Solution Of Economic Dispatch Problem Research Articles

Approaches for smart linear regression in a difficult quasi economic dispatch problem

<span lang="EN-US">Traditional methods indispensably necessitate monotonically increasing characteristic for fuel cost of generators in a thermal power plant. However, in medium and large thermal power plants, this condition is a dream to accomplish. So, to meet out these exigencies heuristic methods like swarm optimization technique, genetic algorithm technique and bee colony based hybrid solar thermal technology (BHSTT) are used to realize the practical nonlinearities associated with valve point loading emanated out of multi-valving effect, associated with power station. However, the heuristic methods too face challenges arising out of bulky thermal power plants adopting cubic cost functions and possessing stringent non-convex economic dispatch problem following multi-valving and erratic behavior of nonlinear loads at the load center. So, at its favor function evaluation method dealing with cubic cost function is attempted in this dissertation to yield a satisfactory optimal solution for economic dispatch problem. This method deals with the real power generation of producing units as well as the complex power of units, as well as dealing with severe nonlinear stringent fuel cost characteristics that are prevalent in today’s bulky thermal power plants. In comparison to previous approaches, the findings achieved are highly encouraging.</span>

Distributed event-triggering algorithm with uncoordinated step sizes for economic dispatch problem over unbalanced directed network

This paper studies the economic dispatch problem of the smart grid based on unbalanced directed graph. An event triggering mechanism is introduced to save communication resources, and each generator broadcasts its information to its neighbors when the event-triggering condition is satisfied. A new distributed Lagrange algorithm with uncoordinated steps is proposed to accelerate the convergence of the algorithm. The row random matrix is introduced to balance the imbalance of the directed network, and convergence of the algorithm is analyzed by the small gain theorem as well. The theoretical analysis shows that when the cost function of the generator is convex and smooth, and the uncoordinated step size satisfies certain conditions. The algorithm can linearly get the optimal solution of economic dispatch problem. Finally, Simulation examples prove the effectiveness and applicability of the proposed algorithm.

Evolutionary algorithm solution for economic dispatch problems

<span>A modified firefly algorithm (FA) was presented in this paper for finding a solution to the economic dispatch (ED) problem. ED is considered a difficult topic in the field of power systems due to the complexity of calculating the optimal generation schedule that will satisfy the demand for electric power at the lowest fuel costs while satisfying all the other constraints. Furthermore, the ED problems are associated with objective functions that have both quality and inequality constraints; these include the practical operation constraints of the generators (such as the forbidden working areas, nonlinear limits, and generation limits) that makes the calculation of the global optimal solutions of ED a difficult task. The proposed approach in this study was evaluated in the IEEE 30-Bus test-bed; the evaluation showed that the proposed FA-based approach performed optimally in comparison with the performance of the other existing optimizers, such as the traditional FA and particle swarm optimization. The results show the high performance of the modified firefly algorithm compared to the other methods.</span>

A Non-Linear-Threshold-Accepting Function Based Algorithm for the Solution of Economic Dispatch Problem

This article introduces a novel heuristic algorithm based on Non-Linear Threshold Accepting Function to solve the challenging non-convex economic dispatch problem. Economic dispatch is a power system management tool; it is used to allocate the total power generation to the generating units to meet the active load demand. The power systems are highly nonlinear due to the physical and operational constraints. The complexity of the resulting non-convex objective cost function led to inabilities to solve the problem by using analytical approaches, especially in the case of large-scale problems. Optimization techniques based on heuristics are used to overcome these difficulties. The Non-Linear Threshold Accepting Algorithm has demonstrated efficiency in solving various instances of static and dynamic allocation and scheduling problems but has never been applied to solve the economic dispatch problem. Existing benchmark systems are used to evaluate the performance of the proposed heuristic. Additional random instances with different sizes are generated to compare the adopted heuristic to the Harmony Search and the Whale Optimization Algorithms. The obtained results showed the superiority of the proposed algorithm in finding, for all considered instances, a high-quality solution in minimum computational time.

