Dynamics and stability of wind turbine generators

Synchronous and induction generators are considered. A comparison is made between wind turbines, steam, and hydro units. The unusual phenomena associated with wind turbines are emphasized. The general control requirements are discussed, as well as various schemes for torsional damping such as speed sensitive stabilizer and blade pitch control. Integration between adjacent wind turbines in a wind farm is also considered

Binary spreading process with parity conservation

Recently there has been a debate concerning the universal properties of the phase transition in the pair contact process with diffusion (PCPD) $2A\to 3A, 2A\to \emptyset$. Although some of the critical exponents seem to coincide with those of the so-called parity-conserving universality class, it was suggested that the PCPD might represent an independent class of phase transitions. This point of view is motivated by the argument that the PCPD does not conserve parity of the particle number. In the present work we pose the question what happens if the parity conservation law is restored. To this end we consider the the reaction-diffusion process $2A\to 4A, 2A\to \emptyset$. Surprisingly this process displays the same type of critical behavior, leading to the conclusion that the most important characteristics of the PCPD is the use of binary reactions for spreading, regardless of whether parity is conserved or not.Comment: RevTex, 4pages, 4 eps figure

A Generalized Duality Transformation of the Anisotropic Xy Chain in a Magnetic Field

We consider the anisotropic $XY$ chain in a magnetic field with special boundary conditions described by a two-parameter Hamiltonian. It is shown that the exchange of the parameters corresponds to a similarity transformation, which reduces in a special limit to the Ising duality transformation.Comment: 6 pages, LaTeX, BONN-HE-93-4

MOD-2 wind turbine farm stability study

The dynamics of single and multiple 2.5 ME, Boeing MOD-2 wind turbine generators (WTGs) connected to utility power systems were investigated. The analysis was based on digital simulation. Both time response and frequency response methods were used. The dynamics of this type of WTG are characterized by two torsional modes, a low frequency 'shaft' mode below 1 Hz and an 'electrical' mode at 3-5 Hz. High turbine inertia and low torsional stiffness between turbine and generator are inherent features. Turbine control is based on electrical power, not turbine speed as in conventional utility turbine generators. Multi-machine dynamics differ very little from single machine dynamics

Control of large wind turbine generators connected to utility networks

This is an investigation of the control requirements for variable pitch wind turbine generators connected to electric power systems. The requirements include operation in very small as well as very large power systems. Control systems are developed for wind turbines with synchronous, induction, and doubly fed generators. Simulation results are presented. It is shown how wind turbines and power system controls can be integrated. A clear distinction is made between fast control of turbine torque, which is a peculiarity of wind turbines, and slow control of electric power, which is a traditional power system requirement

The asymmetric exclusion model with sequential update

We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism which was recently used to solve the model with sublattice-parallel update[1]. It is shown that the matrix-algebra describing the sequential update and sublattice-parallel update are identical and can be mapped onto the random sequential case treated by Derrida et al[2].Comment: 7 pages, Late

Phase transition of the one-dimensional coagulation-production process

Recently an exact solution has been found (M.Henkel and H.Hinrichsen, cond-mat/0010062) for the 1d coagulation production process: 2A ->A, A0A->3A with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with $t^{-1/2}$ density decay law. Here I show that cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates as considered in cond-mat/0010062. Numerical evidence is given that the phase transition universality agrees with that of the annihilation-fission model with low diffusions.Comment: 4 pages, 4 figures include

Matrix Product Eigenstates for One-Dimensional Stochastic Models and Quantum Spin Chains

We show that all zero energy eigenstates of an arbitrary $m$--state quantum spin chain Hamiltonian with nearest neighbor interaction in the bulk and single site boundary terms, which can also describe the dynamics of stochastic models, can be written as matrix product states. This means that the weights in these states can be expressed as expectation values in a Fock representation of an algebra generated by $2m$ operators fulfilling $m^2$ quadratic relations which are defined by the Hamiltonian.Comment: 11 pages, Late

First order phase transition with a logarithmic singularity in a model with absorbing states

Recently, Lipowski [cond-mat/0002378] investigated a stochastic lattice model which exhibits a discontinuous transition from an active phase into infinitely many absorbing states. Since the transition is accompanied by an apparent power-law singularity, it was conjectured that the model may combine features of first- and second-order phase transitions. In the present work it is shown that this singularity emerges as an artifact of the definition of the model in terms of products. Instead of a power law, we find a logarithmic singularity at the transition. Moreover, we generalize the model in such a way that the second-order phase transition becomes accessible. As expected, this transition belongs to the universality class of directed percolation.Comment: revtex, 4 pages, 5 eps figure

Exact results for one dimensional stochastic cellular automata for different types of updates

We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the matrix product formalism. This construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates. Using this connection, we derive explicit relations between the densities and correlation functions for these different stationary states.Comment: 7 pages, Late