Three-phase three-level unidirectional rectifiers are among the most adopted topologies for general active rectification, achieving an excellent compromise between cost, complexity and overall performance. The unidirectional nature of these rectifiers negatively affects their operation, e.g., distorting the input currents around the zero-crossings, limiting the maximum converter-side displacement power factor, reducing the split DC-link mid-point current capability and limiting the converter ability to compensate the low-frequency DC-link mid-point voltage oscillation. In particular, the rectifier operation under non-unity power factor and/or under constant zero-sequence voltage injection (i.e., when unbalanced split DC-link loading occurs) typically yields large and uncontrolled input current distortion, effectively limiting the acceptable operating region of the converter. Although high bandwidth current control loops and enhanced phase current sampling strategies may improve the rectifier input current distortion, especially at light load, these approaches lose effectiveness when significant phase-shift between voltage and current is required and/or a constant zero-sequence voltage must be injected. Therefore, this paper proposes a complete analysis and performance assessment of three-level unidirectional rectifiers under non-unity power factor operation and unbalanced split DC-link loading. First, the theoretical operating limits of the converter in terms of zero-sequence voltage, modulation index, power factor angle, maximum DC-link mid-point current and minimum DC-link mid-point charge ripple are derived. Leveraging the derived zero-sequence voltage limits, a unified carrier-based pulse-width modulation (PWM) approach enabling the undistorted operation of the rectifier in all feasible operating conditions is thus proposed. Moreover, novel analytical expressions defining the maximum rectifier mid-point current capability and the minimum peak-to-peak DC-link mid-point charge ripple as functions of both modulation index and power factor angle are derived, the latter enabling a straightforward sizing of the split DC-link capacitors. The theoretical analysis is verified on a 30kW, 20kHz T-type rectifier prototype, designed for electric vehicle ultra-fast battery charging. The input phase current distortion, the maximum mid-point current capability and the minimum mid-point charge ripple are experimentally assessed across all rectifier operating points, showing excellent performance and accurate agreement with the analytical predictions.