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Optimization of Corridor Observation Method to Solve Environmental and Econom...ijceronline
This paper presents an optimization of corridor observation method (COM) which is an applicable optimization algorithm based on the evolutionary algorithm to solve an environmental and economic Dispatch (EED) problem. This problem is seen like a bi-objective optimization problem where fuel cost and gas emission are objectives. In this method, the optimal Pareto front is found using the concept of corridor observation and the best compromised solution is obtained by fuzzy logic. The optimization of this method consists to find best parameters (number of corridor, number of initial population and number of generation) which improve solution and reduce a computational time. The simulated results using power system with different numbers of generation units showed that the new parameters ameliorate the solution keep her stability and reduce considerably the CPU time (time is minimum divide by 4) comparatively at parameterization with originals parameters.
PuShort Term Hydrothermal Scheduling using Evolutionary Programmingblished pa...Satyendra Singh
In this paper, Evolutionary Programming method
is used for short term hydrothermal scheduling which minimize
the total fuel cost while satisfying the constraints. This paper
developed and studies the performance of evolutionary programs
in solving hydrothermal scheduling problem. The effectiveness of
the developed program is tested for the system having one hydro
and one thermal unit for 24 hour load demand. Numerical results
show that highly near-optimal solutions can be obtained by
Evolutionary Programming.
Comparisional Investigation of Load Dispatch Solutions with TLBO IJECEIAES
This paper discusses economic load dispatch Problem is modeled with nonconvex functions. These are problem are not solvable using a convex optimization techniques. So there is a need for using a heuristic method. Among such methods Teaching and Learning Based Optimization (TLBO) is a recently known algorithm and showed promising results. This paper utilized this algorithm to provide load dispatch solutions. Comparisons of this solution with other standard algorithms like Particle Swarm Optimization (PSO), Differential Evolution (DE) and Harmony Search Algorithm (HSA). This proposed algorithm is applied to solve the load dispatch problem for 6 unit and 10 unit test systems along with the other algorithms. This comparisional investigation explored various merits of TLBO with respect to PSO, DE, and HAS in the field economic load dispatch.
HYBRID PARTICLE SWARM OPTIMIZATION FOR SOLVING MULTI-AREA ECONOMIC DISPATCH P...ijsc
We consider the Multi-Area Economic Dispatch problem (MAEDP) in deregulated power system
environment for practical multi-area cases with tie line constraints. Our objective is to generate allocation
to the power generators in such a manner that the total fuel cost is minimized while all operating
constraints are satisfied. This problem is NP-hard. In this paper, we propose Hybrid Particle Swarm
Optimization (HGAPSO) to solve MAEDP. The experimental results are reported to show the efficiency of
proposed algorithms compared to Particle Swarm Optimization with Time-Varying Acceleration
Coefficients (PSO-TVAC) and RCGA.
An Effectively Modified Firefly Algorithm for Economic Load Dispatch ProblemTELKOMNIKA JOURNAL
This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.
Economic/Emission Load Dispatch Using Artificial Bee Colony AlgorithmIDES Editor
This paper presents an application of the
artificial bee colony (ABC) algorithm to multi-objective
optimization problems in power system. A new multiobjective
artificial bee colony (MOABC) algorithm to
solve the economic/ emission dispatch (EED) problem is
proposed in this paper. Non-dominated sorting is
employed to obtain a Pareto optimal set. Moreover, fuzzy
decision theory is employed to extract the best
compromise solution. A numerical result for IEEE 30-bus
test system is presented to demonstrate the capability of
the proposed approach to generate well-distributed
Pareto-optimal solutions of EED problem in one single
run. In addition, the EED problem is also solved using the
weighted sum method using ABC. Results obtained with
the proposed approach are compared with other
techniques available in the literature. Results obtained
show that the proposed MOABC has a great potential in
handling multi-objective optimization problem.
Optimization of Corridor Observation Method to Solve Environmental and Econom...ijceronline
This paper presents an optimization of corridor observation method (COM) which is an applicable optimization algorithm based on the evolutionary algorithm to solve an environmental and economic Dispatch (EED) problem. This problem is seen like a bi-objective optimization problem where fuel cost and gas emission are objectives. In this method, the optimal Pareto front is found using the concept of corridor observation and the best compromised solution is obtained by fuzzy logic. The optimization of this method consists to find best parameters (number of corridor, number of initial population and number of generation) which improve solution and reduce a computational time. The simulated results using power system with different numbers of generation units showed that the new parameters ameliorate the solution keep her stability and reduce considerably the CPU time (time is minimum divide by 4) comparatively at parameterization with originals parameters.
PuShort Term Hydrothermal Scheduling using Evolutionary Programmingblished pa...Satyendra Singh
In this paper, Evolutionary Programming method
is used for short term hydrothermal scheduling which minimize
the total fuel cost while satisfying the constraints. This paper
developed and studies the performance of evolutionary programs
in solving hydrothermal scheduling problem. The effectiveness of
the developed program is tested for the system having one hydro
and one thermal unit for 24 hour load demand. Numerical results
show that highly near-optimal solutions can be obtained by
Evolutionary Programming.
Comparisional Investigation of Load Dispatch Solutions with TLBO IJECEIAES
This paper discusses economic load dispatch Problem is modeled with nonconvex functions. These are problem are not solvable using a convex optimization techniques. So there is a need for using a heuristic method. Among such methods Teaching and Learning Based Optimization (TLBO) is a recently known algorithm and showed promising results. This paper utilized this algorithm to provide load dispatch solutions. Comparisons of this solution with other standard algorithms like Particle Swarm Optimization (PSO), Differential Evolution (DE) and Harmony Search Algorithm (HSA). This proposed algorithm is applied to solve the load dispatch problem for 6 unit and 10 unit test systems along with the other algorithms. This comparisional investigation explored various merits of TLBO with respect to PSO, DE, and HAS in the field economic load dispatch.
