Analysis of Sub-Harmonics in Power Systems

Zbigniew Leonowicz
Faculty of Electrical Engineering
Wroclaw University of Technology
Wroclaw, Poland,

Abstract—With a wide range of power electronics-related applications in power systems, harmonic currents are increasing at an alarming rate which has greatly deteriorated the power quality in electrical power networks. Moreover, some of electronic controlled equipments used in power systems, such as power converters, produce sub-harmonics, a type of waveform distortion, which can severely degrade the power system performance. Therefore, they must be closely monitored. Moreover, Fast Fourier Transform cannot accurately analyze waveforms containing sub-harmonics because the synchronization of the sampling procedure to sub-harmonics is practically infeasible. The detection of sub-harmonics requires an approach different from that used for harmonics analysis. In most analysis methods the voltage waveform is expected to be a pure sinusoid with a given frequency and amplitude. Standard tools of harmonic analysis based on the Fourier transform assume that only harmonics are present in the investigated signal and the periodicity intervals are fixed, while periodicity intervals in the presence of inter-harmonics and sub-harmonics can be variable and very long. A novel approach to analysis of non-stationary signals, based on the “subspace” methods, is proposed. “Root-Music” harmonic retrieval method is an example of high- resolution eigenstructure-based method

Keywords:- Discrete Fourier Transform, dc arc furnaces
frequency measurement, harmonic analysis, power system,
subspace methods

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Self-perception and Experiential Schemata in the Addicted Brain

Rex Cannon Æ Æ Joel Lubar Æ Æ Debora Baldwin

Abstract This study investigated neurophysiological differences between recovering substance abusers (RSA) and controls while electroencephalogram (EEG) was continuously recorded during completion of a new assessment instrument. The participants consisted of 56 total subjects; 28 RSA and 28 non-clinical controls (C). The participants completed the self-perception and experiential schemata assessment (SPESA) and source localization was compared utilizing standardized low-resolution electromagnetic tomography (sLORETA). The data show significant differences between groups during both the assessment condition and baselines. A pattern of alpha activity as estimated by sLORETA was shown in the right amygdala, uncus, hippocampus, BA37, insular cortex and orbito frontal regions during the SPESA condition. This activity possibly reflects a circuit related to negative perceptions of self formed in specific neural pathways. These pathways may be responsive to the alpha activity induced by many substances by bringing the brain into synchrony if only for a short time. In effect this may represent the euphoria described by substance abusers.

Keywords Addiction  Self-perception  Neurophysiological assessment  EEG biofeedback LORETA

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Mathematically Derived Frequency Correlates in Cerebral Function: Theoretical and Clinical Implications for Neurofeedback Training

Marvin W. Sams, Th.D., R. EEG T., QEEGT., L.Ac.
Technical Edito

Many cortical and subcortical areas of the brain have spontaneously occurring 3644 Hz (’40-Hz”) activity. Across the scalp, the EEG peak frequency of 40 Hz is z 39.5 Hz. A theory is proposed in which the brain has certain resident resonant frequencies that are subharmonics of 40-Hz activity. Some of these EEG frequencies are commonly trainedin  neurotherapy. Two examples are 12-15 Hz and 7-8 Hz activity, which are third and fifth subharmonics. Other frequencies with known cognitive and mental processing relation ships and mathematical associations to 40 Hz include ‘Frontal mid Theta” at 6.5 Hz (sixth subharmonic) and Theta at 4 Hz (tenth subharmonic). Exploring 40 Hz and its sub harmonics may provide further insight into the mechanics of the neurofeedback process and lead to more effective and efficient training. It is also anticipated that if the concept of 40-Hz subharmonics is explored, the mechanisms of cerebral function might be better understood.

