Engineering, 2013, 5, 197-201
doi:10.4236/eng.2013.51b036 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Optimal Load Dispatch of Gas Turbine Power Generation
Units based on Multiple Population Genetic Algorithm
Hua Xiao, Cheng Yang, Jie Wu, Xiaoqian Ma
College of Electric Power, South China University of Technology, Guangzhou 510640, China
Received 2013
ABSTRACT
In this paper, a multiple population genetic algorithm (MPGA) is proposed to solve the problem of optimal load dis-
patch of gas turbine generation units. By introducing multiple populations on the basis of Standard Genetic Algorithm
(SGA) , con necti ng each po pul ation thr ough i mmigr ant op erato r and pr eservi ng the b est ind ividual s of eve ry gene ratio n
through elite strategy, M PGA can enhance the ef ficiency in obtaining the globa l optimal s olution. I n thi s pa per , MPGA
is applied to optimize the load dispatch of 3×390MW gas turbine units. The results of MPGA calculation are compared
with that of equal micro incremental method a nd AGC instruction. MPGA shows the best performance of optimization
under different load conditions. The amount of saved gas consumption in the calculation is up to 2337.45m3N/h, which
indicates that the load dispa tc h o ptimization o f gas t urb i ne uni t s via MPGA approach can be effective.
Keywords: Gas turbine gener a tion units; Load d ispatch; MPGA; Optimizatio n
1. Introduction
The gas turbine centered gas-steam combined cycle with
high thermal efficiency, low pollution discharge, short
building time and advanced start-stop performances is
well-accepted and fast-growing in electricity generation
industry. In this situation, it is important to improve the
efficiency of gas turbine power plants. Load dispatch is
an essential method to improve the economic efficiency
which makes the load dispatch optimization a key point.
In mathematic s, the problem of optimizing load dispatch
is a complex high-dimensional nonlinear problem con-
taining i nteger and conti nuous variables [1-4].
With the development of computer technology and ar-
tificial intelligence, modern intelligent algorithms show
great advantages in solving load dispatch problems,
which mainly includes simulated annealing, artificial
neural network, ant colony optimization, genetic algo-
rithm and chaos optimization [5,6]. Among them, genetic
algorithm has a fast develo pme nt d ue to fewer li mits a nd
requirements for continuous or differentiable objective
function [7]. Moreover, it shows of strong robustness
characteristics, global optimization and parallel compu-
ting in so lvi ng nonli near pr oble m, whic h ma kes it wid el y
applied in optimal operation of power system.
Therefore, this paper is to focus on proposing an effi-
cient algorithm to solve the the problem of optimal load
dispatch of gas turbine generation units. A multiple pop-
ulation genetic algorithm is adopted to optimize the cal-
culation of load dispatch of a gas-turbine plant in this
paper [8-10], which shows a better find-best ability to
solve the problem.
2. Optimal Load Dispatch Model of Gas
Turbine Generation Units
Binomial expression is usually adopted to fit the charac-
teristic curve of gas consumption of gas-turbine genera-
tion uni ts. The f unction o f gas cons umption ha s the for m
as follow.
2
() ()
i iiiiii
f PaPbPc= ++
(1)
where
,,
iii
abc
are the gas consumption characteristic
coefficients of each unit;
i
f
is the gas consumption of
each unit;
i
P
is the load of each unit. Suppose the whole
plant has n unit s which c an be p ut into op eratio n and the
total load demand is
D
P
. So the goal of the load dispatch
is to minimize the total gas consumption by distributing
the load to each of the n units reasonably according to
their gas consumption characteristics. The load dispatch
model can be described as follows.
1
1
min max
max
1
min
1
min( )
..
n
i ii
i
n
ii D
i
i ii
n
ii D
i
n
ii D
i
FU fP
stUP P
P PP
UP P
UP P
=
=
=
=
= •


=


≤≤


≥


≤


∑
∑
∑
∑
(2)

