This tutorial paper is concerned with the identification of hybrid models, i.e. dynamical models whose behavior is determined by interacting continuous and discrete dynamics. Methods specifically aimed at the identification of models with a hybrid structure are of very recent date. After discussing the main issues and difficulties connected with hybrid system identification, and giving an overview of the related literature, this paper focuses on four different approaches for the identification of switched affine and piecewise affine models, namely an algebraic procedure, a Bayesian procedure, a clustering-based procedure, and a bounded-error procedure. The main features of the selected procedures are presented, and possible interactions to still enhance their effectiveness are suggested

This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.

This paper addresses the problem of finding the optimal configuration (number, locations and sizes) of energy storage systems (ESS) in a radial low voltage distribution network with the aim of preventing over- and undervoltages. A heuristic strategy based on voltage sensitivity analysis is proposed to select the most effective locations in the network where to install a given number of ESS, while circumventing the combinatorial nature of the problem. For fixed ESS locations, the multiperiod optimal power flow framework is adopted to formulate the sizing problem, for whose solution convex relaxations based on semidefinite programming are exploited. Uncertainties in the storage sizing decision problem due to stochastic generation and demand, are accounted for by carrying out the optimal sizing over different realizations of the demand and generation profiles, and then taking a worst-case approach to select the ESS sizes. The final choice of the most suitable ESS configuration is done by minimizing a total cost, which takes into account the number of storage devices, their total installed capacity and average network losses. The proposed algorithm is extensively tested on 200 randomly generated radial networks, and successfully applied to a real Italian low voltage network and a modified version of the IEEE 34-bus test feeder.

Demand-side management has been recently recognized as a strategic concept in smart electricity grids. In this context, active demand (AD) represents a demand response scenario in which households and small commercial consumers participate in grid management through appropriate modifications of their consumption patterns during certain time periods in return of a monetary reward. The participation is mediated by a new player, called aggregator, who designs the consumption pattern modifications to make up standardized products to be sold on the energy market. The presence of this new input to consumers generated by aggregators modifies the load behavior, asking for load forecasting algorithms that explicitly consider the AD effect. In this paper, we propose an approach to load forecasting in the presence of AD, based on gray-box models where the seasonal component of the load is extracted by a suitable preprocessing and AD is considered as an exogenous input to a linear transfer function model. The approach is thought for a distribution system operator that performs technical validation of AD products, and therefore possesses full information about the AD schedule in the network. A comparison of the performance of the proposed approach with techniques not using the information on AD and with approaches based on nonlinear black-box models is performed on a real load time series recorded in an area of the Italian low voltage network.