Grid supportive modes integrated within distributed energy resources aim at improving the frequency response. However, hybrid behaviors induced by deadbands and other thresholds and their impact on system frequency remain unclear. This paper employs the parametric metric temporal logic specification for validating such behaviors to ensure adequate frequency response. It allows a richer description of system protections like under-frequency load shedding and can explore the temporal specification of frequency dynamics. The approach is applied on a diesel-wind fed microgrid and appropriate settings of deadband will be obtained, which can be regarded as a guideline for practitioners. The results are expected to be less conservative since the temporal properties are taken into accounts.