1. MEASUREMENT OF IEC GROUPS AND SUBGROUPS USING ADVANCED SPECTRUM ESTIMATION METHODS A. Bracale, G. Carpinelli, Z. Leonowicz, T. Lobos, J. Rezmer Università degli Studi di Napoli “Federico II”, Napoli – Italy Wroclaw University of Technology, Wroclaw – Poland
IMTC Sorrento Italy

2. Harmonic decomposition methods (Prony, ESPRIT, root-MUSIC)
Outline
Introduction
IEC groups & subgroups
Harmonic decomposition methods (Prony, ESPRIT, root-MUSIC)
Investigations
Conclusions

3. Introduction
Spectral representation of waveform distortions in power systems.
Increasing number of power quality (PQ) problems linked to modern power electronic devices, the influence of disturbances on loads and the new liberalized competitive markets, where the PQ has significant economic consequences.
Indices for the characterization of waveform distortions.

4. Introduction
In this paper we propose to estimate the IEC groups and subgroups with advanced spectrum estimation methods: the Prony, ESPRIT and root-MUSIC methods
High accuracy when analysing strongly distorted waveforms with non-stationary behaviour.
DC arc furnace power supply waveforms.

5. IEC groups & subgroups
Amplitudes

6. Modelled DC arc furnace plant
PCC
Short-circuit apparent power: 3500 MVA
Rated voltage: kV
Transformer T1
Rated power: 80 MVA
Rated voltage: 220kV/21kV
Vcc 8%
Winding connection: Y-Δ
Transformer T2
Rated power: 87 MVA
Rated voltage: 21kV/0,638kV/0,638kV
Vcc 10,37%
Winding connection: Y- Δ - Δ
Interphase reactor 150 μH
Arc furnace rated current 96 kA

7. Harmonic decomposition methods
Adaptive Prony method
A waveform can be approximated by M exponential functions:
characteristic polynomial
Vandermonde matrix parameters:

8. Harmonic decomposition methods
Adaptive ESPRIT method
A waveform can be approximated by:
Two selector matrices
shift invariance between discrete time series
parameters in :

9. Harmonic decomposition methods
Adaptive MUSIC (Multiple Signal Classification) method
MUSIC pseudospectrum

10. Short-time harmonic and interharmonic subgroups
defined as the subgroups calculated for a short time window
amplitudes by averaging

11. Investigations – Test signal

12. Investigations –Dc arc furnace current waveform harmonic subgroup amplitudes

13. Investigations –Dc arc furnace voltage waveform harmonic subgroup amplitudes

14. Dc arc furnace current waveform interharmonic subgroup amplitudes

15. Dc arc furnace voltage waveform interharmonic subgroup amplitudes

16. Investigations - Discussion
Harmonic subgroup amplitudes Gsg11 and Gsg-13 ARM, APM and AEM methods give higher values than IEC
The IEC method gives values of the current and voltage harmonic subgroups Gsg-12 significantly greater than the ones obtained with all the adaptive techniques
Interharmonic subgroup amplitudes - all the adaptive methods (ARM, AEM and APM) give values lower than the ones obtained by using the IEC method.
Results obtained by using the subspace-based methods (ARM and AEM) are similar.

17. Conclusions
Advanced spectrum estimation methods are proposed for the evaluation of the harmonic and interharmonic groupings.
Application of Prony, ESPRIT and root-MUSIC methods to a number of short contiguous variable windows inside the ten fundamental periods imposed by IEC Standards.
The number and the duration of the short windows are obtained by applying an adaptive algorithm based on the minimization of the estimation error.

18. Conclusions
The application of the proposed techniques to test defined waveforms and waveforms deriving from simulations of an actual plant has shown very accurate harmonic and interharmonic subgroup estimation.
Even if the use of the IEC Standard technique represents a good compromise among different aims such as the need for good accuracy, simplification and unification, the new proposed approach appears particularly useful for its very high accuracy also in case of particularly complex signals.