 Open Access
 Total Downloads : 365
 Authors : K. C. Meher, R. K. Swain, C. K. Chanda
 Paper ID : IJERTV4IS090295
 Volume & Issue : Volume 04, Issue 09 (September 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS090295
 Published (First Online): 19092015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Solving Dynamic Economic Dispatch Problems Facilitating MetaHeuristic Technique
K. C. Meher1
Department of Electrical Engineering Orissa Engineering College Bhubaneswar
R. K. Swain2
Department of Electrical Engineering Silicon Institute of Technology Bhubaneswar

K. Chanda3
Department of Electrical Engineering Indian Institute of Engineering Science and Technology, Kolkata
Abstract:This paper yields glowworm swarm optimization technique to solve the dynamic economic load dispatch (DELD) problem for minimizing the operation cost in most economical manner. The glowworm swarm based algorithm is considered as metaheuristic based evolutionary approaches where the agents communicate with each other via bioluminescent glowing, that enables them to explore the objective function more effectively. The effectiveness of the proposed method is demonstrated through five unit test systems. The results are compared with the other optimization technique reported in the literature. The fuel cost and other performance of the given approach has been quite impressive. It is shown that the GSO approach can provide the global or near global optimum solutions with a lesser computational time along with higher efficiency and robustness.
KeywordsDynamic economic load dispatch (DELD), glowworm swarm optimization (GSO), luciferin, Valve – point loading effect, Ramp Rate Limits.
find global optimal solution due to their non linear and non convex characteristics of generator input. Many stochastic search algorithm such as genetic algorithm(GA)[7,8], simulated annealing (SA) [9],evolutionary programming (EP) [1013],particle swarm optimization(PSO) [1416], differential algorithm DE [1718] and clonal selection technique (CSA) [19] have been used in an effective manner to solve dynamic economic load dispatch problems. Recent researches have been directed towards the application of Glowworm swarm optimization (GSO) technique to solve DELD problem. The GSO is an efficient global search technique and may be used to find optimal or near optimal solutions to numerical and qualitative problems. It is easy to implement in most programming languages and has been proved to be quite effective and reasonably quick when applied to a diverse set of optimization problems.

INTRODUCTION
Dynamic economic load dispatch (DELD) plays a significant role in power system operation and control. It is a dynamic problem due to dynamic nature of power system and the large variation of load demand. This absolute problem is normally solved by discretization of the entire dispatch period into a no of small time intervals. The load is assumed to be constant and the system is considered to be in accurate steady state dynamic model which finds the best generation schedule for the generating units in real power system framework. The main objective of the dynamic economic dispatch is to minimizing the generation cost, subject to satisfy the physical and operational constraints. In traditional economic dispatch, the cost function is quadratic in nature. In practice, a
In this paper, the GSO based DELD algorithm has addressed for the determination of global or near global optimum dispatch solution. In the proposed work, the operating limit constraints and valve point loading effects are fully incorporated. It has been shown that the algorithm is capable of finding the global or near global optimum solutions for large optimization problems.
.

PROBLEM FORMULATION

The main objective of the dynamic economic dispatch is to determine the outputs of all generating units to minimize the operating cost over a certain period of time under various physical and operational constraints. The formulation of DED problem has expressed as given below.
generating unit cannot exhibit a convex fuel cost function, so T N
a nonconvex characteristics will observe owing to valve point effect. Mathematically, DED problem with valve point
Min F Fit Pit
t 1 i1
(1)
effect can be recognized as a non linear, non convex and large scale optimization problem with various complicated constraints, which finds the optimal result dispatch a new challenge. DED has been recognized as a more accurate problem than the traditional economic dispatch problem.
Many classical optimization techniques have been put on to solve the DED problems. The classical mathematical approaches include linear programming [1], nonlinear programming (NLP) [2], quadratic programming (QP) [3] , Lagrange relaxation(LR) [4,5],and Dynamic Programming (DP) [6]. However, most of these techniques are not able to
F : Total operating cost of all generating units over all dispatch periods.
T : Numbers of hour in the time horizon;
N : Number of generating units;
Fit(Pit): The fuel cost in terms of its real power output Pit at a time t
The fuel cost function with valve point effect of the thermal generating unit is expressed as the sum of a quadratics and sinusoidalfunctions.
F (P ) a P 2 b P c  e (sin( f (P
P )) 
(2)
The number of luciferin level associated with glowworm i at
it it
i i i i i i
i i min i
time t. To update the current position of glowworm i , the
ai , bi
, ci ,
ei and
fi are constants of fuel cost function of
fitness value of the liciferin is given as follows:
ith unit.
li (t) (1 )li (t 1) J (xi (t))
(7)

