[ieee 2010 annual ieee india conference (indicon) - kolkata, india (2010.12.17-2010.12.19)] 2010...

978-1-4244-9074-5/10/$26.00 ©2010 IEEE 2010 Annual IEEE India Conference (INDICON)

Oppositional Biogeography-Based Optimization for Multi-objective Economic Emission Load Dispatch

Aniruddha Bhattacharya Pranab Kumar Chattopadhyay Member IEEE

′Abstract- This Paper presents an Oppositional Biogeography-Based Optimization algorithm to solve complex Economic Emission Load Dispatch (EELD) problems of thermal power systems. Emission of NOx and SOx are considered for case studies. The proposed method is a modification over Biogeography-Based Optimization technique, designed to accelerate its convergence rate and to improve the quality of solution. This method combines opposition-based learning scheme along-with migration concept of BBO. Instead of ordinary random numbers, quasi-reflected numbers have been employed in this work for initialization of population and also for a new operation, namely, generation jumping. The proposed algorithm has been applied for solving multi-objective EELD problems in a 3 Generator system with NOX, SOX emission and in a 6 Generator system with both valve-point loading and NOX emission. The superiority of the proposed method over other alternatives has been demonstrated. Considering the solution quality the proposed method seems to be a promising alternative to solve these problems. Index Terms – Biogeography-Based Optimization, Economic Emission Load Dispatch, Opposition-based learning, Opposite numbers, Quasi-reflected numbers.

I. INTRODUCTION

Economic Load Dispatch (ELD) problem seeks the best generation schedule subject to several equality and inequality constraints to minimize the production cost. However, since 1980s general awareness of common people grew about the ill effects of pollutants like NOX, SOX, etc. that are present in the effluent from a thermal power plant. This has led to enactment of the new clean air policies. Regulations have forced electric utilities and power producers to consider the environmental impact of power generating plants. As a result the concept of Economic Emission Dispatch (EED) has come up. EED is an optimization problem that pursues least emission level of operation of a power system. But operating either at the absolute minimum cost of generation or at the absolute minimum emission may no longer be a desirable. The obvious approach is to figure out the optimal outputs of the generators in the system by minimizing the cost of generation and emission simultaneously. This concept is known as Economic Emission Load Dispatch (EELD).

′ A. Bhattacharya is a Ph.D scholar at Jadavpur University, Kolkata, West

Bengal, 700 032 INDIA (e-mail: [email protected]). Prof. P. K. Chattopadhyay is with the Department of Electrical Engineering, Jadavpur University, Kolkata, West Bengal 700 032 INDIA (e-mail: [email protected]).

Different classical mathematical techniques as well as soft computing techniques have been applied to solve different EELD problems. Recently, Dan Simon proposed a Biogeography-Based Optimization (BBO) method [1]. BBO has already been applied successfully to solve non-convex, large, complex Economic Load Dispatch problems [2].

Initializing the habitats of BBO using quasi-reflected random numbers, instead of ordinary random numbers has developed a modified version of BBO, known as Oppositional BBO (OBBO) [3]. In OBBO, an opposition-based learning (OBL) [3] method has been incorporated into the basic BBO algorithm with a view to enhance the convergence property of the original algorithm. This OBL algorithm is further modified by dynamic domain scaling and weighting the reflection amount based on individual’s fitness in OBBO. OBBO has been successfully applied to different benchmark functions [3] and it has been found to outperform BBO in terms of simulation time and solution quality.

The authors have applied the newly developed algorithm to solve two types of EELD problems, namely, EELD with quadratic cost, NOX & SOX emission function (EELDQNOXSOX) and EELD with valve-point loading effects & NOX emission (EELDVPLNOX).

Section II of the paper provides a mathematical formulation of EELD problems. The BBO approach is described in Section III. Section IV defines opposition based learning. Section V explains the proposed OBBO algorithm. The simulation studies are discussed and conclusion is drawn in Section VI and VII.

