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A nonlinear fractional programming approach for environmental–economic power dispatch

Affiliation:	1. Faculty of Engineering and Applied Science, Univ. of Regina, Regina, Saskatchewan S4S0A2, Canada;2. Institute for Energy, Environment and Sustainability Research, UR-NCEPU, Univ. of Regina, Regina, Saskatchewan S4S 0A2, Canada;3. Institute for Energy, Environment and Sustainability Research, UR-NCEPU, North China Electric Power Univ., Beijing 102206, China;1. Department of Neurology and Institute of Clinical Neuroscience and Medical Psychology, Heinrich Heine University, Duesseldorf, Germany;2. Neuropsychology Unit, IRCCS Istituto Centro San Giovanni di Dio Fatebenefratelli, Brescia, Italy;3. Department of Experimental Psychology, University of Oxford, Oxford OX1 3UD, United Kingdom;4. Max-Planck Institute of Psychiatry, Munich, Germany;5. Berenson-Allen Center for Noninvasive Brain Stimulation and Division for Cognitive Neurology, Department of Neurology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, United States;1. Department of Electrical Engineering, College of Engineering, Taif University, Taif, Saudi Arabia;2. Department of Electrical Engineering, Faculty of Engineering, Minufiya University, Shebin El-Kom, 32511, Egypt;1. Universität Bielefeld, Fakultät für Physik, 33501 Bielefeld, Germany;2. Universität Bochum, Institut für Experimentalphysik, 44780 Bochum, Germany;3. Universität Bonn, Helmholtz-Institut für Strahlen- und Kernphysik, 53115 Bonn, Germany;4. Universität Bonn, Physikalisches Institut, 53115 Bonn, Germany;5. Institute of Scientific Instruments, AS CR, 61264 Brno, Czech Republic;6. Matrivani Institute of Experimental Research & Education, Calcutta 700 030, India;7. Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia;8. Universität Erlangen–Nürnberg, Physikalisches Institut, 91054 Erlangen, Germany;9. Universität Freiburg, Physikalisches Institut, 79104 Freiburg, Germany;10. CERN, 1211 Geneva 23, Switzerland;11. Technical University in Liberec, 46117 Liberec, Czech Republic;12. LIP, 1000-149 Lisbon, Portugal;13. Universität Mainz, Institut für Kernphysik, 55099 Mainz, Germany;14. University of Miyazaki, Miyazaki 889-2192, Japan;15. Lebedev Physical Institute, 119991 Moscow, Russia;p. Ludwig-Maximilians-Universität München, Department für Physik, 80799 Munich, Germany;q. Technische Universität München, Physik Department, 85748 Garching, Germany;r. Nagoya University, 464 Nagoya, Japan;s. Charles University in Prague, Faculty of Mathematics and Physics, 18000 Prague, Czech Republic;t. Czech Technical University in Prague, 16636 Prague, Czech Republic;u. State Scientific Center Institute for High Energy Physics of National Research Center ‘Kurchatov Institute’, 142281 Protvino, Russia;v. CEA IRFU/SPhN Saclay, 91191 Gif-sur-Yvette, France;w. Tel Aviv University, School of Physics and Astronomy, 69978 Tel Aviv, Israel;x. University of Trieste, Department of Physics, 34127 Trieste, Italy;y. Trieste Section of INFN, 34127 Trieste, Italy;z. Abdus Salam ICTP, 34151 Trieste, Italy;11. University of Turin, Department of Physics, 10125 Turin, Italy;12. University of Eastern Piedmont, 15100 Alessandria, Italy;13. Torino Section of INFN, 10125 Turin, Italy;14. National Centre for Nuclear Research, 00-681 Warsaw, Poland;15. University of Warsaw, Faculty of Physics, 00-681 Warsaw, Poland;16. Warsaw University of Technology, Institute of Radioelectronics, 00-665 Warsaw, Poland;17. Yamagata University, Yamagata 992-8510, Japan

Abstract:	A nonlinear fractional programming approach is provided for addressing the environmental–economic power dispatch problems in the thermal power dispatch systems. The objective of this study is to simultaneously minimize the total fuel cost and total emissions of the power dispatch systems, which is realized by two simultaneous models with nonlinear constraints. The first model is to minimize the quotient of two competing and conflicting functions (i.e. total emission function]/total fuel cost function]), and the second one is to minimize the total fuel cost expressed by a quadratic objective function. In particular, the process of solving the first model uses Dinkelbach’s algorithm to convert the minimization problem with the nonlinear fractional objective function into a sequence of non-fractional minimization problems. The effectiveness of this approach is demonstrated through applying to the standard IEEE 30-bus test system. Comparison between the present approach and other existing approaches shows that the proposed approach can generate superior decision alternatives from the view point of realizing a more environmentally friendly and cost-effective scheme and/or considering the power transmission loss rate in the power dispatch systems.

Keywords:	Nonlinear fractional programming Power dispatch Total fuel cost Total emission Environmental–economic scheme
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