This paper proposes a novel modelling approach of multi-machine power systems for the design of decentralized multivariable voltage and speed regulators. In this approach, each generator views the rest of the network as effective instantaneous impedance. The new model contains time-varying parameters representing the interactions among the system generators. The time-varying parameters depend only on the operating conditions of the power system and are independent of the structure of the latter. The advantages of this model are its simplicity, the fact that each generator's terminal voltage and rotor speed are expressed only in terms of local measurable variables and its capability to model inter-machines interactions. A decentralized multi-input multi-output (MIMO) non-linear voltage and speed regulator based on the new model is then used to dampen oscillations in a four-machine power system and to illustrate the advantages of the proposed modelling approach. Simulation results show that voltage, rotor and inter-area oscillations are well damped.