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Harmonic state estimation based on discrete exponential expansion, singular value decomposition and a variable measurement model

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  • Cisneros-Magaña, Rafael
  • Medina-Rios, Aurelio
  • Fuerte-Esquivel, Claudio R.
  • Segundo-Ramírez, Juan

Abstract

In this contribution, a method for harmonic state estimation (HSE) of electrical systems using the discrete exponential expansion (DEE), singular value decomposition (SVD) and a variable measurement model is presented. Variable harmonics, interharmonics, and subharmonics can be estimated using this DEE-SVD time-domain methodology, depending on the number of state variables in the system model and the measurements related through a variable measurement equation, which is proposed as a function of a variable number of measurements and their derivatives to define over, normal and under-determined conditions, respectively. The observability analysis can be verified using the SVD and the resulting null-space vectors, if the electrical system is not completely observable; this analysis can define observable system areas. The HSE regularly receives a limited number of measurements from the system, performs the state estimation and evaluates the global state of the actual harmonic condition. The discrete exponential expansion Newton method determines the periodic steady-state under a particular harmonic condition, obtains a convenient initial steady-state condition to apply the SVD and performs the HSE with a small state estimation error. Noisy measurements adversely affect the state estimation and may increase the state estimation error. The time-domain DEE-HSE can be used to enhance the operation and control of electrical systems under harmonic distortion conditions, e.g., to control active and passive harmonic filters. The state estimation results have been validated through direct comparison against the response obtained with the PSCAD/EMTDC® simulator.

Suggested Citation

  • Cisneros-Magaña, Rafael & Medina-Rios, Aurelio & Fuerte-Esquivel, Claudio R. & Segundo-Ramírez, Juan, 2022. "Harmonic state estimation based on discrete exponential expansion, singular value decomposition and a variable measurement model," Energy, Elsevier, vol. 249(C).
    • Handle: RePEc:eee:energy:v:249:y:2022:i:c:s0360544222006156
    DOI: 10.1016/j.energy.2022.123712
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    References listed on IDEAS

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    1. Khorshidi, Reza & Shabaninia, Faridon & Niknam, Taher, 2016. "A new smart approach for state estimation of distribution grids considering renewable energy sources," Energy, Elsevier, vol. 94(C), pages 29-37.
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    3. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
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