A New Sine Cosine Optimization Algorithm for Solving ...

International Journal on Energy Conversion (I.R.E.CON.), Vol. 5, N. 6 ISSN 2281-5295 November 2017

A New Sine Cosine Optimization Algorithm for Solving Combined Non-Convex Economic and Emission Power Dispatch Problems Rizk M. Rizk-Allah1, Hala M. Abdel Mageed2, Ragab A. El-Sehiemy3, Shady H. E. Abdel Aleem4, Adel El Shahat5 Abstract – The current study presents a modified sine cosine optimization (MSCO) algorithm for solving the non-smooth environmental/economic power dispatch problem. In the proposed MSCO algorithm, random search agents’ population is initialized in the search domain for simultaneous optimization of both the combined economic and environmental objectives. Added to that, the proposed MSCO proposes an opposition strategy to preserve the diversity of solutions purposefully. Hence, the Pareto optimal solutions are customized according to the Pareto front concepts. These solutions are evolved using a modified version of the sine cosine algorithm (SCA), where the best agent is selected randomly from the stored Pareto solutions. Furthermore the parameter-based tuning mechanism is designed to improve the balance between the exploration and exploitation abilities. The correctness and effectiveness of the proposed MSCO are validated through experiments results and comparisons on EELD problem. Simulations were conducted on two test systems with non-smooth fuel cost and emission issues. The first system constitutes 6-unit benchmarking system, while the second one constitutes 10units, and their results are compared with the results of other optimization techniques that were reported in the literature. The numerical comparisons reveal the robustness and effectiveness of the proposed MSCO algorithm. Copyright © 2017 Praise Worthy Prize S.r.l. - All rights reserved.

Keywords: Environmental/Economic Dispatch Problem, Optimization, Pareto Optimal Solution, Sine Cosine Algorithm

Nomenclature Ft ai, bi and ci di, and ei NG PGi αi, βi, γi and ζi PDj NL PLoss min i

PG

D ki

PFk PFkmax

max i

and PG

The best solution so far (destination) of the j dimension in iteration t The previous and current solutions at iterations t and t 1 , respectively Dedicates the absolute value Randomly tuned parameters A constant The maximum number of iterations Indicates the current iteration The lower and upper bounds of candidate search region, respectively The total number of lines

Pj

Nonlinear function that represent the total power generation cost of the system The coefficients of the power generation cost function The coefficients that represent the non-smooth operation of valves The number of generation buses The power generation at bus i The coefficients of power generation emissions The load demand at load bus j The number of load buses The total power losses in the system The minimum and maximum real power bounds, respectively The generalized generation distribution factors (GGDF) for the line k due to the shift in ith generator The real power flow of the line k Upper limit power flow of line k

xti and xti 1

|∙|

r1 , r2 and r3 a

T

t Lb and Ub n

I.

Introduction

Allocating of the power demand among committed generation units considering the economic issue is called economic load dispatch (ELD). The ELD is an important assignment for power system operators [1], [2]. Because of the recent concerns of studying environmental impacts on power systems, a new

Copyright © 2017 Praise Worthy Prize S.r.l. - All rights reserved

https://doi.org/10.15866/irecon.v5i6.14291

180

Rizk M. Rizk-Allah et al.

framework is proposed for the ELD problem to consider the environmental issues due to the increased awareness of the environmental pollution caused by fossil fuelfired thermal power plants. The new framework is defined as environmental/economic load dispatch (EELD) problem. The EELD problem is a multiobjective framework in nature. It has two first objective aims at reducing the fuel costs of generating units, while the environmental objective aims at reducing the emissions while preserving all operational constraints of the power systems. Atmospheric pollutants, such as sulfur oxides and nitrogen oxides, caused by fossilbased thermal units can be modelled separately [3], [4]. Recently, fuel costs have dramatic variation and the increased concerns of environmental issues of power generating units send early alarms for the urgent need of continuous improvement of optimization methodologies that are able to find the best compromise combination between economic and environmental requirements. Therefore, there are continuous interests in the field of conducting optimization methods for solving economic dispatch problem in power systems. Any developed optimization technique for solving the EELD problem must consider the non-convex characteristics, types, models of the available generation units, both of operation and maintenance costs, the operational practical constraints, equipment capabilities and transmission boundaries and be preserving the reliability of the units at different operational situations [5], [6]. Thus, the EELD problem is considered non-convex optimization issue that has objective functions with nonlinear constraints [3]-[7]. These nonlinearities increase even more in practical applications due to the opening process of the steam admission valves that results in a sharp increase in losses. Non-convexities arise from valve points or combined cycle units, zones of prohibited operation of a unit and nonlinear power flow equality constraints [8]. An increase in these nonlinearity characteristics often results in an unsatisfactory solution that is characterized by slow convergence in the case of using some mathematical algorithms. Optimization methods can be classified into conventional and the modern optimization techniques [2]. Lambda iteration and gradient methods were used as alternatives to solve ELD problems [12]. Meanwhile, convex EELD problems are efficiently solved through traditional local search algorithms, such as lambda iteration “which ignores network constraints” [1] and linear programming [2]. However, due to the existence of nonlinearities in generators, the previous methods are not suitable for power systems. In [5], a multi-objective dynamic random neighborhood PSO "DRN-PSO" dynamic search was proposed for solving dual security constrained ELD problem. Other optimization techniques, including nonlinear and dynamic programming, were also applied to the same problem. However, these methods suffer from

non-differential and non-convex objective functions, resulting in local optima trapping. In addition, many multi-objective evolutionary algorithms, such as the niched Pareto genetic algorithm (NPGA) [9], nondominated sorting genetic algorithm (NSGA) [14], particle swarm optimization (PSO) algorithm [15], flower pollination algorithm [16], strength Pareto evolutionary algorithm (SPEA) [17], [18], multiobjective particle swarm optimization (MOPSO) [19] and multi-objective differential evolution (MODE) [7], [11], [20], [21], have been introduced to solve the EED problem with impressive success. The sine cosine algorithm (SCA) is one of the recent metaheuristic algorithms developed in the literature. It was presented in [22] for solving complex optimization problems. SCA is a mathematical algorithm that simulates the behaviour of sine and cosine functions to obtain the best solution (destination). In the SCA, a set of solutions is created randomly, and they are updated based on sine and cosine functions by fluctuating these solutions outwards or towards the destination to create a new population. The SCA has many advantages, such as a simple structure, ease of implementation and low speed to acquire solutions. The optimal power flow solution was investigated by SCA in [23], and the application of the SCA in selection of conductor sizes in radial power systems is presented in [24]. However, a conventional version of SCA has some disadvantages that deteriorate its performance. The first is that the diversity of solutions may not be maintained efficiently which lead to the trapping in local area. The second is that no mechanism is employed to explore and detect the promise regions in the solution space, may lead to poor quality of the outcomes. The third is no representation strategy is introduced in the case of the multi- objective formulation, may stuck to a nondominated solutions. Besides, to the best of our knowledge fewer attempts to utilized SCA in solving single and multi-objective formulations of EELD have been studied in the literature. This study is concerned with solving the non-smooth EELD problem using the proposed modified sine cosine optimization (MSCO) algorithm. The proposed algorithm is employed to obtain the optimum value for each objective as a single goal, and is then employed to optimize the economic and emission objectives simultaneously to obtain the Pareto optimal solution or the Pareto front. The proposed algorithm is tested on two test systems and the results are compared to those published in the literature. The numerical comparisons reveal the robustness and effectiveness of the proposed MSCO algorithm. Thus, proposed MSCO can be an efficient alternative for complex optimization of EELD problems. Then, contributions of this study are stated as follows:  A proposed MSCO algorithm is proposed for solving combined environmental/economic load dispatch problem.  In the proposed MSCO, an opposition strategy is


