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

The interconnection of quadratic droop voltage controllers is a Lotka-Volterra system: implications for stability analysis