HYBRID PARTICLE SWARM OPTIMIZATION FOR SOLVING MULTI-AREA ECONOMIC DISPATCH P...ijsc
We consider the Multi-Area Economic Dispatch problem (MAEDP) in deregulated power system
environment for practical multi-area cases with tie line constraints. Our objective is to generate allocation
to the power generators in such a manner that the total fuel cost is minimized while all operating
constraints are satisfied. This problem is NP-hard. In this paper, we propose Hybrid Particle Swarm
Optimization (HGAPSO) to solve MAEDP. The experimental results are reported to show the efficiency of
proposed algorithms compared to Particle Swarm Optimization with Time-Varying Acceleration
Coefficients (PSO-TVAC) and RCGA.
An Effectively Modified Firefly Algorithm for Economic Load Dispatch ProblemTELKOMNIKA JOURNAL
This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.
Economic/Emission Load Dispatch Using Artificial Bee Colony AlgorithmIDES Editor
This paper presents an application of the
artificial bee colony (ABC) algorithm to multi-objective
optimization problems in power system. A new multiobjective
artificial bee colony (MOABC) algorithm to
solve the economic/ emission dispatch (EED) problem is
proposed in this paper. Non-dominated sorting is
employed to obtain a Pareto optimal set. Moreover, fuzzy
decision theory is employed to extract the best
compromise solution. A numerical result for IEEE 30-bus
test system is presented to demonstrate the capability of
the proposed approach to generate well-distributed
Pareto-optimal solutions of EED problem in one single
run. In addition, the EED problem is also solved using the
weighted sum method using ABC. Results obtained with
the proposed approach are compared with other
techniques available in the literature. Results obtained
show that the proposed MOABC has a great potential in
handling multi-objective optimization problem.
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Optimum designing of a transformer considering lay out constraints by penalty...INFOGAIN PUBLICATION
Optimum designing of power electrical equipment and devices play a leading role in attaining optimal performance and price of equipments in electric power industry. Optimum transformer design considering multiple constraints is acquired using optimal determination of geometric parameters of transformer with respect to its magnetic and electric properties. As it is well known, every optimization problem requires an objective function to be minimized. In this paper optimum transformer design problem comprises minimization of transformers mean core mass and its windings by satisfying multiple constraints according to transformers ratings and international standards using a penalty-based method. Hybrid big bang-big crunch algorithm is applied to solve the optimization problem and results are compared to other methods. Proposed method has provided a reliable optimization solution and has guaranteed access to a global optimum. Simulation result indicates that using the proposed algorithm, transformer parameters such as core mass, efficiency and dimensions are remarkably improved. Moreover simulation time using this algorithm is quit less in comparison to other approaches.
The problem of power system optimization has become a deciding factor in electrical power system engineering practice with emphasis on cost and emission reduction. The economic emission dispatch (EED) problem has been addressed in this paper using a Biogeography-based optimization (BBO). The BBO is inspired by geographical distribution of species within islands. This optimization algorithm works on the basis of two concepts-migration and mutation. In this paper a non-uniform mutation operator has been employed. The proposed technique shows better diversified search process and hence finds solutions more accurately with high convergence rate. The BBO with new mutation operator is tested on ten unit system. The comparison which is based on efficiency, reliability and accuracy shows that proposed mutation operator is competitive to the present one.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
GWO-based estimation of input-output parameters of thermal power plantsTELKOMNIKA JOURNAL
The fuel cost curve of thermal generators was very important in the calculation of economic dispatch and optimal power flow. Temperature and aging could make changes to fuel cost curve so curve estimation need to be done periodically. The accuracy of the curve parameters estimation strongly affected the calculation of the dispatch. This paper aims to estimate the fuel cost curve parameters by using the grey wolf optimizer method. The problem of curve parameter estimation was made as an optimization problem. The objective function to be minimized was the total number of absolute error or the difference between the actual value and the estimated value of the fuel cost function. The estimated values of parameter that produce the smallest total absolute error were the values of final solution. The simulation results showed that parameter estimation using gray wolf optimizer method further minimized the value of objective function. By using three models of fuel cost curve and given test data, parameter estimation using grey wolf optimizer method produced the better estimation results than those estimation results obtained using least square error, particle swarm optimization, genetic algorithm, artificial bee colony and cuckoo search methods.
A Minimum Spanning Tree Approach of Solving a Transportation Probleminventionjournals
: This work centered on the transportation problem in the shipment of cable troughs for an underground cable installation from three supply ends to four locations at a construction site where they are needed; in which case, we sought to minimize the cost of shipment. The problem was modeled into a bipartite network representation and solved using the Kruskal method of minimum spanning tree; after which the solution was confirmed with TORA Optimization software version 2.00. The result showed that the cost obtained in shipping the cable troughs under the application of the method, which was AED 2,022,000 (in the United Arab Emirate Dollar), was more effective than that obtained from mere heuristics when compared.
Stochastic fractal search based method for economic load dispatchTELKOMNIKA JOURNAL
This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based
method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are
introduced in the paper by employing two different random walk generators for diffusion process in which
SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called
SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from
three test system. These systems with 6, 10, and 20 units with different objective function forms and
different constraints are inspected. Numerical result comparison can confirm that the applied approach has
better solution quality and fast convergence time when compared with some recently published standard,
modified, and hybrid methods. This elucidates that the two SFS methods are very favorable for solving
the ELD problem.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Economic Load Dispatch Problem with Valve – Point Effect Using a Binary Bat A...IDES Editor
This paper proposes application of BAT algorithm
for solving economic load dispatch problem. BAT
algorithmic rule is predicated on the localization
characteristics of micro bats. The proposed approach has
been examined and tested with the numerical results of
economic load dispatch problems with three and five
generating units with valve - point loading without
considering prohibited operating zones and ramp rate limits.
The results of the projected BAT formula are compared with
that of other techniques such as lambda iteration, GA, PSO,
APSO, EP, ABC and basic principle. For each case, the
projected algorithmic program outperforms the answer
reported for the existing algorithms. Additionally, the
promising results show the hardness, quick convergence
and potency of the projected technique.
