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 proposes a hybrid approach using fuzzy logic and genetic algorithms to solve the economic load dispatch (ELD) problem. The ELD problem aims to minimize generation costs while meeting load demands and generator constraints. The proposed method combines fuzzy logic and genetic algorithms to adaptively adjust crossover and mutation rates during optimization. Testing on 3-generator and 10-generator systems shows the hybrid approach finds more accurate and economically optimal solutions faster than genetic algorithms or traditional lambda iteration methods. The hybrid approach proves effective for solving the ELD problem in power systems.
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.
This document summarizes the application of computational intelligence techniques like genetic algorithms and particle swarm optimization for solving economic load dispatch problems. It first applies a real-coded genetic algorithm to minimize generation costs for a 6-generator test system with continuous fuel cost equations, showing superiority over quadratic programming. It then uses particle swarm optimization to minimize costs for a 10-generator system with each generator having discontinuous fuel options, showing better results than other published methods. The document provides background on economic load dispatch problems and optimization techniques like quadratic programming, genetic algorithms, and particle swarm optimization.
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 proposes a hybrid approach using fuzzy logic and genetic algorithms to solve the economic load dispatch (ELD) problem. The ELD problem aims to minimize generation costs while meeting load demands and generator constraints. The proposed method combines fuzzy logic and genetic algorithms to adaptively adjust crossover and mutation rates during optimization. Testing on 3-generator and 10-generator systems shows the hybrid approach finds more accurate and economically optimal solutions faster than genetic algorithms or traditional lambda iteration methods. The hybrid approach proves effective for solving the ELD problem in power systems.
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.
This document summarizes the application of computational intelligence techniques like genetic algorithms and particle swarm optimization for solving economic load dispatch problems. It first applies a real-coded genetic algorithm to minimize generation costs for a 6-generator test system with continuous fuel cost equations, showing superiority over quadratic programming. It then uses particle swarm optimization to minimize costs for a 10-generator system with each generator having discontinuous fuel options, showing better results than other published methods. The document provides background on economic load dispatch problems and optimization techniques like quadratic programming, genetic algorithms, and particle swarm optimization.
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.
This document presents a multi-objective optimization method for economic emission load dispatch (EELD) that considers economy, emissions, and transmission line security as objectives. The problem is formulated to minimize total fuel costs and emissions while maximizing line security for a power system. The multi-objective problem is converted to a single objective using goal attainment and then solved using simulated annealing. Results are presented for a 30-bus and 57-bus IEEE test case system to demonstrate the proposed method.
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.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document summarizes a study that uses fuzzy logic to solve the unit commitment problem in power generation systems. The unit commitment problem aims to determine the optimal on/off schedule of generating units to minimize operating costs while meeting demand and constraints. The study models several factors like generator capacity, fuel costs, and startup costs as fuzzy variables. It defines membership functions for these fuzzy inputs and the output of production cost. It then develops 45 fuzzy logic rules relating the inputs to the output. Finally, it uses the centroid defuzzification method to obtain crisp numerical solutions for production cost from the fuzzy model. The goal is to demonstrate that a fuzzy logic approach can efficiently solve the unit commitment problem.
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.
An Adaptive Differential Evolution Algorithm for Reactive Power DispatchIjorat1
This document summarizes an adaptive differential evolution algorithm for solving the reactive power dispatch problem, which involves minimizing real power losses. The problem is formulated as a non-linear constrained optimization problem. An adaptive differential evolution algorithm is proposed that uses time-varying chaotic mutation and crossover to avoid parameter tuning. The algorithm is applied to the IEEE 57-bus and 118-bus test systems and found to provide superior convergence and solution quality compared to classical differential evolution and self-adaptive differential evolution algorithms.
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
This document presents a study that uses the Grey Wolf Optimizer (GWO) method to estimate the input-output parameters of the fuel cost curve for thermal power plants.
The fuel cost curve represents the relationship between a plant's fuel costs and power output, and needs to be periodically re-estimated due to temperature and aging effects. Accurately estimating the curve's parameters is important for economic dispatch calculations.