Real power balance constraints
Where
: Luciferin decay constant whose value lies
N
i1
(3)
Pit

PDt

Plt
0,
t 1,2,T
between (0,1)
: Luciferin enhancement constant
J : Objective function
Where
PDt
is the total power demand during tth dispatch
The individual glowworm i encodes the objective function
period. Plt Total transmission loss during tth dispatch period
J (xi (t) at current position
xi (t) into a luciferin values


Real power operating limits
li (t) and broadcast the same within its neighborhood. The set
Pit min Pit Pit max , i 1,2,T;
of neighborhood Ni (t) is chosen according to higher
t 1,2,T
(4)
luciferin value within dynamic search space domain. The chosen numbers of glow in the local decision range is given
Where
Pi min and
Pi max are the minimum and maximum real
by the following equation
'
power outputs of ith generator respectively.
Ni (t) j : x j (t) x (t) r ;l (t) l j (t)
(8)
i d i

Generator unit ramp rate limit
Where,
N (t) r ' ; r ' is the local updated decision range.
i d d
Pi(t1) Pit DRi ;
i 1,n
(5)
The decision range is bounded by a circular sensor range
r (0 r ' r ) , j N (t)
s d s i
Pit Pi(t 1) URi ;
i 1,n
(6)
ith
x (t) :Glowworm ith position at t iteration
j
l (t) :Glowworm ith luciferin at t iteration
j
URi and DRi are ramp up and ramp down rate limits of
generator respectively and these are expressed in MW/h.
The main objective of DELD problem is to determine the optimal schedule of output powers of online generating units with predicted power demands over a certain period of time to meet the power demand at minimum operating cost
Each glowworm i selects a neighborhood glowworm j with probability Pij (t) .These movements enables the glowworm into a disjoint subgroup which finds the multiple optimal
solutions to the objective function. The selection of the
neighborhood glowworm by using probability distribution is given by
III .OVERVIEW OF GLOWWORM SWARM OPTIMIZATION
P (t)
l j (t) li (t)
(9)
K.N. Krishnanad and D.Ghose [25] developed a glowworm ij
swarm optimization (GSO) based on the behavior of glowworm (insects). The biological behaviors of the
(lk
kNi (t )
(t) li (t))
movement of individuals (e.g. ants, honeybee swarm, fish schools) within a group are the main observation in this algorithm. This algorithm consists of agents, which discover
The updated luciferin movement is given by the following
equation
x j (t) xi (t)
x
i
x (t 1) x (t) s
(10)
the search space and transmit the information regarding i fitness with respect to their correct position. The GSO algorithm searches the agents in a group of individuals similar
j (t) xi (t)
to the other heuristic based optimization methods. All individuals in a swarm approaches to the optimum or quasi optimum through its randomly chosen direction of luciferin.In GSO algorithm, the search space composed Ndimensional agents called glowworm. Initialize the glowworm randomly in
the search space. The position of the glowworm i at time t is
Where s is called moving step size.
In the last phase, the fitness of luciferin within a dynamic decision domain is upgraded in order to limit the range of communication and the updated local decision range is given by the following equation
X i (t) (xi1 (t), xi 2 (t)xiN (t)) . The GSO algorithm has
0, r ' (t)
r ' (t 1) min r , max d
s
(11)
described by the set of variables such as position vector d
(n N )
X i (t) , luciferin level li (t) and neighborhood range ri (t) .
i i
d
r ' (t 1) : is the glowworm i' s local decision range at the
(t 1) iteration

Decision of neighborhood
The better the fitness value, the better the level of luciferin. Each glowworm finds all the glowworms which have the
rs : The sensor range
brighter luciferin level within the local dynamic decision
range r ' . The decision range is bounded by a circular sensor
ni : The neighborhood threshold value
: Constant parameter