II. EELD PROBLEM FORMULATION

EELD is a multi-objective mathematical programming problem which seeks a balance between cost of generation and cost of degradation of environment due to emission and may be formulated as a minimization problem, with the objective function

C (f1, f2, f3) (1) where, f1, f2 and f3 are functions denoting fuel cost, NOx and SOx emission respectively. The fuel cost function f1 may be defined as follows:

21

1 1

( )N N

i i i i i i i

i i

f F P a b P c P= =

= = + +∑ ∑ ($/hr) (2)

The NOX and SOX emission are defined [4] as:

2010 Annual IEEE India Conference (INDICON)

2

22

1 1

( )N N

i i ni ni i ni i

i i

f Fx P P Pα β γ= =

= = + +∑ ∑ (Ton/hr.) (3)

23

1 1

( )N N

i i si si i si i

i i

f Fx P P Pα β γ= =

= = + +∑ ∑ (Ton/hr.) (4)

where, Fi(Pi) is the generation cost, ai, bi, ci are the cost coefficients. f2 and f3 are the total amount of NOX and SOX released from the system in Ton/hr. niα , n iβ , niγ and siα ,

s iβ , siγ are the NOX and SOX emission coefficients of the i-th generator. The constraints to be satisfied are as follows:

A) Real Power Balance constraint:

1

0N

i D L

i

P P P−

=

− =∑ (5)

B) Generator Capacity Constraints: As the power iP generated by each generator shall be within their lower limit miniP or upper limit maxiP , so

min maxi i iP P P≤ ≤ (6) The transmission losses PL can be expressed using B-

coefficients and unit power output as follows:

0 00

1 1 1

N N N

L i ij j i i

i j i

P P B P B P B= = =

= + +∑∑ ∑ (7)

The output power of one of the generators, say the Nth generator (called Slack Generator) is a dependent variable, which may be calculated from the power balance equation (5).

( 1)

1

N

N D L i

i

P P P P−

=

= + − ∑ (8)

The transmission loss ΡL of (7) is a function of outputs all generators, including that of the slack generator and can be rewritten as

1 1 1 12

0 0 001 1 1 1

2 ( )N N N N

L i ij j N Ni i NN N i i N Ni i i i

P PB P P B P B P B P B P B− − − −

= = = =

= + + + + +∑∑ ∑ ∑ (9)

Expanding and rearranging (8) and (9), 1 1 1 1 1

20 0 00

1 1 1 1 1(2 1) ( ) 0

N N N N N

NN N Ni i N N D i ij j i i ii i i i i

B P B P B P P PBP B P P B− − − − −

= = = = =

+ + − + + + − + =∑ ∑∑ ∑ ∑ (10)

The loading of the dependent generator (i.e. Nth) may then be found by solving (10).

The above mentioned multi-objective problem may be converted into a single objective optimization problem by using Price Penalty Factors (PPF) [4] and weighting Factors.

When fuel cost and NOX emission are considered, the overall objective function is

Minimize C = (w)x(f1)+(1-w)x(Pfn)x(f2) ($/hr) (11)

where, Pfn is the Price Penalty Factor for NOX emission, blending the emission costs for NOX emission f2 with the normal fuel cost f1. ‘w’ is the weighting factor whose value varies uniformly between (0, 1).Initially w is set at 0 then increment in steps of 0.01 is made up to 1.

When fuel cost, NOX and SOX emissions are all considered together, the overall objective function can be formulated as per following equation

Minimize C = (f1)+(Pfn).(f2)+(Pfs).(f3) ($/hr) (12)

where, Pfn and Pfs are the Price Penalty Factors for NOX and SOX emission, which blends the NOX and SOX emission costs with the fuel costs. The procedure to find out PPF for NOX, SOX is as follows: a) The fuel cost of each generator is evaluated at its maximum output in $/hr. is

21 max max

1

N

i i i i ii

f a b P c P=

= + +∑ (13)

b) The emission release of each generator for NOX and SOX are evaluated at its maximum output in Ton/hr. is,

2max max

1

N

NOX ni ni i ni i

i

f P Pα β γ=

= + +∑ (14)

2max max

1

N

SOX si si i si ii

f P Pα β γ=

= + +∑ (15)

c) Pfn[i], Pfs[i] (i = 1, 2, 3 ..., n) for each generating unit is calculated from

2

2

max max )1

max max1

([ ]

( )

N

i i i i ii

N

ni ni i ni ii

a b P c PPfn i

P Pα β γ

=

=

+ +=

+ +

∑

∑ (16)

2

2

max max )1

max max1

([ ]

( )