Application of a new constraint handling method for economic dispatch conside...journalBEEI
In this paper, optimal load dispatch problem under competitive electric market (OLDCEM) is solved by the combination of cuckoo search algorithm (CSA) and a new constraint handling approach, called modified cuckoo search algorithm (MCSA). In addition, we also employ the constraint handling method for salp swarm algorithm (SSA) and particle swarm optimization algorithm (PSO) to form modified SSA (MSSA) and modified PSO (MPSO). The three methods have been tested on 3-unit system and 10-unit system under the consideration of payment model for power reserve allocated, and constraints of system and generators. Result comparisons among MCSA and CSA indicate that the proposed constraint handling method is very useful for metaheuristic algorithms when solving OLDCEM problem. As compared to MSSA, MPSO as well as other previous methods, MCSA is more effective by finding higher total benefit for the two systems with faster manner and lower oscillations. Consequently, MCSA method is a very effective technique for OLDCEM problem in power systems.
The optimal synthesis of scanned linear antenna arrays IJECEIAES
In this paper, symmetric scanned linear antenna arrays are synthesized, in order to minimize the side lobe level of the radiation pattern. The feeding current amplitudes are considered as the optimization parameters. Newly proposed optimization algorithms are presented to achieve our target; Antlion Optimization (ALO) and a new hybrid algorithm. Three different examples are illustrated in this paper; 20, 26 and 30 elements scanned linear antenna array. The obtained results prove the effectiveness and the ability of the proposed algorithms to outperform and compete other algorithms like Symbiotic Organisms Search (SOS) and Firefly Algorithm (FA).
A MODIFIED ANT COLONY ALGORITHM FOR SOLVING THE UNIT COMMITMENT PROBLEMaeijjournal
Solving the unit commitment (UC) problem is one of the most complicated issues in power systems that its
exact solving can be calculated by perfect counting of entire possible compounds of generative units. UC is
equated as a nonlinear optimization with huge size. Purpose of solving this problem is to programming the
optimization of the generative units to minimize the full action cost regarding problem constraints. In this
article, a modified version of ant colony optimization (MACO) is introduced for solving the UC problem in
a power system. ACO algorithm is a powerful optimization method which has the capability of fleeing from
local minimums by performing flexible memory system. The efficiency of proposed method in two power
system containing 4 and 10 generative units is indicated. Comparison of obtained results from the proposed
method with results of the past well-known methods is a proof for suitability of performing the introduced
algorithm in economic input and output of generative units.
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Optimum designing of a transformer considering lay out constraints by penalty...INFOGAIN PUBLICATION
Optimum designing of power electrical equipment and devices play a leading role in attaining optimal performance and price of equipments in electric power industry. Optimum transformer design considering multiple constraints is acquired using optimal determination of geometric parameters of transformer with respect to its magnetic and electric properties. As it is well known, every optimization problem requires an objective function to be minimized. In this paper optimum transformer design problem comprises minimization of transformers mean core mass and its windings by satisfying multiple constraints according to transformers ratings and international standards using a penalty-based method. Hybrid big bang-big crunch algorithm is applied to solve the optimization problem and results are compared to other methods. Proposed method has provided a reliable optimization solution and has guaranteed access to a global optimum. Simulation result indicates that using the proposed algorithm, transformer parameters such as core mass, efficiency and dimensions are remarkably improved. Moreover simulation time using this algorithm is quit less in comparison to other approaches.
The problem of power system optimization has become a deciding factor in electrical power system engineering practice with emphasis on cost and emission reduction. The economic emission dispatch (EED) problem has been addressed in this paper using a Biogeography-based optimization (BBO). The BBO is inspired by geographical distribution of species within islands. This optimization algorithm works on the basis of two concepts-migration and mutation. In this paper a non-uniform mutation operator has been employed. The proposed technique shows better diversified search process and hence finds solutions more accurately with high convergence rate. The BBO with new mutation operator is tested on ten unit system. The comparison which is based on efficiency, reliability and accuracy shows that proposed mutation operator is competitive to the present one.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
GWO-based estimation of input-output parameters of thermal power plantsTELKOMNIKA JOURNAL
The fuel cost curve of thermal generators was very important in the calculation of economic dispatch and optimal power flow. Temperature and aging could make changes to fuel cost curve so curve estimation need to be done periodically. The accuracy of the curve parameters estimation strongly affected the calculation of the dispatch. This paper aims to estimate the fuel cost curve parameters by using the grey wolf optimizer method. The problem of curve parameter estimation was made as an optimization problem. The objective function to be minimized was the total number of absolute error or the difference between the actual value and the estimated value of the fuel cost function. The estimated values of parameter that produce the smallest total absolute error were the values of final solution. The simulation results showed that parameter estimation using gray wolf optimizer method further minimized the value of objective function. By using three models of fuel cost curve and given test data, parameter estimation using grey wolf optimizer method produced the better estimation results than those estimation results obtained using least square error, particle swarm optimization, genetic algorithm, artificial bee colony and cuckoo search methods.
A Minimum Spanning Tree Approach of Solving a Transportation Probleminventionjournals
: This work centered on the transportation problem in the shipment of cable troughs for an underground cable installation from three supply ends to four locations at a construction site where they are needed; in which case, we sought to minimize the cost of shipment. The problem was modeled into a bipartite network representation and solved using the Kruskal method of minimum spanning tree; after which the solution was confirmed with TORA Optimization software version 2.00. The result showed that the cost obtained in shipping the cable troughs under the application of the method, which was AED 2,022,000 (in the United Arab Emirate Dollar), was more effective than that obtained from mere heuristics when compared.
