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

Multistability and anomalies in oscillator models of lossy power grids