The study formulates parameter estimation as an optimization problem to minimize errors between actual and estimated fuel costs. It applies GWO to find the parameters for different fuel cost curve models using test data from three power plants. Simulation results show GWO provides better parameter estimates than other estimation 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.
Multi objective economic load dispatch using hybrid fuzzy, bacterialIAEME Publication
The document summarizes a research paper that proposes a new approach for solving the economic load dispatch problem using a hybrid fuzzy, bacterial foraging-Nelder–Mead algorithm. The economic load dispatch problem minimizes generation costs while satisfying load demand under system constraints. The proposed approach considers generation costs, spinning reserve costs, and emission costs simultaneously. It also accounts for valve-point effects, prohibited operating zones, and other practical constraints. A hybrid bacterial foraging and Nelder–Mead algorithm combined with fuzzy logic is used to solve the optimization problem. Simulation results show the advantages of the proposed method in reducing total system costs.
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 document discusses distributed firewalls as an alternative to traditional firewalls. It provides an overview of distributed firewalls, including that they allow security policies to be centrally defined but enforced across individual endpoints. The key advantages of distributed firewalls are that they do not depend on network topology, protect from internal threats, and avoid bottlenecks since there are multiple secure entry points rather than a single point of failure. The document also reviews related work on distributed firewalls and some of their disadvantages, such as increased complexity if the central management system is compromised.
This document summarizes the synthesis and characterization of thin films of pure TiO2 and Sr-doped TiO2 prepared by spin coating technique. Transparent thin films were prepared on glass substrates and annealed at different temperatures from 3000C to 6000C. Structural analysis using GIXRD and Raman spectroscopy confirmed the anatase phase of TiO2. AFM showed a homogeneous globular surface morphology. UV-Vis analysis demonstrated that the optical band gap increased with higher annealing temperatures. Photoluminescence study showed variation in emission peaks for different annealing temperatures and Sr concentrations. Electrical, gas sensing, wettability and self-cleaning properties were also investigated.
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.
This document presents a multi-objective optimization method for economic emission load dispatch (EELD) that considers economy, emissions, and transmission line security as objectives. The problem is formulated to minimize total fuel costs and emissions while maximizing line security for a power system. The multi-objective problem is converted to a single objective using goal attainment and then solved using simulated annealing. Results are presented for a 30-bus and 57-bus IEEE test case system to demonstrate the proposed method.
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.
IJERD (www.ijerd.com) International Journal of Engineering Research and Devel...IJERD Editor
This document summarizes a study that uses fuzzy logic to solve the unit commitment problem in power generation systems. The unit commitment problem aims to determine the optimal on/off schedule of generating units to minimize operating costs while meeting demand and constraints. The study models several factors like generator capacity, fuel costs, and startup costs as fuzzy variables. It defines membership functions for these fuzzy inputs and the output of production cost. It then develops 45 fuzzy logic rules relating the inputs to the output. Finally, it uses the centroid defuzzification method to obtain crisp numerical solutions for production cost from the fuzzy model. The goal is to demonstrate that a fuzzy logic approach can efficiently solve the unit commitment problem.
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.
An Adaptive Differential Evolution Algorithm for Reactive Power DispatchIjorat1
This document summarizes an adaptive differential evolution algorithm for solving the reactive power dispatch problem, which involves minimizing real power losses. The problem is formulated as a non-linear constrained optimization problem. An adaptive differential evolution algorithm is proposed that uses time-varying chaotic mutation and crossover to avoid parameter tuning. The algorithm is applied to the IEEE 57-bus and 118-bus test systems and found to provide superior convergence and solution quality compared to classical differential evolution and self-adaptive differential evolution algorithms.
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
This document presents a study that uses the Grey Wolf Optimizer (GWO) method to estimate the input-output parameters of the fuel cost curve for thermal power plants.
The fuel cost curve represents the relationship between a plant's fuel costs and power output, and needs to be periodically re-estimated due to temperature and aging effects. Accurately estimating the curve's parameters is important for economic dispatch calculations.
The study formulates parameter estimation as an optimization problem to minimize errors between actual and estimated fuel costs. It applies GWO to find the parameters for different fuel cost curve models using test data from three power plants. Simulation results show GWO provides better parameter estimates than other estimation 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.
