Energy and Power Engineering, 2013, 5, 278-282
doi:10.4236/epe.2013.54B054 Published Online July 2013 (http://www.scirp.org/journal/epe)
The Optimal Steam Pressure of Thermal Power
Plant in a Given Load
Yong Hu, Ji-zhen Liu , De-liang Zeng, Wei Wang, Ya-zhe Li
North China Electric Power University, State Key Laboratory of Alternate Electrical Power System with Renewable
Energy Sources, Beijing, China
Received January, 2013
ABSTRACT
As the large change of the grid load, many large capacity units of our country had to change the load in order to meet
the gird need. When a thermal power plant receives a given load instruction from the grid, it is necessary to set an opti-
mal steam pressure to maintain the high efficiency of the plant. In the past optimization methods, during the process of
calculation, the output of the turbine often changed, it was hard to maintain the output constant. Therefo re, in combina-
tion with the theory of variable con dition of turbine, calculation of governing stage and the matrix equation of thermal
power system, an optimization method were put forward and an optimal solution was got in a given load.
Keywords: Given Load; Pressure Optimization; Variable Condition; Thermal Power Plant
1. Introduction
As the development of economy in china, consumption
level of the people have enhanced, which leads to a large
proportion of electricity power is consumed in our daily
life, resulting in the difference between peak and valley
of grid load increased year by year. And in our country,
large-capacity thermal power plants have a large per-
centage in the total installed capacity of power plants,
which makes the large-capacity units with a basic load
have to participate in the load regulation. The units have
to deviate from the original design condition and even
run in the low load area for a long time, which makes
thermal efficiency of the units decrease greatly. Among
the factors that affect the thermal efficiency of power
plant, only the running modes and operating parameters
can be adjusted by operating personnel. Therefore the
resear ch of thermal po wer plants in th e off-design cond i-
tion is of great significance in the selecting of running
modes and operating parameters.
In a given load, when the unit runs in a high steam
pressure, the ideal enthalpy drop of turbine will increase
and the outlet pressure of feed-water pump will rise si-
multaneously. In order to maintain the given unit load, it
is necessary to reduce the steam flow rate through de-
creasing the opening degree of regulating valves, this
will increase the throttling loss of the governing stage.
When the unit runs in a low steam pressure, the th eoreti-
cal thermal efficiency of the unit will reduce, but the
lower steam pressure will make the governing stage to
maintain higher internal efficiency, and the outlet pres-
sure of feed-water pump will decrease. In order to main-
tain the unit load, it has to enlarge th e opening degree of
regulating valves to increase the steam flow rate. There-
fore, in tracking of the grid given load, the unit usually
deviates from the designed condition, how to select the
optimal steam pressure and the running mode has a great
influence on the interest of the power plant.
In the traditional method of the pressure optimization,
it usually assumed the steam pressure was approximately
proportional to the steam flow, when the steam pressure
changed, it calculated the steam flow firstly and then
calculated the back pressure of governing stage accord-
ing to the Flugel formula [1], carried on variable condi-
tion calculation of the governing stage and the whole
turbine. Finally it determined the efficiency of the unit
under the changed steam pressure [2]. But in the practical
operation of the thermal power plant, it must guarantee
the load of the unit equ al to the instruction from the gr id,
when the steam pressure gets higher, it needs to decrease
the opening degree of the regulating valves, lower the
steam flow to ensure the stability of the load, and vice
versa. In the traditional method, due to the approximate
proportional relationship between steam pressure and the
flow, it leads to the load changed in proportion, not in-
variable. In some other literatures, in order to ensure the
load unchanged, it iteratively calculated the steam flow
using the turbine power equation [3], which ignored the
characteristic of the governing stage and caused the de-
viation of the results.

Y. HU ET AL. 279
Therefore, on the base of variable condition calcula-
tion method of governing stage and variable condition
theory of turbine, using thermal economic matrix equa-
tion [4], in order to solve the problems mentioned above,
a new calculation method of optimal steam pressure in a
given load was put forward, the optimal steam pressure
and running modes was got under different loads.
2. Model of Steam Pressure Optimization
2.1. Calculation of the Governing Stage
In the variable condition calculation of the governing
stage, the steam flow through the fu lly opened regulating
valves and the partly opened valve can be expressed as:
'
'2
00
0.648 10
n
n
A
G
pv
  

'
p (1)
''
'''' 2
00
0.648 10
n
n
A
Gp
pv
  
 (2)
Then main steam flow rate can be expressed as:
'
nn
GGG
'
n
'
(3)
In which is the steam flow through the fully
opened valves; is the steam flow through the partly
opened valve;
'
n
G''
n
G'
n
A
is the flow area of fully opened
valves; ''
n
A
is the flow area of partly opened valve; 0
is the pressure of main steam; 0 is the specific volume
of main steam;
p
v
'

