-up
time by keeping the thermal stresses in the thick parts of the heat recovery steam
generator and in the steam turbine under their allowable values. Copyright © 2003 IFAC
Keywords: Power generation, simulation, dynamic modelling, optimization, nonlinear
programming, control engineering.
method, turbine design engineers decide the schedule
parameters in the mismatch chart during the turbine
design stage and install it into the plant control
system. Control engineers may adjust these
parameters when plant operation problems are
encountered during the commissioning operation.
This heuristic approach, however, involves design
and tuning costs, and it is difficult to obtain the
optimal start-up schedule. Moreover, these
parameters may not be adjusted during commercial
operation after commissioning completion.
I. INTRODUCTION
A combined cycle power (CC) plant that combines a
gas turbine and a steam turbine can achieve a higher
thermal efficiency and lower environmental impact,
and have an excellent operation. Therefore, many CC
plants have been installed around the world. The CC
plants are required to have frequent start-up / shutdowns followed by quick loading in order to regulate
power generation rates according to electricity power
demands that frequently change. Consequently, the
time reduction for start-up without shortening the
machine lifetimes has become important for
economical fuel consumption. The decisive factors
for rapid start-up are thermal stresses caused by
temperature gradients in the thick parts of the heat
recovery steam generator (HRSG) and in the steam
turbine. Important functions of the CC plant control
system are to reduce the start-up time and to satisfy
the operational constraints.
Several methods to shorten the start-up time have
been proposed. A model predictive control for a
conventional thermal power plant has been proposed
(Nakai, et aI., 1996). This algorithm predicts the
future thermal stress in the steam turbine rotor and
calculates the optimal future profile of the steam flow
rate. The CC plant, however, has many operational
restrictions, not only thermal stress in the steam
turbine but also loading rates of the gas turbine,
temperature gradients of the HRSG, drum water
levels ofthe HRSG and NOx emission from the plant,
etc. A fuzzy expert system for a CC plant has been
proposed (Akiyama, et al., 1997). To obtain the startup schedule, this system uses an engineer's
experiences in fuzzy rules. It requires additional cost
to obtain this engineering knowledge. Recently,
A start-up schedule for a conventional (simple steam
cycle) thermal power plant is usually generated by a
mismatch chart using the differential temperature
between the steam and steam turbine rotor metal just
before the steam turbine starts (Hanzalek and Ipsen,
1966). The conventional control system of the CC
plant has basically applied the same method. In this
261
100
nonlinear programming using a plant dynamic model
has been studied (Bausa and Tsatsaronis, 2001). This
method is applied to a simplified single pressure CC
plant model. The model includes many assumptions
and simplifications, thus it is not possible to study a
practical problem.
~ 80
-g 60
.3
.,,; 40
"
~
20
o
This paper aims at proposing a method to determine
the practical optimal start-up schedules using a
dynamic simulation and nonlinear programming.
This method does not require any adjustment of the
schedule parameters by engineers. Also, a great deal
of labor is not required in order to prepare the
knowledge base.
100
~ 80
r
t
i:
Stan
Ignite
j
Synchronize;
]60
~
.,,; 40
"
~
20
Time
o.l.-+-_ - - p
t
Synchronize
Stan-up time
f '
Full load
2. COMBINED CYCLE POWER PLANT
Fig. 2. Plant start-up schedule.
2.1 Plant configuration
Many types of CC plants have already been
developed. Here we discuss the multi-shaft type CC
plant, which consists of two gas turbine units, two
HRSG units, and a reheat-type steam turbine unit.
The gas turbines and the steam turbine drive the
generators. Also, the HRSGs generate steam for the
steam turbine using waste heat from the gas turbines.
The configuration of this plant is shown in Fig. I.
This plant generates a total output of 625 MW. The
gas turbines are of the 1300 deg.C class. The HRSGs
are the triple pressure and reheat type with a duct
burner. The steam turbine has a 265 MW rated
capacity.
synchronizing, the first gas turbine goes to a
minimum load of 10 %. The first HRSG warms at the
minimum gas turbine load. When the steam
properties have reached the required conditions, the
steam turbine starts, and the steam turbine is put into
the speed and load control mode. After rub-check,
the steam turbine increases its speed toward a
predefined speed of 800 rpm at an accelerating rate
x I' and maintains this speed during the low-speed
heat soak time x 2. The steam turbine increases its
speed again toward the rated speed, and maintains
this speed during the high-speed heat soak time x 3 .
