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Quantification of Non-stationary Power Quality Events: A New Index Based on $\ell_p$-norm of Energy

Faizal Hafiz, Chirag Naik, Davide La Torre, Akshya Swain

Abstract

The present study proposes a new index to quantify the severity of non-stationary power quality (PQ) disturbance events. In particular, the severity of PQ events is estimated from their energy distribution in temporal-frequency space. The index essentially measures the $\ell_p$-norm between the energy distributions of an event and the nominal voltage signal. The efficacy of the new index is demonstrated considering a wide class of major non-stationary PQ events, including sag, swell, interruptions, oscillatory transients, and simultaneous events. The results of this investigation, with simulated, real and experimental data, convincingly demonstrate that the proposed index is generic, monotonic, easy to interpret, and can accurately quantify the severity of non-stationary events.

Quantification of Non-stationary Power Quality Events: A New Index Based on $\ell_p$-norm of Energy

Abstract

The present study proposes a new index to quantify the severity of non-stationary power quality (PQ) disturbance events. In particular, the severity of PQ events is estimated from their energy distribution in temporal-frequency space. The index essentially measures the -norm between the energy distributions of an event and the nominal voltage signal. The efficacy of the new index is demonstrated considering a wide class of major non-stationary PQ events, including sag, swell, interruptions, oscillatory transients, and simultaneous events. The results of this investigation, with simulated, real and experimental data, convincingly demonstrate that the proposed index is generic, monotonic, easy to interpret, and can accurately quantify the severity of non-stationary events.

Paper Structure

This paper contains 26 sections, 29 equations, 11 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Reformulation of Conventional Indices
  4. Deviation Indices
  5. Preliminaries
  6. Non-stationary PQ Events
  7. Temporal Frequency Decomposition of PQ Events
  8. Proposed Index
  9. Energy Norm Index
  10. Preference Integration
  11. Weighted Index
  12. Segmented Index
  13. Index Selection
  14. Evaluation over Single Non-stationary Events
  15. Sag, Interruption and Swell
  16. ...and 11 more sections

Figures (11)

  • Figure 1: Illustrative sag events and the corresponding energy of wavelet coefficients. The x and y-axes in Fig. \ref{['f:sag1']} respectively denote time (cycles) and magnitude (pu). Pure denotes an ideal 1 (pu) and $50 \ Hz$ sinusoidal voltage signal. The x and y-axes in Fig. \ref{['f:SagBar']} respectively denote frequency bands and the wavelet coefficient energy. $\mathcal{B}_1, \mathcal{B}_2, \dots, \mathcal{B}_8$ denote frequency bands after $7^{th}$ level decomposition as shown in Table \ref{['t:DWT']}.
  • Figure 2: The proposed framework for quantification of non-stationary events.
  • Figure 3: Variations in the monotonicity conditions and $\mathcal{ENI}$ for $sag$ and $swell$ events. $e_{n,j} = 1995$ denotes the nominal energy. All variations in $sag$ and $swell$ events are contained in the regions ($e_{n,j}>e_{x,j}$) and ($e_{n,j}<e_{x,j}$).
  • Figure 4: Selection of an appropriate energy norm index
  • Figure 5: Variations in $\mathcal{ENI}$ for Sags, Interruptions, and Swells. $\mathcal{ENI}$ is determined using $\ell_2-$norm.
  • ...and 6 more figures

Theorems & Definitions (3)

  • proof
  • Remark 1
  • proof