SOLUTION FOR ECONOMIC LOAD DISPATCH USING MODIFIED … · SOLUTION FOR ECONOMIC LOAD DISPATCH USING MODIFIED BAT ALGORITHM P.Girish 1, T.Yuvaraj 2, R. Hariharan 3. 1UG Student, Department

SOLUTION FOR ECONOMIC LOAD DISPATCH USING

MODIFIED BAT ALGORITHM

P.Girish1, T.Yuvaraj2, R. Hariharan3.

1UG Student, Department of Electrical and Electronics Engineering, Saveetha School of

engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India

2,3Assistant Professor, Department of Electrical and Electronics Engineering, Saveetha

School of engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India

1,2,[email protected],[email protected], [email protected]

ABSTRACT

This paper presents a Bio nature inspired Modified Bat algorithm for solving the Economic load dispatch problem. The objective is to minimize the total fuel cost of the generating units through optimal utilization of available sources. This study will further propose modifications

to the original bat algorithm to solve economic load dispatch problem. The simulation results are compared with the previously existing algorithms by using IEEE 6-Bus system, IEEE 14-

Bus system. Keywords: Modified Bat algorithm, Economic load dispatch

1. INTRODUCTION

Economic load dispatch tries to minimize the total operating cost of generating units while

satisfying system equality and inequality constraints. Therefore the main objective of the

optimization of ED problem is to reduce the total generation cost of units while satisfying

constraints. Various mathematical approaches have been suggested to solve the multi-

objective optimization of power plant such as reduction of fuel cost and minimization of the

transmission losses. In the past decade, many efforts have been focused towards solving the

ED problem, incorporating different kinds of constraints through the various optimization

techniques such as conventional methods which include lambda iteration method, base point

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 15957-15968ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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and participation factor method, gradient method, Newton based method, Nonlinear

programming (NLP), Linear programming (LP), Quadratic programming (QP), Mixed-

Integer programming (MIP). In lambda iteration and gradient based methods, the solution to

ELD is obtained by approximately representing the cost function for individual generators in

terms of single quadratic function. These techniques require incremental fuel cost curves

which are piecewise linear and monotonically increasing to find the global optimal solution.

For generators with non-monotonically incremental cost curves, conventional methods

ignores or flattens out portions of incremental cost curve that are not continuous or

monotonically increasing . These limitations of conventional methods were overcome by

modern meta-heuristic approaches like Artificial Neural Networks (ANN), Genetic

Algorithms (GA), Tabu Search (TS), Simulated Annealing (SA), Particle Swarm

Optimization (PSO),Ant colony optimization (ACO),Artificial immune systems (AIS),

Differential Evolution (DE), Bacterial Foraging Algorithm (BFA), Artificial bee colony

(ABC) algorithms [1-4]. Though these methods are not capable in attaining global best

optimal solutions to the ELD problems, to a great extent they produce near optimal solutions.

The purpose of economic dispatch is to produce energy at the low cost to dependably serve

customers, recognizing any operational limits of generation and transmission facilities. The

main plan is that, so as to satisfy the load at a minimum total value, the set of generators with

the bottom marginal costs should be used initial, with the incremental cost of the ultimate

generator required to full fill load setting the system incremental cost. The economic dispatch

involves the solutions of two problems i.e., unit commitment and on-line dispatch. The two

fundamental components of economic dispatch are planning for tomorrow’s dispatch and

dispatching the power today. Planning for tomorrow’s dispatch means scheduling generating

units based on load forecast for each hour of the next day dispatch. The factors that are

considered for planning for tomorrow’s dispatch are generating units operating limits (ramp

rate, maximum and minimum generation levels, amount of time that generator is running),

generating unit characteristics (efficiency, fuel and non-fuel costs) and start-up costs. This is

performed by independent market operator or by generation group. The factors that are

considered for dispatching the power today are ensuring balance of supply and load by

monitoring load, generation and interchange and monitoring transmission system. It is

performed by transmission operator. Normally the input output characteristics of modern

generating units are highly non-linear in nature due to value-point effects, ramp-rate limits

etc. having multiple local minimum points in the cost function.

2. LITERATURE REVIEW

Several authors have given extra comparatively cheap algorithms within the utility of linear

and non-linear programming strategies. Advocate the conversion of the nonlinearly

constrained dispatch trouble to a chain of restricted linear programming issues [5]. Introduces

the combined use of the differential set of rules and therefore the simplex method of

optimization in the safety compelled dispatch [6]. Mentioned a linearized formulation of the

overall finest load float problem and observe minimization technique to an augmented price

characteristic which includes a piecewise differentiable penalty cost characteristic term [7].