N

i i i i ii

N

si si i si ii

a b P c PPfs i

P Pα β γ

=

=

+ +=

+ +

∑

∑ (17)

d) Sets of Pfn[i]and Pfs[i] (i = 1, 2, 3 ..., n) are arrange in ascending order. e) The maximum capacity of each unit, (Pimax) is added one at a time, starting from the smallest Pfn[i] unit for NOX emission & smallest Pfs[i] unit for SOX emission until maxi DP P≥∑ .

f) At this stage Pfn[i] & Pfs[i]associated with the last unit in the process are the price penalty factor Pfn ($/Ton) for NOX emission and Pfs ($/Ton) for SOX emission for that demand PD. Different types of EELD problems solved in this paper are:

1) EELDQNOXSOX: The objective function for this type of EELD problem may be written as (12) and Price Penalty Factors for NOX and SOX emission are calculated as per (16) and (17). Here the problem consists in minimizing (12) satisfying constraints mentioned in (5) and (6).

2) EELDVPLNOX: Fuel cost characteristics with ‘valve-point loadings’ is represented by a more complex formula

21 min

1 1( ) { ( )}

N N

i i i i i i i i i i ii i

f F P a bP cP e Sin f P P= =

= = + + + × × −∑ ∑ (18)

where ai, bi, ci, ei and fi are the cost coefficients of the i-th generator. Pi is the power output of i-th generator. Here, NOX emission is represented by following equation:

2 22

1 1( ) 10 ( ) exp( )

N N

i i i i i i i i i ii i

f Fx P P P Pα β γ ξ λ−

= =

= = + + +∑ ∑ (19)


iα , iβ , iγ , iξ & iλ are emission coefficients of i-th generator. The overall objective function is formed as per (11) after calculating PPF for NOX emission. In this case at the time of calculating PPF, instead of using (2) and (3), equations (18) and (19) are used respectively in step (a) and (b). In step (c), ratios of values obtained from step (a) and (b) are used to calculate PPF. The revised objective function is then minimized subject to the same constraints (5) and (6) for each value of ‘w’. The best compromise generation schedule can be obtained using fuzzy set theory as mentioned below: Best Compromise Solution: The procedure described above generates the non-dominated set of solutions known as the Pareto-optimal solutions. The decision maker may have imprecise or fuzzy goals for each objective function. To aid the power systems operator in selecting an operating point from the obtained set of Pareto-optimal solutions, fuzzy logic theory is applied [5].to each objective function to obtain a fuzzy membership function ifμ

max

max min

1

0

fi fifi fi fiμ

⎧⎪ −⎪= ⎨

−⎪⎪⎩

min

min max

max

i i

i i i

i i

f ff f ff f

≤< <

≥

(20)

The best non-dominated solution can be found when kμ in (21), is maximum where the normalized sum of membership function values for all objectives is highest.

1

1 1

Nk

fik i

M Nk

fik i

μμ

μ=

= =

=∑

∑∑

(21)

Where, M is the number of non-dominated solutions.

III. BIOGEOGRAPHY-BASED OPTIMIZATION (BBO)

BBO [1] is a population based, stochastic optimization technique developed by Dan Simon in 2008. It is based on the concept of biogeography.

In the context of biogeography, a habitat is defined as an Island (area) that is geographically isolated from other Islands. Geographical areas that are well suited as residences for biological species are said to have a high habitat suitability index (HSI). The variables that characterize habitability are called suitability index variables (SIVs). SIVs can be considered as the independent variables of the habitat and HSI calculation is carried out using these variables. The migration of some species from a habitat to an exterior habitat is known as emigration process and an entry into one habitat from outside is known as immigration process. The rate of immigration λ and the emigration μ are functions of the number of species in the habitat. Habitats with a high HSI have a low species immigration rate as they are already saturated with species. As a result, these high HSI habitats are more static in their species distribution than low HSI habitats. On the contrary emigration rate of high HSI habitats are high. The large numbers of species on high HSI islands have many opportunities to emigrate into neighboring habitats having less

number of species and share their characteristics with those habitats. For this reason habitats with a low HSI have a high species immigration rate. Fig. 1 of [1] illustrates a model of species movement process in a single habitat with straight line immigration and emigration curves.

When BBO is applied to any mathematical optimization problem, different terms of biogeography can be correlated with the different terms of optimization problem. A good solution is analogous to a habitat with high HSI. High HSI solutions tend to share their features with low HSI solutions while retaining their identity in high HSI solutions. In this way poor solutions accept lots of new features from good solutions. Addition of these good features to low HSI solutions may raise the quality of them. BBO works based on two mechanisms: - migration and mutation. Details of these are available in [1-2].

