The document describes a hybrid firefly-differential evolution algorithm for solving the economic load dispatch problem. The economic load dispatch problem involves allocating generation among power plants to minimize costs while satisfying constraints. The proposed hybrid algorithm combines the differential evolution and firefly algorithms. It was tested on a 3 unit power system and showed improved efficiency and robustness compared to other existing algorithms for solving the economic load dispatch problem.
This paper introduces a solution of the economic load dispatch (ELD) problem using a hybrid approach of fuzzy logic and genetic algorithm (GA). The proposed method combines and extends the attractive features of both fuzzy logic and GA. The proposed approach is compared with lambda iteration method (LIM) and GA. The investigation reveals that the proposed approach can provide accurate solution with fast convergence characteristics and is superior to the GA and LIM.
THD Optimization in 13 level photovoltaic inverter using Genetic AlgorithmSuman Debnath
Minimum Total Harmonic Distortion (THD) is one of the most important requirements from multilevel inverter concerning good Power Quality. This paper presents the optimization of THD in 13 level Cascaded Multilevel Inverter with unequal dc source using Genetic Algorithm (GA). THD minimization is taken as an optimization problem derived from Selective Harmonic Elimination Pulse width Modulation (SHE-PWM). Results give all possible solutions at each modulation index. Switching strategy, FFT analysis and computational time has been analyzed using MATLAB simulation environment.
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.
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.
5. 9375 11036-1-sm-1 20 apr 18 mar 16oct2017 ed iqbal qcIAESIJEECS
In this paper, Tailored Flower Pollination (TFP) algorithm is proposed to solve the optimal reactive power problem. Comprising of the elements of chaos theory, Shuffled frog leaping search and Levy Flight, the performance of the flower pollination algorithm has been improved. Proposed TFP algorithm has been tested in standard IEEE 118 & practical 191 bus test systems and simulation results show clearly the better performance of the proposed algorithm in reducing the real power loss.
Firefly Algorithm to Opmimal Distribution of Reactive Power Compensation Units IJECEIAES
The issue of electric power grid mode of optimization is one of the basic directions in power engineering research. Currently, methods other than classical optimization methods based on various bio-heuristic algorithms are applied. The problems of reactive power optimization in a power grid using bio-heuristic algorithms are considered. These algorithms allow obtaining more efficient solutions as well as taking into account several criteria. The Firefly algorithm is adapted to optimize the placement of reactive power sources as well as to select their values. A key feature of the proposed modification of the Firefly algorithm is the solution for the multi-objective optimization problem. Algorithms based on a bio-heuristic process can find a neighborhood of global extreme, so a local gradient descent in the neighborhood is applied for a more accurate solution of the problem. Comparison of gradient descent, Firefly algorithm and Firefly algorithm with gradient descent is carried out.
This paper introduces a solution of the economic load dispatch (ELD) problem using a hybrid approach of fuzzy logic and genetic algorithm (GA). The proposed method combines and extends the attractive features of both fuzzy logic and GA. The proposed approach is compared with lambda iteration method (LIM) and GA. The investigation reveals that the proposed approach can provide accurate solution with fast convergence characteristics and is superior to the GA and LIM.
THD Optimization in 13 level photovoltaic inverter using Genetic AlgorithmSuman Debnath
Minimum Total Harmonic Distortion (THD) is one of the most important requirements from multilevel inverter concerning good Power Quality. This paper presents the optimization of THD in 13 level Cascaded Multilevel Inverter with unequal dc source using Genetic Algorithm (GA). THD minimization is taken as an optimization problem derived from Selective Harmonic Elimination Pulse width Modulation (SHE-PWM). Results give all possible solutions at each modulation index. Switching strategy, FFT analysis and computational time has been analyzed using MATLAB simulation environment.
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.
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.
5. 9375 11036-1-sm-1 20 apr 18 mar 16oct2017 ed iqbal qcIAESIJEECS
In this paper, Tailored Flower Pollination (TFP) algorithm is proposed to solve the optimal reactive power problem. Comprising of the elements of chaos theory, Shuffled frog leaping search and Levy Flight, the performance of the flower pollination algorithm has been improved. Proposed TFP algorithm has been tested in standard IEEE 118 & practical 191 bus test systems and simulation results show clearly the better performance of the proposed algorithm in reducing the real power loss.
Firefly Algorithm to Opmimal Distribution of Reactive Power Compensation Units IJECEIAES
The issue of electric power grid mode of optimization is one of the basic directions in power engineering research. Currently, methods other than classical optimization methods based on various bio-heuristic algorithms are applied. The problems of reactive power optimization in a power grid using bio-heuristic algorithms are considered. These algorithms allow obtaining more efficient solutions as well as taking into account several criteria. The Firefly algorithm is adapted to optimize the placement of reactive power sources as well as to select their values. A key feature of the proposed modification of the Firefly algorithm is the solution for the multi-objective optimization problem. Algorithms based on a bio-heuristic process can find a neighborhood of global extreme, so a local gradient descent in the neighborhood is applied for a more accurate solution of the problem. Comparison of gradient descent, Firefly algorithm and Firefly algorithm with gradient descent is carried out.
Reduction of Active Power Loss byUsing Adaptive Cat Swarm Optimizationijeei-iaes
This paper presents, an Adaptive Cat Swarm Optimization (ACSO) for solving reactive power dispatch problem. Cat Swarm Optimization (CSO) is one of the new-fangled swarm intelligence algorithms for finding the most excellent global solution. Because of complication, sometimes conventional CSO takes a lengthy time to converge and cannot attain the precise solution. For solving reactive power dispatch problem and to improve the convergence accuracy level, we propose a new adaptive CSO namely ‘Adaptive Cat Swarm Optimization’ (ACSO). First, we take account of a new-fangled adaptive inertia weight to velocity equation and then employ an adaptive acceleration coefficient. Second, by utilizing the information of two previous or next dimensions and applying a new-fangled factor, we attain to a new position update equation composing the average of position and velocity information. The projected ACSO has been tested on standard IEEE 57 bus test system and simulation results shows clearly about the high-quality performance of the planned algorithm in tumbling the real power loss.
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.
