Stability Analysis of Large-Scale Systems based on Energy Absorption Capacity

Abstract

The problem of stability analysis is the main concern of every Large-Scale System (LSS). Generally the well-known Vector Lyapunov Function (VLF) method is utilized for this purpose. This method face serious difficulties as the size and complexity of the systems grows up. In this paper a new approach is presented to overcome this problem using a new concept “Energy Absorption Capacity (EAC)”. This concept can be defined for every equilibrium point of a system. This point is considered to be stable if it has a positive EAC and is unstable if its absolute EAC is zero. Here, the proposed approach is extended for LSS which initially EAC is defined for very subsystem of LSS. To escape the evaluation of the interaction energy among the subsystems, a lower and upper limit for the interaction energy will be defined which is significantly simpler. Based on the subsystem EAC and the lower and upper limit of the interaction energy, a lower and upper bound of LSS EAC, called EACabs_Low and EACabs_High, is introduced. An equilibrium point of the LSS is considered to be stable if its EACabs_Low is positive and is unstable if its EACabs_High is zero. It is shown that the proposed approach is less conservative compared to VLF method. This fact is because the proposed approach is based on EAC as the scalar extreme value of energy function whereas the VLF method is based on the energy function itself. The effectiveness of the proposed method has been investigated with an illustrative example.