  Oscillator networks with an asymmetric bipolar distribution of natural
frequencies are useful representations of power grids. We propose a mean-field
model that captures the onset, form and linear stability of frequency
synchronization in such oscillator networks. The model takes into account a
broad class of heterogeneous connection structures and identifies a functional
form as well as basic properties that synchronized regimes possess classwide.
The framework also captures synchronized regimes with large phase differences
that commonly appear just above the critical threshold. Additionally, the
accuracy of mean-field assumptions can be gauged internally through two model
quantities. With our framework, the impact of local grid structure on frequency
synchronization can be systematically explored.
