Statistical properties of real-time amplitude estimate of harmonics affected by frequency instability

Abstract This work deals with the statistical characterization of real-time digital measurement of the amplitude of harmonics affected by frequency instability. In fact, in modern power systems both the presence of harmonics and frequency instability are well-known and widespread phenomena mainly due to nonlinear loads and distributed generation, respectively. As a result, real-time monitoring of voltage/current frequency spectra is of paramount importance as far as power quality issues are addressed. Within this framework, a key point is that in many cases real-time continuous monitoring prevents the application of sophisticated algorithms to extract all the information from the digitized waveforms because of the required computational burden. In those cases only simple evaluations such as peak search of discrete Fourier transform are implemented. It is well known, however, that a slight change in waveform frequency results in lack of sampling synchronism and uncertainty in amplitude estimate. Of course the impact of this phenomenon increases with the order of the harmonic to be measured. In this paper an approximate analytical approach is proposed in order to describe the statistical properties of the measured magnitude of harmonics affected by frequency instability. By providing a simplified description of the frequency behavior of the windows used against spectral leakage, analytical expressions for mean value, variance, cumulative distribution function, and probability density function of the measured harmonics magnitude are derived in closed form as functions of waveform frequency treated as a random variable

Consistent circuit technique for zero-sequence currents evaluation in interconnected single/three-phase power networks

This paper deals with a rigorous and mathematically consistent technique for circuit analysis of modern electrical power systems consisting in the interconnection of three-phase components and single-phase active loads. Indeed, it is well known that the standard technique based on the symmetrical components transformation is commonly used in the analysis of symmetrical threephase systems. Nowadays, however, the evolution of power systems towards the custom power conditioning (e.g., active filtering) and the smart grid model requires the inclusion into the analytical tool of single-phase active loads. Starting from the symmetrical components transformation in its rational form instead of its classical form, a rigorous circuit representation of the interconnection of a three-phase system with single-phase active loads is derived in the paper. The proposed circuit representation allows the analysis of complex power systems by means of basic circuit techniques. In particular, the paper focuses on the evaluation of the zero-sequence component of the currents in any branch of the power system. The application of the proposed circuit technique is demonstrated through an example consisting in the analysis of an active filter designed to force to zero the current in the fourth wire of the mains

Combined MTL-fullwave statistical approach for fast estimation of radiated immunity of spacecraft cable assemblies involving multipair bundles

In this work, a computationally-efficient modelling approach is developed to predict the electromagnetic noise induced in the terminal units of random bundles of twisted-wire pairs mounted onboard spacecraft. The proposed model combines the results of a preliminary full wave simulation, aimed at evaluating the electromagnetic field inside the space vehicle’s metallic body, with a stochastic model of a random bundle, based on multiconductor transmission line (MTL) theory. Model assessment versus measurement data obtained characterizing real wiring harness in a full-scale satellite mock-up demonstrates the large sensitivity (up to 40 decibels) of the induced noise levels to different bundle configurations, and corroborates the effectiveness of the proposed simplified modelling strategy for estimating the modal noise voltages induced in the terminal units

Influence of Random Modulated Power Converter on G3 Power Line Communication

Power Line Communication (PLC) technologies are being used in many applications and offer the advantage of utilizing existing power cables for both power and data transmission, thus minimizing cost and complexity. Nevertheless, PLC technology requires further investigation to solve possible co-existence issues. Indeed, recent studies confirmed that alternative modulation schemes such as Random Pulse Width Modulation (RPWM), applied to switching-mode power converters to minimize conducted emissions, detrimentally interfere with the PLC system. This paper presents an experimental test campaign aimed at investigating the effects of RPWM on the G3-PLC system, with the final goal of understanding the conditions under which RPWM schemes can be considered as an effective alternative to conventional Pulse Width Modulation (PWM) in applications involving PLC systems. In details, the effects of different RPWM parameters such as switching frequency, modulation index, and Random Number Update Rate (RNUR) on the G3-PLC is investigated. In addition, different RPWM schemes such as Random Frequency Modulation (RFM) and Random Pulse Position Modulation (RPPM) are compared in terms of performance so as to highlight which RPWM is best suited to assure coexistence with PLC systems. The impact of RPWM on the communication channel is evaluated in terms of Frame Error Rate (FER), Channel Capacity, and Channel Capacity Loss metrics. Experimental results confirmed that randomly modulated converters with switching frequencies near the G3-PLC bandwidth cause more significant disturbance and possible coexistence issues than the switching frequencies out of this range. Results also show that the modulation index and the RNUR of RPWM have a direct effect on the communication channel. Moreover, a trade-off between Electromagnetic Interference (EMI) reduction and coexistence issues is observed: RFM, which is very effective for EMI reduction, is found to be very disruptive for G3-PLC, compared to alternative random modulation techniques such as RPPM

SPICE behavioral modeling of RF current injection in wire bundles

In this work, a measurement-based procedure aimed at deriving a behavioral model of Bulk Current Injection (BCI) probes clamped onto multi-wire cable bundles is proposed. The procedure utilizes the measurement data obtained by mounting the probe onto the calibration jig for model-parameters extraction, and 2D electromagnetic simulations to adapt such parameters to the specific characteristics of the cable bundle under analysis. Outcome of the analysis is a behavioral model which can be easily implemented into the SPICE environment. Without loss of generality, the proposed model is here used to predict the radio-frequency noise stressing the terminal units of a two-wire harness. Model accuracy in predicting the common and differential mode voltages induced by BCI at the line terminals is assessed by EM modeling and simulation of the involved injection setup by the commercial software CST Microwave Studio