Unified control system for three-phase electric drives operating in magnetic saturation region

The research project aims to study and develop control techniques for a generalized three-phase and multi-phase electric drive able to efficiently manage most of the drive types available for traction application. The generalized approach is expanded to both linear and non- linear machines in magnetic saturation region starting from experimental flux characterization and applying the general inductance definition. The algorithm is able to manage fragmented drives powered from different batteries or energy sources and will be able to ensure operability even in case of faults in parts of the system. The algorithm was tested using model-in-the-loop in software environment and then applied on experimental test benches with collaboration of an external company.

Diagnostic techniques for EHD and MHD interaction

The impact of plasma technologies is growing both in the academic and in the industrial fields. Nowadays, a great interest is focused in plasma applications in aeronautics and astronautics domains. Plasma actuators based on the Magneto-Hydro-Dynamic (MHD) and Electro- Hydro-Dynamic (EHD) interactions are potentially able to suitably modify the fluid-dynamics characteristics around a flying body without utilizing moving parts. This could lead to the control of an aircraft with negligible response time, more reliability and improvements of the performance. In order to study the aforementioned interactions, a series of experiments and a wide number of diagnostic techniques have been utilized. The EHD interaction, realized by means of a Dielectric Barrier Discharge (DBD) actuator, and its impact on the boundary layer have been evaluated by means of two different experiments. In the first one a three phase multi-electrode flat panel actuator is used. Different external flow velocities (from 1 to 20m/s) and different values of the supplied voltage and frequency have been considered. Moreover a change of the phase sequence has been done to verify the influence of the electric field existing between successive phases. Measurements of the induced speed had shown the effect of the supply voltage and the frequency, and the phase order in the momentum transfer phenomenon. Gains in velocity, inside the boundary layer, of about 5m/s have been obtained. Spectroscopic measurements allowed to determine the rotational and the vibrational temperature of the plasma which lie in the range of 320 ÷ 440°K and of 3000 ÷ 3900°K respectively. A deviation from thermodynamic equilibrium had been found. The second EHD experiment is realized on a single electrode pair DBD actuator driven by nano-pulses superimposed to a DC or an AC bias. This new supply system separates the plasma formation mechanism from the acceleration action on the fluid, leading to an higher degree of the control of the process. Both the voltage and the frequency of the nano-pulses and the amplitude and the waveform of the bias have been varied during the experiment. Plasma jets and vortex behavior had been observed by means of fast Schlieren imaging. This allowed a deeper understanding of the EHD interaction process. A velocity increase in the boundary layer of about 2m/s had been measured. Thrust measurements have been performed by means of a scales and compared with experimental data reported in the literature. For similar voltage amplitudes thrust larger than those of the literature, had been observed. Surface charge measurements led to realize a modified DBD actuator able to obtain similar performances when compared with that of other experiments. However in this case a DC bias replacing the AC bias had been used. MHD interaction experiments had been carried out in a hypersonic wind tunnel in argon with a flow of Mach 6. Before the MHD experiments a thermal, fluid-dynamic and plasma characterization of the hypersonic argon plasma flow have been done. The electron temperature and the electron number density had been determined by means of emission spectroscopy and microwave absorption measurements. A deviation from thermodynamic equilibrium had been observed. The electron number density showed to be frozen at the stagnation region condition in the expansion through the nozzle. MHD experiments have been performed using two axial symmetric test bodies. Similar magnetic configurations were used. Permanent magnets inserted into the test body allowed to generate inside the plasma azimuthal currents around the conical shape of the body. These Faraday currents are responsible of the MHD body force which acts against the flow. The MHD interaction process has been observed by means of fast imaging, pressure and electrical measurements. Images showed bright rings due to the Faraday currents heating and exciting the plasma particles. Pressure measurements showed increases of the pressure in the regions where the MHD interaction is large. The pressure is 10 to 15% larger than when the MHD interaction process is silent. Finally by means of electrostatic probes mounted flush on the test body lateral surface Hall fields of about 500V/m had been measured. These results have been used for the validation of a numerical MHD code.