Implementation of an Effective Biogeography Based Algorithm
(EBBO) for Economic Load Dispatch (ELD) problems in power system in order to obtain optimal
economic dispatch with minimum generation cost. Approach: A viable methodology has been
implemented for a 20 unit generator system to minimize the fuel cost function considering the
transmission loss and system operating limit constraints and is compared with other approaches such as
BBO, Lambda Iteration and Hopfield Model. Results: Proposed algorithm has been applied to ELD
problems for verifying its feasibility and the comparison of results are tabulated and pictorial
visualization for convergence of EBBO is represented. Conclusion: Comparing with the other existing
techniques, the EBBO gives better result by considering the quality of the solution obtained. This
method could be an alternative approach for solving the ELD problems in practical power system.
NOVEL PSO STRATEGY FOR TRANSMISSION CONGESTION MANAGEMENTelelijjournal
In post deregulated era of power system load characteristics become more erratic. Unplanned transactions
of electrical power through transmission lines of particular path may occur due to low cost offered by
generating companies. As a consequence those lines driven close to their operating limits and becomes
congested as the lines are originally designed for traditional vertically integrated structure of power
system. This congestion in transmission lines is unpredictable with deterministic load flow strategy.
Rescheduling active and reactive power output of generators is the promising way to manage congestion.
In this paper Particle Swarm Optimization (PSO) with varying inertia weight strategy, with two variants
e1-PSO and e-2 PSO is applied for optimal solution of active and reactive power rescheduling for
managing congestion. The generators sensitivity technique is opted for identifying participating generators
for managing congestion. Proposed algorithm is tested on IEEE 30 bus system. Comparison is made
between results obtained from proposed techniques to that of results reported in previous literature.
Capacitor Placement Using Bat Algorithm for Maximum Annual Savings in Radial ...IJERA Editor
This paper presents a two stage approach that determines the optimal location and size of capacitors on radial distribution systems to improve voltage profile and to reduce the active power loss. In first stage, the capacitor locations can be found by using loss sensitivity method. Bat algorithm is used for finding the optimal capacitor sizes in radial distribution systems. The sizes of the capacitors corresponding to maximum annual savings are determined by considering the cost of the capacitors. The proposed method is tested on 15-bus, 33 bus, 34-bus, 69-bus and 85-bus test systems and the results are presented.
Enriched Firefly Algorithm for Solving Reactive Power Problemijeei-iaes
In this paper, Enriched Firefly Algorithm (EFA) is planned to solve optimal reactive power dispatch problem. This algorithm is a kind of swarm intelligence algorithm based on the response of a firefly to the light of other fireflies. In this paper, we plan an augmentation on the original firefly algorithm. The proposed algorithm extends the single population FA to the interacting multi-swarms by cooperative Models. The proposed EFA has been tested on standard IEEE 30 bus test system and simulation results show clearly the better performance of the proposed algorithm in reducing the real power loss.
Determining optimal location and size of capacitors in radial distribution ne...IJECEIAES
In this study, the problem of optimal capacitor location and size determination (OCLSD) in radial distribution networks for reducing losses is unraveled by moth swarm algorithm (MSA). MSA is one of the most powerful meta-heuristic algorithm that is taken from the inspiration of the food source finding behavior of moths. Four study cases of installing different numbers of capacitors in the 15-bus radial distribution test system including two, three, four and five capacitors areemployed to run the applied MSA for an investigation of behavior and assessment of performances. Power loss and the improvement of voltage profile obtained by MSA are compared with those fromother methods. As a result, it can be concluded that MSA can give a good truthful and effective solution method for OCLSD problem.
OPTIMIZATION OF COMBINED ECONOMIC EMISSION DISPATCH PROBLEM USING ARTIFICIAL ...IJCI JOURNAL
Optimal system operation, in general, involves the consideration of economy of operation, system security,
emissions at fossil-fuel plants, optimal release of water at hydro power plants etc. and aim at improving the efficiency of the power system. In this research work, consideration will be given to two aspects of the optimal system operation, emissions and economy of operation, also known as economic dispatch. Generally the heuristic methods like Genetic algorithm, Simulated annealing, Particle Swarm Optimization, Ant Colony techniques and their various modifications have shown marked improvement in the addressing of the economic dispatch problem as well as the combined economic and emission dispatch problem. However there is scope of improvement of the solution to the combined economic and emission dispatch problems, in terms of better convergence, lower losses, faster computation times, reduced fuel costs and reduced emissions. It is worthy of notice that Artificial Bee Colony Method applied in the present work, yielded superior solutions than the heuristic and traditional optimization techniques.
A Hybrid Formulation between Differential Evolution and Simulated Annealing A...TELKOMNIKA JOURNAL
The aim of this paper is to solve the optimal reactive power dispatch (ORPD) problem.
Metaheuristic algorithms have been extensively used to solve optimization problems in a reasonable time
without requiring in-depth knowledge of the treated problem. The perform ance of a metaheuristic requires
a compromise between exploitation and exploration of the search space. However, it is rarely to have the
two characteristics in the same search method, where the current emergence of hybrid methods. This
paper presents a hybrid formulation between two different metaheuristics: differential evolution (based on a
population of solution) and simulated annealing (based on a unique solution) to solve ORPD. The first one
is characterized with the high capacity of exploration, while the second has a good exploitation of the
search space. For the control variables, a mixed representation (continuous/discrete), is proposed. The
robustness of the method is tested on the IEEE 30 bus test system.
Locational marginal pricing framework in secured dispatch scheduling under co...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.
Memory Polynomial Based Adaptive Digital PredistorterIJERA Editor
Digital predistortion (DPD) is a baseband signal processing technique that corrects for impairments in RF
power amplifiers (PAs). These impairments cause out-of-band emissions or spectral regrowth and in-band
distortion, which correlate with an increased bit error rate (BER). Wideband signals with a high peak-to-average
ratio, are more susceptible to these unwanted effects. So to reduce these impairments, this paper proposes the
modeling of the digital predistortion for the power amplifier using GSA algorithm.
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.
