Solution of Different Types of Economic Load Dispatch Problems Using a Pattern Search Method

Direct search (DS) methods are evolutionary algorithms used to solve constrained optimization problems. DS methods do not require information about the gradient of the objective function when searching for an optimum solution. One such method is a pattern search (PS) algorithm. This study presents a new approach based on a constrained PS algorithm to solve various types of power system economic load dispatch (ELD) problems. These problems include economic dispatch with valve point (EDVP) effects, multi-area economic load dispatch (MAED), companied economic-environmental dispatch (CEED), and cubic cost function economic dispatch (QCFED). For illustrative purposes, the proposed PS technique has been applied to each of the above dispatch problems to validate its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method has been assessed and investigated through comparison with results reported in literature. The outcome is very encouraging and suggests that PS methods may be very efficient when solving power system ELD problems

An alternative method to solve combined economic emission dispatch problems using flower pollination algorithm

Flower Pollination Algorithm (FPA) is a new biologically inspired meta-heuristic optimization technique based the pollination process of flowers. FPA mimics the flower pollination characteristics in order to survival by the fittest. This research presents implementation of FPA optimization in solving Combined Economic Emission Dispatch (CEED) problems in power system which minimize total generation cost by minimizing fuel cost and emission. Increasing in power demand requires effective solution to provide sufficient electricity to customer with minimum cost of operation at the same time considering emission. CEED actually is a multi-objective problem and need complex programming to solve it. The problem becomes complicated when there is practical constraints to be considered as well. To simplify the programming, objective of economic dispatch (ED) and emission dispatch (EmD) are combined into a single function by price penalty factor and analysed using weighted sum method to choose the best compromising result. In this research, the valve point loading effect problem in power system also will be considered. The proposed algorithm are tested on four different test systems which are: 6-generating unit and 11-generating unit without valve point effect with no transmission loss, 10-generating unit with having valve point effect and transmission loss, and lastly 40-generating unit with having valve point effect without transmission loss. The results of these four different test cases were compared with the optimization techniques reported in recent literature in order to observe the effectiveness of FPA. Result shows FPA able to perform better than other algorithms by having minimum fuel cost and emission

An Evolutionary Computational Approach for the Problem of Unit Commitment and Economic Dispatch in Microgrids under Several Operation Modes

In the last decades, new types of generation technologies have emerged and have been gradually integrated into the existing power systems, moving their classical architectures to distributed systems. Despite the positive features associated to this paradigm, new problems arise such as coordination and uncertainty. In this framework, microgrids constitute an effective solution to deal with the coordination and operation of these distributed energy resources. This paper proposes a Genetic Algorithm (GA) to address the combined problem of Unit Commitment (UC) and Economic Dispatch (ED). With this end, a model of a microgrid is introduced together with all the control variables and physical constraints. To optimally operate the microgrid, three operation modes are introduced. The first two attend to optimize economical and environmental factors, while the last operation mode considers the errors induced by the uncertainties in the demand forecasting. Therefore, it achieves a robust design that guarantees the power supply for different confidence levels. Finally, the algorithm was applied to an example scenario to illustrate its performance. The achieved simulation results demonstrate the validity of the proposed approach.Ministerio de Ciencia, Innovación y Universidades TEC2016-80242-PMinisterio de Economía y Competitividad PCIN-2015-043Universidad de Sevilla Programa propio de I+D+

Application of Firefly Algorithm for Combined Economic Load and Emission Dispatch

This paper presents an application of Firefly algorithm for multi-objective optimization problem in power system. By economic load scheduling the generations of different plants can be determined such that the total operating cost is minimum. Considering the environmental impacts that grow from the emissions produced by fossil fuelled power plant, the economic dispatch that minimizes only the total fuel cost can no longer be considered as single objective. Application of Firefly algorithm in this paper is based on mathematical modelling to solve combined economic and emissions dispatch problems by a single equivalent objective function. Firefly algorithm has been applied to two realistic systems at different load conditions. Results obtained with proposed method are compared with other techniques presented in literature. Firefly algorithm is easy to implement and much superior to other algorithms in terms of accuracy and efficiency

Hybrid method for achieving Pareto front on economic emission dispatch

In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multi-objective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II

Modified sub-gradient based combined objective technique and evolutionary programming approach for economic dispatch involving valve-point loading, enhanced prohibited zones and ramp rate constraints

A security constrained non-convex power dispatch problem with prohibited operation zones and ramp rates is formulated and solved using an iterative solution method based on the feasible modified sub-gradient algorithm (FMSG). Since the cost function, all equality and inequality constraints in the nonlinear optimization model are written in terms of the bus voltage magnitudes, phase angles, off-nominal tap settings, and the Susceptance values of static VAR (SVAR) systems, they can be taken as independent variables. The actual power system loss is included in the current approach and the load flow equations are inserted into the model as the equality constraints. The proposed modified sub gradient based combined objective technique and evolutionary programming approach (MSGBCAEP) with as decision variable and cost function as fitness function is tested on the IEEE 30-bus 6 generator test case system. The absence of crossover operation and adoption of fast judicious modifications in initialization of parent population, offspring generation and normal distribution curve selection in EP enables the proposed MSGBCAEP approach to ascertain global optimal solution for cost of generation and emission level shown in Table 6 and displayed in Figure 2 and Figure 3 respectively

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