Modulation Techniques for Multi-Phase Converters and Control Strategies for Multi-Phase Electric Drives

The ever-increasing spread of automation in industry puts the electrical engineer in a central role as a promoter of technological development in a sector such as the use of electricity, which is the basis of all the machinery and productive processes. Moreover the spread of drives for motor control and static converters with structures ever more complex, places the electrical engineer to face new challenges whose solution has as critical elements in the implementation of digital control techniques with the requirements of inexpensiveness and efficiency of the final product. The successfully application of solutions using non-conventional static converters awake an increasing interest in science and industry due to the promising opportunities. However, in the same time, new problems emerge whose solution is still under study and debate in the scientific community During the Ph.D. course several themes have been developed that, while obtaining the recent and growing interest of scientific community, have much space for the development of research activity and for industrial applications. The first area of research is related to the control of three phase induction motors with high dynamic performance and the sensorless control in the high speed range. The management of the operation of induction machine without position or speed sensors awakes interest in the industrial world due to the increased reliability and robustness of this solution combined with a lower cost of production and purchase of this technology compared to the others available in the market. During this dissertation control techniques will be proposed which are able to exploit the total dc link voltage and at the same time capable to exploit the maximum torque capability in whole speed range with good dynamic performance. The proposed solution preserves the simplicity of tuning of the regulators. Furthermore, in order to validate the effectiveness of presented solution, it is assessed in terms of performance and complexity and compared to two other algorithm presented in literature. The feasibility of the proposed algorithm is also tested on induction motor drive fed by a matrix converter. Another important research area is connected to the development of technology for vehicular applications. In this field the dynamic performances and the low power consumption is one of most important goals for an effective algorithm. Towards this direction, a control scheme for induction motor that integrates within a coherent solution some of the features that are commonly required to an electric vehicle drive is presented. The main features of the proposed control scheme are the capability to exploit the maximum torque in the whole speed range, a weak dependence on the motor parameters, a good robustness against the variations of the dc-link voltage and, whenever possible, the maximum efficiency. The second part of this dissertation is dedicated to the multi-phase systems. This technology, in fact, is characterized by a number of issues worthy of investigation that make it competitive with other technologies already on the market. Multiphase systems, allow to redistribute power at a higher number of phases, thus making possible the construction of electronic converters which otherwise would be very difficult to achieve due to the limits of present power electronics. Multiphase drives have an intrinsic reliability given by the possibility that a fault of a phase, caused by the possible failure of a component of the converter, can be solved without inefficiency of the machine or application of a pulsating torque. The control of the magnetic field spatial harmonics in the air-gap with order higher than one allows to reduce torque noise and to obtain high torque density motor and multi-motor applications. In one of the next chapters a control scheme able to increase the motor torque by adding a third harmonic component to the air-gap magnetic field will be presented. Above the base speed the control system reduces the motor flux in such a way to ensure the maximum torque capability. The presented analysis considers the drive constrains and shows how these limits modify the motor performance. The multi-motor applications are described by a well-defined number of multiphase machines, having series connected stator windings, with an opportune permutation of the phases these machines can be independently controlled with a single multi-phase inverter. In this dissertation this solution will be presented and an electric drive consisting of two five-phase PM tubular actuators fed by a single five-phase inverter will be presented. Finally the modulation strategies for a multi-phase inverter will be illustrated. The problem of the space vector modulation of multiphase inverters with an odd number of phases is solved in different way. An algorithmic approach and a look-up table solution will be proposed. The inverter output voltage capability will be investigated, showing that the proposed modulation strategy is able to fully exploit the dc input voltage either in sinusoidal or non-sinusoidal operating conditions. All this aspects are considered in the next chapters. In particular, Chapter 1 summarizes the mathematical model of induction motor. The Chapter 2 is a brief state of art on three-phase inverter. Chapter 3 proposes a stator flux vector control for a three- phase induction machine and compares this solution with two other algorithms presented in literature. Furthermore, in the same chapter, a complete electric drive based on matrix converter is presented. In Chapter 4 a control strategy suitable for electric vehicles is illustrated. Chapter 5 describes the mathematical model of multi-phase induction machines whereas chapter 6 analyzes the multi-phase inverter and its modulation strategies. Chapter 7 discusses the minimization of the power losses in IGBT multi-phase inverters with carrier-based pulse width modulation. In Chapter 8 an extended stator flux vector control for a seven-phase induction motor is presented. Chapter 9 concerns the high torque density applications and in Chapter 10 different fault tolerant control strategies are analyzed. Finally, the last chapter presents a positioning multi-motor drive consisting of two PM tubular five-phase actuators fed by a single five-phase inverter.

