  This paper introduces a new grid-forming control for power converters, termed
hybrid angle control (HAC) that ensures the almost global closed-loop
stability. HAC combines the recently proposed matching control with a novel
nonlinear angle feedback reminiscent of (though not identical to) classic droop
and dispatchable virtual oscillator controls. The synthesis of HAC is inspired
by the complementary benefits of the dc-based matching and ac-based
grid-forming controls as well as ideas from direct angle control and nonlinear
damping assignment. The proposed HAC is applied to a high-fidelity nonlinear
converter model that is connected to an infinite bus or a center-of-inertia
dynamic grid models via a dynamic inductive line. We provide insightful
parametric conditions for the existence, uniqueness, and global stability of
the closed-loop equilibria. Unlike related stability certificates, our
parametric conditions do not demand strong physical damping, on the contrary
they can be met by appropriate choice of control parameters. Moreover, we
consider the safety constraints of power converters and synthesize a new
current-limiting control that is compatible with HAC. Last, we present a
practical implementation of HAC and uncover its intrinsic droop behavior,
derive a feedforward ac voltage and power control, and illustrate the behavior
of the closed-loop system with publicly available numerical examples.
