A review on accuracy issues related to solving the non-convex economic dispatch problem

El-Sayed, Wael T.; Hegazy, Yasser G.; Bendary, Fahmy; ElBages, Mohamed S.

doi:10.1016/j.epsr.2016.08.002

Cited by 24 publications

(20 citation statements)

References 59 publications

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“…The equality constraints are the power balance equations. The inequality constraints (depending on the type of generation units) can include minimum and maximum power, prohibited operating zones, multiple fuel options, transmission limits, the valve-point effect, ramp rates, discharge limits, reservoir volume limits, and water dynamic balance equation with transport delay time [13].…”

Section: Typical Power and Energy Problems Solved With Heuristic Methodsmentioning

confidence: 99%

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Chicco

Mazza

2019

Sustainable Energy, Grids and Networks

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Many optimization problems admit a number of local optima, among which there is the global optimum. For these problems, various heuristic optimization methods have been proposed. Comparing the results of these solvers requires the definition of suitable metrics. In the electrical energy systems literature, simple metrics such as best value obtained, the mean value, the median or the standard deviation of the solutions are still used. However, the comparisons carried out with these metrics are rather weak, and on these bases a somehow uncontrolled proliferation of heuristic solvers is taking place. This paper addresses the overall issue of understanding the reasons of this proliferation, showing a conceptual scheme that indicates how the assessment of the best solver may result in the unlimited formulation of new solvers. Moreover, this paper shows how the use of more refined metrics defined to compare the optimization result, associated with the definition of appropriate benchmarks, may make the comparisons among the solvers more robust. The proposed metrics are based on the concept of firstorder stochastic dominance and are defined for the cases in which: (i) the globally optimal solution can be found (for testing purposes); and (ii) the number of possible solutions is so large that practically it cannot be guaranteed that the global optimum has been found. Illustrative examples are provided for a typical problem in the electrical energy systems area -distribution network reconfiguration. The conceptual results obtained are generally valid to compare the results of other optimization problems.2

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Section: Typical Power and Energy Problems Solved With Heuristic Methodsmentioning

confidence: 99%

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Chicco

Mazza

2019

Sustainable Energy, Grids and Networks

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“…Generally, the main purpose of the nonsmooth and nonconvex constrained ELD problems are to reduce the fuel and total operating costs of the thermal generating units with multivalve stream turbines and VPL effects that are usually fed with multiple fuels (MF) sources, as well as possible POZ due to the instability in the certain ranges of power output by opening or closing the steam valve . The global ELD mathematical model can be formulated by a nonsmooth and nonconvex constrained fuel cost function as follows:

italicMin \sum_{i = 1}^{Ng} ((), F_{i} ((), P_{italicGi}))

where

F_{i} ((), P_{italicGi}) = ({, \begin{array}{l} a_{i 1} P_{Gi}^{2} + b_{i 1} P_{Gi} + c_{i 1} + (||, e_{i 1} \times sin ((), f_{i 1} \times ((), P_{italicGi, min} - P_{Gi}))), italicfuel 1, P_{italicGi, min} \leq P_{Gi} \leq P_{italicGi 1} \\ a_{i 2} P_{Gi}^{2} + b_{i 2} P_{Gi} + c_{i 2} + (||, e_{i 2} \times sin ((), f_{i 2} \times ((), P_{italicGi, min} - P_{Gi}))), italicfuel 2, P_{italicGi 1} < P_{Gi} \leq P_{italicGi 2} \\ \dots \\ a_{uk} P_{Gi}^{2} + b_{ik} P_{Gi} + c_{ik} + (||, e_{}) \end{array})

…”