Distributed Incremental Cost Consensus-Based Optimization Algorithms for Economic Dispatch in a Microgrid

The economic dispatch problems (EDPs) in a microgrid (MG) have been extensively investigated by a variety of emerging algorithms. In this paper, we propose two newly distributed dynamic optimization algorithms to respectively study the EDPs under both cases without and with generation constraints under a directed topology network. Two novel dynamic optimization algorithms are based on the distributed incremental cost consensus (ICC), where the mismatch between total demand and power generation is considered. Our algorithms only require the weight matrix of the directed network to be row stochastic. The theoretical analysis on the convergence of the proposed algorithms is presented by using the small gain theorem. It can be found that the algorithms are convergent at the geometric rate. Meanwhile, the power output of the generators are proved to achieve the optimal solution of EDPs based on the proposed algorithms. Finally, the corresponding conditions are also derived, and simulation studies illustrate the correctness of our results.

A Hybrid Metaheuristic Approach for the Solution of Renewables-Incorporated Economic Dispatch Problems

This paper presents a hybrid metaheuristic optimization algorithm developed to solve the Economic Dispatch Problem (EDP) encountered in different combinations of power plants. The algorithm is developed by assimilating the prominent features of Particle Swarm Optimization (PSO) and Bat Algorithm (BA) and improves cost reduction and convergence with lesser computational time. The developed algorithm is employed for the solution of EDP consisting of only Renewable Energy Sources (RESs) implemented at various locations in Pakistan. The all RES based EDP consists of scenarios composed of sub-scenarios having no constraints, with time-varying loads and multi-area economic dispatch (MAED). The algorithm is also tested for three different combinations of power plants, comprising of RES integrated with thermal power plants (TPPs), the small-scaled thermal power system with constraints, and a large-scaled power system with Valve Point Loading (VPL) effect. The comparative analysis of the results for the developed metaheuristic algorithm with various existing techniques shows a reasonable reduction in the cost, improved computational time, and fast convergence.

Distributed approximate Newton algorithms and weight design for constrained optimization

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel distributedapprox − Newton algorithms that approximate the standard Newton optimization method. We first develop the notion of an optimal edge weighting for the communication graph over which agents implement the second-order algorithm, and propose a convex approximation for the nonconvex weight design problem. We next build on the optimal weight design to develop a discrete distributed approx-Newton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full box-constrained problem, we develop a continuous distributed approx-Newton algorithm which is inspired by first-order saddle-point methods and rigorously prove its convergence to the primal and dual optimizers. A main property of each of these distributed algorithms is that they only require agents to exchange constant-size communication messages, which lends itself to scalable implementations. Simulations demonstrate that the distributedapprox − Newton algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods.

Semidefinite programming solution of economic dispatch problem with non-smooth, non-convex cost functions

The paper presents a solution to economic dispatch (ED) problems with non-convex, non-smooth fuel cost functions, which characterize practical generating units. A method involving a unified semidefinite programming (SDP) formulation of different ED problems through cost function decomposition was presented. The solution of the resulting rank-relaxed SDP problem was refined to achieve the rank constraint using the method of convex iteration and branch-and-bound technique. The SDP method was investigated on some test problems in the literature. The results showed that the SDP method compared favorably with other methods, and can efficiently solve non-convex and non-smooth ED problems.

Combined heat and power economic dispatch problem solution by implementation of whale optimization method

Combined heat and power economic dispatch (CHPED) is introduced as a difficult optimization problem, which provides optimal generation scheduling of heat and power units. The CHPED problem aims to minimize the fuel cost of CHP units with the consideration of operational constraints. In this paper, whale optimization algorithm (WOA) is employed to solve CHPED problem. WOA is a new meta-heuristic optimization technique, which is introduced recently for solving optimization problems. Social behavior of humpback whales is the basic idea of proposal of WOA, where the bubble-net hunting strategy inspires this optimization procedure. Three test systems are considered for evaluation of the performance of the WOA in solving the non-convex nonlinear CHPED problem. The first test instance, which includes 24 units, is studied for evaluating WOA performance in finding the optimal solution of CHPED problem. 84-Unit and 96-unit test systems are introduced for the first time in this paper to show the superiority of WOA in solving non-convex CHPED optimization problem. The second test system contains 40 power-only units, 24 CHP units, and 20 heat-only units. Additionally, the third test instance contains 52 power-only units, 24 CHP units, and 20 heat-only units. The obtained optimal solutions represent WOA efficiency and feasibility and capability of obtaining better solutions with respect to other optimization techniques in terms of operational cost and ability of implementation of WOA on large systems.

