Operator formalism for the Wigner phase distribution

The probability distribution for finding a state of the radiation field in a particular phase is described by a multitude of theoretical formalisms; the phase-sensitivity of the Wigner quasi-probability distribution being one of them. We construct a hermitian phase operator for this Wigner phase. We show that this operator is complete and also elucidate a set of complete but non-orthogonal states that seems to be naturally associated with such an operator. Further we show that our operator satisfies a weak equivalence relation with the Pegg-Barnett operator, thus showing that the essential phase information furnished by both formalisms are the same. It is also shown that this operator gives results which are in correct agreement with the expected uniform phase distribution of a Fock state.Comment: 5 page

Phasor-Based Assessment for Harmonic Sources in Distribution Networks

Phasor-based interdependencies of multiple harmonic sources, especially Distributed Energy Resources, on distribution networks are analyzed in this paper. A new index, Phasor Harmonic Index (IPH), is proposed by the authors. IPH considers both harmonic source magnitude and phase angle for different harmonic orders. Other commonly used harmonic indices are based solely on magnitude of waveforms. A very detailed model of a distribution network is used in the harmonic assessment. With the help of the detailed distribution network model, the phase couplings and the phase balancing impacts on harmonic propagation between three phases are investigated. Moreover, effects of harmonic source phase angle deviations are analyzed at both the customer side and the substation side. This paper investigates the importance of phase angles in harmonic assessment and how distribution netw

General modeling of the windings for multi-phase ac machines

This paper, which deals with the winding modeling of ac multi-phase machines with a regular distribution of the stator slots, details an original matrix modeling of the stator winding. First, the properties of the balanced multi-phase windings (with integral-slot and fractional-slot patterns) are analysed. The winding function approach, one of the most common way to model the winding distribution effects on the stator rotating field, is then introduced. For multi-phase machines, it will be shown that the pole number generated by the winding distribution depends on a new parameter: the circularity index. The discrete nature of the winding, imposed by the stator slots, leads to the development of a discrete modeling of the winding obtained from sampling the winding function: two matrices, the winding function matrix and the distribution function matrix, are introduced to characterize the multi-phase winding. This matrix approach is thus a concise way to calculate the winding factors and to estimate the set of self and mutual stator inductances for smooth air gap multi-phase machines. A particularly original method of obtaining an analytical expression for the leakage mutual inductance is described. The results are validated with two experimental 5-phase PM machines by using experimental measurements and numerical simulations

Phase Distribution and Phase Correlation of Financial Time Series

Scaling, phase distribution and phase correlation of financial time series are investigated based on the Dow Jones Industry Average (DJIA) and NASDAQ 10-minute intraday data for a period from Aug. 1 1997 to Dec. 31 2003. The returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of Levy's alpha stable distribution condition. A novel approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study phase distribution and correlation. The analysis of phase distribution concludes return time series fall into a class which is different from other non-stationary time series. The correlation between returns of the two indices probed by the distribution of phase difference indicates there was a remarkable change of trading activities after the event of 911 attack, and this change persisted in later trading activities.Phase Distribution, High Frequency Data, Scaling Analysis, Levy Distribution, Stock Market, Frequency Variant

Overview of three-phase inverter topologies for distributed generation purposes

The increasing presence of single-phase distributed generators and unbalanced loads in the electric power system may lead to unbalance of the three phase voltages, resulting in increased losses and heating. Distribution network operators are seeking to install larger DG units (viz. $>5$kVA in Belgium) by means of three-phase connections instead of single-phase to reduce voltage unbalance. There are several possible topologies to connect the DG units to the three-phase distribution network. These topologies can be divided into three groups: the three-phase three-wire inverters, the three-phase four-wire inverters and the multilevel inverters. In this paper, an overview of the aforementioned topologies is given