Title: A Theory of Solvability for Lossless Power Flow Equations -- Part II: Conditions for Radial Networks,
Abstract: This two-part paper details a theory of solvability for the power flow
equations in lossless power networks. In Part I, we derived a new formulation
of the lossless power flow equations, which we term the fixed-point power flow.
The model is parameterized by several graph-theoretic matrices -- the power
network stiffness matrices -- which quantify the internal coupling strength of
the network. In Part II, we leverage the fixed-point power flow to study power
flow solvability. For radial networks, we derive parametric conditions which
guarantee the existence and uniqueness of a high-voltage power flow solution,
and construct examples for which the conditions are also necessary. Our
conditions (i) imply convergence of the fixed-point power flow iteration, (ii)
unify and extend recent results on solvability of decoupled power flow, (iii)
directly generalize the textbook two-bus system results, and (iv) provide new
insights into how the structure and parameters of the grid influence power flow
solvability.