IMPLEMENTATION OF GSO TO DYNAMIC ELD
This section describes the implementation of GSO algorithm for solving dynamic economic load dispatch problems. This section deals the implementation of the equality and inequality constraints of DELD problems when modifying each individuals search space in the GSO algorithm. For T intervals in the generation scheduling periods, there are T dispatched for the N generating units. An array of decision variable vectors can be expressed as
p11 p12 p1N
P = p21 p22 p2 N
it
pT 1 pT 2 pTN
Where Pit is the real power output of generator i at interval t

Initialization of glowworm
In the initialization procedure, the candidate solution of each individual (generating units power output) is randomly initialized within the feasible range in such a way that it should satisfy the constraint given by Eq. (4). A candidate is initialized as Pit ~ U ( Pit min, Pit max ) , Where U is the uniform distribution of the variables ranging in the interval of (Pit min, Pit max ) .

Fitness function evaluation
The fitness value of individual i is calculated the following equation (2). The number of population is equal to the number of fitness evaluation.

Calculation of luciferin level
Each glowworm carries a luminescent quantity called luciferin. The number of luciferin level associated with each glowworm i at times t . Put the value of objective function
J (xi (t)) into the li (t ) in equation (7). The number of luciferin level is same as the number of glowworms.
d
range. The number of brighter glowworm is calculated by the following equation (8).



Updated local decision range
At each iteration, the dynamic decision range is upgraded by the equation (9). The suitable value of is chosen such that
how it effects the rate of change over the neighborhood range.

Glowworms velocity updated
In this section, each glowworm carries their topical information which enables the glowworm to make their division into a number of subgroups. It gives the multiple local optimal solution of the given objective function. In order to select the proper neighbor, a probability distribution is chosen by the aforesaid equation (10)

Position updated of glowworms
The position of each glowworm is usually updated by the equation (11). The resultant position of individuals is being violated their operating limits and to keep the position as the individual within the boundary.