International Journal on Energy Conversion, Vol. 5, N. 6

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presented to purposefully preserve the diversity of solutions.  The parameter-based tuning mechanism is designed to improve the balance between the exploration and exploitation abilities.  Pareto optimal concepts are proposed to obtain the set of non-dominated solutions for the multi-objective formulation of EELD problem.  The efficiency of the proposed MSCO is validated through experiments results and comparisons on EELD problem. The rest of the work is organized as follows. Section 2 describes the candidate problem. The proposed MSCO algorithm is explained in detail in Section 3. Section 4 describes the tested case studies with a comparative analysis of previously reported works. Finally, Section 5 is devoted to the conclusions of the work.

II.

PGimin  PGi  PGimax

Mathematically, the security formulation in the EELD problem involves a large number of constraints. The power line flow of the transmission line (PFk) can be written in terms of the power generation outputs as [25]: n

PFk 

Sk  S kmax ,k  1, 2,...,n

 di sin

 

ei PGi  PGimin

(1)



III. Proposed Modified Sine Cosine Optimization Algorithm

However, the second objective function that aims to minimize the emission effects is represented as: NG

min Et 

10  2

 i  i PGi   i PGi2



i 1

III.1. Conventional Version The SCA presents a metaheuristic approach that was developed in [22]. It initiates with a random set of points in the search region and then approaches towards the best points through the updating strategy. The updating of solution is based on trigonometric sine and cosine functions, as follows:

(2)

  i exp  i PGi  The previous objective functions in (1) and (2), are subjected to the equality and inequality operational constraints. For equality constraint, the sum of generator’s real power outputs covers the total load demand and transmission line losses. This constraint is expressed as follows: NG i 1

xi  xi  r1  sin  r2   | r3 Pj  xi |

(7)

xi  xi  r1  cos  r2   | r3 Pj  xi |

(8)

Generally, equations (9) and (10) can be merged into one form through switching parameter ( r4 ) that is employed randomly as follows [22]:

NL

 PGi   PD j  PLoss

(6)

For typical power systems, a significant amount of lines have a rather small possibility of being congested. Therefore, the EELD problem may only consider a limited number of lines in congestion conditions, such that the power flowing in these transmission lines may violate or be close to the upper-security limits. In this work, the critical lines term is identified for the congested lines and only the critical lines are taken into account [26]. It should be noted that these lines are considered previously determined by the power system operators. Two security indices are presented the quality of EELD solution obtained by parallel hurricane optimization algorithm in [27]. Several multi-objective frameworks were presented in the literature as fruit fly optimization algorithm [28], gravitational search algorithm [29], ABC-PSO hybrid algorithm [30] and multi-objective cultural algorithm [31].

NG

i 1

(5)

Furthermore, for a transmission line k, its should restrict the kth line loading Sk as given in Eq. (6) as:

The non-smooth formulation of EELD problem aims at finding the optimal scheduling of power generation units that minimize both fuel costs and emissions while satisfying the total required demand. The fuel cost function can be mathematically stated as a quadratic function with superimposed sine components. The superimposed component represents the rippling effects produced by the steam admission valve opening. It can be expressed as follows:

  ai  bi PGi  ci PGi2 

  Dki  PGi  i 1

Problem Description

min Ft 

(4)

(3)

j 1

 xti  r1  sin  r2   | r3 Pjt  xti | if r4  0.5 xti 1   t t t  xi  r1  cos  r2   | r3 Pj  xi | if r4  0.5

The inequality constraint refers to preserving the real power output of each generator within their hard lower and upper limits. It can be simulated as: Copyright © 2017 Praise Worthy Prize S.r.l. - All rights reserved

(9)


182


The parameter r1 is updated to maintain the balance between the exploration search and exploitation ability as:

r1  a  t

a T

III.2.2. Opposition-Based Optimization In the optimization process, the point x and its opposite x is evaluated based on the objective function where the better one replaces the other as shown in Figs. 1, i.e., f  x  replaced with it is corresponding solution x

(10)

based on the fitness function. If f  x  is better than

In this sense, the parameter r1 is responsible for determining the region of next solutions, where this region may be either inside the region between xti and Pj

f  x  then x new  x , otherwise, x new  x . Therefore, the population is updated based on one choice according to the objective function. Thus, this strategy provides a higher chance to attain the promising regions.

or outside them. The pseudo code of the conventional SCA is illustrated in Algorithm 1. Algorithm 1: conventional Sine-Cosine Algorithm Generate a set of solutions randomly Determine the best one among them (destination= P ) repeat Evaluate each solution using the objective function Update the destination Update the random parameters r1 , r2 , r3 and r4 Update the position of each solution by Eq. (12) until ( t < T) Return the global optimum (the best solution obtained so far as)

(a) One dimension

III.2. Opposition Strategy (OS)

(b) Two dimension

The opposition strategy (OS) aims to improve the performances of metaheuristic approaches (MAs). Since, the MAs rely on some random parameters as attempt to obtain the optima; these approaches could not improve the solution through the runs of the MAs. Thus, this can make these approaches suffer from the premature convergence. To overcome these problems, the OS provides a mechanism to search in the opposite direction of the candidate solution, therefore, the diversity of solutions can be improved and the quality of solution can be enhanced.

Figs. 1. The point x and its opposite x

III.3. Multi-Objective Strategy (MOP) Consequently, the EELD can be formulated as a multi-objective problem (MOP). The MOP can be mathematically expressed as follows: Find a vector of the decision variables x  ( x1 , x2 ,..., xn )   with regards to the following objectives: T

Min F  x    f1  x  , f 2  x  ,..., f K  x  

III.2.1. Opposite Number

subject to x  ,

The opposite value ( x ) of a given real number x,x   Lb,Ub  is defined by Tizhoosh [32] as follows: x  Lb  Ub  x



xiL

(11)

space

and

xi   Lbi ,Ubi  ,i  1, 2,...,n .

(13)

,

where F(x), gp(x) and hj (x) are the objective functions, inequality and equality constraint functions with the total number of K, P, and J, respectively. Most real-life applications involve a collection of conflicting objectives. In this respect, there is no single global optimal solution for which all objectives are optimized simultaneously. An increase in one objective will yield a decrease in the other objectives.

