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We present a distributed and price-based control approach for frequencyregulation in power grids with nonzero line conductances. Both grid andcontroller are modeled as a port-Hamiltonian system, where the grid modelconsists of differential as well as algebraic equations. Simulations show thatthe resulting controller asymptotically stabilizes the frequency whilemaintaining minimum overall generation costs in steady state and being robustin terms of clock drifts and uncontrollable loads. Moreover, it is shown thatactive power sharing can be achieved by an appropriate choice of the costfunction.

Steady-State Optimal Frequency Control for Lossy Power Grids with Distributed Communication