Stochastic fractal search based method for economic load dispatchTELKOMNIKA JOURNAL
This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based
method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are
introduced in the paper by employing two different random walk generators for diffusion process in which
SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called
SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from
three test system. These systems with 6, 10, and 20 units with different objective function forms and
different constraints are inspected. Numerical result comparison can confirm that the applied approach has
better solution quality and fast convergence time when compared with some recently published standard,
modified, and hybrid methods. This elucidates that the two SFS methods are very favorable for solving
the ELD problem.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Economic Load Dispatch Problem with Valve – Point Effect Using a Binary Bat A...IDES Editor
This paper proposes application of BAT algorithm
for solving economic load dispatch problem. BAT
algorithmic rule is predicated on the localization
characteristics of micro bats. The proposed approach has
been examined and tested with the numerical results of
economic load dispatch problems with three and five
generating units with valve - point loading without
considering prohibited operating zones and ramp rate limits.
The results of the projected BAT formula are compared with
that of other techniques such as lambda iteration, GA, PSO,
APSO, EP, ABC and basic principle. For each case, the
projected algorithmic program outperforms the answer
reported for the existing algorithms. Additionally, the
promising results show the hardness, quick convergence
and potency of the projected technique.
Application of a new constraint handling method for economic dispatch conside...journalBEEI
In this paper, optimal load dispatch problem under competitive electric market (OLDCEM) is solved by the combination of cuckoo search algorithm (CSA) and a new constraint handling approach, called modified cuckoo search algorithm (MCSA). In addition, we also employ the constraint handling method for salp swarm algorithm (SSA) and particle swarm optimization algorithm (PSO) to form modified SSA (MSSA) and modified PSO (MPSO). The three methods have been tested on 3-unit system and 10-unit system under the consideration of payment model for power reserve allocated, and constraints of system and generators. Result comparisons among MCSA and CSA indicate that the proposed constraint handling method is very useful for metaheuristic algorithms when solving OLDCEM problem. As compared to MSSA, MPSO as well as other previous methods, MCSA is more effective by finding higher total benefit for the two systems with faster manner and lower oscillations. Consequently, MCSA method is a very effective technique for OLDCEM problem in power systems.
The optimal synthesis of scanned linear antenna arrays IJECEIAES
In this paper, symmetric scanned linear antenna arrays are synthesized, in order to minimize the side lobe level of the radiation pattern. The feeding current amplitudes are considered as the optimization parameters. Newly proposed optimization algorithms are presented to achieve our target; Antlion Optimization (ALO) and a new hybrid algorithm. Three different examples are illustrated in this paper; 20, 26 and 30 elements scanned linear antenna array. The obtained results prove the effectiveness and the ability of the proposed algorithms to outperform and compete other algorithms like Symbiotic Organisms Search (SOS) and Firefly Algorithm (FA).
A MODIFIED ANT COLONY ALGORITHM FOR SOLVING THE UNIT COMMITMENT PROBLEMaeijjournal
Solving the unit commitment (UC) problem is one of the most complicated issues in power systems that its
exact solving can be calculated by perfect counting of entire possible compounds of generative units. UC is
equated as a nonlinear optimization with huge size. Purpose of solving this problem is to programming the
optimization of the generative units to minimize the full action cost regarding problem constraints. In this
article, a modified version of ant colony optimization (MACO) is introduced for solving the UC problem in
a power system. ACO algorithm is a powerful optimization method which has the capability of fleeing from
local minimums by performing flexible memory system. The efficiency of proposed method in two power
system containing 4 and 10 generative units is indicated. Comparison of obtained results from the proposed
method with results of the past well-known methods is a proof for suitability of performing the introduced
algorithm in economic input and output of generative units.
Hybrid method for achieving Pareto front on economic emission dispatch IJECEIAES
In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multiobjective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.
Hybrid Particle Swarm Optimization for Solving Multi-Area Economic Dispatch P...ijsc
We consider the Multi-Area Economic Dispatch problem (MAEDP) in deregulated power system environment for practical multi-area cases with tie line constraints. Our objective is to generate allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. This problem is NP-hard. In this paper, we propose Hybrid Particle Swarm Optimization (HGAPSO) to solve MAEDP. The experimental results are reported to show the efficiency of proposed algorithms compared to Particle Swarm Optimization with Time-Varying Acceleration Coefficients (PSO-TVAC) and RCGA.
Dynamic economic emission dispatch using ant lion optimizationjournalBEEI
This paper aims to propose a new meta-heuristic search algorithm, called Ant Lion Optimization (ALO). The ALO is a newly developed population-based search algorithm inspired hunting mechanism of ant lions. The proposed algorithm is presented to solve the dynamic economic emission dispatch (DEED) problem with considering the generator constraints such as ramp rate limits, valve-point effetcs, prohibited operating zones and transmission loss. The 5-unit generation system for a 24 h time interval has been taken to validate the efficiency of the proposed algorithm. Simulation results clearly show that the proposed method outperforms in terms of solution quality when compared with the other optimization algorithms reported in the literature.
A MODIFIED ANT COLONY ALGORITHM FOR SOLVING THE UNIT COMMITMENT PROBLEMAEIJjournal2
Solving the unit commitment (UC) problem is one of the most complicated issues in power systems that its
exact solving can be calculated by perfect counting of entire possible compounds of generative units. UC is
equated as a nonlinear optimization with huge size. Purpose of solving this problem is to programming the
optimization of the generative units to minimize the full action cost regarding problem constraints. In this
article, a modified version of ant colony optimization (MACO) is introduced for solving the UC problem in
a power system. ACO algorithm is a powerful optimization method which has the capability of fleeing from
local minimums by performing flexible memory system. The efficiency of proposed method in two power
system containing 4 and 10 generative units is indicated. Comparison of obtained results from the proposed
method with results of the past well-known methods is a proof for suitability of performing the introduced
algorithm in economic input and output of generative units.
A MODIFIED ANT COLONY ALGORITHM FOR SOLVING THE UNIT COMMITMENT PROBLEMAEIJjournal2
Solving the unit commitment (UC) problem is one of the most complicated issues in power systems that its exact solving can be calculated by perfect counting of entire possible compounds of generative units. UC is equated as a nonlinear optimization with huge size. Purpose of solving this problem is to programming the optimization of the generative units to minimize the full action cost regarding problem constraints. In this article, a modified version of ant colony optimization (MACO) is introduced for solving the UC problem in a power system. ACO algorithm is a powerful optimization method which has the capability of fleeing from
local minimums by performing flexible memory system. The efficiency of proposed method in two power system containing 4 and 10 generative units is indicated. Comparison of obtained results from the proposed
method with results of the past well-known methods is a proof for suitability of performing the introduced
algorithm in economic input and output of generative units.