H. XIAO ET AL.
198
where,
i
U
is the state of unit. 0 and 1 denote closing
down and running of a unit, respectively;
mini
P
is the
minimum load permitted;
maxi
P
is the maximum load
permitted;
D
P
is the total load demand.
It should be noted that the performance of Gas T ur bi ne
Combined Cycle (GTCC) is influenced by the ambient
conditions such as temperature, pressure and so on.
Therefore the performance should have been revised ac-
cording to the ambient consitions. The influence of am-
bient conditions is not discussed in this paper for space
limitations. Generally speaking, the pressure of a certain
place varies so slightly that its influence can be ignored.
And every 1℃depression in inlet air temperature results
in about 0.45% power increase of GTCC and slight vari-
ation in heat consumption rate [11, 12].
3. The Model of Multiple Population Genetic
Algorithm
3.1. Overviews of the Algorithm
Genetic algorithm derives from computer simulation
study of biological systems. It is a self-adaption optimi-
zation algorithm that simulates heredity and evolution of
biology in environment. The basic idea of using genetic
algorithm is expressing the n units as real vectors and
usin g rando m selection or other methods to generate “in-
itial population”. Then individuals in the group of each
generation proceed selection, cross and mutation by cer-
tain probability. According to survival-of-the-fittest me-
chanism, it adopts stepwise iteration method until the
optimal load dispatch results are obtained. Genetic algo-
rithm has less special requirements for objective function.
It can find global optimal solutions in theory. It also can
provide many optional solutions and fits for parallel
processing. Multi-population genetic algorithm (MPGA)
is based on standard genetic algorithm but it has a better
ability of global search and can overcome the problem of
premature convergence compared to standard genetic
algorithm. In MPGA, many populations evolve simulta-
neously which adopt the same methods as standard ge-
netic algorithm (SGA) and realize coevolution through
immigrant operator connecting different populations.
Elite operator is adopted to preserve the best individual
of each generation, which judges the convergence [13,
14]. In all, MPGA mainly includes such steps as: initial
populations, selec tio n, heredity, variation, migration and
artificial selection. The structure of MPGA is shown in
Figure 1.
Figure 1 . Structure diagra m.

H. XIAO ET AL.
199
3.2. Initial Pop ul ati ons
Feasible solutions of load dispatch are coded into chro-
mosomes or individuals. Generally the coding methods
include bit string coding, grey coding, real coding, multi
parameter coding and etc. For load dispatch problems,
the real number coding needs no value conversion and
we can directly carry out genetic manipulation on phe-
notype of solutions. Therefore we choose real coding
method in this paper. Every chromosome is a real vector.
Then, N sets of data representing load dispatch solu-
tions are generated in random. Every set of data is an
individual. MPGA generate t populations and each pop-
ulation consists of N/t individuals. MPGA begins to
evolve with the N data.
3.3. Fitness Function
Fitness function is the function that needs to be opti-
mized. It is the criteria to judge whether an individual is
good or not. Fitness functions are generally converted
from objective functions. For the problem of optimal
load dispatch, the smaller the value of fitness function,
the better the fitness of an individual. For load dispatch
of gas-turbine generation units, the fitness function is
described as follows.
2
11
() ()
nn
ii iiiD
ii
gUf PCUPP
= =
=•+ −
∑∑
(3)
where penalty factor C usually takes a larger value in the
process o f optimizatio n[7]. It will lead to a large value to
the objective function if the solution does not satisfy the
restriction, so that the solution will be eliminated.
3.4. Selecting Operation
Selection is to select those individuals whose fitness
functions values are small to become parents and gener-
ate a new population to rep roduce the indi vidual s of ne xt
generation. The individuals of oversize fitness function
value will be eliminated because of maladjustment.
Selecting operation involves roulette method, cham-
pionship method and etc. In this paper roulette method is
adopted. The probability to enter next generation for
every individual equals to the rate of its own fitness and
the sum of all the individuals’ fitness. The bigger the
fitness value, the greater probability for an individual to
be selected and the greater probability to pass into next
generation are. So the probability of being selected for
individual j is:
1
j
jn
j
j
F
p
F
=
=
∑
(4)
where Fj is the fitness of j, n is the amount of individ uals
in one population.
3.5. Crossover Operation
Cross is to select two individuals from parent generation,
by the crossover of chromosomes, to generate a new
good individual. Real crossover method is used in this
paper. The cross operation method of No. m chromo-
some am and No. n chromosome in position k is de-
scrib ed as fo l l ows.
(1 )
(1 )
mk iknk
nk ikmk
aab ab
aab ab
= −+

= −+

(5)
where b is a random number in region [0, 1].
3.6. Mutation Operation
Mutation is to r andomly select one po int of an individual
from parent generation and mutate the point so as to
generate a random individual. The mutation operation
method of No. j gene of No. i individual is described as
follows[7].
max
min
()(),0.5
()( ),0.5
ij ij
ij ij ij
aa afgr
aa aafgr
+− •≥


=+ −•<


(6)
where amax is the upper bound of gene; aij, amin is the
lower bound of gene aij;
2
2 max
( )(1/)fg rgG= −
, r2 is a
random number, g is current iterations, Gmax is the
maximum evolution time, r is a random number in region
[0,1].
3.7. Elite Strategy
In MPGA, different populations develop through differ-
ent operation parameters to achieve different search tar-
gets. Then it realizes multiple populations’ co-evolution
through the migration operator. The migration operator
compares the best individuals of each population and
substitutes the worst individuals of each population by
globally optimal individual. Then by artificial selection
operator, optimal individuals of each population and
generation are recorded as the criterion of algorithm
convergence[7].
4. Simulation
In [6] the author uses equal micro incremental to optim-
ize the load dispatch of 3×390MW gas turbine genera-
tion u nit s. In t hi s pap er , the g as c ons umpt ion c har acteris-
tic equations from [6] are used for the calculation of the
MPGA.
According to paper [6] the characteristic coefficient of
gas consumption function and bound constraints are
sho wn in Table 1.