Comparison of Emergency Medical Services Delivery Performance using Maximal C...IJECEIAES
Ambulance location is one of the critical factors that determine the efficiency of emergency medical services delivery. Maximal Covering Location Problem is one of the widely used ambulance location models. However, its coverage function is considered unrealistic because of its ability to abruptly change from fully covered to uncovered. On the contrary, Gradual Cover Location Problem coverage is considered more realistic compared to Maximal Cover Location Problem because the coverage decreases over distance. This paper examines the delivery of Emergency Medical Services under the models of Maximal Covering Location Problem and Gradual Cover Location Problem. The results show that the latter model is superior, especially when the Maximal Covering Location Problem has been deemed fully covered.
Dwindling of real power loss by using Improved Bees Algorithmpaperpublications3
Abstract: In this paper, a new Improved Bees Algorithm (IBA) is proposed for solving reactive power dispatch problem. The aim of this paper is to utilize an optimization algorithm called the improved Bees Algorithm, inspired from the natural foraging behaviour of honey bees, to solve the reactive power dispatch problem. The IBA algorithm executes both an exploitative neighbourhood search combined with arbitrary explorative search. The proposed Improved Imperialist Competitive Algorithm (IBA) algorithm has been tested on standard IEEE 57 bus test system and simulation results show clearly the high-quality performance of the projected algorithm in reducing the real power loss.
Keywords: Optimal Reactive Power, Transmission loss, honey bee, foraging behaviour, waggle dance, bee’s algorithm, swarm intelligence, swarm-based optimization, adaptive neighbourhood search, site abandonment, random search.
Solving the Power Purchase Cost Optimization Problem with Improved DE AlgorithmIJEACS
Under the deregulation of generation market in China, all distributed generators will particular in electric power bidding. Therefore power purchase cost optimization (PPCO) problem has been getting more attention of power grid Company. However, under the competition principle, they can purchase power from several of power plants, therefor, there exist continuous and integral variables in purchase cost model, which is difficult to solve by classical linear optimization method. An improved differential evolution algorithm is proposed and employed to solve the PPCO problem, which targets on minimum purchase cost, considering the supply and demand balance, generation and transfer capability as constraints. It yields the global optimum solution of the PPCO problem. The numerical results show that the proposed algorithm can solve the PPCO problem and saves the costs of power purchase. It has a widely practical value of application.
Reduction of Active Power Loss byUsing Adaptive Cat Swarm Optimizationijeei-iaes
This paper presents, an Adaptive Cat Swarm Optimization (ACSO) for solving reactive power dispatch problem. Cat Swarm Optimization (CSO) is one of the new-fangled swarm intelligence algorithms for finding the most excellent global solution. Because of complication, sometimes conventional CSO takes a lengthy time to converge and cannot attain the precise solution. For solving reactive power dispatch problem and to improve the convergence accuracy level, we propose a new adaptive CSO namely ‘Adaptive Cat Swarm Optimization’ (ACSO). First, we take account of a new-fangled adaptive inertia weight to velocity equation and then employ an adaptive acceleration coefficient. Second, by utilizing the information of two previous or next dimensions and applying a new-fangled factor, we attain to a new position update equation composing the average of position and velocity information. The projected ACSO has been tested on standard IEEE 57 bus test system and simulation results shows clearly about the high-quality performance of the planned algorithm in tumbling the real power loss.
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.
Implementation of an Effective Biogeography Based Algorithm
(EBBO) for Economic Load Dispatch (ELD) problems in power system in order to obtain optimal
economic dispatch with minimum generation cost. Approach: A viable methodology has been
implemented for a 20 unit generator system to minimize the fuel cost function considering the
transmission loss and system operating limit constraints and is compared with other approaches such as
BBO, Lambda Iteration and Hopfield Model. Results: Proposed algorithm has been applied to ELD
problems for verifying its feasibility and the comparison of results are tabulated and pictorial
visualization for convergence of EBBO is represented. Conclusion: Comparing with the other existing
techniques, the EBBO gives better result by considering the quality of the solution obtained. This
method could be an alternative approach for solving the ELD problems in practical power system.
NOVEL PSO STRATEGY FOR TRANSMISSION CONGESTION MANAGEMENTelelijjournal
In post deregulated era of power system load characteristics become more erratic. Unplanned transactions
of electrical power through transmission lines of particular path may occur due to low cost offered by
generating companies. As a consequence those lines driven close to their operating limits and becomes
congested as the lines are originally designed for traditional vertically integrated structure of power
system. This congestion in transmission lines is unpredictable with deterministic load flow strategy.
Rescheduling active and reactive power output of generators is the promising way to manage congestion.
In this paper Particle Swarm Optimization (PSO) with varying inertia weight strategy, with two variants
e1-PSO and e-2 PSO is applied for optimal solution of active and reactive power rescheduling for
managing congestion. The generators sensitivity technique is opted for identifying participating generators
for managing congestion. Proposed algorithm is tested on IEEE 30 bus system. Comparison is made
between results obtained from proposed techniques to that of results reported in previous literature.
Capacitor Placement Using Bat Algorithm for Maximum Annual Savings in Radial ...IJERA Editor
This paper presents a two stage approach that determines the optimal location and size of capacitors on radial distribution systems to improve voltage profile and to reduce the active power loss. In first stage, the capacitor locations can be found by using loss sensitivity method. Bat algorithm is used for finding the optimal capacitor sizes in radial distribution systems. The sizes of the capacitors corresponding to maximum annual savings are determined by considering the cost of the capacitors. The proposed method is tested on 15-bus, 33 bus, 34-bus, 69-bus and 85-bus test systems and the results are presented.
Enriched Firefly Algorithm for Solving Reactive Power Problemijeei-iaes
In this paper, Enriched Firefly Algorithm (EFA) is planned to solve optimal reactive power dispatch problem. This algorithm is a kind of swarm intelligence algorithm based on the response of a firefly to the light of other fireflies. In this paper, we plan an augmentation on the original firefly algorithm. The proposed algorithm extends the single population FA to the interacting multi-swarms by cooperative Models. The proposed EFA has been tested on standard IEEE 30 bus test system and simulation results show clearly the better performance of the proposed algorithm in reducing the real power loss.
