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Operating electrical networks by Dynamic Transformer Rating (DTR) unlocks the capacity of grids and allows to increase the exploitation of distributed generation and renewables. However, there is risk associated with the operation of transformers by DTR. Energy dispatch and/or load curtailment must be scheduled before the actual energy delivery, thus DTR and load should be predicted prior the actual transformer loading. Since both are random variables, this problem is prone to be addressed by stress-strength analysis. In this paper, the novel comprehensive probabilistic tool “SmarTrafo” is presented. It allows predicting the probability of the DTR to be greater than the load (i.e., the probability of success) through an exact analytic stress-strength model, and formulating an alarm-setting strategy in order to establish a warning if the expected probability is greater than a threshold. Specifically, the threshold is optimized in a multi-objective formulation, exploiting three different indices which differently evaluate the predictive skill of alarm-setting strategy. Numerical experiments based on actual data confirm the suitability of the proposal in predicting the probability of success and in establishing high-performance alarms based on such predictions. [ABSTRACT FROM AUTHOR]

• A multivariate approach to probabilistic industrial load forecasting is proposed. • Univariate quantile regression and quantile regression forests generate individual forecasts. • A multivariate quantile regression model combines individual forecasts of active and reactive power. • Multivariate quantile regression on quantile regression forests is the best pick for aggregate load. • Multivariate quantile regression on univariate quantile regression is the best pick for a single load. Industrial load takes a big portion of the total electricity demand. Skilled probabilistic industrial load forecasts allow for optimally exploiting energy resources, managing the reserves, and market bidding, which are beneficial to transmission and distribution system operators and their industrial customers. Despite its importance, industrial load forecasting has never been a popular subject in the literature. Most existing methods operate on the active power alone, partially or totally neglecting the reactive power. This paper proposes a multivariate approach to probabilistic industrial load forecasting, which addresses active and reactive power simultaneously. The proposed method is based on a two-level procedure, which consists of generating probabilistic forecasts individually for active and reactive power through univariate probabilistic models, and combining these forecasts in a multivariate approach based on a multivariate quantile regression model. The procedure to estimate the parameters of the multivariate quantile regression model is posed in this paper under a linear programming problem, to facilitate the convergence to the optimal solution. The proposed method is validated using actual load data collected at an Italian factory, under comparison with several probabilistic benchmarks. The proposed multivariate method enhances the skill of forecasts by 6% to 13.5%, with respect to univariate benchmarks. [ABSTRACT FROM AUTHOR]