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RESEARCH ARTICLE

IP-C-PDL: A chaos-embedded trust-region interior-point framework for constrained economic dispatch in large-scale power systems

Jangkung Raharjo1,2 ,  Rifki Rahman Nur Ikhsan1,2* ,  Lindiasari Martha Yustika1,2
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1 School of Electrical Engineering, Telkom University, Jl. Telekomunikasi No. 1, Terusan Buah Batu, Bandung, West Java , Indonesia
2 Center of Excellence of Sustainable Energy and Climate Change, Telkom University, Jl. Telekomunikasi No. 1, Terusan Buah Batu, Bandung, West Java , Indonesia
IJOCTA, 026310188 https://doi.org/10.36922/IJOCTA026310188
Received: 27 July 2026 | Revised: 29 August 2026 | Accepted: 11 September 2026 | Published online: 13 November 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Constrained economic dispatch (ED)—the classical, single-bus, active-poweronly dispatch problem for thermal generation, not an optimal power flow or unit-commitment problem—in large-scale interconnected power systems such as the Java–Madura–Bali (Jamali) network is non-convex and ramprate-coupled: deterministic solvers stall at local optima, while stochastic solvers incur unacceptable run-to-run variance. This paper proposes IP-C-PDL (Interior-Point Chaotic Powell’s Dog-Leg), which, within a single interior-point iteration, couples a Powell’s Dog-Leg trust-region step (Cauchy/quasi-Newton selection via accumulated SR1/BFGS curvature) with a stall-adaptive tentmap chaotic perturbation for ergodic basin escape; a multi-start pool, elite archive, and periodic SQP refinement complete the framework using only three user-specified parameters. On twelve CEC benchmark functions (30 runs, 12 methods), IP-C-PDL ranks 1 in 1 of 12 and top-3 in 7 of 12. On six ED scenarios spanning 5-, 16-, and 42-unit systems (50 runs, 10 methods, single-period and 24-hour horizons), it ranks 1 in 4 of 6 (mean rank 2.17/10) with zero constraint violations, yielding USD 22,239.29/day (σ = USD 0.41) on the 42-unit 24-hour case—0.16% better than the second-ranked comparator (t = −48.26, p < 10−42) and 4.67% better than the worst (t = −180.85, p < 10−70)—confirmed by Friedman, ANOVA, and Wilcoxon–Holm–Bonferroni tests. A five-factor sensitivity analysis identifies multi-start pool size as the dominant factor—with a cliff-edge improvement at just two starts—while the framework is insensitive to the remaining four hyperparameters and stabilises by 400 iterations. A policy sensitivity analysis further links dispatch quality to fiscal savings, Biaya Pokok Penyediaan (BPP) subsidy reduction, and avoided carbon emissions in the Indonesian power sector.

Keywords
Constrained optimisation modelling
Trust-region methods
Interior-point framework
Economic dispatch
Large-scale power systems
Computational intelligence
Funding
This research was supported by the Directorate of Research and Community Service at Telkom University through Agreement/Contract Letter Number No.485/LIT06/PPM-LIT/2024.
