Triangular-current-mode (TCM) modulation guarantees zero-voltage-switching across the mains cycle in AC-DC power converters, eliminating hard-switching with a minor ≈ 30 % penalty in conduction losses over the conventional continuous current mode (CCM) modulation scheme. TCM-operated converters, however, include a wide variation in both switching frequency and switched current across the mains cycle, complicating an analytical description of the key operating parameters to date. In this work, we derive an analytical description for the semiconductor bridge-leg losses in a TCM AC-DC converter, including the rms current and/or conduction losses, switching frequency, and switching losses. For SiC MOSFETs, we introduce a new loss model for switching losses under zero-voltage-switching, which we call "residual ZVS losses". These losses include the constant Coss losses found in previous literature but must also add, we find, turn-off losses that occur at high switched currents. The existence and modeling of these turn-off losses, which are due to currents flowing through the Miller capacitance and raise the inner gate source voltage to the threshold level and accordingly limit the voltage slew rate, are validated on the IMZA65R027M1H 650 V SiC MOSFET. The complete loss model-and the promise of TCM for high power density and high efficiency-is validated on a 2.2 kW hardware bridge-leg demonstrator, which achieves a peak 99.6 % semiconductor efficiency at full load. The proposed, fully-analytical model predicts bridge-leg losses with only 12 % deviation at the nominal load, accurately including residual ZVS losses across load, modulation index, and external gate resistance.