Planned a multipored premiere power glide, nicely modelling the begin-up and shut-down of

thermal devices [8]. Stated regarding Dynamic financial dispatch is companion degree

International Journal of Pure and Applied Mathematics Special Issue

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extension of the usual economic dispatch downside that takes into thought the boundaries at

the ramp fee of the producing devices [9]. Proposed in order to enhance pace and robustness

and those have been implemented successfully [10]. Introduces a brand new method based on

PS optimization to solve various problems of energy gadget ELD [11]. Proposed a unique

heuristic-hybrid op- atomization method designed to remedy the nonconvex monetary

dispatch hassle in energy structures [12]. Discussed the artificial bee colony optimization

that's successfully implemented to economic strength dispatch issues [13]. Discussed about

international warming and haze, environmental difficulty has drawn more attention in every

day optimization operation of electric electricity structures [14]. The blended-integer linear

software is used in [15] for the ED problem. The author proposed an aggregate of C-GRASP

and differential evolution (DE) [16]. Provided a green allotted auction optimization algorithm

(DAOA) based totally on the gossip conversation mechanism for the non-convex economic

dispatch problem [17]. The proposed a multi-objective optimal dispatch model for micro grid

under grid-connected mode [18]. The authors from the above Literature review paper as

proposed mainly forced on the economic problem and also overcome the ELD problem they

were introduced several optimization algorithm to overcome the ELD problem even though

there are several existing algorithm we are concentrated on BAT algorithm due to have the

edible of solving a wide range of problems and highly nonlinear problem efficiently and it

gives promising optimal solution it works well with complicated problems having the quick

response within a short time period

3. PROBLEM FORMULATION

The main aim of this work is to minimize the fuel cost of the generating units through optimal utilization of the available sources. This has to carry out with satisfying all the

operating constraints.

The objective function of the economic dispatch is formulated in mathematically.

(1)

3.1 Operating Constraints

The equality and in equality constraints for economic load dispatch problem are real power

balance

(2)

(3)

Where PD is the total power demand

Is the minimum power generation limits

Is the maximum power generation limits

is the line loss.

4. BAT ALGORITHM

Bat algorithm is proposed by Yang in 2010 [19-22], It is a meta-heuristic algorithm inspired by fascinating abilities of bats such as finding their prey and discriminating different types of


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insects even at complete darkness. The advanced echolocation capability of bats makes them fascinating. Such abilities inspired to researchers on many fields. Bats use typical sonar

called as echolocation to detect prey and to avoid obstacles. Bats, in particular micro-bats, are able to recognize positions of the objects by spreading high and short audio signals and by

collision and reflection of these spread signals. In Bat Algorithm, the echolocation characteristics are idealized within the framework of the

following rules by benefitting such features of bats.

1. All bats use echolocation to sense distance, and they also know the difference between food/prey and background barriers in some magical way. 2. Bats fly randomly with velocity at position with a frequency varying wavelength

and loudness to search for prey. They can automatically adjust the wavelength (or

frequency) of their emitted pulses and adjust the rate of pulse emission r [0, 1], depending on the proximity of their target.

3. Although the loudness can vary in many ways, we assume that the loudness varies from a large (positive) to a minimum constant value Amin. In general the frequency f in a range [Fmin , Fmax] corresponds to a range of wavelengths [min,

max]. Furthermore, we do not necessarily have to use the wavelengths themselves; instead, we can also vary the frequency while fixing the wavelength λ. This is because λ and f are

related due to the fact λf is constant. We will use this later approach in our implementation. For simplicity, we can assume f ∈ [0,

Fmax ]. We know that higher frequencies have short wavelengths and travel a shorter distance. For bats, the typical ranges are a few meters. The rate of pulse can simply be in the range of

[0, 1] where 0 means no pulses at all, and 1 means the maximum rate of pulse emission. Based on these approximations and idealization, the basic steps of the Bat Algorithm (BA) can be summarized. In algorithm we have define the rules for the updating the positions Zi

and velocities Vi in the search space. The position and velocity is given by

(4)

(5)

Where is the random number between [0,1]. is the current best global location.

The new solution or position for the bat can be generated by the equation

(6)

For the local search part, once a solution is selected among the current best solutions, a new solution for each bat is generated locally using random walk.

(7)

Where is the random number between [0, 1].

Is the average loudness of all the bats?

