Practical stability assessment of distributed synchronous generators under variations in the system equilibrium conditions

This paper proposes a method to assess the practical stability of power distribution systems with synchronous generators subject to changes in the system equilibrium conditions due to fast varying loads. The concept of practical stability deals with two known state-space regions Ω1 (which contains all the initial conditions reflecting the perturbations at which the system is subject during its operation) and Ω2 (which represents the operating security region of the power distribution system) satisfying Ω1 ⊂ Ω2. The practical stability problem and the focus of this paper is to determine under which conditions the system trajectories will be confined into a security region of operation for a certain time interval of interest, as the equilibrium point of the model changes. This study was carried out using a mathematical model of the distribution system with synchronous generators in the form of a switched affine system. This proposed model is capable of describing the system behavior over a certain period within which changes on the equilibrium conditions of the system can occur. Sufficient conditions for the power distribution system with synchronous generators described as a switched affine system to be practically stable with respect to its operating security region Ω2 are given in the form of matrix inequalities constraints. The results, obtained for the model of a cogeneration plant of 10 MW added to a distribution network constituted by a feeder and six buses, show that the less stringent properties of the concept of practical stability can be very well-suited to the security analysis of power systems subjected to frequent variations in the load level.