After synchronizing, the steam turbine goes to an
initial load of 3 %, and maintains this load during the
initial-load heat soak time x 4 . During these heat
soak operations, the first gas turbine increases its
load to predefined loads of 25 % and 40 % at loading
rates Xli and x 9 , respectively, so that the steam flow
rate should be secured to drive the steam turbine.
After completing the initial-load heat soak, the
bypass valves of the first unit are closed, then the
steam turbine is put into the inlet pressure control
mode. The second gas turbine and HRSG are started
like the first unit. The second gas turbine goes to a
merged load of 40 %, and maintains this load. The
bypass valves of the second unit are then closed to
merge the second HRSG steam into the first HRSG
steam. Afterwards, both gas turbines increase their
load again toward the rated load at different loading
rates x 5 (40 % to 60 %) and X6 (60 % to 100 %).
2.2 Start-up scheduling method
The start-up process of this plant is shown in Fig. 2.
Initially, the first gas turbine starts, purges, fires, and
increases its speed toward the rated speed. After
..._ _ to Condenser
~_
First unit
Gas turbine rT-~~---r-+l
Duct burner
to Condenser
Bypass valve
to LP Steam turbine
Second unit
to JP Steam turbine
Gas turbine rr--~---_"" to HP Steam turbine
Lastly, after the gas turbines have reached the rated
load, both duct burners fire at a loading rate xl. The
steam turbine reaches the rated load with a time
delay, due to the delay in the steam generation in the
HRSGs.
3. START-UP SCHEDULING PROBLEMS
from HP Steam turbine
' - - - - - from Condenser
The problem of the start-up scheduling is to
determine the above schedule parameters ( x I " · ' ,x 9 )
Fig. I. Plant configuration.
262
in order to minimize the start-up time while
maintaining the operational constraints. The life span
of the power plants is severely affected by thermal
stresses that develop in the steam turbine and HRSG
for reducing the start-up time.
Control center
Optimization
Initial process
values setting
Thermal stresses in the steam turbine occur on the
rotor surfaces and rotor bores at the high-pressure
(HP) part and the intermediate-pressure (IP) part. A
large temperature difference arises between the hot
steam and cold rotor metal when steam enters the
steam turbine, and also, the temperature difference
appears during the gas turbine load-up. As a result,
the thermal stresses are developed by the temperature
distributions in the rotors. The thermal stress of the
thick part of the HP drum is the severest in the
HRSG. In general, this thermal stress is estimated by
the drum temperature gradient.
If the heat soak times (x 2' X 3' x 4 ) are extended, the
steam turbine accelerating rate (x J) and the gas
turbine loading rates ( x 5 • X 8' X 9) decrease, then the
start-up time becomes longer while the thermal
stresses of the steam turbine are reduced, because the
differential temperature between the steam and rotor
metal decrease. On the other hand, the start-up time
is shortened but the thermal stresses of the steam
turbine become greater. Also, the temperature
gradient of the HP drum depends on the gas turbine
loading rates (x 5' XII) and the duct burner loading
rate (Xl
# I Gas turbine #2 Gas turbine Steam turbine
# I HRSG
#2 HRSG
BOP
Combined cycle power plant
Fig. 3. Start-up schedule optimizing system.
).
P,u
The plant operational characteristics have been
intensively studied using a dynamic simulation
method (Maffezzoni, 1992), but it is not easy to
determine the optimal operational parameters
because it is necessary to iterate the dynamic
simulation based on trial and error by the engineer's
intuition and experience. Therefore, in a
conventional operation method, constant values
relating to each start-up mode such as the cold,
warm-I, warm-2, hot-I and hot-2 modes have been
used for a plant operation, and these values are
predetermined during the plant design stage.
=(P'd -
Pa )exp ( -
t,,,-t'd)
k
+ ~I
(I)
where P", is the estimated process values at the time
of the first gas turbine start, P'd is the process values
at the time of the last shut-down, Pa is the ambient
conditions,
t,,,
is the first gas turbine start time,
t,d
is the last shut-down time and k is the cooling
constants. k can possibly be determined from the
actual plant data.
