Optimal generation for wind-thermal power plant systems with multiple fuel sources

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 11, No. 2, April 2021, pp. 1022~1028
ISSN: 2088-8708, DOI: 10.11591/ijece.v11i2.pp1022-1028  1022
Journal homepage: http://ijece.iaescore.com
Optimal generation for wind-thermal power plant systems with
multiple fuel sources
Phan Nguyen Vinh1
, Bach Hoang Dinh2
, Van-Duc Phan3
, Hung Duc Nguyen4
, Thang Trung Nguyen5
1
Faculty of Cinema and Television, The University of Theatre and Cinema Ho Chi Minh City, Vietnam
2,5
Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang
University, Ho Chi Minh City, Vietnam
3
Faculty of Automobile Technology, Van Lang University, Ho Chi Minh City, Vietnam
4
Faculty of Electrical and Electronics Engineering, Ho Chi Minh City University of Technology, Vietnam National
University Ho Chi Minh City, Vietnam
Article Info ABSTRACT
Article history:
Received May 29, 2020
Revised Sep 10, 2020
Accepted Oct 7, 2020
In this paper, the combined wind and thermal power plant systems are
operated optimally to reduce the total fossil fuel cost (TFFC) of all thermal
power plants and supply enough power energy to loads. The objective of
reducing TFFC is implemented by using antlion algorithm (ALA), particle
swarm optimization (PSO) and Cuckoo search algorithm (CSA). The best
method is then determined based on the obtained TFFC from the three
methods as dealing with two study cases. Two systems with eleven units
including one wind power plant (WPP) and ten thermal power plants are
optimally operated. The two systems have the same characteristic of MFSs
but the valve loading effects (VLEs) on thermal power plants are only
considered in the second system. The comparisons of TFFC from the two
systems indicate that CSA is more powerful than ALA and PSO.
Furthermore, CSA is also superior to the two methods in terms of faster
search process. Consequently, CSA is a powerful method for the problem of
optimal generation for wind-thermal power plant systems with consideration
of MFSs from thermal power plants.
Keywords:
Cuckoo search algorithm
Multiple fuel sources
Thermal power plant
Total fossil fuel cost
Wind power plant
This is an open access article under the CC BY-SA license.
Corresponding Author:
Thang Trung Nguyen
Power System Optimization Research Group
Faculty of Electrical and Electronics Engineering
Ton Duc Thang University
19 Nguyen Huu Tho street, Tan Phong ward, District 7, Ho Chi Minh City, Vietnam
Email: nguyentrungthang@tdtu.edu.vn
1. INTRODUCTION
The main text format consists of a flat left-right columns on A4 paper (quarto). The margin text
from the In power system operation, the main target of operating thermal power plants (TPPs) is to determine
the most appropriate active power generation of each thermal power plant (TPP) to reduce TFFC as much as
possible [1-3]. The fact that fossil fuel sources (FFSs) will be exhausted in future and its cost will increase.
So, the optimal use plan of the fuels can enable to last the use time of the sources and power system will be
more stable and work with high reliability. The purpose of using FFSs with lower cost and long time is
encouraged in power systems [4, 5].
The problem of minimizing TFFC from TPPs was concerned in many recent decays. This problem
was called economic load dispatch (ELD) and mathematical modeled by the presence of objective function
and constraints such as limits of generation and active power balance [6-8]. Some first ELD problems

