Switching Markov Gaussian models for dynamic power system inertia estimation

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Abstract

Future power systems could benefit considerably from having a continuous real-time estimate of system inertia. If realized, this could provide reference inputs to proactive control and protection systems which could enhance not only system stability but also operational economics through, for example, more informed ancillary reserve planning using knowledge of prevailing system conditions and stability margins. Performing these predictions in real time is a significant challenge owing to the complex stochastic and temporal relationships between available measurements. This paper proposes a statistical model capable of estimating system inertia in real time through observed steady-state and relatively small frequency variations; it is trained to learn the features that inter-relate steady-state averaged frequency variations and system inertia, using historical system data demonstrated over two consecutive years. The proposed algorithm is formulated as Gaussian Mixture Model with temporal dependence encoded as a Markov chains. Applied within a UK power system scenario, it produces an optimized mean squared error within 0.1s2 for 95% of the daily estimation if being calibrated on a half-hourly basis and maintains robustness through measurement interruptions of up to a period of three hours.
LanguageEnglish
JournalIEEE Transactions on Power Systems
DOIs
Publication statusAccepted/In press - 5 Nov 2015

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System stability
Markov processes
Planning
Economics
Statistical Models

Keywords

  • real-time inertia estimation
  • Gaussian mixture models
  • Markov chain
  • model training

Cite this

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title = "Switching Markov Gaussian models for dynamic power system inertia estimation",
abstract = "Future power systems could benefit considerably from having a continuous real-time estimate of system inertia. If realized, this could provide reference inputs to proactive control and protection systems which could enhance not only system stability but also operational economics through, for example, more informed ancillary reserve planning using knowledge of prevailing system conditions and stability margins. Performing these predictions in real time is a significant challenge owing to the complex stochastic and temporal relationships between available measurements. This paper proposes a statistical model capable of estimating system inertia in real time through observed steady-state and relatively small frequency variations; it is trained to learn the features that inter-relate steady-state averaged frequency variations and system inertia, using historical system data demonstrated over two consecutive years. The proposed algorithm is formulated as Gaussian Mixture Model with temporal dependence encoded as a Markov chains. Applied within a UK power system scenario, it produces an optimized mean squared error within 0.1s2 for 95{\%} of the daily estimation if being calibrated on a half-hourly basis and maintains robustness through measurement interruptions of up to a period of three hours.",
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author = "Xue Cao and Bruce Stephen and Abdulhadi, {Ibrahim Faiek} and Campbell Booth and Graeme Burt",
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AU - Stephen, Bruce

AU - Abdulhadi, Ibrahim Faiek

AU - Booth, Campbell

AU - Burt, Graeme

N1 - (c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

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N2 - Future power systems could benefit considerably from having a continuous real-time estimate of system inertia. If realized, this could provide reference inputs to proactive control and protection systems which could enhance not only system stability but also operational economics through, for example, more informed ancillary reserve planning using knowledge of prevailing system conditions and stability margins. Performing these predictions in real time is a significant challenge owing to the complex stochastic and temporal relationships between available measurements. This paper proposes a statistical model capable of estimating system inertia in real time through observed steady-state and relatively small frequency variations; it is trained to learn the features that inter-relate steady-state averaged frequency variations and system inertia, using historical system data demonstrated over two consecutive years. The proposed algorithm is formulated as Gaussian Mixture Model with temporal dependence encoded as a Markov chains. Applied within a UK power system scenario, it produces an optimized mean squared error within 0.1s2 for 95% of the daily estimation if being calibrated on a half-hourly basis and maintains robustness through measurement interruptions of up to a period of three hours.

AB - Future power systems could benefit considerably from having a continuous real-time estimate of system inertia. If realized, this could provide reference inputs to proactive control and protection systems which could enhance not only system stability but also operational economics through, for example, more informed ancillary reserve planning using knowledge of prevailing system conditions and stability margins. Performing these predictions in real time is a significant challenge owing to the complex stochastic and temporal relationships between available measurements. This paper proposes a statistical model capable of estimating system inertia in real time through observed steady-state and relatively small frequency variations; it is trained to learn the features that inter-relate steady-state averaged frequency variations and system inertia, using historical system data demonstrated over two consecutive years. The proposed algorithm is formulated as Gaussian Mixture Model with temporal dependence encoded as a Markov chains. Applied within a UK power system scenario, it produces an optimized mean squared error within 0.1s2 for 95% of the daily estimation if being calibrated on a half-hourly basis and maintains robustness through measurement interruptions of up to a period of three hours.

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