The initial schedule parameters for the dynamic
simulation are defined using a conventional
mismatch chart. The dynamic simulation In
accordance with the initial schedule simulates the
plant start-up process. The start-up time and process
values are obtained and used for the optimization. A
nonlinear optimization method modifies the schedule
parameters. The function for convergence judgment
decides whether the schedule has reached the
optimum point or not. If it does not converge, the
modified start-up schedule is sent to the dynamic
simulation again. And iterative calculations are
automatical1y occurred until the optimum schedule is
determined.
4. CONTROL CONCEPTS FOR START-UP
4. J Functional structure ofthe system
Fig. 3 shows the functional structure of the start-up
schedule optimizing system proposed in this paper.
This system is instal1ed in a plant control system that
consists of a computer system, machine control
system and operator station (OPS).
The optimum schedule is determined by the
optimization with the dynamic simulation. The initial
process values for the dynamic simulation are
estimated using the cooling curves, and the start-up
initiation time comes from the control center on the
previous day. Process values are estimated according
to equation (1).
After determining the optimum schedule, the
schedule parameters are set in the plant control
system. The plant control system operates the CC
plant according to the schedule obtained by the
optimization.
263
the multiple parts and volumes in which the steam is
stored.
4.2 Dynamic simulation model
The dynamic simulation model consists of the
process equipment model and the control system
model. The first principle is adapted to model the
process equipment that consists of the gas turbine,
HRSG, steam turbine and balance of plant (BOP).
The control system is modeled in order to be
equivalent to the actual control system. This
simulation model is verified by comparison with
actual plant data (Funatsu, et al., 1999).
4.3 Optimization calculation
The start-up problem can be formulated as a function
of the optimization problem with operational
constraints. Among the schedule parameters
(x,,···,x9) in Fig. 2, seven parameters (x,,"',x7)
are selected as optimizing objects and defined as
follows.
Gas turbine model. The gas turbine responds more
quickly than the other equipment. The flow rate and
the temperature of the exhaust gas are represented by
functions of the fuel flow rate. The gas turbine duct
has a time delay because of the large heat capacity.
X
, '
. .. ' x·
... , X7] r
I '
(5)
The others (xli' x9) are defined by the following
relational equations, respectively.
HRSG model.
The HRSG is composed of heat
exchangers that have a long time delay when
compared to the gas turbine and the steam turbine,
and has a significant effect on the starting
characteristics of the entire plant. The dynamic
characteristics of each heat exchanger are calculated
using the mass and energy balance equations as
follows.
dTm
MmC m ~=Qgm -Qmf
= [x
Xli
. 25-10[%])
=max ( 1.0 [%/mm],
.
(6)
x9
. 40-25[%])
= max ( 1.0 [%/mm],
.
(7)
x 2 [mm]
Xl
[mm]
The objective function J r is the start-up time from
the first gas turbine start to the plant base load
operation. The' optimization problem is defined by
equations (8), (9) and (10).
(2)
(8)
dp,
V, ~=Gfi -G,o
(3)
(9)
d{PfH, )
V. t ·
dt
.
(10)
= G.t
I
H .t I - G.t· 0H. 0
t·
+ Qm t·
(4)
where cm; is the maximum process values during
start-up, cii is its limitations, c; is the process
where M is the mass, C is the specific heat, T is
the temperature, Q is the heat flow, V is the volume,
p is the fluid density, G is the fluid mass flow rate,
H is the enthalpy and t is the time. The subscripts
m denote the tube metal, g is the exhaust gas, f is
the internal fluid, i is the inlet and 0 is the outlet.
values, and t is the time. The subscript j stands for
specific locations. The thermal stresses of the steam
turbine are the HP rotor surface (j= 1), HP rotor bore
(j=2), IP rotor surface (j=3) and IP rotor bore (j=4).
The temperature gradients of the HP drum are the
first unit (j=5) and the second unit (j=6).
Steam turbine model. The adiabatic efficiency of
the steam turbine is defined as the function of the
turbine pressure ratio. The steam flow rate through
the steam turbine is calculated using the constant
flow coefficient. The turbine power is calculated
using the enthalpy difference between the inlet and
outlet enthalpies of the steam turbine. No dynamic
effect is evaluated in the flow and pressure relation.
The thermal stress of the steam turbine rotor is
obtained by the temperature distribution, which is
calculated by the dynamic model of the heat
conduction that divides the rotor into several vertical
cylinders.
The operational constraints for equation (9) can be
included in the objective function as the following
penalty function.
