Design of Optimization Methodology for Economic Dispatch of Thermal Generating Units

Abstract

The demand for power supply is increasing day by day to fulfill the energy consumption of people. Renewable and non-renewable energy resources are used for power generation. In thermal units of power generation, the important thing is that efficient operational policies are required in these units, as increasing the power generating units is not only the solution to meet the load demands but essential to optimize the existing generating units effectively. Economic dispatch (ED) generating units are operating economically to fulfill the load demand and losses along with different practical constraints. In order to overcome the non-linear complex problems in power economic dispatch of thermal generating units, an advanced modified Levi Flight Firefly Algorithm (MLFA) is employed on various IEEE standard test systems for validation. The proposed technique/algorithm has been applied on 6, 13, 15, and 20 unit test systems considering various system constraints including valve loading effect, upper and lower limits, transmission losses, etc. In this research, an objective function is formulated on the flashing behavior of fireflies which optimizes the problems. The MATLAB software is used for the implementation of this algorithm. In the end, statistical results are compared with other existing algorithms which revealed that the solution is effectively converged, and the cost is less as compared to other algorithms.

Full text

2022 5th International Conference on Energy Conservation and Efficiency (ICECE)
1
Design of Optimization Methodology for
Economic Dispatch of Thermal Generating Units
Muhammad Tanveer Riaz
Dept. of Mechanical
Mechatronics and
Manufacturing Engineering,
UET Lahore, Faisalabad
Campus Faisalabad, Pakistan
tanveer.riaz@ieee.org
Wajahat Saleem Hashmi
School of Electrical
Engineering, The University of
Faisalabad,
Faisalabad 38000, Pakistan
wajahat44@gmail.com
Saeed Ahmad
Department of Mechanical
Engineering, University of
Sargodha,
Sargodha, Pakistan
saeed.aslam@uos.edu.pk
Sabir Husnain
Dept. of Mechatronics and
Control Engineering, UET
Lahore, Faisalabad Campus,
Faisalabad, Pakistan
sabirhasnain577@gmail.com
Hassan Mujtaba
Dept. of Mechanical
Mechatronics and
Manufacturing Engineering,
UET Lahore, Faisalabad
Campus Faisalabad, Pakistan
hassan.muj@uet.edu.pk
Haider Ali
Dept. of Mechatronics and
Control Engineering, UET
Lahore, Faisalabad Campus,
Faisalabad, Pakistan
haiderali.mechatron@gmail.com
Shahid Atiq
Dept. of Electrical
Engineering, University of
Engineering & Technology,
Faisalabad Campus,
Faisalabad, Pakistan
engineershahid356@gmail.com
Muhammad Mustafa Qureshi
Dept. of Textile Engineering, UET
Lahore, Faisalabad Campus,
Faisalabad, Pakistan
qmuhammadmustafa@gmail.com
Abstract— The demand for power supply is increasing day by day
to fulfill the energy consumption of people. Renewable and non-
renewable energy resources are used for power generation. In
thermal units of power generation, the important thing is that
efficient operational policies are required in these units, as
increasing the power generating units is not only the solution to
meet the load demands but essential to optimize the existing
generating units effectively. Economic dispatch (ED) generating
units are operating economically to fulfill the load demand and
losses along with different practical constraints. In order to
overcome the non-linear complex problems in power economic
dispatch of thermal generating units, an advanced modified Levi
Flight Firefly Algorithm (MLFA) is employed on various IEEE
standard test systems for validation. The proposed
technique/algorithm has been applied on 6, 13, 15, and 20 unit test
systems considering various system constraints including valve
loading effect, upper and lower limits, transmission losses, etc. In
this research, an objective function is formulated on the flashing
behavior of fireflies which optimizes the problems. The MATLAB
software is used for the implementation of this algorithm. In the
end, statistical results are compared with other existing algorithms
which revealed that the solution is effectively converged, and the
cost is less as compared to other algorithms.
