**Development of Floquet Multiplier Estimator to Determine Nonlinear Oscillatory Behavior in Power System Data Measurement**

### **Namki Choi, Hwanhee Cho \* and Byongjun Lee \***

School of Electrical Engineering, Anam Campus, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea; fleminglhr@korea.ac.kr

**\*** Correspondence: whee88@korea.ac.kr (H.C.); leeb@korea.ac.kr (B.L.); Tel.: +82-2-3290-3697 (H.C.); +82-2-3290-3242 (B.L.)

Received: 4 April 2019; Accepted: 7 May 2019; Published: 14 May 2019

**Abstract:** Measurement-based technology has been developed in the area of power transmission systems with phasor measurement units (PMU). Using high-resolution PMU data, the oscillatory behavior of power systems from general electromagnetic oscillations to sub-synchronous resonances can be observed. Studying oscillations in power systems is important to obtain information about the orbital stability of the system. Floquet multipliers calculation is based on a mathematical model to determine the orbital stability of a system with the existence of stable or unstable periodic solutions. In this paper, we have developed a model-free method to estimate Floquet multipliers using time series data. A comparative study between calculated and estimated Floquet multipliers has been performed to validate the proposed method. The results are provided for a sample three-bus power system network and the system integrated with a doubly fed induction generator.

**Keywords:** power systems; floquet multiplier; poincaré map; time series data; DFIG
