J.R. Winkelman

Singular perturbation and iterative separation of time scales

This tutorial paper presents an iterative method for the separation of slow and fast modes, which removes the inconsistencies of the classical quasi-steady-state approach and systematically improves the accuracy of the lower order models. It also serves as a self-contained introduction to singular perturbations. State variable reformulation and time scale identification are discussed and illustrated with power system examples. A correction procedure for nonlinear systems is also presented.

An Analysis of Interarea Dynamics of Multi-Machine Systems

The slow coherency concept is introduced and an algorithm is developed for grouping machines having identical slow motions into areas. The singular perturbation method is used to separate the slow variables which are the area center of inertia variables and the fast variables which describe the intermachine oscillations within the areas. The areas obtained by this method are independent of fault locations. Three types of simulation approximations illustrated on a nonlinear 48 machine system indicate the validity of this algorithm.

Control Design and Performance Analysis of a 6 MW Wind Turbine-Generator

This paper discusses an approach to the modeling and performance for the preliminary design phase of a large (6.2 MW) horizontal axis wind turbine generator (WTG). Two control philosophies are presented, both of which are based on linearized models of the WT mechanical and electrical systems. The control designs are compared by showing the performance through detailed non-linear time simulation. The disturbances considered are wind gusts, and electrical faults near the WT terminals.

Paper: Area decomposition for electromechanical models of power systems

Coherency and time scale properties of power system models are shown to be related by the dichotomic solution of a matrix Riccati equation. A grouping algorithm is proposed which reduces the area decomposition problem to obtaining a basis for the slow subsystem and performing a Gaussian elimination. Since the slow coherency measure allows for a lack of coherency in fast parts of machine transients, the resulting area decomposition is independent of fault locations. The procedure is illustrated by a 16-machine example.

Multi-time-scale analysis of a power system

A time-scale separation procedure is outlined and applied to a three machine interconnected power system modeled with flux linkage and voltage regulator dynamics. Partial models such as the electromechanical model and single machine-infinite bus model are used to identify the slow and fast states of the systems. Linear simulation results in two- and four-time-scales demonstrate the potential applicability of the singular perturbation approach to long-term dynamic studies of power systems.

Coherency based decomposition and aggregation

The relationship between coherency, area decomposition and aggregation is investigated for a class of models of electromechanical networks, including power system models. It is established that coherency conditions and a physically meaningful area-aggregate, reproducing a prescribed set of system modes, depend on external connections only. Coherency with respect to a set of slowest modes (slow coherency) and an earlier developed grouping algorithm are used to identify weakly coupled areas, as demonstrated on a 48-machine model of the United States North-East power system.

Area Decomposition for Electromechanical Models of Power Systems

Abstract The notion of slow coherency is introduced as a less demanding definition of coherency, which allows for a lack of coherency in the fast part of machine transients. The relationship between the time scale properties and the slow coherency is shown to be the dichotomic solution of a matrix Riccati equation. A grouping algorithm is presented which reduces the area decomposition problem to one of obtaining a basis for the slow subsystem and performing a Gaussian elimination. A geometric interpretation of this area grouping algorithm is also presented. The procedure is illustrated with a 3machine and a 16-machine example.

Higher order dynamic equivalents for power systems

Abstract A methodology for obtaining dynamic equivalents of a detailed power system is presented. Two types of reduced order models are developed: a model describing the local behaviour in each area and a model describing the global behaviour between areas. The centre-of-area variables developed for the global model describe equivalent aggregate machines and clarify the nature of the aggregate models. A ten-machine example illustrates the theory.

Multi-Time-Scale Analysis of a Power System

Abstract A time-scale separation procedure is outlined and applied to a three machine interconnected power system modeled with flux and voltage regulator dynamics. Partial models such as the electromechanical model and single machine-infinite bus model are used to identify the slow and the fast states of the systems. Simulation results in two-and four-time-scales show the applicability of the singular perturbation approach to long term dynamic studies of power systems.

Output Feedback Multivariable Control for an Advanced Boiling Water Reactor

This paper presents a preliminary design of an Output Feedback Multivariable Control for use on an ABWR. Although the design is simple and compact, it meets all the major control requirements for use in load following and frequency regulation in a utility power system. The Multivariable Control coordinates three out of four controls with four measurements and integrals of two of these measurements. The design features dynamic control structure switching with a constant gain matrix; recirculation flow is varied above 70% load demand, while control rods are varied below 70% load demand. This paper describes the 23 state model that was used, the Multivariable Control design, and the nonlinear time domain performance of an ABWR with the Multivariable Control.