Solving Economic Load Dispatch Problem Research Articles

Economic Load Dispatch for Thermal Power Plants using Excel Solver

Economic load dispatch (ELD) is a technique used in power system operation to determine the optimal allocation of power generation among available generators to meet the system demand while minimizing the total operating cost. The goal of ELD is to achieve a balance between the demand for electricity and the supply of electricity in the most cost-effective manner. Excel Solver is one of the powerful add-in tools in Microsoft Excel which can be utilized to find global optimum solution for a given optimization problem. It allows users to find the optimal solution to a variety of problems by adjusting specific input variables within certain constraints. In this article, an optimization problem is developed for ELD and Excel Solver is proposed to find the solution. Two case studies viz. 3-unit and 10-unit system are considered and results are obtained using proposed tool. The results show that the proposed tool is effective and user-friendly for solving ELD problem. Overall, this article provides a valuable overview of Excel Solver to solve the ELD problem.

Hybrid Snake Optimizer Algorithm for Solving Economic Load Dispatch Problem with Valve Point Effect

Hybrid Snake Optimizer Algorithm for Solving Economic Load Dispatch Problem with Valve Point Effect

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

Performance of Osprey Optimization Algorithm for Solving Economic Load Dispatch Problem

The osprey optimization algorithm (OOA) is a new metaheuristic motivated by the strategy of hunting fish in seas. In this study, the OOA is applied to solve one of the main items in a power system called economic load dispatch (ELD). The ELD has two types. The first type takes into consideration the minimization of the cost of fuel consumption, this type is called ELD. The second type takes into consideration the cost of fuel consumption and the cost of emission, this type is called combined emission and economic dispatch (CEED). The performance of the OOA is compared against several techniques to evaluate its reliability. These methods include elephant herding optimization (EHO), the rime-ice algorithm (RIME), the tunicate swarm algorithm (TSA), and the slime mould algorithm (SMA) for the same case study. Also, the OOA is compared with other techniques in the literature, such as an artificial bee colony (ABO), the sine cosine algorithm (SCA), the moth search algorithm (MSA), the chimp optimization algorithm (ChOA), and monarch butterfly optimization (MBO). Power mismatch is the main item used in the evaluation of the OOA with all of these methods. There are six cases used in this work: 6 units for the ELD problem at three different loads, and 6 units for the CEED problem at three different loads. Evaluation of the techniques was performed for 30 various runs based on measuring the standard deviation, minimum fitness function, and maximum mean values. The superiority of the OOA is achieved according to the obtained results for the ELD and CEED compared to all competitor algorithms.

Enhanced Honey Badger Algorithm With Lévy Flights for Solving Economic Load Dispatch Problems

Enhanced Honey Badger Algorithm With Lévy Flights for Solving Economic Load Dispatch Problems

A hybrid Harris Hawks optimizer for economic load dispatch problems

This paper proposes a hybridized version of the Harris Hawks Optimizer (HHO) with adaptive-hill-climbing optimizer to tackle economic load dispatch (ELD) problems. ELD is an important problem in power systems that is tackled by finding the optimal schedule of the generation units that minimize fuel conceptions under a set of constraints. Due to the complexity of ELD search space, as it is rigid and deep, the exploitation of HHO is improved by hybridizing it with a recent local search method called adaptive-hill climbing. The HHO can navigate several potential search space regions, while adaptive-hill climbing is used to deeply search for the local optimal solution in each potential region. To evaluate the proposed approach, six versions of ELD cases with various complexities and constraints have been used which are the 6 generation units with 1263 MW of load demand, 13 generation units with 1800 MW of load demand, 13 generation units with 2520 MW of load demand, 15 generation units with 2630 MW of load demand, 40 generation units with 10500 MW of load demand, and 140 generation units with 49342 MW of load demand. Furthermore, the proposed algorithm is evaluated on two ELD real-world cases which are 6 units-1263 MW and 15units-2630 MW. The results show that the proposed algorithm can achieve a significant performance for the majority of the experimented cases. It can achieve the best-reported solution for the ELD case with 15 generation units when compared to 15 well-established methods. Additionally, it obtains the second-best for the ELD case with 140 generation units when compared to 10 well-established methods. In conclusion, the proposed method can be an alternative to solve ELD problems which is efficient.

