Grey Wolf Optimizer Technique to Solve Combined Economic Emission Dispatch (CEED) Problem

Hong Mee Song, Universiti Malaysia Pahang, Malaysia Mohd Herwan Sulaiman, Universiti Malaysia Pahang, Malaysia Mohd Rusllim Mohamed, Universiti Malaysia Pahang, Malaysia

The Asian Conference on Society, Education and Technology 2014 Official Conference Proceedings

Abstract Grey Wolf Optimizer (GWO) is a newly proposed algorithm that developed based on inspiration of grey wolves (Canis Lupus). This GWO algorithm mimics the nature of grey wolves in leadership hierarchy and hunting mechanism. This paper is in the purpose of introducing GWO to solve combined economic emission dispatch problem (CEED) in power system. CEED actually is a bi-objective problem where the objective of economic dispatch (ED) and emission dispatch (EMD) are combined into a single function by using price penalty factor. Hence, CEED is used to minimize total generation cost by minimized fuel cost and emission at the same time determines the optimum power generation. The proposed algorithm will be implemented in two different systems which are 6 and 11-generating unit test system with different constraints on various power load demands. The result was compared with the optimization techniques reported in recent literature in order to observe the effectiveness. Keywords: Combined Economic Emission Dispatch, Grey Wolf Optimizer

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Introduction Economic Dispatch (ED) in power system is for schedule the generators to minimize the total operating cost at the same time to meet load demand of the power system over some appropriate period while satisfying various equality and inequality constraint. The ED basically considers the load balance constraint beside the generating capacity limits. (Harinder Pal Singh 2013) Recently, contribution of power engineering to the environment always questioned since the setup of thermal power plant that generate power from combustion of fossil fuel increasing. Usually power plant which based on lowest fuel cost did not consider the environmental pollution.(Güvenç 2010) Hence, emission dispatch assigned in economic dispatch for the purpose of determine the optimal amount of generated power for the generating units by minimizing the fuel cost and emission level simultaneously subject to various system constraints. In CEED, the emission function is the second objective function to be minimized. The two main emissions of power plant are sulphur dioxide )( 2SO and nitrogen oxide )( xNO . (S.Subramaniam 2010) Quite high numbers of methods have been presented in literature to solve combined economic emission dispatch (CEED) problem. Some also tried to develop these methods in order to improve the results obtained. The most simplest method used in this field is Lagrange Multiplier method which only solves equality constraint and later it was extended by implementing Kuhn Tucker method which solves inequality constraint.(Hassan 2010) To date, nature inspired meta-heuristic optimization technique widely used to solve CEED problems where the effectiveness can be observed vividly compare with conventional method. For example, Abido (Abido 2009) developed a multiobjective evolutionary algorithm that use the strength pareto evolutionary algorithm. Bhuvnesh Khokhar & Singh Parmar(Bhuvnesh Khokhar 2012) introduced novel weight-improved particle swarm optimization by improving function of weight parameter in order to find optimal soltion for CEED. A simplified recursive approach of Dynamic Programming (DP) presented by Balamurugan & Subramaniam in (R.Balamurugan 2008) to solve CEED problem by generalized the equation so that it is easier to implemented in larger system. Similarly, Güvenç(Güvenç 2010) presented genetic algorithm based on similarity crossover to solve CEED which implemented the inspiration of children created by using similarity measurement between parents chromosome. Grey Wolf Optimizer (GWO) is a newly proposed technique by S.Mirjalili, S.M.Mirjalili and A.Lewis (Mirjalili, Mirjalili et al. 2014) in year 2013. The technique is inspired by leadership hierarchy and hunting mechanism of grey wolf (Canis Lupus) which belongs to Canidae family. In this paper, the proposed optimization technique used to solve CEED problem. The study result show that the proposed approach is more efficient in minimizing fuel cost and emission compare with reviewed paper. Problem Formulation

The objective of Combined Economic Emission Dispatch is to minimize the fuel cost and emission while satisfying several equality and inequality constraints. Hence, the problem can be formulated as A. Problem formulation Consider a power system having N generating units, the objective function is formulated as

