Frequency-domain nonlinear modeling approaches for power systems components - A comparison

Harmonic simulations play a key role in studying and predicting the impact of nonlinear devices on the power quality level of distribution grids. A frequency-domain approach allows higher computational efficiency, which has key importance as long as complex networks have to be studied. However, this requires proper frequency-domain behavioral models able to represent the nonlinear voltage-current relationship characterizing these devices. The Frequency Transfer Matrix (FTM) method is one of the most widespread frequency domain modeling approaches for power system applications. However, others suitable techniques have been developed in the last years, in particular the X-parameters approach, which comes from radiofrequency and microwave applications, and the simplified Volterra models under quasi-sinusoidal conditions, that have been specifically tailored for power system devices. In this paper FTM, X-parameters and simplified Volterra approaches are compared in representing the nonlinear voltage-current relationship of a bridge rectifier feeding an ohmic-capacitive dc load. Results show that the X-parameters model reaches good accuracy, which is slightly better than that achieved by the FTM and simplified Volterra models, but with a considerably larger set of coefficients. Simplified Volterra models under quasi-sinusoidal conditions allows an effective trade-off between accuracy and complexity

Metodologia Per la Caratterizzazione di amplificatori a basso rumore per UMTS

In questo lavoro si presenta una metodologia di progettazione elettronica a livello di sistema, affrontando il problema della caratterizzazione dello spazio di progetto dell' amplificatore a basso rumore costituente il primo stadio di un front end a conversione diretta per UMTS realizzato in tecnologia CMOS con lunghezza di canale .18u. La metodologia è sviluppata al fine di valutare in modo quantititativo le specifiche ottime di sistema per il front-end stesso e si basa sul concetto di Piattaforma Analogica, che prevede la costruzione di un modello di prestazioni per il blocco analogico basato su campionamento statistico di indici di prestazioni del blocco stesso, misurati tramite simulazione di dimensionamenti dei componenti attivi e passivi soddisfacenti un set di equazioni specifico della topologia circuitale. Gli indici di prestazioni vengono successivamente ulizzati per parametrizzare modelli comportamentali utilizzati nelle fasi di ottimizzazione a livello di sistema. Modelli comportamentali atti a rappresentare i sistemi RF sono stati pertanto studiati per ottimizzare la scelta delle metriche di prestazioni. L'ottimizzazione dei set di equazioni atti a selezionare le configurazione di interesse per il campionamento ha al tempo stesso richiesto l'approfondimento dei modelli di dispositivi attivi validi in tutte le regioni di funzionamento, e lo studio dettagliato della progettazione degli amplificatori a basso rumore basati su degenerazione induttiva. Inoltre, il problema della modellizzazione a livello di sistema degli effetti della comunicazione tra LNA e Mixer è stato affrontato proponendo e analizzando diverse soluzioni. Il lavoro ha permesso di condurre un'ottimizzazione del front-end UMTS, giungendo a specifiche ottime a livello di sistema per l'amplificatore stesso

Discrete-time linear and nonlinear aerodynamic impulse responses for efficient CFD analyses

This dissertation discusses the mathematical existence and the numerical identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner\u27s function), forced harmonic responses (such as Theodorsen\u27s function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This will establish the aerodynamic discrete-time impulse response function as the most fundamental and computationally efficient aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this dissertation help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories.;Nonlinear aerodynamic impulse responses are identified using the Volterra theory of nonlinear systems. The theory is described and a discrete-time kernel identification technique is presented. The kernel identification technique is applied to a simple nonlinear circuit for illustrative purposes. The method is then applied to the nonlinear viscous Burger\u27s equation as an example of an application to a simple CFD model. Finally, the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code.;Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time systems