Multi objective economic load dispatch using hybrid fuzzy, bacterialIAEME Publication
The document summarizes a research paper that proposes a new approach for solving the economic load dispatch problem using a hybrid fuzzy, bacterial foraging-Nelder–Mead algorithm. The economic load dispatch problem minimizes generation costs while satisfying load demand under system constraints. The proposed approach considers generation costs, spinning reserve costs, and emission costs simultaneously. It also accounts for valve-point effects, prohibited operating zones, and other practical constraints. A hybrid bacterial foraging and Nelder–Mead algorithm combined with fuzzy logic is used to solve the optimization problem. Simulation results show the advantages of the proposed method in reducing total system costs.
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 document discusses distributed firewalls as an alternative to traditional firewalls. It provides an overview of distributed firewalls, including that they allow security policies to be centrally defined but enforced across individual endpoints. The key advantages of distributed firewalls are that they do not depend on network topology, protect from internal threats, and avoid bottlenecks since there are multiple secure entry points rather than a single point of failure. The document also reviews related work on distributed firewalls and some of their disadvantages, such as increased complexity if the central management system is compromised.
This document summarizes the synthesis and characterization of thin films of pure TiO2 and Sr-doped TiO2 prepared by spin coating technique. Transparent thin films were prepared on glass substrates and annealed at different temperatures from 3000C to 6000C. Structural analysis using GIXRD and Raman spectroscopy confirmed the anatase phase of TiO2. AFM showed a homogeneous globular surface morphology. UV-Vis analysis demonstrated that the optical band gap increased with higher annealing temperatures. Photoluminescence study showed variation in emission peaks for different annealing temperatures and Sr concentrations. Electrical, gas sensing, wettability and self-cleaning properties were also investigated.
This document discusses applying a neural network approach to decision making in a self-organizing computing network (SOCN). It proposes using concepts from fuzzy logic and neural networks to build a computing network that can handle mixed data types, like symbolic and numeric data. The network would have input, hidden, and output layers connected by transfer functions. The hidden cells would self-organize based on training data to learn relationships between input and output cells. This approach aims to allow the network to make decisions on data sets with diverse attribute types in a more effective way than other techniques.
Este documento trata sobre diferentes tipos de anemia y angina de pecho. Describe la anemia aplásica como una enfermedad grave de la médula ósea que afecta a los glóbulos rojos, blancos y plaquetas. También explica la anemia en el embarazo, la cual ocurre debido a alteraciones digestivas y el consumo de nutrientes por el feto. Finalmente, define la angina de pecho como un síndrome causado por falta de oxígeno al corazón, con síntomas como dolor en el pecho que puede al
The document describes a proposed clinical decision support system that uses k-means clustering and an artificial neural network with particle swarm optimization to classify patient data and determine diagnoses. It begins with background on clinical decision making and existing systems. It then outlines the proposed system, which involves clustering patient data using k-means, and training an artificial neural network using particle swarm optimization and backpropagation to classify new patient data and determine optimal treatment. The combination of these techniques is meant to improve accuracy, efficiency, time consumption and costs compared to other methods.
This document describes the fabrication of tin oxide (SnO2) thin films using the spray pyrolysis technique. Spray pyrolysis involves spraying a metal salt solution onto a heated substrate where the droplets undergo thermal decomposition to form an oxide thin film. The key deposition parameters that influence the thin film properties are substrate temperature, aerosol transport properties, and precursor decomposition behavior. Higher substrate temperatures result in rougher, more porous films with improved crystallinity and electrical properties. Proper control of deposition parameters allows for the fabrication of thin films with tailored optical and electrical characteristics using the low-cost spray pyrolysis method.
This document summarizes a research paper on a relational database watermarking technique using clustering. The proposed technique clusters database tuples before embedding and detecting a watermark. It uses Mahalanobis distance to measure tuple similarity during clustering. The watermark is then embedded and detected within each cluster by modifying the least significant bits of numeric fields. Majority decision is used in blind detection to determine watermark bits. The technique aims to improve watermark robustness against database operations while maintaining reversibility.
