Hybrid Optimization of the Emission and Economic Dispatch by the Genetic Algorithm
Lahouari ABDELHAKEM KORIDAK^{1*}, Mostefa RAHLI^{2}, Mimoun YOUNES^{3}
^{1, 2} Department of Electrical Engineering, USTO MB BP 1505, Oran El M’naouer, Algeria.
^{3}Department of Mechanical Engineering, USBA BP 89 Sidi Djillali, Sidi Bel Abbes, Algeria.
(* Phone/Fax: 213 41 56 03 01)
Emails: hkoridak@yahoo.fr, rahlim@yahoo.fr, mnyounes@yahoo.fr
Abstract
This paper presents an efficient and reliable technique of optimization with combined economic emission dispatch. This problem has been formulated as a multiobjective problem by considering both economy and emission simultaneously. The biobjective problem is converted into single objective function using hybrid factor in the proposed approach. The optimal solution of problem is determined by genetic algorithm. This approach has been tested on Indian utility62 bus systems consisting of 19 generators with line flow constraints. The solutions obtained are quite encouraging and useful in the present deregulated environment.
Keywords
Nonlinear Programming; Genetic Algorithms; Load Flow; Combined Economic Emission Dispatch.
Introduction
In traditional economic dispatch, the operating cost is reduced by the suitable attribution of the quantity of power to be produced by different generating units. However the optimal production cost can not be the best in terms of the environmental criteria. Recently many countries throughout the world have concentrated on the reduction of the quantity of pollutants from fossil fuel to the production of electrical energy of each unit. The gaseous pollutants emitted by the power stations cause harmful effects with the human beings and the environment like the sulphur dioxide (SO_{2}), nitrogen oxide (NOx) and the carbon dioxide (CO_{2}), etc. Thus, the optimization of production cost should not be the only objective but the reduction of emission must also be taken into account. Considering the difference in homogeneity of the two equations, the equation of the cost of fuel given in $/hr, and the equation of emission of gases to the production of electrical energy given in Kg/hr. In this approach, we optimize the two equations at the same time using a factor of hybridization (Hi). The genetic algorithms are more advanced to solve the problem of multiobjective optimization; the problem consists in combining the economic control system and the gas emission with the production of electrical energy.
Genetic Algorithm
Genetic algorithms (GA) were developed after original work by Holland (1975). These consist of optimization procedures based on principles inspired by natural evolution. Given a problem for which a closedform solution is unidentified, or impossible to obtain with classical methods, an initial randomly generated population of possible solution is created. Its characteristics are then used in an equivalent string of genes or chromosomes that will be later recombined with genes from other individuals. Each solution is assimilated to an individual, who is evaluated and classified in relation with its closeness to the best, yet still unknown, solution to the problem. It can be shown that, by using a Darwinianinspired natural selection process, the method will gradually converge towards the best possible solution.
Figure 1. Outline of a genetic algorithm
Most often, researchers encode individuals using bit string encoding called binarycoded GA. In this work, individuals are represented with floating point or real numbers. In realcoded Gas, an individual is coded as vector of real numbers corresponding to design variables. The realcoded Gas are robust, accurate and efficient because of floating point representation is conceptually closest to the real design space.
Genetic Operators
In this work, the following GA operators are used:
¸ Whole linear crossover: Crossover operator is intended to combine the genetic data of the existing population and generating offspring’s. Pair of chromosomes is recombined on a random basis to form two new individuals. If according to a probability of crossover parameter, pc, there is crossover, then a whole linear crossover is used. From two parents p1 and p2, three offspring’s are generated, namely 0.5p1+0.5p2, 1.5p10.5p2, and 0.5p1+1.5p2. The best two of the three offspring’s are then selected.
¸ Nonuniform mutation: Mutation operator plays a secondary role. It allows new genetic patterns to be formed, thus improving the search method. Occasionally, it protects some useful genetic material loss. During the process, a rate of mutation, pm, determines the possibility of mutating one of the design variables. If a variable is chosen to be mutated, its value is modified as follows:
_{} (1)
_{} (2)
where r is a uniform random number between 0 and 1, T is the maximum generation, and b is a parameter determining the degree of dependency on the generation number (usually chosen between 1 and 5).
¸ Elitist strategy: In standard GA the best possible solution is not preserved, thereby increasing the chance of loosing the obtainable best possible solution. Elitist strategy overcomes this problem by copying the best member of each generation into the next one.
Problem Formulation
The biobjective combined economic emission dispatch problem is converted into single optimization problem by introducing prince hybridization factor.