Solution of Economic Dispatch Problems with Smooth and Non Smooth Cost Function Using Particle Swarm Optimization

This paper deals with solution of economic dispatch problem with smooth and non smooth cost function. With practical consideration, ED will have non smooth cost functions with equality and inequality constraints that make the problem, a large-scale highly constrained nonlinear optimization problem. Here particle swarm optimization (PSO) technique is used to solve economic dispatch. PSO based algorithm is easy to implement and it performs well on optimization problem. To demonstrate the effectiveness of the proposed method it is being applied to test ED problems, with smooth and non smooth cost functions. Comparison with lagrangian relaxation method showed the superiority of the proposed approach to check the efficiency, studies have been performed for 6 generating unit with smooth cost function. Numerical simulations indicate an improvement in total fuel cost savings.

A Versatile Probability Distribution Model for Wind Power Forecast Errors and Its Application in Economic Dispatch

The existence of wind power forecast errors is one of the most challenging issues for wind power system operation. It is difficult to find a reasonable method for the representation of forecast errors and apply it in scheduling. In this paper, a probability distribution model named “versatile distribution” is formulated and developed along with its properties and applications. The model can well represent forecast errors for all forecast timescales and magnitudes. The incorporation of the model in economic dispatch (ED) problems can simplify the wind-induced uncertainties via a few analytical terms in the problem formulation. The ED problem with wind power could hence be solved by the classical optimization methods, such as sequential linear programming which has been widely accepted by industry for solving ED problems. Discussions are also extended on the incorporation of the proposed versatile distribution into unit commitment problems. The results show that the new distribution is more effective than other commonly used distributions (i.e., Gaussian and Beta) with more accurate representation of forecast errors and better formulation and solution of ED problems.

Particle Swarm Optimization (PSO) Technique for Unit Commitment and Economic Dispatch Problem Solution

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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.

Modeling and Solution of Economic Dispatch Problem for GTCC Units

Economic dispatch problem lies at the kernel among different issues in GTCC units’ operation, which is about minimizing the fuel consumption for a period of operation so as to accomplish optimal load dispatch among units. This paper has analyzed the load dispatch model of gas turbine combined-cycle (GTCC) units and utilizes a quantum genetic algorithm to optimize the solution of the model. The performance of gas turbine combined-cycle units varies with many factors and this directly leads to variation of model parameters. To solve the dispatch problem, variable constraints are adopted to correct the parameters influenced by ambient conditions. In the simulation, comparison of dispatch models for GTCC units considering and not considering the influence of ambient conditions indicates that it is necessary to adopt variable constraints for the dispatch model of GTCC units. To optimize the solution of the model, a Quantum Genetic Algorithm is used considering its advantages in searching performance. QGA combines the quantum theory with evolutionary theory of genetic algorithm. It is a new kind of intelligence algorithm which has been successfully employed in optimization problems. Utilizing quantum code, quantum gate and so on, QGA shows flexibility, high convergent rate, and global optimal capacity and so on. Simulations were performed by building up models and optimizing the solutions of the models by QGA. QGA shows better effect than equal micro incremental method used in the previous literature. The operational economy is proved by the results obtained by QGA. It can be concluded that QGA is quite effective in optimizing economic dispatch problem of GTCC units.

Combined heat and power economic dispatch problem solution using particle swarm optimization with time varying acceleration coefficients

In this paper a novel time varying acceleration coefficients particle swarm optimization (TVAC-PSO) algorithm is implemented to solve combined heat and power economic dispatch (CHPED) problem. The CHPED problem is a challenging non-convex and non-linear optimization problem. The acceleration coefficients in PSO algorithm are varied adaptively during iterations to improve solution quality of original PSO and avoid premature convergence. The effect of valve-point in cost function considered with adding an absolute sinusoidal term to conventional polynomial cost function. The proposed method is applied to five test cases with different characteristics. Also, a new large scale test case considering valve-points effects is proposed in this paper. The obtained results demonstrate the superiority of the proposed method in solving non-convex and constrained CHPED problem.

