  High-voltage direct current (HVDC) is a commonly used technology for
long-distance electric power transmission, mainly due to its low resistive
losses. In this paper a distributed controller for multi-terminal high-voltage
direct current (MTDC) transmission systems is considered. Sufficient conditions
for when the proposed controller renders the closed-loop system asymptotically
stable are provided. Provided that the closed loop system is asymptotically
stable, it is shown that in steady-state a weighted average of the deviations
from the nominal voltages is zero. Furthermore, a quadratic cost of the current
injections is minimized asymptotically.
