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Applications of Curve Fitting Techniques in Inertia Estimation of Power System
Research Article | Published: 23 December 2025
Sustainable Energy Control and Optimization Volume 1, Issue 2, 2025: 61-66
Volume 1, Issue 2, Sustainable Energy Control and Optimization
Volume 1, Issue 2, 2025
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Sustainable Energy Control and Optimization, Volume 1, Issue 2, 2025: 61-66

Open Access | Research Article | 23 December 2025
Applications of Curve Fitting Techniques in Inertia Estimation of Power System
by
Altaf Q. H. Badar Altaf Q. H. Badar 1
Bijon Mazumdar Bijon Mazumdar 1
Syed Shahbazuddin Syed Shahbazuddin 1 *
1 Department of Electrical Engineering, National Institute of Technology Warangal, Telangana 506004, India
* Corresponding Author: Syed Shahbazuddin, [email protected]
DOI: 10.62762/SECO.2025.672523
ARK: ark:/57805/seco.2025.672523
Received: 28 September 2025, Accepted: 02 October 2025, Published: 23 December 2025  
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Abstract
The integration of renewable energy sources (RES) into modern power systems is transforming the traditional reliance on synchronous generators, leading to a greener energy portfolio while posing significant challenges to system stability due to reduced inertia. Diminished system inertia results in elevated rates of change of frequency (RoCoF) and larger frequency deviations, potentially culminating in blackouts. Accurate inertia estimation is paramount for implementing virtual inertia control and enhancing frequency support services. This study investigates curve-fitting techniques, with a focus on polynomial fitting, for inertia estimation. Simulations are conducted on a modified IEEE 9-bus system incorporating dynamic models. Transient events involve 10% and 20% load increases at t = 10 s. Results demonstrate that fifth-order polynomials yield the minimum errors (e.g., 9.61% for the 10% load case), with robustness to data loss maintaining errors below 2% for up to 20–30% data reduction.
Graphical Abstract
Applications of Curve Fitting Techniques in Inertia Estimation of Power System
Keywords
curve fitting
frequency stability
IEEE test systems
polynomial fitting
power system inertia
renewable energy sources
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
References
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APA Style
Badar, A. Q. H., Mazumdar, B., & Shahbazuddin, S. (2025). Applications of Curve Fitting Techniques in Inertia Estimation of Power System. Sustainable Energy Control and Optimization, 1(2), 61–66. https://doi.org/10.62762/SECO.2025.672523
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TY  - JOUR
AU  - Badar, Altaf Q. H.
AU  - Mazumdar, Bijon
AU  - Shahbazuddin, Syed
PY  - 2025
DA  - 2025/12/23
TI  - Applications of Curve Fitting Techniques in Inertia Estimation of Power System
JO  - Sustainable Energy Control and Optimization
T2  - Sustainable Energy Control and Optimization
JF  - Sustainable Energy Control and Optimization
VL  - 1
IS  - 2
SP  - 61
EP  - 66
DO  - 10.62762/SECO.2025.672523
UR  - https://www.icck.org/article/abs/SECO.2025.672523
KW  - curve fitting
KW  - frequency stability
KW  - IEEE test systems
KW  - polynomial fitting
KW  - power system inertia
KW  - renewable energy sources
AB  - The integration of renewable energy sources (RES) into modern power systems is transforming the traditional reliance on synchronous generators, leading to a greener energy portfolio while posing significant challenges to system stability due to reduced inertia. Diminished system inertia results in elevated rates of change of frequency (RoCoF) and larger frequency deviations, potentially culminating in blackouts. Accurate inertia estimation is paramount for implementing virtual inertia control and enhancing frequency support services. This study investigates curve-fitting techniques, with a focus on polynomial fitting, for inertia estimation. Simulations are conducted on a modified IEEE 9-bus system incorporating dynamic models. Transient events involve 10% and 20% load increases at t = 10 s. Results demonstrate that fifth-order polynomials yield the minimum errors (e.g., 9.61% for the 10% load case), with robustness to data loss maintaining errors below 2% for up to 20–30% data reduction.
SN  - 3068-7330
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -
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@article{Badar2025Applicatio,
  author = {Altaf Q. H. Badar and Bijon Mazumdar and Syed Shahbazuddin},
  title = {Applications of Curve Fitting Techniques in Inertia Estimation of Power System},
  journal = {Sustainable Energy Control and Optimization},
  year = {2025},
  volume = {1},
  number = {2},
  pages = {61-66},
  doi = {10.62762/SECO.2025.672523},
  url = {https://www.icck.org/article/abs/SECO.2025.672523},
  abstract = {The integration of renewable energy sources (RES) into modern power systems is transforming the traditional reliance on synchronous generators, leading to a greener energy portfolio while posing significant challenges to system stability due to reduced inertia. Diminished system inertia results in elevated rates of change of frequency (RoCoF) and larger frequency deviations, potentially culminating in blackouts. Accurate inertia estimation is paramount for implementing virtual inertia control and enhancing frequency support services. This study investigates curve-fitting techniques, with a focus on polynomial fitting, for inertia estimation. Simulations are conducted on a modified IEEE 9-bus system incorporating dynamic models. Transient events involve 10\% and 20\% load increases at t = 10 s. Results demonstrate that fifth-order polynomials yield the minimum errors (e.g., 9.61\% for the 10\% load case), with robustness to data loss maintaining errors below 2\% for up to 20–30\% data reduction.},
  keywords = {curve fitting, frequency stability, IEEE test systems, polynomial fitting, power system inertia, renewable energy sources},
  issn = {3068-7330},
  publisher = {Institute of Central Computation and Knowledge}
}
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CC BY Copyright © 2025 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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