Optimization of problem has been mathematically formulated is as follows.
_{} (3)
where _{}is the optimal cost of power generation. _{} and _{} are total cost and total emission of generators respectively.
nG represents the number of generators connected in the network. The cost is optimized with the following constraints.
_{} (4)
where P_{Gi} is the real power generation of i^{th} generator, P_{D} is the total load of the system and P_{L} is the transmission losses of the system. The inequality constraints on real power generation P_{Gi} of each generation i are:
_{} (5)
where _{} and _{} are minimum and maximum value of real power allowed at generator
i respectively.
The fuel cost of the production _{} ($/hr) in terms of control variables generator powers can be expressed as,
_{} (6)
where P_{Gi} is the real power output of an i^{th} generator. _{},_{},_{}are the fuel cost curve coefficients.
The total function of emission _{} (kg/hr) can be expressed as,
_{} (7)
where _{}, _{} and _{} are emission coefficients.
The factor of hybridization is exposed like as:
_{} (8)
where i = 1,2,……………..,nG.
The function to minimize can be described as follows.
_{} (9)
Subject to equality constraints,
_{} (10)
and inequality constraints,
_{} (11)
Use of constraints
Constraints may be handled by exterior penalty method; many alternatives are possible, simplest one is to square the violated constraints, multiply by a penalty coefficient and add to the fitness function.
Usually penalty coefficient is a large number.
_{}Subject to_{} the constraints
The constrained function _{} can be transformed to an unconstrained function _{}
_{} (12)
where _{} is the penalty coefficient.
For the application of the genetic algorithm, we transformed our problem of minimization with constraints has a minimization with not constraints by penalty method as follows.
_{} (13)
Equality constraints: _{} and inequality constraints: _{}
Simulation Results
The algorithm was applied to IEEE30 bus system with 06 generating units and 41 transmission lines with four tap changing transformers. The total system load demand is 283.4 MW. The values of fuel cost and emission coefficients are given in Table 1 and the singleline diagram of this system is shown in Figure 2.
Table 1. Generator costs and emission coefficients.
N° Generator 
ai 
bi 
ci 
αi 
βi 
γi 
1 
0.00375 
2.00 
0 
0.0126 
1.1000 
22.983 
2 
0.01750 
1.75 
0 
0.0200 
0.1000 
25.313 
3 
0.06250 
1.00 
0 
0.0270 
0.0100 
25.505 
4 
0.00834 
3.25 
0 
0.0291 
0.0050 
24.900 
5 
0.02500 
3.00 
0 
0.0290 
0.0040 
24.700 
6 
0.02500 
3.00 
0 
0.0271 
0.0055 
25.300 
Figure 2. The singleline diagram of IEEE30bus system
The factor of hybridization Hi for IEEE30 bus system was explained as follows:
Hi = [h1, h2, h3, h4, h5, h6]; Hi = [1.792, 1, 734, 2.230, 2.053, 2.220, 2.338]
S P_{Gi  }Pd  P_{L} = 0 (MW)ÞS P_{Gi}  297.5 = 0
Table 2. Generator operating limits
Bus 
Pmin 
Pmax 
G1 G2 G3 G4 G5 G6 
50 20 15 10 10 12 
200 80 50 35 30 40 
Result of the application
The optimal values of the generated powers, total cost of hybrid function, Fuel cost and Emission output are given by table 3.
Table 3. The best solution for fuel cost and emission gas optimized simultaneous.
N° Generator 
GA method 
EP method 
PG1 Opt (MW) 
139.202 
118.770 
PG2 Opt (MW) 
54.792 
62.246 
PG3 Opt (MW) 
25.618 
34.462 
PG4 Opt (MW) 
29.560 
24.289 
PG5 Opt (MW) 
23.989 
21.621 
PG6 Opt (MW) 
24.340 
28.072 
Best Hybrid function 
1566.177 
2151.570 
Fuel Cost. ($/hr) 
769.677 
840.219 
Emission (Kg/hr) 
353.404 
350.509 
· EP: Evolutionary Programming [4]
· GA: Genetic Algorithm (Proposed approach).
Interpretations
For the results of table 3, we calculated the optimum of the function combined between the fuel cost and the emission gas by introducing the factor to align dimensions of the two functions and we replaced the optimum power to find in both function.
In table 4, we optimized the two functions separately and one replaced the optimum power of the first in the second and conversely.
For our approach we can save 41.09 $/hr of fuel and minimize 3.622 Kg/hr of toxic gas to liberate in the environment.
