Modeling of Combined Economic and Emission Dispatch Using Improved Sand Cat Optimization Algorithm

Combined Economic and Emission Dispatch(CEED)task forms multi-objective optimization problems to be resolved to minimize emission and fuel costs.The disadvantage of the conventional method is its incapability to avoid falling in local optimal,particularly when handling nonlinear and complex systems.Metaheuristics have recently received considerable attention due to their enhanced capacity to prevent local optimal solutions in addressing all the optimization problems as a black box.Therefore,this paper focuses on the design of an improved sand cat optimization algorithm based CEED(ISCOA-CEED)technique.The ISCOA-CEED technique majorly concen-trates on reducing fuel costs and the emission of generation units.Moreover,the presented ISCOA-CEED technique transforms the equality constraints of the CEED issue into inequality constraints.Besides,the improved sand cat optimization algorithm(ISCOA)is derived from the integration of tra-ditional SCOA with the Levy Flight(LF)concept.At last,the ISCOA-CEED technique is applied to solve a series of 6 and 11 generators in the CEED issue.The experimental validation of the ISCOA-CEED technique ensured the enhanced performance of the presented ISCOA-CEED technique over other recent approaches.

Combined Economic and Emission Power Dispatch Control Using Substantial Augmented Transformative Algorithm

The purpose of the Combined Economic Emission Dispatch(CEED)of electric power is to offer the most exceptional schedule for production units,which must run with both low fuel costs and emission levels concurrently,thereby meeting the lack of system equality and inequality constraints.Economic and emissions dispatching has become a primary and significant concern in power system networks.Consequences of using non-renewable fuels as input to exhaust power systems with toxic gas emissions and depleted resources for future generations.The optimal power allocation to generators serves as a solution to this problem.Emission dispatch reduces emissions while ignoring economic considerations.A collective strategy known as Combined Economic and Emission Dispatch is utilized to resolve the above-mentioned problems and investigate the trade-off relationship between fuel cost and emissions.Consequently,this work manages the Substantial Augmented Transformative Algorithm(SATA)to take care of the Combined Economic Emission Dispatch Problem(CEEDP)of warm units while fulfilling imperatives,for example,confines on generator limit,diminish the fuel cost,lessen the emission and decrease the force misfortune.SATA is a stochastic streamlining process that relies upon the development and knowledge of swarms.The goal is to minimize the total fuel cost of fossil-based thermal power generation units that generate and cause environmental pollution.The algorithm searches for solutions in the search space from the smallest to the largest in the case of forwarding search.The simulation of the proposed system is developed using MATLAB Simulink software.Simulation results show the effectiveness and practicability of this method in terms of economic and emission dispatching issues.The performance of the proposed system is compared with existing Artificial Bee Colony-Particle Swarm Optimization(ABC-PSO),Simulated Annealing(SA),and Differential Evolution(DE)methods.The fuel cost and gas emission of the proposed system are 128904$/hr and 138094.4652$/hr.

Black Widow Optimization for Multi Area Economic Emission Dispatch

The optimizationfield has grown tremendously,and new optimization techniques are developed based on statistics and evolutionary procedures.There-fore,it is necessary to identify a suitable optimization technique for a particular application.In this work,Black Widow Optimization(BWO)algorithm is intro-duced to minimize the cost functions in order to optimize the Multi-Area Economic Dispatch(MAED).The BWO is implemented for two different-scale test systems,comprising 16 and 40 units with three and four areas.The performance of BWO is compared with the available optimization techniques in the literature to demonstrate the strategy’s efficacy.Results show that the optimized cost for four areas with 16 units is found to be 7336.76$/h,whereas it is 121,589$/h for four areas with 40 units using BWO.It is also noted that optimization algo-rithms other than BWO require higher cost value.The best-optimized solution for emission is achieved at 9.2784e+06 tones/h,and it is observed that there is a considerable difference between the worst and the best values.Also,the suggested technique is implemented for large-scale test systems successfully with high precision,and rapid convergence occurs in MAED.

A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem

This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.

Finite-time economic model predictive control for optimal load dispatch and frequency regulation in interconnected power systems

This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.