Advanced Energy: An International Journal (AEIJ)AEIJjournal2
Solving the unit commitment (UC) problem is one of the most complicated issues in power systems that its
exact solving can be calculated by perfect counting of entire possible compounds of generative units. UC is
equated as a nonlinear optimization with huge size. Purpose of solving this problem is to programming the
optimization of the generative units to minimize the full action cost regarding problem constraints. In this
article, a modified version of ant colony optimization (MACO) is introduced for solving the UC problem in
a power system. ACO algorithm is a powerful optimization method which has the capability of fleeing from
local minimums by performing flexible memory system. The efficiency of proposed method in two power
system containing 4 and 10 generative units is indicated. Comparison of obtained results from the proposed
method with results of the past well-known methods is a proof for suitability of performing the introduced
algorithm in economic input and output of generative units.
In this study, optimal economic load dispatch problem (OELD) is resolved by
a novel improved algorithm. The proposed modified moth swarm algorithm
(MMSA), is developed by proposing two modifications on the classical moth
swarm algorithm (MSA). The first modification applies an effective formula
to replace an ineffective formula of the mutation technique. The second
modification is to cancel the crossover technique. For proving the efficient
improvements of the proposed method, different systems with discontinuous
objective functions as well as complicated constraints are used. Experiment
results on the investigated cases show that the proposed method can get less
cost and achieve stable search ability than MSA. As compared to other
previous methods, MMSA can archive equal or better results. From this view,
it can give a conclusion that MMSA method can be valued as a useful method
for OELD problem.
Comparative study of the price penalty factors approaches for Bi-objective di...IJECEIAES
One of the main objectives of electricity dispatch centers is to schedule the operation of available generating units to meet the required load demand at minimum operating cost with minimum emission level caused by fossil-based power plants. Finding the right balance between the fuel cost the green gasemissionsis reffered as Combined Economic and Emission Dispatch (CEED) problem which is one of the important optimization problems related the operationmodern power systems. The Particle Swarm Optimization algorithm (PSO) is a stochastic optimization technique which is inspired from the social learning of birds or fishes. It is exploited to solve CEED problem. This paper examines the impact of six penalty factors like "Min-Max", "Max-Max", "Min-Min", "Max-Min", "Average" and "Common" price penalty factors for solving CEED problem. The Price Penalty Factor for the CEED is the ratio of fuel cost to emission value. This bi-objective dispatch problem is investigated in the Real West Algeria power network consisting of 22 buses with 7 generators. Results prove capability of PSO in solving CEED problem with various penalty factors and it proves that Min-Max price penalty factor provides the best compromise solution in comparison to the other penalty factors.
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Abstract: In this paper, an algorithm to solve the optimal unit commitment problem under deregulated environment has been proposed using Particle Swarm Optimization (PSO) intelligent technique accounting economic dispatch constraints. In the present electric power market, where renewable energy power plants have been included in the system, there is a lot of unpredictability in the demand and generation. This paper presents an improved particle swarm optimization algorithm (IPSO) for power system unit commitment with the consideration of various constraints. IPSO is an extension of the standard particle swarm optimization algorithm (PSO) which uses more particles information to control the mutation operation, and is similar to the social society in that a group of leaders could make better decisions. The program was developed in MATLAB and the proposed method implemented on IEEE 14 bus test system.
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Bi-objective Optimization Apply to Environment a land Economic Dispatch Problem Using the Method of Corridor Observations
1. ISSN (e): 2250 – 3005 || Vol, 04 || Issue, 10 || October – 2014 ||
International Journal of Computational Engineering Research (IJCER)
www.ijceronline.com Open Access Journal Page 16
Bi-objective Optimization Apply to Environmental and Economic Dispatch Problem Using the Method of Corridor Observations Salomé Ndjakomo Essiane1, Stève Perabi Ngoffe2, Adolphe Moukengue Imano3, Grégoire Abessolo Ondoa4 1Lecturer, Electronic, Electrotechnic, Automatic and Telecommunications Laboratory, ERSEE, University of Douala - Cameroon 2 Doctorate Student, Electronic, Electrotechnic, Automatic and Telecommunications Laboratory, ERSEE, University of Douala - Cameroon 3 Associate Professor, Electronic, Electrotechnic, Automatic and Telecommunications Laboratory, ERSEE, University of Douala, BP. 8698 Douala - Cameroon 4 Master of Sciences with thesis student, Electronic, Electrotechnic, Automatic and Telecommunications Laboratory, ERSEE , University of Douala - Cameroon
I. INTRODUCTION
The economic dispatching (ED) is one of the key problems in power system operation and planning. The basic objective of economic dispatch is to schedule the committed generating unit outputs so as to meet the load demand at minimum operating cost, while satisfying all equality and inequality constraints. This makes the ED problem a large – scale highly constrained non linear optimization problem. In addition, the increasing public awareness of the environmental protection and the passage of the Clean Air Act Amendments of 1990 have forced the utilities to modify their design or operational strategies to reduce pollution and atmospheric emissions of the thermal power plant. Several strategies to reduce the atmospheric emissions have been proposed and discussed. These include: installation of pollutant cleaning equipment, switching to low emission fuels, replacement of the aged fuel-burners with cleaner ones, and emission dispatching. The first three options require installation of new equipment and/or modification of the existing ones that involve considerable capital outlay and, hence, they can be considered as long-term options. The emission dispatching option is an attractive short-term alternative in which the emission in addition to the fuel cost objective is to be minimized. Thus, the ED problem can be handled as a multi-objective optimization problem with non-commensurable and contradictory objectives. In recent years, this option has received much attention [1–5] since it requires only small modification of the basic ED to include emissions.