Keywords— Thermal Generating Units, Economic Dispatch,
Levi Flight Firefly Algorithm, Modified Levi flight Firefly
Algorithm, Genetic Algorithm
I. INTRODUCTION
The hot issue in the energy sector is power generation,
transmission, and distribution to end users. Economic dispatch
(ED), which raises the system's complexity, is also a major
problem in the power industry. Its aim is to optimize power
generation to achieve satisfactory results in terms of load
demands at a low cost [1]-[3]. Since fuel prices fluctuate on a
daily basis, dealing with this type of problem has become
increasingly important. Since fuel prices fluctuate on a daily
basis, the need for optimization for cost-effective dispatch is
growing by the day [4]. As a result, the primary focus of this
research is on proper economic planning. Without a doubt, the
number of power generation units is growing every day, meeting
the demands of the load, but there is one issue that must be
addressed here that is cost [5]. Its installation costs are high. As
a result, reliable and cost-effective operation of existing
generation units is critical. As compared to other types of
electrical power generation systems, the hydroelectric power
system is the cheapest [6]-[8]. These systems are not only used
to meet people's load demands, but thermal generation units are
also installed to meet established energy demands [9]. ED deals
with generation allocation problems in which existing
generating units work in a cost-effective manner to satisfy load
demands and overcome system losses to the greatest extent
possible under a variety of realistic constraints. These
constraints, such as generator limits, valve loading effect,
prohibited areas, and so on, result in non-linear and non-convex
optimal problems in the system [10]-[12]. The input-output
curve of units must be accurately shown for proper economic
dispatch problem formulation. In the simplest case of a quadratic
function, the convex curve is formed. When some functional
constraints, such as valve loading effect, transmission losses, and
POZ, are taken into account, a non-linear and non-convex curve
emerges [13]-[15]. Because of reducing energy sources, the
generation costs, and the load demand, optimal economic
dispatch is critical. Stochastic algorithms have been used to
solve linear power economic dispatch problems for decades, but
due to the existence of non-linearity in the method, these
algorithms are no longer as efficient [16]. Since traditional
methods such as the gradient method, reduced gradient method,
and lambda iteration are incapable of solving non-linear and
non-convex problems, they can be used to solve convex ED
problems [17]-[20]. A dynamic approach can solve the non-
convex problem, but it has drawbacks as the problem size
increases [21]. Evolutionary techniques and artificial
intelligence approaches, such as Genetic Algorithm (GA),
Evolutionary Programming (EP), Differential Evolution (DE),
and Particle Swarm Optimization (PSO), are used to solve non-
linear economic dispatch problems [22]-[25]. The Levi Flight
Firefly algorithm is one of the most recent Genetic algorithms
for solving nonlinear power economic dispatch optimization
problems [26]-[28]. The following are the objectives of this
proposed research work.
978-1-7281-8680-1/22/$31.00 ©2022 IEEE

2022 5th International Conference on Energy Conservation and Efficiency (ICECE)
• Economic load dispatch problem followed by clear
description & its impacts on power system
• • Development of a Firefly algorithm for solving the ED
Problem.
• • Development of an LFA algorithm for solving the ED
problem.
• • To carry out a cost-effective load dispatch when taking into
account a variety of realistic constraints.
• The proposed algorithm will be applied to various IEEE
standard test systems.
• A comparison of the proposed algorithm's overall generating
cost to that of other available algorithms.
II. MATERIAL AND METHODS
The Levi Flight Firefly algorithm (LFA) is a genetic
algorithm that is used to solve economic power dispatch
problems. A updated version of LFA is used in this study. The
proposed modified Levi flight firefly algorithm (MLFA) has
been tested on three, six, thirteen, fifteen, and twenty-unit test
systems in order to assess its accuracy. When the proposed
algorithm is compared to other approaches, the results show that
the proposed algorithm performs better in terms of efficiency
and effectiveness. Fireflies spontaneously emit flashing lights,
according to the firefly algorithm, and there are over 3000
different types of fireflies. The flashing of fireflies is usually
used for two purposes: communication and prey attraction. Light
intensity decreases as we travel away from the source, and the
reduction ratio follows an inverse square-law.