A multilevel converter structure for grid-connected PV plants

A new conversion structure for three-phase grid-connected photovoltaic (PV) generation plants is presented and discussed in this Thesis. The conversion scheme is based on two insulated PV arrays, each one feeding the dc bus of a standard 2-level three-phase voltage source inverter (VSI). Inverters are connected to the grid by a traditional three-phase transformer having open-end windings at inverters side and either star or delta connection at the grid side. The resulting conversion structure is able to perform as a multilevel VSI, equivalent to a 3-level inverter, doubling the power capability of a single VSI with given voltage and current ratings. Different modulation schemes able to generate proper multilevel voltage waveforms have been discussed and compared. They include known algorithms, some their developments, and new original approaches. The goal was to share the grid power with a given ratio between the two VSI within each cycle period of the PWM, being the PWM pattern suitable for the implementation in industrial DSPs. It has been shown that an extension of the modulation methods for standard two-level inverter can provide a elegant solution for dual two-level inverter. An original control method has been introduced to regulate the dc-link voltages of each VSI, according to the voltage reference given by a single MPPT controller. A particular MPPT algorithm has been successfully tested, based on the comparison of the operating points of the two PV arrays. The small deliberately introduced difference between two operating dc voltages leads towards the MPP in a fast and accurate manner. Either simulation or experimental tests, or even both, always accompanied theoretical developments. For the simulation, the Simulink tool of Matlab has been adopted, whereas the experiments have been carried out by a full-scale low-voltage prototype of the whole PV generation system. All the research work was done at the Lab of the Department of Electrical Engineering, University of Bologna.

Analysis and Implementation of Multiphase-Multilevel Inverter for Open-Winding Loads

Research work carried out in focusing a novel multiphase-multilevel ac motor drive system much suitable for low-voltage high-current power applications. In specific, six-phase asymmetrical induction motor with open-end stator winding configuration, fed from four standard two-level three-phase voltage source inverters (VSIs). Proposed synchronous reference frame control algorithm shares the total dc source power among the 4 VSIs in each switching cycle with three degree of freedom. Precisely, first degree of freedom concerns with the current sharing between two three-phase stator windings. Based on modified multilevel space vector pulse width modulation shares the voltage between each single VSIs of two three-phase stator windings with second and third degree of freedom, having proper multilevel output waveforms. Complete model of whole ac motor drive based on three-phase space vector decomposition approach was developed in PLECS - numerical simulation software working in MATLAB environment. Proposed synchronous reference control algorithm was framed in MATLAB with modified multilevel space vector pulse width modulator. The effectiveness of the entire ac motor drives system was tested. Simulation results are given in detail to show symmetrical and asymmetrical, power sharing conditions. Furthermore, the three degree of freedom are exploited to investigate fault tolerant capabilities in post-fault conditions. Complete set of simulation results are provided when one, two and three VSIs are faulty. Hardware prototype model of quad-inverter was implemented with two passive three-phase open-winding loads using two TMS320F2812 DSP controllers. Developed McBSP (multi-channel buffered serial port) communication algorithm able to control the four VSIs for PWM communication and synchronization. Open-loop control scheme based on inverse three-phase decomposition approach was developed to control entire quad-inverter configuration and tested with balanced and unbalanced operating conditions with simplified PWM techniques. Both simulation and experimental results are always in good agreement with theoretical developments.

