Offshore Wind Energy System with DC Transmission Discrete Mass: Modeling and Simulation

This paper presents an integrated model for an offshore wind energy system taking into consideration a contribution for the marine wave and wind speed with perturbations influences on the power quality of current injected into the electric grid. The paper deals with the simulation of one floating offshore wind turbine equipped with a PMSG and a two-level converter connected to an onshore electric grid. The use of discrete mass modeling is accessed in order to reveal by computing the THD on how the perturbations of the captured energy are attenuated at the electric grid injection point. Two torque actions are considered for the three-mass modeling, the aerodynamic on the flexible part and on the rigid part of the blades. Also, a torque due to the influence of marine waves in deep water is considered. PI fractional-order control supports the control strategy. A comparison between the drive train models is presented.

Control and Supervision of Wind Energy Conversion Systems

This paper is about a PhD thesis and includes the study and analysis of the performance of an onshore wind energy conversion system. First, mathematical models of a variable speed wind turbine with pitch control are studied, followed by the study of different controller types such as integer-order controllers, fractional-order controllers, fuzzy logic controllers, adaptive controllers and predictive controllers and the study of a supervisor based on finite state machines is also studied. The controllers are included in the lower level of a hierarchical structure composed by two levels whose objective is to control the electric output power around the rated power. The supervisor included at the higher level is based on finite state machines whose objective is to analyze the operational states according to the wind speed. The studied mathematical models are integrated into computer simulations for the wind energy conversion system and the obtained numerical results allow for the performance assessment of the system connected to the electric grid. The wind energy conversion system is composed by a variable speed wind turbine, a mechanical transmission system described by a two mass drive train, a gearbox, a doubly fed induction generator rotor and by a two level converter.

Blade pitch control malfunction simulation in a wind energy conversion system with MPC five-level converter

This paper is on a wind energy conversion system simulation of a transient analysis due to a blade pitch control malfunction. The aim of the transient analysis is the study of the behavior of a back-to-back multiple point clamped five-level full-power converter implemented in a wind energy conversion system equipped with a permanent magnet synchronous generator. An alternate current link connects the system to the grid. The drive train is modeled by a three-mass model in order to simulate the dynamic effect of the wind on the tower. The control strategy is based on fractional-order control. Unbalance voltages in the DC-link capacitors are lessen due to the control strategy, balancing the capacitor banks voltages by a selection of the output voltage vectors. Simulation studies are carried out to evaluate not only the system behavior, but also the quality of the energy injected into the electric grid.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

Border figure detection using a phase oscillator network with dynamical coupling

Oscillator networks have been developed in order to perform specific tasks related to image processing. Here we analytically investigate the existence of synchronism in a pair of phase oscillators that are short-range dynamically coupled. Then, we use these analytical results to design a network able of detecting border of black-and-white figures. Each unit composing this network is a pair of such phase oscillators and is assigned to a pixel in the image. The couplings among the units forming the network are also dynamical. Border detection emerges from the network activity.

Modeling Two-Oscillator Circadian Systems Entrained by Two Environmental Cycles

Several experimental studies have altered the phase relationship between photic and non-photic environmental, 24 h cycles (zeitgebers) in order to assess their role in the synchronization of circadian rhythms. To assist in the interpretation of the complex activity patterns that emerge from these ""conflicting zeitgeber'' protocols, we present computer simulations of coupled circadian oscillators forced by two independent zeitgebers. This circadian system configuration was first employed by Pittendrigh and Bruce (1959), to model their studies of the light and temperature entrainment of the eclosion oscillator in Drosophila. Whereas most of the recent experiments have restricted conflicting zeitgeber experiments to two experimental conditions, by comparing circadian oscillator phases under two distinct phase relationships between zeitgebers (usually 0 and 12 h), Pittendrigh and Bruce compared eclosion phase under 12 distinct phase relationships, spanning the 24 h interval. Our simulations using non-linear differential equations replicated complex non-linear phenomena, such as ""phase jumps'' and sudden switches in zeitgeber preferences, which had previously been difficult to interpret. Our simulations reveal that these phenomena generally arise when inter-oscillator coupling is high in relation to the zeitgeber strength. Manipulations in the structural symmetry of the model indicated that these results can be expected to apply to a wide range of system configurations. Finally, our studies recommend the use of the complete protocol employed by Pittendrigh and Bruce, because different system configurations can generate similar results when a ""conflicting zeitgeber experiment'' incorporates only two phase relationships between zeitgebers.

Self-organized distribution of periodicity and chaos in an electrochemical oscillator

We report a detailed numerical investigation of a prototype electrochemical oscillator, in terms of high-resolution phase diagrams for an experimentally relevant section of the control (parameter) space. The prototype model consists of a set of three autonomous ordinary differential equations which captures the general features of electrochemical oscillators characterized by a partially hidden negative differential resistance in an N-shaped current-voltage stationary curve. By computing Lyapunov exponents, we provide a detailed discrimination between chaotic and periodic phases of the electrochemical oscillator. Such phases reveal the existence of an intricate structure of domains of periodicity self-organized into a chaotic background. Shrimp-like periodic regions previously observed in other discrete and continuous systems were also observed here, which corroborate the universal nature of the occurrence of such structures. In addition, we have also found a structured period distribution within the order region. Finally we discuss the possible experimental realization of comparable phase diagrams.

Disagreement between correlations of quantum mechanics and stochastic electrodynamics in the damped parametric oscillator

Intracavity and external third order correlations in the damped nondegenerate parametric oscillator are calculated for quantum mechanics and stochastic electrodynamics (SED), a semiclassical theory. The two theories yield greatly different results, with the correlations of quantum mechanics being cubic in the system's nonlinear coupling constant and those of SED being linear in the same constant. In particular, differences between the two theories are present in at least a mesoscopic regime. They also exist when realistic damping is included. Such differences illustrate distinctions between quantum mechanics and a hidden variable theory for continuous variables.