Journal of Power and Energy Engineering, 2015, 3, 431-437
Published Online April 2015 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2015.34058
How to cite this paper: Cui, L.-L., L i, Y.-F. and Long, P. (2015) Study on Coal Consumption Curve Fitting of the Thermal Pow-
er Based on Genetic Algorithm. Journal of Power and Energy Engineering, 3, 431-437.
http://dx.doi.org/10.4236/jpee.2015.34058
Study on Coal Consumption Curve Fitting
of the Thermal Power Based on
Genetic Algorithm
Le-Le Cui, Yang -Fan Li, Pan Long
State Grid MianYang Electric Power Supply Company, MianYang, Sichuan, China
Received January 2015
Abstract
Coal consumption curve of the thermal power plant can reflect the function relationship between
the coal consumption of unit and load, which plays a key role for research on unit economic oper-
ation and load optimal dispatch . Now get coal consumption curve is generally obtained by least
square method, but which are static curve and these curves remain unchanged for a long time, and
make them are incompatible with the actual operation situation of the unit. Furthermore, coal
consumption has the characteristics of typical nonlinear and time varying, sometimes the least
square method does not work for nonlinear complex problems. For these problems, a method of
coal consumption cu rve fitting of the thermal power plant units based on genetic algorithm is
proposed. The residual analysis method is used for data detection; quadratic function is employed
to the objective function; appropriate parameters such as initial population size, crossover rate
and mutation rate are set; the unit’s actual coal consumption curves are fitted, and compa ring the
proposed method with least squares method, the results indicate that fitting effect of the former is
better than the latter, and further indicate that the proposed method to do curve fitting can best
approximate known data in a certain significance, and they can real-tim ely reflect the interde-
pendence between power output and coal consumption.
Keywords
Thermal Power Plant, Coal Consumption Curve, Unit, Least Squares Method, Genetic Algorithm,
Curve Fitting, Nonlinear Problems
1. Introduction
The structure of electric power in China, by the end of march 2013, the total installed power generating capacity
of the whole country reached 1,123,000,000 kw, the thermal power installed capacity has reached 825,000,000
kw, accounting for 73.52% of the total installed capacity, coal consumption of thermal power plants is growing,
coal energy consumption accounted for the total energy consumption of about 67%. In order to realize energy
saving and emission reduction and low carbon efficient production mode, it needs to optimal load distribution

L.-L. Cui et al.
432
for thermal power plant unit, but realize optimal load distribution the key step is accurate fitting of the unit coal
consumption curve.
At present, coal consumption curve of the thermal power plant is usually obtained by the performance para-
meters which are provided by the manufacturer, or thermal test data, and these curves remain unchanged for a
long time. However, the unit in the actual operation will be affected by the mode of operation, coal quality, de-
vice status, the technical level of operators and other factors, and make these curves have a great differences
with the actual operation situation of the unit. According to this situation, it needs to refit the coal consumption
curve in actual operation. The method of curve fitting most are using least squares on currently, but it is difficult
to solve complex nonlinear problems by this method, sometimes these curves cannot meet requirements of the
actual applications.
Genetic algorithm, or GA for short [1]-[4], is a global optimization algorithm based on selection and natural
genetic, which developed from evolution theory and genetic theory. Compared with the least square method, the
main characteristic of genetic algorithm is not depend on gradient information, especially suited to be used deal
with complex and nonlinear problems which are difficult to be solved by traditional search methods, it makes up
for its shortcomings of the least square method. However, the data of the thermal power plant is huge, strong
nonlinear, this method is used to fit coal consumption curve of the thermal power plant in this paper, and com-
paring the proposed method with least squares method.
2. Data Processing
Since this paper is aimed at nonlinear static system of the coal consumption curve, that is to say it needs to the
unit work on stable state, and use the static data of the unit to model. All the tested unit data are derived from the
bottom of the DCS control system, and because these date are effected by unit operating mode and environmen-
tal conditions, there are errors and noise for the collected data in DCS, if modeling directly use the data in DCS,
it will cause great interference for coal consumption curve, meanwhile it is meaningless if study on coal con-
sumption of the unit under the unit operating exist fluctuation. Therefore, it needs to process original data before
modeling.
There are two main kinds of interference for the data from the DCS: One is the random interference at the
time of data collection, it can be removed by filtering method; the other is jump point that fluctuation is very
conspicuous. In this paper, the method of data detection is residual analysis. Collected data are set to
x
, the da-
ta after process is
y
,
∆
, is the limit value of data changing, under the same sample period, the rate of change
can be judged by the absolute value of the difference between two successive sampling data.
()xk
is the kth
sampling value, to calculate
( )(1)xk xk−−
, if
( )(1)xk xk−− <∆
, there is not outlier,
() ()yk xk =
; if
( )(1)xk xk−− ≥∆
, there may be outliers, we can take another point
( 1)xk+
, if
(1)( )xk xk+ −≤∆
, and
there are same changing trend, we think there is disturbance. Let
()( 1)() y kax kbx k= −+
, where
a
and
b
are weights, and
, (0,1)ab ∈
; if there are opposite trend, we think
()xk
is jump point. Let
( )(1)(1)y kax kbx k=−+ +
; if
(1)( )xk xk+ −≥∆
, we think there are outliers, they should be removed.
3. Coal Consumption Curve Fitting of the Thermal Power Based on Genetic
Algorithm
Now it needs to fit coal consumption curve of the unit for a thermal power plant with 4 × 328.5 MW, operation
energy consumption data of the each unit, as in Table 1 below [5]. In fact, in reality project, just need quadratic
curve then it can meet requirements of the accuracy. Therefore, t he objective function set to the following qua-
dratic function:
2
12 3
F xxPxP=+⋅+ ⋅
, where
123
,,xxx
is the parameters that needs to estimate.
Program object function for the 1# unit, and be saved with the filename ga_curfit.m to Matlab directory.
1# unit fitting results as shown in Figure 1.
The same method can be used to fit coal consumption curve of the other three units, and the fitting results as
shown in Figures 2-4.
Coal consumption curve equations of each unit are fitted by genetic algorithm, which are:
2
1 11
0.0002857929064713220.15229546322378449.7469230797674F PP= ++
2
2 22
0.0004716869196219790.17577929964833743.0063408707241F PP=++

