Economic Load Dispatch Problem Research Articles

Relaxed I-SHOT trust-region algorithm for solving multi-objective economic emission load dispatch problem

ABSTRACTIn this paper, a new algorithm for tackling nonlinear constrained multi-objective optimization problems is introduced. This algorithm, which we call relaxed the interactive sequential hybrid optimization technique (relaxed I-SHOT), is based on a hybrid method between the I-SHOT method and step method (STEM) to transform a multi-objective problem into a single-objective one. An active set strategy is used together with a suggested penalty method to transform a single-objective constrained optimization problem into unconstrained one. A trust-region globalization strategy is added to the algorithm to solve the obtained unconstrained problem to ensure global convergence. The suggested approach is utilized to solve the multi-objective economic emission load dispatch (EELD) problems to assert the effectiveness of the proposed algorithm. The proposed algorithm is tested on the standard IEEE 30-bus 6-generator test system. The results of the proposed approach are compared against those reported in the literature. The comparison asserts the potential of the proposed algorithm to solve the EELD problem.

New Optimization Algorithms for Application to Environmental Economic Load Dispatch in Power Systems

DOI: 10.5152/iujeee.2018.1825 The determination of the most economical generation dispatch in an electrical power system has become a very important issue globally. However, economical dispatch can no longer be considered alone because of environmental problems that are derived from emissions such as nitrogen oxide, carbon dioxide, and sulfur dioxide. In this study, the problem of environmental economic load dispatch (EELD) in a power system of six generators is addressed both by neglecting and including line transmission losses using a modified genetic algorithm and a modified artificial bee colony optimization method. The results of these modified algorithms are compared with those of the unmodified versions. The results demonstrate that the proposed new methods have better economic and environmental distribution performances. Accordingly, it can be concluded that the new methods are more effective and should be adopted.

A Novel Multi-Population Based Chaotic JAYA Algorithm with Application in Solving Economic Load Dispatch Problems

The economic load dispatch (ELD) problem is an optimization problem of minimizing the total fuel cost of generators while satisfying power balance constraints, operating capacity limits, ramp-rate limits and prohibited operating zones. In this paper, a novel multi-population based chaotic JAYA algorithm (MP-CJAYA) is proposed to solve the ELD problem by applying the multi-population method (MP) and chaotic optimization algorithm (COA) on the original JAYA algorithm to guarantee the best solution of the problem. MP-CJAYA is a modified version where the total population is divided into a certain number of sub-populations to control the exploration and exploitation rates, at the same time a chaos perturbation is implemented on each sub-population during every iteration to keep on searching for the global optima. The proposed MP-CJAYA has been adopted to ELD cases and the results obtained have been compared with other well-known algorithms reported in the literature. The comparisons have indicated that MP-CJAYA outperforms all the other algorithms, achieving the best performance in all the cases, which indicates that MP-CJAYA is a promising alternative approach for solving ELD problems.

English

English

Cuckoo Search Algorithm Optimization Approaches for Solving Economic Load Dispatch: A Review

Cuckoo search algorithm (CSA) is an effective and highly reliable swarm intelligence based optimization approach. It is a technique of determining the most efficient, low cost and reliable operation of a power system by dispatching the available electricity generation resources to supply the load on the system. This paper presents a comprehensive review of CSA application in Economic Load Dispatch (ELD) problem. This review will assist power system engineers with a view to enhancing the optimal operation of available thermal plants in electrical power systems.

Dynamic Economic Load Dispatch using Levenberg Marquardt Algorithm

Economic Load Dispatch (ELD) is a very important feature of power system network. This work proposes the novel approach which considers the constraint of ramp rate limit (RRL) to solve the ELD problem. It build up the time varying dynamic economic load dispatch in which load dispatching is calculated for each specified time interval, first it is tested with conventional lambda iteration technique and then the outcomes are used to train artificial neural network (ANN) it is based on Levenberg Marquardt algorithm (LMA).As compared with any other ANN method, the Levenberg Marquardt algorithm based dynamic economic load dispatch is more swift and precise. The propose algorithm is tested on 9 generating unit and results are presented and discussed.