Controllo Vettoriale generalizzato per Macchine Elettriche Trifase

Nell’ambito della presente tesi verrà descritto un approccio generalizzato per il controllo delle macchine elettriche trifasi; la prima parte è incentrata nello sviluppo di una metodologia di modellizzazione generale, ossia in grado di descrivere, da un punto di vista matematico, il comportamento di una generica macchina elettrica, che possa quindi includere in sé stessa tutte le caratteristiche salienti che possano caratterizzare ogni specifica tipologia di macchina elettrica. Il passo successivo è quello di realizzare un algoritmo di controllo per macchine elettriche che si poggi sulla teoria generalizzata e che utilizzi per il proprio funzionamento quelle grandezze offerte dal modello unico delle macchine elettriche. La tipologia di controllo che è stata utilizzata è quella che comunemente viene definita come controllo ad orientamento di campo (FOC), per la quale sono stati individuati degli accorgimenti atti a migliorarne le prestazioni dinamiche e di controllo della coppia erogata. Per concludere verrà presentata una serie di prove sperimentali con lo scopo di mettere in risalto alcuni aspetti cruciali nel controllo delle macchine elettriche mediante un algoritmo ad orientamento di campo e soprattutto di verificare l’attendibilità dell’approccio generalizzato alle macchine elettriche trifasi. I risultati sperimentali confermano quindi l’applicabilità del metodo a diverse tipologie di macchine (asincrone e sincrone) e sono stati verificate nelle condizioni operative più critiche: bassa velocità, alta velocità bassi carichi, dinamica lenta e dinamica veloce.

Evaluation of Human Exposure to Magnetic Fields Generated by Electric Power Systems in Complex Configurations

The international growing concern for the human exposure to magnetic fields generated by electric power lines has unavoidably led to imposing legal limits. Respecting these limits, implies being able to calculate easily and accurately the generated magnetic field also in complex configurations. Twisting of phase conductors is such a case. The consolidated exact and approximated theory regarding a single-circuit twisted three-phase power cable line has been reported along with the proposal of an innovative simplified formula obtained by means of an heuristic procedure. This formula, although being dramatically simpler, is proven to be a good approximation of the analytical formula and at the same time much more accurate than the approximated formula found in literature. The double-circuit twisted three-phase power cable line case has been studied following different approaches of increasing complexity and accuracy. In this framework, the effectiveness of the above-mentioned innovative formula is also examined. The experimental verification of the correctness of the twisted double-circuit theoretical analysis has permitted its extension to multiple-circuit twisted three-phase power cable lines. In addition, appropriate 2D and, in particularly, 3D numerical codes for simulating real existing overhead power lines for the calculation of the magnetic field in their vicinity have been created. Finally, an innovative ‘smart’ measurement and evaluation system of the magnetic field is being proposed, described and validated, which deals with the experimentally-based evaluation of the total magnetic field B generated by multiple sources in complex three-dimensional arrangements, carried out on the basis of the measurement of the three Cartesian field components and their correlation with the field currents via multilinear regression techniques. The ultimate goal is verifying that magnetic induction intensity is within the prescribed limits.