Int J Elec & Comp Eng ISSN: 2088-8708 
Optimal generation for wind-thermal power plant systems with multiple fuel sources (Phan Nguyen Vinh)
1023
considered only single fuel source (SFS) for each TPP and only the minimum and maximum power generation of
the sole SFS was considered. More complicated problems considered total power loss in transmission lines and
ignored other complicated constraints regarding TPPs such as reserve fuel source limits and VLEs [9, 10].
There many algorithm types have been applied for the problem with SFS such as deterministic algorithms
and metaheuristic algorithms. Among the two algorithm groups, the second group was more widely and
successfully applied. The first algorithm group consists of Lagrange method [11], Newton method [12, 13],
dynamic programming [14] and gradient search method [15]. The second group includes PSO [16-17],
genetic algorithm (GA) [18-20], differential evolution (DE) [21], fractal search algorithm (FSA) [22],
teaching learning optimization algorithm (TLOA) [23], bee colony algorithm (BCA) [24], crow optimization
algorithm (COA) [25] and hybrid algorithm (HA) [26]. Deterministic methods had an advantage of using a
low iteration number and reaching the same results for different implementations. However, they suffering
from taking partial derivative with respect to control variables before executing an iterative algorithm. Hence,
they could not be applied for solving ELD problems containing non-differentiable functions. On the contrary,
metaheuristic algorithms did not suffer from the shortcoming of the deterministic algorithms and they could
deal with nondifferentiable function and complicated problem. But the metaheuristic algorithms had the same
disadvantages of falling into local search zones with local optimal solution or a nearby global solution with
worse quality than the best solutions.
As ELD problem is more complicated by considering much complicated fossil fuel cost function
(FFCF) and constraints. VLEs were considered during power increasing or decreasing process of thermal power
plants [26]. A complicated FFCF considered MFSs for burning fuel and driving steam or gas turbines [27].
The combination of VLEs and MFSs was implemented and the solution of the problem was found in the
study [28]. The model with both VLEs and MFSs is the most complicated FFCF in ELD problems. However,
all the considered problems did not consider renewable energies like wind power plants or photovoltaic
systems. Nowadays, wind power plants (WPPs) can produce a very high power and supply electricity to
loads via transmission power network. There were studies combining the wind power plant and thermal
power plants [29-30] for determining TFFC minimization. In the study [29], wind velocity was modeled by a
probability function and its power was dependent on the function. Thermal power plants were in charging of
producing a remaining power after wind power plant can supply its power to loads. The study mainly
introduced the change of wind velocity or considered the uncertainty of wind velocity rather than minimizing
total fuel cost of TPPs. In the study [30], PSO and bat algorithm (BA) were applied to optimize power
generation for TPPs and WPPs. Two systems with 7 plants and 16 plants using SFS were employed in the
study. The demonstration was that power generation from WPP could reduce TFFC of all TPPs and BA was
superior to PSO in terms of reducing TFFC.
In this paper, WPPs and TPPs are combined to produce electricity to loads in which MFSs is
considered in TPPs to produce electricity. In addition, the objective function becomes more complicated
since VLEs is considered during the generation process of the TPPs. Two systems with eleven plants
including one WPP and ten TPPs are taken into account. For reaching the optimal generation of the plants,
three methods including antlion algorithm (ALA) [31], particle swarm optimization (PSO) [32] and cuckoo
search algorithm (CSA) [33] are implemented. The novelty and contribution of the paper is as follows:
 Combine WPPs and TPPs where TPPs consider MFSs and VLEs
 Compare the performance of PSO, ALA and CSA
 Provide optimal solutions for reducing TFFC for the combined system
Other parts of the paper are as follows: Section 2 describes objective function and constraints of the
combined system. Section 3 present Cuckoo search algorithm. Section 4 shows the result comparisons
between CSA and two other methods. Section 5 shows the conclusions.
2. THE PROBLEM FORMULATION
2.1. Objective function of the ELD problem with single fuel option
In optimal operation of the combined system, power generated by WPPs and TPPs is supplied to
loads in which the cost of power from WPPs is supposed to be a constant and it is much less than the cost of
power from TPPs. So, the objective is to use all power from WPPs while the cost from TPPs. The objective is
as follows:
Minimize

 
1
( )
Nt
t t
t
TFFC FFC P (1)
where FFCt is the fossil fuel cost of the tth TPP; Pt is power generation of the tth TPP; Nt is the number of TPPs.