This document discusses the performance analysis of different equalizers used to reduce inter-symbol interference (ISI) in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. It implemented a 2x2 MIMO channel with four equalizers - zero forcing (ZF), minimum mean square error (MMSE), zero forcing parallel interference cancellation (ZFPIC), and maximum likelihood (ML). The results found that the maximum likelihood technique provided the best performance, giving a 2.2 dB improvement over the next best method, ZFPIC. The document provides background on MIMO-OFDM systems and reviews previous research analyzing the performance of different equalization techniques in reducing ISI.
This document summarizes a research paper on face recognition using principal component analysis (PCA). It discusses how PCA can be used to reduce the dimensionality of face images for recognition. The system detects faces in images, extracts features using PCA, and then compares new faces to those in a training database to recognize identities. The results showed an accuracy of 87.09% on a test set of 30 images using this PCA-based approach for face recognition. While effective, the system has limitations when faces vary significantly from the training data. Overall, PCA provides a way to analyze face patterns and identify faces with reasonable accuracy under controlled conditions.
This document compares the performance of link recovery between the EIGRP and OSPF routing protocols through simulation. It finds that EIGRP has faster retransmission times than OSPF when there is a failure in a data transmission link. Specifically, before a link fails the average transmission time is 17.5ms for OSPF and 17.1ms for EIGRP, and after a link fails the times increase to 29ms for OSPF and 28.4ms for EIGRP. Therefore, the research shows that EIGRP has better performance than OSPF in retransmitting data after a link fails.
This document summarizes the design of an optimal discrete Fourier transform (DFT) modulated filter bank with a sharp transition band. It formulates the filter bank design as a non-linear optimization problem. To reduce complexity, it develops a frequency response masking (FRM) technique. The FRM technique uses an interpolated base linear phase filter and masking filters to provide a narrow transition band for the prototype filter while reducing the complexity and filter length. The document presents different cases for applying the FRM technique and analyzes how the filter lengths and number of coefficients are affected based on the transition width and other filter parameters.
This document summarizes a numerical study that examines the effects of fin spacing, fin material, and jet velocity on the heat transfer performance of plate fin heat sinks cooled by impinging air jets. The study considers fin spacings of 2mm, 3mm, and 4mm, and fin materials of aluminum, copper, and steel. Jet velocities of 5m/s, 10m/s, and 15m/s are examined. The results show that heat transfer rate increases with decreasing fin spacing, higher thermal conductivity fin materials like copper, and increasing jet velocity. Copper fins achieved the highest heat transfer rates but are heavier and more expensive than aluminum. A fin spacing of 2mm with aluminum fins and a jet velocity of 15
This paper proposes a method for image denoising using wavelet thresholding while preserving edge information. It first detects edges in the noisy image using Canny edge detection. It then applies a wavelet transform and thresholds the coefficients, preserving values near detected edges. Two thresholding methods are discussed: Visushrink for sparse images and Sureshrink for others. The inverse wavelet transform is applied to obtain the denoised image with preserved edges. The goal is to remove noise while maintaining important image features like edges. The method is described to provide better denoising than alternatives that oversmooth edges.
El documento presenta información sobre los eclipses lunares y solares. Explica que un eclipse ocurre cuando un cuerpo celeste bloquea la luz de otro cuerpo celeste. Un eclipse lunar se produce cuando la Tierra está entre la Luna y el Sol y la sombra de la Tierra oscurece la Luna. Un eclipse solar ocurre cuando la Luna está entre el Sol y la Tierra y proyecta su sombra sobre la superficie terrestre.
This document summarizes a study on assessing deposition rate in metal inert gas (MIG) welding of stainless steel. Four welding parameters - current, voltage, wire speed, and gas flow rate - were examined at two levels each using a Taguchi experimental design. Welding experiments were conducted according to the design and deposition rate was measured for each experiment. The results were analyzed using signal-to-noise ratios and ANOVA to determine the significant welding parameters affecting deposition rate. The optimal levels of parameters will be confirmed with validation experiments.
This document discusses security challenges in underwater wireless communication networks (UWCNs). It provides an overview of the characteristics of underwater acoustic channels that make UWCNs vulnerable to attacks, such as high bit error rates and low bandwidth. Several common attacks on UWCNs are described, such as jamming, wormhole attacks, and selective forwarding. The document also outlines security requirements for UWCNs, including authentication, confidentiality, integrity, and availability. It provides a survey of existing literature on securing UWCNs and discusses open challenges in providing security for these networks.
