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We introduce the concept of complete edge-colored permutation graphs as complete graphs that are the edge-disjoint union of classical permutation graphs. We show that a graph G = (V, E) is a complete edge-colored permutation graph if and only if each monochromatic subgraph of G is a classical permutation graph and G does not contain a triangle with 3 different colors. Using the modular decomposition as a framework we demonstrate that complete edge-colored permutation graphs are characterized in terms of their strong prime modules, which induce also complete edge-colored permutation graphs. This leads to an O (|V|(2))-time recognition algoriyhm. We show, moreover, that complete edge-colored permutation graphs form a superclass of so-called symbolic ultrametrics and that the coloring of such graphs is always a Gallai coloring.

© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., Static energy meters have shown errors beyond the standards due to conducted electromagnetic interference of pulsed currents. This was observed in several case studies and confirmed by laboratory experiments, which showed errors up to 2675%. The extent of this interference case is unknown, because there is limited information about the waveforms occurring in the real on-site scenarios. This article aims to detect critical waveforms in on-site surveyed data that have similar characteristics as the pulses that resulted in metering errors. The time-domain parameters of the laboratory experiments that show static energy meter interference are compared to the on-site waveform data using an interpolation based on an inverse weighting distance function. Using this approach, the waveform characteristics are compared, and an error is estimated. This approach was satisfactorily validated using data from validation experiments that shows a correct estimation of the actual error according to the permissible limits for energy metering for all validation indices. The performed on-site surveys show the existence of nonlinear waveforms. During the survey of three sites for ten days, 19 531 waveforms were captured, of which 14 487 indicate large nonlinearities and 379 are estimated to produce metering errors up to 925%., Peer Reviewed, Postprint (published version)

In 2015, the energy measurement of some static electricity meters was found to be sensitive to specific conducted electromagnetic disturbances with very fast current changes caused by highly nonlinear loads, leading to meter errors up to several hundred percent. This article describes new results on the electromagnetic compatibility (EMC) of 16 different meters from all over Europe when exposed to real-world disturbance signals. Those test signals were obtained from household appliances and onsite measurements at metered supply points all over Europe. The results show that also the interference signals recorded onsite can cause measurement errors as large as several hundred percent, even for meters that pass the present EMC standards. This unambiguously demonstrates that the present immunity testing standards do not cover the most disturbing conducted interference occurring in present daily-life situations due to the increased use of nonlinear electronics. Furthermore, to enable the adoption of potential new test waveforms in future standards for electricity meter testing, artificial test waveforms were constructed based on real-world waveforms using a piece-wise linear model. These artificial test waveforms were demonstrated to cause meter errors similar to those caused by the original real-life waveforms they are representing, showing that they are suitable candidates for use in improved standardization of electricity meter testing., Postprint (published version)

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., This article presents a time-domain waveform model developed to characterize pulsed, nonlinear, current waveforms resulting in electromagnetic interference on static energy meters. The waveform model is calculated by fitting the sampled waveform data into a linear piece-wise function through a process that involves applying algorithms of pulse extraction, change-point detection, and redundancy elimination. The model is applied to data from laboratory experiments that have indicated critical current waveforms resulting in electromagnetic interference problems with static meters. Afterwards, the parameters of the modeled waveforms are calculated in order to correlate them to metering errors. The most relevant parameters that are correlated to significant errors are the maximum slope, crest factor, pulse duration, and charge. The waveform model provides an accurate description of the complex nonlinear waveforms through simplified analytical expressions that reproduce the significant features of the interfering waveforms. This waveform modeling approach could be used to standardize the artificial test signals that are representative of realistic devices and scenarios., Postprint (author's final draft)

For assessing the underlying problem behind the static meter misreadings, a measurement technique must be developed for characterizing the currents that static meters are usually exposed to. In previous studies it was shown that misreadings of the static meters occur when impulsive currents are drawn from the net, even with standalone commercial off the shelf equipment. Time domain electromagnetic interference (EMI) measurements create a novel opportunity for analyzing these noisy waveforms and identifying their fundamental parameters. The next step is extending this measurement approach to on-site scenarios in which these kind of waveforms coexist in superposition with other components that are properly measured by the static meter when they occur alone. This especially holds for up and coming technologies like electric vehicle (EV) charging stations. The characterization is intended in the future for describing realistic waveforms that can be used as new standardized type-testing signals, which will be employed to produce novel standards. Time Domain Electromagnetic Interference Measurement and Post-processing System (TEMPS) software is used in conjunction with a low cost baseband digitizer to measure the waveforms of EV chargers on four different lines, that is the three phases (L1, L2, and L3) and the neutral line (N) simultaneously. To distinguish the impulsive nature of the waveforms a statistical approach is performed in the form of an amplitude probability distribution (APD) diagram. Furthermore the multichannel capability of the low cost digitizer is utilized to achieve a frequency range extension by using two probes simultaneously with different frequency ranges., This project has received funding from the EMPIR pro-gramme co-financed by the Participating States and fromthe European Union’s Horizon 2020 research and innovationprogramme. The results found reflect the author’s view only.EURAMET is not responsible for any use that may be madeof the information it contains. This work was also supportedby a STSM grant from COST Action IC1407 ACCREDIT., Peer Reviewed, Postprint (published version)