Determining optimal location and size of capacitors in radial distribution ne...IJECEIAES
In this study, the problem of optimal capacitor location and size determination (OCLSD) in radial distribution networks for reducing losses is unraveled by moth swarm algorithm (MSA). MSA is one of the most powerful meta-heuristic algorithm that is taken from the inspiration of the food source finding behavior of moths. Four study cases of installing different numbers of capacitors in the 15-bus radial distribution test system including two, three, four and five capacitors areemployed to run the applied MSA for an investigation of behavior and assessment of performances. Power loss and the improvement of voltage profile obtained by MSA are compared with those fromother methods. As a result, it can be concluded that MSA can give a good truthful and effective solution method for OCLSD problem.
OPTIMIZATION OF COMBINED ECONOMIC EMISSION DISPATCH PROBLEM USING ARTIFICIAL ...IJCI JOURNAL
Optimal system operation, in general, involves the consideration of economy of operation, system security,
emissions at fossil-fuel plants, optimal release of water at hydro power plants etc. and aim at improving the efficiency of the power system. In this research work, consideration will be given to two aspects of the optimal system operation, emissions and economy of operation, also known as economic dispatch. Generally the heuristic methods like Genetic algorithm, Simulated annealing, Particle Swarm Optimization, Ant Colony techniques and their various modifications have shown marked improvement in the addressing of the economic dispatch problem as well as the combined economic and emission dispatch problem. However there is scope of improvement of the solution to the combined economic and emission dispatch problems, in terms of better convergence, lower losses, faster computation times, reduced fuel costs and reduced emissions. It is worthy of notice that Artificial Bee Colony Method applied in the present work, yielded superior solutions than the heuristic and traditional optimization techniques.
A Hybrid Formulation between Differential Evolution and Simulated Annealing A...TELKOMNIKA JOURNAL
The aim of this paper is to solve the optimal reactive power dispatch (ORPD) problem.
Metaheuristic algorithms have been extensively used to solve optimization problems in a reasonable time
without requiring in-depth knowledge of the treated problem. The perform ance of a metaheuristic requires
a compromise between exploitation and exploration of the search space. However, it is rarely to have the
two characteristics in the same search method, where the current emergence of hybrid methods. This
paper presents a hybrid formulation between two different metaheuristics: differential evolution (based on a
population of solution) and simulated annealing (based on a unique solution) to solve ORPD. The first one
is characterized with the high capacity of exploration, while the second has a good exploitation of the
search space. For the control variables, a mixed representation (continuous/discrete), is proposed. The
robustness of the method is tested on the IEEE 30 bus test system.
Locational marginal pricing framework in secured dispatch scheduling under co...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.
Memory Polynomial Based Adaptive Digital PredistorterIJERA Editor
Digital predistortion (DPD) is a baseband signal processing technique that corrects for impairments in RF
power amplifiers (PAs). These impairments cause out-of-band emissions or spectral regrowth and in-band
distortion, which correlate with an increased bit error rate (BER). Wideband signals with a high peak-to-average
ratio, are more susceptible to these unwanted effects. So to reduce these impairments, this paper proposes the
modeling of the digital predistortion for the power amplifier using GSA algorithm.
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.
Comparison of Emergency Medical Services Delivery Performance using Maximal C...IJECEIAES
Ambulance location is one of the critical factors that determine the efficiency of emergency medical services delivery. Maximal Covering Location Problem is one of the widely used ambulance location models. However, its coverage function is considered unrealistic because of its ability to abruptly change from fully covered to uncovered. On the contrary, Gradual Cover Location Problem coverage is considered more realistic compared to Maximal Cover Location Problem because the coverage decreases over distance. This paper examines the delivery of Emergency Medical Services under the models of Maximal Covering Location Problem and Gradual Cover Location Problem. The results show that the latter model is superior, especially when the Maximal Covering Location Problem has been deemed fully covered.
Dwindling of real power loss by using Improved Bees Algorithmpaperpublications3
Abstract: In this paper, a new Improved Bees Algorithm (IBA) is proposed for solving reactive power dispatch problem. The aim of this paper is to utilize an optimization algorithm called the improved Bees Algorithm, inspired from the natural foraging behaviour of honey bees, to solve the reactive power dispatch problem. The IBA algorithm executes both an exploitative neighbourhood search combined with arbitrary explorative search. The proposed Improved Imperialist Competitive Algorithm (IBA) algorithm has been tested on standard IEEE 57 bus test system and simulation results show clearly the high-quality performance of the projected algorithm in reducing the real power loss.
Keywords: Optimal Reactive Power, Transmission loss, honey bee, foraging behaviour, waggle dance, bee’s algorithm, swarm intelligence, swarm-based optimization, adaptive neighbourhood search, site abandonment, random search.
Solving the Power Purchase Cost Optimization Problem with Improved DE AlgorithmIJEACS
Under the deregulation of generation market in China, all distributed generators will particular in electric power bidding. Therefore power purchase cost optimization (PPCO) problem has been getting more attention of power grid Company. However, under the competition principle, they can purchase power from several of power plants, therefor, there exist continuous and integral variables in purchase cost model, which is difficult to solve by classical linear optimization method. An improved differential evolution algorithm is proposed and employed to solve the PPCO problem, which targets on minimum purchase cost, considering the supply and demand balance, generation and transfer capability as constraints. It yields the global optimum solution of the PPCO problem. The numerical results show that the proposed algorithm can solve the PPCO problem and saves the costs of power purchase. It has a widely practical value of application.
This paper discusses the possible applications of particle swarm optimization (PSO) in the Power system. One of the problems in Power System is Economic Load dispatch (ED). The discussion is carried out in view of the saving money, computational speed – up and expandability that can be achieved by using PSO method. The general approach of the method of this paper is that of Dynamic Programming Method coupled with PSO method. The feasibility of the proposed method is demonstrated, and it is compared with the lambda iterative method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
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.
Optimal Economic Load Dispatch of the Nigerian Thermal Power Stations Using P...theijes
This paper deals with the optimization of economic load dispatch (ELD) problem; this is to find the optimal combination of generators in order to minimize the operating costs of the system. This is done by using the particle swarm optimization (PSO) algorithm. PSO is applied to search for the optimal schedule of all the generator units that can supply the required demand at minimum fuel cost while satisfying all system constraints. The PSO algorithm has been implemented using MATLAB optimization toolbox and was applied to solve the ELD problem of the Nigeria thermal power stations. The results were compared with published results obtained via micro-GA, conventional-GA and differential evolution (DE) techniques.