The document discusses mining frequent items and item sets from data streams using fuzzy approaches. It describes objectives of mining frequent items from datasets in real-time using fuzzy sets and slices. This involves fetching relevant records, analyzing the data, searching for liked items using fuzzy slices, identifying frequently viewed item lists, making recommendations, and evaluating the results. Algorithms used for mining frequent items from data streams in a single or multiple pass are also reviewed.
This document describes a microcontroller-based gas flow alert system for an industrial furnace. The system monitors the furnace's gas flow mode (manual vs automatic) and uses a GSM modem to send alert messages if the mode is not changed on schedule. This helps reduce wasted nitrogen gas flow and lower production costs by ensuring the optimal gas flow level is maintained based on whether items are actively being loaded into the furnace. The system was designed and assembled with a microcontroller board connected to a GSM modem. It provides alerts if the operator fails to change the furnace mode between shifts, allowing nitrogen usage and costs to be reduced by an estimated Rs. 10,407.93 per month.
This document summarizes a research paper on using active power filters to reduce total harmonic distortion. It provides background on power quality issues caused by harmonics from nonlinear loads. Active power filters inject harmonic currents to cancel out load harmonics. The document describes shunt and series active power filters and their control methods. Simulation results show that a shunt active power filter can reduce the voltage THD from 17.92% to 11.46% and current THD from 0.53% to 0.46% for an AC-DC converter feeding an R-L load. Thus, active power filters are effective in mitigating harmonics and improving power quality.
This document summarizes a research paper that analyzes and evaluates the performance of processing large data sets using Hadoop. It discusses how Hadoop Distributed File System (HDFS) and MapReduce provide parallel and distributed processing of large structured and unstructured data at scale. The paper also presents the results of experiments conducted on Hadoop to classify and cluster large data sets using machine learning algorithms. The experiments showed that Hadoop can process large data sets more efficiently and reliably compared to processing on a single computer.
Economic Load Dispatch Optimization of Six Interconnected Generating Units Us...IOSR Journals
This document describes using particle swarm optimization (PSO) to solve the economic load dispatch (ELD) problem of optimizing the operation of six interconnected generating units. ELD aims to minimize total generation costs while satisfying constraints. PSO is applied to find optimal unit outputs that minimize cost, accounting for transmission losses. The proposed PSO approach is compared to genetic algorithms and conventional methods on a test system, showing PSO provides better solutions faster. Key steps of the PSO algorithm for ELD are initializing particles, evaluating fitness at each iteration, and updating personal and global best positions to iteratively improve solutions.
Economic Dispatch of Generated Power Using Modified Lambda-Iteration MethodIOSR Journals
This document proposes a modified lambda-iteration method for solving economic dispatch problems and minimizing fuel costs. It involves determining the optimal power output of each generator given constraints like load demand and transmission losses. The method is implemented in MATLAB and tested on a 6 generator system. Results found the total power was 1263.0074MW at an incremental cost of 13.2539$/MWh, close to those from a genetic algorithm solution. The proposed method provides a fast, easy to use approach for economic dispatch optimization problems.
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 document summarizes the application of particle swarm optimization (PSO) to solve the economic load dispatch (ELD) problem for Nigeria's thermal power stations. PSO is used to determine the optimal allocation of total power demand among generating units to minimize total fuel costs while satisfying constraints. The PSO algorithm is applied to a 1999 model of Nigeria's power network and results are compared to other heuristic methods. PSO efficiently distributes load to minimize costs and overcomes limitations of traditional optimization techniques for non-linear power system problems.
IRJET- A Genetic based Stochastic Approach for Solving Thermal Unit Commitmen...IRJET Journal
This document summarizes a genetic algorithm approach for solving the unit commitment problem in power systems. The unit commitment problem aims to schedule power generating units in a cost-effective way while satisfying operational constraints. The proposed approach uses a genetic algorithm with an intelligent coding scheme to represent the on/off status of generating units over time. It also uses annular crossover and mutation genetic operators. The algorithm was tested on standard test systems and showed improvements over other approaches in reducing costs and computational time for finding solutions.
