Partial-structure-oriented work-energy theorem (WET) governing the work-energy transformation process of Yagi-Uda array antennas is derived. Driving power as the source to sustain a steady work-energy transformation is introduced. Employing WET and driving power, the essential difference between the working mechanisms of scattering objects and Yagi-Uda array antennas is revealed. The difference exposes that the conventional characteristic mode theory (CMT) for scattering objects cannot be directly applied to Yagi-Uda array antennas. Under WET framework, this paper proposes a generalized CMT for Yagi-Uda antennas. By orthogonalizing driving power operator (DPO), the WET-based CMT can construct a set of energy-decoupled characteristic modes (CMs) for an objective Yagi-Uda antenna, and then can provide an effective modal analysis for the Yagi-Uda antenna. In addition, a uniform interpretation for the physical meaning of the characteristic values / modal significances (MSs) of metallic, material, and metal-material composite Yagi-Uda antennas is also obtained by employing the WET-based modal decomposition and the field-current interaction expression of driving power.