Stability monitoring on the large electric power system

Abstract

The objective 9f this work is development of techniques which provide on line decision on the stability of a large interconnected power system faced by assumed or actual disturbances. Since the system is very large and nonlinear and the time scale only a few seconds at best the only hope for results which are mathematically honest, computable on line, and of sufficient accuracy lies in a set of carefully coordinated approximations founded on precise mathematical theory. Such an approach is discussed in this paper. It divides the problem into four segments in order to narrow down those parts of the sys tern which are actively involved and then represent the critical elements by using approximate transformations and graded precision for remote elements. IRTRODUCTIONMonitoring of the stability of power systems has never really become an o n line tool even in the project sponsored by the US Department of Energy now security, contingency sense. A three year research is attempting to devise approaches which will remedy this situation and, potenzially, even go beyond to m o n i t o r o n g o i n g d y n a m i c p h e n o m e n a o n l i n e , Attainability of the latter goal is not assured but making on line dynamic security monitoring practically feasible would be an accomplishment of major importance. Also valuabie theoretical insights are being developed in this project. This paper s u mmarizes the approach used and the results and insights being achieved at this point in the project The fundamental aim is to establish whether the state will return from a post disturbance initial state to its stable equilibrium, without full pole slips between the various system fragments. Systems and their protection are not built for such asynchronous performances.This, of course, is a formidable computational task for fast moving dynamic phenomena. A combination of organization, precomputation, approximation, new insights, and new results is needed to complete it.This process is divided in Fig.

Synchronization of cyclic power grids: Equilibria and stability of the synchronous state

“…The boundary actually is the upper bound of ∆V II and lower bound of ∆V I , which is close to 2K + Kπ 2 2N calculated by setting P = 0 in Eqs. ( 25) or (27). This does not depend on σ, as can be verified in Figs.…”

“…The stability region has been analyzed by Chiang [6] and independently Zaborsky et al [27,28] and the direct method was developed by Varaiya, Wu, Chiang et al [7,13] to find a conservative approximation to the basin of stability.…”

Synchronization of Power Systems under Stochastic Disturbances

“…The system is exponentially stable if and only if all eigenvalues of the system matrix have strictly negative real part. It has been proven that if 𝑙 𝑖 𝑗 cos 𝛿 * 𝑖 𝑗 ≥ 0, then the system is stable at the synchronous state (𝜹 * , 0) 37,38 , which leads to the security condition…”

Synchronization of power systems under stochastic disturbances

“…The analysis of the eigenvalue of the system matrix is also called small-signal stability analysis. It has been proven that if l ij cos δ * ij ≥ 0, then the system is stable at the synchronous state (δ * , 0) (Zaborsky et al, 1985), which leads to the security condition…”