The internal states of generators obtained by dynamic states estimation (DSE) may provide additional information for the control performances. However, conventional sigma-point Kalman filter (SPKF)-based DSE may experience the loss of positive definiteness and symmetricalness of state noise covariances. This article proposes three numerically stable square-root SPKF (SR-SPKF) algorithms and proposes a novel derivative-free SR-SPKF-based DSE framework to estimate the dynamic states for doubly fed induction generator (DFIG) wind turbines in an interconnected power network. While this article investigates the dynamic behavior of the power grid at a system-level, the DSE of DFIG is achieved in a decentralized manner, which is made possible by the use of phasor measurement units (PMUs) to acquire and transmit voltage and current phasors at DFIG terminal. By utilizing the SR-SPKF-based DSE framework and PMUs data, a comparison study is conducted for square-root unscented Kalman filter, square-root Cubature Kalman filter, square-root central difference Kalman filter, and their conventional versions. The computational burden, estimation accuracy, and mathematical capability of each filtering algorithm are compared and analyzed through simulation studies.