Peak-to-Peak Output Current Ripple Analysis in Multiphase and Multilevel Inverters

Analysis of the peak-to-peak output current ripple amplitude for multiphase and multilevel inverters is presented in this PhD thesis. The current ripple is calculated on the basis of the alternating voltage component, and peak-to-peak value is defined by the current slopes and application times of the voltage levels in a switching period. Detailed analytical expressions of peak-to-peak current ripple distribution over a fundamental period are given as function of the modulation index. For all the cases, reference is made to centered and symmetrical switching patterns, generated either by carrier-based or space vector PWM. Starting from the definition and the analysis of the output current ripple in three-phase two-level inverters, the theoretical developments have been extended to the case of multiphase inverters, with emphasis on the five- and seven-phase inverters. The instantaneous current ripple is introduced for a generic balanced multiphase loads consisting of series RL impedance and ac back emf (RLE). Simplified and effective expressions to account for the maximum of the output current ripple have been defined. The peak-to-peak current ripple diagrams are presented and discussed. The analysis of the output current ripple has been extended also to multilevel inverters, specifically three-phase three-level inverters. Also in this case, the current ripple analysis is carried out for a balanced three-phase system consisting of series RL impedance and ac back emf (RLE), representing both motor loads and grid-connected applications. The peak-to-peak current ripple diagrams are presented and discussed. In addition, simulation and experimental results are carried out to prove the validity of the analytical developments in all the cases. The cases with different phase numbers and with different number of levels are compared among them, and some useful conclusions have been pointed out. Furthermore, some application examples are given.

Power Converters and Electric Drives for Smart Grid Applications

The present dissertation aims to explore, theoretically and experimentally, the problems and the potential advantages of different types of power converters for “Smart Grid” applications, with particular emphasis on multi-level architectures, which are attracting a rising interest even for industrial requests. The models of the main multilevel architectures (Diode-Clamped and Cascaded) are shown. The best suited modulation strategies to function as a network interface are identified. In particular, the close correlation between PWM (Pulse Width Modulation) approach and SVM (Space Vector Modulation) approach is highlighted. An innovative multilevel topology called MMC (Modular Multilevel Converter) is investigated, and the single-phase, three-phase and "back to back" configurations are analyzed. Specific control techniques that can manage, in an appropriate way, the charge level of the numerous capacitors and handle the power flow in a flexible way are defined and experimentally validated. Another converter that is attracting interest in “Power Conditioning Systems” field is the “Matrix Converter”. Even in this architecture, the output voltage is multilevel. It offers an high quality input current, a bidirectional power flow and has the possibility to control the input power factor (i.e. possibility to participate to active and reactive power regulations). The implemented control system, that allows fast data acquisition for diagnostic purposes, is described and experimentally verified.

Design, production and testing of innovative key components of HEV/BEV powertrains

Through modelling activity, experimental campaigns, test bench and on-field validation, a complete powertrain for a BEV has been designed, assembled and used in a motorsport competition. The activity can be split in three main subjects, representing the three key components of an BEV vehicle. First of all a model of the entire powertrain has been developed in order to understand how the various design choices will influence the race lap-time. The data obtained was then used to design, build and test a first battery pack. After bench tests and track tests, it was understood that by using all the cell charac-teristics, without breaking the rules limitations, higher energy and power densities could have been achieved. An updated battery pack was then designed, produced and raced with at Motostudent 2018 re-sulting in a third place at debut. The second topic of this PhD was the design of novel inverter topologies. Three inverters have been de-signed, two of them using Gallium Nitride devices, a promising semiconductor technology that can achieve high switching speeds while maintaining low switching losses. High switching frequency is crucial to reduce the DC-Bus capacitor and then increase the power density of 3 phase inverters. The third in-verter uses classic Silicon devices but employs a ZVS (Zero Voltage Switching) topology. Despite the in-creased complexity of both the hardware and the control software, it can offer reduced switching losses by using conventional and established silicon mosfet technology. Finally, the mechanical parts of a three phase permanent magnet motor have been designed with the aim to employ it in UniBo Motorsport’s 2020 Formula Student car.

