Due to its ability of overcoming the impact of double-fading effect, active intelligent reflecting surface (IRS) has attracted a lot of attention. Unlike passive IRS, active IRS should be supplied by power, thus adjusting power between base station (BS) and IRS having a direct impact on the system rate performance. In this paper, the active IRS-aided network under a total power constraint is modeled with an ability of adjusting power between BS and IRS. Given the transmit beamforming at BS and reflecting beamforming at IRS, the SNR expression is derived to be a function of power allocation (PA) factor, and the optimization of maximizing the SNR is given. Subsequently, two high-performance PA strategies, enhanced multiple random initialization Newton's (EMRIN) and Taylor polynomial approximation (TPA), are proposed. The former is to improve the rate performance of classic Netwon's method to avoid involving a local optimal point by using multiple random initializations. To reduce its high computational complexity, the latter provides a closed-form solution by making use of the first-order Taylor polynomial approximation to the original SNR function. Actually, using TPA, the original optimization problem is transformed into a problem of finding a root for a third-order polynomial.Simulation results are as follows: the first-order TPA of SNR fit its exact expression well, the proposed two PA methods performs much better than fixed PA in accordance with rate, and appoaches exhaustive search as the number of IRS reflecting elements goes to large-scale.