Business Analytics and IT in Smart Grid – Part 2: The Qualitative Mitigation Impact of Piecewise Monotonic Data Approximations on the iSHM Class Map Footprints of Overhead Low-Voltage Broadband over Power Lines Topologies Contaminated by Measurement Differences

Business analytics and IT infrastructure preserve the integrity of the smart grid (SG) operation against the flood of big data that may be susceptible to faults, such as measurement differences. In [1], the impact of measurement differences that follow continuous uniform distributions (CUDs) of different magnitudes has been investigated via initial Statistical Hybrid Model (iSHM) footprints during the operation of overhead low-voltage broadband over power lines (OV LV BPL) networks. In this companion paper, the mitigation efficiency of piecewise monotonic data approximations, such as L1PMA and L2WPMA, is qualitatively assessed in terms of iSHM footprints when the aforementioned measurement difference CUD of different intensities are applied.Citation: Lazaropoulos, A. G. (2020). Business Analytics and IT in Smart Grid – Part 2: The Qualitative Mitigation Impact of Piecewise Monotonic Data Approximations on the iSHM Class Map Footprints of Overhead Low-Voltage Broadband over Power Lines Topologies Contaminated by Measurement Differences. Trends in Renewable Energy, 6, 177-203. DOI: 10.17737/tre.2020.6.2.0011

Power Systems Stability through Piecewise Monotonic Data Approximations – Part 1: Comparative Benchmarking of L1PMA, L2WPMA and L2CXCV in Overhead Medium-Voltage Broadband over Power Lines Networks

This first paper assesses the performance of three well-known piecewise monotonic data approximations (i.e., L1PMA, L2WPMA, and L2CXCV) during the mitigation of measurement differences in the overhead medium-voltage broadband over power lines (OV MV BPL) transfer functions.The contribution of this paper is triple. First, based on the inherent piecewise monotonicity of OV MV BPL transfer functions, L2WPMA and L2CXCV are outlined and applied during the determination of theoretical and measured OV MVBPL transfer functions. Second, L1PMA, L2WPMA, and L2CXCV are comparatively benchmarked by using the performance metrics of the percent error sum (PES) and fault PES. PES and fault PES assess the efficiency and accuracy of the three piecewise monotonic data approximations during the determination of transmission BPL transfer functions. Third, the performance of L1PMA, L2WPMA, and L2CXCV is assessed with respect to the nature of faults —i.e. faults that follow either continuous uniform distribution (CUD) or normal distribution (ND) of different magnitudes—.The goal of this set of two papers is the establishment of a more effective identification and restoration of the measurement differences during the OV MV BPL coupling transfer function determination that may significantly help towards a more stable and self-healing power system.Citation: Lazaropoulos, A. G. (2017). Power Systems Stability through Piecewise Monotonic Data Approximations – Part 1: Comparative Benchmarking of L1PMA, L2WPMA and L2CXCV in Overhead Medium-Voltage Broadband over Power Lines Networks. Trends in Renewable Energy, 3(1), 2-32. DOI: 10.17737/tre.2017.3.1.002

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

This second paper assesses the performance of piecewise monotonic data approximations, such as L1PMA, L2WPMA and L2CXCV, against the measurement differences during the spectral efficiency (SE) calculations in overhead medium-voltage broadband over power lines (OV MV BPL) networks. In this case study paper, the performance of the aforementioned three already known piecewise monotonic data approximations, which are considered as countermeasure techniques against measurement differences, is here extended during the SE computations. The indicative BPL topologies of the first paper are again considered while the 3-30 MHz frequency band of the BPL operation is assumed.Citation: Lazaropoulos, A. G. (2018). 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. Trends in Renewable Energy, 4, 185-212. DOI: 10.17737/tre.2018.4.2.007

Algorithm XXX: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data

Scattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard’s algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data

Power Systems Stability through Piecewise Monotonic Data Approximations – Part 2: Adaptive Number of Monotonic Sections and Performance of L1PMA, L2WPMA, and L2CXCV in Overhead Medium-Voltage Broadband over Power Lines Networks

