A Deep Neural Network Approach for Optimizing Economic Load Dispatch in Power Systems

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

Fossil fuel is considered to be the primary power generation source. As this source is not that eco- and environmentally friendly, researchers are constantly searching for an alternative source for power generation. Renewable energy has drawn much attention in this regard in recent times. For solving economic load dispatch issues, numerous operational constraints must be considered. Due to the restructuring of the power sector, there is competition between different power systems organizations. Increasing fossil fuel costs drive power-producing utilities to adopt a cost-effective technique for dispatching actual power output. Due to the presence of nonlinearity and non-convexity in the fuel of cost function of generators, the economic load dispatch is often considered a complex optimization problem. Many researchers have been optimizing fuel costs to solve the economic power dispatch problem. This paper offers a critical analysis of ELD that takes into account both traditional and non-traditional energy sources. The review covers a variety of algorithms, including hybrid algorithms for integrating renewable energy sources (RES). The paper also focuses on several restricted optimization techniques and contemporary algorithms including PSO, Jaya, GWO, SMO, TLBO, Rao, MRao-2, and MFO to reduce the fuel cost of generation units using large-scale solar PV. Moreover, this paper provides a comprehensive overview of the current state of economic load dispatch and provides valuable insights for electricity researchers and practitioners. It also discusses future technologies and next steps in the field of ELD, emphasizing the need for more environmentally friendly and cost-effective power generation and distribution solutions. Overall, the paper demonstrates the benefits of renewable energy sources as well as optimization techniques for creating a more sustainable and efficient power generation system.

Economic Load Dispatch (ELD) optimization is an important and difficult task in power system planning. Previously, most of the research mainly focused on proposing various evolutionary algorithms (EAs) to pursue better results of ELD problems. However, few comprehensive analysis of the effects of various constraint handling techniques (CHTs) on the performance of EA-based techniques are available so far. In this paper, we try to fill this gap by experimentally testing the algorithmic variants of combining four effective and widely used EAs with three CHTs. From the experimental results on the ELD problems with valve-point and those problems with both valve-point and multiple-fuel effect, several important conclusions can be achieved, including 1) for the low scale ELD problem with valve-point only, the selection of EAs is more important than CHTs; 2) for the large scale problems, CHTs play crucial roles; 3) the appropriate combination of EA and CHT is helpful to achieve better performance. This study is also expected to provide solid basis for further strengthening the robustness of EAs for ELD optimization. It is also interesting to observe that the experimental results obtained in this paper are much better than those of the previous effective ELD optimization algorithms.

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.

The growing incidence of thermal power generation plants and strict environmental laws have constituted the Economic Emission Load Dispatch (EELD) issue into a challenging problem in contemporary power systems operation. This issue comprises the strategy of reducing the cost of fuel and pollutant emission at the same time and meeting the power balance within the system and the operating limits of the generator as well as the transmission losses. Due to the nonlinearity and conflict of these aims, the traditional single-objective optimization methods do not give flexible and environmentally sustainable solutions. An Interactive Fuzzy Goal Programming (IFGP) methodology is suggested in this work to be used to solve the multi-objective EELD problem. The technique converts the economic and emission targets to fuzzy target in terms of linear membership functions based on the ideal and anti-ideal solutions. This is an interactive decision-making mechanism, which enables the levels of aspiration to be updated stochastically until a satisfying compromise solution has been reached. The approach suggested is verified on three generators thermal power system where the transmission losses are modeled using B-coefficients. Extensive graphical explanations such as cost and emission change with demand of load, trade-off properties, and relative comparison with classical Economic Load Dispatch (ELD), are given. The findings indicate a high level of emission reduction by the IFGP approach at a small cost addition to fuel as opposed to traditional ELD. The suggested framework has increased flexibility, clear sightedness, and decision support and is thus a great fit to sustainable and viable power system planning and operation.

Economic dispatch in wind-integrated power systems is a critical challenge, yet many recent metaheuristics suffer from premature convergence, heavy parameter tuning, and limited ability to escape local optima in non-smooth valve-point landscapes. This study proposes a new hybrid optimization framework, the Fractional Grasshopper Optimization algorithm (FGOA), which integrates fractional-order calculus into the standard Grasshopper Optimization algorithm (GOA) to enhance its search efficiency. The FGOA method is applied to the economic load dispatch (ELD) problem, a nonlinear and nonconvex task that aims to minimize fuel and wind-generation costs while satisfying practical constraints such as valve-point loading effects (VPLEs), generator operating limits, and the stochastic behavior of renewable energy sources. Owing to the increasing role of wind energy, stochastic wind power is modeled through the incomplete gamma function (IGF). To further improve computational accuracy, FGOA is hybridized with Sequential Quadratic Programming (SQP), where FGOA provides global exploration and SQP performs local refinement. The proposed FGOA-SQP approach is validated on systems with 3, 13, and 40 generating units, including mixed thermal and wind sources. Comparative evaluations against recent metaheuristic algorithms demonstrate that FGOA-SQP achieves more accurate and reliable dispatch outcomes. Specifically, the proposed approach achieves fuel cost reductions ranging from 0.047% to 0.71% for the 3-unit system, 0.31% to 27.25% for the 13-unit system, and 0.69% to 12.55% for the 40-unit system when compared with state-of-the-art methods. Statistical results, particularly minimum fitness values, further confirm the superior performance of the FGOA-SQP framework in addressing the ELD problem under wind power uncertainty.