Sine Cosine Algorithm for Solving Economic Load Dispatch Problem With Penetration of Renewables

Economic Load Dispatch is used to allocate power demand economically among connected generators by considering various constraints. The thermal generating units are incorporated with renewable sources like wind and solar units to reduce pollution and dependency on fuel cost. The uncertainty of output power from wind and solar plants is considered here. The 2-m point estimation method is used to get generated power from wind and solar units. The population-based Sine Cosine Algorithm is proposed to get the optimum solution of the presented complex ELD problem. The randomly placed search agents find an optimum solution according to their fitness values and keep path towards best solution attained by each search agent. The search agents avoid local optima in exploration stage and move towards the solution exploitation stage using sine and cosine functions. The proposed algorithm has been tested in various four test systems. The results proved that the proposed algorithm gives quite an effective, efficient and promising solution compared to other techniques.

Planning optimal power dispatch schedule using constrained ant colony optimization

In the modern power systems, appropriate power dispatch schedule of the online power generating units is essential for reliable and clean power supply and it is desirable to attain this at the lowest possible operating cost. Mathematical model of such an Economic Load Dispatch (ELD) problem turns out to be a complex non-convex optimization problem with practical constraints involving various factors such as, line loss, valve points effect, prohibited operating zones, ramp rate limits, system spinning reserve, multiple fuel options, etc. Nature inspired algorithms have been extensively used to solve such complex ELD problems. Through this study we propose to contribute to the available pool of efficient methodologies for solving ELD problems. Recently, Kumar et al. (2018) developed an ant colony optimization algorithm, namely ACO-LD which has shown impressive results compared to other efficient algorithms in literature when applied to a set of unconstrained optimization problems. In this study we extend ACO-LD to develop a new Constrained Ant Colony Optimization (ACO) algorithm with Adaptive Penalty (AP) method (Lemonge and Barbosa, 2014), to solve the ELD problem. The proposed algorithm is named CACO-LD-AP and is found to be quite efficient in terms of the quality of the solutions found for ELD problems of varied complexities. In order to validate the efficiency of the proposed algorithm, six power systems have been considered in this study. The performance of CACO-LD-AP is compared with various recently published state of the art algorithms for solving ELD problems. Analysis of the experimental results affirms the robustness and superiority of CACO-LD-AP over other algorithms included in this study.

Lambda Iteration and Genetic Algorithms Application to solve the Economic Load Dispatch Problem of Seven Nigerian Thermal Power Plants

Economic load dispatch (ELD) is a method of earmarking the required load demand between the existing generations in power system and principally determining allocation of generators to each generation for various systems load levels. ELD is an essential component in power system planning and operation. ELD solutions are found by solving the conventional load flow equations, while at the same time ensuring that fuel costs are minimized. There are many methods developed for solving ELD problems, but this work is restricted to two, which are the Lambda Iteration Method (LIM) and the Genetic Algorithm (GA) modified with sorting algorithm. The main objective is to apply the two methods to solve ELD problems in power system networks by comparing the performance of GA method with that of LIM in terms of fuel cost efficiency. The usefulness of LIM and GA to solving economic dispatch problem is emphasized. Simulation results obtained on this network using GA and LIM verify their effectiveness in solving ELD problems. Lastly, GA and LIM approaches have been effectively applied to the harmonization of the Nigerian 32-bus system powered by seven thermal and three hydro generating units. The study shows that GA exhibits better results than LIM from both best possible generation allocations. The results obtained demonstrate that GA based method gave better solution in terms of fuel cost reduction, when compared with those obtained using LIM. By blending the probabilities of crossover and mutation, and the application of sorting techniques, computer usage time can be significantly reduced in the system with better fuel cost reduction. Keywords: Economic load dispatch (ELD), genetic algorithm (GA), lambda iteration method (LIM), optimization, sorting algorithm . DOI: 10.7176/JETP/11-4-04 Publication date: August 31 st 2021