J(X)=a, ·Jr(X)
6
+
La
j='
2j
.K; (cm; (X)-c ii
)2
K j =0, if cm; -5.c ii ,j=1,···,6
K;
= 1,
otherwise
where a, and a 2 are the weighting coefficients.
Pipe model. Since the steam pipe is long and has a
large volume, the pressure in the pipe is modeled by
204
(11 )
(12)
~
In order to obtain a feasible solution, each parameter
is limited as follows.
125 r - - - - - - - - - - - - - - - ,
e:. 100
"C
;
;
First gas turbine speed
ro
o
i
First gas turbine load
--l
~
"C
Q)
Q)
Duct burner i
load
.•
a.
(f)
125
~
~----....,...---l1 00 "C
ro
The optimization method used in this paper is the
successive quadratic programming (SQP) method
(Fukushima, 1986). This method is a kind of
nonlinear programming method using the value of
the gradient. The gradient of the objective function is
approximated as follows.
~
e:.
.3
50
25
.................._ ............._ .......-._-.<-.J..--L.---l0
60
120
180
240
300
o
Time (Minutes)
125 r - - - - - - - - - - - - - - - ,
100 Limitation
"C
C
75
1ii
8
c
50
25
~
0
.~
:c
VJ(X)= J(X +L1X)- J(X)
L1X
75
~
(17)
I-
where L1X is the perturbation of each schedule
parameter. J(X) and J(X +L1X) can be obtained by
the dynamic simulation.
............l-......._ . l -__....l._.........I..o__--I_~
0
Warm-1
Cold
~
~
::::l
m
m
.I, /
~300
/
/
.....
90
70
!!?
co
~
0.150
SO
~
100
50 ~-L.._..u....--Io._""""..J.....I_....L.J_1...--L..---'
12
24
36 48 60 72 84
Standby period (Hours)
96
~
~
G'
Cl
15
500
12
400
9
300
~
6
200
.3
Q)
Q)
~
As a typical example, the result of a cold start-up
when the initial temperature of the rotor is 120 deg.C
(standby period is over 100 hours) is explained. Fig.
5 shows the results of the conventional method. Here,
the normalized thermal stress of the steam turbine is
the maximum value of the four rotors (j=l to 4), and
the normalized temperature gradient of the HP drum
is the first unit (j=5). The start-up time is 264
minutes. In this case, there are some margins for the
operational constraints, and the start-up schedule is
not adequate. Fig. 6 shows the results of the proposed
method. In this case, the initial schedule parameters
were same as the conventional method. The start-up
time is 228 minutes. The proposed method reduces
the start-up time by 36 minutes compared to the
conventional method, and satisfies the operational
constraints.
Q)
o
300
margins. On the other hand, the proposed method
(solid lines) is able to reduce the start-up times by
keeping the thermal stresses under the allowable
values for all the start-up conditions.
80 iii
.<:
60 l-
(jj
0
u
5
0
Fig. 5. Conventional method (Initial schedule).
Ul
Ul
~200
~
¥1o
100 ~
E
_""'...L-L.-.....l----'
-'---L_...L---Io._.J..--J
0
Q)
0
300
I60
120
180
240
0
Time (Minutes)
110
._.-_.-
c
~250
75
50
25
3
,----:f---...-2--.......-+-;:;.;.;.;==-;_=-l 100 ~
,.Ul
240
c
100'~
Q)
c::
Limitation
~350
120
180
Time (Minutes)
125
,.,._......
ro
n.
Numerical studies have been executed for all the
start-up conditions. That is, the initial temperatures
of the rotor are from ]20 deg.C (standby period is
over 100 hours) to 462 deg.C (standby period is 4
hours). A comparison of the conventional method
and the proposed method is shown in Fig. 4. This
figure shows the relationship between the standby
period, the start-up time and thermal stress. Here, the
normalized thermal stress shows the maximum value
of the four rotors (j= I to 4). For the conventional
method (dash dot lines), there are five start-up modes,
i.e., the cold, warm-I, warm-2, hot-] and hot-2
modes that depend on the differential temperature
between the steam and steam turbine rotor metal just
before the steam turbine starts. The schedule
parameters are determined by using the tables of
each start-up mode. In this approach, the start-up
times become discontinuous. In addition, the start-up
times become long because of the thermal stress
Warm-2
60
~
(f)
21 r - - - - - - - - - - - - - - - . , 7 0 0 en
0,
First HRSG
.:L
600 ~
18
5. APPLICATION RESULTS
Hot-2.1
_________________ ~~E~~~~
Q)
108
Fig. 4. Comparison of required start-up time.
