Stellar activity is known to limit exoplanet detection and characterization. Among this activity, stellar convection (``flicker'') evolves during the typical transit timescales (~ hours) and affects the inferred transit parameters. We generated realistic simulations of transiting exoplanets based on solar HMI data. These simulations include planets from 1 to 10 Earth radii with different transit geometries. These simulations comprising hundreds of light curves are available to the community : https://doi.org/10.5281/zenodo.3686871 We analyzed the data using standard MCMC methods assuming the noise is white and Gaussian (WGN), or a Gaussian Process (GP). We show that, in both cases, the resulting planet parameters can be affected by biases, which leads to biased planetary radius measurements. This demonstrates the need to develop robust stellar noise modeling to achieve PLATO's goal of characterizing exoplanets transiting solar-like stars. Next steps of this study will be to investigate i) how other noise sources (e.g., flares, spots and faculae) affect the inferred exoplanet parameters, ii) which noise modeling allows to derive the most accurate transit parameters.