ABSTRACT:
This paper presents a proposed and applicable optimization algorithm based on the evolutionary algorithm to solve an environmental and economic Dispatch (EED) problem. This problem is seen like a bi-objective optimization problem where fuel cost and gas emission are objectives .in this method, the optimal Pareto front is found using the concept of corridor observation and the best compromised solution is obtained by fuzzy logic. The feasibility of this method is demonstrated using power systems with three generation units, and it is compared with the other evolutionary methods of Optimization Toolbox of Matlab in terms of solution quality and CPU time. The simulated results showed that the proposed method is indeed capable of obtaining higher quality solutions in shorter computational time compared to other evolutionary methods. In addition the other advantage is that our approach solves in the same time a unit commitment problem and it can use with n-generation units.
KEYWORDS: bi-objective, corridor observations, Evolutionary algorithm, fuel cost, gas emission, optimal PARETO front, optimization
2. Bi-objective Optimization Apply to…
www.ijceronline.com Open Access Journal Page 17
In the literature concerning environmental/economic dispatch (EED) problem, different technics have
been applied to solve EED problem. In [1, 2] the problem was reduced to a single objective problem by treating
the emission as a constraint. This formulation, however, has a severe difficulty in getting the trade-off relations
between cost and emission. Alternatively, minimizing the emission has been handled as another objective in
addition to the cost [5]. However, many mathematical assumptions have to be given to simplify the problem.
Furthermore, this approach does not give any information regarding the trade-offs involved. In other research
direction, the multi-objective EED problem was converted to a single objective problem by linear combination
of different objectives as a weighted sum [3], [6]. The important aspect of this weighted sum method is that a set
of non-inferior (or Pareto-optimal) solutions can be obtained by varying the weights. Unfortunately, this
requires multiple runs as many times as the number of desired Pareto-optimal solutions. Furthermore, this
method cannot be used in problems having a non-convex Pareto optimal front. To overcome it, certain method
optimizes the most preferred objective and considers the other objectives as constraints bounded by some
allowable levels [5]. The most obvious weaknesses of this approach are that, then are time-consuming and tend
to observed weakly non-dominated solutions [5].
The other direction is to consider both objectives simultaneously as competing objectives. The recent
review to the Unit Commitment and Methods for Solving [7] showed that evolutionary algorithms are the most
used in this case; certainly because they can efficiently eliminate most of the difficulties of classical methods
[5]. The major problems of these algorithms, is to find the pareto optimal front and to conserve the non-dominated
solutions during the search. In this paper we perform and apply one optimization method proposed in
[9] to solve the EED problem. The particularity of this method is based to the fact that the search of front and
optimal Pareto is found by the concept of corridor, and the archives is dynamic. This dynamism reduce the loses
of the non-dominated solution during the different generations. In the second part of this paper, we present
materials and methods to solve the problem, and the third part, present simulation and results obtained.
II. MATERIALS AND METHODS
In this part, we formulate the EED problem and present our approach to solve it.
2.1. Problem formulation
The EED problem is to minimize two competing objective functions, fuel cost and emission, while satisfying
several equality and inequality constraints. Generally the problem is formulated as follows :
2.1.1. Problem objectives
Minimization of fuel cost
The generator cost curves are represented generally by quadratic functions. The total fuel cost ($/h) in terms of
period T, can be expressed as:
(1)
Where
2
, , , ( ) fi i t i i i t i i t c p a b p c p (2)
and ( ) fi i , t c p is the generator fuel cost function; ai, bi and ci are the cost coefficients of ith generator; Pi,t, is the
electrical output of ith generator; Ng is the number of generators committed to the operating system ; Ii,tthestatut
of differents generators ; STi the start-up cost .
Minimization of gas emission
The atmospheric pollutants such as sulpher dioxides (SO2) and nitrogen oxides (NOX) caused by fossil-fueled
thermal units can be modeled separately. However, for comparison purposes, the total emission (ton/h) in one
period T of these pollutants can be expressed as:
i t i t
T
t
Ng
i
i t fi E p e p I , ,
1 1
, ( )
(3)
where
( ) ( )
2
fi i , t i i i , t i i , t e P p p (4)
and αi, βi, δi are the emission coefficients of the ith generator.
i t i t i t i t i t
T
t
Ng
i
i t fi F p c p I ST I I , , , , 1 ,
1 1
, ( ) (1 )
3. Bi-objective Optimization Apply to…
www.ijceronline.com Open Access Journal Page 18
2.1.2. Objective constraints
Power balance constraint
Ng
i
load t i t i t p p I
1
, , , 0
(5)
Spinning reserve constraint :
Ng
i
load t t i i t p R p I
1
, max, , 0
(6)
Generation limit constraints :
i i t i t i i t p I p p I min, , , max, , , i 1 ...... Ng
(7)
Minimum up and down time constraint :
or otherwise
if T T
if T T
I
down
i
off
i
up
i
on
i
i t
0 1
0
1
,
(8)
Where Ti
up represent the minimum up time of unit i; Ti
down the minimum down time of unit iTi
off is the
continuously off time of unit i and Ti
on the continuously on time of unit- i .
Start-up cost
down
i
cold
i
off
i i
cold
i
down
i
off
i
down
i i
i
CST if T T T
HST if T T T T
ST
2.2. The proposed approach
2.2.1. Algorithm of corridors observations method
The different steps of the proposed approach to solve EED problem is summarize in the follow figure
Figure 1: Different steps of the algorithms
Step 1
In the first step, we start with to the status of different unit generation, were we create randomly the initial
population. Each individual is a combination of each power generation unit
Step 2
In the second, using equations (1) and (3) we evaluate the objective functions of this population
Step 3
Generate initial
population
· Evaluate function cost
· Evaluate emission cost
Segment objectives space function
in corridor
Search the best persons in
corridors
Archive the best persons
Stopping criteria
determine the pareto front
determine the best compromize
solution
End
Apply cross and mutation operator
Form a new population
4. Bi-objective Optimization Apply to…
www.ijceronline.com Open Access Journal Page 19
Using the minimum of the different objective functions of individuals who respect the constraints (5) to (8), we
define the space solution and segment it to the corridors observation following the different axes which are
specify by each function.