The

opposite of x  x1 ,x2 ,...,xn  is given by x  x1 ,x2 ,...,xn  as follows:

xi  Lbi  Ubi  xi

 xi 

xiU

 p  1, 2,...,P  ,  j  1, 2,...,J  , and  i  1, 2,...,n 

On the other hand, this concept can be generalized in the higher dimension as defined in [32]. Let x  x1 ,x2 ,...,xn  be an n-dimensional point in the search



  x  n | g p  x   0  h j  x   0 ,

(12)



183


Accordingly, a set of solutions should be attained and the concept of the so-called Pareto optimal set or Pareto front. In the literature, the preliminaries of ‘‘domination’’ and Pareto optimality are outlined as follows [17]-[19]: Definition 1 (Domination): for the minimization problem, the solution x1  , where   n is the

denote jth generation of the ith solution and its opposite solution, respectively. Step 2 (Constraints satisfaction mechanism): in this step, the solutions are collected in one pool denoted by   such that   PG  PG . j ,i

Afterwards each solution is repaired or improved so that the overall generators satisfy the equality constraints, as well as the generation limits. The procedure demonstrating this step is shown in Fig. 2.

feasible region, is dominating a solution x2  , briefly written as x1 > x2 for minimization, if and only if it is superior or equal in all objective functions and at least superior in one objective. This can be expressed by Eq. (14):

Constraints satisfaction mechanism Input: PD  PLoad  PLosses ;

  PG j ,i , PG j ,i ,   PG j ,i  PG j ,i , PG j ,max , PG j ,min .

  i  1, 2 ,...,K : fi  x1   fi  x 2  , (14) x1  x 2 , if    j  1, 2 ,...,K : f j  x1   f j  x 2  .

 i , i  1, 2,..., 2m NG 1

 NG  PD   j 1  j If  NG  PG NG ,max

Definition 2 (Pareto optimality): If x1  is an arbitrary solution vector, then: (a) The solution vector x1  is said to be nondominated regarding the set Ω  Ω if and only if there is no solution vector x2 in Ω can dominate x1. (b) The decision (parameter) vector x1 is called Pareto optimal, if and only if x1 is non-dominated in the whole parameter space  .

 

   NG  PG NG ,max ;    j



   ( j )     j





 PG j ,max



NG 1 j 1

; PG NG ,max

NG 1 j 1



  PG NG ,min   NG ;   PG j ,min

III.4. The Proposed MSCO Procedure





NG 1 j 1

 

 j

NG 1 j 1

;  NG  PG NG ,min

NG 1 j 1

  [  NG ] Output :  , put PG  

The proposed MSCO algorithm is developed through four improvements on the traditional SCA as follows:  The first improvement is based on the opposition strategy that maintains the diversity of search agents.  The second improvement is based on Pareto concept which is utilized to generate a set of non-dominated solutions. Here, the aim is to help the operators to choose the best operating one from the operating point of view.  The third improvement is based the weighted sum method which is employed to convert the multiple functions into a single one through different weights.  The last improvement presents a new modification to enhance the exploration and exploitation searches based on the adaptive adjustment of parameter r1 . Accordingly, the main steps of the MSCO algorithm can be summarized as follows: Step 1 (Initialization): a population of solutions is randomly initialized within the feasible solution region as well as the opposite solutions are obtained using the Equations (15) and (16):



 PG j ,i  PG j ,max  PG j ,min  PG j ,i



j 1

Else if  NG  PG NG ,min





NG 1

  [  NG ]

   ( j )      j

PG j ,i  PG j ,min  rand  PG j ,max  PG j ,min

j ,i



Fig. 2. Constraints satisfaction mechanism

Step 3 (Evaluation): in this step each search agent is evaluated according to the optimization process either single function (SF) or multiple functions (MFs) as follows:

  w1 Ft  w2 Et   F  xi     w F  w E 2 t  1 t

wk 

rand k   K

MFs

 randk 

(17)

k

w1  0, w2  1 w1  1, w2  0

SF

Step 4 (Determination of Pareto solutions): In this step, the obtained solutions are evaluated according to the Pareto concept that divides the solutions into two categories (i.e., non-dominated solutions and dominated solutions). The procedure by two archives namely, N to store non-dominated solutions and M to store the dominated solutions. The steps of obtaining the Pareto solutions are showed in Fig. 3. Step 5 (Updating Pareto solutions): through the run of the algorithm, we obtain new Pareto solution; this solution can be inserted into the archive of the nondominated solutions N according to the concept of the non-dominated. The mechanism of updating the archive is shown in Fig. 4.

(15) (16)

where j  1, 2,...,NG  1 is the jth generation unit,

 i  1, 2,...,m is the ith solution; PG j ,i and PG j ,i



184


Input:

 

1. Two empty archives N , M and the population POP  PG ,i

m

i 1



 t a max  a min max  r1   a   T 

.

2. For i  1: m 3. For j  1: m , i  j 4. Check if PG i worse than PG j , then M  M  PG ,i 

t

 

(19)

where t is the present iteration, T is the maximum number of iterations, amax is the maximum radius and amin is the minimum radius. Also, this aims to enhance the solutions by updating the search agents by using the best solution so far and the Pareto optimal solution during iteration to guide the search agents to explore more diverse and distributed solutions. Step 6 (Stopping criteria): if t  T , stop the MSCO algorithm; otherwise, go to Step 2. Finally, these modifications can improve the solution equality and accelerate the convergence to the Pareto optimal solutions in the MSCO algorithm.

 

5. Else N  N  PG ,i 6. End; End

7. Output : N (Pareto solutions) Fig. 3. Determination of the Pareto solutions Input: 1. Let we have archive N and new solution PG 2. If  PG  N PG  PG then 3. N  N  PG (adding to archive) 4. Else if  PG  N

  ,   0.98

PG  PG then

 

5. N  N  PG  \ PG ( removing from archive)

IV.

6. End 7. Output : N

Applications

The proposed MSCO algorithm is applied for solving EELD problems on two test systems with a non-smooth fuel cost function and emission issues. To demonstrate the performance of the proposed method, other common optimization methods are compared with the results obtained with the proposed MSCO algorithm to validate its effectiveness.

