In power-hardware-in-the-loop (PHIL) digital simulation testing, a power device, also known as device-under-test (DUT), is virtually exchanging power with a power amplifier governed by the reference signals coming from the point of interface (POI) in the power system implemented on a digital real-time simulation platform. Indeed, the power amplifier (also known as grid simulator) is the integral of any PHIL testing, and its dynamics are greatly impacting the accuracy of the PHIL testing. The dynamics of an industrial power amplifier is certainly not an ideal transfer function, i.e., unity. In fact, it is going to degrade the accuracy of the testing especially when the interested frequency range of the power system studies is within the frequency response of the power amplifier's dynamics. Consequently, having an industrial power amplifier's dynamics is very helpful in order to judge the accuracy of the PHIL testing. In this paper, experimental results of an industrial power amplifier have been used, and mathematical linear discrete-time models of the industrial power amplifier have been extracted using different linear system identification methods. Designing input signals, pre-processing data, estimating time delay, estimating model order and parameters, calculating confidence intervals, representing frequency-domain of models, and validating different models are shown in this paper. ARX, ARMAX, BJ, and OE estimated models, which benefit from prediction error method (PEM), are employed in this paper.