A modified crow search algorithm (MCSA) for solving economic load dispatch problem

This paper presents a novel evolutionary optimization algorithm namely the modified crow search algorithm (MCSA) for solving the non-convex economic load dispatch (ELD) problem which improves the crow search algorithm (CSA) by an innovative selection of the crows and adaptive adjustment of the flight length. MCSA is a population-based technique based on the intelligent behavior of the crows in finding food sources. In MCSA, each crow saves its food in hiding-places for the time it needs. Also, each crow searches environment to find the better foods by stealthily following other crows to discover their hiding-places. The proposed MCSA develops the search capability of crows in the original CSA and introduces a new way by which a destination is selected by a crow to follow. To indicate the applicability of MCSA in the ELD problem, it is applied on five different well-known test systems. The results are compared in terms of the solution quality, robustness, and computing time with other methods implying that the proposed method has a superior performance than the other techniques.

Hybrid artificial algae algorithm for economic load dispatch

A hybrid artificial algae algorithm (HAAA) has been proposed in this paper that hybridizes the artificial algae algorithm (AAA) and simplex search method (SSM) to solve economic load dispatch problem. The AAA simulates the life cycle of microalgae which comprises helical movement, evolutionary and adaptation phases. The helical movement phase provides the exploration while the evolutionary and adaptation phases provide the exploitation of search space. The exploration provided by the helical movement completely depends upon energy and shear-force parameters. In the proposed algorithm, the AAA acts as global optimizer while SSM provides local search. The SSM improves the exploitation capability by performing a local search. Dynamic tuning of parameters enhances the exploration capability of the proposed method. An iterative heuristic repair algorithm is applied to handle the equality constraint of economic load dispatch problem. Further, the operation in prohibited operating zones is avoided heuristically. The performance of HAAA is evaluated with CEC’05 standard test functions and small, medium and large-scale economic load dispatch problems. The simulation results advocate that the proposed algorithm produces better or comparable results than the well-established and popular algorithms. Finally, the Wilcoxon sign rank test is performed to validate the results.

Economic Power Dispatch with Emission Constraint and Valve Point Loading Effect Using Moth Flame Optimization Algorithm

Economic dispatch (ED) is an important optimization task in power system which involves determination of the optimal combination of power outputs for all generating units which will minimize the total fuel cost while satisfying load constraints. There are three criteria in solving the economic load dispatch problem. They are minimizing the total generator operating cost, total emission cost and multi-objective (cost and emission). This paper proposes Moth Flam Optimization (MFO) algorithm for solving the economic dispatch problem with valve point effects and emissions. It determines the optimal generation schedule of generating units by minimizing three criteria. Two test systems consisting of 6 generating units and isolated microgrid have been used to illustrate the effectiveness of the proposed MFO method. The results obtained from MFO is compared with different algorithms. The results show better global convergence and also gives good optimum solution by reducing system generation cost and emission cost.

Natural selection methods for artificial bee colony with new versions of onlooker bee

Artificial bee colony (ABC) algorithm is one of the most recent swarm intelligence-based algorithms simulate the foraging behavior of honey bees in their hive. ABC starts with a colony of artificial bees with sole aim of discovering the place of food sources with high nectar amount using the solution search equation in the employed bee and onlooker bee operators. However, the solution search equation is good in exploration and poor in exploitation. In this paper, the solution search equation of the onlooker bee is modified by using a value of the fittest food sources selected by a set of selection schemes inspired from the evolutionary algorithms. This is to guide the search process of onlooker bee toward the fittest food sources from the population in order to empower the exploitation capability and convergence. Four selection schemes are incorporated with the ABC algorithm to choose the fittest food sources in four versions as follows: global-best, tournament, linear rank, and exponential rank. For evaluation purposes, 10 classical benchmark optimization functions are used to study the sensitivity analysis of each ABC algorithm to its parameters. The performance of the proposed ABC versions is compared with the original ABC version in order to study the effectiveness of the modifications. In addition, a comparative evaluation of ABC algorithms is carried out against the state-of-the-art methods that worked on CEC2005 benchmark functions, CEC2015 benchmark functions, and two real-world cases of economic load dispatch problem. The experimental results show that the selection schemes incorporated within the search equation of the onlooker bee directly affects the performance of ABC algorithm.