H. XIAO ET AL.
200
Table 1 . Gas co nsumption cha racter co efficient a nd limit of
load.
date unit ai bi ci [pmin, pma x]
7.25
7.25
10.26
10.26
1
2
1
3
0.11837
0.12583
0.058427
0.12681
84.002
75.695
117.29
71.863
16725
18274
11904
17860
[234, 390]
[234, 390]
[234, 390]
[234, 390]
Take total load PD=505MW on July 25, 2007 as an
example. Fitness function is described as follow.
33
2
11
() ()
ii iiiD
ii
gUf PCUPP
= =
=⋅+−
∑∑
(7)
The units in operation are just 1# and 2#, so U1=U2=1，
U3=0. Take 100 for the penalty factor C.
2
1111
2
222 2
( )0.1183784.00216725
( )0.1258375.69518274
fPP P
fPPP
= ++

= ++


(8)
In this multiple population genetic algorithm model,
the amount of the populations is set to 10. Cross proba-
bility pc of each population randomly generates between
0.7 and 0.9, Mutation p robab ility p m ra ndoml y generat es
between 0.01 and 0.05. The size of population is set to
40.
Through the optimization of MPGA, the minimum
value of fitness function reaches 90833.33, with the load
of 1# unit 242.84MW and 2# unit 261.46MW. The total
gas consumption is 90771.60m3N/h. The evolution
process of this calculation is sho wn as Figure 2.
In a similar way, all the results of load dispatch calcu-
lation are obtained and compared with results of other
methods , as shown in Ta b l e 2 and Table 3.
0 2 46 810 12
9. 082
9. 083
9. 084
9. 085
9. 086
9. 087
9. 088
9. 089
9. 09
9.091 x 10
4
ev ol ut i onary generati on
v al ue of fitnes s func t i on
Figure 2. Evolution process.
Table 2. Load dispatch results of 1#,2# by different methods On July 25,2007.
Load
MW
P1
(MPGA)
MW
P2
(MPGA)
MW
1#
gas consumption
(MPGA) m3 N /h
2#
gas consumption
(MPGA) m3 N /h
Tot al g as co n sum p-
tion (MPG A) m3 N /h
Equal micro
incremental method
m3 N /h
AGC
m3 N /h
505 242.84 261.46 44104.47 46667.12 90771.60 90870.67 98274.51
542 261.87 279.39 46839.93 49244.56 96084.49 96192.57 98427.58
600 291.00 307.00 51193.27 53371.72 104564.99 104871.10 1 04935.59
660 322.68 336.52 56155.73 57996.59 114152.32 114280.70 117339.50
700 343.26 355.91 59506.76 61153.74 120660.50 120797.70 1 22443.95
Table 3. Lo ad disp a tch r esults of 1#,3# by different methods O n October 26,2 007.
Load
MW
P1
(MPGA)
MW
P3
(MPGA)
MW
1#
gas consumption
(MPGA) m3 N /h
3#
gas consumption
(MPGA) m3 N /h
Tot al g as co n sum ption
(MPGA) m3 N /h
Equal micro
incremental method
m3 N /h
AGC
m3 N /h
491 234.39 256.1 42560.04 43008.05 85563.06 87114.16 88041.39
500 234.10 265 .26 42563.81 43606.07 86169.88 88507.33 87778.98
600 290.00 309 .16 50831.87 50820.74 101652.61 103229.10 103538.45
651 322.78 327 .46 55850.32 54654.14 110504.46 111009.30 119029.83
701 356.27 343.93 61106.92 58492.97 118569.89 118737.80 119029.83

