Valve Point Loading Effect Research Articles

Environmental and economic power dispatch of thermal generators using modified NSGA-II algorithm

This paper presents the solution to the problem in fabricating Environmental and Economic Power Dispatch (EEPD) of thermal generators with valve-point loading effect and multiple prohibited operating zones (POZ). The valve-point effect introduces ripples in the input–output characteristics of generating units, and the existence of POZ breaks the operating region of a generating unit into isolated sub-regions, thus forms a nonconvex decision space. The EEPD problem becomes a nonsmooth optimization problem because of these valve-point effect and POZ. Accuracy of the solution for a practical system is improved by considering the nonlinearities of valve-point loading effect and multiple POZ in the EEPD problem. The multi-objective evolutionary algorithms, namely non-dominated sorting genetic algorithm-II (NSGA-II) and modified NSGA-II (MNSGA-II) have been applied for solving the multi-objective nonlinear optimization EEPD problem. To improve the uniform distribution of non-dominated solutions, dynamic crowding distance is considered in the NSGA-II and developed MNSGA-II. These multi-objective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus and IEEE 118-bus test systems. Real-coded genetic algorithm is used to generate reference Pareto-front, which is used to compare with the Pareto front obtained using NSGA-II and MNSGA-II. Numerical results reveal that MNSGA-II is effectively capable for appreciable performance than NSGA-II to solve the different power system nonsmooth EEPD problem. Moreover, three different performance metrics such as convergence, diversity and Inverted Generational Distance are calculated for the evaluation of closeness of obtained Pareto fronts to the reference Pareto-front. In addition, an approach based on Technique for ordering Preferences by Similarity to Ideal Solution is applied to extract best compromise solution from the obtained non-domination solutions. Copyright © 2014 John Wiley & Sons, Ltd.

Solution to economic dispatch problem with valve-point loading effect by using catfish PSO algorithm

This paper proposes application of a catfish particle swarm optimization (PSO) algorithm to economic dispatch (ED) problems. The ED problems considered in this paper include valve-point loading effect, power balance constraints, and generator limits. The conventional PSO and catfish PSO algorithms are applied to three different test systems and the solutions obtained are compared with each other and with those reported in literature. The comparison of solutions shows that catfish PSO outperforms the conventional PSO and other methods in terms of solution quality though there is a slight increase in computational time.

Chemical reaction optimisation for different economic dispatch problems

This study presents a real coded chemical reaction algorithm to solve economic load dispatch (ELD) problems involving different constraints such as power balance, ramp rate limits and prohibited operating zone constraints. Effects of valve-point loading and multi-fuel options of large-scale thermal plants are also studied. System transmission loss has also been considered in a few cases. Chemical reaction optimisation mimics the interactions of molecules in a chemical reaction to reach from a higher energy unstable state to a low energy stable state. A real coded version, known as real-coded chemical reaction optimisation is implemented here to solve ELD problems. The simulation results establish that the proposed approach outperforms several other existing optimisation techniques in terms of quality of solution obtained and computational efficiency. The results also prove the robustness of the proposed methodology to solve ELD problems.

A New modified particle swarm Optimization (PSO) Technique for Non-Convex Economic Dispatch

This paper gives a new modified technique for evaluating non-convex economic dispatch (NCED) problem having non-linear, discontinuous cost function. This new particle swarm optimization technique incorporates time varying acceleration coefficients (NPSOTVAC). The highly non-linear cost function due to ramp rate limit, prohibited operating zones and valve point loading effect is considered in the proposed method. The effectiveness of proposed NPSOTVAC algorithm is proved through test on 6 and 15 unit test systems.

Solving Economic Load Dispatch Using WI-PSO

This paper presents a weight improved particle swarm optimization (WIPSO) algorithm to solve economic load dispatch problem of fossil fuel generating plants. The proposed methodology takes care of economic dispatch problems considering constraints such as power balance loading, ramp rate limits and generating limit. Particle swarm optimization is a population based technique that can be applied to a wide range of engineering problems. Particle swarm optimization with a weight improved-search strategy called WIPSO, enhances the ability of particles to explore the solution spaces more effectively and increases their convergence rate.To demonstrate the qualitiveness and effectiveness of the proposed approach, a test system consisting of three-unit generating unit, within co-orporation of power balance constraints, operating limits and ramp rate limits are taken into account.. The current proposal reveals the effectiveness and robustness as compared to other heuristic algorithms reported in literature Keywords: Economic load Dispatch (ELD), Weight improved particle swarm optimization (WIPSO), Valve point effect, Ramp Rate Limits. In this paper, the WIPSO is proposed for solving economic load dispatch (ELD) problem. The proposed WIPSO is an improvement of particle swarm optimization method with weight improvement parameter for better optimal solution and faster computation. The proposed algorithm has the ability to explore the solution space than in a standard PSO. This method focuses on solving the economic load dispatch with valve point loading effect and generator ramp rate limits constraint. The feasibility of the proposed method demonstrated for the test data of three generator system. The result obtained through the proposed approach is compared with other PSO techniques reported in recent literatures. .