Modified Shuffled Frog Leaping Algorithm for Solving Economic Load Dispatch Problem

In the recent restructured power system scenario and complex market strategy, operation at absolute minimum cost is no longer the only criterion for dispatching electric power. The economic load dispatch (ELD) problem which accounts for minimization of both generation cost and power loss is itself a multiple conflicting objective function problem. In this paper, a modified shuffled frog-leaping algorithm (MSFLA), which is an improved version of memetic algorithm, is proposed for solving the ELD problem. It is a relatively new evolutionary method where local search is applied during the evolutionary cycle. The idea of memetic algorithm comes from memes, which unlike genes can adapt themselves. The performance of MSFLA has been shown more efficient than traditional evolutionary algorithms for such type of ELD problem. The application and validity of the proposed algorithm are demonstrated for IEEE 30 bus test system as well as a practical power network of 203 bus 264 lines 23 machines system.

Multiple objective particle swarm optimization technique for economic load dispatch

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Com- parison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

Comparison between dynamic programming and genetic algorithm for hydro unit economic load dispatch

The hydro unit economic load dispatch （ELD） is of great importance in energy conservation and emission reduction. Dynamic programming （DP） and genetic algorithm （GA） are two representative algorithms for solving ELD problems. The goal of this study was to examine the performance of DP and GA while they were applied to ELD. We established numerical experiments to conduct performance comparisons between DP and GA with two given schemes. The schemes included comparing the CPU time of the algorithms when they had the same solution quality, and comparing the solution quality when they had the same CPU time. The numerical experiments were applied to the Three Gorges Reservoir in China, which is equipped with 26 hydro generation units. We found the relation between the performance of algorithms and the number of units through experiments. Results show that GA is adept at searching for optimal solutions in low-dimensional cases. In some cases, such as with a number of units of less than 10, GA＇s performance is superior to that of a coarse-grid DP. However, GA loses its superiority in high-dimensional cases. DP is powerful in obtaining stable and high-quality solutions. Its performance can be maintained even while searching over a large solution space. Nevertheless, due to its exhaustive enumerating nature, it costs excess time in low-dimensional cases.

Economic Load Dispatch with Daily Load Patterns Using Particle Swarm Optimization

ELD （economic load dispatch） problem is one of the essential issues in power system operation. The objective of solving ELD problem is to allocate the generation output of the committed generating units. The main contribution of this work is to solve the ELD problem concerned with daily load pattern. The proposed solution technique, developed based PSO （particle swarm optimization） algorithm, is applied to search for the optimal schedule of all generations units that can supply the required load demand at minimum fuel cost while satisfying all unit and system operational constraints. The performance of the developed methodology is demonstrated by case studies in test system of six-generation units. The results obtained from the PSO are compared to those achieved from other approaches, such as QP （quadratic programming）, and GA （genetic algorithm）.

A Multi-Agent Particle Swarm Optimization for Power System Economic Load Dispatch

A new versatile optimization, the particle swarm optimization based on multi-agent system (MAPSO) is presented. The economic load dispatch (ELD) problem of power system can be solved by the algorithm. By competing and cooperating with the randomly selected neighbors, and adjusting its global searching ability and local exploring ability, this algorithm achieves the goal of high convergence precision and speed. To verify the effectiveness of the proposed algorithm, this algorithm is tested by three different ELD cases, including 3, 13 and 40 units IEEE cases, and the experiment results are compared with those tested by other intelligent algorithms in the same cases. The compared results show that feasible solutions can be reached effectively, local optima can be avoided and faster solution can be applied with the proposed algorithm, the algorithm for ELD problem is versatile and efficient.

Economic Load Dispatch Based on Efficient Population Utilization Strategy for Particle Swarm Optimization

In this paper, the efficient population utilization strategy for particle swarm optimization (EPUSPSO) is proposed to solve the economic load dispatch (ELD) problem of power system. This algorithm improves the accuracy and the speed of its convergence by changing the number of particles effectively, and improving the velocity equation and position equation. In order to verify the effectiveness of the algorithm, this algorithm is tested in three different ELD cases of power system include IEEE 3-unit case, 13-unit case, and 40-unit case, and the obtained results are compared with those obtained from other algorithms using the same system parameters. The compared results show that the algorithm can find the optimal solution effectively and accurately, and avoid falling into the local optimal problem;meanwhile, faster speed can be ensured in the case.