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 11, No. 2, April 2021 : 1022 - 1028
1024
As MFSs is considered, FFCt of the tth TPP is represented as follows:
    

   

 

    

2
1 1 1 ,1,min ,1,max
2
2 2 2 ,2,min ,2,max
2
, ,min , ,max
( )
...
t t t t t t t t
t t t t t t t t
t t
tM t tM t tM t M t t M
a P b P c for P P P
a P b P c for P P P
FFC P
a P b P c for P P P
(2)
where M is the number of fuels; Pt,M,min and Pt,M,max are the lower bound and upper bound of power generation
of the tth TPP for the Mth fuel.
As considering the VLEs in the generation process, FFCt of the tth TPP is represented as follows:
 
 
 
       
       

       
2
1 1 1 1 1 ,min ,1,min ,1,max
2
2 2 2 2 2 ,min ,2,min ,2,max
2
,min , ,min ,
sin( ( ))
sin( ( ))
( )
...
sin( ( ))
t t t t t t t t t t t t
t t t t t t t t t t t t
t t
tM t tM t tM tM tM t t t M t t M
a P b P c P P for P P P
FFC P






 ,max
(3)
The FFCt without and with VLEs is plotted in Figure 1.
Figure 1. FFC with and without VLEs
2.2. Power generation of wind turbines
Wind turbines can produce and supply electricity to loads but their stability is not certain due to the
influence of wind velocity. If wind velocity is high, power generation of the wind turbines is high and vice
versa. The generation of the wind turbines is determined as follows: [29]:
 


  

 

  



,
,
0
0
w rate
w
w rate
if V Vi
V Vi
WP if Vi V Vr
WP Vr Vi
WP if Vr V Vo
else
(4)
where WPw and WPw, rate are Power generation and rated power generation of the wth WPP; V and Vr, are
speed of wind, rated speed of wind at the wth WPP; and Vi and Vo are the minimum and maximum speed of
wind for power generation.
2.3. Constraints of the problem
2.3.1. Constraints of WPPs
Wind power is dependent on values of velocity. So, as the velocity has the lowest value, the power
is minimum and as the velocity has the highest value, the power is maximum. As a results, limits of wind
power are as follows:

1025
  
,min ,max
; 1,...,
w w w
WP WP WP w Nw (5)
where WPw is power generation of the wth WPP; WPw,min and WPw,min are the lower bound and upper bound
of power generation of the wth WPP; and Nw is the number of WPPs.
2.3.2. Constraints of TPPs
Active power generation limits: In the problem, the fossil fuel sources at TPPs are supposed to be
plentiful and unlimited. However, the power generation of each TPP is constrained due to the limits of
gas/steam turbines and generators. The generation restriction is described as follows:
 
,min ,max
t t t
P P P (6)
In the constraint, Pt,min and Pt,max are the minimum and maximum active power generation of the tth TPP.
Because the TPPs use MFSs, Pt,min and Pt,max are, respectively, equal to Pt,1,min and Pt,M,max, which are shown in
(2) and (3).
2.3.3. Constraints of system
The power system constrains the balance of power between supply side and consume side. If the
balance is achieved, the frequency of the system can be stable and system is working stably. The supply side
consists of TPPs and WPPs where consume side is load demand. The balance constraint is as follows:
 
 
 
1 1
Nt Nw
t w demand
t w
P WP P (7)
where Pdemand is the active power of all loads in the system.
3. CUCKOO SEARCH ALGORITHM (CSA)
3.1. Lévy flights
Lévy flights is a power search technique of CSA thank to the use of an infinite step size by using
Lévy distribution. The technique is used to update new solutions as shown in the following equation:
. ; 1,...,
new
s s po
Sol Sol Levy s N

   (8)
where ε is scale factor; Levy is Lévy distribution [33]; and Npo is population size.
3.2. Mutation technique
Mutation technique is employed in CSA to update new solutions for the second time. However, the
technique does not update the whole population but it selects solutions based on the comparison condition
between a random number cs and mutation factor MF. The technique is shown as follows:
1 2
.( )
s rp rp s
new
s
s
Sol c Sol Sol if c MF
Sol
Sol otherwise
  


 


(9)
where Solrp1 and Solrp2 are picked solutions by using randomization.
4. NUMERICAL RESULTS
In this section, PSO, ALA and CSA are executed for reaching the optimal solutions of two test
systems. Each method is run fifty trials on Matlab platform and a PC with processor of 2.2GHz and RAM of
4.0GB. The detail of simulation result is presented in the two following sections.
4.1. The first wind-thermal power plant system
In this section, the data of ten TPPs with MFSs and without VLEs is taken from [34] while the data
of WPP is taken from [35]. The rated speed of wind and the rated power of the WPP is 15 m/s and 120 MW.