Fig. 4. Updating Pareto solutions

Step 5 (Update the agent locations): In this step, a new modification on original SCA in introduced, where mutation probability is employed to update the solution either the best solution or random solution from the archive N , as follows:

IV.1. Results: Six-Unit System

t pi  0.4  0.4 , i  1, 2,...., PS T PGi ,t 1 

The first tested system is a six-unit system constituted of forty-one lines and six generators with non-smooth fuel cost and emission functions. The total power demand equals 1200 MW. Table I shows the cost and emission coefficients for this system and their minimum and maximum limits of power. The upper and down ramp rate limits are considered as ±10%. To assess the efficiency of the proposed MSCO algorithm, it was applied to EELD problems where the objective functions can be either smooth or non-smooth. Hence, three cases are considered for the six-unit system, as follows: Case 1: Minimization of the fuel costs only. Case 2: Minimization of the generation emissions only. Case 3: optimizing both objective functions simultaneously. All numerical calculations were completed using Matlab 7.12.0.635 “R2011a” on a processor core I5 Dell Inspiron N5010. Case 1: Fuel cost minimization. To investigate the effectiveness of the proposed algorithm, the system is considered with losses. Table II gives the MSCO solution compared with the real code genetic algorithm “RCGA” [3], the dynamic random neighborhood particle swarm optimization algorithm "DRN-PSO" [5] and the multi-objective fruit fly optimization algorithm (MOFOA) [28]. It is obvious that, the proposed MSCO algorithm is superior to the RCGA with regards to the

(18)

 PGi ,t  r1  sin  r2   | r3 Pi ,t  xi ,t | r4  0.5  r5  pi   PGi ,t  r1  cos  r2   | r3 Pi ,t  xi ,t | r4  0.5    PG  r  sin r  | r Pa  x | r  0.5  2  3 i ,t i ,t 4   i ,t 1  r  pi  PGi ,t  r1  cos  r2   | r3 Pai ,t  xi ,t | r4  0.5 5 where the symbol P denotes the best solution (destination), P=PG* is evaluated using the combined objective function and Pa denotes the Pareto optimal solution that is randomly chosen from the archive N . Afterwards, the opposition strategy is employed. In the original SCA, the new location is produced by picking the candidate region in a linear manner, but this is unsatisfactory for some applications as the algorithm will need a large number of iterations to find the promised region for large search space. Accordingly, the performance of the SCA is improved to overcome this drawback by tuning the parameter r1, such that dynamically tunes the search space around the destination solution, so that the search space is gradually shrunken with increasing number of iterations, as follows:



185


609

statistical measures, i.e., mean, best and worst values and the related standard deviation for 100 runs. In addition to the lower emission at best fuel costs in the proposed algorithm, the best fuel cost is found as 600.5800 ($/hr) compared to the RCGA result which was 615.5482 ($/hr). The solutions of the DRN-PSO and MOFOA neglect the system losses. Fig. 5 shows the convergence of the solution under fuel cost minimization. Case 2: Emission minimization. In this case, the emission objective function is considered alone. Table III indicates that the solution obtained using the proposed algorithm is better than the other competitive algorithms in terms of the lowest objective function. It gives the lowest emission level compared to the RCGA results. In addition, the convergence characteristic of the solution under emission function solution, Case 2, is shown in Fig. 6.

Generatori

PG1 PG2 PG3 PG4 PG5 PG6

Limits PGimin

PGimax

(per unit) 0.05 0.05 0.05 0.05 0.05 0.05

(per unit) 0.5 0.6 1 1.2 1 0.6

608 607

Cost ($/hr)

606 605 604 603 602 601 600

0

50

100

150

200

300

350

400

Fig. 5. Convergence of fuel cost solution for Case 1 with the six-unit system

TABLE I GENERATION LIMITS, COST, EMISSION COEFFICIENTS FOR THE 6-UNIT SYSTEM Cost coefficients Emission coefficients ai ($/MW2)

bi ($/MW)

ci ($)

di ($)

ei (MW-1)

αi (ton/MW2)

βi (ton/MW)

γi (ton)

ζi (ton)

λi (MW-1)

10 10 20 10 20 10

200 150 180 100 180 150

100 120 40 60 40 100

32.4 32.4 32.4 23.4 24 24

0.047 0.047 0.047 0.063 0.063 0.063

4.091 2.543 4.258 5.326 4.258 6.131

-5.554 -6.047 -5.094 -3.550 -5.094 -5.555

6.490 5.638 4.586 3.380 4.586 5.151

2.0×10-4 5.0×10-4 1.0×10-6 2.0×10-3 1.0×10-6 1.0×10-5

2.857 3.333 8.000 2.000 8.000 6.667

TABLE II BEST FUEL COST-BASED EELD SOLUTION OF CASE 1 FOR THE SIX-UNIT SYSTEM RCGA [3] DRN-PSO [5] MOFOA [27] PG1 (per unit) 0.1727 0.1764 0.3388 PG2 (per unit) 0.3966 0.2852 0.3802 PG3 (per unit) 0.5679 0.4691 0.9438 PG4 (per unit) 1.1079 0.8981 0.5974 PG5 (per unit) 0.2194 0.6350 0.2838 PG6 (per unit) 0.3949 0.3029 0.2900 Best fuel cost ($/hr) 615.5482 591.1517 478.2092 Mean fuel cost ($/hr) 623.3722 602.2351 561.3540 Median NA NA NA Worst fuel cost ($/hr) 634.9026 619.1436 619.3516 Standard deviation 5.7289 6.0778 62.6440 Emission at best fuel costs (ton/hr) 0.2285 0.215 0.2118 Run time (s) 0.29364 NA NA NA: Not Available

PG1 (per unit) PG2 (per unit) PG3 (per unit) PG4 (per unit) PG5 (per unit) PG6 (per unit) Best emission (ton/hr) Mean emission (ton/hr) Median Worst emission (ton/hr) Standard deviation Fuel cost at best emission ($/hr) Run time (s)

250

Iteration

TABLE III BEST EMISSION-BASED EELD SOLUTION OF CASE 2 FOR THE SIX-UNIT SYSTEM RCGA [3] DRN-PSO [5] MOFOA [28] 0.3969 0.3850 0.1884 0.4566 0.4396 0.2373 0.6015 0.6230 0.5877 0.3853 0.4218 0.7331 0.5366 0.4702 0.4875 0.5064 0.5200 0.6000 0.1932 0.1949 0.2069 0.2018 0.2016 0.1231 NA NA NA 0.2194 0.2128 0.1308 0.0056 0.0036 0.0033 691.3766 643.8616 615.8101 0.0502 NA NA


Proposed MSCO 0.0991 0.2927 0.5457 1.0432 0.4520 0.4014 600.5800 601.9624 601.8460 602.9957 0.5924 0.2243 0.5568

Proposed MSCO 0.4323 0.4442 0.5577 0.3858 0.5527 0.5113 0.1942 0.1945 0.1945 0.1949 0.0002 650.3365 0.99427


186


worst and standard deviation are shown in Table VII. Furthermore, the convergence performance of the fuel cost and emission objectives are demonstrated in Figs. 8(a) and (b), respectively.

