Constrained angle control in power grids comprising virtual synchronous machines

In order to ensure synchronism in a power grid, the relative electric angles of the (virtual) synchronous generators in this grid must remain close to a desired stable equilibrium point, which implies that these angles should remain small. In particular, asynchronous rotations must be avoided, as they may cause the protections to disconnect generators and may even lead to a breakdown of the system. This can happen as the result of a fault, when the grid impedances between the individual machines become too large, so that the coupling between generators may become too weak. Maintaining synchronism is a classical and well studied problem in power systems, but the emergence of power systems comprising inverters operated as virtual synchronous machines (VSMs) opens up new horizons. Most importantly, such VSMs will be embedded in modern communication infrastructures, such that a real time exchange of information between individual machines becomes conceivable. In such systems we may apply control techniques that are not feasible for traditional generators, such as instantaneous frequency droop and virtual friction. Here we propose to apply constrained control inspired by projected dynamical systems theory, to limit the allowed deviation of the relative angles of VSMs, thus preventing asynchronous rotations, and helping the power grid to more easily recover after a large disturbance.