Automated stability evaluation of interconnected systems for spacecraft power systems

Stability, the tendency of a system to return to a given operating point following a perturbation, is a very important property in most engineered systems. In the context of supervisory control of spacecraft power systems, it is important that the controller select stable sets of operating points at which the system should operate. In this way, the controller can achieve the system control objectives while maintaining stable operation of the power system. In this study, an automated method to evaluate the small-signal stability of spacecraft power systems about given operating points is presented. Generalized power systems are regarded as interconnections of specific components. Each of these components has specific sets of parameters that correspond to its physical parameters and its operating condition, and the components are represented using component-level systems of differential algebraic equations (DAEs). The automated method described herein combines the DAEs for each of the components based on their interconnections, resulting in a system-level system of DAEs. The method locates the system equilibrium point by solving the system-level system of DAEs and performs linearization about the equilibrium point. This results in a linear small-signal ordinary differential equation model of the system about the equilibrium point. The stability of the linearized model is evaluated to determine the small-system stability of the power system about the equilibrium point. The method is demonstrated for several example systems. The results for these systems are presented along with a comparison to time domain simulation results. It is found that the automated approach is capable of determining the local stability properties of the demonstration systems correctly and efficiently.