L.-L. Cui et al.
433
Table 1. Power output-coal consumption table.
1# unit 2# unit 3# unit 4# unit
Power
output
(MW)
Coal
consumption
(t/h)
Power
output
(MW)
coal
consumption
(t/h)
Power
output
(MW)
coal
consumption
(t/h)
Power
output
(MW)
coal
consumption
(t/h)
189.85 90.00 170.00 85. 00 174.00 1 01.62 163.70 103.00
217.59 95.00 190.00 93. 00 192.92 1 07.96 192.96 108.00
220.00 96.00 205.92 100.00 210.83 113.02 208.15 111.00
240.00 104.00 220.00 107.00 220.00 114.00 222.96 120.00
250.00 105.00 230.00 112.00 222.92 120.00 232.22 126.00
260.00 111.00 240.00 107.00 245.00 128.14 244.81 128.00
271.86 112.00 250.00 117.00 253.39 125.46 252.96 130.00
280.00 116.00 260.00 123.00 277.08 147.91 260.00 137.00
290.00 114.00 277.00 128.00 290.83 153.02 271.10 145.00
300.00 123.00 296.00 131.00 300.00 156.05 284.07 151.00
310.00 122.00 300.00 137.00 312.08 158.00 300.00 156.00
315.00 126.00 318.00 148.00 320.00 159.00 315.00 160.00
320.00 130.00 320.00 150.00 325.00 164.31 320.00 169.20
Figure 1. Coal consumption curve of unit 1.
2
33
0.0005028912845690650.184153363892838 52.6593691773213PP++
2
4 44
0.001012822443036500.0599965442023200 83.1580882142092F PP= −+
4. Coal Consumption Curve Fitting of the Thermal Power Based on Least Square
Method
For comparison purposes, methods and results of least squares fitting curve are given.
180 200 220 240 260 280 300 320
85
90
95
100
105
110
115
120
125
130
Power output P（MW）
Coal consumption F （ t /h）
Coal consumption curve of unit 1
Original data
Coal consumption curve

L.-L. Cui et al.
434
Figure 2. Coal consumption curve of unit 2.
Figure 3. Coal consumption curve of unit 3.
Figure 4. Coal consumption curve of unit 4.
160 180200220 240260280300 320
80
90
100
110
120
130
140
150
Power output P（MW）
Coal consumption F （ t /h）
Coal consumption curve of unit 2
Original data
Coal consumption curve
160 180 200 220 240 260 280 300 320 340
100
110
120
130
140
150
160
170
Power output P（MW ）
Coal consumption F （
t /h）
Coal consumption curve of unit 3
Original data
Coal consumption curve
160 180 200 220 240 260 280 300 320
90
100
110
120
130
140
150
160
170
Power output P（MW）
Coal consumption F （ t /h）
Coal consumption curve of unit 4
Original data
Coal consumption curve

