Network theoretic conditions for existence and uniqueness of steady state solutions to electric power circuits

Surveys available network theoretic results on conditions under which the unique and operationally acceptable load flow solution exists. The main topic is the problem of establishing system-dependent bounds on input and network topology within which the unique solution exists. Both decoupled real-power-phase angle and reactive-power-voltage problems are studied. The particular emphasis is on the conservativeness of the sufficient conditions under which the power network has the properties of a nonlinear resistive network. Several new results and open questions are reported regarding conservativeness of sufficient conditions for solution existence.