Step 4
In each corridor, we search the best individual who have the minimum objectives functions, and the non feasible
solutions are classified using the number and the rate of violation constraints. Those solutions will be used to
increase the number of feasible solutions.
Step 5
We keep in the archives those best individuals
Step 6
We verify the stoping criteria define as [9] :
ln( d )
(9)
where
F N
j
cl
i
t
j i
t
j i
F F
F F
Cl
d
1 1 max min
1
1 , ,
explain the metric progression of the best individuals in each corridor. NF is the number of objectives functions ;
Cl the number of corridor ; Ft
j,i , Ft-1
j,i the jth objective function of the best individual in ith corridor ; Fmin and Fmax
the minimum and maximum of the j function ; t is the present generation, t-1 the anterior generation. At times
the maximum number of generation can be the alternative stopping criteria
step 7
If the stopping criteria is not verified, we construct the new population using the selection ,cross and mutation
operators apply to the archive population and we return to step 2.
Step 8
If the stopping criteria is verified we find the best compromise solution among the individuals of the Pareto
front. Due to imprecise nature of the decision maker’s judgment, each objective function of the i-th solution is
represented by a membership i function defined as
max
min max
max min
max
min
0
1
i i
i i i
i i
i i
i i
i
if F F
F F F
F F
F F
if F F
For each non-dominated solution, the normalized membership function is k
calculated as:
M
k
N
i
k
i
N
i
k
i
k
F
F
1 1
1
where M is the number of non-dominated solutions. The best compromise solution is the one having the
maximum of k
.
2.2.2. Implementation and strategy to search solution
To find the problem solution algorithm, we have to :
Explore space solutions
During this step, the algorithm explore space solutions with using 0.9 percentage of random mutation operator
and 0.1 percentage of uniform cross operator, it corresponding to the inequality 8 .
Exploit space solutions
To exploit space solutions, the algorithm applied to the population random mutation a percentage of 0.9 and
0.1 percentage of arithmetic cross operator. it corresponding to the inequality 18 12 .
Apply hybrid mode
It’s a transition between exploration and exploitation which correspond to 0.5 percentage of cross probability
and 0.5 percentage of mutation probability. The range of stopping criteria is: 12 8
(11)
(12)
(10)
5. Bi-objective Optimization Apply to…
www.ijceronline.com Open Access Journal Page 20
III. SIMULATION AND RESULTS
In order to validate the proposed procedure and to verify the feasibility of the corridor method to solve
the EED, a 3-units generation system is tested [10] and extent to 6, 10 and 15 units génération. The proposed
method is implemented with Matlab 2010.b on a core i3 2.1 GHz and the results are compared with other
evolutionary algorithms (GA and GA multi-obj) of optimization tool. The data concerning the unit generation is
given in table 1 to table 2 [10].
Table 1. The 3-units system data
Unit Pi
max
(MW)
Pi
min
(MW)
a
($ /h)
b
($ /MWh)
c
($ /MW2h)
Ri
up
($ /MW)
Ri
down
($ /MWh)
1 600 150 561 7.29 0.00156 100 100
2 400 100 310 7.85 0.00194 80 80
3 200 50 78 7.97 0.00482 50 50
Table 2. SO2 and NOx coefficients emission gas data of 3-units
Units
so 2 (tons/h)
Nox
(tons/h) so 2 (tons/MWh)
Nox (tons/MWh)
so 2 (tons/MW2h)
Nox
(tons/MW2h)
1 0,5783298 0,04373254 0,00816466 -9,4868099 e-6 1,6103e-6 1,4721848 e-7
2 0,3515338 0,055821713 0,00891174 -9,7252878 e-5 5,4658 e-6 3,0207577 e-7
3 0,0884504 0,027731524 0,00903782 -3,5373734 e-4 5,4658 e-6 1,9338531 e-6
In the implementation, we add the different coefficients of each gas per groups to have the coefficient of the
whole gas.
3.1 Achievement of Pareto front
The Pareto front is obtained, keeping the best individuals (individuals who have the minimum fuel cost are
conserved in relation to the emission axes and vice versa) that respect all the contraints in each corridor during
the evolution. To simulate the evolution of pareto front we have initialize the population size at 300 , the
maximum generation at 1000 ,the number of corridor at 50 and load demand is 1000MW.
9260 9270 9280 9290 9300 9310 9320
10.5
10.55
10.6
10.65
10.7
10.75
10.8
10.85
10.9
Cost
Emission
generation 764
individual of population
feasible individual
Best compromise solution
Figure 2 : Pareto optimal front at the end of process (1000MW load demand).
In the search of the best solution in each corridor, at the beginning the algorithm could not find the best feasible
solutions but in the process of evolution the number of these solutions increases up to the Pareto optimal front.
3.1. Study of convergence
The curve convergence show that until one number of generations the algorithm finds the best solution,
from this times gas emission and fuel cost is uniform. It expresses the performance of stopping criteria.
6. Bi-objective Optimization Apply to…
www.ijceronline.com Open Access Journal Page 21
0 100 200 300 400 500 600 700 800 900 1000
9255
9260
9265
9270
9275
9280
cost convergence with generation
generation
cost($)
0 100 200 300 400 500 600 700 800 900 1000
10.7
10.75
10.8
10.85
10.9
10.95
emission convergence with generation
generation
emission globale(ton/h)
Figure 3: Convergence of fuel cost($) and gas emissions(ton/h) objective functions (1000MW).
3.2. Apply of method to 24 hours
To present the effectiveness of our approach to unit commitment and EED, we have apply it to plan the
production of 3-units during 24 hours.
