The energy consumption of cloud servers accounts for about 25% of the total energy of cloud data centers. Reducing and optimizing this energy consumption is thus extremely important in energy saving in cloud data centers. Power model is fundamental in energy efficiency optimization scheduling for cloud computing. However, systems and tools for power measurement in the cloud computing environment are relatively scarce, and power models of cloud servers cannot keep up with the times. Therefore, we propose a new CPU power model named power-exponent function model (PEFM) is proposed, which provides higher accuracy in estimating the CPU power of the latest cloud servers than the current linear, polynomial and power function models. A novel hardware-aware CPU power measurement (HCPM) is also proposed, that can select an appropriate CPU power model through the launch year of CPU without power model training. For validating the efficacy of PEFM and HCPM, a set of experiments including OpenStack cluster experiment, based on a distributed energy meter (DEM) implemented by our team were conducted. The experimental results indicate that the proposed PEFM and HCPM not only improve the accuracy of CPU power estimation in cloud servers in cloud environment, but also reduce the difficulty of model training and simplify system deployment.