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.
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 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.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Optimal Power Flow with Reactive Power Compensation for Cost And Loss Minimiz...ijeei-iaes
One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile
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.
This document provides an overview of economic dispatch and unit commitment in power systems. It discusses:
1. Economic dispatch is the process of determining generator outputs to meet demand at minimum cost, taking into account generator costs and constraints. It can be solved graphically or using the KKT conditions.
2. Unit commitment determines which generators will operate over different time periods to meet forecasted load at minimum cost, while considering generator operating constraints like minimum up/down times. It is solved using techniques like mixed integer programming and Lagrangian relaxation.
3. Mixed integer programming and Lagrangian relaxation are commonly used optimization methods for unit commitment. Mixed integer programming formulates it as an optimization problem with discrete and continuous variables.
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.
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.
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 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.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Optimal Power Flow with Reactive Power Compensation for Cost And Loss Minimiz...ijeei-iaes
One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile
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.
This document provides an overview of economic dispatch and unit commitment in power systems. It discusses:
1. Economic dispatch is the process of determining generator outputs to meet demand at minimum cost, taking into account generator costs and constraints. It can be solved graphically or using the KKT conditions.
2. Unit commitment determines which generators will operate over different time periods to meet forecasted load at minimum cost, while considering generator operating constraints like minimum up/down times. It is solved using techniques like mixed integer programming and Lagrangian relaxation.
3. Mixed integer programming and Lagrangian relaxation are commonly used optimization methods for unit commitment. Mixed integer programming formulates it as an optimization problem with discrete and continuous variables.
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.
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.
Combining both Plug-in Vehicles and Renewable Energy Resources for Unit Commi...IOSR Journals
This document presents a study that combines plug-in electric vehicles with vehicle-to-grid technology (V2G), renewable energy resources like wind and solar, and existing power plants, to optimize unit commitment in smart grids. The goal is to minimize total costs and emissions. A genetic algorithm is used to optimize scheduling of generation units, V2G vehicles providing spinning reserves, and time-varying renewable sources over a 24-hour period to meet load demand at lowest cost while satisfying constraints. Simulation results validate that integrating V2G and renewable energy sources can effectively reduce costs and emissions for the smart grid.
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.
Economic Dispatch using Quantum Evolutionary Algorithm in Electrical Power S...IJECEIAES
Unpredictable increase in power demands will overload the supply subsystems and insufficiently powered systems will suffer from instabilities, in which voltages drop below acceptable levels. Additional power sources are needed to satisfy the demand. Small capacity distributed generators (DGs) serve for this purpose well. One advantage of DGs is that they can be installed close to loads, so as to minimise loses. Optimum placements and sizing of DGs are critical to increase system voltages and to reduce loses. This will finally increase the overall system efficiency. This work exploits Quantum Evolutionary Algorithm (QEA) for the placements and sizing. This optimisation targets the cheapest generation cost. Quantum Evolutionary Algorithm is an Evolutionary Algorithm running on quantum computing, which works based on qubits and states superposition of quantum mechanics. Evolutionary algorithm with qubit representation has a better characteristic of diversity than classical approaches, since it can represent superposition of states.
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.
Comparative study of the price penalty factors approaches for Bi-objective di...IJECEIAES
One of the main objectives of electricity dispatch centers is to schedule the operation of available generating units to meet the required load demand at minimum operating cost with minimum emission level caused by fossil-based power plants. Finding the right balance between the fuel cost the green gasemissionsis reffered as Combined Economic and Emission Dispatch (CEED) problem which is one of the important optimization problems related the operationmodern power systems. The Particle Swarm Optimization algorithm (PSO) is a stochastic optimization technique which is inspired from the social learning of birds or fishes. It is exploited to solve CEED problem. This paper examines the impact of six penalty factors like "Min-Max", "Max-Max", "Min-Min", "Max-Min", "Average" and "Common" price penalty factors for solving CEED problem. The Price Penalty Factor for the CEED is the ratio of fuel cost to emission value. This bi-objective dispatch problem is investigated in the Real West Algeria power network consisting of 22 buses with 7 generators. Results prove capability of PSO in solving CEED problem with various penalty factors and it proves that Min-Max price penalty factor provides the best compromise solution in comparison to the other penalty factors.
