**Dynamic State Estimation for Synchronous Machines Based on Adaptive Ensemble Square Root Kalman Filter**

#### **Dongliang Nan 1,2, Weiqing Wang 1, Kaike Wang 2, Rabea Jamil Mahfoud 3, Hassan Haes Alhelou 4,\* and Pierluigi Siano 5,\***


Received: 13 November 2019; Accepted: 26 November 2019; Published: 29 November 2019

**Abstract:** Dynamic state estimation (DSE) for generators plays an important role in power system monitoring and control. Phasor measurement unit (PMU) has been widely utilized in DSE since it can acquire real-time synchronous data with high sampling frequency. However, random noise is unavoidable in PMU data, which cannot be directly used as the reference data for power grid dispatching and control. Therefore, the data measured by PMU need to be processed. In this paper, an adaptive ensemble square root Kalman filter (AEnSRF) is proposed, in which the ensemble square root filter (EnSRF) and Sage–Husa algorithm are utilized to estimate measurement noise online. Simulation results obtained by applying the proposed method show that the estimation accuracy of AEnSRF is better than that of ensemble Kalman filter (EnKF), and AEnSRF can track the measurement noise when the measurement noise changes.

**Keywords:** dynamic state estimation (DSE); synchronous machine; ensemble square root filter (EnSRF); Sage–Husa algorithm