Economic and Emission Dispatch using Whale Optimization Algorithm (WOA) IJECEIAES
This paper work present one of the latest meta heuristic optimization approaches named whale optimization algorithm as a new algorithm developed to solve the economic dispatch problem. The execution of the utilized algorithm is analyzed using standard test system of IEEE 30 bus system. The proposed algorithm delivered optimum or near optimum solutions. Fuel cost and emission costs are considered together to get better result for economic dispatch. The analysis shows good convergence property for WOA and provides better results in comparison with PSO. The achieved results in this study using the above-mentioned algorithm have been compared with obtained results using other intelligent methods such as particle swarm Optimization. The overall performance of this algorithm collates with early proven optimization methodology, Particle Swarm Optimization (PSO). The minimum cost for the generation of units is obtained for the standard bus system.
Genetic Algorithm for Solving the Economic Load DispatchSatyendra Singh
In this paper, comparative study of two approaches, Genetic Algorithm
(GA) and Lambda Iteration method (LIM) have been used to provide
the solution of the economic load dispatch (ELD) problem. The ELD
problem is defined as to minimize the total operating cost of a power
system while meeting the total load plus transmission losses within
generation limits. GA and LIM have been used individually for solving
two cases, first is three generator test system and second is ten
generator test system. The results are compared which reveals that GA
can provide more accurate results with fast convergence characteristics
and is superior to LIM.
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.
Optimal Unit Commitment Based on Economic Dispatch Using Improved Particle Sw...paperpublications3
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.
This paper presents the implementation of multiple distributed generations planning in distribution system using computational intelligence technique. A pre-developed computational intelligence optimization technique named as Embedded Meta EP-Firefly Algorithm (EMEFA) was utilized to determine distribution loss and penetration level for the purpose of distributed generation (DG) installation. In this study, the Artificial Neural Network (ANN) was used in order to solve the complexity of the multiple DG concepts. EMEFA-ANN was developed to optimize the weight of the ANN to minimize the mean squared error. The proposed method was validated on IEEE 69 Bus distribution system with several load variations scenario. The case study was conducted based on the multiple unit of DG in distribution system by considering the DGs are modeled as type I which is capable of injecting real power. Results obtained from the study could be utilized by the utility and energy commission for loss reduction scheme in distribution system.
Hybrid method for solving the non smooth cost function economic dispatch prob...IJECEIAES
This article is focused on hybrid method for solving the non-smooth cost function economic dispatch problem. The techniques were divided into two parts according to: the incremental cost rates are used to find the initial solution and bee colony optimization is used to find the optimal solution. The constraints of economic dispatch are power losses, load demand and practical operation constraints of generators. To verify the performance of the proposed algorithm, it is operated by the simulation on the MATLAB program and tests three case studies; three, six and thirteen generator units which compared to particle swarm optimization, cuckoo search algorithm, bat algorithm, firefly algorithm and bee colony optimization. The results show that the proposed algorithm is able to obtain higher quality solution efficiently than the others methods.
This paper proposed the integration of solar energy resources into the conventional unit commitment. The growing concern about the depletion of fossil fuels increased the awareness on the importance of renewable energy resources, as an alternative energy resources in unit commitment operation. However, the present renewable energy resources are intermitted due to unpredicted photovoltaic output. Therefore, Ant Lion Optimizer (ALO) is proposed to solve unit commitment problem in smart grid system with consideration of uncertainties .ALO is inspired by the hunting appliance of ant lions in natural surroundings. A 10-unit system with the constraints, such as power balance, spinning reserve, generation limit, minimum up and down time constraints are considered to prove the effectiveness of the proposed method. The performance of proposed algorithm are compared with the performance of Dynamic Programming (DP). The results show that the integration of solar energy resources in unit commitment scheduling can improve the total operating cost significantly.
Bi-objective Optimization Apply to Environment a land Economic Dispatch Probl...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
1. International Journal of Research in Advent Technology, Vol.2, Issue.8, August 2014
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A Hybrid Firefly-DE Algorithm For Economic Load Dispatch
Mr.Mandeep Loona1, Mrs. Shivani Mehta2, Mr.Sushil Prashar3
Department Electrical Engineering, D.A.V.I.E.T., Jalandhar, Punjab, India1, 2, 3
Student, Master of Technology, mandeeploona@gmail.com1
Assistant Professor, shivanimehta7@gmail.com2
Assistant Professor, prashar_sushil@yahoo.com3
Abstract- Economic load dispatch (ELD) is an important optimization task in power system. It is the process of allocating generation among the committed units such that
the constraints imposed are satisfied and the energy requirements are minimized. There are three criteria in solving the economic load dispatch problem. They are minimizing
the total generator operating cost, total emission cost and scheduling the generator units Economic Load Dispatch (ELD) problem in power systems has been solved by
various optimization methods in the recent years, for efficient and reliable power generation. This paper introduces a solution to ELD problem using a new metaheuristic
nature-inspired Hybrid algorithm called DE-Firefly Algorithm (FFA). The proposed approach has been applied to 3 unit test system. The results proved the efficiency and
robustness of the proposed method when compared with the other Existed algorithm.
Keywords - Economic Load Dispatch, Differential Evolution, Firefly Algorithm, Hybrid DE-Firefly Algorithm
1. INTRODUCTION
To manage with the increasing demand for electric power, the electric power
industry has witnessed major changes i.e. deregulated
electricity markets. These competitive markets reduce costs. The increased
diffusion of non-dispatchable renewable sources, such as wind and solar, adds
another degree of complexity to the scheduling of economic power dispatch. It
becomes even more complex when more than one objective function is considered
with various types of practical generators constraints. All these factors contribute
to the increasing need for fast and reliable optimization methods, tools and
software that can address both security and economic issues simultaneously in
support of power system operation and control.
