Optimization techniques for economic load dispatch problem in power plant

Economical dispatch of power is a significant real time optimization problem in the operation of power system, which allocates the loads on the committed generating units to reduce the generation cost, while meeting all the inequality and equality constraints. Traditionally, economic load dispatch problems have been formulated as convex optimization problem and various classical methods such as gradient methods, base-point participation factor method, etc. have been used for solving them. The traditional formulation is a quadratic input-output curve or piece wise linear cost curve, which are continuous and convex, however, real generating units have valve loading effects, which make the cost curve discontinuous and non-convex and hence the economic dispatch problem is no longer simple to handle. Thus, the classical methods cannot be employed for non-convex problems. The non-convex, non-linear and discontinuous economic dispatch (ED) problem can be better solved by metaheuristic approaches. Such approaches often require tuning of their respective evolutionary parameters. Although, solution to such type of problem have already been solved by different metaheuristic optimization techniques in previous studies as well, however, the algorithm employed in this paper to solve Power Economic Load Dispatch (PELD) problem is adaptive real coded quantum-inspired evolutionary algorithm, which does not require tuning of evolutionary parameters and performs better than some of the existing techniques on standard 6-bus 3 machine system and IEEE 14 bus 5 unit system.

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

Using suitable solution techniques to the unit commitment (UC) and economic load dispatch (ELD) problems play major role on finding an optimal power scheduling in electrical power system. The UC and ELD problems are to decide when and which generating units to commit and decommit, in order to minimize the total fuel cost over specified period subject to a large number of difficult constraints. Lagrangian relaxation (LR) has been widely used to solve UC and ELD. Recently bundling method (BM) has appeared to be one of the best multipliers updated techniques for LR. This method has promising and the fastest convergence characteristics for UC and ELD problems. For that reason, this paper is to solve the UC and ELD problems via LR, BM and interior point method. This paper explores also the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

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.

This paper is an extension made in biogeography based optimization (BBO) by modifying its migration models to make it more realistic. This BBO technique is then applied on simple economic load dispatch (ELD) problem and ELD with valve point effect to analyze the effect of different migration models. Our analysis concludes that the quadratic and sinusoidal models provide the best result for the ELD and ELD valve point effect problem respectively.

In this paper, an effective and reliable variant of particle swarm optimization with time-varying acceleration coefficients (PSO-TVAC) technique is proposed for the economic load dispatch problem considering valve-point loading effect. Main objective of the economic load dispatch (ELD) problem is to minimize the fuel cost by allocating the generation of the committed units subjected to the equality and inequality constraints. Equation of the economic dispatch objective function gets modified with the addition of a new parameter which represents the effect of valve-point loading. While exploring the use of PSO and its other variants to the economic dispatch problem, a number of research works have not considered the transmission losses properly. This paper represents the usefulness of the proposed PSO-TVAC algorithm to significantly reduce the fuel cost while taking into account the effect of transmission losses along with the non-convex characteristic due to valve loading. The results have been demonstrated for three-generator and ten-generator test systems.

Economic load dispatch can be defined as a technique of generation allocation among the units committed with an objective of fuel cost minimization by meeting the set constraints. This paper presents a novel DNLP approach using general algebraic modeling system (GAMS) software for scheduling generators for obtaining electrical power more economically. In power systems for optimal planning and efficient operation, economic load dispatch (ELD) problem is considered essential and vital. It is a highly nonlinear type of constrained optimization problem. The suggested approach is tested on three distinct well-known test systems to demonstrate its applicability in the ELD problem. In comparison with other methods for robustness, quality, and time of computation, the proposed method outperforms in all aspects. In this paper, both the losses of transmission and valve-point effects are considered for various test systems with 13, 40, and 10 generators.KeywordsEconomic load dispatchValve-point effectsTransmission line lossGeneral algebraic modeling system

An optimal solution to the unit commitment (UC) and economic load dispatch (ELD) problems lead to remarkable saving in the power system operational cost. UC and ELD main problems are to find the maximum profit and fast computation simulation time for the scheduling program. Lagrangian relaxation (LR) has become one of the best solution methods in solving the UC and ELD problems. The approach is claimed to be more efficient and easier than other methods in solving large-scale problems. When applying LR, the dual function needed to be updated at the higher level. Lately, bundling method (BM) is one of the best solution methods to Lagrangian dual problem. This paper presents LR technique, BM and interior point method for solving the UC and ELD problems. It will also explore the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

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.

