This study introduces a cutting-edge Matrix Pencil-based Dual Grid Energy Management System (MP-DEMS) aimed at seamlessly integrating electric vehicles (EVs) into power grids while enhancing power quality (PQ) and reliability (PR). Operating within an AC-DC hybrid microgrid (HMG) framework, the MP-DEMS reduces the necessity for additional conversion devices, simplifying the integration of EVs and batteries. The core of the proposed DEMS comprises three key modules: the Wind Energy Management Module (WEMS), Smart Storage and EV Power Coordination (SS-EVPC), and Coordinated Power Conversion Control (CPCC). These modules work together to optimize energy usage, leverage renewable sources effectively, and manage EV charging/discharging schedules to minimize grid impact. An innovative aspect of the MP-DEMS is its use of Matrix Pencil-based techniques, offering several advantages over traditional Discrete Fourier Transform (DFT) methods. These advantages include swift dynamic response, resilience to voltage variations, and precise voltage phase estimation. Software simulations and Hardware-in-the-Loop (HIL-402) testing validate the efficacy of the MP-DEMS approach, showcasing enhanced power transfer capabilities, improved harmonic performance, and superior voltage/frequency regulation within EV-HMS applications. Overall, the MP-DEMS presents a promising solution for advancing the integration of EVs into microgrid systems, contributing to a more sustainable and reliable energy future.