We consider the problems of stability, frequency restoration and optimal steady-state resource allocation in a heterogeneous and structure-preserving differential-algebraic equation (DAE) power system model. Thereby, we include constant-power-controlled loads (CPCLs) and constant-power-controlled sources (CPCSs) explicitly in the analysis and network control design. This results in a power system model with mixed algebraic as well as first- and second-order differential dynamics. We show that the abovementioned control objectives can be achieved via a distributed averaging proportional integral (DAPI) control and, in particular, extend the stability proof in [1] to the resulting closed-loop DAE system.
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