M.A. Zorrozua 1 , J. Lazaro 2 , J.F. Miñambres 1 , B. Larrea 2 and M.Sanchez 2

1 Department of Electrical Engineering

2 Department of Applied Mathematics

E.T.S.I., University of the Basque Country (UPV/EHU)

Alda. Urquijo s/n, 48013 Bilbao (Spain)

Phone/Fax number:+0034 94 6014056 / +0034 94 6014200, e-mail: miguelangel.zorrozua @ehu.es

Abstract. A new simple method is presented in order to analyze the full harmonic spectrum (harmonic and interharmonic) of a transient signal. The proposed algorithm features a trade-off between accuracy and computational burden. The results obtained show that this method significantly improves the estimation of power system harmonics and inter-harmonics.

Key words – Harmonic analysis, interharmonics, spectral analysis.

**1. Introduction**

As it is well known, electrical signals (voltages or currents) in actual power systems are not ideal. They can

be considered as the sum of a series of different components superimposed over a fundamental component. According to IEC 61000-2-1 and IEC 61000-2-2, their analysis leads to the definition of the following types of components:

– Fundamental component. It is a sinusoidal wave at fundamental frequency (f) of the power system (f = 50 Hz or 60 Hz).

– Harmonic components. They are sinusoidal waves having frequencies (f h ) that are whole multiples of the fundamental frequency. The ratio of the harmonic frequency to the fundamental frequency is called harmonic order (h). h·f f h where h is an integer greater than zero – Interharmonic components. IEC-61000-2-1 establishes that “Between the harmonics of the power frequency voltage and current, further frequencies can be observed which are not an integer of the fundamental. They can appear as discrete frequencies or as a wide-band spectrum”. Consequently, interharmonic frequency (f h ) is defined as h·f f h where h is an integer greater than zero By analogy with harmonics, h is called interharmonic

order.

– Subharmonic components. They are only a particular case of interharmonic of a frequency (f m ) less than the fundamental frequency. m·f f m where 0 < m < 1

– Aperiodic components. The constant dc offset and the decaying dc offset are the typical aperiodic components present in an electrical signal. The presence of harmonic and aperiodic components is very usual in electrical signals, above all during transient periods. In recent years, the interharmonics have increasing importance. Fundamental sources of this last type of components are:

Arcing loads as those provided by arc furnaces and welding machines. Arc furnaces usually produce significant interharmonics during the initial phase of melting. Welding operations tend to generate a particular spectrum associated with each process.

Ripple controls such as the metering devices used to regulate the usage of energy at certain times of the day. Ripple control metering is growing in importance nowadays as an attempt to slow global warming and reducing the need for drilling and mining for energy resources.

Static converters are increasingly used for the integration of distributed power generators, such as photovoltaic systems and speed-variable windmills, into the grid.

Variable load electric drives such as motors with variable-torque loading. Also, induction motors can generate interharmonics in association with saturation of the magnetic circuit (slot harmonics), natural asymmetry or rotor misalignment.