Nonlinear Modeling and Identification of Unsteady Aerodynamics at Stall

For an aircraft with delta wing shape, aerodynamics in stall angles-of-attack at both low and high-subsonic Mach conditions is known to be unsteady and nonlinear in nature. In these conditions, the longitudinal aerodynamic loads depend on the history of angle-ofattack and side-slip. The classical method of using damping or acceleration aerodynamic derivatives for modeling the unsteady variation of coefficients is unsuitable. Hence, two novel approaches for modeling aerodynamic loads in these conditions are proposed in this thesis. The unsteady effect in stall conditions at low Mach number is reflected in forced oscillation wind tunnel tests as dependence of longitudinal loads on amplitude and frequency of sinusoidal angle-of-attack input. The variations in longitudinal loads are nonlinear as their power spectrum contains super-harmonics of input frequency. The approaches presented in literature are equivalent when these are reduced to equivalent linear transfer function formulation, while their nonlinear adaptations are semi-empirical or adhoc. Hence, Volterra Variational Modeling (VVM) is proposed as a systematic approach to capture the nonlinear nature of unsteady variations. The VVM is derived from Volterra series as a set of parametric differential equations of the so-called kernel states. The kernel-states have special harmonic input response properties which are leveraged to develop a systematic methodology to capture the nonlinear unsteady variations in pitching moment coefficient. VVM is shown to inherently reproduce the nonlinear features of unsteady aerodynamic loads like amplitude dependence of nonlinear variations, different effective time-scale for pitch-up and pitchdown motions and same number of super-harmonics as seen in the experimental data. Hence, it offers several advantages compared to all the modeling approaches in literature. The VVM is a powerful approach due to following features: (i) Mathematically rigorous structure, (ii) Physical interpretations of parameters, (iii) it facilitates linear analysis of the flight modes (iv) simple identification methodology using forced oscillation wind tunnel test data (v) open to innovations in model structure and estimation technique. These concepts are demonstrated for the Generic Tailless Aircraft and F16XL aircraft using comprehensive sets of wind tunnel test data . The unsteady phenomena at high sub-sonic Mach number is called AbruptWing Stall, and novel model called ”Bifurcational Model of Aerodynamic Asymmetry” is proposed for modeling it. It shown to be a topologically rich structure which can model the static hysteresis and unsteady variations in rolling moment coefficient versus the side-slip angle, in order to reproduce the effects of Abrupt Wing Stall on flight dynamics

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems

Density waves in the shearing sheet I. Swing amplification

The shearing sheet model of a galactic disk is studied anew. The theoretical description of its dynamics is based on three building blocks: Stellar orbits, which are described here in epicyclic approximation, the collisionless Boltzmann equation determining the distribution function of stars in phase space, and the Poisson equation in order to take account of the self-gravity of the disk. Using these tools I develop a new formalism to describe perturbations of the shearing sheet. Applying this to the unbounded shearing sheet model I demonstrate again how the disturbances of the disk evolve always into `swing amplified' density waves, i.e. spiral-arm like, shearing density enhancements, which grow and decay while the wave crests swing by from leading to trailing orientation. Several examples are given how such `swing amplification' events are incited in the shearing sheet.Comment: small corrections, uses new A&A style fil

Identification of the dynamic characteristics of nonlinear structures

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Identification scheme for fractional Hammerstein Models with the delayed Haar Wavelet

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix (HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods

Analog dithering techniques for highly linear and efficient transmitters

The current thesis is about investigation of new methods and techniques to be able to utilize the switched mode amplifiers, for linear and efficient applications. Switched mode amplifiers benefit from low overlap between the current and voltage wave forms in their output terminals, but they seriously suffer from nonlinearity. This makes it impossible to use them to amplify non-constant envelope message signals, where very high linearity is expected. In order to do that, dithering techniques are studied and a full linearity analysis approach is developed, by which the linearity performance of the dithered amplifier can be analyzed, based on the dithering level and frequency. The approach was based on orthogonalization of the equivalent nonlinearity and is capable of prediction of both co-channel and adjacent channel nonlinearity metrics, for a Gaussian complex or real input random signal. Behavioral switched mode amplifier models are studied and new models are developed, which can be utilized to predict the nonlinear performance of the dithered power amplifier, including the nonlinear capacitors effects. For HFD application, self-oscillating and asynchronous sigma delta techniques are currently used, as pulse with modulators (PWM), to encode a generic RF message signal, on the duty cycle of an output pulse train. The proposed models and analysis techniques were applied to this architecture in the first phase, and the method was validated with measurement on a prototype sample, realized in 65 nm TSMC CMOS technology. Afterwards, based on the same dithering phenomenon, a new linearization technique was proposed, which linearizes the switched mode class D amplifier, and at the same time can reduce the reactive power loss of the amplifier. This method is based on the dithering of the switched mode amplifier with frequencies lower than the band-pass message signal and is called low frequency dithering (LFD). To test this new technique, two test circuits were realized and the idea was applied to them. Both of the circuits were of the hard nonlinear type (class D) and are integrated CMOS and discrete LDMOS technologies respectively. The idea was successfully tested on both test circuits and all of the linearity metric predictions for a digitally modulated RF signal and a random signal were compared to the measurements. Moreover a search method to find the optimum dither frequency was proposed and validated. Finally, inspired by averaging interpretation of the dithering phenomenon, three new topologies were proposed, which are namely DLM, RF-ADC and area modulation power combining, which are all nonlinear systems linearized with dithering techniques. A new averaging method was developed and used for analysis of a Gilbert cell mixer topology, which resulted in a closed form relationship for the conversion gain, for long channel devices