 ISSN: 2088-8708
1026
The wind speed at the scheduling hour is 14 m/s and the power generation of the WPP is 108MW.
The TPPs and the WPP supply electricity to a 2400 MW load. In order to get results for PSO, ALA and CSA,
Npo and Nit (which is the number of iterations) are respectively set to 20 and 100 for PSO and ALA, and 10
and 100 for CSA. The results are summarized in Figures 2 and 3. Figure 2 shows that CSA can reach the
smallest cost with $437.7 while PSO is the worst method with the highest cost of $441.4. Similarly, CSA and
PSO are the best and the worst methods with the smallest and highest maximum cost. The comparisons of
mean cost of 50runs can indicate the best stability of CSA since that of the method is the smallest. Figure 3
can confirm the best stability of CSA one more time since all runs of CSA have much less cost than those of PSO
and ALA.
Figure 2. Comparisons of result for the first system Figure 3. TFFC comparisons of 50 trial runs for the
first system
4.2. The second wind-thermal power plant system
In this section, the data of ten TPPs with MFSs and VLEs is taken from [35] while the data of WPP
is taken from [36]. The rated speed of wind and the rated power of the WPP is 15 m/s and 80 MW. The wind
speed at the scheduling hour is 14.5 m/s and the power generation of the WPP is 76MW. The TPPs and the
WPP supply electricity to a 2700 MW load.
For running PSO, ALA and CSA, Npo and Nit are respectively set to 20 and 200 for PSO and ALA,
and 10 and 200 for CSA. The Figures 4 and 5 show the best performance of CSA because CSA can reach the
smallest minimum, mean and maximum cost. ALA is the second best method whereas PSO is still the worst
performance method. TFFC of 50 runs from CSA is approximately lied on a line while that of PSO and ALA
have the high fluctuations. The analysis can lead to a conclusion that CSA is superior to PSO and ALA for
the system with MFSs, VLEs and wind power plants. Optimal solutions of the two systems are shown
Table A1 in Appendix.
Figure 4. Comparisons of result for the second
system
Figure 5. TFFC comparisons of 50 trial runs for the
second system

1027
5. CONCLUSION
In this paper, PSO, ALA and CSA solved two wind-thermal power plant systems where TPPs used
multiple fuel sources to generate electricity to loads. The two system had the same number of power plants,
ten TPPs and one WPP in which the first system did not consider valve loading effects on TPPs during the
power increase or decrease process but the second system did. The result comparison indicated that CSA was
more robust than PSO and ALA in reaching the optimal power generation and the search stability. CSA could
reach the smallest minimum, mean and maximum cost among three executed methods. In addition, the cost
from fifty runs of CSA was approximately lied on a line without fluctuations whilst the cost of PSO and ALA
had high fluctuations. Consequently, CSA is recommended as a powerful search algorithm for the optimal
generation of wind-thermal power plant systems.
APPENDIX
Table A1. Optimal generation of the two systems found by PSO, ALA and CSA methods
Pt (MW)
System 1 System 2
PSO ALA CSA PSO ALA CSA
P1 168.9 182.7 179.8 207.8 195.3 208.4
P2 208.6 197.3 196.8 303.2 273.6 271.3
P3 220.9 239.9 239.6 265.0 237.6 237.5
P4 220.2 232.2 230.4 298.8 244.9 270.0
P5 225.7 214.1 223.7 235.8 244.4 235.9
P6 223.5 229.2 229.8 295.2 290.9 278.1
P7 261.7 236.2 235.1 234.0 234.4 238.5
P8 224.2 230.0 229.1 330.4 394.7 409.6
P9 327.0 300.8 306.5 208.8 276.6 262.8
P10 211.1 229.5 221.2 244.9 231.7 211.8
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