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
The document presents an improved particle swarm optimization (IPSO) algorithm for solving the optimal unit commitment problem in power systems. The IPSO algorithm extends the standard PSO algorithm by using additional particle information to control mutation and mimic social behaviors. The algorithm was implemented on the IEEE 14 bus test system in MATLAB. Results showed the IPSO approach committed units to meet load demand over 24 hours while satisfying constraints, with bus voltages maintained between 1.0017 and 1.0751 per unit. Total costs including fuel, startup, and shutdown costs were minimized at each hour.
A Decomposition Aggregation Method for Solving Electrical Power Dispatch Prob...raj20072
This document proposes a decomposition/aggregation method to solve large-scale economic dispatch problems with many generators. It decomposes a power system into areas, each containing generators and loads. An evolutionary programming technique optimizes dispatch in each area locally. The area solutions are then aggregated to solve the overall system problem while minimizing total cost. The method is demonstrated on 5-bus and 26-bus test systems decomposed into two areas each. Local area problems are solved as subproblems, while the overall system solution is the "master problem". Results are compared to a centralized approach. The decomposition/aggregation method shows promise in solving economic dispatch with large numbers of generators.
This document presents a traditional approach called the lambda iteration method to solve the economic load dispatch (ELD) problem considering generator constraints. The ELD problem aims to minimize the total fuel cost while meeting demand and generator constraints. The lambda iteration method is implemented on a three-unit and six-unit system, with and without transmission losses, in MATLAB. The results show that considering transmission losses provides a more accurate solution to the ELD problem compared to ignoring losses. The lambda iteration method provides an effective traditional technique for solving the ELD problem.
A novel approach for solving Optimal Economic load dispatch problem in power ...IRJET Journal
This document presents a novel approach for solving the optimal economic load dispatch problem in power systems using the Lion Optimization Algorithm (LOA), a meta-heuristic algorithm. LOA simulates the behavior of lion prides to find optimal solutions. The economic load dispatch problem aims to minimize total fuel costs while satisfying constraints like power balance and generator limits. Environmental emissions are also considered to minimize pollution. LOA is applied to solve the economic and emission dispatch problem and results show it performs better than other algorithms like PSO and GA, finding lower-cost solutions that satisfy constraints.
IRJET- Economic Load Dispatch using Metaheuristic AlgorithmsIRJET Journal
This document discusses various metaheuristic algorithms that can be used to solve the economic load dispatch problem in power systems, which is the process of allocating optimal load to committed generators to minimize fuel costs while satisfying constraints. It describes artificial bee colony, genetic, particle swarm optimization, and simulated annealing algorithms. The artificial bee colony algorithm is inspired by honey bee behavior and models artificial bees searching for food sources. Genetic algorithms use genetic operators like crossover and mutation to evolve solutions over generations. Particle swarm optimization models potential solutions as particles that adjust their positions based on their own experiences and neighboring particles' information.
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.
Stable Multi Optimized Algorithm Used For Controlling The Load Shedding Probl...IOSR Journals
This document discusses using multi-agent based particle swarm optimization (MAPSO) and genetic algorithms (MAGA) to solve the load shedding problem in power systems. MAPSO integrates a multi-agent system with PSO, allowing agents to cooperate and compete with neighbors to find optimal load shedding solutions quickly. MAGA applies genetic algorithm concepts like reproduction, crossover and mutation to agents. The document outlines the load shedding problem formulation and constraints. It also describes PSO, genetic algorithms, multi-agent systems and how MAPSO and MAGA combine these approaches to determine the most appropriate loads to shed during under frequency or voltage conditions.
This document summarizes research on using particle swarm optimization to improve a distribution system with multiple distributed generators. It presents methods for optimally siting and sizing distributed generators using genetic algorithms and particle swarm optimization. The methods are tested on the IEEE 33-node test feeder, and particle swarm optimization is able to reduce total power losses by up to 66.68 kW compared to 29.65 kW for genetic algorithms when placing three distributed generators.
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.
