Initial Conditions Of State Variables Research Articles

The Analysis of Sub-Synchronous Resonance in a Wind Farm for a Doubly-Fed Induction Generator Using Modern Analytical Method

The occurrence of Sub-Synchronous Resonance (SSR) phenomena can be attributed to the interaction that takes place between wind turbine generators and series-compensated transmission lines. The Doubly-Fed Induction Generator (DFIG) is widely recognized as a prevalent generator form employed in wind energy conversion systems. The present paper commences with an extensive exposition on modal analysis techniques employed in a series of compensated wind farms featuring Doubly Fed Induction Generators (DFIGs). The system model encompasses various components, including the aerodynamics of a wind turbine, an induction generator characterized by a sixth-order model, a second-order two-mass shaft system, a series compensated transmission line described by a fourth-order model, controllers for the Rotor-Side Converter (RSC) and the Grid-Side Converter (GSC) represented by an eighth-order model, and a first-order DC-link model. The technique of eigenvalue-based SSR analysis is extensively utilized in various academic and research domains. The eigenvalue technique depends on the initial conditions of state variables to yield an accurate outcome. The non-iterative approach, previously employed for the computation of initial values of the state variables, has exhibited issues with convergence, lack of accuracy, and excessive computational time. The comparative study evaluates the time-domain simulation outcomes under different wind speeds and compensation levels, along side the eigenvalue analysis conducted using both the suggested and non-iterative methods. This comparative analysis is conducted to illustrate the proposed approach efficacy and precision. The results indicate that the eigenvalue analysis conducted using the proposed technique exhibits more accuracy, as it aligns with the findings of the simulations across all of the investigated instances. The process of validation is executed with the MATLAB program. Within the context of the investigation, it has been found that increasing compensation levels while simultaneously decreasing wind speed leads to system instability. Therefore, modifying the compensation level by the current wind speed is advisable.

Particle filter combined with data reconciliation for nonlinear state estimation with unknown initial conditions in nonlinear dynamic process systems

State estimation is very crucial for process control and optimization in dynamic processes. The particle filter (PF) is a novel and suitable technique for state estimation of nonlinear dynamic process systems. Conventional PFs for nonlinear dynamic process systems rely on the known initial conditions for state variables, such as the known probability density function (PDF) of initial states or the known values of initial states, but the initial conditions of a nonlinear dynamical system are usually unknown in actual industrial processes. In this paper, a novel methodology, PF combined with data reconciliation, is proposed and applied to nonlinear dynamic process systems for state estimation with unknown initial conditions. The measurement test criterion and data reconciliation with sequentially increasing data information are proposed to derive reliable initial values of the state variables under sufficient information of measurements. The interactive information between PF and data reconciliation problems can improve the initial values iteratively. Finally, accurate results of state estimation can be achieved. The effectiveness of the methodology is demonstrated through two nonlinear dynamic systems.

Effective recursive parallelotopic bounding for robust output-feedback control

In this paper an approach is studied to guaranteed (set-membership) state estimation for robust output-feedback model predictive control (MPC) with hard input and state constraints. Uncertainties are assumed to arise in a dynamic system from unknown initial conditions of state variables and due to unknown-but-bounded measurement noise. The uncertainty in the state variables is represented as a parallelotopic set. The employed state-estimation algorithm recursively outbounds the feasible set that is given by an intersection of model predictions with obtained measurement information. Along with the well-known minimum-volume criterion for parallelotopic outbounding, three alternative criteria are proposed and studied. The aim is to identify the best outbounding approach for improving performance of the robust MPC.

A terminal invariance criterion in deterministic motion control systems

A matrix-vector criterion for the terminal invariance of the state variables at the terminal point in time under nonzero initial conditions in a deterministic control system of a plant motion is proposed. In distinction from the scalar third terminal invariance form studied earlier, the proposed criterion makes it possible to take into account nonzero initial conditions for state variables.