A Novel Solution Based on Differential Evolution for Short-Term Combined Economic Emission Hydrothermal Scheduling

This paper presents a novel approach based on differential evolution for short-term combined economic emission hydrothermal scheduling, which is formulated as a bi-objective problem: 1) minimizing fuel cost and 2) minimizing emission cost. A penalty factor approach is employed to convert the bi-objective problem into a single objective one. In the proposed approach, heuristic rules are proposed to handle water dynamic balance constraints and heuristic strategies based on priority list are employed to repair active power balance constraints violations. A feasibility-based selection technique is also devised to handle the reservoir storage volumes constraints. The feasibility and effectiveness of the proposed approach are demonstrated and the test results are compared with those of other methods reported in the literature. Numerical experiments show that the proposed method can obtain better-quality solutions with higher precision than any other optimization methods. Hence, the proposed method can well be extended for solving the large-scale hydrothermal sched-uling.

An Efficient Multi-objective Approach Based on Golden Jackal Search for Dynamic Economic Emission Dispatch

Dynamic Economic Emission Dispatch(DEED)aims to optimize control over fuel cost and pollution emission,two conflicting objectives,by scheduling the output power of various units at specific times.Although many methods well-performed on the DEED problem,most of them fail to achieve expected results in practice due to a lack of effective trade-off mechanisms between the convergence and diversity of non-dominated optimal dispatching solutions.To address this issue,a new multi-objective solver called Multi-Objective Golden Jackal Optimization(MOGJO)algorithm is proposed to cope with the DEED problem.The proposed algorithm first stores non-dominated optimal solutions found so far into an archive.Then,it chooses the best dispatching solution from the archive as the leader through a selection mechanism designed based on elite selection strategy and Euclidean distance index method.This mechanism can guide the algorithm to search for better dispatching solutions in the direction of reducing fuel costs and pollutant emissions.Moreover,the basic golden jackal optimization algorithm has the drawback of insufficient search,which hinders its ability to effectively discover more Pareto solutions.To this end,a non-linear control parameter based on the cosine function is introduced to enhance global exploration of the dispatching space,thus improving the efficiency of finding the optimal dispatching solutions.The proposed MOGJO is evaluated on the latest CEC benchmark test functions,and its superiority over the state-of-the-art multi-objective optimizers is highlighted by performance indicators.Also,empirical results on 5-unit,10-unit,IEEE 30-bus,and 30-unit systems show that the MOGJO can provide competitive compromise scheduling solutions compared to published DEED methods.Finally,in the analysis of the Pareto dominance relationship and the Euclidean distance index,the optimal dispatching solutions provided by MOGJO are the closest to the ideal solutions for minimizing fuel costs and pollution emissions simultaneously,compared to the latest published DEED solutions.

Data-driven Surrogate-assisted Method for High-dimensional Multi-area Combined Economic/Emission Dispatch

Multi-area combined economic/emission dispatch(MACEED)problems are generally studied using analytical functions.However,as the scale of power systems increases,ex isting solutions become time-consuming and may not meet oper ational constraints.To overcome excessive computational ex pense in high-dimensional MACEED problems,a novel data-driven surrogate-assisted method is proposed.First,a cosine-similarity-based deep belief network combined with a back-propagation(DBN+BP)neural network is utilized to replace cost and emission functions.Second,transfer learning is applied with a pretraining and fine-tuning method to improve DBN+BP regression surrogate models,thus realizing fast con struction of surrogate models between different regional power systems.Third,a multi-objective antlion optimizer with a novel general single-dimension retention bi-objective optimization poli cy is proposed to execute MACEED optimization to obtain scheduling decisions.The proposed method not only ensures the convergence,uniformity,and extensibility of the Pareto front,but also greatly reduces the computational time.Finally,a 4-ar ea 40-unit test system with different constraints is employed to demonstrate the effectiveness of the proposed method.

