Application of the Levenberg-Marquardt Algorithm in Solving the Economic Emission Dispatch Problem Integrating Renewable Energy
Received: 21 April 2022 | Revised: 16 May 2022 | Accepted: 18 May 2022 | Online: 7 August 2022
Corresponding author: T. Dridi
The Economic Emission Dispatch (EED) is a multi-objective optimization problem that seeks to find the optimal balance between the reduction of the generation costs and the pollutant emissions of power thermal plants while respecting power balance and several operational restrictions. This balance could be carried out by proper scheduling power generation of the committed units to fulfill the power demands considering emissions. This paper presents a novel application of the conventional Levenberg-Marquardt Algorithm (LMA) optimization approach to solve the EED problem with the integration of renewable energy. Wind and solar energy were chosen to be injected into the system’s power balance constraint. The combined EED objective function with Valve Point Effects (VPE) consideration was modeled using price penalty and weight factors. This study showed the effectiveness of the chosen optimization technique and the influence of injecting renewable energy along with traditional power resources on reducing total cost and pollutant emissions. The proposed method was applied to the IEEE 9-bus test system and tested in Matlab.
Keywords:economic emission dispatch, levenberg-marquardt algorithm, wind, solar, valve point effects
"BP Statistical Review of World Energy 2020 : les chiffres clés de l’énergie dans le monde | Connaissances des énergies," 2020. https://www.connaissancedesenergies.org/bp-statistical-review-world-energy-2020-les-chiffres-cles-de-lenergie-dans-le-monde-220218.
S. Shafiee and E. Topal, "When will fossil fuel reserves be diminished?," Energy Policy, vol. 37, no. 1, pp. 181–189, Jan. 2009. DOI: https://doi.org/10.1016/j.enpol.2008.08.016
J. H. Talaq, F. El-Hawary, and M. E. El-Hawary, "A summary of environmental/economic dispatch algorithms," IEEE Transactions on Power Systems, vol. 9, no. 3, pp. 1508–1516, Dec. 1994. DOI: https://doi.org/10.1109/59.336110
Y. H. Song and I. K. Yu, "Dynamic load dispatch with voltage security and environmental constraints," Electric Power Systems Research, vol. 43, no. 1, pp. 53–60, Oct. 1997. DOI: https://doi.org/10.1016/S0378-7796(97)01160-7
K. Shamganth and Martin. J. N. Sibley, "A survey on relay selection in cooperative device-to-device (D2D) communication for 5G cellular networks," in 2017 International Conference on Energy, Communication, Data Analytics and Soft Computing (ICECDS), Chennai, India, Dec. 2017, pp. 42–46. DOI: https://doi.org/10.1109/ICECDS.2017.8390216
V. Suresh, S. Sreejith, S. K. Sudabattula, and V. K. Kamboj, "Demand response-integrated economic dispatch incorporating renewable energy sources using ameliorated dragonfly algorithm," Electrical Engineering, vol. 101, no. 2, pp. 421–442, Jun. 2019. DOI: https://doi.org/10.1007/s00202-019-00792-y
N. Kherfane, R. L. Kherfane, M. Younes, and F. Khodja, "Economic and Emission Dispatch with Renewable Energy Using HSA," Energy Procedia, vol. 50, pp. 970–979, Jan. 2014. DOI: https://doi.org/10.1016/j.egypro.2014.06.116
S. Brini, H. H. Abdallah, and A. Ouali, "Economic Dispatch for Power System included Wind and Solar Thermal energy," Leonardo Journal of Sciences, no. 14, pp. 204–220, 2009.