5. MODIFICATIONS

5.1 Add Bad Experience Component


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A new variant to the classical PSO was introduced by Selvakumar and Thanushkodi by

splitting the correction component into two components. These components were called the good and bad experience components. A particle tries to achieve a better position while

trying to avoid the bad positions it has encountered. This paper proposes to add bad experience component to the velocity update equation. This modification is intended for enhancing the exploration capability of the algorithm. The modified equation is can be

mathematically written as

(8)

Where and are the global best and worst positions. And are the

personal best and worst positions. And are parameters that accelerate the particle

towards the global best and personal best positions respectively. And are constants that

accelerate the particle away the swarm worst and personal worst positions respectively.

5.2 NONLINEAR INERTIA WEIGHT

A variant of the bat algorithm called improved bat algorithm (IBA) has recently been

presented by Jamil. He proposed adding an inertia weight coefficient to the velocity

component in the velocity update equation. The paper proposes the weight component

decrease linearly from its maximum value to its minimum value. The purpose of the weight is

to provide balance between global and local exploration and better convergence rate. This

paper proposes using a nonlinear weight. The reason for using nonlinear weight is to have to

ability to control the transition between the global and local exploitation so that it can be

tailored for a specific problem. In this paper the following three equations have been derived

to get a better control over the transition between global and local exploitation.

(9)

Where and are maximum and minimum bounds of inertia weight coefficient.

Is maximum allowed iterations? The constants calculated using the following equations.

(10)

(11)

The final modified velocity updated equation is

(12)


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6. FLOW CHART

Fig.1 Modified Bat algorithm flowchart

7. RESULTS AND DISCUSSION

The bat algorithm is used for solving the economic load dispatch problems. In this the IEEE 6

bus system is used to compare with the fruit fly algorithm(FA), practical swarm

optimization(PSO), cuckoo search algorithm (CSA), flower pollination algorithm (FPA), The

simulation results is done by MATLAB. The six generator system consists of six busses. In

the system the P, Q is the real power and the reactive power.

The table 1 shows the comparative results of proposed algorithm with compared algorithms

PSO, FA, FPA, and CSA. The proposed method shows the best results when compared to the

other algorithms. The IEEE 6 bus system power delivering units are 325.51MW, 78.24MW,

150MW, 49MW, 55.25MW, 52MW respectively.

Start

Initialize random bat position and calculate fitness where

i=1, n

Generate pulse frequency

Ca lculate new frequency and calculate new bat pos i tion

Ca lculate new fi tness

Ini tia l i ze pulse rate and loudness

U(0,1) >

Terminate

<

U(0,1) < and

Random walk around best

solution

Update and

Accept new solution update pulse and loudness

End

Yes

No

Yes

No

Yes

No

Yes


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The power loss reduced by the proposed method is 10.86MW. Here the power loss reduced

by the other algorithms is 11.03MW, 11.44MW, 11.73MW, 11.02MW. From the above

discussion it could be concluded that the proposed method shows the best results when

compared to the other algorithms.

IEEE 6-Bus system

The six unit test system consisting of six thermal units, 26 buses, and 46 transmission lines is

used for simulation of proposed problem of economic load dispatch. This system is simulated

for 50 iterations.

Fig 2 IEEE six bus generating units

Parameters CSA

[12]

FA

[12]

PSO

[12]

FPA

[12]

Proposed

method [MBA]

P1 (MW) 324.1 293.3 288.6 323.995 325.51

P2 (MW) 76.86 79.54 82.75 76.84 78.24

P3 (MW) 158.1 123.33 132.9 158.2 150

P4 (MW) 50 69.7 50 50 49

P5 (MW) 51.96 79.54 99.5 51.98 55.25

P6 (MW) 51.96 63.77 57.5 50 52

Ploss (MW) 11.03 11.44 11.73 11.02 10.86

Fuel Cost($) 8356.06 8388.4 8401.45 8356.05 8199.4

Table 1 comparative results of modified bat algorithm

The result of comparison between CSA, FA, PSO, and FPA obtained from table1 shows that

the method of modified bat algorithm gives better results. Additionally the advantages of

modified bat algorithm are it is easier to implement and there are fewer parameters to adjust

and it shows the best results when compared to the other algorithms.

