We present a parameter study of self-consistent models of protoplanetary disks around Herbig AeBe stars. We use the code developed by Dullemond and Dominik, which solves the 2D radiative transfer problem including an iteration for the vertical hydrostatic structure of the disk. This grid of models will be used for several studies on disk emission and mineralogy in followup papers. In this paper we take a first look on the new models, compare them with previous modeling attempts and focus on the effects of various parameters on the overall structure of the SED that leads to the classification of Herbig AeBe stars into two groups, with a flaring (group I) or self-shadowed (group II) SED. We find that the parameter of overriding importance to the SED is the total mass in grains smaller than 25um, confirming the earlier results by Dullemond and Dominik. All other parameters studied have only minor influences, and will alter the SED type only in borderline cases. We find that there is no natural dichotomy between group I and II. From a modeling point of view, the transition is a continuous function of the small dust mass. We also show that moderate grain growth produces spectra with weak or no 1um feature, both for flaring (Group I) and non-flaring (Group II) sources. The fact that sources with weak features have been found mostly in Group I sources is therefore surprising and must be due to observational biases or evolutionary effects.
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