Probabilistic wind power forecasting approaches have significantly advanced in recent decades. However, forecasters often assume data completeness and overlook the challenge of missing values resulting from sensor failures, network congestion, etc. Traditionally, this issue is addressed during the data preprocessing procedure using methods such as deletion and imputation. Nevertheless, these ad-hoc methods pose challenges to probabilistic wind power forecasting at both parameter estimation and operational forecasting stages. In this paper, we propose a resilient probabilistic forecasting approach that smoothly adapts to missingness patterns without requiring preprocessing or retraining. Specifically, we design an adaptive quantile regression model with parameters capable of adapting to missing patterns, comprising two modules. The first is a feature extraction module where weights are kept static and biases are designed as a function of missingness patterns. The second is a non-crossing quantile neural network module, ensuring monotonicity of quantiles, with higher quantiles derived by adding non-negative amounts to lower quantiles. The proposed approach is applicable to both missing-at-random and missing-not-at-random cases. Case studies demonstrate that our proposed approach achieves state-of-the-art results in terms of the continuous ranked probability score, with acceptable computational cost.

Demand response (DR) is regarded as a solution to the issue of high electricity prices in the wholesale market, as the flexibility of the demand can be harnessed to lower the demand level for price reductions. As an across-the-board DR in a system is impractical due to the enrollment budget for instance, it is necessary to select a small group of nodes for DR implementing. Current studies resort to intuitive yet naive approaches for DR targeting, as price is implicitly associated with demand, though optimality cannot be ensured. In this paper, we derive such a relationship in the security-constrained economic dispatch via the multi-parametric programming theory, based on which the DR targeting problem is rigorously formulated as a mixed-integer quadratic programming problem aiming at reducing the averaged price to a reference level by efficiently reducing targeted nodes’ demand. A solution strategy is proposed to accelerate the computation. Numerical studies demonstrate compared with the benchmarking strategy, the proposed approach can reduce the price to the reference point with less efforts in demand reduction. Besides, we empirically show that the proposed approach is immune to inaccurate system parameters, and can be generalized to variants of DR targeting tasks.

Prediction intervals (PIs) offer an effective tool for quantifying uncertainty of loads in distribution systems. The traditional central PIs cannot adapt well to skewed distributions, and their offline training fashion is vulnerable to the unforeseen change in future load patterns. Therefore, we propose an optimal PI estimation approach, which is online and adaptive to different data distributions by adaptively determining symmetric or asymmetric probability proportion pairs for quantiles of PIs’ bounds. It relies on the online learning ability of reinforcement learning (RL) to integrate the two online tasks, i.e., the adaptive selection of probability proportion pairs and quantile predictions, both of which are modeled by neural networks. As such, the quality of quantiles-formed PI can guide the selection process of optimal probability proportion pairs, which forms a closed loop to improve PIs’ quality. Furthermore, to improve the learning efficiency of quantile forecasts, a prioritized experience replay (PER) strategy is proposed for online quantile regression processes. Case studies on both load and net load demonstrate that the proposed method can better adapt to data distribution compared with online central PIs method. Compared with offline-trained methods, it obtains PIs with better quality and is more robust against concept drift.

We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow~(CNF). In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches) and can directly yield continuous probability densities, hence avoiding quantile crossing. It relies on a base distribution and a set of bijective mappings. Both the shape parameters of the base distribution and the bijective mappings are approximated with neural networks. Spline-based conditional normalizing flow is considered owing to its universal approximation capability. Over the training phase, the model sequentially maps input examples onto samples of base distribution, where parameters are estimated through maximum likelihood. To issue probabilistic forecasts, one eventually map samples of the base distribution into samples of a desired distribution. Case studies based on open datasets validate the effectiveness of the proposed model, and allows us to discuss its advantages and caveats with respect to the state of the art. Code will be released upon publication.