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Accurate dynamic models of power plants are essential for Transmission System Operators (TSOs) to assess the security and reliability of the grid operation, especially as the loss of system inertia amplifies the impact of disturbances. Yet, parameterizing these models remains a challenge in deregulated systems due to limited data availability and restricted access to proprietary information. This paper proposes an identification framework for estimating the parameters of grey-box linear state-space dynamic equivalents of synchronous machines and their regulators directly from terminal measurements. The method applies a two-step constrained least-squares routine to initialize the system state and subsequently identify the model parameters. Validation is performed on a dynamic IEEE 9-bus test system under different operating conditions, enabling analysis of the identification performance. Convergence tests confirm the method’s consistency against large perturbations to the initial parameter guess. Designed for non-intrusive and online use, the proposed approach provides TSOs with a computationally efficient tool for dynamic model inference and/or validation, and subsequent system security studies.