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References
  1. Wood AJ, Wollenberg BF, Sheblé Power Generation, Operation, and Control. 3rd ed. New York, NY: Wiley-Interscience; 2013. Accessed June 15, 2026. https://bcs.wiley.com/he-bcs/Books?action=index&itemId=0471790559&bcsId=8646
  2. Gao Y, Sosnowski M, Grabowska K, et al. Economic dispatch optimization strategies and problem formulation: A comprehensive review. Energies. 2024;17:550. https://doi.org/10.3390/EN17030550
  3. Li L, Pei J, Shen Q. A review of research on dynamic and static economic dispatching of hybrid wind-thermal power microgrids. 2023. https://doi.org/10.3390/en16103985
  4. Visutarrom T, Chiang TC. Economic dispatch using metaheuristics: Algorithms, problems, and solutions. Appl Soft Comput. 2024;150:110891. https://doi.org/10.1016/J.ASOC.2023.110891
  5. Carolina M. Evaluasi kritis perusahaan listrik negara (PLN) persero terhadap kebijakan subsidi. Jurnal Budget. 2021;6(1):121-143. https://doi.org/10.22212/jbudget.v6i2.112
  6. PT PLN (Persero), Ministry of Energy and Mineral Resources, Republic of Indonesia. Electricity supply business plan (RUPTL) 2025-2034. Jakarta: Kementerian Energi dan Sumber Daya Mineral; 2025. Accessed June 15, 2026. https://climatepolicydatabase.org/policies/electricity-supply-business-plan-ruptl-2025-2034
  7. Ma H, Shahidehpour SS. Economic dispatch with ramp-rate limits. IEEE Trans Power Syst. 1994;9(1):254-261. https://doi.org/10.1109/59.317581
  8. Fu Y, Shahidehpour M, Li Z. Security-constrained unit commitment with AC constraints. IEEE Trans Power Syst. 2005;20(3):1538-1550. https://doi.org/10.1109/TPWRS.2005.854375
  9. Roldán-Blay C, Miranda V, Carvalho L, Roldán-Porta C. Optimal generation scheduling with dynamic profiles for the sustainable development of electricity grids. Sustainability. 2019;11. https://doi.org/10.3390/su11247111
  10. Ji Y, Wei H. An approximate dynamic programming method for unit-based small hydropower scheduling. Front Energy Res. 2022;10. https://doi.org/10.3389/fenrg.2022.965669
  11. Shilaja C, Arunprasath T, Priya P. Day-ahead optimal scheduling of microgrid with adaptive grasshopper optimization algorithm. Int J Commun Syst. 2022;35. https://doi.org/10.1002/dac.4133
  12. Zein H, Wachjoe CK. Dynamic scheduling with unit commitment, constraints and real transmission losses. In: *7th International Conference on Control, Decision and Information Technologies, CoDIT 2020*. Piscataway, NJ: Institute of Electrical and Electronics Engineers; 2020:1209-1214. https://doi.org/10.1109/CoDIT49905.2020.9263830
  13. Ismail FB, Randhawa GS, Al-Bazi A, Alkahtani AA. Intelligent optimization systems for maintenance scheduling of power plant generators. Inf Sci Lett. 2023;12:1319-1332. https://doi.org/10.18576/isl/120322
  14. Muthana SA, Ku-Mahamud KR. Tri-objective generator maintenance scheduling model based on sequential strategy. PLoS One. 2022;17. https://doi.org/10.1371/journal.pone.0276225
  15. Moyo L, Nwulu NI, Ekpenyong UE. Generator maintenance scheduling using exchange mark et al MethodsX. 2020;7. https://doi.org/10.1016/j.mex.2020.100932
  16. Ramsamooj N, Ramdath L, Bahadoorsingh S, Sharma C. A comparison of memetic algorithms in a generator maintenance scheduling problem for Trinidad and Tobago. West Indian J Eng. 2019:4-12. Accessed June 15, 2026. https://journals.sta.uwi.edu/ojs/index.php/wije/article/view/9197
  17. Aditya IA, Simaremare AA, Raharjo J, Suyanto, Wijayanto I. Komodo mlipir algorithm to solve generator scheduling problems. In: Proceedings - 2022 2nd International Conference on Electronic and Electrical Engineering and Intelligent System, ICE3IS 2022. Piscataway, NJ: IEEE; 2022:84-88. https://doi.org/10.1109/ICE3IS56585.2022.10010294
  18. Puspitasari KMD, Raharjo J, Sastrosubroto AS, Rahmat B. Generator scheduling optimization involving emission to determine emission reduction costs. Int J Eng Trans B Appl. 2022;35. https://doi.org/10.5829/IJE.2022.35.08B.02