Economic dispatch by optimization techniquesIJECEIAES
The current paper offers the solution strategy for the economic dispatch problem in electric power system implementing ant lion optimization algorithm (ALOA) and bat algorithm (BA) techniques. In the power network, the economic dispatch (ED) is a short-term calculation of the optimum performance of several electricity generations or a plan of outputs of all usable power generation units from the energy produced to fulfill the necessary demand, although equivalent and unequal specifications need to be achieved at minimal fuel and carbon pollution costs. In this paper, two recent meta-heuristic approaches are introduced, the BA and ALOA. A rigorous stochastically developmental computing strategy focused on the action and intellect of ant lions is an ALOA. The ALOA imitates ant lions' hunting process. The introduction of a numerical description of its biological actions for the solution of ED in the power framework. These algorithms are applied to two systems: a small scale three generator system and a large scale six generator. Results show were compared on the metrics of convergence rate, cost, and average run time that the ALOA and BA are suitable for economic dispatch studies which is clear in the comparison set with other algorithms. Both of these algorithms are tested on IEEE-30 bus reliability test system.
This chapter will focus on the optimization and security of a power system. basically it will focus on economic dispatch analysis without considering transmission line losses.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
IRJET- Particle Swarm Intelligence based Dynamics Economic Dispatch with Dail...IRJET Journal
This document discusses particle swarm intelligence techniques for solving economic load dispatch problems. It begins with an abstract that introduces economic load dispatch as a technique for allocating power generation levels among generating units to minimize costs while meeting demand and operational constraints. It then provides background on economic load dispatch and describes how particle swarm optimization can be applied to solve non-convex economic dispatch problems. Finally, it reviews several related works applying evolutionary algorithms like particle swarm optimization, genetic algorithms, and cuckoo search to economic load dispatch problems.
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.
Evolutionary algorithm solution for economic dispatch problemsIJECEIAES
A modified firefly algorithm (FA) was presented in this paper for finding a solution to the economic dispatch (ED) problem. ED is considered a difficult topic in the field of power systems due to the complexity of calculating the optimal generation schedule that will satisfy the demand for electric power at the lowest fuel costs while satisfying all the other constraints. Furthermore, the ED problems are associated with objective functions that have both quality and inequality constraints, these include the practical operation constraints of the generators (such as the forbidden working areas, nonlinear limits, and generation limits) that makes the calculation of the global optimal solutions of ED a difficult task. The proposed approach in this study was evaluated in the IEEE 30-Bus test-bed, the evaluation showed that the proposed FA-based approach performed optimally in comparison with the performance of the other existing optimizers, such as the traditional FA and particle swarm optimization. The results show the high performance of the modified firefly algorithm compared to the other methods.
IRJET- A Comparative Study of Economic Load Dispatch Optimization MethodsIRJET Journal
This document presents a comparative study of different optimization methods for solving the economic load dispatch (ELD) problem in power systems. The ELD problem involves minimizing generation costs while meeting demand, and is formulated as a non-linear optimization problem with constraints. Various conventional and evolutionary algorithms have been used to solve ELD, but more recently bio-inspired algorithms like flower pollination algorithm and Jaya optimization have shown better performance. The paper evaluates these nature-inspired algorithms and compares their results for the ELD problem to demonstrate their effectiveness.
Optimal unit commitment of a power plant using particle swarm optimization ap...IJECEIAES
Economic load dispatch among generating units is very important for any power plant. In this work, the economic load dispatch was made at Egbin Thermal Power plant supplying a total load of 600MW using six generating units. In carrying out this study, transmission losses were assumed to be included into the load supplied. Also, three different combinations in the form of 6, 5- and 4-units commitment were considered. In each case, the total load was optimally dispatched between committed generating units using Particle Swarm Optimization (PSO). Similarly, the generation cost for each generating unit was determined. For case 1, the six generators were committed and the generation cost is 2,100,685.069$/h. For case 2, five generators were committed and the generation cost is 2,520,861.947$/h. For case 3, four generators were committed and the generation cost is 3,150,621.685$/h. From all considered cases, it was found that, the minimum generation cost was achieved when all six generating units were committed and a total of 420,178.878$/h was saved.
Optimal Operation of Wind-thermal generation using differential evolutionIOSR Journals
This document presents an optimal operation model for a wind-thermal power generation system using differential evolution (DE). DE is an evolutionary algorithm inspired by biological evolution that can solve complex constrained optimization problems. The paper formulates the economic dispatch problem to minimize total generation cost of the wind and thermal plants subject to various constraints like power balance, generator limits, ramp rates, and valve point loading effects. Five different DE mutation strategies are analyzed for solving the wind-thermal economic dispatch problem on a test system with 10 thermal units. The results show that the best mutation strategy and control parameter values (mutation rate and crossover rate) depend on the problem and can significantly impact the solution quality and consistency obtained by the DE algorithm.
