Multi-thread security constraint economic dispatch with exact loss formulation

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect

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.

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.

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.

International Journal of Computational Engineering ScienceVol. 05, No. 01, pp. 81-89 (2004) No AccessEVOLUTIONARY PROGRAMMING BASED ECONOMIC DISPATCH WITH LINE FLOW CONSTRAINTSP. SOMASUNDARAM, K. KUPPUSAMY, and R. P. KUMUDINI DEVIP. SOMASUNDARAMSchool of Electrical and Electronics Engineering, Anna University, Chennai, Tamil Nadu 600 025, India Search for more papers by this author , K. KUPPUSAMYSchool of Electrical and Electronics Engineering, Anna University, Chennai, Tamil Nadu 600 025, India Search for more papers by this author , and R. P. KUMUDINI DEVISchool of Electrical and Electronics Engineering, Anna University, Chennai, Tamil Nadu 600 025, India Search for more papers by this author https://doi.org/10.1142/S1465876304002277Cited by:1 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThis paper presents an efficient, simple and new method for solving Economic Dispatch (ED) problem with line flow constraints through the application of Evolutionary Programming (EP). The controllable system quantities in the base-case state are optimized to minimize some defined objective function subject to the base-case operating constraints. A 10-bus system is taken for investigation. The ED results obtained using EP are compared with those obtained using quadratic programming. The investigations reveal that the proposed algorithm is relatively simple, reliable, efficient and suitable for on-line applications.Keywords:Power System OptimizationEconomic DispatchEvolutionary ProgrammingLine Flow Constraints References B. H. Chowdhury and S. Rahman, IEEE Transaction on power systems 5(4), 1248 (1990). Crossref, Google Scholar Nanda, L. Hari and M. L. Kothari, IEE Proceedings-C 141(1), 1 (1994). Google ScholarJ. Nandaet al., IEE Proceedings-C 139(1), 39 (1992). Google ScholarJ. Y. Fan and L. Zhang, IEEE Transactions on Power Systems 13(2), 320 (1998). Crossref, Google ScholarP. K. Hota, R. Chakrabarti and P. K. Chattopadhyay, Institute of Engineers (India) Journal-EL 81, 21 (2000). Google ScholarJ. Nanda and R. Badri Narayanan, Electrical Power and Energy Systems 24, 723 (2002). Crossref, Google Scholar D. B. Fogel , Evoluationary Computation: Toward a New Philosophy of Machine Intelligence ( IEEE Press , USA , 1995 ) . Google ScholarL. L. Lai and J. T. Ma, IEEE Transactions on Power Systems 12(1), 198 (1997). Crossref, Google ScholarH. T. Yang, P. C. Yang and C. L. Huang, IEEE Transactions on Power Systems 11(1), 112 (1996). Crossref, Google ScholarK. P. Wong and J. Yuryevich, IEEE Transactions on Power Systems 13(2), 301 (1998). Google ScholarT. Jayabarathi, G. Sadasivam and V. Ramachandran, Electric Power Systems Research 52, 261 (1999). Crossref, Google ScholarT. Jayabarathi and G. Sadasivam, European Transaction on Electrical Power 10(3), 167 (2000). Crossref, Google ScholarP. Attaviriyanupapet al., IEEE Transactions on Power Systems 17(2), 411 (2002). Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 1FDR PSO-based Transient Stability Constrained Optimal Power Flow Solution for Deregulated Power IndustryM. Anitha, S. Subramanian and R. Gnanadass28 Aug 2007 | Electric Power Components and Systems, Vol. 35, No. 11 Recommended Vol. 05, No. 01 Metrics History KeywordsPower System OptimizationEconomic DispatchEvolutionary ProgrammingLine Flow ConstraintsPDF download

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

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.

This paper deals with dynamic combined economic emission dispatch problem of an electric power system consisting of thermal, hydro and photovoltaic (PV) power plants. Mathematical models of these plants as well as the model of dynamic combined economic-environmental nonlinear optimization problem are given. The proposed optimization model was implemented in publicly available GAMS software, and the result is the optimal load distribution among the plants during a one-day optimization period. The software is applied to the power system without PV power plants and with a number of new PV plants added to the existing hydrothermal system. The results quantify the positive effects of PV power plants on both fuel cost and greenhouse gas reduction and recommendations are given related to the application of PV generation in modern systems. Software efficiency in solving both dynamic economic dispatch (DED) and dynamic combined economic emission dispatch (DCEED) problems is discussed, and the conclusions are drawn about its application possibilities.