Integration of renewable energy sources in dynamic economic load dispatch problem using an improved fireworks algorithm

In electrical power system, economic load dispatch is a generic operation for optimal sharing of generation units to meet the system load. With the rapid development of the renewable infrastructure and wide encouragement for green energy have emerged hybrid generating systems in power systems. However, there continuous ever-increasing production is creating challenges as well as implicating economic factor also in operation. A collective cost function is considered with the conventional thermal generators along with the consideration of renewable energy sources to envisage the economic factor. For these renewable sources, like wind and solar, the proportional cost, their uncertainty and variability by overestimation and underestimation cost are considered. To achieve this economic day-ahead scheduling, dynamic operation in time scale of 1 h interval is performed. The stochastic nature of wind and solar is modelled by Weibull and Beta distributions, respectively. Moreover, economic optimisation is obtained by a newly developed algorithm called improved fireworks algorithm with non-uniform operator (IFWA-NMO). This introduces adaptive dimension strategy, limiting mapping operator and non-uniform operator. The effectiveness of proposed IFWA-NMO is investigated on standard dynamic economic load dispatch (DELD) system and also employed to solve conventional DELD with wind-solar system.

Application of Firefly Optimization Technique for Solving Convex Economic Load Dispatch of Generation On Nigerian 330 kV, 24-Bus Grid System

Firefly optimization is a population based technique in which the attractiveness of a firefly is determined by its attractiveness which is then encoded as the objective function of the optimization problems. Firefly algorithm is one of the newest meta-heuristic algorithms based on the mating or flashing behavior of fireflies. Economic load dispatch of generation allocates power generation to match load demand at minimal possible cost without violating power units and system constraints. This paper presents application of firefly optimization technique (FFOT) for solving convex economic load dispatch of generation. The economic load dispatch problem was formulated to minimize the total fuel cost for the heat optimal combination of thermal generators without violating any of the system constraints using quadratic fuel cost model of Sapele, Delta, Afam and Egbin power stations as case studies. The equality and inequality constraints used on the system were the power balance equation and the transmission line constraints respectively. Firefly optimization technique was then developed using appropriate control parameters for a faster convergence of the technique. The optimization technique was tested and validated on the IEEE 30-bus system and Nigerian 24-bus system. The results obtained from the IEEE 30-bus system were compared to published results obtained via Differential Evolution (DE), Ant Colony Optimization (ACO) and Genetic Algorithm (GA). The comparison confirms the superiority, fast convergence and proficiency of the algorithm.

Application of Firefly Optimization Technique for Solving Convex Economic Load Dispatch of Generation On Nigerian 330 kV, 24-Bus Grid System

Firefly optimization is a population based technique in which the attractiveness of a firefly is determined by its attractiveness which is then encoded as the objective function of the optimization problems. Firefly algorithm is one of the newest meta-heuristic algorithms based on the mating or flashing behavior of fireflies. Economic load dispatch of generation allocates power generation to match load demand at minimal possible cost without violating power units and system constraints. This paper presents application of firefly optimization technique (FFOT) for solving convex economic load dispatch of generation. The economic load dispatch problem was formulated to minimize the total fuel cost for the heat optimal combination of thermal generators without violating any of the system constraints using quadratic fuel cost model of Sapele, Delta, Afam and Egbin power stations as case studies. The equality and inequality constraints used on the system were the power balance equation and the transmission line constraints respectively. Firefly optimization technique was then developed using appropriate control parameters for a faster convergence of the technique. The optimization technique was tested and validated on the IEEE 30-bus system and Nigerian 24-bus system. The results obtained from the IEEE 30-bus system were compared to published results obtained via Differential Evolution (DE), Ant Colony Optimization (ACO) and Genetic Algorithm (GA). The comparison confirms the superiority, fast convergence and proficiency of the algorithm.