Economic Load Dispatch (ELD) seeks the best generation schedule for the
generating plants to supply the required demand plus transmission loss with the
minimum generation cost. Significant economical benefits can be achieved by
finding a better solution to the ELD problem. So, a lot of researches have been
done in this area. Previously a number of calculus-based approaches including
Lagrangian Multiplier method have been applied to solve ELD problems. These
methods require incremental cost curves to be monotonically increasing/piece-wise
linear in nature. But the input-output characteristics of modern generating
units are highly non-linear in nature, so some approximation is required to meet
the requirements of classical dispatch algorithms. Therefore more interests have
been focused on the application of artificial intelligence (AI) technology for
solution of these problems. Several AI methods, such as Genetic Algorithm
Artificial Neural Networks, Simulated Annealing, Tabu Search, Evolutionary
Programming , Particle Swarm Optimization, Ant Colony Optimization,
Differential Evolution, Harmony search Algorithm, Dynamic Programming, Bio-
2. International Journal of Research in Advent Technology, Vol.2, Issue.8, August 2014
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geography based optimization, Intelligent water drop Algorithm have been
developed and applied successfully to small and large systems to solve ELD
problems in order to find much better results. Very recently, in the study of social
insects behaviour, computer scientists have found a source of motivation for the
design and execution of optimization algorithms.
2 ECONOMIC LOAD DISPATCH
A major challenge for all power utilities is to not only satisfy the consumer
demand for power, but to do so at minimal cost. Any given power system can be
comprised of multiple generating stations, each of which has its own characteristic
operating parameters. The cost of operating these generators does not usually
correlate proportionally with their outputs; therefore the challenge for power
utilities is to try to balance the total load among generators that are running as
efficiently as possible. In fig 2.1 the operating costs of a fossil fired generator is
shown. The min Pgi
is the minimum loading limit below which the operating unit
proves to be uneconomical ( or may be technically infeasible ) and Pgi
max is the
maximum output limit.
Fig 2.1 Operating costs of a fossil fired generator
2.1 Cost Function
Mathematically, economic dispatch problem considering valve point loading is
defined as :
Minimize operating cost
= Σ ∗
+
3. ∗ + …. (2.1)
Subject to:-
Energy balance equation
= + ... (2.2)
Σ
The inequality constraints
≤ ≤
= 1,2,…. , ! ...(2.3)
Where
,
4. , ,, # are cost coefficients of the ith unit
is load demand
is real power generation and will act as decision variable
is power transmission loss
! is the number of generator buses.
2.2 Loss formula:-
One of the most important, simple but approximate method of expressing
transmission loss as a function of generator power is through B-coefficients. This
method uses the fact that under normal operating conditions, the transmission loss
5. International Journal of Research in Advent Technology, Vol.2, Issue.8, August 2014
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is quadratic in the injected bus real powers. The general form of the loss formula
using B-coefficients is [31]
= Σ Σ $%
$ '( ...(2.4)
Where
$ and $ are the real power generations at the ith and jth buses
% are the loss coefficients which are constant under certain assumed conditions.
! is number of generation buses
The transmission loss formula of Eq. 2.4 is known as George’s formula.
Another more accurate form of transmission loss expression given by Kron’s loss
formula is [31]
= %)) Σ %)$
+
$ '( ...(2.5)
Σ Σ $%
Where
%)), %), % are the loss coefficients which are constant under certain assumed
conditions NG is number of generation buses.
3 DIFFERENTIAL EVOLUTIONS
Differential Evolution (DE) is a type of evolutionary algorithm originally
proposed by Price and Storn for optimization problems over a continuous domain.
DE is exceptionally simple, significantly faster and robust. The basic idea of DE is
to adapt the search during the evolutionary process. Differential Evolution (DE) is
a parallel direct search method which utilizes NP D-dimensional parameter
vectors xi,g, i = 1, 2, . . . .NP as a population for each generation G. NP does not
change during the minimization process. The initial vector population is chosen
randomly and should cover the entire parameter space. At the start of the
evolution, the perturbations are large since parent populations are far away from
each other. As the evolutionary process matures, the population converges to a
small region and the perturbations adaptively become small. As a result, the
evolutionary algorithm performs a global exploratory search during the early
stages of the evolutionary process and local exploitation during the mature stage
of the search. In DE the fittest of an offspring competes one-to-one with that of
corresponding parent which is different from other evolutionary algorithms. This
one-to-one competition gives rise to faster convergence rate. Price and Storn gave
the working principle of DE with simple strategy in. Later on, they suggested ten
different strategies of DE . The key parameters of control in DE are population
size (NP), scaling or mutation factor (F) and crossover constant (CR). The
optimization process in DE is carried out with three basic operations: mutation,
crossover and selection. The DE algorithm is described as follows:
3.1 Initialization
The initial population comprises combinations of only the candidate dispatch
solutions, which satisfy all the constraints and are feasible solutionsof economic
dispatch. It consists of
= 1,2,…, !; + = 1,2,…, , trail parent individuals.
The elements of a parent are the combinations of power outputs of the generating
units, which are chosen randomly by a random ranging over[
,
] [10].
=
+ /01
−
3 = 1,2,…, !; + = 1,2,…, ,
... (3.1)
Where rand () is uniform random number ranging from over [0,1].
is the upper bound of the nth variable of the problem ,
Where
is the
lower bound of the nth variable of the problem, rand (0,1) is a uniformly
distributed number within the limits(0,1). The elements of parent/offspring
may violate constraints Eq. (3.6). This violation is corrected by fixing them either
at lower or upper limits as described below:
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=
;
4 5 6
;
;
≤
≤
9 …(3.1a)
= 1,2,…, !; + = 1,2,…, ,
3.2 Evaluation of Objective Function
In order to satisfy the power balance constraints, a generator is arbitrarily selected
as a dependent generator d. In this we are considering PL=0 means transmission
losses are neglected. Output of dependent or slack generator is given below
:
+ = 1,2,…, ,
;
;:
= − Σ ;
...(3.2)
Similarly, if the output of the dependent generator violates its limits . After
limiting the value of the dependent generator as above, a penalty term is
introduced in the objective function Eq. (3.4) to penalize its fitness value. When
so introduced, Eq. (3.4) is changed to the following generalized form:
3 + + = 1,2,…, , (3.3)
= = 1
Where
Penalty factor is given by
= ?
