Recently, event-triggered model predictive control (MPC) is addressed as a promising and powerful technique for power converter systems. The core idea behind this technique is to explicitly provide a feasible solution to reduce switching actions. However, it is prone to suffer from unknown uncertainties and large tracking error that hinder its potential when medium to high accuracy is desired. To tackle the difficulties caused by the uncertainties and tracking error, our work takes a step forward toward addressing a modified data-driven event-triggered model-free predictive control architecture leveraging a two-step event-triggered protocol subject to parametric uncertainties. Meanwhile, an integral error term is embedded into this proposal so as to enhance the tracking performance under low switching frequency (SF) operation. Compared to previous studies, we show that this modification not only endows with uncertainties and SF as well as tracking error attenuating capabilities but also inspires new works in the intersection of event-driven control technique and MPC theory, without requiring a priori knowledge of model dynamics and weighting factors. Finally, numerical examples illustrate the interest and efficacy of this proposal.