The Economic Load Dispatch (ELD) is considered to minimize the only fuel cost in power system planning and operation. Due to environmental issues, the emission amount released by thermal power generation should be considered in minimizing the total cost generation as well. This make the power dispatch problem become multi-objective problem that called Economic and Emission Load Dispatch (EELD). This paper investigates the performances of Artificial Bee colony (ABC) algorithm for determining optimal solution for EELD problem. In this paper, the EELD problem is formulated as a single objective problem by taking minimization of total cost and emission level as separated objective. The cost characteristic of thermal generator considered the effect of opening and closing of the valve for practical application. The ABC algorithm has been tested on standard test systems which is 10-generating unit test system in order to validate the effectiveness of proposed ABC algorithm. The results obtained have been compared with reported result by other methods in literature. From the result, it found that ABC algorithm is better than other methods for minimizing fuel cost of thermal power generation and obtained comparative results in reducing the emission level.

ABSTRACTThe novelty behind this research is to develop enhanced models for real‐time power system monitoring in a platform‐independent and distributed platform. Distributed models for power system applications have been implemented using Remote Method Invocation (RMI), Common object Request Broker Architecture and. NET remoting technologies. The interoperability among the heterogeneous power system clients in a distributed platform has been achieved through XMLization of power system data which provides meaningful solution to the legacy issues associated with power systems. A RMI‐based model for real‐time power system monitoring in a distributed platform had been implemented and discussed in detail. A component model for real‐time power system monitoring has also been proposed and implemented to increase the reusability and scalability of the system. A location transparent model has been developed using Common object Request Broker Architecture with RMI‐Internet Inter‐Orb Protocol for load flow monitoring and the idea is extended to solve real‐time economic load dispatch and dynamic security monitoring. The detailed monitoring on performance of the proposed models has been done with load flow monitoring, dynamic security monitoring and economic load dispatch problems. A. NET remoting architectural model has been developed for real‐time economic load dispatch in a distributed platform. This research paper explores various issues in deploying power system applications in a distributed platform. It will serve the purpose of stimulating interest among power engineers and also will be extremely useful for electric power utilities.

This paper presents using the Bees algorithm approach to multi-objective optimal economic dispatch of electrical power systems. The generation of electricity from the fossil fuel releases several contaminants, such as sulfur oxides, nitrogen oxides and carbon dioxide, into the atmosphere. Genetic algorithmic approach to power system optimization, as reported here for a case of economic power dispatch, consists essentially of minimizing the objective function while gradually satisfying the constraint relations. In the Multi-objective problem formulation, four important non-commensurable objectives in an electrical thermal power system are considered. These are economy and environmental impacts because of NOx, SO2, CO2 emissions. The suitability of the proposed approach is described to multiobjective optimal economic dispatch of electrical power systems.

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.

The primary goal of any electric power generation system is to provide a sufficient amount of electricity to consumers without jeopardizing the system's economic viability. The modernization of the power grid has resulted in a significant rise in power demand, which has increased the cost of producing electrical energy. When the cost of output rises, so does the cost of transferring energy to the end consumer. As a result, the output of energy at various stages of a power system must be optimized. As a result, the cost per unit of thermal energy output is reduced while load demand requirements and transmission losses are maintained. These complex non-linear quadratic functions with Multiple Fuels lead to a non-Convex problem for steam thermal generating systems, according to previous studies. Perfect Economic Load Dispatch (ELD) modelling for steam thermal generating units is possible with multiple fuels. Because acute variations and disruptions in the incremental cost function are possible, it is difficult to simplify the non-convex problem using existing techniques. Oppositional Teaching Learning Based Optimization (OTLBO) is used to address the ELD problem in this research. Under various load demands, the proposed solution was applied to a 6-unit test system, a 10-unit test system, and a 14-unit test system, and the results were evaluated using the Teaching Learning Based Optimization (TLBO) algorithm.

Guest Editorial: Situational awareness of integrated energy systems

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.

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

Economic load dispatch is one of the optimization problems in power systems. This paper presents an improved genetic algorithm for economic load dispatch with valve-point loadings. New crossover and mutation operations are introduced. The solutions of the economic load dispatch with valve-point loadings under three cases are solved by the improved genetic algorithm. Test results are given and compared with those from different published genetic algorithms. It is shown that the proposed improved genetic algorithm performs better than the published genetic algorithms.