()=
 (1)
where r is the absorption coefficient and Is is the light intensity
at the source. As light travels through an absorbent medium, its
intensity decreases. The flashing actions of fireflies can be used
to formulate an objective function that can be used in an
optimization problem. The objective function is directly
proportional to the brightness in a simple optimal problem.
While the attractiveness is measured and discovered by another
Firefly algorithm. It is determined by the distance between
fireflies I and j. Furthermore, as the distance from the source
increased, the light intensity decreased, and at the same time,
luminous is absorbed by passing through a medium. As can be
seen in equation 1, this phenomenon follows the inverse square-
rule so, in Gaussian form, it will be
= (2)
where r is the distance between two fireflies and n is the number
of fireflies. Although the source location's original light
intensity is I o. The attraction of fireflies is directly proportional
to the amount of light they see.
= (3)
When r = 0 then βo will be attractiveness. Equation (iii) is for
rapid calculation,
=
1 + 
In a practical situation, attractiveness is decreasing
monotonically and it is generally
=  > 1 (4)
The distance amongst the firefly i and j generally represent
equation (v).
 =  (5)
While the movement of firefly due to another firefly attraction
is
=+
 + (6)
Where 
  is for attraction and 
randomization with the most important scaling element α. It is
necessary to determine the convergence rate of the absorption
parameter that demonstrates the variation of attractiveness.
Simulations in MATLAB are carried out to ensure the
robustness of the MLFA for Economic Dispatch. MATLAB
R2013b was used to run all of the simulations. The proposed
methodology is validated and statistically compared to other
approaches that endorse the MLFA approach using different
IEEE test systems.
TABLE 1: MLFA CONTROL PARAMETERS
MLFA Control Parameters
No. of fireflies
20
Maximum iteration
50
Total no of Trials
35
Alpha
0.5
A minimum value of beta
0.2
Gamma
1
Alpha is the scaling parameter, Beta is the attractiveness
parameter, and Gamma is the absorption coefficient. The value
of alpha is reduced iteratively for quick convergence, while in
the ideal Firefly algorithm, it is a constant value between zero
and one.
αk+1 =(1/2kmax)1/kmax *α (7)
The value of alpha has a significant influence on algorithm
behaviour, so it should be carefully chosen. When an alpha value
is modified in each iteration, the solution can experience
premature convergence or divergence. The proposed MLFA
Algorithm's flow diagram is in figure 1.
III. RESULTS AND DISCUSSIONS
In this paper, the Modified Levi Flight Firefly Algorithm
(MLFA) is used to solve power economic dispatch problems. Its
formulation is done on the basis of the Levi Flight Firefly
Algorithm (LFA). In order to implement a given algorithm, the
MATLAB software is used. The problem with the proposed
technique is examined using a variety of IEEE standard test
systems, which include

2022 5th International Conference on Energy Conservation and Efficiency (ICECE)
Figure 1: Flow diagram for proposed MLFA Algorithm
• 3- Thermal units’ system
• 6- Thermal units’ system
• 13- Thermal units’ system
• 15- Thermal units’ system
• 20- Thermal units’ system
These test systems take into account realistic constraints such
as generator upper and lower limits, valve loading impact,
transmission losses, ramp rate limits, and prohibited zones,
among others. For the reader's convenience, data for 3 and 15
thermal generating units are listed in this paper. Based on the
results of these studies, it has been determined that the Modified
Levi Flight Firefly Algorithm (MLFA) is the most efficient
approach for solving complex and large optimization problems
and provides promising results when compared to other
approaches.
