This study investigated Type I error rates for tests of fixed effects in mixed linear models using Wald F-statistics with the Kenward-Roger adjustment. Data were generated using 15 covariance structures. Correct covariance structures as well as those selected using the Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (BIC) criteria were examined. Performance of the AIC and BIC criteria in selecting the true covariance structure was also studied. Type I error rates for the correct models were often adequate depending on the sample size and complexity of covariance structure. Type I error rates for the best AIC and BIC models were always higher than target values, but those obtained using BIC were closer to the target value than those obtained using AIC. For unbalanced data, Type I error rates for the between-subjects effect were closer to target values for positive pairing while those for the within-subject effect were closer for negative pairing. Success of AIC and BIC in selecting the correct covariance structure was low.

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The main objective of this paper is to obtain the duty‐cycle probability forecast functions of cooling and heating aggregated residential loads. The method consists of three steps: first, the single loads are modelled using systems of stochastic differential equations based on perturbed physical models; second, intensive numerical simulation of the stochastic system solutions is performed, allowing several parameters to vary randomly; and third, smoothing techniques based on kernel estimates are applied to the results to derive non‐parametric estimators, comparing several kernel functions. The use of these dynamical models also allows us to forecast the indoor temperature evolution under any performance conditions. Thus, the same smoothing techniques provide the indoor temperature probability forecast function for a load group. These techniques have been used with homogeneous and non‐homogeneous device groups. Its main application is focused on assessing Direct Load Control programs, by means of comparing natural and forced duty‐cycles of aggregated appliances, as well as knowing the modifications in customer comfort levels, which can be directly deduced from the probability profiles. Finally, simulation results which illustrate the model suitability for demand side – bidding – aggregators in new deregulated markets are presented.

This paper describes and assesses a physically based load model of residential Electric Thermal Storage (ETS) devices, for both static and dynamic loads. This load model is based on an energy balance between the indoor environment, the dwelling constructive parameters, the ETS device, and the internal mass through a discrete state-space equation system. Therefore, detailed information about several physical magnitudes of the whole system are given along the time: ceramic brick temperature, electrical demand, heat fluxes, and indoor temperature. The main application of this load model has been oriented towards the simulation of the ETS device performances, in order to assess load management (LM) programs.The proposed model has been implemented and validated using data collected for the last two years in residential areas, in order to evaluate its accuracy and flexibility. Finally, a simulation case study is presented to show the possibilities of limiting and reducing the actual winter-peak by means of an LM program, proposed by the authors, that takes into account customer minimum comfort levels and the experimental data of residential load curve profiles.

The purpose ofthis paper is to describe a useful tool for the initial analysis to assess the possibilities of residential Electric Thermal Storage (ETS), taking into account heat storage and cool storage devices. These load models are based on an energy balance between the indoor environment, the dwelling constructive parameters, the ETS device and the internal mass through a discrete statespace equation system. The main application of this load model has been oriented towards the simulation of ETS performance in order to evaluate the possibilities of Load Management in the new de-regulated structures of Electrical Power Systems. The proposed model has been implemented and validated for heat storage, using real data collected during the last years in residential areas to evaluate its accuracy and flexibility. Finally, a simulation case study is presented to show the possibilities of modifying the actual residential demand profile through a storage period re-scheduling proposed by the authors, taking into account the customer minimum comfort levels and avoiding program rejection. Index Term-Demand-side bidding, residential load modeling, Electrical Thermal Storage I. INTRODUCTTONWO different approaches have been used to solve the Electrical Energy Systems. The fust one is focused on adding new resources and expanding the Power System so that the new energy requirements can be met -Supply Side Management (SSM)-. The second one is to try to influence on customers in order to reduce their demand peaks andior modify their habits. Thus, Demand-Side Management (DSM) technologies -and specifically Load Management (LM) programs-have been applied in the United States and the European Union countries for over the last two decades. The main objective is to manage the timing, magnitude and sharpness of daily and seasonal load curves to provide, economically and technically mechanisms matching load to supply. Nowadays, and throughout the world, the electric power industry is moving toward a deregulated framework in T .