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Register a new userA hybrid model of kernel density estimation and quantile regression for GEFCom2014 probabilistic load forecasting
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We present a model for generating probabilistic forecasts by combining kernel density estimation (KDE) and quantile regression techniques, as part of the probabilistic load forecasting track of the Global Energy Forecasting Competition 2014. The KDE method is initially implemented with a time-decay parameter. We later improve this method by conditioning on the temperature or the period of the week variables to provide more accurate forecasts. Secondly, we develop a simple but effective quantile regression forecast. The novel aspects of our methodology are two-fold. First, we introduce symmetry into the time-decay parameter of the kernel density estimation based forecast. Secondly we combine three probabilistic forecasts with different weights for different periods of the month.
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In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single time frames, followed by the application of a suitable kinetic model to time activity curves (TACs) at the voxel or region-of-interest level. The relatively new field of 4D PET direct reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Existing 4D direct models are based on a deterministic description of voxels TACs, captured by the chosen kinetic model, considering the photon counting process the only source of uncertainty. In this work, we introduce a new probabilistic modeling strategy based on the key assumption that activity time course would be subject to uncertainty even if the parameters of the underlying dynamic process were known. This leads to a hierarchical Bayesian model, which we formulate using the formalism of Probabilistic Graphical Modeling (PGM). The inference of the joint probability density function arising from PGM is addressed using a new gradient-based iterative algorithm, which presents several advantages compared to existing direct methods: it is flexible to an arbitrary choice of linear and nonlinear kinetic model; it enables the inclusion of arbitrary (sub)differentiable priors for parametric maps; it is simpler to implement and suitable to integration in computing frameworks for machine learning. Computer simulations and an application to real patient scan showed how the proposed approach allows us to weight the importance of the kinetic model, providing a bridge between indirect and deterministic direct methods.
The recent advent of smart meters has led to large micro-level datasets. For the first time, the electricity consumption at individual sites is available on a near real-time basis. Efficient management of energy resources, electric utilities, and transmission grids, can be greatly facilitated by harnessing the potential of this data. The aim of this study is to generate probability density estimates for consumption recorded by individual smart meters. Such estimates can assist decision making by helping consumers identify and minimize their excess electricity usage, especially during peak times. For suppliers, these estimates can be used to devise innovative time-of-use pricing strategies aimed at their target consumers. We consider methods based on conditional kernel density (CKD) estimation with the incorporation of a decay parameter. The methods capture the seasonality in consumption, and enable a nonparametric estimation of its conditional density. Using eight months of half-hourly data for one thousand meters, we evaluate point and density forecasts, for lead times ranging from one half-hour up to a week ahead. We find that the kernel-based methods outperform a simple benchmark method that does not account for seasonality, and compare well with an exponential smoothing method that we use as a sophisticated benchmark. To gauge the financial impact, we use density estimates of consumption to derive prediction intervals of electricity cost for different time-of-use tariffs. We show that a simple strategy of switching between different tariffs, based on a comparison of cost densities, delivers significant cost savings for the great majority of consumers.
Distribution network operators (DNOs) are increasingly concerned about the impact of low carbon technologies on the low voltage (LV) networks. More advanced metering infrastructures provide numerous opportunities for more accurate load flow analysis of the LV networks. However, such data may not be readily available for DNOs and in any case is likely to be expensive. Modelling tools are required which can provide realistic, yet accurate, load profiles as input for a network modelling tool, without needing access to large amounts of monitored customer data. In this paper we outline some simple methods for accurately modelling a large number of unmonitored residential customers at the LV level. We do this by a process we call buddying, which models unmonitored customers by assigning them load profiles from a limited sample of monitored customers who have smart meters. Hence the presented method requires access to only a relatively small amount of domestic customers data. The method is efficiently optimised using a genetic algorithm to minimise a weighted cost function between matching the substation data and the individual mean daily demands. Hence we can show the effectiveness of substation monitoring in LV network modelling. Using real LV network modelling, we show that our methods perform significantly better than a comparative Monte Carlo approach, and provide a description of the peak demand behaviour.
The increasing use and spread of low carbon technologies are expected to cause new patterns in electric demand and set novel challenges to a distribution network operator (DNO). In this study, we build upon a recently introduced method, called buddying, which simulates low voltage (LV) networks of both residential and non-domestic (e.g. shops, offices, schools, hospitals, etc.) customers through optimization (via a genetic algorithm) of demands based on limited monitored and customer data. The algorithm assigns a limited but diverse number of monitored households (the buddies) to the unmonitored customers on a network. We study and compare two algorithms, one where substation monitoring data is available and a second where no substation information is used. Despite the roll out of monitoring equipment at domestic properties and/or substations, less data is available for commercial customers. This study focuses on substations with commercial customers most of which have no monitored `buddy, in which case a profile must be created. Due to the volatile nature of the low voltage networks, uncertainty bounds are crucial for operational purposes. We introduce and demonstrate two techniques for modelling the confidence bounds on the modelled LV networks. The first method uses probabilistic forecast methods based on substation monitoring; the second only uses a simple bootstrap of the sample of monitored customers but has the advantage of not requiring monitoring at the substation. These modelling tools, buddying and uncertainty bounds, can give further insight to a DNO to better plan and manage the network when limited information is available.
In several recent publications, Bettencourt, West and collaborators claim that properties of cities such as gross economic production, personal income, numbers of patents filed, number of crimes committed, etc., show super-linear power-scaling with total population, while measures of resource use show sub-linear power-law scaling. Re-analysis of the gross economic production and personal income for cities in the United States, however, shows that the data cannot distinguish between power laws and other functional forms, including logarithmic growth, and that size predicts relatively little of the variation between cities. The striking appearance of scaling in previous work is largely artifact of using extensive quantities (city-wide totals) rather than intensive ones (per-capita rates). The remaining dependence of productivity on city size is explained by concentration of specialist service industries, with high value-added per worker, in larger cities, in accordance with the long-standing economic notion of the hierarchy of central places.
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