TABLE 2: THREE THERMAL GENERATING UNITS
Unit
P
i
min
(MW)
P
i
max
(MW)
a
($/MW2)
B
($/MW)
c
($)
e
($/h)
f
1 100 600 0.001562 7.92 561 300 0.0315
2 50 200 0.004820 7.95 78 150 0.063
3 100 400 0.001940 7.85 310 200 0.042
A. Case Studies Implementation
For the evaluation of the proposed algorithm, different test
cases have been studied and analyzed. It is tested on 3, 6, 13, 15,
20 and 40 generation units subject to satisfaction of different
restraints. The case study for 3 and 15-generating units are given
here,
1) IEEE standard 3-Generating Units
In this case, 3 thermal generating units are taken. The data is
given in Table 2, the load demand, in this case, is 850MW. Data
for three thermal units (IEEE standard) of generating capacity
and cost coefficients
Figure 2: Comparison via a bar chart for three thermal units’ test
system with other techniques
The proposed algorithm of Modified Firefly results on
MATLAB Software shows less fuel cost as compare to other
available techniques as mentioned in Table 3.
TABLE 3: FUEL COST COMPARISON OF DIFFERENT ALGORITHMS
Sr. No
Method Name
Fuel Cost
1
MPSO[10]
8234.07
2
PSO[11]
8234.1
3
PS[12]
8234.1
4
GA-PS-SQP[13]
8234.07
5
BSA[14]
8234.07
6
FA[15]
8234.07
7
MLFA
8226.62
Figure 3: Graph of cost with respect to trials

2022 5th International Conference on Energy Conservation and Efficiency (ICECE)
Figure 3 shows the results of the proposed MLFA after 35
Nos. of trials.
2) IEEE standard 15-Generating Units
With ramp rate limits, POZ, and transmission losses
restrictions, fifteen generating unit test systems are used in this
case. Table 4 shows the details. Table 5 contains data on ramp
rate limits and POZ, as well as transmission line coefficients. In
this case, the load demand is 2630MW. The results of this case
are shown in Table 4, with the power outputs of generating units
in column 2 and the fuel cost of each unit in column 4. In
comparison to the other techniques listed in the introduction
section, the results show that MLFA performs better. Figure 4
depicts a graph of 35 trials versus fuel cost.
TABLE 4: COMBINATION OF OUTPUT POWER FOR 15-THERMAL
GENERATING UNITS ALONG WI TH COST
Output power (MW)for
each unit using
Proposed MLFA
Cost of fuel ($/h)
for each unit using
Proposed MLFA
P1
388.3574
F1
4638.5056
P2
395.4531
F2
4636.2399
P3
99.6383
F3
1261.9960
P4
123.4867
F4
1477.8532
P5
178.2828
F5
2268.1725
P6
456.3237
F6
5281.5466
P7
393.3177
F7
4440.8241
P8
121.5540
F8
1576.3989
P9
151.0493
F9
1784.6399
P10
110.1920
F10
1346.3739
P11
60.2431
F11
779.4212
P12
47.4300
F12
691.9591
P13
73.9601
F13
1106.9465
P14
43.5669
F14
830.8208
P15
22.5192
F15
581.4936
Losses
(MW)
35.9187
Total
generation
2630
Total
fuel cost
32703.1918
Figure 4: Comparison via a bar chart for Fifteen thermal units’ test
system with other techniques
TABLE 5: FUEL COST COMPARISON WITH OTHER ALGORITHMS
Method Name
Fuel Cost
PSO[24]
32858
GA[24]
33113
SOH_PSO[12]
32751
CPSO1[40]
32835
CPSO2[40]
32834
BF[41]
32784.5
FA[16]
32704.5
MLFA
32703.1918
IV. CONCLUSION
The key problem in power system and control is ED, which
becomes extremely non-linear and non-convex due to various
functional constraints such as multiple fuels and prohibited
operating zones. For convex problems, conventional methods
based on mathematical programming are useful. It has no ability
to handle non-convex complex problems. For the solution of
complex non-convex problems, Artificial Intelligence
algorithms are used. Artificial Intelligence techniques include
Genetic Algorithm (GA), Differential Evolution (DE), Artificial
Neural Network (ANN), Particle Swarm Optimization (PSO),
Gravitational Search Algorithm (GSA), Ant Colony
Optimization (ACO), Virtual Bees Algorithm (VBA) and Firefly
Algorithm (FA) other nature-inspired algorithms. The modified
Levi flight firefly algorithm (MLFA) is used in FA to help
achieve the global minimum. Other algorithms should stick to
local minima instead of a global one when solving multimodal
functions. On the other hand, when the same type of problems
are solved using the suggested algorithms, MLFA performs
better, as seen in the results and discussion section. In these
cases, the solution converges rapidly while still being cost-
effective. A modified firefly algorithm can also be used to
improve the cost-effectiveness of complex problem dispatching.
