The ongoing efforts by many countries worldwide to increase the share of renewable energy sources in power generation has changed the nature of existing power grids and introduced numerous stability-related issues. To address these problems, more extensive and detailed stability analysis studies are therefore needed. Driven by this need, in this article, we present a passivity-based framework for stability analysis and control design that allows more accurate modeling of both the network and the power system components while facilitating the derivation of completely decentralized stability results. In particular, the proposed approach relies on the formulation of the network as a dynamical multivariable system, which is shown to be passive, even when the network’s dynamic and lossy nature are taken into account. The application of decentralized passivity conditions on bus dynamics is then further exploited, together with the incorporation of more accurate dynamical models for the power system components, to guarantee the asymptotic stability of the interconnected system. Moreover, we discuss the opportunities provided by the proposed approach regarding the incorporation of higher order dynamics, the derivation of significant stability results in a completely decentralized manner and the design of effective distributed control mechanisms. These opportunities are finally verified through the design of a demand-side voltage droop controller and several dynamic simulations on two typical test systems.