  This paper studies the stability of voltage dynamics for a power network in
which nodal voltages are controlled by means of quadratic droop controllers
with nonlinear AC reactive power as inputs. We show that the voltage dynamics
is a Lotka-Volterra system, which is a class of nonlinear positive systems. We
study the stability of the closed-loop system by proving a uniform ultimate
boundedness result and investigating conditions under which the network is
cooperative. We then restrict to study the stability of voltage dynamics under
a decoupling assumption (i.e., zero relative angles). We analyze the existence
and uniqueness of the equilibrium in the interior of the positive orthant for
the system and prove an asymptotic stability result.