This document summarizes a research paper that examines pricing strategy in a two-stage supply chain consisting of a supplier and retailer. The supplier offers a credit period to the retailer, who then offers credit to customers. A mathematical model is formulated to maximize total profit for the integrated supply chain system. The model considers three cases based on the relative lengths of the credit periods offered at each stage. Equations are developed to represent the profit functions for the supplier, retailer and overall system in each case. The goal is to determine the optimal selling price that maximizes total integrated profit.
The document discusses melanoma skin cancer detection using a computer-aided diagnosis system based on dermoscopic images. It begins with an introduction to skin cancer and melanoma. It then reviews existing literature on automated melanoma detection systems that use techniques like image preprocessing, segmentation, feature extraction and classification. Features extracted in other studies include asymmetry, border irregularity, color, diameter and texture-based features. The proposed system collects dermoscopic images and performs preprocessing, segmentation, extracts 9 features based on the ABCD rule, and classifies images using a neural network classifier to detect melanoma. It aims to develop an automated diagnosis system to eliminate invasive biopsy procedures.
This document summarizes various techniques for image segmentation that have been studied and proposed in previous research. It discusses edge-based, threshold-based, region-based, clustering-based, and other common segmentation methods. It also reviews applications of segmentation in medical imaging, plant disease detection, and other fields. While no single technique can segment all images perfectly, hybrid and adaptive methods combining multiple approaches may provide better results. Overall, image segmentation remains an important but challenging task in digital image processing and computer vision.
This document presents a test for detecting a single upper outlier in a sample from a Johnson SB distribution when the parameters of the distribution are unknown. The test statistic proposed is based on maximum likelihood estimates of the four parameters (location, scale, and two shape) of the Johnson SB distribution. Critical values of the test statistic are obtained through simulation for different sample sizes. The performance of the test is investigated through simulation, showing it performs well at detecting outliers when the contaminant observation represents a large shift from the original distribution parameters. An example application to census data is also provided.
This document summarizes a research paper that proposes a portable device called the "Disha Device" to improve women's safety. The device has features like live location tracking, audio/video recording, automatic messaging to emergency contacts, a buzzer, flashlight, and pepper spray. It is designed using an Arduino microcontroller connected to GPS and GSM modules. When the button is pressed, it sends an alert message with the woman's location, sets off an alarm, activates the flashlight and pepper spray for self-defense. The goal is to provide women a compact, one-click safety system to help them escape dangerous situations or call for help with just a single press of a button.
- The document describes a study that constructed physical fitness norms for female students attending social welfare schools in Andhra Pradesh, India.
- Researchers tested 339 students in classes 6-10 on speed, strength, agility and flexibility tests. Tests included 50m run, bend and reach, medicine ball throw, broad jump, shuttle run, and vertical jump.
- The results showed that 9th class students had the best average time for the 50m run. 10th class students had the highest flexibility on average. Strength and performance generally improved with increased class level.
This document summarizes research on downdraft gasification of biomass. It discusses how downdraft gasifiers effectively convert solid biomass into a combustible producer gas. The gasification process involves pyrolysis and reactions between hot char and gases that produce CO, H2, and CH4. Downdraft gasifiers are well-suited for biomass gasification due to their simple design and ability to manage the gasification process with low tar production. The document also reviews previous studies on gasifier configuration upgrades and their impact on performance, and the principles of downdraft gasifier operation.
This document summarizes the design and manufacturing of a twin spindle drilling attachment. Key points:
- The attachment allows a drilling machine to simultaneously drill two holes in a single setting, improving productivity over a single spindle setup.
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Paper id 28201438
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:
6. International Journal of Research in Advent Technology, Vol.2, Issue.8, August 2014
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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
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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
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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.
REFERENCES
[1] R Subramanian, K. Thanushkodi and A. Prakash, “An efficient Meta Heurisitc
Algorithm to Solve Economic Load Dispatch Problems”. Iranian Journal of
Electrical and Electronics Engineering. Vol. 9, No.4 Dec 2013.
12. International Journal of Research in Advent Technology, Vol.2, Issue.8, August 2014
E-ISSN: 2321-9637
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[2] Xin-She Yang, Xingshi He,” Firefly Algorithm: Recent Advances and
Applications” arXiv:1308.3898v1, 18 Aug 2013.
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