L.-L. Cui et al.
435
Set
01
, ,...,
n
ϕϕ ϕ
are the functions of linear independence on
[,]Cab
, and let
01
{ ,,...,}
n
span ϕϕ ϕ Φ=
. Set
()fx
be a given discrete function on
1m+
nodes which are
01
...
m
ax xxb=< <<=
, least squares method is
find
*
s∈Φ
to make
*2 2
00
()[()()]min()[() ()]
mm
jjjjj j
s
jj
x fxsxx fxsx ρρ
∈Φ
= =
−= −
∑∑
, where
()x ρ
is weight func-
tion on
[,]ab
. Then we call
*()sx
as the least squares solution for
()fx
which on
1m+
nodes, also called
as the least squares fitting [6].
According to above principle, the coal consumption curve which is used by quadratic polynomial is:
2
FmPtP k= ++
(1)
where
F
—coal consumption of the unit power supply (t/h);
P
—generation power of the unit (MW);
,,mtk
—Energy consumption characteristic parameters.
Use least squares method to determine the binomial coefficient
,,mtk
. Set there are n experiments discrete
data points (
i
F
,
i
P
)
Let
22
1
()
n
ii i
i
JmPtPk F
=
=+ +−
∑
, to make the
J
minimum, and then let:
22
1
2( )0
n
iii i
i
JP mPtPkF
m=
∂=+ +−=
∂
∑
(2)
2
1
2() 0
n
ii ii
i
JP mPtPkF
t
=
∂=+ +−=
∂∑
(3)
2
1
2() 0
n
ii i
i
JmPtPk F
k
=
∂=+ +−=
∂
∑
(4)
After put in order we can get :
4 322
1 111
()()() ()
n nnn
ii iii
i iii
PmP tPkFP
== ==
++ =
∑ ∑∑∑
(5)
32
11 11
() ()()( )
nn nn
iiiii
ii ii
PmPtP kFP
=== =
++=
∑∑ ∑∑
(6)
2
11 1
()( )
nn n
ii i
ii i
PmPtnkF
= ==
+ +=
∑∑ ∑
(7)
Coal consumption parameters
,,mtk
can be obtained by solve the linear equations.
Using least square method to fit coal consumption curve, and the results as shown in Figures 5-8.
Coal consumption curve equations of each unit are fitted by least square method, which are:
2
11 1
0.000580241018610.00488999810271 67.81118406745974 FPP= ++
2
22 2
0.00043327714310.1952337909269940.62061826123973FP P=++
2
33 3
0.00041365759690.22857182978488 47.30730098461958FP P=++
2
444
0.001021187304230.06561283911416 84.01621840672190FPP= −+
5. Fitting Error Analysis
The curve fitting is good or not judged by SSE (sum of square error), the sum of square error are obtained by
these two algorithms as shown in Table 2.
Notes: SSE1 is sum of square error based on genetic algorithm and SSE2 is sum of square error based on least
square method in the table.
From the table we can see that the error based on genetic algorithm is significantly less than least square me-
thod for unit 1, 2 and 3, and the error of both methods are very close for unit 4. Show that fitting effect based on

L.-L. Cui et al.
436
Figure 5. Coal consumption curve of unit 1.
Figure 6. Coal consumption curve of unit 2.
Figure 7. Coal consumption curve of unit 3.
180 200 220 240 260280 300 320
85
90
95
100
105
110
115
120
125
130
Power output P(MW)
Coal consumption F(t/h)
Coal consumption curve of unit 1
Original data
Coal consumption curve
160 180200 220 240 260 280300 320
80
90
100
110
120
130
140
150 Coal consumption curve of unit 2
Power output P(MW)
Coal consumption F(t/h)
Original data
Coal consumption curve
160 180 200 220 240 260 280 300 320 340
90
100
110
120
130
140
150
160
170
Power output P(MW)
Coal consumption F(t/h)
Coal consumption curve of unit 3
Original data
Coal consumption curve

L.-L. Cui et al.
437
Figure 8. Coal consumption curve of unit 4.
Table 2. Error sum of square.
1# unit 2# unit 3# unit 4# unit
SSE1(
2
(/ )th
)
SSE2(
2
(/ )th
)
43.17
44.88 95.30 95.32 134.25 134.90 83.88 83.82
genetic algorithm is significantly better than based on least square method, the original data are more fall on the
curve or distributed around the curve, and more truly reflect the relationship between coal consumption and
power output.
6. Conclusion
The experiments show that it is practicable use genetic algorithm to fit coal consumption curve. From the fitting
results can be seen that the fitting curve can approximate the original data points, and it can better predict the
coal consumption trend. But genetic algorithm also has its shortcomings, premature convergence, non direction-
al genetic operator, and every time the search results are not fixed, these problems are expected next step to be
improved.
References
[1] Wu, J., Ma, X. a nd Hou, R. (2011) Optimization of APF LCL Output Filter Based on Genetic Algorithm. Transactions
of China Electrotechnical Society, 26, 159-164.
[2] Ma, X.-F. and Cui, H.-J. (2011) An Improved Genetic Algorithm for Distribution Network Planning With Distributed
Generation. Transactions of China Electrotechnical Society, 26, 175-181.
[3] Wang, X.-P. (2002) Genetic Algorithms—Theory, Application and Software Implementation. Xi’an Jiaotong Univer-
sity Press.
[4] Zhou , W.-Y., Lü, F.-P. an d Li, H. (2013) Method for the Combination of Power System Operation Mode Based on
Genetic Algorithm. Power System Protection and Control, 41, 51-55.
[5] Zhao, L.-Q. (2008) Research on the Plant’s Optimal Unit Co mmitment. North China Electric Power University.
[6] Liu, X. (2007) Research on the Plant’s Optimal Load Dispatch and Unit Commitment of Thermal Power Plant Based
on Genetic Algorithm. North China Electric Power University.
160 180 200 220240 260 280 300320
100
110
120
130
140
150
160
170
Power output P(MW)
Coal consumption F(t/h)
Coal consumption curve of unit 4
Original data
Coal consumption curve