A tool for stability and power sharing analysis of a generalized class of droop controllers for high-voltage direct-current transmission systems

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.