Figure 3. The best generator setting of GA
Table 4. The best solution for fuel cost and emission gas optimized individually.

Best Fuel Cost 
Best Emission Gas 
P_{G1 (MW)} 
178.954 
117.516 
P_{G2 (MW)} 
046.703 
052.192 
P_{G3 (MW)} 
020.790 
032.167 
P_{G4 (MW)} 
025.763 
033.362 
P_{G5 (MW)} 
010.042 
027.147 
P_{G6 (MW)} 
015.248 
035.114 
Fuel cost ($/hr) 
810.767 
876.403 
Emission ( Kg/hr) 
402.546 
357.026 
Conclusion
In this article, an approach based on a genetic algorithm was presented and applied to the fuel cost and the function of emission gas in electric power network. The problem was formulated as multiobjective function environmental / economic dispatch, the problem is to optimize the fuel cost of the production and the emission gas on the environment at the same time.
For reason of the difference dimensioning of the two functions, we have to use the factor of hybridization for the first test (table 3), and for the second test (table 4) we have to optimize both separately function.
The genetic algorithm thus gave us well satisfactory results. This shows that it is much faster and more effective than the traditional techniques by dealing with the multi objective problems of optimization.
Certainly, we compared the minimal cost calculated in the first test with the minimal in the second test. We carried out in test 1 a reduction of 86.93 Kg/day pollutant gas (Nox, SO2, CO2, CO) emitted in the atmosphere and we have to gain has little close 987 $/day.
References
1. D.E. Goldberg, Genetic Algorithm in Search Optimisation and Machine Learning AddisonWesley, 1989.
2. M. Rahli et P. Pirotte, Dispatching Economique par une Nouvelle Méthode de Programmation Non Linéaire à la Répartition Economique des Puissances Actives dans un Réseaux d’Energie Electrique, (CIMASI’96, Casablanca, Maroc, 1416, pp 325330, novembre 1996.
3. M. Rahli ,Contribution à l’Etude de la Répartition Optimale des Puissances Actives dans un Réseau d’Energie Electrique,(thèse de doctorat, 06 janvier 1996, USTO. Algérie).
4. R. Ouiddir et M. Rahli, Dispatching Economique Actif dans un Réseau d’Energie Electrique par un Algorithme Génétique, (2^{nd} International Conférence on Electrotechnics, 1315 Novembre 2000, ICEL2000,USTOran, Algérie).
5. Claire Desarmenien et Fabien Laurent, Approximation Polygonal par un Algorithme Génétique, (Internet).
6. L. AbdelhakemKoridak, M. Rahli et R. Ouidir, Application des Algorithmes Génétiques à la Répartition Optimale des Puissances dans un Réseau d’Energie Electrique, ( CIMASI’2002, du 23 au 25 Octobre 2002 Casablanca, Maroc).
7. M.A. Abido, A Niched Pareto genetic algorithm for Multiobjective Environmental/Economic Dispatch, (Electrical Power and Energy Systems N°25, 2003, 97105).
8. Yokoyama R, Bae SH, Morita T, Sasaki H., Multiobjective Generation Dispatch Based on Probability Security Criteria, (IEEE Trans Power Syst 1988; 3(1): 317–24).
9. Farag A, AlBaiyat S, Cheng TC., Economic Load Dispatch Multiobjective Optimization rocedures Using Linear Programming Techniques, ( IEEE Trans Power Syst 1995; 10(2):731–8).
10. A .Immanuel Selva Kumar, K. Dhanushkodi, J. Jaya Kumar et C. Kumar Charlie Paul, Particle Swarm Optimization Solution to Emission and Economic Dispatch Problem,( 078037651X/ 03/ 2003 IEEE ).
11. L. AbdelhakemKoridak , Etude d’un Dispatching Economique par l’Algorithme Génétique, (Thèse de magister, 19 mars 2003, USTO. Algérie).
12. L.AbdelhakemKoridak, M. Rahli et R. Ouidir, Optimisation par l’Algorithmes Génétiques du Coût de Production dans un Réseau d’Energie Electrique, (CIMNA1,du 14 au 15 Novembre 2003, Beyrouth Liban).
13. L. AbdelhakemKoridak, M. Rahli , Application d’un Algorithme Génétique à la Fonction Multi Objective Environnement/ Economique de la Production d’Energie Electrique, 5^{ème} conférence régionale des comités CIGRE des pays arabes, du 21au 23 juin 2004, Algeri