0.1985 0.198

Emission (ton/hr)

0.1975 0.197

5

x 10

0.1965

1.072 0.196 0.1955

1.07 Cost ($/hr)

0.195 0.1945 0.194

0

50

100

150

200

250

300

350

1.068

1.066

400

Iteration 1.064

Fig. 6. Convergence of emission solution for Case 2 with the six-unit system

1.062

Case 3: Both objectives are optimized simultaneously. For Case 3, Pareto concept is applied to find the multi-objective case of the EELD problem as reported in Tables IV and V. Applying the MSCO algorithm, the obtained Pareto front is shown in Fig. 7. The results clearly reveal that the obtained solutions were welldistributed and covered the entire Pareto front of Case 3 compared with the reported solutions using the MODE, MOPSO, NSGA, NPGA and SPEA.

100

150

200 250 Iteration

300

350

400

(a)

3820

Emission (Ib/hr)

3800

0.225

Emission (ton/hr)

50

3780 3760 3740 3720

0.22

3700

0.215

3680

0.21

50

100

150

0.205

200 250 Iteration

300

350

400

(b) 0.2

Figs. 8. Convergence curves for Cases 1 and 2 with the ten-unit system. (a) Case 1 (minimum cost), (b) Case 2 (minimum emission

0.195 0.19 600

4300 610

620

630

640

650

660

Cost ($/hr)

4200

Fig. 7. Pareto front of the proposed algorithm for Case 3 with the six-unit system

Emission (Ib/hr)

4100

IV.2. Results: Ten-Unit System The second test system has 10 units with non-smooth fuel cost and emission issues applied to verify the efficiency of the proposed SCA algorithm. The total power demand equals 2000 MW. Tables VI and VII show the cost and emission coefficients of the tengenerator system with their minimum and maximum power limits, respectively. Firstly, the system is considered a lossless system and the above three cases are implemented, the fuel cost and emission are optimized individually, and the obtained results concerning the statistical measures, i.e., best, mean,

4000 3900 3800 3700 3600 1.06

1.07

1.08

1.09 Cost ($/hr)

1.1

1.11

1.12 5

x 10

Fig. 9. Set of non-dominated solutions by optimizing both objectives with the ten-unit system



187


Fig. 9 shows the set of non-dominated solutions. It is evident that the proposed algorithm gives a broad range of solutions and they are well distributed on the Pareto front. The feature of visualizing the set of nondominated solutions is to aid decision makers and engineers to extract the ‘preferred’’ or best compromise solution. Table VIII demonstrates the best compromise solutions considering the non-dominated solutions considering two states the best cost and the

corresponding emission solution and the best emission and the corresponding cost. For each state, the optimal solutions are obtained from the non-dominated set. Secondly, when the transmission losses are considered and the same scenarios are repeated. Table IX shows the best solutions for cost and emission when they are optimized separately with the statistical results reported. Table X demonstrates the best compromise solutions for the two fronts.

PG1 PG2 PG3 PG4 PG5 PG6 Fuel cost Emission

TABLE IV BEST SOLUTIONS OF COST WITH THE SIX ALGORITHMS OF CASE 3 FOR THE SIX-UNIT SYSTEM MODE MOPSO NSGA NPGA SPEA 0.1332 0.1207 0.1447 0.1425 0.1279 0.2727 0.3131 0.3066 0.2693 0.3163 0.6018 0.5907 0.5493 0.5908 0.5803 0.9747 0.9769 0.9894 0.9944 0.9580 0.5146 0.5155 0.5244 0.5315 0.5258 0.3617 0.3504 0.3542 0.3392 0.3589 606.126 607.790 607.98 608.06 607.86 0.2195 0.2193 0.2191 0.2207 0.2176

Proposed MSCO 0.1342 0.2429 0.5482 0.9867 0.5655 0.3576 600.9326 0.2208

PG1 PG2 PG3 PG4 PG5 PG6 Fuel cost Emission

TABLE V BEST SOLUTIONS OF EMISSION WITH THE SIX ALGORITHMS OF CASE 3 FOR THE SIX-UNIT SYSTEM MODE MOPSO NSGA NPGA SPEA 0.39266 0.4101 0.3929 0.4064 0.4145 0.46256 0.4594 0.3937 0.4876 0.4450 0.56311 0.5511 0.5815 0.5251 0.5799 0.40309 0.3919 0.4316 0.4085 0.3847 0.5676 0.5413 0.5445 0.5386 0.5348 0.47826 0.5111 0.5192 0.4992 0.5051 642.849 644.740 638.98 644.23 644.77 0.1942 0.1942 0.1947 0.1943 0.1943

Proposed MSCO 0.4128 0.4799 0.5260 0.3885 0.5703 0.5144 652.1679 0.1942

Generatori

Limits PGimin

PG1 PG2 PG3 PG4 PG5 PG6 PG7 PG8 PG9 PG10

TABLE VI GENERATION LIMITS AND COST, EMISSION COEFFICIENTS FOR THE TEN-UNIT SYSTEM Cost coefficients Emission coefficients

PGimax

ai 2 (per unit) (per unit) ($/MW ) 10 55 0.04702 20 80 0.04652 47 120 0.04652 20 130 0.04652 50 160 0.0042 70 240 0.0042 60 300 0.0068 70 340 0.0068 135 470 0.0046 150 470 0.0046

bi ($/MW)

ci ($)

di ($)

−3.9864 −3.9524 −3.9023 −3.9023 0.3277 0.3277 −0.5455 −0.5455 −0.5112 −0.5112

360.0012 350.0056 330.0056 330.0056 13.8593 13.8593 40.2669 40.2669 42.8955 42.8955

0.25475 0.25475 0.25163 0.25163 0.2497 0.2497 0.248 0.2499 0.2547 0.2547

ei αi βi (MW-1) (ton/MW2) (ton/MW) 0.01234 0.01234 0.01215 0.01215 0.012 0.012 0.0129 0.01203 0.01234 0.01234

0.12951 0.10908 0.12511 0.12111 0.15247 0.10587 0.03546 0.02803 0.02111 0.01799

40.5407 39.5804 36.5104 39.5104 38.539 46.1592 38.3055 40.3965 36.3278 38.2704

γi (ton)

ζi (ton)

λi (MW-1)

1000.403 950.606 900.705 800.705 756.799 451.325 1243.531 1049.998 1658.569 1356.659

33 25 32 30 30 20 20 30 60 40

0.0174 0.0178 0.0162 0.0168 0.0148 0.0163 0.0152 0.0128 0.0136 0.0141

TABLE VII BEST SOLUTIONS FOR INDIVIDUALLY OPTIMIZED COST AND EMISSION FOR CASES 1 AND 2 FOR THE TEN-UNIT SYSTEM Unit Cost minimization (Case 1) Emission minimization (Case 2) PG1 (MW) 55.0000 55.0000 PG2 (MW) 80.0000 77.1866 PG3 (MW) 91.4067 80.6376 PG4 (MW) 73.8654 81.9068 PG5 (MW) 70.5700 160.0000 PG6 (MW) 70.0000 240.0000 PG7 (MW) 282.6504 300.0000 PG8 (MW) 340.0000 260.0389 PG9 (MW) 470.0000 362.8871 PG10 (MW) 466.5075 382.3431 Best fuel cost ($/hr) 106198.0226 3660.7106 Mean fuel cost ($/hr) 1.0632 3660.7106 Worst fuel cost ($/hr) 1.0645 3660.7106 -4 Standard deviation 6×10 0.0000 Emission at best fuel cost (ton/hr) 4.2747×103 1.1202×105 Run time 0.909999 0.751742



