This paper considers a network of energy harvesting wireless nodes transmitting simultaneously in a Gaussian interference channel and investigates a distributed power allocation algorithm that maximizes the sum-rate. The power consumption model is based on a series of step functions that allow to model, among others, radio frequency circuits being on/off and the startup power consumption of the transmitter. After showing that the sum-rate maximization problem is nonsmooth, nonconvex, and NP-hard, the Iterative Smooth and Convex approximation Algorithm (ISCA) is proposed, which successively approximates the step functions by proper smooth functions to obtain a sequence of smooth nonconvex problems that can be solved by means of the successive convex approximation method. It is demonstrated that the ISCA distributedly converges to a stationary solution of the sum-rate maximization problem. For the particular case of point to point communications, the numerical results show that the ISCA is able to avoid bad stationary solutions, performing close to the globally optimal solution. The performance of the ISCA is also evaluated in the interference channel and with real solar energy harvesting data.