H. XIAO ET AL.
201
According to the results above, MPGA has an obvious
decrease of total gas consumption compared to the equal
micro incremental method and AGC instruction. When
the total load demand is 500MW on October 26, 2007,
the largest amount of gas consumption is obtained of all
the cases listed compared to equal micro incremental
method. The load dispatch results of unit 1# and 3# are
234.10MW and 265.26MW. The gas consumption is
42563.81m3N/h and 43606.07m3N/h respectively. The
total gas consumption is 86169.88m3N/h, which has a
reduction of 2337.45m3N/h compared to equal micro
incremental method and 1609.1m3N/h compared to AGC
instruction. It indica tes that using MPGA to optimize the
load dispatch problem of gas turbine units can improve
the economic effic iency of the units .
5. Conclusions
Cons ide ring t he i mport ance of ga s-fired gener ati on i n the
field of energy, it is necessary to improve the efficiency
of gas t ur b ine powe r p la nt s. Due to the co mplexit y o f gas
turbine oper ation, the require ment for algorithms of good
performance is strong.
Multiple population genetic algorithm is based on
standard genetic algorithm and introduces multiple pop-
ulations into optimal search process. In MPGA, different
populations evolve simultaneously and are connected by
the migration operator. The elite strategy can ensure
message to be exchange d among a ll kind s of the popula-
tions and takes full advantage of knowledge accumula-
tion in evolutiona ry process, so the solutions of the me-
thod are more reasonable.
By establishing fitness function, crossover, mutation
and elite strategy, the theory of MPGA is used to build
up a load dispatch model of the gas turbine generation
units to optimize the load dispatch. Compared with the
results of equal micro incremental method and AGC in-
struction, MPGA shows a decrease of gas consumption.
Therefore, it indicates that MPGA has an advantage in
the optimization of operation of gas turbine units. This
work will contribute to the operation of gas turbine pow-
er plants.
6. Acknowledgment
The authors gratefully acknowledge the projects sup-
ported by “electric power research institute of China
Southern Power Grid” and “the Fundamental Research
Funds for the Central Universities” (Grant No.2009ZM-
0229and No. 2012ZM0015).
REFERENCES
[1] Abdolsaeid Ganjeh Kaviri, Mohammad Nazri Mohd.
Jaafar, Tholudin Mat Lazim. “Modeling and Mul-
ti-objective Exergy Based Optimization of a Combined
Cycle Power Plant Using A Genetic Algorithm,” Energy
Conve r si on an d Managem e nt , 20 12, 58: 94–103.
[2] Narges Kaveshgar, Nathan Huynh, Saeed Khaleghi Ra-
himian. “An Efficient Genetic Algorithm for Solving the
Quay Crane Scheduling Problem,” Expert Systems with
Applications, 2012, 39: 13108–13117.
[3] Ma Xiaoqian, Wang Yi, Liao Yanfen. “Design and Rea-
lization of Power Plant Unit Load Optimization Sch edul-
ing Software Syst em,”. Journal of South China University
of Technology, 2006,34(6): 116-120.
[4] Huang Wenhua, Wang Renming, Liu Fen. “Hybrid Ge-
netic Algorithm Applies on Power Plant Load Scheduling
Problem,” J of China Three Gorges Univ,2006,8(5):
400-403.
[5] Canforag, Dipentam, Espositor, Villaniml. “A Light
Weight Approach for QoS-aware Service Composition,”
Proc. of the 2th International Conference on Service
Oriented Computing. New York, 2004, 232- 239
[6] Peng Xiangang, Zhang Conghui, Wang Xinghua. “Ap-
plication Research of Optimal Load Dispatch on LNG
Power Plant,” Power System Protection and Con-
trol,2010,38(14): 84-87.
[7] Shi Feng, Wang Hui, Yu Lei. “30 Case Analysis of
MATLAB Intelligent Algorithm,” Beijing: BEIHANG
UNIVERSITY PRESS, 2011.
[8] Gong Jiawei, Chen Jun, Deng Haojiang. CA Selection
“Method of Service Composition Based on Improved
Genetic Algorithm,” Micro Computer Applications,
2010 ,31(10): 1-6.
[9] Y. Toh, M. Koizumi, M. Oshima. “Analysis of toxic ele-
ments by MPGA,” Journal of Radioanalytical and Nuc-
lear Chemist ry, 2010, 272 (2): 303-305.
[10] Wen Xianyang. “An improved genetic algorithm adopting
immigration operator,” Intelligent Data Analysis, 2004
8:385-401.
[11] Wen H, Naru la RG, “Econ omics o f Gas Turbine Inlet Air
Cooling for Combined Cycle Plants,” Proceedings of the
American power conference, Chicago, USA;2000. p.
100–105.
[12] Cheng Yang, Zeliang Yang, Ruixian Cai. “Analytical
Method For Evaluation of Gas Turbine Inlet air Cooling
in Combined Cycle Power Plant,” Applied Energy 86
(2009) 84 8–856
[13] Jeffery K. Cochran, Shwu-Min Horng, John W. Fowler.
“A Multi-population Genetic Algorithm to Solve Mul-
ti-objective Scheduling Problems for Parallel Machines,”
Computers & Operations Research, June 2003, 30(7):
1087–1102.
[14] Y. G. Li, M. F. Abdul Ghafir, L. Wang. “Nonlinear Mul-
tiple Points Gas Turbine Off-Design Performance Adap-
tation Using a Genetic Algorithm,”. Journal of Engineer-
ing for Gas Turbines and Power, J ul y 2011, Vol. 133.