(Abridged) The archetypal Seyfert 1 galaxy NGC 5548 was observed in 2013-2014 in the context of an extensive multiwavelength campaign, which revealed the source to be in an extraordinary state of persistent heavy obscuration. We re-analyzed the archival grating spectra obtained by XMM-Newton and Chandra between 1999 and 2007 in order to characterize the classic warm absorber (WA) using consistent models and up-to-date photoionization codes and atomic physics databases and to construct a baseline model that can be used as a template for the WA in the 2013 observations. The WA in NGC 5548 is composed of 6 distinct ionization phases outflowing in 4 kinematic regimes in the form of a stratified wind with several layers intersected by our line of sight. If the changes in the WA are solely due to ionization or recombination processes in response to variations in the ionizing flux among the different observations, we are able to estimate lower limits on the density of the WA, finding that the farthest components are less dense and have a lower ionization. These limits are used to put stringent upper limits on the distance of the WA components from the central ionizing source, with the lowest ionization phases <50, <20, and <5 pc, respectively, while the intermediately ionized components lie at <3.6 and <2.2 pc from the center, respectively. The highest ionization component is located at ~0.6 pc or closer to the AGN central engine. The mass outflow rate summed over all WA components is ~0.3 Msun/yr, about six times the nominal accretion rate of the source. The total kinetic luminosity injected into the ISM is a small fraction (~0.03%) of the bolometric luminosity of the source. After adding the contribution of the UV absorbers, this value augments to ~0.2% of the bolometric luminosity, well below the minimum amount of energy required by current feedback models to regulate galaxy evolution.
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