  A problem of load balancing in isolated DC microgrids is considered in this
paper. Here, a DC load is fed by multiple heterogenous DC sources, each of
which is connected to the load via a boost converter. The gains of the DCC's
provide for a means to control the division of load current amongst the DC
sources. The primary objective of the control scheme is to minimise the total
losses in the network, while maintaining the output voltage within a desired
range, serving the load current demand and adhering to VI-characteristics of
the power sources. Under assumptions of
concavity/monotonocity/piece-wise-linearity of the VI-characteristics, the
problem is solved using a convex relaxation. It is shown that the solution to
the relaxed problem is tight. Thus, the resulting algorithm is guaranteed to
reach global optimality in a numerically efficient manner. Simulations are
provided for corroboration.