Economic Load Dispatch Incorporating Wind Power Using Hybrid Biogeography-Based Optimization

This article represents salp swarm algorithm (SSA) for the most favourable operating solution of economic load dispatch (ELD). For making the convergence first along with SSA, another optimization algorithm (i.e., BBO [biogeography;based optimization]) is also used. For lowering the operational cost, wind power is employed with thermal units. SSA is inspired by swarming behaviour of salp, which belongs to salpiside family. Salp possess a special kind of swarm while hunting for food and navigating. The recommended algorithm is executed on two systems of SIX units and 40 units. In both of the cases, load dispatch problem is carried out with renewable sources and also without renewable sources. Individually, BBO, SSA, and hybrid BBO-SSA are applied to all the test systems to justify effectiveness of hybrid BBO-SSA. Obtained results assure the prospective and advantages of recommended algorithm in contrast to algorithms mentioned in the article. Results come out to be very satisfying and reveal that hybrid BBO-SSA is a powerful algorithm to solve ELD problems.

Dual objective multiconstraint swarm optimization based advanced economic load dispatch

In electric power system, the vital topic to be mooted is economic load dispatch (ELD). It is a non-linear problem with some unavoidable constraints such as valve point loading and ramp rate constraint. For solving ELD problem distint methods were devised and tried for different electric supply systems yielding slow convergence rates. To achieve fast convergence, dual objective multi constraint swarm optimization based advanced economic load dispatch (DOMSOBAELD) algorithm is proposed making use of simulated values of real power outages of a thermal power plant as initial estimates for PSO technique embedded in it and used for optimizing economic dispatch problem in this article. DOMSOBAELD method was developed in the form of amalgamating fluids. Presence of power line losses, multiple valves in steam turbines, droop constraints and inhibited zones were utilized to optimize the ELD problem as genuinely approximate as possible. The results obtained from DOSOBAELD are compared with particle swarm optimization (PSO), PSOIW and differential particle swarm optimization (DPSO) techniques. It is quite conspicuous that DOMSOBAELD yielded minimum cost values with most favourable values of real unit outputs. Thus the proposed method proves to be advantageous over other heuristic methods and yields best solution for ELD by selecting incremental fuel cost as the decision variable and cost function as fitness function.

Simulated Annealing-Based Optimization (SA) Approach for Solving Economic Load Dispatch Problems

The economic dispatch problem with non smooth cost function has become a major issue with depletion of coal and increasing fuel prices. A proper schedule of available generating units may save millions of dollars per year in production cost. In this paper, Simulated Annealing Optimization (SA) algorithm is proposed for solving economic load dispatch (ELD) problems. Simulated annealing is a random-search technique which exploits an analogy between the way in which a metal cools and freezes into a minimum energy crystalline structure (the annealing process) and the search for a minimum in a more general system; it forms the basis of an optimization technique for combinatorial and other problems Simulated annealing can deal with highly nonlinear models, chaotic and noisy data and many constraints. It is a robust and general technique. Its main advantages over other local search methods are its flexibility and its ability to approach global optimality. In all cases, the proposed algorithm either matches or outperforms the solution reported for the existing algorithms. The proposed technique is also easy to implement and capable of finding feasible near global optimal solution.

