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Abstract
In this article, a non-linear coordinated control of generator excitation and a static synchronous compensator is proposed to enhance the transient stability of an electrical power system. The coordinated controller proposed is designed via immersion and invariance methodology. In particular, a non-linear model of the power system and immersion and invariance design method are used to achieve not only power angle stability but also frequency and voltage regulations following a large disturbance (a symmetrical three-phase short-circuit fault) on one transmission line or a small perturbation to mechanical power input to synchronous generators in the system. The controller design is validated using a simulation study on a single-machine infinite bus. Simulation results show that the proposed controller can not only keep the system transiently stable but also simultaneously achieve power angle stability and frequency and voltage regulation.
Appendix
FBL Controller [22]
To design a non-linear coordinated controller based on the FBL scheme used to compare with the proposed controller, the output is defined as
then the power system in Eq. (Equation13
(13) ) is a three-input three-output non-linear system, which can be written as
(A.1) where
With the help of the differential geometry theory, the relative degree of the non-linear system in Eq. (EquationA1
(A.1) ) at xe becomes r = 1 + 1 = 2 < 4; therefore, based on the stability theory of the zero dynamics, the change of coordinates is selected as follows:
and it is assumed that the Jacobian matrix of Φ(x) at xe is non-singular (
). Further, it is easy to express the non-linear system in Eq. (EquationA1
(A.1) ) as
(A.2)
For the linear system in Eq. (EquationA2(A.2) ), the linear optimal law v can be obtained as
where P is the positive definite matrix satisfying the Riccati equation for the linear systems in Eq. (EquationA2
(A.2) ). Hence, it is easy to obtain the non-linear coordinated and optimal control law based on the FBL methodology as follows:
Notes
It is assumed that all functions and mappings are throughout this article.
Additional information
Notes on contributors
Adirak Kanchanaharuthai
Adirak Kanchanaharuthai received the B. Eng degree in control engineering from King Mongkut’s Institute of Technology Ladkrabang, Thailand, the M. Eng. degree in electrical engineering from Chulalongkorn University, Thailand, and the Ph.D. degree in systems and control engineering from Case Western Reserve University, OH, USA, in 1995, 1997, and 2012, respectively. His main research interests are in the field of nonlinear systems and power systems stability and control.