53 research outputs found
Recovering Multiple Nonnegative Time Series From a Few Temporal Aggregates
Motivated by electricity consumption metering, we extend existing nonnegative
matrix factorization (NMF) algorithms to use linear measurements as
observations, instead of matrix entries. The objective is to estimate multiple
time series at a fine temporal scale from temporal aggregates measured on each
individual series. Furthermore, our algorithm is extended to take into account
individual autocorrelation to provide better estimation, using a recent convex
relaxation of quadratically constrained quadratic program. Extensive
experiments on synthetic and real-world electricity consumption datasets
illustrate the effectiveness of our matrix recovery algorithms
Scalable visualisation methods for modern Generalized Additive Models
In the last two decades the growth of computational resources has made it
possible to handle Generalized Additive Models (GAMs) that formerly were too
costly for serious applications. However, the growth in model complexity has
not been matched by improved visualisations for model development and results
presentation. Motivated by an industrial application in electricity load
forecasting, we identify the areas where the lack of modern visualisation tools
for GAMs is particularly severe, and we address the shortcomings of existing
methods by proposing a set of visual tools that a) are fast enough for
interactive use, b) exploit the additive structure of GAMs, c) scale to large
data sets and d) can be used in conjunction with a wide range of response
distributions. All the new visual methods proposed in this work are implemented
by the mgcViz R package, which can be found on the Comprehensive R Archive
Network
Day-ahead probabilistic forecasting for French half-hourly electricity loads and quantiles for curve-to-curve regression
The probabilistic forecasting of electricity loads is crucial for effective scheduling and decision-making in volatile and competitive energy markets with ever-growing uncertainties. We propose a novel approach to construct the probabilistic predictors for curves (PPC) of electricity loads, which leads to properly defined predictive bands and quantiles in the context of curve-to-curve regression. The proposed predictive model provides not only accurate hourly load point forecasts, but also generates well-defined probabilistic bands and day-long trajectories of the loads at any probability level, pre-specified by managers. We also define the predictive quantile curves that exhibit future loads in extreme scenarios and provide insights for hedging risks in the supply management of electricity. When applied to the day-ahead forecasting for French half-hourly electricity loads, the PPC outperform several state-of-the-art time series and machine learning predictive methods with more accurate point forecasts (mean absolute percentage error of 1.10%, compared to 1.36%–4.88% for the alternatives), a higher coverage rate of the day-long trajectory of loads (coverage rate of 95.5%, against 31.9%–90.7% for the alternatives) and a narrower average length of the predictive bands. In a series of numerical experiments, the PPC further demonstrate robust performance and general applicability, achieving accurate coverage probabilities under a variety of data-generating mechanisms
Human spatial dynamics for electricity demand forecasting: the case of France during the 2022 energy crisis
Accurate electricity demand forecasting is crucial to meet energy security
and efficiency, especially when relying on intermittent renewable energy
sources. Recently, massive savings have been observed in Europe, following an
unprecedented global energy crisis. However, assessing the impact of such
crisis and of government incentives on electricity consumption behaviour is
challenging. Moreover, standard statistical models based on meteorological and
calendar data have difficulty adapting to such brutal changes. Here, we show
that mobility indices based on mobile network data significantly improve the
performance of the state-of-the-art models in electricity demand forecasting
during the sobriety period. We start by documenting the drop in the French
electricity consumption during the winter of 2022-2023. We then show how our
mobile network data captures work dynamics and how adding these mobility
indices outperforms the state-of-the-art during this atypical period. Our
results characterise the effect of work behaviours on the electricity demand
Target Tracking for Contextual Bandits: Application to Demand Side Management
We propose a contextual-bandit approach for demand side management by
offering price incentives. More precisely, a target mean consumption is set at
each round and the mean consumption is modeled as a complex function of the
distribution of prices sent and of some contextual variables such as the
temperature, weather, and so on. The performance of our strategies is measured
in quadratic losses through a regret criterion. We offer upper bounds
on this regret (up to poly-logarithmic terms)---and even faster rates under
stronger assumptions---for strategies inspired by standard strategies for
contextual bandits (like LinUCB, see Li et al., 2010). Simulations on a real
data set gathered by UK Power Networks, in which price incentives were offered,
show that our strategies are effective and may indeed manage demand response by
suitably picking the price levels
Clustering electricity consumers using high-dimensional regression mixture models
Massive informations about individual (household, small and medium enterprise) consumption are now provided with new metering technologies and the smart grid. Two major exploitations of these data are load profiling and forecasting at different scales on the grid. Customer segmentation based on load classification is a natural approach for these purposes. We propose here a new methodology based on mixture of high-dimensional regression models. The novelty of our approach is that we focus on uncovering classes or clusters corresponding to different regression models. As a consequence, these classes could then be exploited for profiling as well as forecasting in each class or for bottom-up forecasts in a unified view. We consider a real dataset of Irish individual consumers of 4,225 meters, each with 48 half-hourly meter reads per day over 1 year: from 1st January 2010 up to 31st December 2010, to demonstrate the feasibility of our approach
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