This work presents a passivity-based stability guarantee for the decentralized control of nonlinear power flow systems. This class of systems is characterized using a graph-based modeling approach, where vertices represent capacitive elements that store energy and edges represent power flow between these capacitive elements. Due to their complexity and size, these power flow systems are often decomposed into dynamically coupled subsystems, where this coupling stems from the exchange of power between subsystems. Each subsystem has a corresponding model predictive controller that can be part of a decentralized, distributed, or larger hierarchical control structure. By exploiting the structure of the coupling between subsystems, stability of the closed-loop system is guaranteed by augmenting each model predictive controller with a local passivity constraint. (C) 2017 Elsevier Ltd. All rights reserved.