  In this article, we consider a dynamic model of a three-phase power system
including nonlinear generator dynamics, transmission line dynamics, and static
nonlinear loads. We define a synchronous steady-state behavior which
corresponds to the desired nominal operating point of a power system and obtain
necessary and sufficient conditions on the control inputs, load model, and
transmission network, under which the power system admits this steady-state
behavior. We arrive at a separation between the steady-state conditions of the
transmission network and generators, which allows us to recover the
steady-state of the entire power system solely from a prescribed operating
point of the transmission network. Moreover, we constructively obtain necessary
and sufficient steady-state conditions based on network balance equations
typically encountered in power flow analysis. Our analysis results in several
necessary conditions that any power system control strategy needs to satisfy.
