A reduced-order method for estimating the stability region of power systems with saturated controls

Abstract

In a modern power system, there is often large difference in the decay speeds of transients. This could lead to numerical problems such as heavy simulation burden and singularity when the traditional methods are used to estimate the stability region of such a dynamic system with saturation nonlinearities. To overcome these problems, a reduced-order method, based on the singular perturbation theory, is suggested to estimate the stability region of a singular system with saturation nonlinearities. In the reduced-order method, a low-order linear dynamic system with saturation nonlinearities is constructed to estimate the stability region of the primary high-order system so that the singularity is eliminated and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proven and the method is validated using a test power system with 3 buses and 5 machines.saturation nonlinearity, power system stabilizer, linear matrix inequality, singular perturbation method, reduced-order method

Estimating the stability region of singular perturbation power systems with saturation nonlinearities: an linear matrix inequality-based method

“…Garcia et al [17,20] provided a useful method to stabilise singular perturbation systems and under some conditions they also provided a method to estimate the stability region of closed-loop systems. Similar work was done by Liu [21] and Gan et al [14], etc. In those methods, the singular perturbation system is decomposed into a slow and a fast subsystem, and this decomposition is possible because feedback control only need slow states.…”

“…We remark that in the above analysis the load model is considered to be constant impedance model. If we consider the dynamic models such as the motor models for some loads, it is easy to verify that the dynamical model can still be written as the form of expression (14), and the states of motors should be classified into the fast variables since the inertial of a motor is far less than that of a generator. Thus, the structure of A 33 is still alike that of (14) except that some elements are added in the diagonal position.…”

“…If we consider the dynamic models such as the motor models for some loads, it is easy to verify that the dynamical model can still be written as the form of expression (14), and the states of motors should be classified into the fast variables since the inertial of a motor is far less than that of a generator. Thus, the structure of A 33 is still alike that of (14) except that some elements are added in the diagonal position. Moreover, there are many methods for the choice of an appropriate parameter 1 [22] in order to formulate the standard singular perturbation model, readers are referred to [22,23] and the references therein for more information.…”

“…Problem 1: for a given sufficiently small 1 . 0, how to estimate the stability region of system (14) which can contain a largest set X 0 , and meanwhile solve the difficulties adhere to singular perturbation systems by considering the specialty of this kind of systems, where set X 0 is a given referenced set defined as…”

“…Motivated by this, in this paper, we aim to propose a new method to estimate the stability region for the small-signal dynamical models in power systems based on our recent results [13,14] and some related singular perturbation theories. We will establish a set of conditions under which the stability region can be decomposed into the Cartesian product of a contractive high-dimensional ellipse and a sufficiently large ball.…”