Fig 4
Footprints of the real OV LV BPL topologies of the TIM database. (a) mSHM footprint of OV LV BPL topologies with one branch. (b) mSHM footprint of OV LV BPL topologies with two branches.
Contexts in source publication
Context 1
... the mSHM footprint of the real OV LV BPL topologies with one branch are regarded, the TIM BPL topology database specifications are assumed to be the same with the ones of the iSHM footprint case. With reference to the mSHM class map of Fig. 2(c), the mSHM footprint of the real OV LV BPL topologies with one branch is illustrated as white areas in Fig. 4(a). Similarly, the mSHM footprint of the real OV LV BPL topologies with two branches is illustrated in Fig. 4(b) when the TIM BPL topology database specifications are assumed to be the same with the ones of the mSHM footprint ...
Context 2
... specifications are assumed to be the same with the ones of the iSHM footprint case. With reference to the mSHM class map of Fig. 2(c), the mSHM footprint of the real OV LV BPL topologies with one branch is illustrated as white areas in Fig. 4(a). Similarly, the mSHM footprint of the real OV LV BPL topologies with two branches is illustrated in Fig. 4(b) when the TIM BPL topology database specifications are assumed to be the same with the ones of the mSHM footprint ...
Context 3
... the opposite direction. Same observations can be expressed for the case of OV LV BPL topologies with two branches, where OV LV BPL topologies of two branches remain in the suburban case area with similar branch length behavior regarding the relative location in the class map suburban case area with the case of a single branch. • With reference to Figs. 4(a) and 4(b), the mSHM footprints of OV LV BPL topologies with one and two branches are clearly confined in the rural and suburban case areas, respectively. Although the number of the examined OV LV BPL topologies remains the same given the number of branches, the main difference between iSHM and mSHM footprints is first their extent; this is due ...
Context 4
... of the mSHM class maps and demonstrated as white spots through the practical approximation of Frobenius distance analyzed in Sec.4.1 of [1]. As the number of spacings of the horizontal and vertical axes of the mSHM class maps of Figs. 2(a)-(c) is both equal to 10, all the white spots of Figs. 3(a) and 3(b) are classified into 8 white spots in Figs. 4(a) and 4(b), respectively. It is evident that as the number of spacings of the horizontal and vertical axes increases so does the number of white spots of the mSHM footprints of the real OV LV BPL topologies since a larger set of available pairs can be ...
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Citations
... 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. ...
... In the frequency range 3-30MHz of interest, -60 dBm/Hz are the FCC Part 15 IPSD limits suitable for the operation of OV LV BPL networks [25], [26], [73]; (vi) Noise PSD levels: Already been mentioned in Sec.3.1, FL noise model of [62], [74] is adopted for the capacity computations in the 3-30MHz frequency range [25], [26], [30], [52], [75]; say -105 dBm/Hz is assumed to be the default AWGN PSD limit level for OV LV BPL networks; and (vii) Best CASD with respect to its capacity estimation: This is one of the main objective of the companion paper of [76] to be determined for the OV LV BPL networks. Anyway, in accordance with [36], [37], it has been demonstrated for the iSHM that Weibull and Wald CASDs perform the best capacity estimations in OV MV and UN MV power grid types, respectively, regardless of the examined BPL topology subclass when the respective default operation settings concerning IPSD limits, noise PSD levels and applied coupling scheme are assumed. ...
... Based on the findings of [36] and [45], it has been demonstrated for the iSHM that Weibull and Gaussian CASDs perform the best capacity estimations in OV MV and OV HV BPL networks, respectively, regardless of the examined BPL topology subclass when the aforementioned default operation settings are adopted. Anyway, one of the main interest of the companion paper of [76] is the identification of the best CASD for the OV LV BPL networks with respect to the best capacity estimations when the default operation settings are applied. ...
... Finally, as the default operation settings of the definition procedures are concerned, these are further divided into two groups: (i) iSHM definition procedure default operation settings: With respect to FL1.05 of Fig. 3(a), the number of spacings for the horizontal and vertical axis (i.e., and , respectively) is assumed to be equal to 10 in both cases. Note that the most suitable CASD with respect to its capacity estimation is going to be determined in [76] where the spacings for the horizontal and vertical axis are there applied; and (ii) mSHM definition procedure default operation settings: Since Empirical CASD is the only examined CASD, CDFs are of interest and not MLEs. With respect to FL2.05 of Fig. 3(b), the number of spacings for the horizontal and vertical axis (i.e., and , respectively) is assumed to be equal to 10 in both cases. ...
... In accordance with the BPMN diagram of iSHM [18] and during the preparation of iSHM footprints, Phase C computes all the related iSHM Weibull CASD MLEs of the examined real indicative OV LV BPL topology, namely either for the theoretical coupling scheme channel attenuation difference (i.e, ̂M LE,theor ). In accordance with [36]- [38], the iSHM class map of OV LV BPL topologies, which acts as the graphical basis for the demonstration of all the kinds of iSHM footprints, is plotted in Fig. 1 of [2] with respect to ̂M LE Weibull , ̂M LE Weibull and the average capacity of each OV LV BPL topology subclass when the default operation settings of [1], [34] and the modified BPL frequency range settings of [2] are assumed. Through the prism of iSHM footprints, the effect of measurement differences and the countermeasures of piecewise monotonic data approximations against the measurement differences have been illustrated in Figs. ...