Discussion of “Continuous quick group search optimizer for solving non-convex economic dispatch problems” by Moradi-Dalvand et al. [Electr. Power Syst. Res. 93 (2012) 93–105

This short communication presents a discussion of “Continuous quick group search optimizer for solving non-convex economic dispatch problems” by Moradi-Dalvand et al. [Electr. Power Syst. Res.] 93 (2012) 93–105. The discussed paper presented economic dispatch problem by experimenting with five example systems considering 6, 10, 20, 40 and 140-unit test systems considering non-convex cost function with valve point loading effects, multi-fuel effects and prohibited operating zones. However, in the reported results for the 6 and 20-unit test system, the total generation, total loss and the cost quoted were different for the given generation schedule. In this communication, the corrected data of the 6-unit test system and clarification regarding power transmission losses and cost calculations are presented.

Oppositional Real Coded Chemical Reaction Optimization for different economic dispatch problems

This paper proposes an effective oppositional Real Coded Chemical Reaction algorithm (ORCCRO) to solve Economic Load Dispatch (ELD) problems involving different equality and inequality constraints. Effects of valve-point loading, multi-fuel options of large-scale thermal plants are also studied. System transmission loss has also been considered in few cases. Chemical Reaction Optimization (CRO) imitates the interaction of molecules in a chemical reaction to reach from a higher energy unstable state to a low energy stable state. A real coded version of it, known as Real-coded chemical reaction optimization (RCCRO). Oppositional based RCCRO (ORCCRO) have been used here to improve the effectiveness and quality of solutions in minimum time. The proposed opposition-based RCCRO (ORCCRO) of the present work employs opposition-based learning for population initialization and also for generation wise update operation. In the present work, quasi-opposite numbers have been utilized instead of pseudo random numbers to improve the convergence rate of the RCCRO. Simulation results establish that the proposed approach outperforms several other existing optimization techniques in terms quality of solution obtained and computational efficiency. Results also prove the robustness of the proposed methodology to solve ELD problems.

A Multiobjective Bacterial Foraging Algorithm to Solve the Environmental Economic Dispatch Problem

In this article, multi-objective bacterial foraging with non-dominated sorting procedure is applied to solve the non-linear constrained environmental/economic dispatch problem. In the proposed work, we have considered the standard IEEE 30-bus 6-generator test system with fuel cost and emission as two conflicting objectives to be optimized simultaneously. The limits on generator real power and reactive power outputs, bus voltages and power flow of transmission lines, ramp rate limits and prohibited operating zones are considered as the constraints. The proposed work also includes the effect of having non-smooth cost characteristics to mimic the valve point loading effect. The simulation result reveals that the proposed approach is a competitive one to the existing methods for finding the best optimal Pareto front of two conflicting objectives and has the better robustness.

OPF Solution for Thermal Power Plant Generating Units with Valve-Point Loading Effects and Multiple Fuels Using IGSA

In this paper, a new solution method, which is an improved version of gravitational search algorithm (IGSA), is proposed to solve discrete optimal power flow (OPF) problem that has both discrete and continuous variables considering valve-point loading effects and multiple fuels .IGSA is based on the Newton’s law of gravity and mass interactions. In the proposed algorithm, the searcher agents are a collection of masses that interact with each other using laws of gravity and motion of Newton. The OPF problem is formulated as a single-objective mix-integer nonlinear problem, where optimal setting of the OPF control variables for minimization of total fuel cost considering without valve point loading effects, with valve point loading effects and multiple fuels are obtained .The IEEE 30-bus test system is presented to demonstrate the application of the proposed problem .The obtained results are compared to other methods recently published in the literatures and the superiority of the proposed approach over other methods is verified.

A Solution to the Combined Economic and Emission Dispatch Using Hybrid HB-SA Algorithm on Large Scale Power System

In the current scenario Economic Dispatch problem has taken a suitable twist as the public has become increasingly concerned with environmental matters. The dispatch of systems to minimise pollutants, as well as to achieve minimum cost are the two main constraints to be dealt with. In this paper, Global optimization techniques such as Honey Bee’s and Simulated Annealing techniques are employed together (HB-SA) to solve the Combined static Economic and Emission dispatch (CEED) problems in power system. This paper clearly is justified with the results, separately obtained for the above two techniques and is also provided with the results on applying both the algorithms separately. With practical consideration, Economic Dispatch will have non-smooth cost functions with equality and inequality constraints that make the problem, a large-scale highly constrained non linear optimization problem. As to demonstrate the effectiveness of the proposed method, it is subjected to the CEED problems considering (or) handling valve point loading effects. Comparison with other optimization techniques showed the superiority of the proposed HB-SA approach and confirmed its potential for solving nonlinear CEED problems.