An adjoint data assimilation approach for estimating parameters in a three-dimensional ecosystem model

In this paper an ecosystem model, including phytoplankton, zooplankton, nitrate, ammonium, phosphate and detritus, is described. The model is driven by physical fields derived from a three-dimensional physical transport model. Simulation includes nitrate input from a river. Simulated results are then sampled and the sampled data are used in sequential numerical experiments to assess the ability of using an adjoint data assimilation approach for estimating the poorly known parameters of the ecosystem model, such as growth and death rate, half-saturation constant of nutrients, etc. Data with different spatial and temporal resolution over 1 week are assimilated into the ecosystem model. Assimilation of data at 30 grid stations with a sampling interval of 6 h is proved to be adequate for recovering all the parameters of the ecosystem model. Both the spatial and temporal resolution of the data are mutually complementary in the assimilative model. Thus, improvement of either of them can result in improvement of model parameter recoveries. The assimilation of phytoplankton data is essential to recover the model parameters. Phytoplankton is the core of the food web and without the information on phytoplankton, the structure of the ecosystem cannot be constructed correctly. The adjoint method can work well with the noisy data. In the twin experiments with noisy data, the parameters can be recovered but the error is increased. The results of the model and parameter recovery are sensitive to the initial conditions of state variables, so the determination of the initial condition is as important as that of the model parameter. The spatial and temporal resolution and the data type of the observations in Analysis and Modelling Research of the Ecosystem in the Bohai Sea (AMREB) are suitable for the recovery of the model parameters used in this study.

PANSYM: a symbolic equation generator for mathematical modelling, analysis and control of metabolic and pharmacokinetic systems

Software is presented for automatic generation of fist-order ordinary differential equations (ODE) that arise from lumped parameter representations of metabolic and pharmacokinetic systems. The definition of system structures is accomplished by fractional transfer rates between state variables, together with input/output equations and initial conditions of state variables. General non-linear mathematical expressions can be assigned to all structure definition items. The software parses and interprets the system definitions and generates symbolically the mathematical expression of the model's set of ODE. In addition, symbolic derivatives of state equations are determined with respect to model parameters, state variables and external inputs. These derivatives represent the constituents of systems of sensitivity-differential and adjoint-differential equations that arise in identification and optimal control problems. Finally, output routines generate source code that, once compiled and linked to simulation programs, allows efficient numerical integration of the system of ODE. This software has been developed in PROLOG on Macintosh computers and has been extensively used with the programming environment MATLAB ™. Possible applications of this software include model building, sensitivity analysis, identification, optimal experiment design and numerical solution of optimal control problems.

Analysis of common switching converters using Z transform

The method uses state-space formulation to analyze the converter transient and steady-state behavior in each cycle, whereby the initial conditions of state variables in each cycle are treated as discrete quantities. The difference equation for such quantities is solved in closed analytical form, using the Z-transform. The method is illustrated by the application of a three-storage-element two-configuration DC-to-AC resonant inverter. The resonant curve of such an inverter is obtained and shows that the resonance can occur on different switching frequencies. >

Interactive software tools, BGS-II and BGS-III, for ecological simulation

Interactive processing is vital to software for constructing ecological models. Two versions of interactive software have been developed, and named biological growth simulators BGS-II and BGS-III. BGS-II is portable (machine-independently accessible) as it is written in Fortran; BGS-III embodies high-quality graphical output. These are both designed for constructing models which are described by simultaneous ordinary differential equations. In BGS-II, a model is written as a Fortran subroutine which follows a particular pattern. Parameters of the model, initial conditions for state variables and some additional information to control simulation are requested in terms of menu and/or prompting messages on an interactive terminal. Five integration methods (Euler, modified Euler, Runge-Kutta, Runge-Kutta-Gill and Milne methods) are prepared. Integration methods and step size can be changed at any stage of the simulation process. The outputs generated from the simulation are obtained in table and/or graph (printed and/or plotted). Five results are saved in disk files to be compared with one another or with experimental data. BGS-III is interactive simulation programs running on a local computer network. Although BGS-II runs on a host computer including character display unit, BGS-III operates on a system which is composed of host computer and intelligent graphic terminal (TOSBAC UX-300). Host computer supports the same simulation functions as run in BGS-II. The terminal has a data transmission program (UX-NET) which assigns input and output functions of the simulation. The screen of the graphic display controlled by UX-NET is divisible into four sections. Three sections display simulation states, prompting messages and output information. Commands are entered in the other section. A model and equations necessary to the model definition are entered by request of prompting messages in this version. BGS-III has lost portability in input and output functions, but has gained more effective man-machine communication.