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The existing spectral discretization-based methods (SDMs) are capable of accurately computing critical eigenvalues of large power systems when time delays in wide-area damping control loops are considered. However, SDMs suffer from huge dimension of the discretized matrices of spectral operators, which is usually dozens of times of actual system states. To resolve the problem, an idea of partial spectral discretization (PSD) is proposed in this paper where only the retarded state variables instead of all system states are discretized. Following the PSD idea, a partial and explicit infinitesimal generator discretization (PEIGD) method is presented for highly efficient eigen-analysis of large closed-loop delayed cyber-physical power system (DCPPS). In contrast to the original EIGD method, the order of the resultant discretized matrix of the infinitesimal generator is greatly reduced and close to the number of actual state variables. The computational burden of PEIGD can be an order of magnitude less than that of EIGD and nearly the same as eigen-analysis of a system without time delay. Moreover, PEIGD is endowed with exactly the same accuracy as EIGD in capturing critical oscillation modes. Both theoretical analyses and intensive tests on the 16-generator 68-bus test system as well as a 516-bus and a 33028-bus real-life large power systems verify the accuracy and efficiency of the presented method. [ABSTRACT FROM AUTHOR]