The document discusses electric power system operation and control. It addresses the objectives of power system operation which are to provide continuous quality service to energy users at minimum cost. This includes supplying power at acceptable voltage and frequency while minimizing environmental impact and ensuring security and reliability. The tasks of operation planning, control and accounting are described. Operation planning involves scheduling generation and transmission facilities to meet load demand at minimum cost over various time periods. Operation control functions like economic dispatch, load frequency control and operating reserve calculation aim to satisfy instantaneous load demands. Optimization of generation dispatch to minimize total operating costs is formulated as a constrained optimization problem solved using methods like Lagrange multipliers and iterative techniques. Transmission losses are also accounted for in the optimal load dispatch model
Coyote multi-objective optimization algorithm for optimal location and sizing...IJECEIAES
This document summarizes a research paper that proposes using a new optimization algorithm called the coyote optimization algorithm (COA) to determine the optimal location and sizing of renewable distributed generators (RDGs) in radial distribution systems. The objectives are to minimize power losses, maximize voltage stability index, and reduce total operation cost. The COA is applied to the IEEE 33 bus and IEEE 69 bus test systems. The results demonstrate the effectiveness of using COA to optimally site and size RDGs in distribution networks.
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.
Multi Area Economic Dispatch Using Secant Method and Tie Line MatrixIJAPEJOURNAL
In this paper, Secant method and tie line matrix are proposed to solve multi area economic dispatch (MAED) problem with tie line loss. Generator limits of all generators in each area are calculated at given area power demands plus export (or import) using secant method and the generator limits of all generators are modified as modified generator limits. Central economic dispatch (CED) problem is used to determine the output powers of all generators and finally power flows in all tie lines are determined from tie line matrix. Here, Secant method is applied to solve the CED problem. A modified tie line matrix is used to find power flow in each tie line and then tie line loss is calculated from the power flow in each tie line. The proposed approach has been tested on two-area (two generators in each area) system and four-area (four generators in each area) system. It is observed from various cases that the proposed approach provides optimally best solution in terms of cost with tie line loss with less computational burden.
This paper focuses on the artificial bee colony (ABC) algorithm, which is a nonlinear optimization problem. is proposed to find the optimal power flow (OPF). To solve this problem, we will apply the ABC algorithm to a power system incorporating wind power. The proposed approach is applied on a standard IEEE-30 system with wind farms located on different buses and with different penetration levels to show the impact of wind farms on the system in order to obtain the optimal settings of control variables of the OPF problem. Based on technical results obtained, the ABC algorithm is shown to achieve a lower cost and losses than the other methods applied, while incorporating wind power into the system, high performance would be gained.
The optimal solution for unit commitment problem using binary hybrid grey wol...IJECEIAES
The aim of this work is to solve the unit commitment (UC) problem in power systems by calculating minimum production cost for the power generation and finding the best distribution of the generation among the units (units scheduling) using binary grey wolf optimizer based on particle swarm optimization (BGWOPSO) algorithm. The minimum production cost calculating is based on using the quadratic programming method and represents the global solution that must be arriving by the BGWOPSO algorithm then appearing units status (on or off). The suggested method was applied on “39 bus IEEE test systems”, the simulation results show the effectiveness of the suggested method over other algorithms in terms of minimizing of production cost and suggesting excellent scheduling of units.
Fourier analysis uses Fourier series and Fourier integrals to represent functions. Fourier series represent periodic functions as the sum of sines and cosines, while Fourier integrals extend this to non-periodic functions using integrals of sines and cosines instead of series. Orthogonal function systems like sines and cosines allow determining the coefficients using formulas like the Euler formulas. Extensions include replacing sines and cosines with other orthogonal functions and applying Fourier methods to functions of any period by changing variables.
This document provides information about an optimization course taught by Assoc. Prof. Pelin Gündeş. It includes the instructor's contact information, textbook recommendations, course schedule, prerequisites, and grading policy. An example problem is also provided to illustrate optimization concepts such as design variables, objective functions, constraint surfaces, and plotting constraint curves. The goal is to design a column with minimum cost subject to stress and dimensional constraints.
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Combining both Plug-in Vehicles and Renewable Energy Resources for Unit Commi...IOSR Journals
This document presents a study that combines plug-in electric vehicles with vehicle-to-grid technology (V2G), renewable energy resources like wind and solar, and existing power plants, to optimize unit commitment in smart grids. The goal is to minimize total costs and emissions. A genetic algorithm is used to optimize scheduling of generation units, V2G vehicles providing spinning reserves, and time-varying renewable sources over a 24-hour period to meet load demand at lowest cost while satisfying constraints. Simulation results validate that integrating V2G and renewable energy sources can effectively reduce costs and emissions for the smart grid.