Economic load dispatch is one of the vital purposes in electrical power system operation, management and planning. Economic dispatch problem is one of the most important problems in electric power system operation. In large scale system, the problem is more complex and difficult to find out optimal solution because it is nonlinear function and it contains number of local optimal. Combined economic emission dispatch (CEED) problem is to schedule the committed generating units outputs to meet the required load demand at minimum operating cost with minimum emission simultaneously. The main aim of economic load dispatch is to reduce the total production cost of the generating system and at the same time the necessary equality and inequality constraints should also be fulfilled. This leads to the development of CEED techniques. There are various techniques proposed by several researchers to solve CEED problem based on optimization techniques. But still some problems such as slower convergence and higher computational complexity exist in using the optimization techniques such as GA for solving CEED problem. This paper proposes an efficient and reliable technique for combined fuel cost economic optimization and emission dispatch using the Modified Ant Colony Optimization algorithm (MACO) to produce better optimal solution. The simulation results reveal the significant performance of the proposed MACO approach.

A social spider algorithm for solving the non-convex economic load dispatch problem

Microgrid is a novel small-scale system of the centralized electricity for a small-scale community such as villages and commercial area. Microgrid consists of micro-sources like distribution generator, solar and wind units. A microgrid is consummate specific purposes like reliability, cost reduction, emission reduction, efficiency improvement, use of renewable sources and continuous energy source. In the microgrid, the Energy Management System is having a problem of Economic Load Dispatch (ELD) and Combined Economic Emission Dispatch (CEED) and it is optimized by meta-heuristic techniques. The key objective of this paper is to solve the Combined Economic Emission Dispatch (CEED) problem to obtain optimal system cost. The CEED is the procedure to scheduling the generating units within their bounds together with minimizing the fuel cost and emission values. The newly introduced Interior Search Algorithm (ISA) is applied for the solution of ELD and CEED problem. The minimization of total cost and total emission is obtained for four different scenarios like all sources included all sources without solar energy, all sources without wind energy and all sources without solar and wind energy. In both scenarios, the result shows the comparison of ISA with the Reduced Gradient Method (RGM), Ant Colony Optimization (ACO) technique and Cuckoo Search Algorithm (CSA) for the two different cases which are ELD without emission and CEED with emission. The results are calculated for different Power Demand of 24 h. The results obtained to ISA give comparatively better cost reduction as compared with RGM, ACO and CSA which shows the effectiveness of the given algorithm.

Economic Load Dispatch (ELD) problems are nonlinear constrained problems which occupy an important role in the economic operation of power system. Recently, as an alternative to the conventional mathematical approaches, evolutionary algorithms have been given much attention by researchers due to their ability to find good solutions in ELD problems. In this paper, a biogeography based-optimization approach is validated. Biogeography is the study of the geographical distribution of biological organisms. Furthermore, a new approach of the biogeography based-optimization methodology combined with predator-prey approach were proposed and validated for two test systems consisting of 15 and 20 generation units (thermal generators), respectively. Simulation results are compared with those of other studies reported in the literature.

Hybrid artificial algae algorithm for economic load dispatch

In this study, we propose an algorithm based on a recently proposed metaheuristic called the Harris Hawk Optimization (HHO). We utilized a dynamic control strategy to enhance the exploration capability. To further avoid trapping in local optima, we incorporate opposition-based learning (OLB) and a multi-restart strategy. The proposed algorithm is used to solve economic load dispatch (ELD) problems with non-smooth cost functions. The ELD problems have a very large search space and therefore it is difficult to find global optimum using analytical methods. The results of the proposed approach are very competitive compared with notable results from previous research.