GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

Analyzing multi-fiber reconstruction in high angular resolution diffusion imaging using the tensor distribution function

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

Provisioning a 3.3 MW PhotoVoltaic generation system onto a distribution authority’s 11 kV rural feeder

This paper describes part of an engineering study that was undertaken to demonstrate that a multi-megawatt Photovoltaic (PV) generation system could be connected to a rural 11 kV feeder without creating power quality issues for other consumers. The paper concentrates solely on the voltage regulation aspect of the study as this was the most innovative part of the study. The study was carried out using the time-domain software package, PSCAD/EMTDC. The software model included real time data input of actual measured load and scaled PV generation data, along with real-time substation voltage regulator and PV inverter reactive power control. The outputs from the model plot real-time voltage, current and power variations throughout the daily load and PV generation variations. Other aspects of the study not described in the paper include the analysis of harmonics, voltage flicker, power factor, voltage unbalance and system losses.

Impact of electric energy storage scheduling on reliability of distribution system

The development of Electric Energy Storage (EES) integrated with Renewable Energy Resources (RER) has increased use of optimum scheduling strategy in distribution systems. Optimum scheduling of EES can reduce cost of purchased energy by retailers while improve the reliability of customers in distribution system. This paper proposes an optimum scheduling strategy for EES and the evaluation of its impact on reliability of distribution system. Case study shows the impact of the proposed strategy on reliability indices of a distribution system.

Data driven modeling for power transformer lifespan evaluation

Large sized power transformers are important parts of the power supply chain. These very critical networks of engineering assets are an essential base of a nation’s energy resource infrastructure. This research identifies the key factors influencing transformer normal operating conditions and predicts the asset management lifespan. Engineering asset research has developed few lifespan forecasting methods combining real-time monitoring solutions for transformer maintenance and replacement. Utilizing the rich data source from a remote terminal unit (RTU) system for sensor-data driven analysis, this research develops an innovative real-time lifespan forecasting approach applying logistic regression based on the Weibull distribution. The methodology and the implementation prototype are verified using a data series from 161 kV transformers to evaluate the efficiency and accuracy for energy sector applications. The asset stakeholders and suppliers significantly benefit from the real-time power transformer lifespan evaluation for maintenance and replacement decision support.

Effects of fish density distribution and effort distribution on catchability

The effects of fish density distribution and effort distribution on the overall catchability coefficient are examined. Emphasis is also on how aggregation and effort distribution interact to affect overall catch rate [catch per unit effort (cpue)]. In particular, it is proposed to evaluate three indices, the catchability index, the knowledge parameter, and the aggregation index, to describe the effectiveness of targeting and the effects on overall catchability in the stock area. Analytical expressions are provided so that these indices can easily be calculated. The average of the cpue calculated from small units where fishing is random is a better index for measuring the stock abundance. The overall cpue, the ratio of lumped catch and effort, together with the average cpue, can be used to assess the effectiveness of targeting. The proposed methods are applied to the commercial catch and effort data from the Australian northern prawn fishery. The indices are obtained assuming a power law for the effort distribution as an approximation of targeting during the fishing operation. Targeting increased catchability in some areas by 10%, which may have important implications on management advice.

Development of innovative robust stability enhancement algorithms for distribution systems containing distributed generators

This project was a step forward in improving the voltage profile of traditional low voltage distribution networks with high photovoltaic generation or high peak demand. As a practical and economical solution, the developed methods use a Dynamic Voltage Restorer or DVR, which is a series voltage compensator, for continuous and communication-less power quality enhancement. The placement of DVR in the network is optimised in order to minimise its power rating and cost. In addition, new approaches were developed for grid synchronisation and control of DVR which are integrated with the voltage quality improvement algorithm for stable operation.

Probabilistic load flow for distribution systems with uncertain PV generation

Large integration of solar Photo Voltaic (PV) in distribution network has resulted in over-voltage problems. Several control techniques are developed to address over-voltage problem using Deterministic Load Flow (DLF). However, intermittent characteristics of PV generation require Probabilistic Load Flow (PLF) to introduce variability in analysis that is ignored in DLF. The traditional PLF techniques are not suitable for distribution systems and suffer from several drawbacks such as computational burden (Monte Carlo, Conventional convolution), sensitive accuracy with the complexity of system (point estimation method), requirement of necessary linearization (multi-linear simulation) and convergence problem (Gram–Charlier expansion, Cornish Fisher expansion). In this research, Latin Hypercube Sampling with Cholesky Decomposition (LHS-CD) is used to quantify the over-voltage issues with and without the voltage control algorithm in the distribution network with active generation. LHS technique is verified with a test network and real system from an Australian distribution network service provider. Accuracy and computational burden of simulated results are also compared with Monte Carlo simulations.

New genetic loci link adipose and insulin biology to body fat distribution

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10−8). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms.

A flexible tool for integrated planning of active distribution networks

This paper presents a flexible and integrated planning tool for active distribution network to maximise the benefits of having high level s of renewables, customer engagement, and new technology implementations. The tool has two main processing parts: “optimisation” and “forecast”. The “optimization” part is an automated and integrated planning framework to optimize the net present value (NPV) of investment strategy for electric distribution network augmentation over large areas and long planning horizons (e.g. 5 to 20 years) based on a modified particle swarm optimization (MPSO). The “forecast” is a flexible agent-based framework to produce load duration curves (LDCs) of load forecasts for different levels of customer engagement, energy storage controls, and electric vehicles (EVs). In addition, “forecast” connects the existing databases of utility to the proposed tool as well as outputs the load profiles and network plan in Google Earth. This integrated tool enables different divisions within a utility to analyze their programs and options in a single platform using comprehensive information.