Dynamic formulation and approximation methods to solve economic dispatch problems

Economic dispatch (ED) is an optimisation tool that is used to allocate active load demands to the generating units through optimising the fuel generation cost function subject to the different operational constraints. The high non-linearity of the power system imposes mathematical challenges in formulating the generation cost function models, which makes the ED problem hard to solve. This study introduces two ideas to solve issues related to the ED problem. First, a dynamic formulation technique is developed to optimally allocate the change in the total active load demand to the generating units. This technique is shown to be insensitive to the optimality of the initial active load distribution unlike the base point and participation factor method. Moreover, it guarantees an optimal distribution among the generating units due the change in the active load demand. Second, a novel approximation of the non-convex generation cost function is developed to solve non-convex ED problem with the transmission losses. This approximation enables the use of gradient and Newton techniques to solve the non-convex ED problem with valve point loading effect and transmission losses in an analytic approach. This approximation is compared with some heuristic optimisation techniques.

Interactive DE for solving combined security environmental economic dispatch considering FACTS technology

This paper presents an efficient interactive differential evolution (IDE) to solve the multi-objective security environmental/economic dispatch (SEED) problem considering multi shunt flexible AC transmission system (FACTS) devices. Two sub problems are proposed. The first one is related to the active power planning to minimize the combined total fuel cost and emissions, while the second is a reactive power planning (RPP) using multi shunt FACTS device based static VAR compensator (SVC) installed at specified buses to make fine corrections to the voltage deviation, voltage phase profiles and reactive power violation. The migration operation inspired from biogeography-based optimization (BBO) algorithm is newly introduced in the proposed approach, thereby effectively exploring and exploiting promising regions in a space search by creating dynamically new efficient partitions. This new mechanism based migration between individuals from different subsystems makes the initial partitions to react more by changing experiences. To validate the robustness of the proposed approach, the proposed algorithm is tested on the Algerian 59-bus electrical network and on a large system, 40 generating units considering valve-point loading effect. Comparison of the results with recent global optimization methods show the superiority of the proposed IDE approach and confirm its potential for solving practical optimal power flow in terms of solution quality and convergence characteristics.

Modified shuffled frog leaping algorithm with genetic algorithm crossover for solving economic load dispatch problem with valve-point effect

This paper addresses a hybrid solution methodology involving modified shuffled frog leaping algorithm (MSFLA) with genetic algorithm (GA) crossover for the economic load dispatch problem of generating units considering the valve-point effects. The MSFLA uses a more dynamic and less stochastic approach to problem solving than classical non-traditional algorithms, such as genetic algorithm, and evolutionary programming. The potentiality of MSFLA includes its simple structure, ease of use, convergence property, quality of solution, and robustness. In order to overcome the defects of shuffled frog leaping algorithm (SFLA), such as slow searching speed in the late evolution and getting trapped easily into local iteration, MSFLA with GA cross-over is put forward in this paper. MSFLA with GA cross-over produces better possibilities of getting the best result in much less global as well as local iteration as one has strong local search capability while the other is good at global search. This paper proposes a new approach for solving economic load dispatch problems with valve-point effect where the cost function of the generating units exhibits non-convex characteristics, as the valve-point effects are modeled and imposed as rectified sinusoid components. The combined methodology and its variants are validated for the following four test systems: IEEE standard 30 bus test system, a practical Eastern Indian power grid system of 203 buses, 264 lines, and 23 generators, and 13 and 40 thermal units systems whose incremental fuel cost function take into account the valve-point loading effects. The results are quite promising and effective compared with several benchmark methods.

Multi-objective optimization for combined heat and power economic dispatch with power transmission loss and emission reduction

The growing concern over environmental considerations and the increasing fuel cost call for operating the energy station in a more economical and environmentally friendly way. This paper develops a multi-objective model for the CHPED (combined heat and power economic dispatch) problem to conventional energy stations, where the competing fuel cost and environmental impact objectives are simultaneously optimized. To model the problem accurately, both non-linear fuel cost functions with valve-point loading effects and power transmission loss are explicitly considered in this model. A novel MLCA (multi-objective line-up competition algorithm) is proposed to handle the problem as a nonlinear constrained multi-objective optimization problem. Some diversity-preserving mechanisms are employed in the MLCA to produce well-distributed Pareto-optimal solutions. Moreover, a fuzzy decision-making process is applied to extract the best compromise nondominated solution from the Pareto-optimal set. The performance of the proposed method is validated by two typical systems. Comparison results have demonstrated the superiority of the proposed approach and confirmed its potential to solve the larger multi-objective CHPED problem.

