The aim of this paper is to present a novel phasor measurement unit (PMU) data-based cable temperature monitoring method with an intended application towards facilitating dynamic line rating. First part of the paper presents the method to estimate and track the temperature of a 3-phase cable segment.The benefit of this temperature monitoring method is that no additional temperature measurement sensors are required to be placed along the cable. The method is based on a novel algorithm which gives accurate resistance estimates for 3-phase cable segments even in the presence of random and bias errors in the grid measurements. The performance of the method is demonstrated by utilizing data from PMUs in a distribution grid. The results from the grid data show that the method is capable of monitoring the cable temperature up to an accuracy of ±5°C. The later part of the paper presents a system to utilize the temperature estimates given by the monitoring method to predict the dynamic thermal state of the cable for forecasted power-flow scenarios. This is demonstrated by using the available temperature estimates to initialize and solve the system of equations given by the thermoelectric equivalent (TEE) model the cable

Aggregated Norton’s equivalent models, with parallel impedance and current injection at different harmonic frequencies are used to model the distribution grid in harmonic studies. These models are derived based on measurements and/or prior knowledge about the grid. The measurement-based distribution (sub-)grid impedance estimation method uses harmonic phasors of 3-phase current and voltage measurements to capture the response of the distribution (sub-)grid before and after an event in the utility side of the grid. However, due to increasing non-linear components in the grid, knowledge about uncertainty in parameters of such equivalent models which intrinsically describe a linear grid becomes important. The aim of this paper is to present two novel methods to calculate the uncertainty of the measurement-based Norton’s equivalent harmonic model of the distribution (sub-)grids as seen from the utility side at the Point of Common Coupling (PCC). The impedance and the uncertainty calculations are demonstrated on a simulated network.

Modelling of Multiple Steady-state Behaviour and Control of a Continuous Bioreactor

This paper focuses on studying the phenomenon of harmonic distortion propagation through distribution networks. This phenomenon is governed by a combination of factors involving the nature of harmonic loads and their dynamic interaction, the influence of background voltage distortion, and harmonic impedance values. The objective of the proposed research includes evaluation of the network response at different nodes to harmonic current injections via utilizing a time-synchronized distributed measurement system. The study is performed in a fully controlled and flexible test network with three medium voltage/low voltage (MV/LV) distribution substations and several managed LV harmonic sources, namely PV inverter, single-phase EV charger and emulated harmonic load with reference current injections. A selection of the results is analyzed and interpretation of the observed phenomena is given with implications that synchronized harmonic measurements can be considered as potential powerful instruments for analyzing power quality disturbances.

This paper proposes a new regression-based method to estimate resistance, reactance, and susceptance parameters of a 3-phase cable segment using phasor measurement unit (PMU) data. The novelty of this method is that it gives accurate parameter estimates in the presence of unknown bias errors in the measurements. Bias errors are fixed errors present in the measurement equipment and have been neglected in previous such attempts of estimating parameters of a 3-phase line or cable segment. In power system networks, the sensors used for current and voltage measurements have inherent magnitude and phase errors whose measurements need to be corrected using calibrated correction coefficients. Neglecting or using wrong error correction coefficients causes fixed bias errors in the measured current and voltage signals. Measured current and voltage signals at different time instances are the variables in the regression model used to estimate the cable parameters. Thus, the bias errors in the sensors become fixed errors in the variables. This error in variables leads to inaccuracy in the estimated parameters. To avoid this, the proposed method uses a new regression model using extra parameters which facilitate the modeling of present but unknown bias errors in the measurement system. These added parameters account for the errors present in the non- or wrongly calibrated sensors. Apart from the measurement bias, random measurement errors also contribute to the total uncertainty of the estimated parameters. This paper also presents and compares methods to estimate the total uncertainty in the estimated parameters caused by the bias and random errors present in the measurement system. Results from simulation-based and laboratory experiments are presented to show the efficacy of the proposed method. A discussion about analyzing the obtained results is also presented.

This study presents a novel measurement‐based method for modelling harmonic current injections of low‐voltage power electronics equipment. The aim of the developed methodology is to accurately represent harmonic current phase angle in response to the applied harmonic background voltage at the terminals of modelled device. In this method, the harmonic angles are analysed with the techniques of circular statistics. The performed study proves the adequacy of representing phase angles as sets of directional data rather than linear. After graphical and quantitative analysis, the regression models with underlying von Mises distribution are derived in the form of algebraic equation. This algebraic equation features sine and cosine terms and explains relationship between independent variable – voltage harmonic angle and dependent variable – current harmonic angle. The subsequent analysis of the residuals allows to conclude that models developed by applying this technique can be used in commercial simulation packages and allow to account on any value of background harmonic voltage angle.