Analysis and improvements of four-wire power converters for electric vehicle chargers

A robust and well-distributed backbone charging network is the priority to ensure widespread electrification of road transport, providing a driving experience similar to that of internal combustion engine vehicles. International standards set multiple technical targets for on-board and off-board electric vehicle chargers; output voltage levels, harmonic emissions, and isolation requirements strongly influence the design of power converters. Additionally, smart-grid services such as vehicle-to-grid and vehicle-to-vehicle require the implementation of bi-directional stages that inevitably increase system complexity and component count. To face these design challenges, the present thesis provides a rigorous analysis of four-leg and split-capacitor three-phase four-wire active front-end topologies focusing on the harmonic description under different modulation techniques and conditions. The resulting analytical formulation paves the way for converter performance improvements while maintaining regulatory constraints and technical requirements under control. Specifically, split-capacitor inverter current ripple was characterized as providing closed-form formulations valid for every sub-case ranging from synchronous to interleaved PWM. Outcomes are the base for a novel variable switching PWM technique capable of mediating harmonic content limitation and switching loss reduction. A similar analysis is proposed for four-leg inverters with a broad range of continuous and discontinuous PWM modulations. The general superiority of discontinuous PWM modulation in reducing switching losses and limiting harmonic emission was demonstrated. Developments are realized through a parametric description of the neutral wire inductor. Finally, a novel class of integrated isolated converter topologies is proposed aiming at the neutral wire delivery without employing extra switching components rather than the one already available in typical three-phase inverter and dual-active-bridge back-to-back configurations. The fourth leg was integrated inside the dual-active-bridge input bridge providing relevant component count savings. A novel modified single-phase-shift modulation technique was developed to ensure a seamless transition between working conditions like voltage level and power factor. Several simulations and experiments validate the outcomes.

