Tecniche di ottimizzazione per la stima e il monitoraggio di sistemi elettrici di potenza

The evolution of modern electric power grids requires increasingly complex, flexible, and effective management and control tools. These rely on data obtained from monitoring systems consisting of measurement instruments with advanced features but still characterized by uncertainty, and of estimation methods influenced by all the uncertainty sources of the measurement chain. Consequently, the availability of mathematical tools able to effectively model estimation problems, fully exploiting the characteristics of measurement instruments and a priori knowledge, is increasingly important. The thesis explores an approach based on optimization techniques to some relevant problems of estimation and monitoring designed for the power systems. The aim is to optimize the estimation performance through the integration in the problem formulation of a priori information on the domain under investigation and on the state to be reconstructed, exploiting the available knowledge on measurement errors. The considered optimization formulations involve two terms: the approximation error and the regularization term. The first one, also called fitting term, evaluates how well the solution matches the available measurements, while the regularization term considers the a priori information on the solution to be recovered. The estimation problems addressed in the thesis are the estimation of the main sources of harmonic pollution, i.e., the Harmonic Source Estimation (HSoE), in a distribution network and the simultaneous estimation of transmission line parameters and systematic errors in the measurement chain. In both cases, synchronized phasor measurements (at fundamental or harmonic frequency), available from a new generation of measurement devices, are considered. The identification of the prevailing harmonic sources is modelled as an underdetermined problem with a sparse solution and is addressed by using the Compressive Sensing approach as an L1 minimization. The problem is faced using first the L1 minimization with equality constraints, then, starting from the theoretical aspects involved in the evaluation of measurement uncertainties, and aiming at the reduction of their impact on HSoE algorithms, a new formulation based on the L1 minimization with quadratic constraints is proposed. To maximize the algorithm performance, a whitening matrix that allows retrieving the information on the distributions of the measurement errors, and thus estimating the corresponding energy bounds, is presented. The effectiveness of the presented solution is evaluated by simulations on appropriate test networks. The simultaneous estimation of line parameters and systematic errors of the measurement chain is addressed by a new method based on synchronized measurements by phasor measurement units (PMUs). The method is conceived to exploit a multiple-branch approach and a potentially large number of obtained measurements, corresponding to multiple operating conditions. The method is designed in the context of Tikhonov regularization and allows exploiting the high accuracy and reporting rate of PMUs more effectively, to improve the estimation of line parameters and to refine the compensation of systematic measurement errors, particularly from instrument transformers. The validity of the proposal has been verified through simulations performed on the IEEE 14-bus test system. The validity of the proposed paradigm has been confirmed by all the applications and experiments conducted. The flexibility of the optimization techniques discussed in this thesis has in fact made it possible to model the various a priori information about the considered domain and the state to be recovered, exploiting any type of available knowledge on measurement errors. These techniques can therefore be considered a valid, flexible, and effective tool for addressing the new measurement problems posed by modern electric power grids.