IV. OPPOSITION-BASED LEARNING (OBL)

Opposition-based learning (OBL) is proposed in [6]. The main principle involved in OBL is to utilize opposite numbers to approach the solution as it was found that the opposite of a random number is likely to be closer to the solution than the original random number. Again, in [3], it has been demonstrated that a quasi-reflected number is usually closer to the solution than its opposite number.

Opposite, quasi-opposite, quasi-reflected numbers in one dimensional space have been defined below for easy reference. These may easily be extended to higher dimensions. Definition 1: Let x be any real number between [a, b]. Its opposite, xo, is defined as

xo = a + b − x Definition 2: Let x be any real number between [a, b]. Its quasi-opposite point, xqo, is defined as

xqo = rand(c,xo) where ‘c’ is the centre of the interval [a, b] and can be calculated as (a + b)/2 and rand(c,xo) is a random number uniformly distributed between ‘c’ and ‘xo’. Same logic can be applied to reflect the quasi-opposite point xqo, to obtain the quasi-reflected point, xqr. Definition 3: Let x be any real number between [a, b]. Then the quasi-reflected point, xqr, is defined as

xqr = rand(c,x) where, rand(c,x) is a random number uniformly distributed between c and x.

Figure 1. Opposite points defined in domain [a, b]. c is the centre of the domain and x is an estimated solution, generated by an EA. xo is the opposite of x, and xqo and xqr are the quasi-opposite and quasi-reflected points respectively lies in the region mentioned by arrows. Figure 1 illustrates a point x, its opposite point xo, the domain for its quasi-opposite point xqo and quasi-reflection xqr.

Table I in [3] indicates that the most cost effective opposition method is to create a quasi-reflected population.

x c xo b

xqr xqo

a


4

V. OPPOSITIONAL BIOGEORAPHY-BASED OPTIMIZATION

In OBBO algorithm, performance of two main steps of BBO, e.g., habitat initialization and migration operation are enhanced using the OBL scheme to accelerate its convergence speed and to find better and faster solution. Brief description of the algorithm of proposed approach (OBBO) is given in Table II of [3]. Different steps of OBBO are described briefly here.

A. Opposition-Based Habitat Initialization OBBO creates each SIV (i.e. each member of solution set) of

each habitat set (H) using uniformly distributed random number. By utilizing OBL, a quasi-reflected habitat (OH) is generated. Table I shows the implementation of opposition-based initialization for OBBO.

TABLE I QUASI-REFLECTED OPPOSITE POPULATION INITIALIZATION PSEUDO CODE, WHERE NP IS THE HABITAT SIZE, D IS THE PROBLEM DIMENSION, H IS THE

CURRENT HABITAT, OH IS THE OPPOSITE HABITAT. 1. Generate uniformly distributed random habitat H; 2. Find the absolute min, max and median for the whole

habitat 3. Create reflection weight, τ ∈ [0, 1], which determines the

reflection amount based on individual’s fitness. 4. Create OH based on the dynamic domain and reflection

weight: 5. for i = 1 : Np 6. for j = 1: D 7. if Hi,j < Median 8. OHi,,j = Hi,,j + (Median − Hi,,j)* τi 9. else 10. OHi,,j = Median + (Hi,j − Median)* τi 11. end 12. end 13. end 14. Calculate the HSI value of each individual of total Original

Habitat and Opposite Habitat. 15. Select Np fittest individuals from the set of (H, OH) as

initial population H, based on their HSI value. 16. The elite habitat (p) is stored separately. B. Immigration and Emigration based Migration

Immigration rate λ and emigration rate µ are used to modify each non-elite habitat by migration operation. This operation is same as BBO operation. Details are available in [1-2]. C. Implementation of Opposite Habitat Jumping

Jumping rate, 0 ≤ Jr ≤ 1, is a control parameter, used to select whether quasi-reflected population will be created at certain generation or quasi-reflected population creation will be skipped at certain generations to save computational time. OBBO also adds dynamic domain scaling [3] to speed up the optimization process. Pseudo-code is given in Table – III of [3]. D. BBO Algorithm for EELD Problem

The search procedure for minimization of the EELD problem involving both equality and inequality using OBBO algorithm is as shown below:

1) No. of Generators N , no. of Habitats H are Read in. The OBBO parameters like Habitat Modification Probability modP ,

Mutation Probability, maximum mutation rate maxm , max. immigration rate I, max. emigration rate E , step size for numerical integration dt, elitism parameter ‘p’ are initialized.

