Balanced Realization Technique Research Articles

Accurate and Reduced Order Identification of Propagation Function for Electromagnetic Transient Analysis of Cables

This paper proposes a set of fitting features that enables identifying propagation function of cables accurately in the form of multi-delay rational transfer functions while maintaining reduced order of approximation. Frequency domain partitioning and adaptive weighting techniques are applied directly in phase domain for the evaluation of poles and residues simultaneously to ensure the precision of fitting of all entries including the low-magnitude off-diagonal elements. The objective is not only to obtain a precise fitting in phase domain but also to account for intrinsic modal decomposition so that integration errors in time domain are not magnified. The order of approximation is considerably reduced by post-processing the fitting using the balanced realization technique. When the proposed fitting approach is combined with a precise integration technique in time domain, it leads to accurate evaluation of transients as demonstrated in this paper, eliminating the spurious oscillations or numerical instabilities that may be encountered in the universal line model regardless of the integration or interpolation technique.

Order Reduction in Linear Dynamical Systems by Using Improved Balanced Realization Technique

In this article, a new model order reduction scheme is proposed for the simplification of large-scale linear dynamical models. The proposed technique is based on the balanced realization method, in which the steady-state gain problem of the balanced truncation is circumvented. In this method, the denominator coefficients of the reduced system are evaluated by using the balanced realization, and the numerator coefficients are obtained by using a simple mathematical procedure as given in the literature. The proposed technique has been illustrated through some standard large-scale systems. This method gives the least performance error indices compared to some other existing system reduction methods. The time response of the approximated system, evaluated by the proposed method, is also shown which is the excellent matching of the response of the actual model when compared to the responses of other existing techniques.

A novel approach for determining optimal number and placement of static var compensator device to enhance the dynamic performance in power systems

Increasing in the scale and complexity of interconnected power systems was because of the growth of electricity demands, leading to multiple electromechanical oscillations despite having support of the power system stabilizer (PSS). Therefore, the dynamic performance of the existing networks should enhance. One type of flexible alternating current transmission system devices, namely the static var compensator (SVC), can be installed at the buses to maintain and/or control particular parameters of the electrical power system by exchanging capacitive and/or inductive current. However, the performance of SVC device highly depends upon its parameters, sizes, and suitable number and location in the power network. Hence, the optimal location for SVC has become a key issue; in this paper, we propose a novel approach for the suitable number and location for SVC by using critical energy analysis based on the Gramian matrices that the solution framework applied an algorithm based on the Lyapunov equations and the balanced realization technique. The optimal placement is determined by (1) analyzing the small-signal stability to seek number of feasible locations and (2) comparing these feasible locations by analyzing the transient stability through various simulation cases. The effectiveness of the proposed method is compared with the other optimal method and verified on the 39-bus New England system by the simulation results based on the power system simulation engineering (PSS/E) and MATLAB programs. The obtained result shows that the SVC is installed at the single or multi-location having the total maximum Gramian energy.

Model order reduction of random parameter-dependent linear systems

This paper proposes a new method to perform model reduction of linear time invariant (LTI) systems where parameters are random variables governed by probabilistic laws. It combines the well-known truncation balanced realization (TBR) technique together with the generalized polynomial chaos (GPC) formalism, a powerful tool for uncertainty propagation. GPC formalism is used to represent and compute a random parameter-dependent balancing transformation (RPD-BT) which puts the random LTI system in a balanced form almost surely within the probabilistic range of the uncertain parameters. Model reduction is then performed by truncating almost surely weakly controllable and observable states, yielding a random parameter dependent truncated balanced realization (RPD-TBR). The truncation error’s moments are shown to be bounded by Hankel singular values’ moments, which are also estimated using GPC formalism. As an illustrative example, the proposed method is applied to a simple mechanical model of a two-degrees of freedom mass–spring system with uncertain stiffness and damping.

Model reduction of descriptor systems using frequency limited Gramians

Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, some applications require approximation over a certain band of frequency than whole frequency range. Different model reduction techniques are available for descriptor systems. However, for limited frequency interval, no such work exists in the literature. A frequency limited balanced truncation method for general descriptor systems is proposed. The method is an extension of truncated balanced realization method for the general descriptor system. The proposed technique generalizes the results of Gawronski and Juang technique for large-scale descriptor systems using frequency interval Gramians. Simple algorithms are also given for preserving the stability of reduced-order models. The work also extends Poor Man׳s truncated balanced realization technique to include frequency limited Gramians for descriptor systems. Practical numerical examples are incorporated to show the successful application of the proposed method in the desired frequency range.

