The studied power flow controller is an electronic device capable of controlling the power flows at a node in a meshed low voltage DC grid. It is made of m buck-boost converters connected in parallel on their high voltage-side to a reservoir capacitor. This paper proposes a nonlinear control method achieving robust regulation of the power in each line and of the reservoir voltage inside the converter. This control law only requires measurements of local currents and voltages, and the knowledge of the maximum possible resistance of the grid, whereas prior control laws required the full knowledge of some nominal parameters. Proofs of stability are given for every possible uncertain parameters of the studied grid model whereas prior control laws were only valid at nominal parameters and their neighbourhood. The performance of this control method is asserted through a tenth-scale experimental set-up. Stochastic simulations are conducted to estimate the basin of attraction.