Each iteration of the firefly algorithm produces a different result
due to randomness. The results of the MLFA algorithm are much
better to those of other heuristic algorithms.
ACKNOWLEDGMENT
This research work is done by the mutual funding of NTDCL
(National Transmission and Dispatch Company) and the
Mechatronics and Control Engineering Department, UET
Lahore (FSD Campus).
REFERENCES
[1] G. Chen et al., “Modified Firefly Algorithm for handling optimal power
flow control with operational constraints” Chinese Automation Congress
(CAC), 2018
[2] M. T. Riaz, M. M. Afzal, S. M. Aaqib and H. Ali, "Analysis and
Evaluating the Effect of Harmonic Distortion Levels in Industry," 2021
4th International Conference on Energy Conservation and Efficiency
(ICECE), 2021, pp. 1-7, doi: 10.1109/ICECE51984.2021.9406283.
[3] S. Pothiya, I. Ngamroo, and W. Kongprawechnon, "Ant colony
optimisation for economic dispatch problem with non-smooth cost
functions," International Journal of Electrical Power & Energy Systems,
vol. 32, pp. 478-487, 2010.
[4] S. Affijulla and S. Chauhan, "A new intelligence solution for power
system economic load dispatch," in Environment and Electrical
Engineering (EEEIC), 2011 10th International Conference on, 2011, pp.
1-5.

2022 5th International Conference on Energy Conservation and Efficiency (ICECE)
[5] M. T. Riaz et al., "The Intelligent Transportation Systems with Advanced
Technology of Sensor and Network," 2021 International Conference on
Computing, Electronic and Electrical Engineering (ICE Cube), 2021, pp.
1-6, doi: 10.1109/ICECube53880.2021.9628331.
[6] X. Liao, J. Zhou, R. Zhang, and Y. Zhang, "An adaptive artificial bee
colony algorithm for long-term economic dispatch in cascaded
hydropower systems," International Journal of Electrical Power & Energy
Systems, vol. 43, pp. 1340-1345, 2012.
[7] M. T. Riaz et al., “Wireless Android Based Home Automation System,”
Advances in S cience, Tech nology and Engineering Systems Journal, 2(1),
234–239, 2017. DOI: 10.25046/aj020128
[8] P. Eser, A. Singh, N. Chokani, and R. S. Abhari, “Effect of increased
renewables generation on operation of thermal power plants,” Appl.
Energy, vol. 164, pp. 723–732, 2016.
[9] M. T. Riaz et al., "Wireless Model for High Voltage Direct Current
Measurement using Hall Sensor," 2021 International Bhurban Conference
on Applied Sciences and Technologies (IBCAST), 2021, pp. 642-647,
doi: 10.1109/IBCAST51254.2021.9393186.
[10] M. H. Sulaiman, M. W. Mustafa, Z. N. Zakaria, O. Aliman, and S. A.
Rahim, "Firefly algorithm technique for solving economic dispatch
problem," in Power Engineering and Optimization Conference (PEDCO)
Melaka, Malaysia, 2012 Ieee International, 2012, pp. 90-95.
[11] X.-S. Yang, S. S. S. Hosseini, and A. H. Gandomi, "Firefly algorithm for
solving non-convex economic dispatch problems with valve loading
effect," Applied soft computing, vol. 12, pp. 1180-1186, 2012.