A direct Newton–Raphson economic emission dispatch

Economic dispatch is considered as one of the critical advancement errand and operational choice which gives a financial condition to control framework. The principle emphasis of economic dispatch is the means by which a power system network can be arranged with the goal that we have minimum cost of electric generation to take care of the load demand, while meeting all the balance and imbalance constraints. Economic load dispatch arrangements are found by explaining the customary techniques, for example lambda iteration technique, gradient search technique, linear programming technique, dynamic programming technique and so on. Out of every single traditional technique the convergence rate of lambda iteration method is very fast and it gives accurate results and precise outcomes. This work has been made by utilizing MiPower version9 programming to distinguish the best scheduling of generator. Lambda iteration method is utilized to take care of economic dispatch issue for 6 generating unit framework with and without transmission losses.

This chapter discusses the application of linear programming (LP) techniques to find the optimal solution of the economic dispatch (ED) problem without considering transmission losses. The ED problem is concerned with optimizing the power generated by several generating units. The objective is to find the optimal power produced by each unit to supply the required load at minimum total cost. The generation cost associated with each unit is usually in the form of a quadratic or cubic function of the power produced. To apply LP, these nonlinear cost functions have to be linearized. The optimal solution is then determined by LP based on the approximate linear model. Piece-wise linearization methodology is adopted in this chapter. To evaluate the performance of the linearization method, a comprehensive set of benchmark test problems is used. LP solutions of linearized ED problems are compared with several other techniques from the literature. The LP technique with piece-wise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction.

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.

This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. In particular, convex optimization problems are formulated for both the EDP and the load shedding problem. For the EDP, an extension of the problem considering the transmission losses is presented. Furthermore, emphasis is placed on scheduling the load shedding when there exist some priorities on the loads. To solve the EDP and the load shedding problem in a distributed setting, we develop a method that combines the dual decomposition approach and the extragradient-based strategy. Notably, this work provides a fixed step size-based scheme for a strongly convex resource allocation problem considering general nonaffine coupled constraints. We show the proposed algorithm converges to the optimal solution under the assumption that the underlying graph is undirected. In addition, the method has an ergodic convergence rate of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(1/k)</i> in terms of the optimality residuals and the constraint violations. Simulation results are presented to demonstrate the effectiveness of the proposed optimization problems and distributed algorithm.

The electric power industries worldwide have undergone considerable changes especially from vertical structure to full deregulated entities. These changes are now introducing new problems in terms of operations, controls and planning of the entire grid systems. This calls for a more reliable analytical tool ever than before. One feasible solution is to perform the Optimal Economic Dispatch (OED) paradigm on this restructured power system so as to provide fairness to all operators. In this paper, the economic dispatch problem with voltage and line flow constraints has been formulated for the hydro-thermal generating units feeding the Nigerian power system. In order to solve the arising power flow problem a MATLAB based simulation package, MATPOWER version 3.0 has been suitably modified to obtain feasible solutions for different loading system scenarios. The results obtained showed that the OED offered a better optimal power schedules, power loss minimization and reduced total fuel cost than earlier work based on Micro-Genetic Algorithm, (MGA) and Conventional Genetic Algorithm (CGA).

The major issue in power system is economic dispatch (ED) problem. The Economic dispatch problem is aim to distribute electrical power generators in some active electrical system to minimize the total of cost of generators. Here, the purpose of this paper is to achieve the combination of power output, maximum total of demand with the transmission losses, minimum the total cost of generating unit and design web based application to simplify the calculation of economic dispatch problem for user at PT. Indonesia Power. This paper introduces a solution to ED problem using Dr. Xin She Yang developed firefly algorithm. The result obtained by the proposed algorithm have been compared with the result from the data source and that results is more optimal using firefly algorithm than the results of the data source. Based on the result, it can be concluded that this web based application is very useful to user in calculating the economic dispatch problem with transmission losses at PT. Indonesia Power.