Recently, it has been demonstrated that graphene nano-ribbons (GNRs) exhibit superior thermoelectric performance compared to graphene sheets. However, the underlying mechanism behind this enhancement has not been systematically investigated and significant opportunity remains for further enhancement of the thermoelectric performance of GNRs by optimizing their charge carrier concentration. In this work, we modulate the carrier concentration of graphene-based nano-structures using a gate voltage and investigate the resulting carrier-concentration-dependent thermoelectric parameters using the Boltzmann transport equations. We investigate the effect of energy dependent scattering time and the role of substrate-induced charge carrier fluctuation in optimizing the Seebeck coefficient and power factor. Our approach predicts the scattering mechanism and the extent of the charge carrier fluctuation in different samples and explains the enhancement of thermoelectric performance of GNR samples. Subsequently, we propose a route towards the enhancement of thermoelectric performance of graphene-based devices which can also be applied to other two-dimensional materials.