This second paper investigates the role of the number of monotonic sections during the mitigation of measurement differences in overhead medium-voltage broadband over power lines (OV MV BPL) transfer functions. The performance of two well-known piecewise monotonic data approximations that are based on the number of monotonic sections (i.e., L1PMA and L2WPMA) is assessed in comparison with the occurred measurement differences and L2CXCV, which is a piecewise monotonic data approximation without considering monotonic sections.The contribution of this paper is double. First, further examination regarding the definition of the optimal number of monotonic section is made so that the accuracy of L1PMA can be significantly enhanced. In fact, the goal is to render piecewise monotonic data approximations that are based on the optimal number of monotonic sections as the leading approximation against the other ones without monotonic sections. Second, a generic framework concerning the definition of an adaptive number of monotonic sections is proposed for given OV MV BPL topology.Citation: Lazaropoulos, A. G. (2017). Power Systems Stability through Piecewise Monotonic Data Approximations – Part 2: Adaptive Number of Monotonic Sections and Performance of L1PMA, L2WPMA, and L2CXCV in Overhead Medium-Voltage Broadband over Power Lines Networks. Trends in Renewable Energy, 3(1), 33-60. DOI: 10.17737/tre.2017.3.1.003

Big Data and Neural Networks in Smart Grid - Part 2: The Impact of Piecewise Monotonic Data Approximation Methods on the Performance of Neural Network Identification Methodology for the Distribution Line and Branch Line Length Approximation of Overhead Low-Voltage Broadband over Powerlines Networks

Τhe impact of measurement differences that follow continuous uniform distributions (CUDs) of different intensities on the performance of the Neural Network Identification Methodology for the distribution line and branch Line Length Approximation (NNIM-LLA) of the overhead low-voltage broadband over powerlines (OV LV BPL) topologies has been assessed in [1]. When the αCUD values of the applied CUD measurement differences remain low and below 5dB, NNIM-LLA may internally and satisfactorily cope with the CUD measurement differences. However, when the αCUD values of CUD measurement differences exceed approximately 5dB, external countermeasure techniques against the measurement differences are required to be applied to the contaminated data prior to their handling by NNIM-LLA. In this companion paper, the impact of piecewise monotonic data approximation methods, such as L1PMA and L2WPMA of the literature, on the performance of NNIM-LLA of OV LV BPL topologies is assessed when CUD measurement differences of various αCUD values are applied. The key findings that are going to be discussed in this companion paper are: (i) The crucial role of the applied numbers of monotonic sections of the L1PMA and L2WPMA for the overall performance improvement of NNIM-LLA approximations as well as the dependence of the applied numbers of monotonic sections on the complexity of the examined OV LV BPL topology classes; and (ii) the performance comparison of the piecewise monotonic data approximation methods of this paper against the one of more elaborated versions of the default operation settings in order to reveal the most suitable countermeasure technique against the CUD measurement differences in OV LV BPL topologies.Citation: Lazaropoulos, A. G., & Leligou, H. C. (2024). Big Data and Neural Networks in Smart Grid - Part 2: The Impact of Piecewise Monotonic Data Approximation Methods on the Performance of Neural Network Identification Methodology for the Distribution Line and Branch Line Length Approximation of Overhead Low-Voltage Broadband over Powerlines Networks. Trends in Renewable Energy, 10, 67-97. doi: https://doi.org/10.17737/tre.2024.10.1.0016

Applications of the best piecewise monotonic approximation to peak estimation of NMR data