2) The initial position of SIV of each habitat H should be randomly distributed across the domain of the optimization problem. Each habitat set H should satisfy equality and inequality constraints (5) and (6). Several numbers of habitats depending upon the habitat size is generated. This forms the habitat matrix H . The quasi-reflected habitat, OH is also created from H matrix. Each habitat set of H and OH matrix is a potential solution to the given problem.

3) The HSIi (i=1, 2….H) for each set of habitat and their quasi-reflected habitat for a given emigration rate μ , immigration rate λ and Species S are calculated. In EELD problem HSIi indicates the overall cost of fuel and emission due to i-th set of Generation value (i.e. i-th habitat) in $/hr.

4) The best S set of solutions based on their HSI values, from the S set of Habitat (H) and S set of Quasi-reflected Habitat (OH) are sorted out. The new habitat matrix H then created.

5) Identify elite habitats (i.e. those habitats whose HSI values are optimum). Top ‘p’ habitat sets are retained in the next iteration without making any modification.

6) Migration operation is performed on those SIVs of non-elite habitats that are selected probabilistically. After migration operation new habitat sets are generated.

7) ‘Opposite Habitat Jumping’ process is performed based on the Pseudo code given in Table – III of [3]. Restore Elite Individuals within habitat matrix (H).

8) If current iteration is greater than or equal to the maximum iteration, iterations are terminated. In case of bi-objective problem (i.e. when fuel cost and one emission substance are considered), the results obtained are kept in an array (known as Pareto-optimal set); otherwise steps 3 to 7 are repeated. In case of tri-objective problem (i.e. when fuel cost and two emission substances are considered), output obtained at the end of step 8 directly gives optimum solution.

9) In case of bi-objective problem (represented by (11)), the value of ‘w’ is incremented in step of 0.01 starting from w=0. For each value ‘w’ step 1 to 8 of the algorithm are repeated. This process is continued until the value of ‘w’ reaches to 1.

9) Best Compromise Solution:-The algorithm described above generates the non-dominated set of solutions known as the Pareto-optimal solutions. The best non-dominated solution is found using (20) and (21). After completing the process Best solution of EELD problem is found.

VI. NUMERICAL EXAMPLES AND SIMULATION RESULTS

Proposed OBBO algorithm has been applied to EELD problems for minimization of operating cost and emissions in two different test systems. After performing several trials with different combinations of OBBO parameters, following optimum values of them have finally been settled for all cases: Habitat size=30, Habitat Modification Probability=1, Immigration Probability bounds per gene= [0, 1], step size for numerical integration=1, maximum immigration and


emigration rate for each island=1, number of elite habitat p=2, Jumping Rate (Jr) = 0.3 and without any Mutation process.

A. Description of the Test Systems 1) Test Case 1: A system with 3 generators, NOX and SOX emission is used to demonstrate the efficiency of the proposed approach. The input data are adapted from [4]. The load demand is 850MW. Results obtained from proposed OBBO, BBO, NSGA-II [4], Tabu Search [7] have been compared in tables I, II, III and IV. A pareto optimal front for fuel cost and NOx emission, for fuel cost and SOx emission are shown in Figure 2 & 3 respectively. 2) Test Case 2: It is slightly more complex system having 6 thermal units with valve-point loading and NOX emission. The input data are given in [8]. The load demand is 2.834 p.u. on 100 MVA base i.e. 283.4 MW. Solutions obtained from OBBO, BBO, PSO [8] are shown in tables V, VI and VII. Pareto-optimal solution obtained by OBBO algorithm is shown in Figure 4.

Comparative Study 1) Solution Quality: From the results in tables I, II, III, V and VI, it is seen that the OBBO method can obtain either lower or equal fuel cost and lower emission level than other methods. The overall cost is calculated by adding fuel cost to emission cost (multiplying emission level with corresponding Price Penalty Factor). Tables IV and VII show best compromising costs obtained by OBBO and other methods. The overall cost of compromising generation in OBBO is less than those in BBO and other algorithms. This indicates superiority and reliability of the proposed algorithm. Moreover, the average simulation times of OBBO in all cases are much better than that of BBO, which reflects its superior speed of convergence.