265
The path to search for the optimal solution is shown
in the case of the warm-2 start-up in Fig. 7, where
the initial temperature of the rotor is 258 deg.C
(standby period is 48 hours). Iterating about ten
times minimized the objective function (I I}, and the
optimal solution is obtained. It is necessary to
calculate the dynamic simulation eight (number of
125 r - - - - - - - - - - - - - - - ,
~
~ 100
ro
o
I
"0
Q)
Q)
(j)
~
~
C
.~
U;
§u
:g
:c
:J
I-
i
/f
Duct burner i
First gas turbine load
-l
c.
1
First gas turbine speed
"0
125
100
75
50
25
'--..........u._'--............l._""'of..-L........l._L-~ 0
o
60
120
180
240
300
Time (Minutes)
125r--------------,
Limitation
100
75
50
25
0
125
Limitation 100
75
50
25
St~~~t·~~bi~~·
speed
load
-'
6. CONCLUSIONS
<f.
"0
ro
A method is proposed to optimize the operational
parameters of the combined cycle power plants. The
proposed method consists of the optimization
calculation and the dynamic simulation.
S
"0
Q)
~
(j)
The proposed method makes it possible to determine
the optimal operational parameters by taking into
account the dynamic characteristics of the plant.
---------
------------------
.l..-... O
.......-L............- -......- _ . . . " , l I L -
Future work will add other operational restrictions
(e.g., NOx emission from the plant, etc.).
C
.~
~o
REFERENCES
§
0
Hanzalek, F. J. and P. G. Ipsen (1966). Thermal
Stress Influence Starting, Loading of Bigger
Boilers. Electrical World, VoI. 165, No. 6, pp.
58 - 62.
Nakai, A., et al. (1996). Turbine Start-up Algorithm
Based on Prediction of Rotor Thermal Stress.
Proceedings of IFAC 13th Triennial World
Congress, pp. 25 - 30. San Francisco, U.S.A..
Akiyama, T., et al. (1997). Dynamic Simulation and
its Applications to Optimum Operation Support
for Advanced Combined Cycle Plants. Energy
Conversion and Management, VoI. 38, No. 1517, pp. 1709-1723. Elsevier Science Ltd., U.K..
Bausa, J., and G. Tsatsaronis (2001). Dynamic
Optimization of Startup and Load-Increasing
Processes in Power Plants - Part I: Method, Part
11: Application. Transactions of the ASME,
Journal of Engineering for Gas Turbines and
Power, VoI. 123, pp. 246-254.
Maffezzoni, C. (1992). Issues in Modelling and
Simulation of Power Plants. Proceedings of
IFAC International Symposium on Control of
Power Plants and Power Systems 1992, Vol. 1,
pp. 19 - 27. Munich, Germany.
Funatsu, T., et al. (1999). An Evaluation of Dynamic
Simulation via 1300 deg.C Class Combined
Cycle Plant. Proceedings ofASME PWR-Vol. 34,
1999 International Joint Power Generation
Conference (IJPGC-99), Vol. 2, pp. 735 - 740.
San Francisco, U.S.A ..
Fukushima, M. (1986). A Successive Quadratic
Programming Algorithm with Global and Superlinear Convergence Properties. Mathematical
Programming, Vol. 35, pp. 253 - 264.
u
300
Fig. 6. Proposed method (Optimal solution).
~
eft
105
Warm-2 start-up
Standby period is 48 hours
-; 100
o
95
.2
g
Q)
90
13
Q)
85
o
80
.~
:c
o
1 2
3
4
5
6
7
8
parameters + 1) times in order to obtain the gradient
vector equation (17) for each iteration step. Therefore,
the computation time strongly depends on the
dynamic simulation. It takes about 2 minutes to
calculate the dynamic simulation once using a
personal computer (Intel® Pentium® 4 processor 2.20
GHz), so that it needs about 180 minutes to obtain
the optimal solution. The computation time depends
on the start-up conditions. In a word, the hot start-up
condition requires a shorter computation time, and
the cold start-up condition requires a longer
computation time.
9 10 11 12
Number of iterations
Fig. 7. Convergence history.
266