C)Min f(FC,EF T = (1) B. Minimization of Fuel Cost The generator cost curve are represented by quadratic functions and the total fuel cost FC in ($/h) can be expressed as FC = ( )∑ =

++N

i iiiii cPbPa12 (2)

where N is the number of generators; iii cba ,, are the cost coefficients of the thi generator and P is the vector of real power outputs of generators and defined as

[ ]PPPP Νi ,,, ……21= (3)

C. Minimization of Emission The total emission EC in (Kg/h) can be expressed as

( )∑ =++=

N

i iiiii γPβPαEC1

2 (4)

where N is the number of generators; iii γβα ,, are the emission coefficients of the thi generator.

D. Constraints 1.) Power Balance/Equality Constraint The total generated power must cover the total load power which can be defined as

01

=−∑ =

N

i iload PP (5) 2.) Generation Capacity/Inequality Constraint For stable operation, the real power output of each generator is restricted by lower and upper limits as follows:

,maxmin PPP iii ≤≤ i = 1, 2… N (6) E. Price Penalty Factor The bi-objective of combined economic emission dispatch actually can be converted into single objective function by implementing price penalty factor ih .(Venkatesh, Gnanadass et al. 2003) The price penalty factor of each generator is the ratio between the fuel cost and emission at its maximum power output.

γβα iiiii

iiiiii PP

cPbPah++

++=

max2max

max2max (7)

F. Total Cost of Generation The total generating cost actually is sum of minimized fuel cost and minimized emission where the emission (Kg/h) is converted into emission cost ($/h).

( ) ( )γPβPαhcPbPaF iiiii

N

i iiiiiiTMin +++++=∑ =

2

1

2 (8)

The transmission losses of the system have been ignored in this paper due to mathematical simplicity and comparison with reviewed paper. Grey Wolf Optimizer Algorithm GWO actually inspired by grey wolf which are the apex predators where they are stands at the top of the food chain. They mostly live in group which consist 5-12 members. Their leadership hierarchy is as shown in Figure 1. The alpha in the figure shown can be represented as leader where it is decision maker and dictator of the group. The beta wolf in the hierarchy plays the role as consultant to the alpha wolf where help alpha wolf to make decision. It will be appointed as alpha in case the former alpha is passed away or too weak. The lowest ranking in the hierarchy is omega wolves where it plays the role as scapegoat. The losing of omega wolf will cause the entire group facing internal fighting. Omega wolves also can be described as babysitters of the group. Delta wolves in the hierarchy also described as subordinate. It has to submit to alpha and beta but dominate the omega. There are few roles in this category which consists of scouts, sentinels, elders, hunters, and caretakers. The most common social behaviour of grey wolves is group hunting. Hunting of grey wolf can be divided into phases as follows (Mirjalili, Mirjalili et al. 2014),(C. Muro 2011):

• Tracking, chasing, and approaching prey. • Pursuing, encircling, and harassing the prey until it stops moving. • Attack towards the prey.

In the mean of design GWO, the hunting techniques and the leadership hierarchy of the grey wolves are mathematically modelled.

Figure 1: Hierarchy of grey wolf

To model the mathematical computation, the first stage is social hierarchy where the fittest solution is α followed by β and δ. The rest of the candidate solution is assumed as ω. In the stage of encircling prey, the proposed equations are

( ) ( )tt. XXCD p

!!!!−= (9)

DAtXtX p

!!!!.)()1( −=+

(10)

araA !!!!−= 1.2

(11)

2.2 rC !!=

(12) Where t indicates the current iteration, A

!and C

!are coefficient vectors, pX

!is the

position vector of the prey, and X!

indicates the position vector of a grey wolf. A!

and C!

actually can be calculated as shown in equation (11) and (12) where a! linearly decreased from 2 to 0 over the course of iterations and 1r , 2r are random vectors. The position of grey wolf (X,Y) can be updated according to the position of prey (X*,Y*). The mathematical formulation during the stage of hunting is as follow

|.||,.||,.| 321 XXCDXXCDXXCDx!!!!!!!!!!!!

−=−=−= δδββα (13)

).(),.(),.( 332211 δδββαα DAXXDAXXDAXX!!!!!!!!!!!!