Modified Cuckoo Search Algorithm: A Novel Method to Minimize the Fuel Cost

Economic load dispatch (ELD) is an important optimization problem for operating and controlling modern power systems, and if ELD is effectively executed, power systems work stably and economically. The main objective of this paper is to develop a novel method to solve the ELD with the purpose of minimizing the total fuel cost of all available generating units while requirements are to satisfy all constraints regarding thermal units, generators, and transmission power networks. The proposed high performance cuckoo search algorithm (HPCSA) is developed from the efficient technique for the second new solution generation of conventional cuckoo search algorithm (CCSA), called adaptive mutation technique. This proposed technique diversifies the local search ability based on a new comparison criterion. The HPCSA is verified on difference systems under special conditions, namely the 10-unit system with multi fuels, 15-unit system considering prohibited operating zones, and three IEEE systems with 30, 57, and 118 buses considering transmission power network constraints. The specific evaluation of the HPCSA is compared to that of Lagrange optimization-based methods (LMS), neural network-based methods (NNMS), CCSA, and other popular methods such as Particle swarm optimization (PSO) variants, Differential evolution (DE) variants, Genetic Algorithm (GA) variants, and state-of-the-art methods. In comparison with CCSA, the proposed method is always more effective and more robust since the proposed method can find most solutions with better quality and faster convergence speed. In comparison with LMS and NNMS, the proposed method can also find solutions with approximate or equal quality. In comparison with popular methods and state-of-the-art methods, the proposed method has more potential since it can reach faster convergence to valid solutions with approximate or better quality. Consequently, it can be concluded that the proposed HPCSA is an effective optimization tool for dealing with ELD problems.

A Solution to Non-convex/Convex and Dynamic Economic Load Dispatch Problem Using Moth Flame Optimizer

Moth flame optimization algorithm is novel nature inspired heuristic paradigm inspired by navigation method of moths in nature and based on the concept that the moth eventually converges toward the light. This paper presents the application of MFO algorithm for the solution of non-convex and dynamic economic load dispatch problem of electric power system. The performance of MFO algorithm is tested for non-convex, convex and dynamic economic load dispatch problem of seven IEEE benchmarks and the results are verified by a comparative study with lambda iteration method, particle swarm optimization algorithm, genetic algorithm (GA), artificial bee colony, evolutionary programming (EP) and grey wolf optimizer (GWO). Also, in the proposed research, the impact of renewable energy sources (i.e. wind and solar) has been taken into consideration along with conventional thermal power generating units. Also, critical analysis has been made for percentage cost saving with due consideration of solar and wind power units and it has been experimentally observed that the addition of renewable energy sources to conventional thermal power system results in significant cost saving. Comparative results show that the performance of Moth Flame Optimizer Algorithm is better than recently developed GWO algorithm and other well known heuristics and meta-heuristics search algorithms.

Implementation of Smooth and Non-Smooth Fuel Cost Function for Economic Load Dispatch using Cuckoo Search Method

Economic Load Dispatch (ELD) is an important topic in the operation of power plants which can help to build up effecting generating management plans. The ELD problem has no smooth cost function with equality and inequality constraints which make it difficult to be effectively solved. The paper presents an application of Cuckoo Search Algorithm (CSA) to solve Economic Load Dispatch (ELD) problems with smooth and non-smooth fuel cost objective functions. Main objective of ELD is to determine the most economic generating dispatch required to satisfy the predicted load demands including line losses over a certain period of time while relaxing various equality and inequality constraints. The unit Min/Max operational constraints, effects of valve-point loading ripples and line losses are considered for the practical applications. This paper describes the implementation of smooth and non smooth fuel cost function by CSA Method and its comparison with BAT method. We have used 6 and 12 bus system for calculating their total fuel cost.

