Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows

Abstract

The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level to increase efficiency and ensure reliable control. However, high fluctuations and increasing electrification cause huge forecast variability, not reflected in traditional point estimates. Probabilistic load forecasts take future uncertainties into account and thus allow more informed decision-making for the planning and operation of low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein polynomial normalizing flows, where a neural network controls the parameters of the flow. In an empirical study with 363 smart meter customers, our density predictions compare favorably against Gaussian and Gaussian mixture densities. Also, they outperform a non-parametric approach based on the pinball loss for 24h-ahead load forecasting for two different neural network architectures.

Sample-based Uncertainty Quantification with a Single Deterministic Neural Network

“…DISCO Net (and DN+) differs from recent approaches based on NF (Sick et al, 2020;Charpentier et al, 2020;Dumas et al, 2021;Sendera et al, 2021;Jamgochian et al, 2022;Rittler et al, 2022;März and Kneib, 2022;Arpogaus et al, 2022;Cramer et al, 2022) in a number of ways. First, NF estimates the joint density p(x, y) to derive the conditional density p(y|x) while DISCO Net directly models the latter with no recourse to the former.…”

“…NF is a generative model that uses a composition of multiple differentiable bijective maps modeled by NN to transform a simple (such as uniform or Gaussian) distribution to a more complex distribution of real data. Examples of probabilistic forecast based on NF can be found in (Sick et al, 2020;Charpentier et al, 2020;Dumas et al, 2021;Sendera et al, 2021;Jamgochian et al, 2022;Rittler et al, 2022;März and Kneib, 2022;Arpogaus et al, 2022;Cramer et al, 2022).…”

Creating Probabilistic Forecasts from Arbitrary Deterministic Forecasts using Conditional Invertible Neural Networks

“…To create probabilistic forecasts, cINNs, also referred to as normalising flows (Ardizzone et al, 2019), are combined with other machine learning methods. Arpogaus et al (2022), for example, apply normalising flows to learn the parameters of Bernstein polynomials, which are in turn used to create a probabilistic forecast. Moreover, Rasul et al (2020) combine normalising flows with recurrent neural networks to create probabilistic forecasts.…”

Probabilistic load forecasting for the low voltage network: Forecast fusion and daily peaks

“…Importantly, the quantile forecasts at the smart meter level are shown to be more skilful than an advanced parametric approach based on the Gaussian distribution. Bernstein polynomials have also been proposed for producing non-parametric density forecasts in [13] which show improvement over Gaussian and Gaussian mixture density forecasts. Finally, multivariate forecasts are generated for a hierarchy of smart meters in [14], where a coherency constraint is placed on the samples of the multivariate distribution, i.e.…”