Elementary Transfer Functions Research Articles

Uneven internal time-step adjustment for fast power system dynamic simulations based on Trapezoidal integration of elementary transfer function blocks

With the development of renewable energy sources, the scale and complexity of power systems are continuously increasing, resulting in a high requirement for the efficiency of dynamic simulation. Increasing the simulation time-step is a possible measure for the fixed time-step (FTS) method to accelerate the simulation, yet also a potential cause for deteriorating the simulation accuracy. To improve the overall power system dynamic simulation speed without jeopardizing the expected accuracy, this paper proposes a novel Uneven Internal Time-Step Adjustment method based on Trapezoidal integration of elementary transfer function blocks (ETFBs). For ETFBs with different time constants, three different integration modes are defined, including single-step integration, multiple-step integration, and static approximation. Each ETFB can select an appropriate integration mode and adjust its internal time-step, automatically expanding the size of the simulation time-step. Implementation of static approximation for ETFBs with small time constants is given. Discussion on the determination of threshold values of internal time-step is provided, which mainly affect the accuracy of the system. The proposed method is applied to the open-source Simulation Toolkit for Electrical Power Systems (STEPS). Different cases are tested to obtain the maximum simulation time-step that can maintain numerical stability and validate the efficiency and accuracy of the proposed method.

Bode Plots Revisited: a Software System for Automated Generation of Piecewise Linear Frequency Response Plots

The paper presents an algorithm for automatic generation of piecewise linear Bode plots. The algorithm is complete in the sense it covers for all posible locations of poles and zeros of transfer functions, including unstable poles and poles and zeroes at the imaginary axis. The starting transfer function is factored into a canonical form, and thirteen elementary transfer function types are defined by their canonical forms. The thirteen elementary transfer function types are shown to be derived from just five generic transfer function types, and piecewise linear Bode plots are defined and depicted for all five of the generic types. For all thirteen elementary transfer function types the nodes they introduce in the piecewise linear plots are specified, as well as the algorithms how they affect the node altitudes. Finally, a three stage algorithm that produces both the Bode plots and the exact numerically computed frequency response plots is described. The algorithm is implemented in a command line based program, illustrated in a filter example, and future work directions are indicated, aiming a graphical user interface and integration of the program to a linear system symbolic analysis software suite.

Assisted Optimization of the Servo Driving by Using Virtual Labview Instrumentation and the Elementary Transfer Functions and Neural Network Methods

In the optimisation stage of the systems one of the more important step is the optimisation of the dynamic behavior of all elements with priority the elements what have the slow frequency, like motors. The paper try to show how will be possible to optimise very easily the dynamic behavior of elements and systems, using LabVIEW propre instrumentation and the application of the transfer functions and neural tnetwork theory. By appling the virtual LabVIEW instrumentation is possible to choose on-line the optimal values for each constructive and functional parameters of the elements and the systems to obtain one good dynamic answer: maximal acceleration without vibration, minimum answer time and maximal precision. The paper presents some of the more important used transfer functions in the assisted analyse of the elements and systems and some practical results of the assisted optimisation by using the neural network method. In the research were been used some different way to optimize the convergence process, for example: using one time- delay of the first and second output from the neural layers; using the recursive link and time- delay; using the bipolar sigmoid hyperbolic tangent sensitive function replacing the sigmoid simple sensitive function. By on-line simulation of the neural network was possible to know what will be the influences of all network parameters like the input data, weight, biases matrix, sensitive functions, closed loops and time- delay, to the gradient errors, in a convergence process. In the optimization research we used the minimization of the gradient error function between the output and the target.

Stability and resonance conditions of elementary fractional transfer functions

Elementary fractional transfer functions are studied in this paper. Some basic properties of elementary transfer functions of the first kind are recalled. Then, two main results are presented regarding elementary fractional transfer functions of the second kind, written in a canonical form and characterized by a commensurate order, a pseudo-damping factor, and a natural frequency. First, stability conditions are established in terms of the pseudo-damping factor and the commensurate order, as a corollary to Matignon’s stability theorem. They extend the previous result into conditions that are simpler to check. Then, resonance conditions are established numerically in terms of the commensurate order and the pseudo-damping factor and give interesting information on the frequency behavior of fractional systems. It is shown that elementary transfer functions of the second kind might have up to two resonant frequencies. Moreover, three abaci are given allowing to determine the pseudo-damping factor and the commensurate order for, respectively, a desired normalized gain at each resonance, a desired phase at each resonance, and a desired normalized first or second resonant frequency.

From a Model of Lossy Flared Pipes to a General Framework for Simulation of Waveguides

This paper deals with the theory and application of waveguide modeling of lossy flared acoustic pipes, relying on the Webster-Lokshin equation. This model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar waves or spherical waves. Solving this model for a piece of pipe leads to a two-port system made of four transfer functions which mimic the global acoustic effects. Moreover, introducing some relevant physical interpretations makes it possible to separate elementary effects due to the geometry of the piece of pipe (section, slope, and curvature) and isolate corresponding elementary transfer functions. From this decomposition a framework is obtained which allows to recover some digital waveguide models introduced earlier in the literature. This work contributes to the standardization of some different waveguide models, and brings a higher level of refinement that is visco-thermal losses combined with curvature effects.

DIFFUSIVE REPRESENTATIONS FOR THE ANALYSIS AND SIMULATION OF FLARED ACOUSTIC PIPES WITH VISCO-THERMAL LOSSES

Acoustic waves travelling in axisymmetric pipes with visco-thermal losses at the wall obey a Webster–Lokshin model. Their simulation may be achieved by concatenating scattering matrices of elementary transfer functions associated with nearly constant parameters (e.g. curvature). These functions are computed analytically and involve diffusive pseudo-differential operators, for which we have representation formula and input-output realizations, yielding direct numerical approximations of finite order. The method is based on some involved complex analysis.

Partially coherent imaging and spatial coherence wavelets

A description of spatially partially coherent imaging based on the propagation of second-order spatial coherence wavelets and marginal power spectra (Wigner distribution functions) is presented. In this dynamics, the spatial coherence wavelets will be affected by the system through its elementary transfer function. The consistency of the model with the both extreme cases of full coherent and incoherent imaging was proved. In the last case we obtained the classical concept of optical transfer function as a simple integral of the elementary transfer function. Furthermore, the elementary incoherent response function was introduced as the Fourier transform of the elementary transfer function. It describes the propagation of spatial coherence wavelets form each object point to each image point through a specific point on the pupil planes. The point spread function of the system was obtained by a simple integral of the elementary incoherent response function.

Conditions for the application of reactor transfer functions

An equivalent complex amplification coefficient for a reactor can be defined, not only for a given law of variation of the input, but also for a given law of variation of the output. The results obtained can be used in the programmed control of the period and power of a reactor, and they also make possible the determination of conditions of applicability of elementary transfer functions for a reactor, and the estimation of the errors made when this is done. New formulas are introduced for the approximation of transfer functions for subcritical, critical, and supercritical reactors.