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Abstract: This paper applies the point estimate method to account for the uncertainties that affect the evaluation of the steady state operating condition of an unbalanced three-phase power system. Moreover, since the point estimate method requires that the input random variables are uncorrelated, a suitable adjustment to take into account the correlation is applied. Different point estimate schemes (2m, 2m +1 and 4m +1 schemes) are presented and tested. The accuracy of the proposed techniques is tested on a three-phase unbalanced IEEE 34-bus test system; the results obtained applying the Monte Carlo simulation are assumed as reference . Both correlated and uncorrelated input random variables are considered, and multimodal probability density functions are tested. The conclusion is that the 2m +1 scheme gives the best solution in terms of accuracy and computational efforts; in the case of correlated input random variables, an adequate procedure to take into account the correlation must be applied. [Copyright &y& Elsevier]

• 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]

• The features of a real trolley-bus that crosses over the center of Naples are studied. • Electrical measurements were recorded on the actual bus. • The main BESS technologies for the electric vehicles are also presented. • The substitution of the conventional ICE with an on-board BESS is proposed. • To design the unit, a new two steps optimized procedure is proposed and validated. The paper investigates the renewal of a hybrid trolley-bus, powered by a 600 V DC overhead electrical grid. The analysis focuses on replacing the on-board internal combustion engine (ICE) with a battery-based power unit. A novel two-step optimization procedure is proposed for this purpose. The procedure compares the solutions in terms of the total cost sustained by the ownership. By means of an iterative method, the optimal size of the battery unit is designed as a function of power and energy requirements, taking into account cycle life, depth of discharge, working temperature, replacement, and the requirements of the transport service operator. Using the real measurements taken on a trolley-bus operating in the city center of Naples (Italy), several numerical simulations are performed. The simulations examine three alternative Lithium high specific power and energy batteries. The comparison of the results allows to select the best solution among the different technologies for the proposed application. [ABSTRACT FROM AUTHOR]