− :
:
:
; :
− :
:
; :
:
≤ :
0 ; :
≤ :
9 ... (3.3a)
3.3 Mutation
A new population named mutant population is generated whose size is same as
that of the initial population (NG* L). Among the various strategies used for
mutation in DE, the addition of the weighted difference vector between the two
population members to the third member is adopted in this approach. Here three
different members namely Pr1 ,Pr2 and Pr3 are chosen from the current population
.Then the difference between any two of these members is scaled by a scalar
number F, which is then added to the third member. The value of F is usually in
between 0.4 and 1. In each generation, a donor vector is created in order to change
the population member vector. Therefore the jth member of the donor vector Zi(t)
is expressed
as
Zij
(t+1) = Pr1j( t ) + F*( Pr2j( t ) - Pr3j( t ) ) + = 1,2,…, !; + ≠ , = 1,2,…, ,
...(3.4)
3.4 Crossover
In order to increase the diversity of the perturbed parameter vectors, crossover is
introduced. A new population is created by suitably combining the parent
population and the mutant population. The process of crossover is based on the
CR which is in between (0,1). Binomial crossover scheme is used which is
performed on all D variables and can be expressed as:
Uij(t) = Zij(t) if R4(j ) ≤ CR ...(3.5)
Uij(t) = Pij(t) else...
where Uij(t) is the child which is obtained after crossover operation where j = 1,2,
... NG,
i= 1,2, ..... L. Here, rand ensures that the newly generated vector is different for
both Zij(t) and Pij(t).
3.5 Selection
After calculating the objective function = using L number of variables for using
initial and crossover population , a new population with the least objective
function ( minimum fuel cost) is formed for the next generation. This is given by
BC = D
BC = = E
E
BC =
B = 1,2,…, !; = 1,2,…, ,
B FGℎ#/IJ# … 3.6 9
The process is repeated until the maximum number of generations or no
improvement is seen in the real power generation cost after many generations. The
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global optimum searching capability and the convergence speed of DE are very
sensitive to the choice of control parameters L, F and CR. The crossover rate CR
is between [0.3 , 0.9]. Mutation Factor (F) should not be smaller than a certain
value to prevent premature convergence.
3.6 Stopping criterion
There are various criteria available to stop a stochastic optimization algorithm. In
this
maximum number of iterations is chosen as the stopping criterion
4. FIREFLY ALGORITHM
The Firefly Algorithm ( FA) is a Meta heuristics, nature-inspired, optimization
algorithm which is based on the flashing behaviour of fireflies, or lighting bugs,
in the summer sky in the tropical temperature regions . Firefly Algorithm was
developed by Dr. Xin-She Yang at Cambridge University in 2007, and it is based
on the swarm behaviour such as insects or birds present in nature. The firefly
algorithm is identical with other algorithms which are based on the so-called
swarm intelligence, such as Particle Swarm Optimization (PSO), Artificial Bee
Colony optimization (ABC), and Bacterial Foraging (BFA) algorithms, it is
indeed much simpler both in concept and implementation Furthermore, according
to recent bibliography, It is more efficient and can outperform other conventional
algorithms, such as genetic algorithms, for solving many optimization problems;
a fact that has been justified in a recent research, where the statistical
performance of the firefly algorithm was measured against other well-known
optimization algorithms using various standard stochastic test functions . Its main
advantage is the fact that it uses mainly real random numbers, and it is based on
the global communication among the swarming particles.
4.1 The firefly algorithm has three rules which are based on some of the
major flashing characteristics of real fireflies.
The characteristics are as follows: a) All fireflies are unisex and they will move
towards more attractive and brighter ones regardless their sex.
b) The degree of attractiveness of a firefly is proportional to its brightness which
decreases as the distance from the other firefly increases. This is due to the fact
that the air absorbs light. If there is not a brighter or more attractive firefly than a
particular one, it will then move randomly.
c) The brightness or light intensity of a firefly is determined by the value of the
objective function of a given problem. For maximization problems, the light
intensity is proportional to the value of the objective function.
4.2 Attractiveness:
In the firefly algorithm, the form of attractiveness function of a firefly is given by
the following monotonically decreasing function
M/ = M) ∗ #NO−P/
) with m≥1 …(4.1)
Where, r is the gap between two fireflies.
M) is the attractiveness in the starting when distance r=0
γ is an absorption coefficient which controls the decrease of light intensity.
4.3 Distance:
The distance between two fireflies i j, at positions N 0 N.it can be defined as
a Cartesian.
/ = ǁ N − N ǁ = QΣ N,; − N,;
:;
…(4.2)
Where N,; is the Kth component of the spatial coordinate N of the ith firefly and
d is the number of dimensions we have, for d=2 , we have
/ = RN − N
− S − S
…(4.3)
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However, the calculation of a distance r can also be defined using other distance
metrics, based on the nature of problem, such as manhattan distance.
4.4 Movement:
The movement of the firefly which is attracted by a more attractive. Firefly + is
given by is given by:
N = N+M) ∗ exp −
P/
)*(N − N)+α*/0 −
...(4.4)
Where the first term is the current position of a firefly, the second term is used for
considering a firefly’s attractiveness to light intensity seen by adjacent fireflies
and third term is used for the random movement of fireflies in case there are no
brighter ones. The coefficient α is a randomization parameter determined by the
problem of interest. Rand is a random number generator uniformly in the
distributed space [0,1].
5. HYBRID DIFFERENTIAL EVOLUTION (DE) FIREFLY
ALGORITHM
We have noticed that the meta-heuristic methods are very efficient for the search
of global solution for complex problems better than deterministic methods.
However their disadvantage is the time of convergence which is due the high
number of the agents and iterations. To solve this problem we have developed a
hybrid method with the combination of two algorithms, the firefly algorithm and
the Differential Evolution with a lower number of ants and fireflies as possible,
the explanation of computation procedure of hybrid method and its concept.
ALGORITHM
Step1: Read the system data such as cost coefficients, minimum and maximum
power limits of all generator units, power demand and B-coefficients.
Step 2: Initialize the parameters and constants of Firefly Algorithm. They are
noff, αmax, αmin, β0, γmin, γmax and itermax (maximum number of iterations).
Step 3: Generate noff number of fireflies (xi) randomly between λmin and λmax .
Step 4: Set iteration count to 1.
Step 5: Calculate the fitness values corresponding to noff number of fireflies.
Step 6: Obtain the best fitness value EbestFV by comparing all the fitness values
and also obtain the best firefly values EbestFF corresponding to the best fitness
value EbestFV.
