Active powers from generation units are required to track changes of automatic generation control (AGC) commands from power grid dispatch centers. Maximum ramp rates are the fastest speeds in making required changes of active powers, and are valuable performance metrics for dispatching AGC commands to quickly suppress frequency fluctuations in power grids. This article proposes a method to estimate maximum ramp rates from historical data samples of active powers. The proposed method is composed by three steps to address some technical challenges. The first step resolves a challenge in separating original data samples of active powers into isolated data segments in piece-wise linear representations, from which amplitude changes and time durations of active powers are obtained. The second step selects pairs of large amplitude changes and short time durations being associated with sufficient local densities; doing so deals with the second challenge to achieve a maximum ramp rate estimate representing a repeatable rapidity, instead of an occasional largest ramp rate. In order to alleviate and quantify the negative noise effects as the third challenge, the last step of the proposed method builds linear regression models on the selected pairs of amplitude changes and time durations, and estimates the maximum ramp rates with their confidence intervals afterwards. Existing methods in the literature do not fully consider the three challenges, so that resulting estimates are either the mixtures of fast and slow ramp rates, or the contaminated ones with large errors. Numerical and industrial examples are provided to illustrate the proposed method and compare with existing ones.