Operating-Point Identification from Dimensions of Alternating Signal Based on Incremental Iterative Mapping Mechanism for Analyzing Dynamics of AC Systems

Increasing occurrences of oscillations of unknown mechanisms in today's power systems ask for recalling the first principle of operating. AC systems in general work with all units of supplies and loads to build up internal voltage of a certain amplitude/frequency, ensuring transferring and balancing of power in the system while subjected to varied disturbances. The dynamics following are therefore closed-loop iterations between power balancing - internal voltage relations in units and internal voltage - power relations in networks. Operating points and small disturbances associated will then have to be defined from such iterative processes with nonlinear relations among the increments that can be approximated at the initial period of disturbance, so linear system mathematics will be applicable for dynamic analysis. Conventional methodologies from varied fields are unfortunately not rooted from first principle physics and are therefore especially not suited for today's new scenario with increasing penetration of renewables. Taking a small disturbance dynamic process of a converter interfaced system as an example, this paper thus aims to propose an operating-point identification methodology from dimensions of AC signal by first revealing the incremental iterative mapping mechanism from the first principle of operating, and by then clarifying the self-consistency of the relevant electrical variables, as well as relations among them during iterations. It is recognized that during a certain time period following the disturbance, amplitude/frequency of internal voltage in the converter and active/reactive current at the network interface evolve in the form of the complex exponential, among which we can see linearizable weak-nonlinear relations, and thus should be defined as operating points. Based on the above operating points and relevant increments of the internal-voltage amplitude/frequency and active/reactive current, fundamental steps and challenges linearizing AC systems are finally summarized for analyzing grid dynamics.