PENERAPAN LAGRANGE MULTIPLIER UNTUK MENGOPTIMALKAN RUGI DAYA PADA RANGKAIAN LISTRIK

Ilham Afn

Abstract


Penelitian ini membahas penerapan metode Lagrange Multiplier untuk meminimalkan kerugian daya resistif dalam sirkuit listrik, khususnya pada sistem non-planar yang kompleks. Kerugian daya resistif merupakan salah satu penyebab utama penurunan efisiensi transmisi energi listrik. Upaya tradisional seperti meningkatkan luas penampang konduktor dianggap tidak efisien dari segi biaya dan ruang, sehingga diperlukan pendekatan matematis untuk menemukan kondisi optimal antara tegangan dan arus. Melalui penerapan Hukum Ohm dan analisis nodal, dibentuk sistem persamaan yang mewakili hubungan antara tegangan, arus, dan resistansi. Sistem tersebut kemudian diformulasikan menjadi fungsi Lagrange sebagai fungsi tujuan dan fungsi kendala. Proses optimasi dilakukan menggunakan bahasa pemrograman Python dengan Sympy/Numpy untuk perhitungan simbolik dan numerik. Hasil optimasi menunjukkan bahwa metode Lagrange Multiplier mampu menentukan nilai tegangan dan arus yang meminimalkan kerugian daya total sebesar 663.257575757577 Watt.


Keywords


Lagrange Multiplier, Kerugian Daya Resistif, Analisis Nodal, Hessian Terbatas, Sirkuit Non-Planar.

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References


Cence Power. (2022, December 20). Can We Eliminate These 3 Types of Line Losses in Transmission Systems?. Cance Power Blog.

Boyce, W. E., & DiPrima, R. C. (2017). Elementary Differential Equations and Boundary Value Problems (11th ed.). Wiley.

Dorf, R. C., & Svoboda, J. A. (2020). Introduction to Electric Circuits (10th ed.). Wiley.

Rao, S. S. (2019). Engineering Optimization: Theory and Practice (5th ed.). Wiley.

Oliphant, T. E. (2006). A Guide to NumPy. Trelgol Publishing.

Vadlamani, S. K., Xiao, T. P., & Yablonovitch, E. (2020). Physics successfully implements Lagrange multiplier optimization. Proceeding of the National Academy of Sciences, 117(46), 28525-28531.

Bordered Hessian For Constrained Optimisation. (n.d.). Youtube. Upload by Youtube. https://www.youtube.com/watch?v=qk_Jfkfc7i8.

William H. Hayt, Jr., Jack E. Kemmerly, Steven M. Durbin. Terbit sejak 1962 oleh McGraw-Hill Companies. Engineering Circuit Analysis, Six Edition.

Faouri, A. O., & Kasap, P. (2023). Classical optimization techniques. In Science & Engineering Researches (Chapter XIX, pp. 301–323). Ondokuz Mayıs University.

Law, E. (2022, December 20). 3 Types of Line Losses in Power Transmission. Cence Power.

Castro, L.M., & colleagues. (2020). Efficient method for the optimal economic operation including point-to-point VSC-HVDC using Lagrange multipliers. Energy Conversion and Management.

Mohajan, H. K., & Mohajan, D. (2022). A bordered Hessian approach for second-order conditions in constrained optimization.

Tran, H. G., & colleagues. (2023). Lagrange multiplier-based optimization for hybrid energy management in migrogrids. Electronics, 12(21), 4513.

Meng, L. (2024). Bound-constrained optimization using Lagrange multiplier methods: comparisons and KKT considerations. Computers & Structures.

Elazab, R. (2025). Optimazing stand-alone microgrids with Lagrange multiplier methods: sizig and planning. Jurnal of Cleaner Production / Renewable Energy.

Oliphant, T. E. (2020). NumPy and scientific Python tools for optimazation and simulation (update tutorial/documentation). SciPy / Trelgol Publishing.

The SymPy Development Team. (2024). SymPy documentation – Lagrange multipliers and symbolic optimization examples.

Authors. (2021). A Lagrange multiplier-based state enumeration for reliability assessment in power system with renewables. Konferensi / Prosiding.

Jiang, X. (2025). Understanding the Lagrangian in constrained optimization.

Arora, J. S. (2011). Introduction to optimum design (3th ed.). Elsevier.




DOI: https://doi.org/10.52447/jkte.v11i1.9016

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