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.