1:0.9725

1:0.91

P=55MW

Q=13MV

ar 1.05/0

P=50MW

Q=5MVar

P=30MW

Q=18MVar

P=50MW

V=1.1

1

2

3

6 5

4


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Fig 3 The performance analysis of six bus system

the above figure 3 shows the performance analysis of six bus system.the graph has been

drawn for fuel cost and power loss from the above graph it is very clear that our proposed

method shows the least values of power lost and fuel cost.whereas the other alogirthms

csa,fa,pso,fpa alogirthms shows the highest values of power loss and fuel cost when

compared to our proposed alogirthm mba.

IEEE 14-Bus system

The IEEE 14 bus system consists of 14 busses and 16 inter connecting nodes among

the busses and 32 transmission lines is used for simulation of proposed problem of economic

load dispatch.

parameters QP GA Proposed

method MBA

PG1(MW) 200 199.8 203

PG2(MW) 25.79 24.28 26

PG3(MW) 15 15.77 16

PG6(MW) 10 10.41 8

PG8(MW) 10 10.48 8

Power loss(MW)

13.54 13.42 13.24

Fuel cost($) 860.7250 805.55 803.45

Table 2 comparative results of MBA with other optimization algorithms

8356.06

8388.4 8401.45

8356.05

8199.4

711.03

711.4

711.73

711.02

710.86

710.4

710.6

710.8

711

711.2

711.4

711.6

711.8

8050

8100

8150

8200

8250

8300

8350

8400

8450

CSA FA PSO FPA

MBA

PO

WER

LO

SS(M

W)

FUEL

CO

ST($

)

FUEL COST($) POWER LOSS(MW)


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Fig 4 IEEE 14 bus generating units

The table 2 shows the comparative results of proposed method with compared algorithm

CSA, FPA, PSO, FA. The proposed method shows the best result by using IEEE 14 bus

system the power delivering units are 13.54 MW, 13.42 MW, 13.24 MW respectively.

The fuel cost reduced by the proposed method is 803.45 where the fuel cost obtained by the

other algorithms QP, GA are 860.7250, 805.55 respectively.

21

C

c

16

11

G1

3

C

2

G1

Bus 14 Bus 13

Bus 11

Bus 12

Bus 10

Bus 8

Bus 9

Bus 6 Bus 7

Bus 2 Bus 3

Bus 1 Bus 5 Bus 4

30 22 31 32 26

18 2

29

20

19 25

24 27

17 23

3 1 5 6 14 15

16 12

2

10

11

4 13 9 7

8

8

1

7

4

6

10

9

13

14

12

15


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Fig.5 The performance analysis of 14 bus system

The above figure 5 shows the performance analysis of 14 bus system. The above graph has

been plotted for fuel cost and power loss. Whereas our proposed method modified bat

algorithm shows the least values where compared with other optimization alogirthms

quadratic programming and genetic algorithm shows the higher values.

CONCLUSION

This paper proposes a new bio-nature inspired Modified Bat algorithm for solving the

economic load dispatch problem. For a normal bat algorithm the modification s have done.

And the Modified bat algorithm is compared with the Cuckoo search algorithm(CSA),

Practical swarm optimization(PSO), Fruit fly(FA) ,Flower pollination(FPA), algorithms but

from the graph that is very clear that the MBA shows best results when compared to the other

algorithms. From the graph it is clear that the modified bat algorithm has more accuracy and

computational time when compared to the other optimization algorithms, although the

proposed algorithm had been successfully applied to Economic load dispatch with valve point

loading effect including a few constraints.

REFERENCES

1. Yuvaraj, T., Devabalaji, K. R., & Ravi, K. (2015). Optimal placement and sizing of

DSTATCOM using harmony search algorithm. Energy Procedia, 79, 759-765. 2. Devabalaji, K. R., Yuvaraj, T., & Ravi, K. (2016). An efficient method for solving the

optimal sitting and sizing problem of capacitor banks based on cuckoo search

algorithm. Ain Shams Engineering Journal. 3. Yuvaraj, T., Ravi, K., & Devabalaji, K. R. (2017). Optimal allocation of DG and

DSTATCOM in radial distribution system using cuckoo search optimization algorithm. Modelling and Simulation in Engineering, 2017.

4. Thangaraj, Y., & Kuppan, R. (2017). Multi-objective simultaneous placement of DG

and DSTATCOM using novel lightning search algorithm. Journal of Applied Research and Technology, 15(5), 477-491.

