  The analysis of dissipatively coupled oscillators is challenging and highly
relevant in power grids. Standard mathematical methods are not applicable, due
to the lack of network symmetry induced by dissipative couplings. Here we
demonstrate a close correspondence between stable synchronous states in
dissipatively coupled oscillators, and the {winding partition} of their state
space, a geometric notion induced by the network topology. Leveraging this
winding partition, we accompany this article with an algorithms to compute all
synchronous solutions of complex networks of dissipatively coupled oscillators.
These geometric and computational tools allow us to identify anomalous
behaviors of lossy networked systems. Counterintuitively, we show that loop
flows and dissipation can increase the system's transfer capacity, and that
dissipation can promote multistability. We apply our geometric framework to
compute power flows on the IEEE RTS-96 test system, where we identify two high
voltage solutions with distinct loop flows.