G. A. Alshammari, F. A. Alshammari, T. Guesmi, B. M. Alshammari, A. S. Alshammari, and N. A. Alshammari, "A New Particle Swarm Optimization Based Strategy for the Economic Emission Dispatch Problem Including Wind Energy Sources," Engineering, Technology & Applied Science Research, vol. 11, no. 5, pp. 7585–7590, Oct. 2021. DOI: https://doi.org/10.48084/etasr.4279
D. W. Marquardt, "An Algorithm for Least-Squares Estimation of Nonlinear Parameters," Journal of the Society for Industrial and Applied Mathematics, vol. 11, no. 2, pp. 431–441, Jun. 1963. DOI: https://doi.org/10.1137/0111030
K. Levenberg, "A Method for the Solution of Certain Non-Linear Problems in Least Squares," Quarterly of Applied Mathematics, vol. 2, no. 2, pp. 164–168, 1944. DOI: https://doi.org/10.1090/qam/10666
P. Wilson and H. A. Mantooth, "Chapter 10 - Model-Based Optimization Techniques," in Model-Based Engineering for Complex Electronic Systems, P. Wilson and H. A. Mantooth, Eds. Oxford: Newnes, 2013, pp. 347–367. DOI: https://doi.org/10.1016/B978-0-12-385085-0.00010-5
Τ. M. Kumar and Ν. A. Singh, "Environmental Economic Dispatch with the use of Particle Swarm Optimization Technique based on Space Reduction Strategy," Engineering, Technology & Applied Science Research, vol. 9, no. 5, pp. 4605–4611, Oct. 2019. DOI: https://doi.org/10.48084/etasr.2969
M. H. Mansor, M. M. Othman, I. Musirin, and S. A. Mohd Saleh, "Solving non-convex economic dispatch problem using computational intelligence technique," in 2017 Computing Conference, London, UK, Jul. 2017, pp. 168–172. DOI: https://doi.org/10.1109/SAI.2017.8252099
H. C. S. Rughooputh and R. T. F. A. King, "Environmental/economic dispatch of thermal units using an elitist multiobjective evolutionary algorithm," in IEEE International Conference on Industrial Technology, 2003, Maribor, Slovenia, Sep. 2003, vol. 1, pp. 48-53.
Ι. Marouani, A. Boudjemline, T. Guesmi, and H. H. Abdallah, "A Modified Artificial Bee Colony for the Non-Smooth Dynamic Economic/Environmental Dispatch," Engineering, Technology & Applied Science Research, vol. 8, no. 5, pp. 3321–3328, Oct. 2018. DOI: https://doi.org/10.48084/etasr.2098
M. Albadi, "Power Flow Analysis," in Computational Models in Engineering, K. Volkov, Ed. London, UK: IntechOpen, 2019, pp. 67–88. DOI: https://doi.org/10.5772/intechopen.83374
Ciornei and E. Kyriakides, "Recent methodologies and approaches for the economic dispatch of generation in power systems," International Transactions on Electrical Energy Systems, vol. 23, no. 7, pp. 1002–1027, 2013. DOI: https://doi.org/10.1002/etep.1635
T. Dridi, H. Jouini, E. Dafaoui, A. El Mhamedi, and A. Mami, "Comprative Study of two Classical Optimization Algorithms Solving Economic Dispatch Problem," presented at the 13the International Conference on Modeling, Optimization and Simulation - MOSIM’20, Agadir, Morocco, Aug. 2020.
"IEEE 3-Units ELD Test System," Power Systems and Evolutionary Algorithms. https://al-roomi.org/economic-dispatch/3-units-system.
G. Chandrakala, V. Ramakrishna, and J. B. Shaik, "Solving economic dispatch with valve point loading effects by using optimization techniques," International Journal of Engineering Science Invention, vol. 3, no. 9, Sep. 2014.
D. C. Walters and G. B. Sheble, "Genetic algorithm solution of economic dispatch with valve point loading," IEEE Transactions on Power Systems, vol. 8, no. 3, pp. 1325–1332, Dec. 1993. DOI: https://doi.org/10.1109/59.260861
J.-B. Park, K.-S. Lee, J.-R. Shin, and K. Y. Lee, "A particle swarm optimization for economic dispatch with nonsmooth cost functions," IEEE Transactions on Power Systems, vol. 20, no. 1, pp. 34–42, Oct. 2005. DOI: https://doi.org/10.1109/TPWRS.2004.831275
U. T. Bekabil, "Empirical Review of Production, Productivity and Marketability of Soya Bean in Ethiopia," International Journal of u- and e-Service, Science and Technology, vol. 8, no. 1, pp. 61–66, Jan. 2015. DOI: https://doi.org/10.14257/ijunesst.2015.8.1.06
P. M. Anderson and A. Bose, "Stability Simulation Of Wind Turbine Systems," IEEE Transactions on Power Apparatus and Systems, vol. PAS-102, no. 12, pp. 3791–3795, Sep. 1983. DOI: https://doi.org/10.1109/TPAS.1983.317873
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