188


TABLE VIII BEST COMPROMISE SOLUTION FOR SIMULTANEOUS OPTIMIZATION OF COST AND EMISSION FOR THE TEN-UNIT SYSTEM Unit Best Cost Best Emission PG1 (MW) 55.0000 55.0000 PG2 (MW) 61.5513 70.5223 PG3 (MW) 99.6468 67.0209 PG4 (MW) 76.3147 86.6577 PG5 (MW) 82.4439 160.0000 PG6 (MW) 74.0702 224.6021 PG7 (MW) 270.9732 300.0000 PG8 (MW) 340.0000 259.5438 PG9 (MW) 470.0000 397.8528 PG10 (MW) 470.0000 378.8003 Fuel cost ($/hr) 1.0632×105 1.1135×105 3 Emission (Ib/hr) 4.2681×10 3.6869×103 TABLE IX BEST SOLUTIONS FOR INDIVIDUALLY OPTIMIZED COST AND EMISSION CONSIDERING LOSSES FOR CASES 1 AND 2 WITH THE TEN-UNIT SYSTEM Cost minimization Emission minimization Unit (Case 1) (Case 2) PG1 (MW) 55.0000 55.0000 PG2 (MW) 67.9089 73.4504 PG3 (MW) 81.2391 78.5249 PG4 (MW) 76.6677 82.2898 PG5 (MW) 90.3652 157.9873 PG6 (MW) 104.3364 240.0000 PG7 (MW) 300.0000 300.0000 PG8 (MW) 340.0000 262.6415 PG9 (MW) 470.0000 372.9576 PG10 (MW) 470.0000 449.4574 Best fuel cost ($/hr) 110065.6702 3880.2243 Mean fuel cost ($/hr) 1.1021×105 3.9056 Worst fuel cost ($/hr) 1.1047×105 3.9244 Standard deviation 0.0013 0.0121 Emission at best fuel cost (Ib/hr) 4.3410×103 1.1581×105 Losses (MW) 55.5174 72.3089 Run time (s) 1.049039 1.099903 TABLE X BEST COMPROMISE SOLUTION FOR SIMULTANEOUS OPTIMIZATION OF COST AND EMISSION CONSIDERING LOSSES FOR THE TEN-UNIT SYSTEM Unit Best Cost Best Emission PG1 (MW) 54.1633 55.0000 PG2 (MW) 80.0000 70.0919 PG3 (MW) 78.3482 85.7924 PG4 (MW) 95.5942 95.3848 PG5 (MW) 112.5969 160.0000 PG6 (MW) 143.0026 240.0000 PG7 (MW) 300.0000 258.2294 PG8 (MW) 276.6827 266.0778 PG9 (MW) 433.5148 333.3267 PG10 (MW) 470.0000 470.0000 Fuel cost ($/hr) 1.1009×105 1.1389×105 3 Emission (Ib/hr) 4.1207×10 3.8647×103 Losses (MW) 43.9027 33.9030

Outputs PG1 (MW) PG2 (MW) PG3 (MW) PG4 (MW) PG5 (MW) PG6 (MW) PG7 (MW) PG8 (MW) PG9 (MW) PG10 (MW) Fuel cost×105($) Emission (Ib) Losses (MW) Run time (s)

TABLE XI COMPARISON BETWEEN THE PROPOSED MSCO ALGORITHM AND OTHER ALGORITHMS FOR THE TEN-UNIT SYSTEM MODE [17] NSGAII [17] PDE [17] SPEA-2 [17] GSA [29] ABC_PSO [30] EMOCA [31] FPA [16] Proposed MSCO 54.9487 51.9515 54.9853 52.9761 54.9992 55 55 53.188 52.8995 79.975 74.5821 67.2584 79.3803 72.813 79.9586 80 80 74.9428 78.105 79.4294 73.6879 83.9842 78.1128 79.4341 81.14 83.5594 97.4068 97.119 80.6875 91.3554 86.5942 83.6088 85.0000 84.216 84.6031 95.9554 152.74 136.8551 134.0522 144.4386 137.2432 142.1063 138.3377 146.5632 131.8702 163.08 172.6393 174.9504 165.7756 172.9188 166.5670 167.5086 169.2481 200.5119 258.61 283.8233 289.4350 283.2122 287.2023 292.8749 296.8338 300 227.9224 302.22 316.3407 314.0556 312.7709 326.4023 313.2387 311.5824 317.3496 303.6511 433.21 448.5923 455.6978 440.1135 448.8814 441.1775 420.3363 412.9183 366.3189 466.07 436.4287 431.8054 432.6783 423.9025 428.6306 449.1598 434.3133 470.0000 1.13484

1.13539

1.1351

1.1352

1.1349

1.1342

1.13445

1.1337

1.1087

4124.9 84.33 3.82

4130.2 84.25 6.02

4111.4 83.9 4.23

4109.1 84.1 7.53

4111.4 83.9869 NA

4120.1 84.1736 NA

4113.98 83.56 2.90

3997.7 84.3 2.23

3940.6 21.4789 1.8265



189


non-dominated solutions. Finally, the feasibility of using the proposed approach for handling multiobjective EELD is approved. The simulation results indicate that the MSCO algorithm has an effective performance in realizing the ability to obtain the global solution. As presented in Table XI, the proposed solution by the MSCO algorithm that is picked from the Pareto front dominates the other solutions according to the dominance concept. Also, convergence characteristics with better performance have been proved compared to other algorithms presented in the literature. Thus, it is concluded that the proposed MSCO algorithm is capable of efficiently and quickly solving several optimization problems in power systems.

5

x 10 1.12 1.118 1.116 Cost ($/hr)

1.114 1.112 1.11 1.108 1.106 1.104 1.102 50

100

150

200 250 Iteration

300

350

400

(a) Case 1 (minimum cost)

V.

This work has proposed the application of a modified version of sine cosine algorithm for solving the nonlinear constrained EELD problem for enhanced operation of power grids. The proposed method provides an effective generating management plan. Numerical applications were conducted on two test systems with 6- and 10- units test systems. The obtained results have compared with previous optimization techniques those reported in the literature. It confirms the effectiveness and the superiority of the proposed MSCO approach over the other approaches in terms of the solution quality. The proposed algorithm improves the economic issue as well as enhancing the power system operation in the considered technical point. Thus, the proposed algorithm can be considered as a promising alternative algorithm for solving practical problems in large-scale power system studies. The main features of this study can be summarized as follows:  The proposed MSCO algorithm has been effectively applied to solve the multi-objective EELD problem.  The mechanism of the MSCO algorithm has four improvements that add more merits over other algorithms reported in the literature, such as improving the search space, the simplicity of the approach and low computational time.  The Pareto front solutions are well distributed and have satisfactory diversity characteristics. This is useful in giving a reasonable freedom in choosing an operating point from the available finite alternative.  The opposition strategy has been proposed to improve the performances of the MSCO.  The proposed approach is efficient for solving nonconvex multi-objective optimization problems where multiple Pareto-optimal solutions can be found in one simulation run.

