Small signal stability criteria for descriptor form power network model

ABSTRACT

This work considers the problem of small signal stability of a lossless power network by representing its mathematical model in descriptor form. A stability criterion is derived by constructing two orthogonal projectors corresponding to the system model. These projectors are then used in (i) constructing a Lyapunov function and (ii) deriving another criterion to identify the presence of poles (finite) of the system to the right of a given vertical line in the complex plane. The latter criterion is required to analyse whether the dominant low-frequency electro-mechanical modes, that cause oscillatory instability in the power network, settle down within a specified time limit. Using the derived criteria, linear matrix inequality feasibility problems are formulated to analyse small signal instability and oscillatory instability. Power network examples, including an IEEE benchmark system, are considered to demonstrate the developed approach.

KEYWORDS:

• Linear systems
• descriptor systems
• power networks
• stability

Acknowledgments

The author would like to acknowledge the helpful comments and suggestions of the editor and the anonymous reviewers for preparing this article. The discussion on power network examples with Dr. Mukesh Das is acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. We have considered the structure-preserving classical model of a PN where a generator is represented with constant magnitude voltage source behind a transient reactance (Sauer Pai, 1998, Chapter 7).

2. The parameters $G_{ik}$'s are set to 0, since the linearised PN model (2(2) $E\dot{x}=Ax+Bu$(2) ) is obtained by assuming lossless transmission lines. Note that, the proposed stability criteria (9(9) $X{E}^{+}A{Z}_d+Z_d^T{A}^T(E^{+}{)}^{T}X=-P_{d}Q{P}_d.$(9) ) and (26(26) $X{E}^{+}A{Z}_d+Z_d^T{A}^T(E^{+}{)}^{T}X+2\gamma P_{d}X{P}_d=-P_{d}Q{P}_d.$(26) ) can still be used for a linearised PN model when it is obtained without assuming lossless transmission lines.