Figure 2. Pareto-optimal front for fuel cost & NOx emission (Test Case1)

2) Comparison of Best Generation Cost: The best fuel cost, NOX and SOX emission obtained by OBBO for the 3-unit system are compared with BBO, NSGA-II [4] and other methods in tables I, II and III. The results show that OBBO obtains the minimum fuel cost 8344.5875 $/hour, minimum NOX emission 0.095923 Ton/hour and minimum SOX emission 8.965931 Ton/hour. Best fuel cost and emission results for 6-unit system are compared with result of BBO, PSO [8] & mentioned in tables

V, VI. The minimum fuel cost & minimum NOX emission obtained in this test case are 613.335079 $/hour & 0.194179 Ton/hour. These results are either improved or same as that of BBO technique. When the best compromised overall costs are compared, it has been seen from tables IV and VII that performance of OBBO is better than those of BBO and others.

Figure 3. Pareto-optimal front for fuel cost & SOx emission (Test Case 1)

Figure 4. Pareto-optimal front for fuel cost & NOx emission (Test Case 2)

TABLE I MINIMUM FUEL COST FOR THREE GENERATOR SYSTEM (PD = 850 MW)

Unit Power Output

Minimum Fuel CostOBBO BBO Tabu

Search [7]NSGA-II

[4]P1 (MW) 435.1981 435.1966 435.69 436.366P2 (MW) 299.9697 299.9723 298.828 298.187P3 (MW) 130.6604 130.6600 131.28 131.228

Total Power (MW) 865.8282 865.8289 865.798 865.781Ploss (MW) 15.8282 15.8289 15.798 15.781

Fuel Cost $/hour 8344.5875 8344.5927 8344.598 8344.651SOX Emission

Ton/hour 9.021948 9.02195 9.02146 9.02541

NOX Emission Ton/hour 0.098686 0.098686 0.09863 0.098922

Simulation Time (Sec.)

1.7642 1.9891 - -

TABLE II MINIMUM SOX EMISSION FOR THREE GENERATOR SYSTEM (PD = 850 MW)

Unit Power Output

Minimum SOX EmissionOBBO BBO Tabu

Search [7]NSGA-II

[4]P1 (MW) 552.1113 552.1111 549.247 538.527P2 (MW) 219.4441 219.4441 234.582 227.817P3 (MW) 92.9597 92.96053 81.893 98.185


Fuel Cost $/hour 8396.4616 8396.4665 8403.485 8385.177

8340 8350 8360 8370 8380 8390 8400

8.97

8.98

8.99

9

9.01

9.02

9.03

9.04

Fuel Cost ($/hr.)

SOx

Emis

sion

(Ton

/hr.)

610 620 630 640 650 660 670 6800.19

0.195

0.2

0.205

0.21

0.215

0.22

0.225

Fuel Cost ($/hr.)

NO

x Em

issi

on (T

on/h

r.)

8340 8345 8350 8355 8360 8365 83700.0955

0.096

0.0965

0.097

0.0975

0.098

0.0985

0.099

0.0995

0.1

0.1005

Fuel Cost ($/hr.)

NO

x Em

issi

on (T

on/h

r.))


6

SOX Emission Ton/hour

8.965931 8.965937 8.974 8.96670 NOX Emission

Ton/hour0.096817 0.096817 0.0974 0.096325

Simulation Time (Sec.) 1.7549 1.9820 - -

TABLE III MINIMUM NOX EMISSION FOR THREE GENERATOR SYSTEM (PD = 850 MW)

Unit Power Output

Minimum NOX EmissionOBBO BBO Tabu

Search [7]NSGA-II

[4]P1 (MW) 508.5800 508.5813 502.914 508.367P2 (MW) 250.4423 250.4433 254.294 250.444P3 (MW) 105.7228 105.7212 108.592 105.934


Fuel Cost $/hour 8365.1088 8365.1146 8371.143 8364.993SOX Emission

Ton/hour8.973662 8.973667 8.9860 8.97374

NOX Emission Ton/hour

0.095923 0.095923 0.0958 0.095924 Simulation Time

(Sec.) 1.7519 1.9806 - -

TABLE IV BEST COMPROMISE SOLUTION OF FUEL COST & SOX , NOX EMISSION FOR 3

GENERATOR SYSTEM (PD = 850 MW)

Unit Power Output Best Compromise Solution OBBO BBO NSGA-II [4]

