An investigation into the power flow distribution is conducted to better understand the vulnerability of power grids. The distribution of number of links connected to any random node of the power grid follows an exponential distribution. Hence, network theory based topological degree distribution of power grids does not provide useful information about critical elements (e.g., nodes and links). Hence, the distribution of an alternative functional parameter of power grids, node flow, is scrutinized with a view to gain understanding of the paradoxical robust but fragile characteristics explained by power-law distribution. We show that, although the node flow follows the exponential distribution, a meticulous examination of the distribution of high power flow nodes reveals the scale-free characteristics.