Step 7: Determine alpha(α) value of current iteration using the following
equation: α (iter)= αmax -(( αmax - αmin) (current iteration number )/ itermax)
Step 8: Determine the rij values of each firefly using the following equation:
rij= EbestFV -FV
rij is obtained by finding the difference between the best fitness value EbestFV
(EbestFV is the best fitness value i.e., jth firefly) and fitness value FV of the ith
firefly.
Step 9: New xi values are calculated for all the fireflies using the equation(4.4)
Step 10: EbestFF gives the optimal solution of the Economic Load Dispatch
problem and the results are printed. The WXYZB value of the Firefly Algorithm is
given to the Differential Evolution as Input Value. Read the input Data
Step 11 : Generate an array of ( Ng * L ) of uniform random numbers. Set
population counter , i=0 and increment the population counter to, i=i+1, set the
generation counter, j=0 and increment the generation counter j=j+1.
Step 12: Compute Pid using Eq. (3.2), check limits and adjust using Eq. (3.1a).
Then compute penalty factor, 0 = using Eq. (3.3a) and (3.3).
9. International Journal of Research in Advent Technology, Vol.2, Issue.8, August 2014
E-ISSN: 2321-9637
69
Step 13: Generate an array of uniform random numbers and generate three
different integer random numbers within the range 1 to L. . IF (j ≠ d) THEN
compute t Zij
using eq.(3.4)
Step 14: Compute Uij(t+1) using Eq. (3.6), check limits and adjust using Eq.
(3.1a). Then compute penalty factor, 0 = using Eq. (3.3a) and (3.3).
Step 15 After calculating the objective function = using L number of variables
for using initial and crossover population , a new population with the least
objective function ( minimum fuel cost) is formed for the next generation. This is
given by
BC = D
BC = = E
E
BC =
B
B FGℎ#/IJ# 9 5.7
Here = 1,2,…, !; = 1,2,…, ,
Step 16: The process is repeated until the maximum number of generations or no
improvement is seen in the real power generation cost after many generations. The
global optimum searching capability and the convergence speed of DE are very
sensitive to the choice of control parameters L, F and CR.
Step 17: There are various criteria available to stop a stochastic optimization
algorithm. In this maximum number of iterations is chosen as the stopping
criterion
6. SIMULATION RESULTS
The effectiveness of the proposed firefly algorithm is tested with three unit
system. Firstly the problem is solved by Firefly Algorithm and then the DE-FIREFLY
Algorithm is used to solve the problem
6.1 Three-Unit System The generator cost coefficients, generation limits and B-coefficient
matrix of three unit system are given below. Economic Load Dispatch
solution for three unit system is solved using conventional Firefly Algorithm and
DE-Firefly Hybrid algorithm method. Test results of DE-Firefly method are given
in table 6.2.Test results of Firefly Algorithm are given in Table 6.3 Comparison
of test results of DE-Firefly Hybrid and Firefly algorithm are shown in table 6.4.
Table 6.1: Cost Coefficients and Power limits of 3 Unit system
The loss Coefficients matrix of 3 Unit
0.000071 0.000030 0.000025
0.000030 0.000069 0.000032
0.000025 0.000032 0.000080
% = [
`
Table 6.2: Test results of DE-FIREFLY Algorithm for 3-Unit System
Sr
.
N
o
Power
Demand(M
W)
P1(MW) P2(MW) P3(MW) abZZ
(MW
)
Fuel
Cost(Rs/Hr)
1 350 64.093328 160.37892
2
126 .471 18383.6015
63
2 400 66.373126 187.51756
0
146.11005
8
.495 20487.5694
76
3 450 42.825634 191.52132
7
215.65403
6
0.5 22785.9526
05
S.NO
11. International Journal of Research in Advent Technology, Vol.2, Issue.8, August 2014
E-ISSN: 2321-9637
70
4 500 64.499424 232.19894
3
203.30282
3
1 24974.4656
26
5 550 69.139309 209.38136
6
271.48079
6
1 27324.1050
80
6 600 71.333083 290.43716
0
238.23067
3
1.5 29641.5252
77
7 650 137.00242
5
298.97173
1
214.52776
3
1.7 31935.1862
30
8 700 141.85293
3
292.66473
9
266.48456
3
1.8 34273.7316
41
Table 6.3: Test results of FIREFLY Algorithm for 3-Unit system
Sr.
No
.
Power
Demand(
MW)
P1
(MW)
P2 (MW) P3
(MW)
abZZ
(MW)
Fuel Cost
(RS/Hr)
1 350 43 159 149 1 18482.8966
15
2 400 36 216.6681
30
149.831
467
1.25 20933.6645
47
3 450 43.074777 170.1702
86
238 1.245 23019.5606
55
4 500 93 209 199 1 25070.6061
05
5 550 210 173 168 1 27820.2673
10
6 600 190.244315 213.0304
29
196.726
834
1.5 29751.5693
98
7 650 45.427961 308 298 1.65 32408.3787
30
8 700 160 276 266 2 34582.5818
76
Table4 : Comparison of test Results of Firefly Algorithm and DE-FIREFLY
Algorithm for 3 unit System
Sr No. Power Demand Fuel Cost (Rs/Hr)
Firefly Algorithm
Fuel Cost (Rs/Hr)
DE-Firefly
Algorithm
1 350 18482.896615 18383.601563
2 400 20933.664547 20487.569476
3 450 23019.560655 22785.952605
4 500 25070.606105 24974.465626
5 550 27820.267310 27380.105080
6 600 29751.569398 29641.525277
7 650 32408.378730 31935.186230
8 700 34582.581876 34273.731641
7. CONCLUSION
Economic Load Dispatch problem is solved by using Firefly Algorithm and DE-Firefly
Hybrid Algorithm. The programs are written in MATLAB software
package. The solution algorithm has been tested for three generating units. The
results obtained from DE-Firefly Algorithm are compared with the results of
Firefly Algorithm. Comparison of test results of both methods reveals that DE-Firefly
Hybrid Algorithm is able to give more optimal solution than Firefly. Thus,
it develops a simple tool to meet the load demand at minimum operating cost
while satisfying all units and operational constraints of the power system.
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