... As already been mentioned, the iSHM class map of OV LV BPL topologies, which is depicted in [36]- [38], acts as the graphical basis for the demonstration of the various iSHM footprints and is shown in Fig. 1. Similarly to [2], the iSHM footprint due to measurement differences of the arbitrary 5dB maximum value CUD for the real indicative OV LV BPL urban case A is also depicted in Fig. 1 as superimposed white circles on the iSHM class map as well as the iSHM footprint due to the application of L1PMA of the traditional aspect against the aforementioned measurement differences is shown as superimposed cyan squares when 4 monotonic sections are assumed. ...
... On the basis of the well-validated DHM for transmission and distribution power grids [10], [11], [15]- [18], the proposed SHM framework, which consists of its iSHM and mSHM versions, has recently been proposed in [19]- [21]. Also, new tools that are integrated with SHM and further exploit its operation are available in [1], [2], [22]- [24], namely: (i) The definition procedure: This procedure enriches the existing BPL topology classes with virtual BPL topology subclasses statistically defined in terms of the applied SHM version and its corresponding successful CASD parameter pairs (i.e, MLEs and CDF for iSHM and mSHM CASDs, respectively); (ii) The class maps: 2D contour plots illustrate the borders between adjacent BPL topology classes while CASD parameter pairs with the corresponding BPL topology subclass average capacities are represented on the class map; and (iii) The class map footprints of critical events of the operation of power grids: The real OV LV BPL topologies, the real OV LV BPL topologies with a sole branch line fault and the real OV LV BPL topologies with a single hook for energy theft can be illustrated as superimposed white areas upon the class maps for given power grid type, SHM version, CASD, coupling scheme, IPSD limits and noise levels. In accordance with [2], the most descriptive class map footprints are the iSHM ones, which are going to be exploited in this paper, since their representation depends on a straightforward procedure rather than the approximation of mSHM ones. ...
... Also, new tools that are integrated with SHM and further exploit its operation are available in [1], [2], [22]- [24], namely: (i) The definition procedure: This procedure enriches the existing BPL topology classes with virtual BPL topology subclasses statistically defined in terms of the applied SHM version and its corresponding successful CASD parameter pairs (i.e, MLEs and CDF for iSHM and mSHM CASDs, respectively); (ii) The class maps: 2D contour plots illustrate the borders between adjacent BPL topology classes while CASD parameter pairs with the corresponding BPL topology subclass average capacities are represented on the class map; and (iii) The class map footprints of critical events of the operation of power grids: The real OV LV BPL topologies, the real OV LV BPL topologies with a sole branch line fault and the real OV LV BPL topologies with a single hook for energy theft can be illustrated as superimposed white areas upon the class maps for given power grid type, SHM version, CASD, coupling scheme, IPSD limits and noise levels. In accordance with [2], the most descriptive class map footprints are the iSHM ones, which are going to be exploited in this paper, since their representation depends on a straightforward procedure rather than the approximation of mSHM ones. Until now, the results of iSHM and its accompanying tools have exploited as inputs the theoretical numerical results came from the operation of DHM. ...
... where is the flat-fading subchannel start frequency, is the flat-fading subchannel frequency spacing, is the number of subchannels in the examined 3-30MHz frequency range, is the 1×Q line vector that consists of the flat-fading subchannel start frequencies , (•) is the applied IPSD limits in dBm/Hz, (•) is the applied AWGN PSD levels in dBm/Hz and 〈•〉 L is an operator that converts dBm/Hz into a linear power ratio (W/Hz). More details concerning the applied coupling scheme, IPSD limits and AWGN PSD levels are given in [1], [2]. ...
... As the BPL channel modeling is concerned, the recently proposed iSHM, which is based on the well-validated DHM, can be deployed for the broadband channel description of transmission and distribution power grids [19]- [23], [28]- [31]. Also, a plethora of related broadband iSHM tools, such as the definition procedure, the class maps and the iSHM footprints, have been so far demonstrated and tested in order to assist the operation of iSHM towards a more accurate statistical description of the communications channel [32]- [35]. Except for the communications channel itself, measurement differences between the experimental and theoretical results during the channel attenuation determination, briefly denoted as measurement differences, may occur due to a number of practical reasons and "real-life" difficulties that may critically influence iSHM operation, the interaction of broadband iSHM tools with iSHM and finally the SG big data with the related decisions. ...
... In accordance with the BPMN diagram of iSHM [29], the CASD MLEs of iSHM are computed at the Phase C of Fig. 2(a) of [24]. In accordance with [35], Weibull CASD MLEs are going to be used in this paper since Weibull CASD performs the best performance among the available iSHM CASDs with reference to the percentage change and average absolute percentage change when OV LV BPL topology main subclasses are examined. In accordance with [33]- [35], the iSHM class map of OV LV BPL topologies, which acts as the graphical basis for the demonstration of iSHM footprints due to measurement differences, is plotted in Fig. 1 with respect to ̂M LE Weibull , ̂M LE Weibull and the average capacity of each OV LV BPL topology subclass when the default operation settings of [1], [24] and the modified BPL frequency range settings of Sec.2.2 are assumed. ...
... In accordance with [35], Weibull CASD MLEs are going to be used in this paper since Weibull CASD performs the best performance among the available iSHM CASDs with reference to the percentage change and average absolute percentage change when OV LV BPL topology main subclasses are examined. In accordance with [33]- [35], the iSHM class map of OV LV BPL topologies, which acts as the graphical basis for the demonstration of iSHM footprints due to measurement differences, is plotted in Fig. 1 with respect to ̂M LE Weibull , ̂M LE Weibull and the average capacity of each OV LV BPL topology subclass when the default operation settings of [1], [24] and the modified BPL frequency range settings of Sec.2.2 are assumed. ...
