Inter-cell interference is one of the main limiting factors in current Heterogeneous Cellular Networks (HCNs). Uplink Fractional Power Control (FPC) is a well known method that aims to cope with such limiting factor as well as to save battery live. In order to do that, the path losses associated with Mobile Terminal (MT) transmissions are partially compensated so that a lower interference is leaked towards neighboring cells. Classical FPC techniques only consider a set of parameters that depends on the own MT transmission, like desired received power at the Base Station (BS) or the path loss between the MT and its serving BS, among others. Contrary to classical FPC, in this paper we use stochastic geometry to analyze a power control mechanism that keeps the interference generated by each MT under a given threshold. We also consider a maximum transmitted power and a partial compensation of the path loss. Interestingly, our analysis reveals that such Interference Aware (IA) method can reduce the average power consumption and increase the average spectral efficiency. Additionally, the variance of the interference is reduced, thus improving the performance of Adaptive Modulation and Coding (AMC) since the interference can be better estimated at the MT.