, ''

is the function of ,
; is the steam pressure behind fully opened
valve; is the steam pressure behind partly opened
valve; 2 is the back pressure of governing stage;
'
20
p/p
''
20
/pp'
0
p
'
0
p
p

is the efficiency of governing stage; a
x
is the speed
ratio of governin g stage.
In general, when the steam flows through the fully
opened valves, the throttle loss is smaller, so it can be
assumed 0
; when the steam flows through
the partly opened valve, the opening degree of partly
opened valve is x(), since the annular chamber
after the nozzle is in communicatio n with each other, the
steam pressure 1 behind the nozzle of each nozzle
group are the same, the steam pressure behind the un-
opened regulating valve (i.e., the pressure before the
nozzle of unopened valve) is also equal to 1. When the
opening degree of valve x gradually changes from 0 to 1,
the pressure beh ind partly opened valve will change
from to . In order to facilitate the calcula-
00
11
xp is assumed (this as-
sumption is only convenient to calculate ''
0
p, it has no
effect on the optimization results). So when the opening
degree of all the regulating valves is known, the main
steam flow can be expres
'
0
0.95p
[0x
p
''
0
p
0
0.95p
(0.95pp
p
tion,
sed as:
)

,1]
) 
p
1
p'' p
02
(,,)
n
Gfpxp (4)
Therefore, the main steam flow can be determined by
0 and 2, then on basis of the variable condition
calculation of governing stage, the steam enthalpy of
governing stage can be got.
,px p
tj
h
2.2. Calculation of the Intermediate Stage and
Last Stage
In the variable condition calculation of turbine, because
the flow area of intermediate stage is constant, when the
load of the unit is changed, if the variation of temperatur e
before all stages is ignored, the pressure before interme-
diate stage is proportional to th e steam flow of this stage,
so pressure ratio is invariant, the efficiency of intermedi-
ate stage is unchanged, the ideal enthalpy drop of each
stage is also unchanged [5]. Therefore, when the pa-
rameters of governing stage are known, the steam en-
thalpy of each extraction point can be expressed as:
(1)110 (1)0
(
iiii
hhhh


 (5)
In which i is the steam enthalpy of stage; sub-
script 0 represents the designed condition; subscript 1
represents the variable condition.
hith
For the last stage of steam turbine, we calculated from
the last stage to the prior stage, found the superheated
steam extraction point and set it as stage. The steam
after the stage does adiabatic expansion in the tur-
bine, so the entropy is constant. Combined with the
steam pressure of extraction point, the ideal steam en-
thalpy of this stage could be got, according to (6), we
could get the steam enthalpy of this stage and calculated
one stage by one stage until to the last stage.
ith
ith
(1)11,1 1(1)1
(
iiiiii
hh hh 


)

(6)
In which (1)1iis the ideal steam enthalpy of h
(1)i

stage, ,1ii


is the efficiency of stage. (1)i
2.3. Calculation of the Boiler Feed-Water Pump
Turbine
When the main steam pressure and flow rate change, the
output of Boiler Feed-Water Pump Turbine (BFPT) will
change too. Therefore, the influence of BFPT on the
thermal efficiency cannot be ignored.
From the outlet of feed-water pump to the main steam
valve, the phase of working fluid changed. In this process,
there exists the loss of resistance along the way and the
loss of local resistance [5], both loss can be expressed as:
2
2
C
p 

 (7)
In which p

is the pressure drop;

is the average
density of fluid; is the flow rate of fluid; C

is the
loss coefficient which depends on the characteristic of
pipe. We use subscript represent the parameters of d

Y. HU ET AL.
280
design-condition, then the outlet pressure of feed-water
pump can be expressed as:
2
202 0
() (
nd )
p
pd d
nd
G
ppp p
G


 (8)
In which 2
p
p is the outlet pressure of feed-water
pump; 0 is the main steam pressure; n is the main
steam flow. When the feed-water flows through the
pump, the pressure of feed-water will rise because of the
working of pump, this will make the feed-water enthalpy
rise. This process can be regarded as isentropic flow [6],
so the enthalpy- rise of feed-water can be expressed as:
p G
21
()
pp
p
vp p
h


 (9)
In which 1
p
p is the inlet pressure of feed-water pump;
v is the average specific volume of feed-water;
p

is
the efficiency of feed-water pump. According to the law
of conservation of energy, the extraction flow for BFPT
can be got.
21
4
()
()
np p
BFPT
p
cpj
Gpp v
Dhh



 (10)
In which 4 is the inlet steam enthalpy of BFPT; h
p
c is the exhaust enthalpy of BFPT;
h
j

is the effi-
ciency of BFPT.
3. Optimization Method of Steam Pressure
in a Given Load
3.1. Optimization Method
In order to maintain the output of the unit and overcome
the shortcomings of traditional optimization methods, in
the process of optimization, we adopted the sequential
calculation method, combining with assumption, verifi-
cation and iterative adjustment. If the load and an initial
steam pressure were given, we could get the steam flow,
opening degrees of regulating valves, back pressure of
governing stage and thermal efficiency of the unit, then a
unique m appin g relations hip was fo rmed among them .
Step1. According to the load instruction, use Figure 1
to determine the feasible range of steam pressure [7] and
the number of fully opened valves.
Step2. Assume a certain back pressure of governing
stage and the degree of partly opened valve to determine
the main steam flow, the enthalpy and temperature of
governing stage.
Step3. According to the enthalpy and temperature of
the governing stage, carry on the variable condition cal-
culation of intermediate stage and last stage, get the out-
put of turbine.
Step4. Judge the parameters of governing stage using
(11). Equation (11) is the Flugel formula [1]. If the equa-
tion does not hold, adjust the back pressure of governing
stage, and then go to step 2.
22
2
22 2
2
nc
nd dcd
GppT
GT pp



