This paper deals with the modeling of trading activity on the European electricity intraday market by a self-exciting point process. This type of process (also known as a Hawkes process) enriches the modeling to tackle the issue of trade clustering during a fixed time period. It gives some empirical evidence of self-excitement on the European market from EPEX SPOT data, and discusses the time homogeneity of the baseline of the process: a piecewise constant baseline is found as a relevant choice to fit the increasing intensity of trades at the end of the trading period. With the aim of finding a tractable parametric model, the question of the functional shape of the intensity kernel is also addressed: a nonparametric estimator, based on spline functions, is implemented and suggests the use of an exponential kernel. Finally, a parameter estimation procedure is derived for the model with a nonconstant baseline, based on maximization of the likelihood.