SIMULATION RESULTS AND DISCUSSION
The proposed GSO algorithm has been applied to DELD problems by considering five generating unit systems to investigate the effectiveness and robustness. The result obtained from proposed approach has been compared with EAPSO [20] and other previously developed techniques. The software has been written in MATLAB7.5 language and executed on a 2.3GHz Pentium IV personal computer with 512MB RAM. For implementing the GSO technique in ELD problems, the maximum number of generation (iteration) of 5000 is taken for simulation study of the five unit test systems.
Description of Case Study for the 5unit Test Systems: Initially, the proposed GSO technique is applied on a small test system, consisting of five generating unit with a ramp rate limit and valve point effects The system data of this test have been taken from [20].Table I indicates the generator data of system. Table II yields the variation of load demand for 24 hours. The results obtained for this case study are given in table III, which shows that the GSO has better solution without violating any operating constraints The best fuel cost result obtained from proposed GSO and other optimization algorithms are compared in table IV. From table IV, it is clearly visible that the proposed method outperforms all other methods in terms of best fuel cost and simulation time. Fig 1.shows the variation of power generation with time and Fig
2. shows the convergence behavior of the proposed technique.
TABLE I
Generator data for the 5unit test system
/tr>
Units
ai
bi
ci
di
ei
Pi max
Pi min
DRi
URi
1
25
2.0
0.0080
100
0.042
75
10
30
30
2
60
1.8
0.0030
140
0.040
125
20
30
30
3
100
2.1
0.0012
160
0.038
175
30
40
40
4
120
2.0
0.0010
180
0.037
250
40
50
50
5
40
1.8
0.0015
200
0.035
300
50
50
50
TABLE II
Load Variation for 24hours
Load Demand(MW)
Hour
Load
Hour
Load
Hour
Load
Hour
Load
1
410
7
626
13
704
19
654
2
435
8
654
14
690
20
704
3
475
9
690
15
654
21
680
4
530
10
704
16
580
22
605
5
558
11
720
17
558
23
527
6
608
12
740
18
608
24
463
Fig.1.Power Generation of five unit systems with time
TABLE III VI. CONCLUSION
Best Solution of Proposed Method for five unit systems
Hour
Unit 1 (MW)
Unit 2 (MW)
Unit 3 (MW)
Unit4 (MW)
Unit5 (MW)
Load (MW)
1
17.2944
99.1647
30.1945
124.5679
139.7079
410.7399
2
19.2021
99.7085
51.1479
126.0288
139.9210
435.8877
3
10.6900
98.7549
71.6084
155.4974
139.8204
475.7750
4
10.5866
98.7642
77.4776
204.7948
140.4001
531.0706
5
10.3069
96.2009
108.1316
205.9634
139.6188
559.3281
6
39.4206
106.5602
113.3428
210.7621
140.3704
609.9846
7
68.2616
98.1121
112.8731
210.1602
139.0849
628.0831
8
74.2339
101.0520
113.2912
213.1890
154.8241
655.9041
9
70.3845
97.9287
112.3251
209.8157
202.0374
692.0525
10
55.8620
98.8737
112.3839
209.7366
229.5768
706.1667
11
72.4644
98.3169
112.5360
209.5947
229.5910
722.6415
12
67.7412
98.7137
136.9351
209.7345
229.5732
743.0782
13
56.0396
98.5365
112.3371
210.0573
229.4653
706.5003
14
41.0388
98.7888
112.9186
209.9416
229.7016
691.9781
15
34.2447
98.5367
112.7467
180.2379
230.1968
655.5823
16
10.8238
97.3308
112.5992
131.5030
229.1279
581.2506
17
11.0130
97.7050
97.7086
124.3342
228.4528
559.2045
18
17.2650
98.5567
112.9927
150.5157
230.2600
609.4548
19
17.1378
98.9317
112.3211
198.3132
229.4672
655.5492
20
46.6632
101.2134
112.8768
210.1392
235.5337
706.1987
21
31.8222
98.3838
113.0804
209.5952
229.4778
681.7967
22
10.4036
98.3138
108.6966
160.1477
229.0916
606.5144
23
10.7665
98.5560
112.1879
125.0940
181.7279
528.1315
24
10.5248
82.8039
108.1656
124.9296
137.7758
464.0102
A simple and an efficient optimization technique based on GSO is addressed for solving DELD problems, taking account of the valve point effect. By considering a fiveunit test system, it is observed that the proposed algorithm has better convergence characteristics, robustness and computational efficiency as compared to other heuristic methods. It is also clear from the result obtained that by different trials, the proposed GSO technique can avoid the shorting of premature convergence of other optimization to obtain good quality results. When more complex fuel cost characteristics is considered, the solution quality and computational efficiency are significantly better than other methods. Because of these dominant characteristics, GSO becomes an important tool for solving more complex optimization problems in power system.
5.1
5
4.9
Cost $/h
4.8
4.7
4.6
4.5
4.4
4.3
4
x 10
TABLE IV
Comparison of Various Methods
Methods
Minimum
Cost($/h)
Simulation
time(sec)
MSL[24]
49216.81
1.4
SA[21]
47356.00
351.98
APSO[22]
44678
—
SOA
SQP[23]
40701.42
—
EAPSO[20]
43784
2.00
GSO
43414.12
1.39
5 unit System with GSO
VII. REFERENCES

R.Jabr, A.Coonick and B Corry. A homogeneous linear programming algorithm for the security constrained economic dispatch problem, IEEE Transaction s on Power System. Vol. 15, issue 3, pp 930937;
Aug.2000

S.Takriti &B.Krasenbrink A decomposition approach for the fuel constrained economic powerdispatch problem, European journal of operational research .Vol. 112, issue 2, pp.460466, 199

L.Papageorgiou and E. Fraga. A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones, Electric Power System Research, vol. 77, issue 10, pp.12921296, 2007

A.Keib, H. Ma, and J. Hart, Environmentally constrained economic dispatch using the Lagrangian relaxation method, IEEE Transaction son PowerSystem.vol.9, issue 4, pp. 17231727, 1994

K. Hindi and M. Ghani, Dynamic economic dispatch for largescale power systems: A Lagrangian relaxation approach, Electric Power system research, vol.13, issue1pp.5156, 19

D.Travers, and R Kaye, Dynamic dispatch by constructive dynamic programming, IEEE Transactions on Power System. vol.3, issue 1, pp.7278, 1998

S.Basker, P. Subbaraj, and M Rao, Hybrid real coded genetic algorithm solution to economic dispatch problem, Computers and Electrical Engineering. vol.29, issue 3,pp. 407419, 2003

C. Chiang, Improved genetic algorithm for power economic dispatch of units with valuepoint effects and multiple fuels, IEEE Transactions on Power System. vol. 20, issue 4, pp. 16901699, 2005.