P1 (MW) 507.11971 507.11954 496.328P2 (MW) 251.64200 251.64262 260.426P3 (MW) 106.00030 106.00042 108.144

Total Power Output (MW) 864.76251 864.76258 864.898Ploss (MW) 14.76251 14.76258 14.898

Fuel Cost ($/hour) 8364.30627 8364.31126 8358.896SOX Emission (Ton/hour) 8.974195 8.974201 8.97870SOX Price Penalty Factor

($/Ton) 970.03157

0 970.031570 970.031570

Equivalent Cost of SOX Emission ($/hour)

8705.2525 8705.25828552557

8709.622457559

NOX Emission (Ton/hour) 0.0959248 0.0959248 0.09599 NOX Price Penalty Factor

($/Ton) 147582.78

814 147582.7881

4 147582.7881

4Equivalent Cost of NOX

Emission ($/hour) 14156.849435771872

14156.849435771872

14166.4718335586

Total Cost ($/hour) 31226.40958 31226.41898 31234.99029 TABLE V

MINIMUM FUEL COST FOR 6 GENERATOR SYSTEM (PD = 2.834 P.U (MW))

Unit Power Output Minimum Fuel Cost OBBO BBO PSO [8]

P1 (MW) 0.050000 0.050004 0.099441P2 (MW) 0.399999 0.400006 0.36248P3 (MW) 0.687498 0.687522 0.48349P4 (MW) 0.949998 0.949992 0.87359P5 (MW) 0.549995 0.550009 0.66428P6 (MW) 0.230949 0.230916 0.39004

Total Power (MW) 2.868439 2.868449 2.873321Ploss (MW) 0.034439 0.034449 0.039321

Fuel Cost ($/hour) 613.335079 613.342347 626.96NOX Emission (Ton/hour) 0.223368 0.223369 0.21392

Simulation Time (Sec.) 1.9274 2.2471 -TABLE VI

MINIMUM NOX EMISSION FOR 6 GENERATOR SYSTEM (PD = 2.834 P.U (MW)) Unit Power Output Minimum NOX Emission

OBBO BBO PSO [8]P1 (MW) 0.410500 0.410500 0.37883P2 (MW) 0.463289 0.463289 0.39323P3 (MW) 0.543820 0.543820 0.49948P4 (MW) 0.389949 0.389949 0.53439P5 (MW) 0.544118 0.544118 0.57341P6 (MW) 0.515173 0.515173 0.48651

Total Power (MW) 2.866849 2.866849 2.86585Ploss (MW) 0.032849 0.032849 0.03185

Fuel Cost ($/hour) 679.184988 679.184988 659.44NOX Emission (Ton/hour) 0.194179 0.194179 0.19567

Simulation Time (Sec.) 1.9194 2.2409 -

TABLE VII BEST COMPROMISE SOLUTION OF FUEL COST & NOX EMISSION FOR 6

GENERATOR SYSTEM (PD=2.834 P.U (MW)) Unit Power Output Best Compromise Solution

OBBO BBO PSO [8]P1 (MW) 0.385228 0.1846 0.14089P2 (MW) 0.399999 0.4000 0.34415P3 (MW) 0.474999 0.6875 0.67558P4 (MW) 0.499999 0.6500 0.83971P5 (MW) 0.549995 0.5500 0.49043P6 (MW) 0.559999 0.3901 0.39797

Total Power Output 2.870219 2.8622 2.88873Ploss (MW) 0.036219 0.0282 0.05473

Fuel Cost ($/hour) 649.969241 628.5743 639.65NOX Emission 0.19536903 0.2028 0.21105

NOX Price Penalty Factor ( $/Ton)

6046.173677

6046.173677

6046.173677

Equivalent Cost of NOX Emission ($/hour)

1181.235103

1226.164022

1276.044954

Total Cost ($/hour) 1831.20434 1854.73832 1915.69495

VII. CONCLUSION

In this paper, the OBBO has been successfully implemented to solve multi-objective EELD problems for minimization of both fuel cost and emission of thermal power plants. This approach has been tested and examined on two different systems to demonstrate its effectiveness. It has been observed that the OBBO has the ability to reduce both, the fuel costs and emission levels in a faster manner than that of conventional BBO. Therefore, it may be concluded that for solving EELD problems, OBBO is superior to BBO and other algorithms in terms of solution quality and computational efficiency.

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