  The problem of primary control of high-voltage direct current transmission
systems is addressed in this paper, which contains four main contributions.
First, to propose a new nonlinear, more realistic, model for the system
suitable for primary control design, which takes into account nonlinearities
introduced by conventional inner controllers. Second, to determine necessary
conditions - dependent on some free controller tuning parameters - for the
existence of equilibria. Third, to formulate additional (necessary) conditions
for these equilibria to satisfy the power sharing constraints. Fourth, to
establish conditions for stability of a given equilibrium point. The usefulness
of the theoretical results is illustrated via numerical calculations on a
four-terminal example.
