The problem of soft-sensing of directly immeasurable variables in the synchronous generator， such as the power angle， the d and q axis transient electromotive forces， the d and q axis stator circuit currents， is investigated. Firstly， the model of synchronous generator suitable for soft-sensing is proposed， which includes the directly measurable variables of generator， such as the active and reactive powers， the amplitude of current， etc. The proposed model is a type of nonlinear differential-algebraic sub-systems. Secondly， aiming at the specialty of the proposed model， an expanded left-inversion soft-sensing algorithm is proposed for the soft-sensing of synchronous generator. Then， a left-inversion soft-sensor is designed considering the 4-order transient practical model of synchronous generator， and all directly immeasurable variables in the model can be soft-sensed. Finally， simulations are performed using MATLAB/ SimPowerSystems， in which a 6-order sub-transient practical model of generator is used， and the results demonstrate the validity of the proposed method.