An Improved Symbiosis Particle Swarm Optimization for Solving Economic Load Dispatch Problem

To realize the sustainable development of social economy, energy conservation and emission reduction has become one of the problems that must be considered in the current power system. Under the electric power market system, the economic load dispatch problem not only is important but also has practical significance and broad application prospects. In order to minimize the costs of electric-power generation, the load capacity should be reasonably assigned among many different generating sets. In this paper, an improved symbiosis particle swarm optimization algorithm was proposed, aiming at providing a better solution to this problem. First of all, a mathematical model was established with certain constraints, which successfully converted the practical problem into a mathematical one. Then, to balance the global optimization and local search capability, an improved symbiosis particle swarm optimization algorithm with mutualistic symbiosis strategy in nature was presented. The improved symbiosis particle swarm optimization algorithm consisted of three swarms inspired by the proverb “two heads are better than one,” and its specific analysis was through the standard test functions. At last, the economic load dispatch problem could be optimized by the proposed improved symbiosis particle swarm optimization algorithm. In addition, two different kinds of practical examples were also adopted for algorithm evaluation. From the simulation results, it can be seen clearly that the costs of electric-power generation gained were the lowest compared with the results of particle swarm optimization algorithm, improved chaos particle swarm optimization algorithm, and symbiotic organisms search algorithm, well demonstrating the effectiveness of the improved symbiosis particle swarm optimization algorithm in solving the economic load dispatch problem.

A New Aggrandized Class Topper Optimization Algorithm to Solve Economic Load Dispatch Problem in a Power System.

Optimization techniques are widely being used to solve large and complex economical load dispatch (ELD) and combined emission economical dispatch (CEED) problems in power systems. These techniques can solve these problems in a short computational time. In this article, a new human intelligence-based metaheuristic optimization technique, that is, aggrandized class topper optimization (CTO), is proposed to solve ELD and CEED problems. This proposed algorithm is an upgraded form of classical CTO in which the concept of remedial classes is incorporated to enhance the learning ability of weak students of a class. To validate the exploration, exploitation, convergence, and local minima avoidance capabilities of the proposed algorithm, 29 benchmark functions are considered. Furthermore, seven different test cases for the ELD problem and four test cases for a CEED problem are considered to test the effectiveness of the proposed algorithm to solve these complex problems. The result analysis proves that the proposed algorithm provides better and effective results in almost each test case.

Economic Load Dispatch With Multiple Fuel Options and Valve Point Effect Using Cuckoo Search Algorithm With Different Distributions

The cuckoo search algorithm (CSA), a new meta-heuristic algorithm based on natural phenomenon of the cuckoo species and Lévy flights random walk has been widely and successfully applied to several optimization problems so far. In the article, two modified versions of CSA, where new solutions are generated using two distributions including Gaussian and Cauchy distributions in addition to imposing bound by best solutions mechanisms are proposed for solving economic load dispatch (ELD) problems with multiple fuel options. The advantages of CSA with Gaussian distribution (CSA-Gauss) and CSA with Cauchy distribution (CSA-Cauchy) over CSA with Lévy distribution and other meta-heuristic are fewer parameters. The proposed CSA methods are tested on two systems with several load cases and obtained results are compared to other methods. The result comparisons have shown that the proposed methods are highly effective for solving ELD problem with multiple fuel options and/nor valve point effect.

A comparative study of Economic Load Dispatch with complex non-linear constraints using Salp Swarm Algorithm

Economic Load Dispatch (ELD) is an important part of cost minimization procedure in power system operation. Different derivative and probabilistic methods are used to solve ELD problems. This paper proposes a powerful Salp Swarm Algorithm (SSA) to explain the ELD issue including equality and inequality restrictions. The main aim of ELD is to satisfy the entire electric load at minimum cost. The SSA is a population based probabilistic method which guides its search agents that are randomly placed in the search space, towards an optimal point using their fitness function and also keeps a track of the best solution achieved by each search agent. SSA is being used to solve the ELD problem with their high exploration and local optima escaping technique. This algorithm confirms that the promising areas of the search space are exploited to have a smooth transition from exploration to exploitation using the movement of Salps in the sea. Simulation results prove that the proposed algorithm surpasses other existing optimization techniques in terms quality of solution obtained and computational efficiency. The final results also prove the robustness of the SSA.