Section: Cfa For Solving Eld Problemsmentioning

confidence: 99%

“…Ghasemi et al 78 10, 15, 40, 140-unit Yes Yes Yes Yes Yes Artificial bee colony (ABC) 79,80 2007 AydıN and Özyön 81 3, 5, 6, 40-unit Yes No Yes Yes Yes Jadhav and Roy 82 6, 15, 40-unit Yes No Yes Yes Yes Basu 83 6, 10, 40-unit Yes Yes Yes No Yes Hemamalini and Simon 84 10, 13, 15, 40-unit Yes Yes Yes No Yes Shayeghi and Ghasemi 85 6, 14, 40-unit Yes No Yes No Yes Secui 86 6, 13, 40, 52-unit Yes No Yes Yes Yes Firefly algorithm (FFA) 87 2008 Yang et al 88 92 6, 13, 20, 40, 110-unit Yes No Yes Yes Yes Xiong et al 93 13, 15, 38, 40-unit Yes No Yes Yes Yes Cuckoo search algorithm (CSA) 94 2009 Vo et al 95 10, 15, 20, 30, 40, 80, 140, 160-unit 98 3, 6, 15, 40-unit Yes No Yes Yes Yes Gravitational search algorithm (GSA) 99 2009 Güvenç et al 100 6,10,11, 108 6, 13, 20, 40, 160-unit Yes Yes Yes Yes Yes Chemical reaction optimization (CRO) 109 2010 Bhattacharjee et al 110 13,40,110, No No Yes (Continues) load dispatch (ELD) problem that considers the units constraints is a very significant optimization problem in the power system operation. [1][2][3][4] The ELD problem is a nonlinear, nonconvex, and nonsmooth optimization problem because of the characteristics of valve-point loading (VPL) effect as a result of the multivalve steam turbine, the network transmission power losses, the ramp rate limits, and the prohibited operating zones (POZ) of power generation units. [4]…”

Section: 10 54-unit Yes Yes Yes Yes Yesmentioning

confidence: 99%

“…Generally, the main purpose of the nonsmooth and nonconvex constrained ELD problems are to reduce the fuel and total operating costs of the thermal generating units with multivalve stream turbines and VPL effects that are usually fed with multiple fuels (MF) sources, as well as possible POZ due to the instability in the certain ranges of power output by opening or closing the steam valve. [1][2][3][4] The global ELD mathematical model can be formulated by a nonsmooth and nonconvex constrained fuel cost function as follows 2 :…”

Section: Eld Problems Formulationmentioning

confidence: 99%

“…The fuel cost function of units may be segmented according to different piecewise quadratic types. Economic load dispatch (ELD) problem that considers the units constraints is a very significant optimization problem in the power system operation …”

Section: Introduction With Brief Overview Of Proposed Algorithms For mentioning

confidence: 99%

See 2 more Smart Citations

CFA optimizer: A new and powerful algorithm inspired by Franklin's and Coulomb's laws theory for solving the economic load dispatch problems

Ghasemi

Ghavidel

Aghaei

et al. 2018

Int Trans Electr Energ Syst

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Summary This paper presents a new efficient algorithm inspired by Franklin's and Coulomb's laws theory that is referred to as CFA algorithm, for finding the global solutions of optimal economic load dispatch problems in power systems. CFA is based on the impact of electrically charged particles on each other due to electrical attraction and repulsion forces. The effectiveness of the CFA in different terms is tested on basic benchmark problems. Then, the quality of the CFA to achieve accurate results in different aspects is examined and proven on economic load dispatch problems including 4 different size cases, 6, 10, 15, and 110‐unit test systems. Finally, the results are compared with other inspired algorithms as well as results reported in the literature. The simulation results provide evidence for the well‐organized and efficient performance of the CFA algorithm in solving great diversity of nonlinear optimization problems.

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Solution of Economic Load Dispatch Using Flower Pollination Algorithm

Mahto¹,

Sarwagya²,

Ranjan³

et al. 2021

Advances in Intelligent Systems and Computing

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A review on accuracy issues related to solving the non-convex economic dispatch problem

Cited by 24 publications

References 59 publications

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

CFA optimizer: A new and powerful algorithm inspired by Franklin's and Coulomb's laws theory for solving the economic load dispatch problems

Solution of Economic Load Dispatch Using Flower Pollination Algorithm

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