The increasing demand for reliable and efficient energy supply under variable operating conditions has accelerated the development of hybrid trigeneration systems (electricity, heating, and cooling). This study analyzes an autonomous trigeneration system comprising an internal combustion engine, heat recovery unit, absorption refrigeration machine, and thermal energy storage. System performance is evaluated using energy and exergy analyses under design and off-design operating conditions, including grid-disconnected (so called, island mode) operation conditions. The impact of load variation and thermal energy storage capacity on system efficiency and operational stability is evaluated. A modified exergy performance indicator is proposed to account for the prioritized supply of critical loads during transient operation. Results indicate that control strategies for maximum steady-state efficiency lead to significant performance degradation under disturbance conditions, reducing the system’s capability to meet critical energy demands. The integration of thermal energy storage operational flexibility, mitigates the effects of load fluctuations, and improves system stability. In a 48-hour island mode case, thermal energy storage increases the coverage of critical loads. The findings demonstrate that exergy analysis provides a more rigorous assessment of system performance than energy analysis, and enables the identification of operational limitations. This approach supports the design and control of resilient and flexible trigeneration systems for decentralized energy applications.