Cuckoo Search for Solving Economic Dispatch Load Problem

Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. In this paper, two test systems of the ELD problems are solved by adopting the Cuckoo Search (CS) Algorithm. A comparison of obtained simulation results by using the CS is carried out against six other swarm intelligence algorithms: Particle Swarm Optimization, Shuffled Frog Leaping Algorithm, Bacterial Foraging Optimization, Artificial Bee Colony, Harmony Search and Firefly Algorithm. The effectiveness of each swarm intelligence algorithm is demonstrated on a test system comprising three-generators and other containing six-generators. Results denote superiority of the Cuckoo Search Algorithm and confirm its potential to solve the ELD problem.

CSO Algorithm for Economic Dispatch Decision of Hybrid Generation System

The aim of this research is to study the optimal economic dispatch （ED） through Cat Swarm Optimization （CSO） algorithm. Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the CSO can, therefore, be effectively applied to different optimization problems. In this paper, the CSO is also extended to coordinate wind and thermal dispatch and to minimize total generation cost. Results indicated that the CSO is superior to PSO in the fast convergence and better performance to find the global best solution.

Sequential Approach with Matrix Framework for Various Types of Economic Thermal Power Dispatch Problems

This paper presents a sequential approach with matrix framework for solving various kinds of economic dispatch problems. The objective of the economic dispatch problems of electrical power generation is to schedule the committed generating units output so as to meet the required load demand while satisfying the system equality and inequality constraints. This is a maiden approach developed to obtain the optimal dispatches of generating units for all possible load demands of power system in a single execution. The feasibility of the proposed method is demonstrated by solving economic load dispatch problem, combined economic and emission dispatch problem, multiarea economic dispatch problem and economic dispatch problem with multiple fuel options. The proposed methodology is tested with different scale of power systems. The generating unit operational constraints are also considered. The simulation results obtained by proposed methodology for various economic dispatch problems are compared with previous literatures in terms of solution quality. Numerical simulation results indicate an improvement in total cost saving and hence the superiority of the proposed method is also revealed for economic dispatch problems.

Economic Dispatch with Multiple Fuel Options Using CCF

This paper presents an efficient analytical approach using Composite Cost Function (CCF) for solving the Economic Dispatch problem with Multiple Fuel Options (EDMFO). The solution methodology comprises two stages. Firstly, the CCF of the plant is developed and the most economical fuel of each set can be easily identified for any load demand. In the next stage, for the selected fuels, CCF is evaluated and the optimal scheduling is obtained. The Proposed Method (PM) has been tested on the standard ten-generation set system;each set consists of two or three fuel options. The total fuel cost obtained by the PM is compared with earlier reports in order to validate its effectiveness. The comparison clears that this approach is a promising alterna-tive for solving EDMFO problems in practical power system.

Addressing Economic Dispatch Problem with Multiple Fuels Using Oscillatory Particle Swarm Optimization

Economic dispatch has a significant effect on optimal economical operation in the power systems in industrial revolution 4.0 in terms of considerable savings in revenue.Various non-linearity are added to make the fossil fuel-based power systems more practical.In order to achieve an accurate economical schedule,valve point loading effect,ramp rate constraints,and prohibited operating zones are being considered for realistic scenarios.In this paper,an improved,and modified version of conventional particle swarm optimization(PSO),called Oscillatory PSO(OPSO),is devised to provide a cheaper schedule with optimum cost.The conventional PSO is improved by deriving a mechanism enabling the particle towards the trajectories of oscillatory motion to acquire the entire search space.A set of differential equations is implemented to expose the condition for trajectory motion in oscillation.Using adaptive inertia weights,this OPSO method provides an optimized cost of generation as compared to the conventional particle swarm optimization and other new meta-heuristic approaches.

Economic Dispatch with Convex and Non-Convex Fuel Cost Functions Including Line Losses Using Pattern Search

This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is to determine the most economic generating dispatch required to satisfy the predicted load demands including line losses. Relaxing various equality and inequality constraints are considered. The unit operation minhnum/maximum constraints, effects of valve-point and line losses are considered for the practical applications. Several case studies were tested and verified, which indicate an improvement in total fuel cost savings. The robustness of the proposed PS method have been assessed and investigated through intensive comparisons with reported results in recent researches. The results are very encouraging and suggesting that PS may be very useful tool in solving power system ELD problems.