Table 3. Unit commitment and EED during 24 hours
Hours
(H)
Demands
(MW)
P1
(MW)
P2
(MW)
P3
(MW)
Fuel cost
X103($)
Emission
gas
(ton/h)
Starting
cost
($/MWh)
Total cost
($)
1 550 0 0 549.9 5.0415 5.6380
2 600 0 0 599.9 5.4957 6.1468
3 650 108.0382 0 541.8742 5.9646 6.6979 50
4 700 114.5484 0 585.351 6.4169 7.2059
5 750 150.228 0 599.67 6.8777 7.7323
6 800 0 224.27 575.62 7.4424 8.5731 80
7 850 0 250.314 599.58 7.8893 9.1188
8 900 0 300.541 599.3621 8.3352 9.7188
9 950 114.9563 239.4409 595.5072 8.8142 10.1626 50
10 1000 128.8152 275.9956 595.0968 9.2607 10.7347
11 1050 141.965 308.5501 599.3873 9.7144 11.3159
12 900 0 300.03 599.8287 8.3342 9.7188
13 850 0 250.0713 599.8287 7.8894 9.1184
14 800 0 225.58 574.3207 7.4419 8.5747
15 750 150.7585 0 599.1479 6.8779 7.7327 50
16 700 114.5434 0 585.355 6.4116 7.2059
17 650 108.0326 0 541.8732 5.9646 6.6979
18 600 0 0 599.9 5.4957 6.1468
19 730 130.2853 0 599.6148 6.6913 7.5171 50
20 820 0 233.9595 585.9423 7.6209 8.7892 80
21 860 0 260.1659 599.7343 7.9778 9.2361
22 900 0 300.531 599.3721 8.3352 9.7188
23 950 114.9553 239.4419 595.5072 8.8142 10.1626 50
24 1000 128.8152 275.9956 595.0968 9.2607 10.7347
Total 178.368 410 178778
In function of demand we see that some unit could be on and other off, to minimize the fuel cost and emission
gas. The plan production of different units is represent in follow figure
7. Bi-objective Optimization Apply to…
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Figure 3: Production plan of different units
3.3. Comparison of results
To show the effectiveness of the proposed method, we have compared it with other evolutionary algorithm of optimization tool of matlab. The same parameter is considered and the criteria for comparisons are cost and average CPU times. Tableau 4: Comparison methods with 1000MW of load demand
GA
GA multi-obj.
corridor P1 (MW) 400.0587 399,999 598.4477
P2 (MW)
399.9885
399,999
275.8265 P3(MW) 199.9518 199,999 125.6293
Fuel Cost($ /h)
9879.2053
9878,988
9260,6 Emission ton/h 11.755 11,644 10.5768
Average CPU times
244.9135
261.9536
23.29854
This table show that our method is best in term of fuel cost and emission gas
3.4. Impact of numbers of units to fuel cost, gas emission and average CPU times
To show this impact, we have multiplied the number of units of our 3-units. The results are presented to follow table. Tableau 5: Impact of numbers of units to fuel cost, gas emission and average CPU times
Number of units
3
6
10
15 Fuel cost($) 9.2606 9.1911 9.176 9.177
Gas emission(ton/h)
10.7347
10.2771
10.3679
10.3683 Average times(s) 23.29 31.92 49.40 104.61
This table show that when the number of units increases, the fuel cost, gas emission and average CPU decrease.
IV. CONCLUSION
In this paper, an approach based on the evolutionary algorithm has been presented and applied to environmental/economic power dispatch optimization problem. The problem has been formulated as a bi- objective optimization problem with competing fuel cost and environmental impact objectives. The proposed approach has a diversity-preserving mechanism to find Pareto-optimal solution. The optimal Pareto front is obtained from minimizing each objective function in each corridor and keeping the best individuals in dynamic achieves. Moreover, a fuzzy-based mechanism is employed to extract the best compromise solution over the trade-off curve. The results show that the proposed approach is efficient for solving bi-objective optimization
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where multiple Pareto-optimal solutions can be found in one simulation run. In addition, the non-dominated solutions in the obtained Pareto-optimal set are well distributed and have satisfactory diversity characteristics. Comparatively to other approach, the most important aspect of the proposed approach is the reduce time to find optimal Pareto front, fuel cost, gas emission, the consideration of unit commitment problem and the possibility to manage system which have n-generation units and best compromise. REFERENCES [1] Brodesky S. F, Hahn R. W. Assessing the influence of power pools on emission constrained economic dispatch. IEEE Trans Power Syst 1986;1(1).pp:57–62. [2] Granelli G. P, Montagna M, Pasini G. L, Marannino P. Emission constrained dynamic dispatch. Electr Power Syst Res 1992;24.pp: 56–64. [3] Chang C. S, Wong K. P, Fan B. Security-constrained multiobjective generation dispatch using bicriterion global optimization. IEE Proc—GenerTransmDistrib 1995;142(4):406–14. [4] R Manoj Kumar. Bavisetti, T.KranthiKiran. Optimization Of Combined Economic and Emission Dispatch Problem – A Comparative Study for 30 Bus Systems. IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) 2012 ;Vol 2 : PP 37-43 [5] M. A. Abido. Environmental/Economic Power Dispatch Using Multiobjective Evolutionary Algorithms. IEEE Transactions On Power Systems ; 2003 VOL. 18, NO. 4. Pp :1529-1537 [6] Alkhalil Firas. «Supervision, économie et impact sur l’environnement d’un système d'énergie électrique associé à une centrale photovoltaïque »thèse de Doctorat Paris tech. 2011 [7] Samani.h, Razmezani.M and Naseh.M.R. (2013). Unit Commitment and Methods for Solving; a Review .J. Basic. Appl. Sci. Res., 3(2s) 358-364 [8] Lubing Xie, Songling Wang & Zhiquan Wu. Study on Economic, Rapid and Environmental Power Dispatch. Modern applied sciences vol.3 N06. 2009. pp :38-44 [9] Jean Dipama. « Optimisation Multi-Objectif Des Systèmes Énergétiques ».thèse soutenue à l’université de Montréal. 2010 [10] Farid Benhamida, Rachid Belhachem. Dynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network .Power Engineering And Electrical Engineering.Volume: 11 N01 .2013.pp :1-9