Due to the ever-increasing demand for more detailed and accurate power system simulations, the dimensions of mathematical models increase. Although the traditional direct linear equation solvers based on LU factorization are robust, they have limited scalability on the parallel platforms. On the other hand, simulations of the power system events need to be performed at a reasonable time to assess the results of the unwanted events and to take the necessary remedial actions. Hence, to obtain faster solutions for more detailed models, parallel platforms should be used. To this end, direct solvers can be replaced by Krylov subspace methods (conjugate gradient, generalized minimal residuals, etc.). Krylov subspace methods need some accelerators to achieve competitive performance. In this article, a new preconditioner is proposed for Krylov subspace-based iterative methods. The proposed preconditioner is based on the spectral projectors. It is known that the computational complexity of the spectral projectors is quite high. Therefore, we also suggest a new approximate computation technique for spectral projectors as appropriate eigenvalue-based accelerators for efficient computation of power flow problems. The convergence characteristics and sparsity structure of the preconditioners are compared to the well-known black-box preconditioners, such as incomplete LU, and the results are presented.