Inter-cell interference is one of the main limiting factors in current heterogeneous cellular networks. Uplink fractional power control (FPC) is a well-known method that aims to cope with such a limiting factor and to save the battery life of the mobile terminals (MTs). In order to do that, the transmit power of each MT is adjusted as a function of a set of parameters that usually depend only on the link between MTs and serving base station (BS), such as the desired received power at the serving BS or the path loss between the MT and its serving BS. Contrary to these classical FPC schemes, 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. Our analysis reveals that such an interference aware method can reduce the average power consumption and increase the average spectral efficiency at once. In addition, the variance of the interference is reduced, thus improving the performance of adaptive modulation and coding schemes, since the interference can be better estimated.