K. Wong, C. Fong, Simulated annealing based economic dispatch algorithm, IEEE proceedings on Generation, Transmission and Distribution. vol.140, issue 6, pp. 509515, 1993

T.Jayabarathi, K.Jayaprakash, and D.Jeyakumar, Evolutionary programming techniques for different kinds of economic dispatch problems, Electric Power System Research. vol.73, issue 2, pp. 169 176, 2005

T. Victoire, and A. Jeyakumar, A modified hybrid EPSQP for dynamic economic dispatch with valvepoint effect, International journal of Electrical Power and Energy Systems. vol. 27, issue 8, pp. 594601, 2005

T. Victoire, and A. Jeyakumar, Hybrid EPSQP for dynamic economic
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Iterations
Fig.2.Convergence behavior of proposed GSO
dispatch with valvepoint effect, Electric Power System Research,vol.71, issue 1, pp. 5159, 2004

P. Attaviriyanupap, H. Kita, E. Tanaka, J. Hasegawa, A hybrid EP and SQP for dynamic economic dispatch with non smooth fuel cost function, IEEE Trans. Power Syst.2002; vol.17, issue 2, pp.411416, 2002.

T.A.A. Victoire, and A.E. Jeyakumar, Deterministically guided PSO for dynamic dispatch considering valvepoint effect, Electric Power Syst. Res. vol. 73, issue 3, pp. 313322, 2005

Victoire, T.A.A., and Jeyakumar,A.E.Reserved constrained dynamic dispatch of units with valve point effects. IEEE. Trans. Power Syst.2005; 20(3): 12731282

Su A Yuan, Y Yuan. et al., An improved PSO for dynamic load dispatch of generators with valvepoint effects. Energy. vol. 34, issue 1, pp. 6774, 2009

X Yuan, L Wang, and Y Yuan. et al, A modified differential evolution approach for dynamic economic dispatch with valvepoint effects, Energy Conversion and Management, vol. 49, issue 12, pp. 34473453, 2008

X Yuan, L Wang, and Y Yuan. et al, A hybrid differential evolution method for dynamic economic dispatch with valvepoint effects, Expert system with Applications. vol. 36, issue 2, pp. 40424048, 2009

R.K.Swain, A.K.Barisal, P.KHota and R.Chakrabarti, Short Term Hydrothermal Scheduling Using Clonal Selection Algorithm, International Journal in Electrical Power and Energy System. Vol. 33, issue 3, pp. 647657, March. 2011

T.Niknam, F.Golestaneh, Enhanced adaptive particle swarm optimization algorithm for dynamic economic dispatch of units considering valve point effects and ramp rates, IET Gener.Transm.Distrib, 2012, Vol6, issue5,pp424435.

Panigrahi.C.K,Chattopadhyay.P.K,.Chakrabarty.R.N,,Basu.M simulated annealing technique for dynamic economic dispatch Elect power compt.syst,2006,34pp577586

Panigrahi, B,. Ravikumar, P.V,. Das,S,. Adaptive particle swarm optimization approach for static and dynamic for static and dynamic economic load dispatch. Energy conversion Mang., 2008,49,pp1407 1422

Sivasubramani, S. Swarup, K.S.: 'Hybrid SOASQP algorithm for dynamic economic dispatch with valve point effects Energy, 2010, 35.(12),pp50315036

Hemamalini,S,.Simon,S.P .Dynamic economic dispatch using artificial using Maclaurin series based Lagrangian method Energy cover, Manage,2010,5,pp22122219.

Krishnanand,K.N.D.Ghose,D.Glowworm swarm optimization: a new model for optimizing multimodal functions, Computational Intelligence Studies,1(1):93119,2009