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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.
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Unpredictable increase in power demands will overload the supply subsystems and insufficiently powered systems will suffer from instabilities, in which voltages drop below acceptable levels. Additional power sources are needed to satisfy the demand. Small capacity distributed generators (DGs) serve for this purpose well. One advantage of DGs is that they can be installed close to loads, so as to minimise loses. Optimum placements and sizing of DGs are critical to increase system voltages and to reduce loses. This will finally increase the overall system efficiency. This work exploits Quantum Evolutionary Algorithm (QEA) for the placements and sizing. This optimisation targets the cheapest generation cost. Quantum Evolutionary Algorithm is an Evolutionary Algorithm running on quantum computing, which works based on qubits and states superposition of quantum mechanics. Evolutionary algorithm with qubit representation has a better characteristic of diversity than classical approaches, since it can represent superposition of states.
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.
Comparative study of the price penalty factors approaches for Bi-objective di...IJECEIAES
One of the main objectives of electricity dispatch centers is to schedule the operation of available generating units to meet the required load demand at minimum operating cost with minimum emission level caused by fossil-based power plants. Finding the right balance between the fuel cost the green gasemissionsis reffered as Combined Economic and Emission Dispatch (CEED) problem which is one of the important optimization problems related the operationmodern power systems. The Particle Swarm Optimization algorithm (PSO) is a stochastic optimization technique which is inspired from the social learning of birds or fishes. It is exploited to solve CEED problem. This paper examines the impact of six penalty factors like "Min-Max", "Max-Max", "Min-Min", "Max-Min", "Average" and "Common" price penalty factors for solving CEED problem. The Price Penalty Factor for the CEED is the ratio of fuel cost to emission value. This bi-objective dispatch problem is investigated in the Real West Algeria power network consisting of 22 buses with 7 generators. Results prove capability of PSO in solving CEED problem with various penalty factors and it proves that Min-Max price penalty factor provides the best compromise solution in comparison to the other penalty factors.
Economic dispatch by optimization techniquesIJECEIAES
The current paper offers the solution strategy for the economic dispatch problem in electric power system implementing ant lion optimization algorithm (ALOA) and bat algorithm (BA) techniques. In the power network, the economic dispatch (ED) is a short-term calculation of the optimum performance of several electricity generations or a plan of outputs of all usable power generation units from the energy produced to fulfill the necessary demand, although equivalent and unequal specifications need to be achieved at minimal fuel and carbon pollution costs. In this paper, two recent meta-heuristic approaches are introduced, the BA and ALOA. A rigorous stochastically developmental computing strategy focused on the action and intellect of ant lions is an ALOA. The ALOA imitates ant lions' hunting process. The introduction of a numerical description of its biological actions for the solution of ED in the power framework. These algorithms are applied to two systems: a small scale three generator system and a large scale six generator. Results show were compared on the metrics of convergence rate, cost, and average run time that the ALOA and BA are suitable for economic dispatch studies which is clear in the comparison set with other algorithms. Both of these algorithms are tested on IEEE-30 bus reliability test system.
This chapter will focus on the optimization and security of a power system. basically it will focus on economic dispatch analysis without considering transmission line losses.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
IRJET- Particle Swarm Intelligence based Dynamics Economic Dispatch with Dail...IRJET Journal
This document discusses particle swarm intelligence techniques for solving economic load dispatch problems. It begins with an abstract that introduces economic load dispatch as a technique for allocating power generation levels among generating units to minimize costs while meeting demand and operational constraints. It then provides background on economic load dispatch and describes how particle swarm optimization can be applied to solve non-convex economic dispatch problems. Finally, it reviews several related works applying evolutionary algorithms like particle swarm optimization, genetic algorithms, and cuckoo search to economic load dispatch problems.
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.
Evolutionary algorithm solution for economic dispatch problemsIJECEIAES
A modified firefly algorithm (FA) was presented in this paper for finding a solution to the economic dispatch (ED) problem. ED is considered a difficult topic in the field of power systems due to the complexity of calculating the optimal generation schedule that will satisfy the demand for electric power at the lowest fuel costs while satisfying all the other constraints. Furthermore, the ED problems are associated with objective functions that have both quality and inequality constraints, these include the practical operation constraints of the generators (such as the forbidden working areas, nonlinear limits, and generation limits) that makes the calculation of the global optimal solutions of ED a difficult task. The proposed approach in this study was evaluated in the IEEE 30-Bus test-bed, the evaluation showed that the proposed FA-based approach performed optimally in comparison with the performance of the other existing optimizers, such as the traditional FA and particle swarm optimization. The results show the high performance of the modified firefly algorithm compared to the other methods.