Optimization Of Combined Economic and Emission Dispatch Problem – A Comparative Study for 30 Bus Systems

This paper presents an evolutionary computation (EC) method called Genetic Algorithm (GA) and a metaheuristic algorithm called Ant Colony Search Algorithm (ACSA) to solve the combined Economic and Emission dispatch (EED) problem with transmission losses. Economic Load Dispatch (ELD) and Economic Emission Dispatch (EED) have been applied to obtain optimal fuel cost and optimal emission of generating units, respectively. Combined Economic Emission Dispatch (CEED) problem is obtained by considering both the economy and emission objectives. A real coded GA has been implemented to minimize both the dispatch cost as well as emission while satisfying all the equality and inequality constraints. ACSA is also developed to provide a means of comparison and it is a new cooperative agents approach, which is inspired by the observation of the behaviors of real ant colonies on the topic of ant trail formation and foraging methods. In the ACSA, a set of cooperating agents called ants cooperates to find a good solution for economic dispatch problem. The merits of ACSA are parallel search and optimization capabilities. The feasibility of the proposed method is tested on a power system network and the experimental results of both GA and ACSA are compared with the solutions of conventional Lamda iteration method.

Solution of economic dispatch problems by seeker optimization algorithm

Seeker optimization algorithm (SOA), a novel heuristic population-based search algorithm, is utilized in this paper to solve different economic dispatch (ED) problems of thermal power units. In the SOA, the act of human searching capability and understanding are exploited for the purpose of optimization. In this algorithm, the search direction is based on empirical gradient by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple fuzzy rule. The effectiveness of the algorithm has been tested on four different small, as well as, large scale test power systems to solve the ED problems. The outcome of the present work is to establish the SOA as a promising alternative approach to solve the ED problems in practical power systems. Both the near-optimality of the solution and the convergence speed of the algorithm are promising. The results obtained are compared with those published in the recent literatures.

A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions

This paper develops a Novel Stochastic Search (NSS) method for the solution of economic dispatch problems with non-convex fuel cost functions. The NSS solution procedure consists of three steps, namely Direct Search (DS), Goal Neighborhood Approximation (GNA) and Marginal Cost Dispatch (MCD). The DS step identifies a set of feasible solutions in accordance with prescribed equality and inequality constraints. The GNA step processes those feasible solutions to identify an appropriate direction for searching the global optimal solution. Finally, in the MCD step, the marginal cost of each generating unit is regulated in order to establish the global optimal solution. The proposed NSS scheme is applied to solve three examples systems of increasing complexity. The results are compared to those obtained using the conventional Simulated Annealing (SA), Genetic Algorithm (GA), and Evolutionary Programming (EP) methods. The results demonstrate that the NSS method provides a fast, robust and highly effective scheme for the solution of economic dispatch.

Combined Hybrid Differential Particle Swarm Optimization Approach for Economic Dispatch Problems

The economic dispatch problem is concerned with the optimal allocation of a load among different generators for a given demand, minimizing fuel cost, emission, etc. This article presents a new, improved combined hybrid differential particle swarm optimization algorithm that combines hybrid differential evolution with particle swarm optimization for the solution of economic dispatch problems. This new algorithm combines the vibrancy and explorative nature of particle swarm optimization with the superior exploitative nature of hybrid differential evolution in such a manner that the merits of both remain intact. The results obtained are compared with a few other existing non-conventional methods, and the applicability and effectiveness of the proposed algorithm to power system optimization problems are indicated.

Economic Dispatch Using an Enhanced Hopfield Neural Network

This article introduces some modifications to the conventional Hopfield neural network (HNN) to enhance its performance. A comprehensive study of the effect of the HNN parameters on the solution quality of the economic dispatch problem (EDP), as a case study, has been made. By investigating the describing curves, the best values for the HNN parameters are tuned. To further improve the solution quality, an adaptive correction factor is proposed and introduced to the EDP solution obtained by the HNN. To investigate the effect of the modifications on the solution quality of the EDP, three case studies are selected and solved. Comparisons of results are then made with others to prove the validity and effectiveness of the proposed modifications.