Hybrid microgrids with high penetration of inverter-based renewable energy require reliable modelling and control to ensure stable and secure operation, particularly during transitions between grid-connected and islanded modes. This paper presents the modelling and simulation of the hybrid microgrid at the Åland University of Applied Sciences Energy Lab using MATLAB Simulink and Simscape. The system includes a 60 kWp photovoltaic plant, a 10.2 kWh battery energy storage system, two 100 kW diesel generators, and a range of controllable loads. A detailed component-level model was developed to represent the electrical and dynamic behaviour of generation, storage, and load subsystems. A supervisory control strategy was implemented to enable power balancing, load management, and coordinated source synchronisation. Simulation studies were conducted for grid-connected operation, planned islanding, black start, and grid resynchronisation. The results demonstrate stable voltage and frequency regulation and effective coordination between energy sources during operating mode transitions. The developed simulation model provides a platform for analysing hybrid microgrid performance and supports further research, control development, and education for resilient and sustainable energy systems..