Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

An Analytical Method for Nodal Inertia Estimation of Power Systems
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1Department of Electrical and Electronic Engineering, Imperial College London, London, SW7 2AZ, U.K.;2School of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, U.K.;3Department of Electrical Engineering, Indian Institute of Technology Roorkee, Uttarakhand, 247667, India;4Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016, India

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This work was supported by the Resilient Operation of Sustainable Energy Systems (ROSES) EPSRC-NSFC Programme on Sustainable Energy Supply (No. EP/T021713/1), 2020-2023. The work of D. Brahma was supported in part by a Leverhulme International Professorship (No. LIP-2020-002) and in part by the Engineering and Physical Sciences Research Council (No. EP/Y025946/1).

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    Abstract:

    The significance of system inertia, especially its non-uniform spatial distribution, is becoming paramount in the power system. The scope of inertia estimation has traditionally been the estimation of overall or total system inertia. However, as frequency dynamics become increasingly localized with the increasing penetration level of inverter-based resources (IBRs), the need for higher spatial resolution (geographically localized estimation) and faster temporal resolution (online or continuous estimation) in inertia estimation becomes paramount. This paper proposes an analytical method to estimate the spatial inertia distribution down to the transmission bus level, i.e., nodal inertia. Depending on data availability, the proposed method is flexible and can be used in two ways to estimate nodal inertia under any given operating condition (or snapshot), or to continuously estimate nodal inertia under both ambient and transient conditions using available measurements from local phasor measurement units (PMUs). The novelty of the proposed method lies in its analytical formulation, which does not require rate of change of frequency (ROCOF) measurements or rate of change of power injections, making it immune to the noise associated with the estimation of these derived quantities. Additionally, the proposed method does not require defining near-zero ROCOF thresholds, which is a system-specific and non-trivial problem. The proposed method is mode-agnostic, which makes it more general than the dominant mode-based linearized methods. The applicability of the proposed method is demonstrated through simulation studies performed on the IEEE 39-bus and IEEE 68-bus test systems with varying penetration levels of IBRs. The robustness of the proposed method is numerically assessed against modeling and measurement uncertainties.

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History
  • Received:March 10,2025
  • Revised:August 27,2025
  • Adopted:
  • Online: May 27,2026
  • Published:
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