This paper explores the concept of system model identification through input-output data analysis. It focuses on three prominent mathematical approaches: Balanced Proper Orthogonal Decomposition (BPOD), Eigensystem Realization Algorithm (ERA), and Observer/Kalman Filter Identification (OKID). A six-state microgrid (MG) system serves as the test case, further exposed to noise during data collection to bridge the gap between simulation and real-world conditions. To assess the performance of each approach under noise, MATLAB simulations are employed. The results reveal that while BPOD exhibits the highest noise tolerance, its real-world applicability is limited due to implementation constraints. Conversely, OKID demonstrates a balance of robustness and accuracy, making it a more viable option for practical system model identification.