Application of the slow coherency decomposition method to the Yemeni network

International Journal of Electrical Engineering Education, Jan 2004 by Badeeb, Omer M Awed, Hazza, Gamal A W

Abstract

This paper reviews the slow coherency method for decomposing multi-machine power systems into coherent areas. The slow coherency method identifies weakly coupled groups of generators with the slowest inter-area modes of oscillation. This decomposition method has a sound mathematical basis. A case study is described in which the decomposition technique is applied to a power system (the Yemeni electrical network), and its dynamic equivalency is determined. This selection was based on choosing an already developed network. Results obtained indicate the necessity for performing such an analysis to improve the performance of developed networks.

Keywords coherent machines; dynamic equivalents; slow coherency; synchronous generator

The simulation of large electric power systems for planning and operational studies involves a large set of differential algebraic equations describing the interaction of generating plants and their controls through the transmission network. Because of the limitations, the system is usually divided into a 'study system', the response of which is of direct interest and is represented in great detail, and the rest of the system, known as the 'external system', which is represented by a simplified dynamic equivalent. The dynamic equivalent should reflect the same behaviour as the individual machine that it represents when the power system is subjected to a disturbance.

The available methods of simplifying system models can be classified into three main categories. The first category has methods that are based in modal analysis.1,2 References [1,2] present a method for the construction of the dynamic equivalent of a group of machines (the external system). The comprehensive differential and algebraic equations of the external system representation are transformed to canonical form in order to ease separation of the external modes. Then, the canonical form is reduced further by ignoring the contribution to the responses of rapidly varying modes as well as unobservable and uncontrollable modes. The basis for deleting these modes is the large magnitude of their eigenvalues in comparison with other, retained eigenvalues. The physical interpretation is that, for a step disturbance, these deleted modes will settle quickly to a new steady state.

The second category is for methods based on the so-called coherency concept. In this approach, dynamic equivalents are determined based on their coherency property, that is their ability to swing together as a coherent group following a disturbance. The reduced model obtained using coherency-based methods has the same electromechanical characteristics as the detailed power system model it represents. The coherency-based approach to determine dynamic equivalents involves two steps:

* identification of coherent groups of generators;

* replacement of coherent generators by a single equivalent model.

Many methods have been proposed for identifying coherent generators. Podmore3 proposes a method based on the solution of a simplified linear model. This technique tends to identify slow coherent groups far away from the disturbance. Although it is an efficient method, it requires many iterations to ensure selection of the appropriate disturbance and it is time consuming. Chow4 proposed a slow coherency aggregation method, which identifies those coherent groups of generators with the lowest frequency. Time-scale properties of the dynamic networks and singular perturbation have been used to develop a decomposition-aggregation methodology for dynamic networks with weak connections.5~7 There are other methods8�9 that claim to be efficient, however, they may be either computationally time consuming or require simulations of the swing curve to identify coherent generators.

The final category can be classified as methods that adopt a compromise which combines modal analysis and coherency concepts by introducing different measures and indices using modal-coherency concepts as well as different probability approaches to identify coherent generators.10"12

The main focus of this paper is the study of a coherency-based method for power system dynamic equivalencing. The case study results obtained show the necessity for conducting a thorough investigation when applying similar techniques to different sizes of networks.

Mathematical model

Slow coherency method

When a power system is subjected to a disturbance, different system modes have different responses. This allows for the separation of the time-scales of the system response. For example, when the power system is perturbed, it is found that interarea modes have a slow oscillation in comparison with inter-area modes, which will have fast oscillations and can be damped quickly. The slow coherency method associates coherent srouos of machines with the lowest freauency.

Although, this method has a strong mathematical basis, it still requires lengthy computation of the eigen subspaces (especially in large power systems) and a robust method for the optimum selection of the number of coherent areas. To overcome these computational problems, different proposed improvements have been suggested.13'14'15 Here, a mathematical measure, termed the residual norm, is proposed in the following section to determine the optimal number of coherent areas.