Nonparametric End-to-End Probabilistic Forecasting of Distributed Generation Outputs Considering Missing Data Imputation

TL;DR

Addresses probabilistic forecasting of distributed renewable generation when data are incomplete. It proposes a nonparametric end-to-end framework using an LSTM-based forecast model to produce quantiles $x_{t+l|t}^{\alpha}$ via $F(\boldsymbol{X}_t, \alpha; \theta)$, without assuming a parametric distribution. Imputation is integrated into training through iterative median forecasts $x_{t+1|t}^{0.5}$ and a pinball-loss objective. On wind-power data with MCAR missing, it achieves superior reliability, sharper prediction intervals, and higher skill scores than two-phase and end-to-end baselines, demonstrating robustness to missing data.

Abstract

In this paper, we introduce a nonparametric end-to-end method for probabilistic forecasting of distributed renewable generation outputs while including missing data imputation. Firstly, we employ a nonparametric probabilistic forecast model utilizing the long short-term memory (LSTM) network to model the probability distributions of distributed renewable generations' outputs. Secondly, we design an end-to-end training process that includes missing data imputation through iterative imputation and iterative loss-based training procedures. This two-step modeling approach effectively combines the strengths of the nonparametric method with the end-to-end approach. Consequently, our approach demonstrates exceptional capabilities in probabilistic forecasting for the outputs of distributed renewable generations while effectively handling missing values. Simulation results confirm the superior performance of our approach compared to existing alternatives.

Figures (4)

• Figure 1: Nonparametric end-to-end framework for probabilistic forecasting of distributed energy resources considering missing data imputation.
• Figure 2: LSTM layer and model. (a) is a demonstration of the calculation steps in one LSTM layer. (b) is the structure of the nonparametric probabilistic forecast model.
• Figure 3: End-to-end training considering missing data imputation.
• Figure 4: Probabilistic forecasting of distributed energy resources' outputs.