IRJET- A Comparative Study of Economic Load Dispatch Optimization MethodsIRJET Journal
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A Decomposition Aggregation Method for Solving Electrical Power Dispatch Problems.pdf
1. A Decomposition/ Aggregation Method for Solving
Electrical Power Dispatch Problems
M. H. Mansor
Universiti Tenaga Nasional
(UNITEN), Malaysia
E-mail:mhelmi@uniten.edu.my
M. R. Irving
Brunel Institute of Power Systems,
UK
E-mail: Malcolm.Irving@brunel.ac.uk
G. A. Taylor
Brunel Institute of Power Systems,
UK
E-mail:Gareth.Taylor@brunel.ac.uk
Abstract-This paper presents a new approach to solving the
Economic Dispatch (ED) Problem for a large number of
generators using a decomposition / aggregation method. A
program has been developed to demonstrate the algorithm using
the MATLAB programming language. A 5-bus test system and
the IEEE 26-bus test system are used as demonstration systems.
Each test system is decomposed into small areas and each area
has been solved for Economic Dispatch (locally) using an
Evolutionary Programming (EP) technique. It was ensured that
each area contains at least one generating unit and one supplied
load. The EP will minimise the objective funtion for each area,
minimising the local operating cost including the effects of real
power losses in each area. The optimisation problem for each
area can be regarded as a sub-problem of the decomposition
scheme. Subsequently, the solutions from the areas are
combined (aggregated) to solve the overall system problem. The
results obtained using the decomposition / aggregation method
are compared with the results found when the ED Problem was
solved using a centralised EP approach and the base-case results
found from solving a (non-optimal) load flow. It was found that
applying the aggregation method is a prospective approach for
solving economic dispatch problems with a large numbers of
generators in a power system.
Index Terms--Economic Dispatch (ED), Decompositon,
Aggregation, Evolutionary Programming (EP).
I. INTRODUCTION
Demand for electricity in homes and business has increased
rapidly. The available supply may not be enough to dispatch
sufficient amount of electricity to cater for the demand in 5
years time. This situation will result in unreliable energy for
the consumers [1]. Therefore, more generating units or power
plants need to be built in order to handle the situation. In ten
years time there would be many more than 200 generating
units in the grid system in the UK to serve the high demand.
Today, there are various computer methods existing for the
dispatch of generator power outputs. These include two types
of optimisation techniques: mathematical optimisation
methods and heuristics optimisation. Papers that apply
mathematical optimisation methods such as linear
programming, quadratic programming, integer and mixed-
integer programming, dynamic programming, Lagrangian
relaxation method include [2-10]. Many of the latest papers
for solving the ED Problem use heuristics optimisation
methods such as evolutionary algorithms, simulated
annealing, tabu search, neural networks, fuzzy programming,
hybrid techniques, etc [11-18].
Unfortunately, all the above methods are only efficient for
problems involving up to about 200 generators. For systems
that have many hundreds or thousands of generators, a new
approach is required. This project presents a new approach
for dispatching generator power outputs and shceduling of
generator on / off status for a large scale problerm. The new
approach to dispatching generator power outputs, that is
presented in this paper, is decomposition/ aggregation
method.
This paper presents an investigation into applying the
decomposition/ aggregation methods in conjunction with the
Evolutionary Programming (EP) optimisation technique to
solve the ED problem. EP is one of the Evolutionary
Algorithm (EA) Optimisation Techniques [19]. This approach
is suitable for a general Economic Dispatch problem
formulation.
II. ECONOMIC DISPATCH
Economic Dispatch (ED) is one of the electrical power
systems problems. ED also known as electrical power
dispatch. The definition of economic dispatch (ED) provided
by FERC (E P Act section 1234) is stated as follows: “The
operation of generation facilities to produce energy at the
lowest cost, to reliably serve consumers, recognizing any
operational limits of generation and transmission
facilities.”[20]. Likewise, Ross Baldick (2004) gave the
following definition: “Economic dispatch is sharing
generation between generators to minimize the total fuel
costs” [21]. From above definitions, ED can generally be
identified as a method of determining the lowest cost of
dispatching electrical power from the generating units to the
demand on the system with respect to the system constraints
and the unit constraints [20]. The systems constraints can be
the real power balance between the generation and the
demand, reserve generation capacity, transmission network
limits, network security, etc. Furthermore, the unit constraints
are the operating limits of generators, ramp rate limits,
minimum ‘up time’, etc.