  19. Imbulana Arachchi J, Managi S. Preferences for energy sustainability: Different effects of gender on knowledge and importance. Renew Sustain Energy Rev. 2021;141:110767. https://doi.org/10.1016/J.RSER.2021.110767
  20. Jin M, Wang M. Research on the economic dispatch of power systems with a high proportion of renewable energy based on improved PSO. In: Journal of Physics: Conference Series. Vol 2465. Bristol, UK: Institute of Physics; 2023. https://doi.org/10.1088/1742-6596/2465/1/012024
  21. Nocedal J, Wright SJ. Numerical Optimization. 2nd ed. New York, NY: Springer; 2006. https://doi.org/10.1007/978-0-387-40065-5
  22. Chowdhury BH, Rahman S. A review of recent advances in economic dispatch. IEEE Trans Power Syst. 1990;5(4):1248-1259. https://doi.org/10.1109/59.99376
  23. Duman S, Yorukeren N, Altas IH. A novel modified hybrid PSOGSA based on fuzzy logic for non-convex economic dispatch problem with valve-point effect. Int J Electr Power Energy Syst. 2015;64:121-135. https://doi.org/10.1016/j.ijepes.2014.07.031
  24. Ikhsan RRN, Raharjo J, Rahmat B. Vectorized lambda iteration method for swift economic dispatch analysis. Evergreen. 2024;11:435-447. https://doi.org/10.5109/7172306
  25. Chen J, Zhang Y. A Lagrange relaxation-based alternating iterative algorithm for non-convex combined heat and power dispatch problem. Electric Power Syst Res. 2019;177:105982. https://doi.org/10.1016/J.EPSR.2019.105982
  26. Bai C, Li Q, Zhou W, Li B, Zhang L. Fast distributed gradient descent method for economic dispatch of microgrids via upper bounds of second derivatives. Energy Rep. 2022;8:1051-1060. https://doi.org/10.1016/J.EGYR.2022.08.110
  27. Azevedo AT, Oliveira ARL, Soares S. Interior point method for long-term generation scheduling of large-scale hydrothermal systems. Ann Oper Res. 2009;169:55-80. https://doi.org/10.1007/s10479-008-0389-z
  28. Gbadega PA, Sun Y. Primal-dual interior-point algorithm for electricity cost minimization in a prosumer-based smart grid environment: A convex optimization approach. Energy Rep. 2022;8:681-695. https://doi.org/10.1016/j.egyr.2022.10.144
  29. Mataifa H, Krishnamurthy S, Kriger C. An efficient primal-dual interior-point algorithm for volt/var optimization in rectangular voltage coordinates. IEEE Access. 2023;11:36890-36906. https://doi.org/10.1109/ACCESS.2023.3266421
  30. Jain S, Kanwar N. Day ahead optimal scheduling of generators using dynamic programming method. In: *2019 8th International Conference on Power Systems: Transition towards Sustainable, Smart and Flexible Grids, ICPS 2019*. Piscataway, NJ: Institute of Electrical and Electronics Engineers; 2019. https://doi.org/10.1109/ICPS48983.2019.9067555
  31. Gaing ZL. Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans Power Syst. 2003;18(3):1187-1195. https://doi.org/10.1109/TPWRS.2003.814889
  32. Prakash O, Rai A, Das S, Gopal Y, Singh HR, Somassoundaram T. Minimization of fuel cost for generator systems with valve point effect using modified PSO. Franklin Open. 2024;7:100090. https://doi.org/10.1016/j.fraope.2024.100090
  33. Xu Y, Liu J, Cui Z, et al. Economic scheduling model of an active distribution network based on chaotic particle swarm optimization. Information. 2024;15. https://doi.org/10.3390/info15040225
  34. Sinha N, Chakrabarti R, Chattopadhyay PK. Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Comput. 2003;7(1):83-94. https://doi.org/10.1109/TEVC.2002.806788
  35. Faseela CK, Vennila H. Economic and emission dispatch using whale optimization algorithm (WOA). Int J Electr Comput Eng. 2018;8:1297-1304. https://doi.org/10.11591/ijece.v8i3.pp1297-1304
  36. Chao IM, Hsiung SC, Liu JL. Improved whale optimization algorithm based on inertia weights for solving global optimization problems. Adv Technol Innov. 2020;5:147-155. https://doi.org/10.46604/AITI.2020.4167
  37. Bhesdadiya RH, Pandya MH, Trivedi IN, Jangir N, Jangir P, Kumar A. Price penalty factors based approach for combined economic emission dispatch problem solution using dragonfly algorithm. In: *2016 International Conference on Energy Efficient Technologies for Sustainability, ICEETS 2016*. Piscataway, NJ: IEEE; 2016:436-441. https://doi.org/10.1109/ICEETS.2016.7583794