Το πρόβλημα εκτίμησης κορυφών εμφανίζεται εγγενώς στη φασματοσκοπία. Στη φασματοσκοπία πυρηνικού μαγνητικού συντονισμού (NMR), για παράδειγμα, ο μαγνητικός συντονισμός βασίζεται στην ιδιότητα της ύλης ανάλλογα μέσω της έκθεσης του δείγματος σε συγκεκριμένη συχνότητα ραδιοκυμάτων. Παράγεται ηλεκτρικό σήμα και φαίνεται από το ύψος των κορυφών. Φασματοσκοπία NMR είναι μια από τις πιο κοινές τεχνικές φασματοσκοπίας μοριακής δόμησης για την αξιολόγηση των μοριακών κινήσεων σε πολύ υψηλές στάθμες δόνησης και των ειδών δακτυλικών αποτυπωμάτων. Για αυτά τα φάσματα, η θέση των κορυφών και οι εντάσεις τους είναι η ένδειξη μιας οργανικής ή ανόργανης ένωσης ή ιστού. Η μέθοδος προσέγγισης τμηματικών μονοτονικών δεδομένων σε σειρά κάνει τη μικρότερη αλλαγή στα δεδομένα, έτσι ώστε οι πρώτες διαφορές των αλλαγών των εξομαλυνσμένων τιμών να είναι ανάλογες ενός προκαθορισμένου αριθμού. Οι αλγόριθμοι που έχουν αναπτυχθεί για αυτόν τον δύσκολο συνδυαστικό υπολογισμό είναι πολύ αποτελεσματικοί παρέχοντας βέλτιστες λύσεις σε τετραγωνική πολυπλοκότητα σε σχέση με τον αριθμό των δεδομένων. Πρόκειται να διερευνήσουμε την αποδοτικότητα και την αποτελεσματικότητα της μεθόδου κατά προσέγγιση μονοτονικών δεδομένων για την εκτίμηση κορυφών των δεδομένων NMR που θα ληφθούν από τις βάσεις δεδομένων που σχετίζονται με τον μεταβολισμό Στόχος μας είναι να παρουσιάσουμε τα αποτελέσματα της τμηματικής μονοτονικής μεθόδου σε ένα φάσμα NMR. Επομένως, τα αποτελέσματά μας είναι χρήσιμα για να δείξουμε ότι η τμηματική μονοτονική μέθοδος είναι ιδιαίτερα κατάλληλη για εκτίμηση αιχμής σε δεδομένα NMR.Peak estimation problems appear inherently in spectroscopy. In nuclear magnetic resonance (NMR) spectroscopy, for example, magnetic resonance is based on matter property by analyzing the sample at a specific frequency of radio waves. An electrical signal is produced and is shown by the height of the peaks. NMR spectroscopy is the most common vibrational spectroscopy techniques for assessing molecular motion and fingerprinting species. For these spectra, the location of peaks and their intensities are the signature of a sample of an organic or an inorganic compound or a tissue. Piecewise monotonic data approximation method makes the smallest change to the data such that the first differences of the smoothed values change sign a prescribed number of times. The algorithms that have been developed for this challenging combinatorial calculation are very efficient providing optimal solutions in quadratic complexity with respect to the number of data. We are going to investigate the efficiency and the efficacy of the piecewise monotonic data approximation method to peak estimation of NMR data that will be received from metabolomics data bases. Our intention is to present results of the piecewise monotonic method on a muter of NMR spectrum. Therefore, our results are helpful in showing that piecewise monotonic method is particularly suitable for peak estimation in NMR data

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

This paper assesses the performance of the main line fault localization methodology (MLFLM) when its application is extended to underground medium- and low-voltage broadband over power lines (UN MV and UN LV BPL) networks, say UN distribution BPL networks.  This paper focuses on the localization of main distribution line faults across UV MV and UN LV BPL networks. By extending the MLFLM procedure, which has successfully been applied to overhead medium-voltage (OV MV) BPL networks, the performance assessment of MLFLM is investigated with respect to the nature of the main distribution line faults, the intensity of the measurement differences and the fault location across the main distribution lines of the underground distribution power grid (either MV or LV grid).Citation: Lazaropoulos, A. G. (2017). Main Line Fault Localization Methodology (MLFLM) in Smart Grid – The Underground Medium- and Low-Voltage Broadband over Power Lines Networks Case. Trends in Renewable Energy, 4, 15-42. DOI: 10.17737/tre.2018.4.1.004

Algorithm 863: L2WPMA, a Fortran 77 package for weighted least-squares piecewise monotonic data approximation

Fortran software is developed that calculates a best piecewise monotonic approximation to n univariate data contaminated by random errors. The underlying method minimizes the weighted sum of the squares of the errors by requiring k - 1 sign changes in the first divided differences of the approximation, where k is a given positive integer. Hence, the piecewise linear interpolant to the fit consists of k monotonic sections, alternately increasing and decreasing. This calculation can have about O(nk) local minima, because the positions of the turning points of the fit are integer variables of the problem. The method, however, by employing a dynamic programming technique divides the data into at most k disjoint sets of adjacent data and solves a k = 1 problem (monotonic fit or isotonic regression) for each set. So it calculates efficiently a global solution in only O(nσ + kσ2) computer operations when k 3, where σ is the number of local minima of the data, always bounded by n/2. This complexity reduces to only O(n) when k = 1 or k = 2 (unimodal case). At the end of the calculation a spline representation of the solution and the corresponding Lagrange multipliers are provided. The software package has been tested on a variety of data sets showing a performance that does provide in practice shorter computation times than the complexity indicates in theory. An application of the method on identifying turning points and monotonic trends of data from 1947 - 1996 on the U.K. pound over the U.S. dollar exchange rate is presented. Generally, the method may have useful applications as, for example, in estimating the turning points of a function from some noisy measurements of its values, or in image and signal processing, or in providing a preliminary or complementary smoothing phase to further analyses of the data. © 2007 ACM