Aiming at low reliability and long time-consuming of existing system power deficit estimation algorithms, a fast power deficit estimation algorithm based on local frequency information is proposed. Firstly, it is proved that local frequency deviation is composed of the linear component and n-1 electro-mechanical （EM） modes via solving the initial value problem of ordinary differential equations. Furthermore, the linear component of each local frequency deviation is identical to the center of inertia （COI） frequency deviation in the early stages of system disturbance. Based on this property, a remote-communication-independent system power deficit estimation method is proposed. In the proposed method, the center of inertia （COI） frequency can be estimated via extracting the linear component of local frequency based on least-squares fitting. Then, the system power deficit is estimated by combining system inertia level. Finally, New England 39-bus system is built in PSCAD/EMTDC to verify the correctness of the property and the effectiveness of the proposed power deficit estimation method.