−=−=−= (14)

3)1( 321 XXXtX

!!!! ++

=+

(15)

Figure 2: Pseudo code of the GWO algorithm

GWO for Combined Economic Emission Dispatch Problem The parameter that needs to be set in GWO is search agents and number of iteration. The solution of GWO for CEED is initialized based a set of candidate, ngsaX , . This comprises of the number of generations of the system that will be optimized which resulted minimum total cost, fuel cost and emission by fulfilling all the constraints. The search agent variables of the CEED can be expressed as follows:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=sang

sa

ng

ji

xx

xxX

!"#"

!

1

111

,

(16)

where sa is the number of search agents and gn is the number of generator plant in the system. To achieve the targeted objective which is to solve CEED, Eq. (17) was applied in the performance of evaluation. GWO algorithm chooses the boundaries values when the solution obtained exits the boundaries in any iteration for equality constraint. At the same time for equality constraint, the penalty factor PF implemented in objective functions when it is violated. The implementation of PF is as follows

)]([*)(1∑ =

−+=N

i iD PPabsPFFCF (17)

)]([*)(1∑ =

−+=N

i iD PPabsPFECE (18) The algorithm will continue until the maximum iteration is met and the optimum result is obtained (M.H. Sulaiman 2014). Results & Discussion

The proposed method is tested on six-generator test system taken from (Güvenç 2010) for solving CEED problem while ignoring power losses. The fuel cost coefficient, emission coefficient and generator capacity limit are given in Table 1 and 2.

Table 1: Fuel cost coefficients and generation limits of six-generator system Generator 1a

($/MW²h) 1b

($/MWh) 1c

($/h) min1P

(MW) max1P

(MW) 1 0.1525 38.540 756.800 10 125 2 0.1060 46.160 451.325 10 150 3 0.0280 40.400 1050.000 35 225 4 0.0355 38.310 1243.530 35 210 5 0.0211 36.328 1658.570 130 325 6 0.0180 38.270 1356.660 125 315

Table 2: Emission coefficients of six-generator system

Generator 1α (Kg/MW²h)

1β (Kg/MWh)

1γ (Kg/h)

1 0.0042 0.3300 13.860 2 0.0042 0.3300 13.860 3 0.0068 -0.5455 40.267 4 0.0068 -0.5455 40.267 5 0.0046 -0.5112 42.900 6 0.0046 -0.5112 42.900

Table 3 presents the best optimal power output with minimum total cost, fuel cost and emission using GWO algorithm with the power demand varies from 500-1100 MW for six generator system. While Table 4 gives the comparative result of GWO with other optimization techniques for six-generator test system with power demand of 500-1100 MW. Table 3: CEED solution for six-generator system

Load (MW) Power load (MW) 500 600 700 800 900 1000 1100

Unit 1 (MW) 31.8794

46.0089

60.2174

74.2786

88.5183

102.7083

116.9031

Unit 2 (MW) 24.4049

40.5243

56.8850

73.1641

89.3756

105.8075

122.0459

Unit 3 (MW) 88.0607

102.1737

116.1917

130.3291

144.3443

158.4078

172.5360

Unit 4 (MW) 89.0580

102.9178

116.6627

130.5462

144.2855

157.9717

171.7070

Unit 5 (MW) 134.3870

155.2392

175.9522

196.5394

217.2205

238.1182

258.7316

Unit 6 (MW) 132.2100

153.1361

174.0911

195.1427

216.2557

236.9865

258.0764

Fuel Cost ($/h) 27195.7055

31827.1352

36637.3658

41621.2525

46781.8156

52121.9668

57634.8291

Emission Output (Kg/h)

257.1116

331.2539

422.5478

531.0997

656.8470

799.7291

959.8889

Price Penalty Factor 48.3216

Total Cost ($/h) 39619.7593

47833.8643

57055.5655

67284.8559

78521.7367

90766.1846

104018.2309

Table 4: Comparison of fuel cost, emission and total cost for six-generator system

Fuel cost ($/h)

