Flexible models for aggregated residential loads are needed to analyze the impact of demand response policies and programs on the minimum comfort setting required by end-users. This impact has to be directly deduced from the probability profiles of thermal and electrical performance variables. The purpose of this paper is to compare different aggregation techniques in order to estimate, as accurately and flexibly as possible, the probability distribution function of thermal and electrical variables of thermostatically controlled loads. Two different approaches are considered: on the one hand, intensive numerical simulations-Monte Carlo process-combined with either Euler-Maruyama discrete approximation method or smoothing techniques; and, on the other hand, a numerical resolution of the Fokker-Planck partial differential equations. In all cases, a stochastic differential equation system-based on perturbed physical models-is used to model the individual load behavior. This individual system was previously developed and validated by the authors.

The purpose of this paper is to describe and assess a new characterization and classification method of voltage dips. The proposed method allows us to classify multistage and real voltage dips when measurement errors or transients are present in the recorded data. Different real voltage dips are used to assess this method, comparing the results with previous approaches. For visualization purposes, a voltage-space vector representation is introduced in order to clarify the global voltage dip evolution along the time. The classification of all the voltage dips, measured from a one-year field measurement campaign in wind farms located in the Spanish region of Castilla-La Mancha, is also presented and characterized according to the proposed method.

This paper describes the application of sliced inverse regression to model the electrochemical process of aluminum smelter plants. Real data measurements obtained during several years in a Spanish industrial environment are used to illustrate the main dependencies between parameters. Nonlinear relations between the output variables and relevant linear combinations of input variables are deduced. An exploratory statistical analysis is also presented, checking for correlations and possible linear dependencies. The developed model is used to analyze the range of electrical power demand variations as a consequence of modifications in chemical and electrical parameters. An example is described maintaining constant the aluminum production. The results can be considered for future load flexibility programs, which might include aluminum smelter plants as a flexible industrial customer.