Statistical Channel Modeling of Overhead Low Voltage Broadband over Power Lines (OV LV BPL) Networks – Part 2: The Numerical Results of Class Map Footprints of Real OV LV BPL Topologies, Branch Line Faults and Hook Style Energy Thefts

Abstract

In [1], the theoretical framework for the interoperability of DHM, iSHM, mSHM, the definition procedure and the class maps has been first presented for OV LV BPL networks. But the main interest of the first paper has focused on the theory of the OV LV BPL topology footprints of TIM, FIIM and HS-DET method on the class maps. In this paper, the numerical results concerning the application of iSHM, mSHM, the definition procedure and the class maps to OV LV BPL networks are first shown. Then, given the iSHM and mSHM class maps, the footprints of TIM, FIIM and HS-DET method databases for the OV LV BPL topologies are highlighted. Finally, a technique for the detection of branch line faults and hook style energy thefts that is based on iSHM and mSHM footprints is proposed.

Management Information Systems and Data Science in the Smart Grid – Inner Class Area Capacity Distribution of the iSHM Class Maps of Overhead Low-Voltage Broadband over Power Lines Topologies

“…Also, iSHM supports five CASDs with their corresponding MLEs (i.e., Gaussian, Lognormal, Wald, Weibull and Gumbel CASDs). According to [20], each iSHM CASD exhibits different performance depending on the input parameters but Weibull CASD performs the best performance among the available ones in terms of the performance capacity metrics of the absolute threshold of percentage change and the average absolute percentage change when OV LV BPL topologies are examined. Hence, the CASD approximation accuracy to the real capacity results of [20] mandates the use of Weibull CASD for the further analysis of OV LV BPL topologies in this paper, which is anyway reevaluated for its accuracy during the critical events assumed in this paper.…”

“…iSHM footprints that are added on the class maps as groups of white spots can graphically assess the impact of the intrinsic parameter changes or the existence of critical events during the power grid operation and can help towards the quick identification of the critical events for future actions by the management information system of the smart grid. The theoretical definition of iSHM footprints has been presented in [23] while a variety of applications of iSHM footprints has been presented so far, such as the iSHM footprints of the real OV LV BPL topologies, of the OV LV BPL topologies with a sole branch line fault and of the OV LV BPL topologies with a single hook for energy theft [20]. By studying iSHM footprints of OV LV BPL topologies, it is clear that the iSHM footprint extent, size, white spot positions and white spot group direction with respect to the real indicative OV LV BPL topologies may imply the intrinsic parameter change or the nature of the occurred critical events during the power grid operation.…”

“…Until now, the impact of a variety of parameters on the iSHM simulation results has been investigated so far such as the topology length, the interconnections between branches / main lines, branch lengths, distances between branches, branch terminations and channel attenuation measurement differences between the theoretical and practical results due to the real operation conditions [8], [18], [19]. Apart from the impact of the aforementioned intrinsic parameters, critical events during the operation of power grids, such as branch line faults and hook-style energy thefts, can be detected even if real operation conditions occur by exploiting the class maps footprints of iSHM [20], [21]; here, it should be reminded that a class map is a 2D contour plot that: (i) graphically classifies real and virtual BPL topologies in terms of their CASD Maximum Likelihood Estimator (MLE) parameter pairs and capacity; (ii) illustrates the borders between the BPL topology classes; and (iii) corresponds each CASD MLE parameter pair to its BPL topology subclass average capacity for given power grid type, CASD, coupling scheme, Injected Power Spectral Density Limits (IPSD) limits and noise Power Spectral Density (PSD) levels; while class map footprints are the graphical correspondence of CASD MLE parameter pair with the capacity that are represented on the class maps and may assess the impact of the intrinsic parameter change or the existence of critical events during the power grid operations. As the OV LV BPL topologies are examined in this paper, when changes of intrinsic parameters or the aforementioned critical events occur the respective CASD MLE parameters of the modified OV LV BPL topologies tend to change their iSHM footprint locations on the class maps following patterns of the same capacity behavior as presented in [20], [22].…”

“…Apart from the impact of the aforementioned intrinsic parameters, critical events during the operation of power grids, such as branch line faults and hook-style energy thefts, can be detected even if real operation conditions occur by exploiting the class maps footprints of iSHM [20], [21]; here, it should be reminded that a class map is a 2D contour plot that: (i) graphically classifies real and virtual BPL topologies in terms of their CASD Maximum Likelihood Estimator (MLE) parameter pairs and capacity; (ii) illustrates the borders between the BPL topology classes; and (iii) corresponds each CASD MLE parameter pair to its BPL topology subclass average capacity for given power grid type, CASD, coupling scheme, Injected Power Spectral Density Limits (IPSD) limits and noise Power Spectral Density (PSD) levels; while class map footprints are the graphical correspondence of CASD MLE parameter pair with the capacity that are represented on the class maps and may assess the impact of the intrinsic parameter change or the existence of critical events during the power grid operations. As the OV LV BPL topologies are examined in this paper, when changes of intrinsic parameters or the aforementioned critical events occur the respective CASD MLE parameters of the modified OV LV BPL topologies tend to change their iSHM footprint locations on the class maps following patterns of the same capacity behavior as presented in [20], [22]. In this paper, the inner class area capacity distribution of the iSHM class maps of OV LV BPL topologies is first investigated while the differences between the capacity of the aforementioned modified OV LV BPL topologies and the respective BPL topology subclass average capacities, which are used in class maps, for given CASD MLE parameter pairs is computed.…”

“…The rest of this short paper, which may act as a companion paper of [18], [20], [22], [23], is organized as follows: Section 2 briefly presents the theory concerning the iSHM class maps and iSHM class map footprints of OV LV BPL topologies. In Section 3, the simulation results regarding the inner class area capacity distribution are demonstrated as well as and the capacity differences between the modified OV LV BPL topologies and the respective BPL topology subclass average capacities of iSHM class maps.…”