Grey Wolves Optimization for Economic Load Dispatch with Practical Constraints

This paper manifests the applicability of grey wolf’s optimization (GWO) for solving economic load dispatch (ELD) problems by considering practical constraints of power generation, but effects of valve-point loading are not considered. This recommended technique is a evolutionary strategy of upgrade with fundamental structure and single control parameter to handle the complex mathematic as well as complicated engineering problems. It is a groundbreaking technique for adequately investigating the exploration and exploitation to locate the optimal solution within a low calculation time. The six generating tests-system have been utilized to exhibit the proficiency of GWO to solve ELD problem. The outcomes are contrasted with a several methods of optimization to confirm the elite of GWO for tackling the problem of ELD.

Noninferior Solution Grey Wolf Optimizer with an Independent Local Search Mechanism for Solving Economic Load Dispatch Problems

The economic load dispatch (ELD) problem is a complex optimization problem in power systems. The main task for this optimization problem is to minimize the total fuel cost of generators while also meeting the conditional constraints of valve-point loading effects, prohibited operating zones, and nonsmooth cost functions. In this paper, a novel grey wolf optimization (GWO), abbreviated as NGWO, is proposed to solve the ELD problem by introducing an independent local search strategy and a noninferior solution neighborhood independent local search technique to the original GWO algorithm to achieve the best problem solution. A local search strategy is added to the standard GWO algorithm in the NGWO, which is called GWOI, to search the local neighborhood of the global optimal point in depth and to guarantee a better candidate. In addition, a noninferior solution neighborhood independent local search method is introduced into the GWOI algorithm to find a better solution in the noninferior solution neighborhood and ensure the high probability of jumping out of the local optimum. The feasibility of the proposed NGWO method is verified on five different power systems, and it is compared with other selected methods in terms of the solution quality, convergence rate, and robustness. The compared experimental results indicate that the proposed NGWO method can efficiently solve ELD problems with higher-quality solutions.

Implementation of Improved Grasshopper Optimization Algorithm to Solve Economic Load Dispatch Problems

The costs of different fuels are increasing gradually, for operation of power production units. Thus new optimization techniques are needed to tackle the problems of Economic Load Dispatch (ELD). Metaheuristics are very helpful for policy makers in achieving the best results by minimizing the cost function. In this paper, we have updated the Grasshopper Optimization Algorithm (GOA) with a better initialization strategy to balance the search capability of GOA. The new algorithm is named as Improved Grasshopper Algorithm (IGOA). GOA is inspired by the swarms of grasshopper and mimics their biological behavior. Furthermore, IGOA is used to solve the ELD problems by tacking four case studies from literature. The objective in these problems is to find best decision variables for dispatching the available power with lowest cost, efficiency and reliability. To validate the efficiency of our proposed algorithm, we have tested it by solving 4 case studies of ELD with 1263MW, 600MW, 800MW and 2500MW demands respectively. IGOA is better in terms of convergence rate and quality of solutions obtained for the problems considered in literature for other metaheuristics.

Particle Swarm Optimization for Solving Economic Load Dispatch Problem

This work deals with the optimization of power flow through interconnected system. The work deals with efficient and reliable evolutionary based approach to solve the economic load dispatch (ELD) with line flows and voltage constraints. The work employs PSO algorithm for ELD. PSO is a robust, stochastic computational technique based on movement and intelligence of swarm. The work introduces a conceptual overview and detailed explanation of PSO algorithm as well as shows how it can be used for solving ELD problems. Inherent shortcoming of the traditional methods of finding the ELD is discussed along with other evolutionary methods of finding ELD. A comparative study of different evolutionary programming technique is done and it is shown that particle swarm optimization offer a better result with greater repeatability and lesser time. The feasibility of the proposed method is demonstrated by using a six generator interconnected system having different cost functions and voltage constraints. The results are compared with those obtained by G.A.