The emergence of distributed energy resources can lead to congestion in distribution grids. DC distribution grids are becoming more relevant as more sources and loads connected to the low voltage grid use dc. Bipolar dc distribution grids with asymmetric loading can experience partial congestion resulting in a nodal price difference between the two polarities if a respective market model is applied. In order to take into account this price difference, this paper presents an optimal power flow (OPF) model formulated in terms of voltage and current. In the case of bipolar dc distribution grids, the single line approximation is no longer valid because current can flow in the neutral conductors as well. Moreover, loads and sources can be connected between any two nodes in the network. The proposed exact OPF formulation includes bilinear equations. The locational marginal prices (LMP) are derived by linearizing the problem at the optimal solution. Example cases show the various phenomena that can appear under asymmetric loading, such as pole-to-pole connections combined with pole-to-neutral connections, parallel sources, meshed grids and their effect on the LMP.@en