Economic Dispatch plays an important role in improving
the economy of generating unit operation effectively and
hence minimise the total generation cost. This is because the
latest optimisation techniques for solving the ED Problem
give reliable and convincing solutions, as all constraints (the
systems constraints and the unit constraints) are considered in
the formulation of the ED problem. Furthermore, the latest
ED problems may also consider some of the the dynamic
2. characteristics of the system. Today, power systems operators
(dispatchers) rely on the ED solution as a reference in making
judgements and decisions for daily operation of a grid system
at the lowest feasible operating cost.
The objective function of the ED problem (i.e., total
production cost) can be written as follows:
Minimise ( )
∑
=
=
n
i
i
i
total P
C
C
1
(1)
Where total
C is the total production cost.
( )
i
i P
C is the fuel cost function of unit i in terms of real
power output, Pi. The fuel cost function can be expressed in
the form of a quadratic equation as follows:
( ) ∑
=
+
+
=
n
i
i
i
i
i
i
i
i c
P
b
P
a
P
C
1
2
Where ai, bi and ci are cost coefficients of generating unit i,
subject to the constraints:
i. Real power balance
∑
=
=
+
n
i
i
loss
demand P
P
P
1
(2)
Where demand
P is the total system load demand and loss
P is
the total system loss.
ii. Generator operating limits
max
min i
i
i P
P
P ≤
≤ , i = 1, …, n (3)
Where min
i
P and max
i
P are the minimum and the maximum
real power outputs of ith generator, respectively.
III. PROPOSED APPROACH
The proposed approach is illustrated in Figure 1.
The process of the proposed approach starts with
decomposing an electrical power system in to a set of areas
that contain a number of generators and loads. The number of
areas depends on the size of the system. This paper mainly
concerns the application of the decomposition / aggregation
method in solving the economic dispatch problem, rather than
the choice of how to subdivide the network. Each area must
have at least one generating unit and one supplied load. The
individual areas will be solved for ED by using the EP
technique. The EP will minimise the objective function for
each area, minimising the local operating cost in each area.
The optimisation problem for each area can be regarded as a
sub-problem of the decomposition scheme. Subsequently, the
solutions from the areas are combined (aggregated) to solve
the co-ordination optimisation problem.
The co-ordination optimisation problem can be regarded as
the ‘master problem’ of the decomposition / aggregation
scheme. The master objective function is to minimise the sum
of the costs in area 1, in area 2 and upto area (n), subject to
proper interaction balance of the real power (P) and the
reactive power (Q) flows in and out of each sub-problem.
Hence, the local cost and the real and reactive power
produced by each area, calculated by the EP technique will be
added to obtain the total cost and total loss of the whole
system. The variables and control parameters for the dispatch
problem are the real power generated by each generating unit.
The real power balance and the generator operating limits are
considered as contraints.
A. 5-Bus Test System
A program has been developed to demonstrate the
algorithm using the MATLAB programming language. A
small 5-bus test system and a 26-bus test system are used as
demonstration systems. The 5-bus test system data are
tabulated in Table 1 and Table 2.
TABLE 1: GENERATOR DATA AND COST COEFFICIENTS OF 5-
BUS TEST SYSTEM.
Bus No. Generator
1 (G1)
Generator
2 (G2)
Generator
3 (G3)
Size (MW) 10 to 85 10 to 80 10 to 80
Generator
Cost
Coefficients
a ($/MW2
H) 200 180 140
b ($/MWH) 7.0 6.3 6.8
c ($/H) 0.008 0.009 0.007
TABLE 2: THE SYSTEM LOAD DEMAND OF 5-BUS TEST SYSTEM.
Bus No. Bus 2 (L2) Bus 3 (L3) Bus 4 (L4) Bus 5 (L5)
Real Power
(MW)
20 20 50 60
Reactive
Power (Mvar)
10 15 30 40
The 5-bus system was decomposed into two areas. As
stated earlier, it was ensured that each area contains at least
one generating unit and one supplied load. The decomposed
areas are as shown in Figure 2.
There are two areas in the decomposed electrical system,
separated via the dotted line shown in Figure 2. The top part
of the figure is Area 1 and the bottom part of the figure is
Area 2. These two areas linked together with four
transmission lines f1, f3, f4 and f7. Each area was solved for
Economic Dispatch (locally) using an Evolutionary
Programming (EP) technique. Only transmission lines f2 and
f6 are considered for solving the ED problem in Area 1. For
Area 2 transmission line f5 is considered. The transmission
lines f1, f3, f4 and f7 are paralled together to be approximated
by one equivalent transmission line when solving the master
problem. Since the system is divided into two areas, two sub-
problem need to be solved within each master problem
iteration.