860.725

805.55 803.45

13.54

13.42

13.24

13.05

13.1

13.15

13.2

13.25

13.3

13.35

13.4

13.45

13.5

13.55

13.6

770

780

790

800

810

820

830

840

850

860

870

QP GA MBA

PO

WER

LO

SS(M

W)

FUEL

CO

ST($

)

FUEL COST($) POWER LOSS(MW)


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5. Mehmed, et al., "A Modified Method for Solving the Economic Dispatching Problem," IEEEE Transactions on Power Apparatus and Systems, Vol. PAS-96 (I),

pp. 124-133, January February, 1977. 6. R. Luta, “Security Constrained Dispatch,"IEEE Transactions on Power Apparatus and

Systems, Vol. PAS-98 (I), pp. 270-274, JanuarylFebruary, 1979. 7. R. Mote-Palomino, and V. Quintana, "A Penalty Function - Linear Programming

Method and Solving Power System Constrained Economic Operation Problems,"

IEEE Transactions on Powel Apparatus and Systems, Vol. PAS-I03 (6), pp. 1414-1422, June,1984.

8. R. Becher, H. P. Van Metermen, "Real-Time Power Flow on Automatic Generation Control, "IEEE Transactions on Power Systems,Vol. 3(4), pp. 1518-1529, Nov. 1988.

9. B.H. Chowdhury, Sai fur Rahman “A review on recent advantages on economic

dispatch” IEEE Transactions on Power Systems, Vol. 5, No. 4, November 1990. 10. Po-Hung Chen, Hong-Chan Chang,” Large scale economic dispatch by genetic

algorithm” IEEE Transactions on Power System. Vol. 10. No. 4. November 1995. 11. K. Abdul-Rahman, M. Shahidehpour, M. Agnatic, S. Mohair “An efficient approach

to short term resource scheduling based on the augmented Lagrangian relaxation

method” Jan. 1996. 12. M.Aganagic, B. Awobamise, G. Raina, A.I. Mc Cortney, “Economic dispatch with

generation contingency constraints” IEEE Transactions on Power Systems, Vol. 12, Issue 3, pp 1229-1236, Aug 1997.

13. Nidus Sinha, R. Chakraborty, and P. K. Chattopadhyay,” Evolutionary

Programmingg Techniques for Economic Load Dispatch”, IEEE Transactions on evolutionary computation, Vol. 7, No, 1, February 2003.

14. J.S. Al-omit, J.K. Skulks, A.K. Othman,” Solution of different types of economic load dispatch problems using a pattern search method”2008.

15. Belkacem Mahdi, K. Sari, T. Boulter improved parallel PSO solution to economic dispatch with practical generator constraints 2010.

16. Gaurav Prasad Dixit, Hari Mohan Dubey, Manatee Pundits, B. K. Panigrahi

“Artificial Bee Colony Optimization for Combined Economic Load and Emission Dispatch”, Sustainable Energy and Intelligent Systems (SEISCON 2011),

International Conference on 20-22 July 2011. 17. Irina cornier, Elias Kyriakos’s,” A GA-API solution for the economic dispatch

of generation in power system operation”, IEEE Transactions on power systems, Vol.

27 No. 1, February 2012. 18. Sunny Orica and David W. Crone “Improved Evolutionary Algorithms for Economic

Load Dispatch Optimization Problems”, Published in Computational Intelligence (UKCI), 2012 12th UK Workshop on 5-7 Sep 2012.

19. Yuvaraj, T., Ravi, K., & Devabalaji, K. R. (2017). DSTATCOM Allocation in the

Radial Distribution Networks with Different Stability Indices using Bat Algorithm. GAZI UNIVERSITY JOURNAL OF SCIENCE, 30(4), 314-328.

20. Yuvaraj, T., Devabalaji, K. R., & Ravi, K. (2018). Optimal Allocation of DG in the Radial Distribution Network Using Bat Optimization Algorithm. In Advances in Power Systems and Energy Management (pp. 563-569). Springer, Singapore.

21. Yuvaraj, T., Ravi, K., & Devabalaji, K. R. (2015). DSTATCOM allocation in distribution networks considering load variations using bat algorithm. Ain Shams

Engineering Journal. 22. T.K.Sethuramalingam, 2B.Nagaraj A COMPARATIVE APPROACH ON PID CONTROLLER

TUNING USING SOFT COMPUTINGTECHNIQUES International Journal of Innovations in

Scientific and Engineering Research (IJISER)


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Documents

SOLUTION FOR ECONOMIC LOAD DISPATCH USING MODIFIED … · SOLUTION FOR ECONOMIC LOAD DISPATCH USING MODIFIED BAT ALGORITHM P.Girish 1, T.Yuvaraj 2, R. Hariharan 3. 1UG Student, Department