  38. Zitar RA, Al-Betar MA, Awadallah MA, Doush IA, Assaleh K. An intensive and comprehensive overview of JAYA algorithm, its versions and applications. Arch Comput Methods Eng. 2022;29:763-792. https://doi.org/10.1007/S11831-021-09585-8
  39. Degertekin SO, Lamberti L, Ugur IB. Sizing, layout and topology design optimization of truss structures using the Jaya algorithm. Appl Soft Comput. 2018;70:903-928. https://doi.org/10.1016/J.ASOC.2017.10.001
  40. Awadallah MA, Al-Betar MA, Hammouri AI, Alomari OA. Binary Jaya algorithm with adaptive mutation for feature selection. Arab J Sci Eng. 2020;45:10875-10890. https://doi.org/10.1007/S13369-020-04871-2
  41. Bakare MS, Abdulkarim A, Zeeshan M, Shuaibu AN. A comprehensive overview on demand side energy management towards smart grids: challenges, solutions, and future direction. Energy Inform. 2023;6:1-59. https://doi.org/10.1186/S42162-023-00262-7
  42. Abrar Mohamed Hafiz, Abdelrahman ME, Temraz H. Economic dispatch in power system networks including renewable energy resources using various optimization techniques. Arch Electr Eng. 2021;70:643-655. https://doi.org/10.24425/aee.2021.137579
  43. Selvakumar AI, Thanushkodi K. A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans Power Syst. 2007;22(1):42-51. https://doi.org/10.1109/TPWRS.2006.889132
  44. Niu Q, Zhang H, Li K. An improved TLBO with elite strategy for parameters identification of solar cells and modules. Energy Convers Manag. 2013;71:150-160. https://doi.org/10.1016/j.enconman.2013.04.019
  45. Iqbal MN, Bhatti AR, Butt AD, Sheikh YA, Paracha KN, Ashique RH. Solution of economic dispatch problem using hybrid multi-verse optimizer. Electric Power Syst Res. 2022;208:107912. https://doi.org/10.1016/J.EPSR.2022.107912
  46. Hassan MH, Kamel S, Jurado F, Desideri U. Global optimization of economic load dispatch in large scale power systems using an enhanced social network search algorithm. Int J Electr Power Energy Syst. 2024;156:109719. https://doi.org/10.1016/J.IJEPES.2023.109719
  47. Elsakaan AA, El-Sehiemy RA, Kaddah SS, Elsaid MI. An enhanced moth-flame optimizer for solving non-smooth economic dispatch problems with emissions. Energy. 2018;157:1063-1078. https://doi.org/10.1016/J.ENERGY.2018.06.088
  48. Dehbalaee MRG, Shaeisi GH, Valizadeh M. A proposed improved hybrid hill climbing algorithm with the capability of local search for solving the nonlinear economic load dispatch problem. Int J Eng. 2020;33:575-585. https://doi.org/10.5829/IJE.2020.33.04A.09
  49. Powell MJD. A new algorithm for unconstrained optimization. In: Rosen JB, Mangasarian OL, Ritter K, eds. Nonlinear Programming. New York, NY: Academic Press; 1970:31-65. https://doi.org/10.1016/B978-0-12-597050-1.50006-3
  50. Conn AR, Gould NIM, Toint PL. Trust-Region Methods. Philadelphia, PA: SIAM; 2000. https://doi.org/10.1137/1.9780898719857
  51. El-sobky B, Abo-elnaga Y, Elsaid A, Foda A. Relaxed i-shot trust-region algorithm for solving multi-objective economic emission load dispatch problem. J Taibah Univ Sci. 2018;12:573-583. https://doi.org/10.1080/16583655.2018.1503796
  52. Gianto R, Purwoharjono. Trust-region method for load flow solution of three-phase unbalanced electric power distribution system. J Electr Comput Eng. 2022;2022. https://doi.org/10.1155/2022/5415300
  53. Yang KE, Tsai CY, Shen HH, et al. Trust-region method with deep reinforcement learning in analog design space exploration. In: Proceedings - Design Automation Conference. Vol 2021-December. Piscataway, NJ: IEEE; 2020:1225-1230. https://doi.org/10.1109/DAC18074.2021.9586087
  54. Rosen DM, Kaess M, Leonard JJ. RISE: An incremental trust-region method for robust online sparse least-squares estimation. IEEE Trans Robot. 2014;30:1091-1108. https://doi.org/10.1109/TRO.2014.2321852
  55. Li B, Jiang WS. Optimizing complex functions by chaos search. Cybern Syst. 1998;29(4):409-419. https://doi.org/10.1080/019697298125678
