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Transmission loadability is decided by thermal and protective constraints. In stressed states, such as voltage depression, the relay loadability may replace the thermal loadability, leading to undesirable relay operation and cascading events. In this paper, the operation margins of overload, overcurrent, and underimpedance constraints are quantified. The sensitivity model of the transmission loadability to the bus voltages and the field currents is newly proposed. Numerical results show that: 1) both overexcitation and reinforced excitation control may contribute to undesirable relay operation; 2) overload and underimpedance constraints may over- or underestimate the thermal loadability under voltage depression; and 3) relay loadability is dependent on the protection schemes and the relay settings.