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Activation of Human Cerebral and Cerebellar Cortex by Auditory Stimulation at 40 Hz

Maria A. Pastor, 1 Julio Artieda, 1 Javier Arbizu, 2 Josep M. Marti-Climent, 2 Ivan Pen ˜uelas, 2 and
Jose C. Masdeu 1
Departments of 1 Neurology and 2 Nuclear Medicine, University of Navarra School of Medicine, 31080 Pamplona, Spain
We used functional brain imaging with positron emission to-mography (PET)-H 2 15 O to study a remarkable neurophysiological finding in the normal brain. Auditory stimulation at various frequencies in the gamma range elicits a steady-state scalp electroencephalographic (EEG) response that peaks in amplitude at 40 Hz, with smaller amplitudes at lower and higher stimulation frequencies. We confirmed this finding in 28 healthy subjects, each studied with monaural trains of stimuli at 12 different stimulation rates (12, 20, 30, 32, 35, 37.5, 40, 42.5, 45, 47.5, 50, and 60 Hz). There is disagreement as to whether the peak in the amplitude of the EEG response at 40 Hz corresponds simply to a superimposition of middle latency auditory evoked potentials, neuronal synchronization, or increased cortical synaptic activity at this stimulation frequency. To clarify this issue, we measured regional cerebral blood flow (rCBF) with PET-H 2

15 O in nine normal subjects at rest and during auditory stimulation at four different frequencies (12, 32, 40, and 47 Hz) and analyzed the results with statistical parametric mapping. The behavior of the rCBF response was similar to the steady-state EEG response, reaching a peak at 40 Hz. This finding suggests that the steady-state amplitude peak is related to increased cortical synaptic activity. Additionally, we found that, compared with other stimulation frequencies, 40 Hz selectively activated the auditory region of the pontocerebellum, a brain structure with important roles in cortical inhibition and timing.

Key words: steady-state auditory evoked potentials; gamma oscillatory activity; regional cerebral blood flow; positron emission tomography; cerebellum; auditory cortex

Estimation of Power System Harmonics and Interharmonics in the Presence of Aperiodic Components

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

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

– 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.

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Measurement of Subharmonics in Power Voltages

J. Barros, Senior Member IEEE, M. de Apraiz, and R. I. Diego

Abstract—This paper presents the results of the monitoring of sub-harmonic voltages in a low-voltage distribution network using an IEC harmonic measurement instrument. The time evolution and the statistical analysis of the r.m.s. voltage magnitude of the subharmonic group and subgroup, defined as grouping of the output bins of an IEC harmonic measurement instrument below 50 Hz, are investigated in a low-voltage distribution system. The results obtained show higher magnitude of these components than was expected, showing similar time evolution to the magnitudes of the 1st and 2nd order interharmonic groups and the flicker severity indices simultaneously measured in the same power supply system.

Index Terms—Harmonics, Power quality, Power distribution systems, Subharmonics

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The Electromagnetic Induction of Mystical and Altered States within the Laboratory

Michael A. Persinger* , Kevin S. Saroka, Stanley A. Koren & Linda S. St-Pierre Consciousness Research Laboratory, Behavioural Neuroscience & Biomolecular Sciences Programs Laurentian University, Sudbury, Ontario Canada P3E 2C6


The human brain is the locus of all human experiences. The substantial microstructural and neuroelectrical differences between the two cerebral hemispheres predicts two major classes of mystical experiences which involve the sensed presence and the out-of-body experience. Their occurrence and their attributions to cosmic origins have been reported for centuries and have been the bases for social belief systems. Direct cerebral electrical stimulation during the 20th century evoked these experiences. In the 21st century the non-invasive, external transcerebral application of complex, physiologically-patterned weak magnetic fields has been shown to produce similar experiences that can be correlatively mapped by quantitative electroencephalographic inferences of interhemispheric coherence. The experimental production and control of these powerful experiences by more sophisticated technologies might be employed to understand the intricate nature and function of mystical/altered states within large populations of human beings. Key Words: mystical states, out-of-body-experiences, sensed presence, biofrequency electromagnetic fields, consciousness.

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