Electrode Materials for Ionic Liquid Based-Supercapacitors

The development of safe, high energy and power electrochemical energy-conversion systems can be a response to the worldwide demand for a clean and low-fuel-consuming transport. This thesis work, starting from a basic studies on the ionic liquid (IL) electrolytes and carbon electrodes and concluding with tests on large-size IL-based supercapacitor prototypes demonstrated that the IL-based asymmetric configuration (AEDLCs) is a powerful strategy to develop safe, high-energy supercapacitors that might compete with lithium-ion batteries in power assist-hybrid electric vehicles (HEVs). The increase of specific energy in EDLCs was achieved following three routes: i) the use of hydrophobic ionic liquids (ILs) as electrolytes; ii) the design and preparation of carbon electrode materials of tailored morphology and surface chemistry to feature high capacitance response in IL and iii) the asymmetric double-layer carbon supercapacitor configuration (AEDLC) which consists of assembling the supercapacitor with different carbon loadings at the two electrodes in order to exploit the wide electrochemical stability window (ESW) of IL and to reach high maximum cell voltage (Vmax). Among the various ILs investigated the N-methoxyethyl-N-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide (PYR1(2O1)TFSI) was selected because of its hydrophobicity and high thermal stability up to 350 °C together with good conductivity and wide ESW, exploitable in a wide temperature range, below 0°C. For such exceptional properties PYR1(2O1)TFSI was used for the whole study to develop large size IL-based carbon supercapacitor prototype. This work also highlights that the use of ILs determines different chemical-physical properties at the interface electrode/electrolyte with respect to that formed by conventional electrolytes. Indeed, the absence of solvent in ILs makes the properties of the interface not mediated by the solvent and, thus, the dielectric constant and double-layer thickness strictly depend on the chemistry of the IL ions. The study of carbon electrode materials evidences several factors that have to be taken into account for designing performing carbon electrodes in IL. The heat-treatment in inert atmosphere of the activated carbon AC which gave ACT carbon featuring ca. 100 F/g in IL demonstrated the importance of surface chemistry in the capacitive response of the carbons in hydrophobic ILs. The tailored mesoporosity of the xerogel carbons is a key parameter to achieve high capacitance response. The CO2-treated xerogel carbon X3a featured a high specific capacitance of 120 F/g in PYR14TFSI, however, exhibiting high pore volume, an excess of IL is required to fill the pores with respect to that necessary for the charge-discharge process. Further advances were achieved with electrodes based on the disordered template carbon DTC7 with pore size distribution centred at 2.7 nm which featured a notably high specific capacitance of 140 F/g in PYR14TFSI and a moderate pore volume, V>1.5 nm of 0.70 cm3/g. This thesis work demonstrated that by means of the asymmetric configuration (AEDLC) it was possible to reach high cell voltage up to 3.9 V. Indeed, IL-based AEDLCs with the X3a or ACT carbon electrodes exhibited specific energy and power of ca. 30 Wh/kg and 10 kW/kg, respectively. The DTC7 carbon electrodes, featuring a capacitance response higher of 20%-40% than those of X3a and ACT, respectively, enabled the development of a PYR14TFSI-based AEDLC with specific energy and power of 47 Wh/kg and 13 kW/kg at 60°C with Vmax of 3.9 V. Given the availability of the ACT carbon (obtained from a commercial material), the PYR1(2O1)TFSI-based AEDLCs assembled with ACT carbon electrodes were selected within the EU ILHYPOS project for the development of large-size prototypes. This study demonstrated that PYR1(2O1)TFSI-based AEDLC can operate between -30°C and +60°C and its cycling stability was proved at 60°C up to 27,000 cycles with high Vmax up to 3.8 V. Such AEDLC was further investigated following USABC and DOE FreedomCAR reference protocols for HEV to evaluate its dynamic pulse-power and energy features. It was demonstrated that with Vmax of 3.7 V at T> 30 °C the challenging energy and power targets stated by DOE for power-assist HEVs, and at T> 0 °C the standards for the 12V-TSS and 42V-FSS and TPA 2s-pulse applications are satisfied, if the ratio wmodule/wSC = 2 is accomplished, which, however, is a very demanding condition. Finally, suggestions for further advances in IL-based AEDLC performance were found. Particularly, given that the main contribution to the ESR is the electrode charging resistance, which in turn is affected by the ionic resistance in the pores that is also modulated by pore length, the pore geometry is a key parameter in carbon design not only because it defines the carbon surface but also because it can differentially “amplify” the effect of IL conductivity on the electrode charging-discharging process and, thus, supercapacitor time constant.

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Earthquake forecasting and seismic hazard analysis: some insights on the testing phase and the modeling

This thesis is divided in three chapters. In the first chapter we analyse the results of the world forecasting experiment run by the Collaboratory for the Study of Earthquake Predictability (CSEP). We take the opportunity of this experiment to contribute to the definition of a more robust and reliable statistical procedure to evaluate earthquake forecasting models. We first present the models and the target earthquakes to be forecast. Then we explain the consistency and comparison tests that are used in CSEP experiments to evaluate the performance of the models. Introducing a methodology to create ensemble forecasting models, we show that models, when properly combined, are almost always better performing that any single model. In the second chapter we discuss in depth one of the basic features of PSHA: the declustering of the seismicity rates. We first introduce the Cornell-McGuire method for PSHA and we present the different motivations that stand behind the need of declustering seismic catalogs. Using a theorem of the modern probability (Le Cam's theorem) we show that the declustering is not necessary to obtain a Poissonian behaviour of the exceedances that is usually considered fundamental to transform exceedance rates in exceedance probabilities in the PSHA framework. We present a method to correct PSHA for declustering, building a more realistic PSHA. In the last chapter we explore the methods that are commonly used to take into account the epistemic uncertainty in PSHA. The most widely used method is the logic tree that stands at the basis of the most advanced seismic hazard maps. We illustrate the probabilistic structure of the logic tree, and then we show that this structure is not adequate to describe the epistemic uncertainty. We then propose a new probabilistic framework based on the ensemble modelling that properly accounts for epistemic uncertainties in PSHA.