3. Figure 1: Overview of the decomposition/ aggregation method for solving ED problem.
Figure 2: Decomposed 5-Bus Test System.
4. There are two areas in the decomposed electrical
system, separated via the dotted line shown in Figure 2.
The top part of the figure is Area 1 and the bottom part of
the figure is Area 2. These two areas linked together with
four transmission lines f1, f3, f4 and f7. Each area was
solved for Economic Dispatch (locally) using an
Evolutionary Programming (EP) technique. Only
transmission lines f2 and f6 are considered for solving the
ED problem in Area 1. For Area 2 transmission line f5 is
considered. The transmission lines f1, f3, f4 and f7 are
paralled together to be approximated by one equivalent
transmission line when solving the master problem. Since
the system is divided into two areas, two sub-problem
need to be solved within each master problem iteration.
Sub-problem 1 (Area 1)
The cost functions for generating units in Area 1 are as
follows:
Generator 1:
(4)
Generator 2:
(5)
The total operating cost in Area 1 is
Cost3
Cost1
1
Area
of
Cost
Total +
= (6)
Hence, the objective function of ED problem of Area 1 can
be written as
Minimise Cost3
Cost1
1
Area
of
Cost
Total +
= (7)
Sub-problem 2 (Area 2)
There is only one generating unit in Area 2 which is
generator 2. the cost function for generator 2 is:
Generator 1:
2
g2
0.009P
g2
6.3P
180
Cost2 +
+
= (8)
The objective function of ED problem of Area 2 can be
written as
Minimise Cost2
2
Area
of
Cost
Total = (9)
Master problem
The solutions from solving the ED problem in Area 1
and Area 2 are used to solve the master problem. The
solutions include the total operating cost and the real and
reactive power available in each area. The master objective
function is to minimise the sum of the costs in area 1 and
in area 2.The master problem objective function can be
written as:
Minimise =
Cost
Overall
2
Area
of
Cost
Total
1
Area
of
Cost
Total +
(10)
The transmission lines that connected between these
two areas are paralleled and assumed it connected between
two busbars. The real and reactive power of each area
found from the EP optimisation technique will be used as
the parameters for these two buses for solving the master
problem. Area 1 will be the slack bus for the master
problem. Therefore, only the real power of area 1 will be
varied to solve the master problem. While minimising the
overall cost of the system as shown in equation 10, the
master problem will keep updating the real power
generation required for each generating units in the 5-bus
system until the best set of real power generation to supply
the demand, while minimising the overall operating cost
and also the system losses, is found.
B. 26-Bus Test System
The aggregation/ decomposition program also
demonstrated on 26-bus system. The 26-bus test system
data are tabulated in Table 1 and Table 2.
TABLE 3: GENERATOR DATA AND COST
COEFFICIENTS OF 26-BUS TEST SYSTEM.
The 26-bus system was decomposed into two areas. As
stated earlier, it was ensured that each area contains at
least one generating unit and one supplied load. The
decomposed areas are as shown in Figure 2.
Bus No. Size
(MW)
Generator Cost Coefficients
a ($/MW2
H) b ($/MWH) c ($/H)
Generator 1
(G1)
10 to 500 240 7 0.007
Generator 2
(G2)
50 to 200 200 10 0.0095
Generator 3
(G3)
80 to 300 220 8.5 0.009
Generator 4
(G4)
50 to150 200 11 0.009
Generator 5
(G5)
50 to 200 220 10.5 0.008
Generator 26
(G26)
50 to 120 190 12 0.0075
2
g1
0.008P
g1
7.0P
200
Cost1 +
+
=
2
g3
0.007P
g3
6.8P
140
Cost3 +
+
=
5. Figure 3: Decomposed 26-Bus Test System.
There are two areas in the decomposed electrical
system, separated via the dotted line shown in Figure 3.
The left part of the figure is Area 1 and the right part of the
figure is Area 2. Each area was solved for Economic
Dispatch (locally) using an Evolutionary Programming
(EP) technique. The transmission lines connecting these
two areas are paralled together to be approximated by one
equivalent transmission line when solving the master
problem. Since the system is divided into two areas, two
sub-problem need to be solved within each master problem
iteration.