4000

Emission (Ib/hr)

3980 3960 3940 3920 3900

50

100

150

200 250 Iteration

300

350

400

(b) Case 2 (minimum emission) Figs. 10. Convergence curves for Cases 1 and 2 considering losses with the ten-unit system 4150

Emission (Ib/hr)

4100 4050 4000 3950 3900 3850 1.1

1.105

1.11

1.115

1.12

1.125

Cost ($/hr)

1.13

1.135

Conclusion

1.14 5

x 10

Fig. 11. Pareto solutions for the ten-unit system considering losses

To assess the proposed MSCO, Table XI presents the comparisons between the proposed algorithms with different algorithms in the literature. The results show that the proposed MSCO algorithm outperforms and outlasts other algorithms in obtaining better cost and better emission values. The convergence of the cost and emission against iterations are depicted in Figs. 10(a) and (b), respectively. Fig. 11 shows the set of nondominated solutions, where it is evident that the proposed algorithm gives a well-distributed front of the

References [1]


Sinha, Nidul, R. Chakrabarti, and P. K. Chattopadhyay. "Evolutionary programming techniques for economic load dispatch." IEEE Transactions on evolutionary computation 7, no. 1 (2003): 83-94.


190


[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

https://doi.org/10.1109/TEVC.2002.806788 Zhu, J.: 'Optimization of Power System Operation', John Wiley & Sons, Inc. Publication, IEEE, 2009. https://doi.org/10.1002/9780470466971 El-Sehiemy, Ragab A., Mostafa Abdelkhalik El-Hosseini, and Aboul Ella Hassanien. "Multiobjective real-coded genetic algorithm for economic/environmental dispatch problem." Studies in Informatics and Control 22, no. 2 (2013): 113-122. https://doi.org/10.24846/v22i2y201301 Rizk M. Rizk-Allah, Ragab A. El-Sehiemy, Gai-Ge Wang, "A novel parallel hurricane optimization algorithm for secure emission/economic load dispatch solution, Applied Soft Computing, Volume 63, 2018, pp. 206-222. https://doi.org/10.1016/j.asoc.2017.12.002 El-Hosseini, M.A., El-Sehiemy, R.A., Haikal, A.Y.: 'Multiobjective optimization algorithm for secure economical/emission dispatch problems', Journal of Engineering & Applied Science, 2014, 61, (1), pp. 83–103. Yang, X.S.: 'Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect', Applied Soft Computing, 2012, 12, (3), pp. 1180–1186. https://doi.org/10.1016/j.asoc.2011.09.017 Sayah, S., Abdellatif, H.: 'A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems', Applied Soft Computing, 2013, 13, (4), pp. 1608–1619. https://doi.org/10.1016/j.asoc.2012.12.014 Damousis, I.G., Bakirtzis, A.G., Dokopoulos, P.S.: 'Networkconstrained economic dispatch using real-coded genetic algorithm', IEEE Transactions on Power Systems, 2003, 18, (1), pp. 198–205. https://doi.org/10.1109/TPWRS.2002.807115 Abido, M.A.: 'A niched Pareto genetic algorithm for multiobjective environmental/economic dispatch', Electrical Power and Energy Systems, 2009, 25, pp. 97–105. https://doi.org/10.1016/S0142-0615(02)00027-3 Gjorgiev, B., Cepin, M.: 'A multi-objective optimization based solution for the combined economic-environmental power dispatch problem', Engineering Applications of Artificial Intelligence, 2013, 26, pp. 417–429. https://doi.org/10.1016/j.engappai.2012.03.002 Wu, L.H., Wang, Y.N., Yuan, X.F., Zhou, S.W.: 'Environmental/economic power dispatch problem using multiobjective differential evolution algorithm', Electric Power Systems Research, 2010, 80, pp. 1171–1181. https://doi.org/10.1016/j.epsr.2010.03.010 Soliman, A.S., Abdel-Aal, H.M.: 'Modern Optimization Techniques with Applications in Electric Power Systems: Optimal Power Flow, Energy Systems Series, ISSN 1867-8998, pp. 281346, 2012. Abou El-Ela, A.A., Bishr, M.A., Allam, S.M., El-Sehiemy, R.A.: 'Optimal preventive control actions using multi-objective fuzzy linear programming technique', Electric Power Systems Research, 2005, 74, (1), pp. 147–155. https://doi.org/10.1016/j.epsr.2004.08.014 Abou El-Ela, A.A., Bishr, M.A., Allam, S.M., El-Sehiemy, R.A.: 'An Emergency Power System Control Based on the Multi-stage Fuzzy Based Procedure', Electric Power Systems Research, 2007, 77, (5-6), pp. 421–429. https://doi.org/10.1016/j.epsr.2006.04.004 Abou El-Ela, A.A., El-Sehiemy, R.A.: 'Optimized Generation costs using modified particle Swarm optimization version', WSEAS transactions on power systems, 2007, pp. 225–232. Abdelaziz AY, Ali ES, Abd Elazim SM. Implementation of flower pollination algorithm for solving economic load dispatch and combined economic emission dispatch problems in power systems. Energy 2016;101:506–18. https://doi.org/10.1016/j.energy.2016.02.041 Abido, M.A.: 'Environmental/economic power dispatch using multiobjective evolutionary algorithms, IEEE Trans. Power Syst., 2003, 18, (4), pp. 1529–1537. https://doi.org/10.1109/TPWRS.2003.818693 Abido, M.A.: 'Multiobjective evolutionary algorithms for electric power dispatch problem', IEEE Trans. Evol. Comput. 2006, 10,

[19]

[20]

[21]