2 d
(11)
Step5. Judge th e output of turb ine. If the output of tur-
bine is not equal to the load instruction, adjust the degree
of partly opened valve and go to step 2.
The flow chart of the pressure calculation is shown in
Figure 2.
Figure 1. The feasible range of steam pressure.
0minmax
[]
p
pp
0i
0min
0.1
p
pi
x
2
p
n
G
tj
h
2
T
22
22
22
22
ncd
ndd cd
GppT
GppT



e
PN
x
2
p
Figure 2. The flow chart of the optimization method.

Y. HU ET AL. 281
3.2. Application Examples
We took the Oriental steam turbine N1000-25.0/600/600
as an example, the impact of the overlap of regulating
valves was not considered and we ignored the influence
of environmental factors on the thermal economy of the
unit. In the ideal condition of 100% load, there were
three regulating valves fully opened and one valve closed.
First, we took the 100% THA condition as an example,
analyze and validate the optimization method, the results
were shown in Table 1. In the 100% THA condition, in
order to maintain the unit load, as the decline of main
steam pressure, the regulating valves had to be opened
larger to increase the main steam flow, and the power
consumed by feed-water pump was decrease too. The
thermal efficiency of the unit was decline as the steam
pressure became lower. But when the main steam pres-
sure reduced to 22.76 Mpa, four regulating valves were
all fully opened, the throttling losses was least at this
moment, so the efficiency of the unit rebounded a little.
From the dates of Table 1, the variation tendency of
pressure and efficiency consistent with the theoretical
analysis, so this method can be used to optimize other
conditions of the unit.
Figure 3 shows the thermal efficiency change as the
number of fully opened valves change from 2 to 4 in dif-
ferent load. As the increasing of the opening degree, the
Table 1. The analysis of efficiency in a design condition.
Steam
Pressure
(Mpa)
Main
Steam
Flow(t/h)
Degree of
Regulating
Valves
Thermal
Efficiency
The Energy
Consumption of
Feed-water Pump (MW)
25.00 2850.95 75.00% 49.0875% 34.6134
24.00 2880.56 79.25% 48.8659% 33.7388
23.60 2885.50 83.75% 48.8319% 33.2834
23.20 2889.22 90.50% 48.8106% 32.8091
23.00 2889.43 94.50% 48.8095% 32.5484
22.76 2888.78 100.0% 48.8159% 32.2231
50 60 708090 100
46.5
47
47.5
48
48.5
49
The opening degree of the adjusting valves( %)
Thermal efficiency(%)
80%
70%
60%
50%
Figure 3. The relation between thermal efficiency and valve
opening.
50 60 70 80 90100
46
46.5
47
47.5
48
48.5
49
49.5
The unit load
(
%
)
Th erm al ef fi ci ency(%)
50 60 70 80 90100
12
14
16
18
20
22
24
26
28
30
Steam pressure(Mpa)
50 60 70 80 90100
12
14
16
18
20
22
24
26
28
30
Steam pressure of mode 1
Thermal effic ienc y of mode 2
Thermal effic ienc y of mode 1
Steam pressure of mode 2
Thermal effic iency of mode 2
Thermal effic iency of mode 1
Figure 4. The comparison curves of the two modes.
main steam pressure dropped, the thermal efficiency de-
clined, but in the fully opened points, there existed a lo-
cal optimal point.
Figure 4 shows the efficiency of the unit in different
sliding pressure operation mode. In mode 1, the unit took
a fixed pressure operation mode with 25Mpa steam
pressure first, when the output of the load decreased to
the 80%, the unit took the sliding pressure operation
mode with 2 regulating valves fully opened. In mode 2,
the unit took the sliding pressure operation mode with 3
regulating valves fully opened beginning from the 100%
THA condition. It can be seen from the picture, the effi-
ciency of mode 1 was higher than mode 2, especially in
the low load region.
4. Conclusions
Basing on the variable condition calculation method of
governing stage and variable conditions theory of turbine,
a new optimization method was put forward for the op-
timal operation of thermal power plant, and we took the
Oriental steam turbine as an example, got the optimal
steam pressure of different load and the optimal sliding
pressure curve. Therefore, operating personnel can adopt
this method, combined with the characteristic of the unit
and the factor of environment, drawing the optimal pres-
sure curves, which can be used as a reference in the prac-
tical operation.
5. Acknowledgements
This work was support ed by the National Basic Research
Program of China (“973” Project) (Grant No. 2012CB-
215203) and the National Natural Science Major Fund
Project (Grant No. 51036002)
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