Method Load (MW) 500 600 700 800 900 1000 1100

ϒ-Iteration (Güvenç 2010),(R.Balamurugan 2008)

27092.50

31628.70

36314.00

41148.40

46131.80

51264.60

56546.40

Recursive (Güvenç 2010),(R.Balamurugan 2008)

27092.50

31628.60

36313.90

41148.30

46131.80

51264.50

56546.20

PSO (Güvenç 2010),(R.Balamurugan 2008)

27097.50

31634.90

36314.20

41160.30

46160.60

51269.60

56556.70

DE (Güvenç 2010),(R.Balamurugan 2008)

27098.10

31629.20

36314.00

41152.60

46152.60

51264.60

56546.60

Simplified recursive (Güvenç 2010),(R.Balamurugan 2008)

27092.50

31628.60

36313.90

41148.30

46131.80

51264.60

56546.20

Similarity crossover of GA (Güvenç 2010)

27089.45

31626.79

36310.80

41144.47

46124.54

51262.31

56542.01

Proposed GWO 27195.7055

31827.1352

36637.3658

41621.2525

46781.8156

52121.9668

57634.8291

Emission Output (Kg/h) ϒ-Iteration (Güvenç 2010),(R.Balamurugan 2008)

261.6350

338.9930

434.3800

547.7970

679.2410

828.7200

996.2240

Recursive (Güvenç 2010),(R.Balamurugan 2008)

261.6340

338.9920

434.3800

547.7960

679.2410

828.7150

996.2180

PSO (Güvenç 2010),(R.Balamurugan 2008)

262.2250

339.8200

434.6050

547.8440

679.7240

828.8630

996.6720

DE (Güvenç 2010),(R.Balamuru

261.8590

339.0650

434.4530

547.8020

679.2830

828.7150

996.2220

gan 2008) Simplified recursive (Güvenç 2010),(R.Balamurugan 2008)

261.6340

338.9920

434.3800

547.7960

679.2410

828.7150

996.2180

Similarity crossover of GA (Güvenç 2010)

261.3307

338.4397

433.6409

546.7831

678.2906

827.2612

994.5205

Proposed GWO 257.1116

331.2539

422.5478

531.0997

656.8470

799.7291

959.8889

Total cost ($/h)

ϒ-Iteration 39735.1218

48009.3841

57303.9366

67618.8275

78953.8119

91309.6764

104685.5376

Recursive 39735.0735

48009.2358

57303.8366

67618.6792

78953.8119

91309.3347

104685.0477

PSO 39768.6316

48055.5461

57315.0090

67632.9986

79005.9512

91321.5863

104717.4857

DE 39751.5459

48013.3633

57307.4641

67623.2691

78976.6414

91309.4347

104685.6410

Simplified recursive

39735.0735

48009.2358

57303.8366

67618.6792

78953.8119

91309.4347

104685.0477

Similarity crossover of GA

39717.3676

47980.7378

57265.0221

67565.9042

78900.6271

91236.8948

104598.8318

Proposed GWO 39619.7593

47833.8643

57055.5655

67284.8559

78521.7367

90766.1846

104018.2309

In Table 3, proposed GWO obtained minimum total cost by minimizes fuel cost and emission. When the load varied from 500-1100 MW, the algorithm demonstrated its efficiency well by choosing optimal power of generating unit with minimum cost of operation. The comparison with other techniques showed that GWO have the most minimum total cost of generation for six-generator system when the same price penalty factor applied to the value of other techniques. The optimum minimization in emission successfully minimized the total operating cost of the system. Conclusion In this paper, the recent natures-inspired Grey Wolf Optimizer (GWO) technique discussed to solve CEED problems with loss less. It has been tested with six-generator system to observe its effectiveness and robustness. From the simulation, it can be concluded that the proposed GWO algorithm performed better than other optimization compared by minimizes the total generating cost. The technique chooses to minimize the emission more rather than fuel cost in terms to minimize the total operating cost with generated price penalty factor. Acknowledgement The authors would like to acknowledge Universiti Malaysia Pahang (UMP) and Ministry of Higher Education Malaysia (MOHE) for the financial supports and facilities provided to conduct this research. Grant #RDU130104.

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