[12] K. Zare, M. T. Haque, and E. Davoodi, "Solving non-convex economic
dispatch problem with valve point effects using modified group search
optimizer method," Electric Power Systems Research, vol. 84, pp. 83-89,
2012.
[13] M. Modiri-Delshad and N. A. Rahim, "Solving non-convex economic
dispatch problem via backtracking search algorithm," Energy, vol. 77, pp.
372-381, 2014.
[14] X.-S. Yang, "Firefly algorithms for multimodal optimization," in
International Symposium on Stochastic Algorithms, 2009, pp. 169-178.
[15] C. Yaşar and S. Özyön, "A new hybrid approach for nonconvex economic
dispatch problem with valve-point effect," Energy, vol. 36, pp. 5838-
5845, 2011
[16] P. Chakraborty, G. G. Roy, B. Panigrahi, R. Bansal, and A. Mohapatra,
"Dynamic economic dispatch using harmony search algorithm with
modified differential mutation operator," Electrical Engineering, vol. 94,
pp. 197-205, 2012.
[17] J. Cai, Q. Li, L. Li, H. Peng, and Y. Yang, "A fuzzy adaptive chaotic ant
swarm optimization for economic dispatch," International journal of
electrical power & energy systems, vol. 34, pp. 154-160, 2012.
[18] J.-C. Lee, W.-M. Lin, G.-C. Liao, and T.-P. Tsao, "Quantum genetic
algorithm for dynamic economic dispatch with valve-point effects and
including wind power system," International Journal of Electrical Power
& Energy Systems, vol. 33, pp. 189-197, 2011.
[19] X.-S. Yang, "Firefly algorithm, Levy flights and global optimization," in
Research and development in intelligent systems XXVI, ed: Springer,
2010, pp. 209-218.
[20] M.T. Riaz et al., “A wireless controlled intelligent healthcare system for
diplegia patients”, Mathematical Biosciences and Engineering, 19(1):
456-472, 2022. doi: 10.3934/mbe.202202
[21] M.A. Akbar et al., “Multicriteria Decision Making Taxonomy of Cloud-
Based Global Software Development Motivators”, IEEE Access, 8,
185290-185310, 2020. DOI: 10.1109/ACCESS.2020.3030124
[22] M. A. Akbar et al., "Identification and Prioritization of Cloud Based
Global Software Development Best Practices," in IEEE Access, vol. 8, pp.
191242-191262, 2020, doi: 10.1109/ACCESS.2020.3031365.
[23] M. Taiyaba et al., "Secure V2X Environment using Blockchain
Technology." In Proceedings of the Evaluation and Assessment in
Software Engineering, pp. 469-474. 2020. DOI:
https://doi.org/10.1145/3383219.3383287
[24] M. A. Akbar et al., "Requirements Change Management Challenges of
Global Software Development: An Empirical Investigation," in IEEE
Access, vol. 8, pp. 203070-203085, 2020, doi:
10.1109/ACCESS.2020.3035829.
[25] T. Kamal et al., “Energy management and switching control of PHEV
charging stations in a hybrid smart micro-grid system,” Electronics, vol.
7, no. 9, p. 156, 2018.
[26] S. Z. Hassan et al., “Intelligent Control of Wind-Assisted PHEVs Smart
Charging Station,” Energies, vol. 12, no. 5, p. 909, 2019.
[27] M. Awais, S. Z. Hassan, T. Kamal, A. Zahoor, M. A. Khan, and M. T.
Riaz, “Control System for Spinning Machine Induction Motor using
PLC,” in 2019 International Conference on Electrical, Communication,
and Computer Engineering (ICECCE), 2019, pp. 1–6.
[28] H.A. Javaid et al., Classification of Hand Movements Using MYO
Armband on an Embedded Platform. Electronics, 10, 1322, 2021. DOI:
10.3390/electronics10111322