Practical stability assessement of distributed synchronous generators under load variations

This paper proposes a method to assess the practical stability of distribution systems with synchronous generators subject to changes in the system equilibrium conditions due to load variations. 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 the minimum amount of time in which the system is required to stay in a particular loading condition, such that the system trajectories from an initial condition in Ω₁ will be confined in the security region of operation Ω₂ for the whole time interval of interest. This study was carried out using a mathematical model of the distribution system with synchronous generators in the form of a switched affine system. Sufficient conditions for the power distribution system with synchronous generators described as a switched affine system to be practically stable with respect to Ω₁ and Ω₂ are given in the form of matrix inequalities constraints. Numerical results were obtained for a model of a cogeneration plant of 10 MW added to a distribution network constituted by a feeder and six buses.