Teaching learning based optimization for short-term hydrothermal scheduling problem considering valve point effect and prohibited discharge constraint

This article presents a novel teaching learning based optimization (TLBO) to solve short-term hydrothermal scheduling (HTS) problem considering nonlinearities like valve point loading effects of the thermal unit and prohibited discharge zone of water reservoir of the hydro plants. TLBO is a recently developed evolutionary algorithm based on two basic concept of education namely teaching phase and learning phase. In first phase, learners improve their knowledge or ability through the teaching methodology of teacher and in second part learners increase their knowledge by interactions among themselves. The algorithm does not require any algorithm-specific parameters which makes the algorithm robust. Numerical results for two sample test systems are presented to demonstrate the capabilities of the proposed TLBO approach to generate optimal solutions of HTS problem. To test the effectiveness, three different cases namely, quadratic cost without prohibited discharge zones; quadratic cost with prohibited discharge zones and valve point loading with prohibited discharge zones are considered. The comparison with other well established techniques demonstrates the superiority of the proposed algorithm.

Economic Load Dispatch in Power System using Genetic Algorithm

Evolutionary algorithms are becoming an important aspect of artificial intelligence and are successfully applied to a variety of optimization problems. This paper presents genetic algorithm and quadratic programming concepts in solving economic load dispatch in which the total cost of generating power is minimized with a valve point loading effect while satisfying the load demand irrespective of transmission line losses. This work aims in modeling the economic load dispatch problem with transmission loss and is being applied to the test systems i.e. IEEE 14 BUS and IEEE 30 BUS using MATLAB.

Discussion of “Combined heat and power economic dispatch problem solution using particle swarm optimization with time varying acceleration coefficients” by Mohammadi-Ivatloo et al. “Electric Power Systems Research” 95 (2013) 9–18

The recent paper [Combined heat and power economic dispatch problem solution using particle swarm optimization with time varying acceleration coefficient by Mohammadi-Ivatloo et al., Electric Power Systems Research 95 (2013) 9–18] presented CHPED problem by experimenting with five test systems considering valve-point loading effects and transmission losses. In this short discussion we point out that some results of the discussed paper for case III are affected by imprecision as some system test data have been mis-reported. In this discussion, the corrected data of the test system III and clarifications regarding generation cost and power transmission losses are presented.

A New Improved Particle Swarm Optimization for Solving Nonconvex Economic Dispatch Problems

This paper proposes a new improved particle swarm optimization (NIPSO) for solving nonconvex economic dispatch (ED) problem in power systems including multiple fuel options (MFO) and valve-point loading effects (VPLE). The proposed NIPSO method is based on the self-organizing hierarchical (SOH) particle swarm optimizer with time-varying acceleration coefficients (TVAC). The self-organizing hierarchical can handle the premature convergence of the problem by re-initialization of velocity whenever particles are stagnated in the search space. During the optimization process, the performance of TVAC is applied for properly controlling both local and global explorations with cognitive component and social component of the swarm to obtain the optimum solution accurately and efficiently. The proposed NIPSO algorithm is tested in different types of non-smooth cost functions for solving ED problems and the obtained results are compared to those from many other methods in the literature. The results have revealed that the proposed NIPSO method is effective and feasible in finding higher quality solutions for non-smooth ED problems than many other methods.

Shuffled differential evolution for large scale economic dispatch

In this paper, a novel metaheuristic optimization methodology is proposed to solve large scale nonconvex economic dispatch problem. The proposed approach is based on a hybrid shuffled differential evolution (SDE) algorithm which combines the benefits of shuffled frog leaping algorithm and differential evolution. The proposed algorithm integrates a novel differential mutation operator specifically designed to effectively address the problem under study. In order to validate the SDE methodology, detailed simulation results obtained on three standard test systems 13, 40, and 140-unit test system are presented and discussed. Transmission losses are considered along with valve point loading effects for 13 and 40-unit test systems and calculated using B-coefficient matrix. A comparative analysis with other settled nature-inspired solution algorithms demonstrates the superior performance of the proposed methodology in terms of both solution accuracy and convergence performances.

Shuffled differential evolution for economic dispatch with valve point loading effects

This paper proposes a novel metaheuristic optimization methodology aimed at solving economic dispatch problem considering valve point loading effects. The proposed approach is based on a hybrid shuffled differential evolution (SDE) algorithm which combines the benefits of shuffled frog leaping algorithm and differential evolution. The SDE algorithm integrates a novel differential mutation operator specifically designed to effectively address the problem under study. In order to validate the proposed methodology, detailed simulation results obtained on three standard test systems are presented and discussed. A comparative analysis with other settled nature-inspired solution algorithms demonstrates the superior performance of the proposed methodology in terms of both solution accuracy and convergence performances.