Spectrum-domain stability assessment and intrinsic oscillation for aggregated mobile energy storage in grid frequency regulation

This paper assesses the aggregation stability of mobile energy storage for the grid frequency regulation, which employs distributed electric-vehicle capacities. To reveal the aggregation dynamics, a multiple-aggregator model is established in the state space, which introduces aggregation factors coupled with the time for distributed vehicles. Interlinking the aggregated model of mobile energy storage system with the electrical grid model, an integration model is developed for the stability assessment. According to the transcendental model feature, an efficient stability region extraction method is then proposed to disclose the unstable risk, which consists of four sequential stages: quasi-polynomial formulation, Dixon-resultant based spectrum estimation, oscillation spectrum extraction, and stability map determination. In the first stage, Rekasius substitution is deployed converting the notoriously complicated model to a quasi-polynomial form. Since the real and imaginary parts of the quasi-polynomial have to vanish simultaneously, an elimination method called Dixon resultant is utilized, which constructs the necessary and sufficient assessment condition. After that, the discriminant is carried out to generate the imaginary spectra bound, which is scanned to finally determine the oscillation spectrum. It is revealed that the aggregation of mobile energy storage system might induce an oscillation spectrum due to asynchronous processes. Besides, the bound of the oscillation caused by the aggregation process is disclosed. Moreover, the established mapping relationship between the kernel curve and their offspring curves visualizes the complete stability map. The whole model and stability analysis are theoretically derived and verified through a typical grid frequency regulation system with mobile energy storage.