In this paper we present two sets of parallel algorithms for identifying real-time, small-signal dynamic models of power systems using multiple sources of Synchrophasor data. The first problem is posed in terms of identifying the transfer matrix of single-input multiple-output (SIMO) power system models using linear least-squares (LLS), where parallelism can be implemented through parallel execution of matrix multiplications using multiple processors or workers. Given the constraints of sequential communication and limited local memory, which may arise due to multiple applications running in the workers at the same time, a novel scheduling algorithm is proposed to enable flexible deadlines that meet these constraints. The scheduling algorithm minimizes the total time of execution under constraints, and can be solved via integer programming. The second problem is posed as a similar parallel algorithm for identifying a linearized state-variable (SV) model of a power system using both linear and nonlinear least-squares (NLS) in presence of scheduling. The performance of all the algorithms are studied via simulations of an IEEE 145-bus, 50-machine power system model, and compared with their centralized, non-parallel implementation.