Low frequency full wave electromagnetic modeling is of great importance to a number of applications. But it is also a great challenge in the research of computational electromagnetics (CEM). To address this issue, in this paper, we will discuss incorporating the augmented electric field integral equation (A-EFIE) into the low frequency augmented equivalence principle algorithm (A-EPA) method. It effectively improves the low frequency simulation stability. But this method involves the calculation of the translation process which is exceptionally time-consuming and memory-consuming. In order to surmount this problem, we use the adaptive cross approximation (ACA) to accelerate the calculation of this process. Benchmarks for A-EPA with A-EFIE using ACA will be presented at the end of this paper.