[22] [23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

(3), pp. 315–329. https://doi.org/10.1109/TEVC.2005.857073 Abido, M.A.: 'Multiobjective particle swarm optimization for environmental/economic dispatch problem', Electr. Power Syst. Res., 2009, 79, (7), pp.1105–1113. https://doi.org/10.1016/j.epsr.2009.02.005 Wu, L.H., Wang, Y.N., Yuan, X.F., Zhou, S.W.: 'Environmental/economic power dispatch problem using multiobjective differential evolution algorithm', Electr. Power Syst. Res., 2010, 80, pp. 1171–1181. https://doi.org/10.1016/j.epsr.2010.03.010 Basu, M.: 'Economic environmental dispatch using multiobjective differential evolution', Int. J. Appl. Soft Comput., 2011, 11, pp. 2845–2853. https://doi.org/10.1016/j.asoc.2010.11.014 Seyedali, M.: SCA: A Sine Cosine Algorithm for Solving Optimization Problems, Knowledge-Based Systems, 2016. Abdel Fattah Attia, El-Sehiemy, R.A, Hany Hasaneen, Optimal Power Flow Solution in Power Systems Using a Novel SineCosine Algorithm, International Journal of Electrical Power and Energy Systems 99C (2018) pp. 331-343. S. M. Ismael, S. H. E. Abdel Aleem, and A. Y. Abdelaziz, "Optimal selection of conductors in Egyptian radial distribution systems using sine-cosine optimization algorithm," presented at the 19th International Middle-East Power Systems Conference, MEPCON' 2017, Cairo, Egypt. December 19-21, 2017. Ahmed Ahmed El-Sawy, Elsayed M. Zaki, and R.M. Rizk-Allah: 'A hybrid multi-objective optimization algorithm for Environmental/economic power dispatch', Eighth Egyptian Rural Development Conference (ERDC-8), Oct. 23-25, 2012, Mounifia, Egypt. Bouchekara, H.R.E.H., Chaib, A.E., Abido, M.A., El-Sehiemy, R.A.: 'Optimal power flow using an Improved Colliding Bodies Optimization algorithm', Applied Soft Computing, 2016, 42, pp. 119–131. https://doi.org/10.1016/j.asoc.2016.01.041 Rizk-Allah, Rizk M., Ragab A. El-Sehiemy, and Gai-Ge Wang. "A novel parallel hurricane optimization algorithm for secure emission/economic load dispatch solution." Applied Soft Computing 63 (2018): 206-222. https://doi.org/10.1016/j.asoc.2017.12.002 A. Abou El-Ela, Ragab A. El Sehiemy, R.M. Rizk-Allah, D. Abdel Fatah: 'Multi-Objective Fruit Fly Optimization Algorithm for Solving Economic Power Dispatch Problem', International Conference on New Trends for Sustainable Energy (ICNTSE), pp. 17–22, 2016. Güvenç, U., Sonmez, Y., Duman, S., Yorükeren, N.: 'Combined economic and emission dispatch solution using gravitational search algorithm', Sci. Iran. D Comput. Sci. Eng. Electr. Eng., 2012, 19, (6), pp. 1754–1762. Manteaw, E.D., Odero, N.A.: 'Combined economic and emission dispatch solution using ABC-PSO hybrid algorithm with valve point loading effect', Int. J. Sci. Res. Publ, 2012, 2, (12), pp. 1–9. Zhang, R., Zhou, J., Mo, L., Ouyang, S., Liao, X.: 'Economic environmental dispatch using an enhanced multi-objective cultural algorithm', Electr. Power Syst. Res., 2013, 99, pp. 18–29. https://doi.org/10.1016/j.epsr.2013.01.010 Tizhoosh HR. Opposition-Based Learning: A New Scheme for Machine Intelligence. Comput Intell Model Control Autom 2005 Int Conf Intell Agents, Web Technol Internet Commer Int Conf 2005;1:695–701. https://doi.org/10.1109/CIMCA.2005.1631345

Authors’ information 1

Basic Engineering Science Department, University of Minoufia, Shebin El-Kom, Egypt. 2

3

National Institute of Standards (NIS), 12211, Giza, Egypt.

Electrical Engineering Department, Kafrelsheikh University, Egypt


Faculty

of

Engineering,


191


4

Higher Institute of Engineering, Mathematical, Physical & Life Sciences, 15th of May City, Helwan, Cairo, 11731, Egypt

Shady H. E. Abdel Aleem received the B.Sc. and M.Sc. and Ph.D. degrees in Electrical Power and Machines from the Faculty of Engineering, Helwan University, Helwan, Egypt, in 2002, and the Faculty of Engineering, Cairo University, Egypt, in 2010 and 2013 respectively. Currently, he is an Assistant Professor at 15th of May Higher Institute of Engineering. He is working in the field of electric machines, power quality, electric circuits, and engineering mechanics. Dr. Shady is a member of the Institute of Electrical and Electronics Engineers. Also, he is a member of the IET. He regularly reviews papers for many IEEE Transactions and journals in his areas of interest. Dr. Shady is author or co-author of many journal and conference papers. Areas of research include harmonic problems in power systems, power quality, solar energy, wind energy, green energy, electric machines, distributed generation, economics and engineering mechanics.

5

Department of Electrical and Computer Engineering, Georgia Southern University (GSU), USA Rizk Masoud Rizk-Allah received his B.Sc. with honors in 2004 from Department of Electrical Engineering and M.Sc. degree in 2010 from Department of Basic Engineering Science, both at Faculty of Engineering, Menoufia University, Egypt. On June 2013, he received his doctoral degree from the Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Egypt. His research interests include: nonlinear programming problems, multi criteria decision making, many objectives optimization problems, resource allocation Problem, fuzzy sets, metaheuristic algorithms, combinatorial optimization and Engineering applications.

Adel El Shahat is currently an Assistant Professor of Electrical Engineering in the Department of Electrical and Computer Engineering at Georgia Southern University (GSU), USA. He is the Founder and Director of the innovative Power Electronics and NanoGrids Research Lab (iPenG) at GSU. He received his B.Sc. in Electrical Engineering from Zagazig University, Zagazig, Egypt, in 1999. He received his M.Sc. in Electrical Engineering (Power & Machines) from Zagazig University, Zagazig, Egypt in 2004. He received his Ph.D. degree (Joint Supervision) from Zagazig University, Zagazig, Egypt, and The Ohio State University (OSU), Columbus, OH, USA, in 2011. His research focuses on various aspects of Smart Grid Systems; Nano & MicroGrids; Power Electronics; Electric Machines; Drive Systems; Smart Homes, Distributed Generation; Renewable Energy Systems (Photovoltaic, Wind, …etc); Power Systems; Energy Storage & Conservation; Optimization; Neural Networks, Genetic; Power System Stability; Control Systems; Micro-generators Design; Micro-turbine operation; FACTS; Capacitive Deionization; Modeling and Simulation techniques.

Hala M. Abdel Mageed received M.Sc. and Ph.D. degrees in Electrical Power and Machines from the Faculty of Engineering, Cairo University, Egypt in 2004 and 2010, respectively. She is an associate professor in the National Institute of Standards (NIS), Egypt. She is an author of many refereed journal and conference papers. Her areas of expertise are electrical measurements, electrical metrology, renewable energy and green energy. Currently she is the head of high voltage laboratory and proficiency testing lab at NIS, Egypt. Ragab A. El-Sehiemy was born at Minoufiya, 1973. He received his B.Sc., M.Sc., and Ph.D. degrees in 1996, 2005, and 2008, respectively. He is an associate professor at the department of electrical engineering, faculty of engineering, Kafrelsheikh University, Kafrel-Sheikh, Egypt. His research interests involve power system operation, control, and planning, applications of modern optimization techniques for variant electric power systems applications, renewable sources, and smart grid.



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