Best L1 Piecewise Monotonic Data Approximation in Overhead and Underground Medium-Voltage and Low-Voltage Broadband over Power Lines Networks: Theoretical and Practical Transfer Function Determination

Abstract

This paper investigates the efficiency and accuracy of the best L1 piecewise monotonic data approximation (best L1PMA) in order either to approximate the transfer functions of distribution BPL networks or to reveal the aforementioned transfer functions when various faults occur during their determination. The contribution of this paper is quadruple. First, based on the inherent piecewise monotonicity of distribution BPL transfer functions, a piecewise monotonic data approximation is first applied in BPL networks; best L1PMA is outlined and applied during the determination of distribution BPL transfer functions. Second, suitable performance metrics such as the percent error sum (PES) and fault PES are reported and applied so as to assess the efficiency and accuracy of the best L1PMA during the determination of distribution BPL transfer functions. Third, the factors of distribution BPL networks that influence the performance of best L1PMA are identified. Fourth, the accuracy of the best L1PMA is assessed with respect to its inherent properties, namely, the assumed number of monotonic sections and the nature of faults, that is, faults that follow either continuous uniform distribution (CUD) or normal distribution (ND), during the determination of distribution BPL transfer functions. Finally, best L1PMA may operate as the necessary intermediate antifault method for the theoretical and practical transfer function determination of distribution BPL networks.

Smart Energy and Spectral Efficiency (SE) of Distribution Broadband over Power Lines (BPL) Networks – Part 2: L1PMA, L2WPMA and L2CXCV for SE against Measurement Differences in Overhead Medium-Voltage BPL Networks

“…On the basis of the minimization of the moduli sum between the output data (L1PMA approximation data of SE) and input data into the separate monotonous sections, L1PMA achieves to mitigate the uncorrelated SE differences, which come from the assumed measurement differences, by neglecting the existence of few large ones [33], [36], [37]. The L1PMA application is based on the Fortran software package that is freely available online in [42] receives as inputs the measured SE, the measurement frequencies and the number of monotonic sections (i.e., either user-or computer-defined) and primarily gives as output the best fit of the measured SE.…”

“…In accordance with [33], [36], PES is the main performance metric that is employed to assess the approximation accuracy when piecewise monotonic data approximation methods are applied in BPL networks. More specifically, in this paper, PES expresses as a percentage the total sum of the relative differences between the examined SE and the theoretical SE for all the used frequencies.…”

“…On the basis of these application properties, the application of the piecewise monotonic data approximations is extended to the SE results in order to reveal the theoretical SE values by ignoring the fluctuations of channel attenuation computations due to the measurement differences and without knowing the CUD measurement difference properties (i.e., maximum and minimum values of the CUD measurement distributions). The countermeasure efficiency of the L1PMA, L2WPMA and L2CXCV against the measurement differences during the SE computation is assessed for comparison reasons on the basis of: (i) the main performance metric of the piecewise monotonic data approximation method [33], [36], that is the percent error sum (PES); and (ii) the statistical performance metrics of set A and B that already been applied in [4].…”

Main Line Fault Localization Methodology (MLFLM) in Smart Grid – The Underground Medium- and Low-Voltage Broadband over Power Lines Networks Case

“…The strong point of MLFLM towards the mitigation of measurement differences is the adoption of PMAs during the process of measurement data of channel attenuation and coupling reflection coefficient in BPL networks [21]- [23], [33]- [38]. The application of PMAs, such as L1PMA [24]-[30], L2WPMA [31] and L2CXCV [32], drastically improve the fault localization efficiency even in the case of significant measurement differences.…”

“…Initially, a great convenience towards the aforementioned problems has been offered by the combined operation of the well-established hybrid method [4]- [8], [11]- [23] with piecewise monotonic data approximations (PMAs), such as L1PMA, L2WPMA and L2CXCV [24]- [32]. Their application to measurement data, such as channel attenuations and reflection coefficients, has allowed the restoration of theoretical transfer functions and the reflection coefficients, respectively, even if measurement differences of various intensities may occur [21], [33]- [36]. On the basis of the mitigation of measurement differences and the retrieval of the transfer functions and reflection coefficients for a given BPL topology, Topology Identification Methodology (TIM) suggests that the determination of the topological characteristics of the examined topology is a straightforward process through an identification procedure that compares PMA approximated data with the respective ones of a detailed BPL topology database [22], [37].…”