  56. Alatas B, Akin E, Ozer AB. Chaos embedded particle swarm optimization algorithms. Chaos Solitons Fractals. 2009;40(4):1715-1734. https://doi.org/10.1016/j.chaos.2007.09.063
  57. Karthik N, Rajagopalan A, Bajaj M, et al. Chaotic self-adaptive sine cosine multi-objective optimization algorithm to solve microgrid optimal energy scheduling problems. Sci Rep. 2024;14. https://doi.org/10.1038/s41598-024-69734-4
  58. Wu X, Gao S, Iu HHC, et al. Multi-scroll regulation and control of a programmable memristive Hopfield neural network with FPGA implementation. Sci China Technol Sci. 2026;69(9):1920406. https://doi.org/10.1007/s11431-025-3273-y
  59. Gao S, Zhang Z, Iu HHC, et al. A parallel color image encryption algorithm based on a 2-D logistic-Rulkov neuron map. IEEE Internet Things J. 2025;12(11):18115-18124. https://doi.org/10.1109/JIOT.2025.3540097
  60. Ding S, Shi F, Erkan U, et al. Design of a three-dimensional logistic map and its application to seafood image encryption. J Supercomput. 2026;82(4):225. https://doi.org/10.1007/s11227-025-08196-5
  61. Gao S, Iu HHC, Erkan U, et al. A 3D memristive cubic map with dual discrete memristors: design, implementation, and application in image encryption. IEEE Trans Circuits Syst Video Technol. 2025;35(8):7706-7718. https://doi.org/10.1109/TCSVT.2025.3545868
  62. Gao S, Zhang Z, Li Q, et al. Encrypt a story: A video segment encryption method based on the discrete sinusoidal memristive Rulkov neuron. IEEE Trans Dependable Secure Comput. 2025;22(6):8011-8024. https://doi.org/10.1109/TDSC.2025.3603570
  63. Lin Y, Wei Y, Chen D, et al. Cryptanalysis and improvement of a video cryptosystem via chaos and S-box. ACM Trans Multimedia Comput Commun Appl. 2026;22(6):1-28. https://doi.org/10.1145/3808699
  64. El-Shorbagy MA. Trust region based chaotic search for solving multi-objective optimization problems. Expert Syst. 2024;41(12):e13705. https://doi.org/10.1111/exsy.13705
  65. Epitropakis MG, Li X, Engelbrecht A. IEEE WCCI/CEC 2020 competition on niching methods for multimodal optimization. 2020. Accessed June 15, 2026. https://www.epitropakis.co.uk/cec20-niching/competition/
  66. Li X, Engelbrecht A, Epitropakis MG. Benchmark functions for CEC'2013 special session and competition on niching methods for multimodal function optimization. Technical report. Melbourne, Australia: Evolutionary Computation and Machine Learning Group, RMIT University; 2013.
  67. Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum Associates; 1988. https://doi.org/10.4324/9780203771587
  68. Vargha A, Delaney HD. A critique and improvement of the CL common language effect size statistics of McGraw and Wong. J Educ Behav Stat. 2000;25(2):101-132. https://doi.org/10.3102/10769986025002101
  69. Ministry of Energy and Mineral Resources, Republic of Indonesia (ESDM). Harga batubara acuan (HBA): Indonesian coal reference price. Jakarta: Kepmen ESDM; 2024. Accessed June 15, 2026. https://www.esdm.go.id/id/media-center/arsip-berita/menteri-esdm-tetapkan-harga-acuan-untuk-batubara-dan-mineral-bulan-mei-2024
  70. Institute for Global Environmental Strategies (IGES). List of grid emission factors: Indonesia (Jamali and regional grids). Technical report. Joint Crediting Mechanism (JCM), Ministry of Environment, Japan; 2023. Accessed June 15, 2026. https://www.iges.or.jp/jp/pub/list-grid-emission-factor/en
  71. Lasota A, Mackey MC. Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics. Applied Mathematical Sciences. Vol 97. 2nd ed. New York, NY: Springer-Verlag; 1994. https://doi.org/10.1007/978-1-4612-4286-4
  72. Devaney RL. An Introduction to Chaotic Dynamical Systems. 2nd ed. Redwood City, CA: Addison-Wesley; 1989. https://doi.org/10.1201/9780429280801
  73. Elaydi SN. Discrete Chaos: With Applications in Science and Engineering. 2nd ed. Boca Raton, FL: Chapman and Hall/CRC; 2008. https://doi.org/10.1201/9781420011043
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