Sub-problem 1 (Area 1)
The cost functions for generating units in Area 1 are as
follows:
Generator 1:
2
g1
0.007P
g1
7.0P
240
Cost1 +
+
= (11)
Generator 5:
2
g3
0.008P
g3
10.5P
220
Cost5 +
+
= (12)
Generator 26:
2
g3
0.0075P
g3
12.0P
190
Cost26 +
+
= (13)
The total operating cost in Area 1 is
Cos26
Cost5
Cost1
1
Area
of
Cost
Total +
+
= (14)
Hence, the objective function of ED problem of Area 1
can be written as
Minimise
6
Cost5_Cos2
Cost1
1
Area
of
Cost
Total +
= (15)
Sub-problem 2 (Area 2)
6. The cost functions for generating units in Area 2 are as
follows:
Generator 2:
2
g2
0.0095P
g2
10.0P
200
Cost2 +
+
= (16)
Generator 3:
2
g2
0.009P
g2
8.5P
220
Cost3 +
+
= (17)
Generator 4:
2
g2
0.009P
g2
11.0P
200
Cost4 +
+
= (18)
The objective function of ED problem of Area 2 can be
written as
Minimise
Cos4
Cos3
Cost2
2
Area
of
Cost
Total +
+
= (19)
Master problem
The master objective function is to minimise the sum
of the costs in area 1 and in area 2.The master problem
objective function for 26-bus test system can be written as:
Minimise
=
Cost
Overall
2
Area
of
Cost
Total
1
Area
of
Cost
Total + (20)
As mentioned previously, the transmission lines that
connected between these two areas are paralleled and
assumed it connected between two busbars.
IV. RESULTS AND DISCUSSION
Prior to the decomposition / aggregation scheme, the
ED problem of 5-bus system and 26-bus system were
solved using a centralised EP approach and also was
solved for a load flow (non-optimal) solution. These tests
are for the purpose of comparison. The comparison of the
results found from the three methods are shown in Table 4
and Table 5. It is important to compare the results found
using decomposition / aggregation method with the other
approach in order to know the advantage of this approach
over the standard methods.
TABLE 4: COMPARED RESULTS OF LOAD FLOW,
CENTRALISED EP AND THE PROPOSED
DECOMPOSITION/ AGGREGATION METHOD FOR
5-BUS SYSTEM
Representation Load Flow
(Non-Optimal)
Centralised EP Decomposition/
Aggregation Method
Pg1 (MW) 83.051 77.3216 26.3368
Pg2 (MW) 40.000 37.2568 43.3350
Pg3 (MW) 30.000 52.6737 82.1591
Total Generation
Cost ($/h)
2028.2 1608.3 1606.0
Total System
Loss (MW)
3.0526 2.5081 2.6731
TABLE 5: COMPARED RESULTS OF LOAD FLOW,
CENTRALISED EP AND THE PROPOSED
DECOMPOSITION/ AGGREGATION METHOD FOR
26-BUS SYSTEM
Representation Load Flow
(Non-Optimal)
Centralised EP Decomposition/
Aggregation Method
Pg1 (MW) 719.5341 473.8551 477.4357
Pg2 (MW) 79 172.3794 200.316
Pg3 (MW) 20 246.5948 223.6499
Pg4 (MW) 100 113.1528 146.6501
Pg5 (MW) 300 179.8036 166.1310
Pg26 (MW) 60 92.7484 54.2673
Total Generation
Cost ($/h)
17289 15457.9 13505.4
Total System
Loss (MW)
15.534 13.0190 10.0759
From Table 4 and Table 5, it is found that the total
generation cost obtained using decomposition /
aggregation method for 5-bus system and 26-bus system
are 16060 $/h and 13505.4 $/h respectively. The cost is
lesser than the total generation cost obtained using the
centralized EP and load flow (non-optimal) solution.
V. CONCLUSION
An approach of using a decompostion / aggregation
method has been presented in this paper. The method were
implemented on a 5-bus system and 26-bus system. It has
been found that applying the decomposition / aggregation
method is a suitable prospective approach for solving
economic dispatch problems with a large numbers of
generators in a power system. As stated earlier, the main
concern of this paper is not selection of the number and
definition of decomposed areas, but to begin to investigate
the the advantage of implementing the decomposition /
aggregation method in solving ED problem. The number
of decomposed area will be higher as the number of buses
is increased. It is hoped that this approach can be
developed further to allow the electrical power dispatch
problem to be expanded to cope with increasing numbers
of generators in the future.
7. ACKNOWLEDGEMENTS
The work presented in the present paper is sponsored by
Universiti Tenaga Nasional (UNITEN), Malaysia.
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