A Comparison of Some Model Order Reduction Methods for Fast Simulation of Soft Tissue Response using the Point Collocation-based Method of Finite Spheres (PCMFS).

In this paper we develop the Point Collocation-based Method of Finite Spheres (PCMFS) to simulate the viscoelastic response of soft biological tissues and evaluate the effectiveness of model order reduction methods such as modal truncation, Hankel optimal model and truncated balanced realization techniques for PCMFS. The PCMFS was developed in [1] as a physics-based technique for real time simulation of surgical procedures. It is a meshfree numerical method in which discretization is performed using a set of nodal points with approximation functions compactly supported on spherical subdomains centered at the nodes. The point collocation method is used as the weighted residual technique where the governing differential equations are directly applied at the nodal points. Since computational speed has a significant role in simulation of surgical procedures, model order reduction methods have been compared for relative gains in efficiency and computational accuracy. Of these methods, truncated balanced realization results in the highest accuracy while modal truncation results in the highest efficiency.

Controller Reduction by the Block Balanced Realization Using the General Representation of H.INF. Controllers

In this paper, we propose a new controller reduction method using the closed-loop block balanced realization technique. To decrease the closed-loop performance degradation, it is need to take account the closed-loop configuration in controller reduction process. The block balanced realization technique was developed from the open-loop balanced realization method to consider the closed-loop configuaration. In our method, we employ the block balanced realization method to reduce the order of H∞ controllers, and to consider robustness for controller variation, we use the general representation of H∞ controllers. A numerical example is presented to illustrate the effectiveness of our method.

Adaptation of the balanced realization to the coupling of reduced order models for the modelling of the thermal behavior of buildings

This work is devoted to the field of building physics and related to the reduction of heat conduction transfer models. The aim is to enlarge the model libraries of heat and mass transfer codes through limiting the considerable dimensions reached by the numerical systems during the modelling process of a multizone building. We show that the balanced realization technique, specifically adapted to the coupling of reduced order models with the other thermal phenomena, turns out to be very efficient.

PLS, balanced, and canonical variate realization techniques for identifying VARMA models in state space

This paper demonstrates the application of PLS regression, balanced realization, and canonical variate (CV) state space modeling techniques in identifying stationary vector autoregressive moving average (VARMA) type of time series models in state space. An example VARMA process model is used to generate data, carry out modeling activities, and compare the three model development techniques. All realization methods provide equivalent state space models. Balanced realization can not handle singularities in the covariance matrix of past observations while all other methods can accommodate such singularities. Balanced realization and classical PLS do not provide minimal state variables that are orthogonal. `Orthogonal states' PLS and canonical variate state space realization give orthogonal state variables that provide robust parameter estimates from real data, however the PLS method requires an additional singular value decomposition step.

H2-optimal controller reduction by frequency-weighted balanced realization

In this paper, we propose a new controller reduction method which considers maintaining the index value of H2-optimal controller. In the method, a frequency-weighted balanced realization technique developed by Enns is employed to obtain low order controllers. The fractional representation is used to reduce the order of unstable controllers effectively. To illustrate the effectiveness of our method, two numerical examples are presented.

Plant and controller reduction problems for closed-loop performance

Model reduction problems which consider preserving closed-loop performance (H/sub 2/, H/sub infinity /, and mu ) in the presence of reduction error are developed. These are formulated as weighted multiplicative error problems (for plant reduction) and weighted additive error problems (for controller reduction), with the weight function incorporating explicitly such control information as the desired sensitivity operator bound, the setpoint/disturbance spectrum, and the plant uncertainties. These problems are efficiently solved using the frequency-weighted balanced realization technique. The benefits of these reduction problems are illustrated with examples taken from the control of a binary distillation column. >

Identification and model reduction from impulse response data

Two new algorithms for identification and model reduction of stable linear continuous systems are proposed, based on the weighted impulse response gramians (Agathoklis and Sreeram 1988 b). In identification, the model parameters are obtained from the solution of a linear system of equations with coefficients obtained from the numerical evaluation of the weighted impulse response gramians. The reduction technique is based on retaining part of the original weighted impulse response gramians obtained as the solutions to the Lyapunov equation for the original system in controllability canonical form. This yields different stable models for different values of the weighting factor. The model corresponding to zero weighting factor matches the impulse response norm of the original system and its derivatives exactly. Finally, the method is illustrated by a numerical example and is compared with well-known balanced realization techniques.

Model reduction using balanced realizations with improved low frequency behaviour

Model reduction using balanced realization techniques is known to give a better approximation of the high frequency behaviour than the low frequency one. In this paper, a simple modification to the technique is proposed to get a better approximation of the low frequency behaviour of the original system. The proposed technique is illustrated by numerical examples.