Formal and Compositional Analysis of Power Systems Using Reachable Sets

Power system stability analysis becomes more important in the presence of ever increasing variations in operating conditions. Traditionally, the operation of power systems is verified for specific operating conditions. In this work, the stability analysis is performed for a set of operating conditions using reachability analysis, which makes it possible to compute the bounds of all possible system trajectories. Thus, reachability analysis can be used to rigorously check specifications. Contrary to previous work, the presented approach does not require model simplifications when the system is described by semi-explicit, nonlinear, index-1 differential-algebraic equations. The main obstacle in reachability analysis is the scalability towards larger systems, which is addressed by investigating compositional techniques. As a result, transient stability and variable energy production can be analyzed for the IEEE 14-bus and 30-bus benchmark systems, for which the computation times are orders of magnitude faster than the simulation of all cases starting in the corners of the set of possible initial states.