A novel method to solve sustainable economic power loading dispatch problem

PurposeThe purpose of this paper is to deal with the economic requirements of power system loading dispatch and reduce the fuel cost of generation units. In order to optimize the scheduling of power load, an improved chicken swarm optimization (ICSO) is proposed to be adopted, for solving economic load dispatch (ELD) problem.Design/methodology/approachThe ICSO increased the self-foraging factor to the chicks whose activities were the highest. And the evolutionary operations of chicks capturing the rooster food were increased. Therefore, these helped the ICSO to jump out of the local extreme traps and obtain the global optimal solution. In this study, the generation capacity of the generation unit is regarded as a variable, and the fuel cost is regarded as the objective function. The particle swarm optimization (PSO), chicken swarm optimization (CSO), and ICSO were used to optimize the fuel cost of three different test systems.FindingsThe result showed that the convergence speed, global search ability, and total fuel cost of the ICSO were better than those of PSO and CSO under different test systems. The non-linearity of the input and output of the generating unit satisfied the equality constraints; the average ratio of the optimal solution obtained by PSO, CSO, and ICSO was 1:0.999994:0.999988. The result also presented the equality and inequality constraints; the average ratio of the optimal solution was 1:0.997200:0.996033. The third test system took the non-linearity of the input and output of the generating unit that satisfied both equality and inequality constraints; the average ratio was 1:0.995968:0.993564.Practical implicationsThis study realizes the whole fuel cost minimization in which various types of intelligent algorithms have been applied to the field of load economic scheduling. With the continuous evolution of intelligent algorithms, they save a lot of fuel cost for the ELD problem.Originality/valueThe ICSO is applied to solve the ELD problem. The quality of the optimal solution and the convergence speed of ICSO are better than that of CSO and PSO. Compared with PSO and CSO, ICSO can dispatch the generator more reasonably, thus saving the fuel cost. This will help the power sector to achieve greater economic benefits. Hence, the ICSO has good performance and significant effectiveness in solving the ELD problem.

Combined Economic and Emission Load Dispatch Problem Solving by ITLBO Algorithm

Recent trends in economic and emission dispatch problem which turn has to promote the rise in the number of power generating stations and their capacity of generation. The Sulphur Dioxide (S02), Nitrogen Oxides (N2O) and Carbon Dioxide (CO2) are yields the CEED problem and they are created from generation of electricity from fossil fuel. Combined economic and emission load dispatch problem is a procedure to determine the generation of electrical power isdevoted generating units in a power system so that the both total generation costand total emission of the system is minimized, while fulfilling the load demand in directly. Improved teaching learning based optimization algorithm is used to solve combined economic emission load dispatch problem with constraints in generation of power system. This method was verified by thirteen generating bus and use with different load demand and compared with other existing techniques display the advantage of the proposed algorithm. The simulation has been done in MATLAB/Simulink with required formulation and the result is gotten in graph and numerical.

Island bat algorithm for optimization

Structured population in evolutionary algorithms is a vital strategy to control diversity during the search. One of the most popular structured population strategies is the island model in which the population is divided into several sub-populations (islands). The EA normally search for each island independently. After a number of predefined iterations, a migration process is activated to exchange specific migrants between islands. Recently, bat-inspired algorithm has been proposed as a population-based algorithm to mimic the echolocation system involved in micro-bat. The main drawback of bat-inspired algorithm is its inability to preserve the diversity during the search and thus the prematurity can take place. In this paper, the strategy of island model is adapted for bat-inspired algorithm to empower its capability in controlling its diversity concepts. The proposed island bat-inspired algorithm is evaluated using 25 IEEE-CEC2005 benchmark functions with different size and complexity. The sensitivity analysis for the main parameters of island bat-inspired algorithm is well-studied to show their effect on the convergence properties. For comparative evaluation, island bat-inspired algorithm is compared with 17 competitive methods and shows very successful outcomes. Furthermore, the proposed algorithm is applied for three real-world cases of economic load dispatch problem where the results obtained prove considerable efficiency in comparison with other state-of-the-art methods.

Determination of Optimal Reserve Requirement for Fuel Cost Minimization of a Microgrid Under Load and Generation Uncertainties

In this paper, economic load dispatch (ELD) problem of a microgrid is formulated considering load and renewable generation uncertainties. Both load and generation uncertainties are modeled using triangular fuzzy numbers. The ELD problem minimizes the fuel cost of the dispatchable distributed generators (DGs) in the microgrid. The reserve requirement for generation and load uncertainties is formulated. Next, the reserve requirement for a stable transition of a grid-connected microgrid to islanded mode under load and generation uncertainties is also formulated. Moreover, the reserve requirement for a stable transition of an islanded microgrid to grid-connected mode under load and generation uncertainties is also formulated in this paper. The effects of these constraints on the daily fuel cost of dispatchable DGs are then investigated. A three-area microgrid test system is considered for the simulation. Each area in the microgrid comprises dispatchable DGs, loads, wind power DGs and solar power DGs. The economic dispatch problem is solved using four different techniques: (i) bisection method, (ii) regula falsi method, (iii) golden section method, and (iv) teaching–learning-based optimization (TLBO) technique. Simulation is carried out considering 24 h load, wind generation and solar generation profiles.