In this paper, the voltage regulation in power systems is addressed from the perspective of the modern paradigm of control logic supported by phasor measurement units. The information available from measurements is used to better adapt the regulation actions to the actual operation point of the system. The use of the online measurement data allows for identifying the sensitivity matrix and for improving the regulation performances with respect to the fast load variations that increasingly affect modern power systems. With the aim of estimating the sensitivity matrices, a preliminary action is necessary to reconstruct the phases of the network voltages, which are assumed not to be provided by the phasor measurement units. This allows for obtaining a model-free adaptive control method. It is then shown how the regulation problem can be formulated in terms of a linear quadratic Gaussian problem, properly considering the load modeling in terms of the stochastic Ornstein–Uhlenbeck process. This control strategy has the advantage of avoiding dangerous oscillations of power flows, as demonstrated through the results of some simulations on a classical test network. Particularly, the advantage of the proposed approach is shown in the presence of different levels of load disturbances.