A Layered Matrix Cascade Genetic Algorithm and Particle Swarm Optimization Approach to Thermal Power Generation Scheduling

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.

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.

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

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.

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. Comparison 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.

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.

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.

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

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.

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

Hybrid artificial algae algorithm for economic load dispatch

The economic load dispatch problem is a very important practical problem in electric power systems operation, where an efficient solution can lead to cost and emissions reductions. The use of metaheuristics, as the Firefly Algorithm, for the solution of economic load dispatch problems has been shown to be a more appropriate alternative than classical optimisation methods. In this work, we have proposed a new variant for the Firefly Algorithm, considering a non-homogeneous population. This new variant was validated using ten benchmark functions, and then applied to solve a 15-units economic load dispatch problem, considering transmission line losses, power limits, ramp limits and prohibited zones for each generator, and a 13-units non-convex system with valve-point loading effect in the cost function and power generation limits. The results show that the proposed non-homogeneous variant is able to reach better solutions than the original Firefly Algorithm, using both penalty and non-penalty power balance constraint handling methods. In general, the non-penalty approach reached better results than the penalty method. Moreover, the new variant presented relatively competitive results for the economic load dispatch problems considered, when compared to the best results found in the literature.

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.

Electric power system problems are amongst the most complex and challenging problems of electric industry market. The main aim of economic load dispatch in power system operation control and planning is to satisfy the energy demand at the least cost while fulfilling all the equality and inequality constraints. This paper presents the mathematical formulation of optimal load dispatch problem by considering the sources of energy generation from conventional power plants and all the important constraints of the realistic power system. In the proposed research the memetic optimizer is developed by hybridizing slime mould algorithm with pattern search algorithm. The proposed hSMA-PS has been tested to obtain the solution of economic load dispatch problem and experimentally it has been observed that the proposed memetic optimizer is providing cost effective solution to complex economic load dispatch problem of electric power system.