Abstract
With thermal power sources taken into account, the IEEE 57-bus and IEEE 118 bus system’s probabilistic optimal power flow (OPF) solution is being reached. In this article, incorporate renewable energy sources (RES), energy storage system (ESS) and flexible ac transmission system (FACTS) i.e thyristor controlled series compensator (TCSC), thyristor controlled phase shifter (TCPS) and Static VAR compensator (SVC) with frequency security-constrained into the OPF. The reduction of generation costs, emissions and frequency deviations are the main goals. Five situations have been studied in this article: OPF without frequency security restriction, probabilistic OPF with frequency security constraint, OPF integrating FACTS devices (TCSC, TCPS and SVC) with frequency security requirement, OPF incorporating RES (wind and PV), ESS (aqua electrolyzer fuel cell (AEFC) and ultra capacitor), FACTS with frequency security constraint comprises FOPID controller and OPF integrated RES, ESS on IEEE 118-bus system with frequency security constraint. In order to show the balance between generation and consumption, the system’s frequency needs to be kept within a safe range. Therefore, the power flow optimisation system should maintain frequency stability in addition to having the lowest generation cost under operational conditions. Frequency security is a new limitation on the power dispatch problem that is necessary to enable this approach. The test results show that using RES (wind and PV), ESS (AEFC and ultra capacitor) and FACTS with frequency security constraints improves the OPF problem’s resolution. The overall fuel cost and emissions are decreased by 16.59% and 34.95%, respectively, after integrating the FACTs device with security constraints. Additionally, by integrating RES, ESS, and FACTS with frequency security limitation using a FOPID controller, the overall fuel cost and emissions are lowered by 36.41% and 41%, respectively, at 50% load. Furthermore the overall fuel cost and emissions are decreased by 26.11% and 36% at 80% load. Driving training-based optimization (DTBO) has been utilized to identify the optimal solution. The experimental results show that the DTBO outperforms the biography based optimization (BBO) and grey wolf optimization (GWO). Statistical techniques like one-way ANOVA (analysis of variance) demonstrate that the recommended approach has yielded superior results.
Data availability
Not Applicable.(This manuscript does not report data generation or analysis.)
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Mr. A.R.: Data curation, conceptualization, formal analysis, writing review and editing. Dr. S.D.: Methodology, resources, software, writing , original draft-validation. Dr. S.B.: Formal analysis, investigation, methodology. Dr. A.B.: Methodology, resources, software, writing, original draft-validation, writing. Mr. S.G.: Data curation, conceptualization, formal analysis, writing review. Dr. S.B.: Original draft-validation, writing review and editing.
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Appendices
Appendix A
\({{{B}}_{{1}}},{{{B}}_{{2}}}={0}.{42}{{{5}}_{{}}}{p}.{u} {MW}/{Hz};\) \({{{R}}_{{1}}},{{{R}}_{{2}}}={2}.{4Hz}/{pu};\) \({{{T}}_{{G1}}}={0}.{08s};\) \({{{T}}_{{T1}}}={0}.{3s};\) \({{{T}}_{{r1}}}={10s};\) \({{{K}}_{{r1}}}={0}.{3s};\) \({{{K}}_{{P1}}}= {120Hz}/{puMW};\) \({{{K}}_{{P2}}}={120Hz}/{pu}~{MW};\) \({{{T}}_{{P1}}}={{{T}}_{{P2}}}\) \(={20s};{Ptie12}= {200}{MW};\) \({a12}=-{1}, {{{X}}_{{G}}}={0}.{6s};\) \({{{Y}}_{{G}}}={1}.{1s};\) \({{{K}}_{{T1}}}={{{K}}_{{T2}}}={0}.{6};\) \({{{T}}_{{RH}}}={41}.{6}{s},{{{T}}_{{R}}}= {5}{s};\) \({{{T}}_{{GH}}}={0}.{51}{s},{{{T}}_{{W}}}={1}{s},{{{K}}_{{H1}}}={{{K}}_{{H2}}}={0}.{3}, {{{C}}_{{g}}}={1};\) \({{{b}}_{{g}}}={0}.{049s};\) \({{{T}}_{{F}}}={0}.{239s};\) \({{{T}}_{{CR}}}={0}.{01s};\) \({{{T}}_{{CD}}} ={0}.{2s};\) \({RLP}=\pm {0}.{02p}.{u}( {Mw})\) \({{a}}={900};\) \({{b}}={-18};\) \({{d}}={50};\) \({{d}}={50};\) \({50\% loading condition}\).
Appendix B
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Roy, A., Dutta, S., Biswas, S. et al. Probabilistic OPF and LFC of conventional with RES, energy storage and FACTS using DTBO. Sci Rep (2026). https://doi.org/10.1038/s41598-026-43847-4
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DOI: https://doi.org/10.1038/s41598-026-43847-4
