Reversible system for storing and extracting electricity, comprising: - an electrochemical converter comprising at least one solid oxide electrochemical cell each formed of an H 2 electrode, an O 2 electrode and an electrolyte interposed between these two electrodes, the converter being designed to operate as a high-temperature water vapour electrolysis reactor (SOEC) and, reversibly, as a fuel cell (SOFC), and vice versa; - a hydrogen storage and extraction reservoir, designed to store hydrogen or, reversibly, to supply hydrogen to the converter or, if appropriate, to a methanation reactor upstream of the converter; - an air compressor; - an air storage reservoir, designed to store air that comes from the compressor in electricity storage mode and to supply air to the converter in electricity extraction mode; - a supply line for supplying liquid water to the converter; - a heat exchanger designed to exchange heat between the supply line and the air compressor; the system being configured such that: • when the system operates in electricity storage mode and the converter operates in electrolysis mode, the compressor introduces the heat produced during the air compression to the liquid water via the exchanger in order to vaporize the water before it enters the H 2 electrode of the converter, while the air compressed by the compressor is stored in the air reservoir and the hydrogen produced is stored in the hydrogen reservoir; • when the system operates in electricity extraction mode and the converter operates reversibly as a fuel cell, the hydrogen reservoir supplies hydrogen to the H 2 electrode of the converter or, if appropriate, the methanation reactor which itself supplies a mixture of methane and water to the H 2 electrode of the converter, while the air reservoir supplies air to the O 2 electrode of the converter. - an electrochemical converter comprising at least one solid oxide electrochemical cell each formed of an H 2 electrode, an O 2 electrode and an electrolyte interposed between these two electrodes, the converter being designed to operate as a high-temperature water vapour electrolysis reactor (SOEC) and, reversibly, as a fuel cell (SOFC), and vice versa; - a hydrogen storage and extraction reservoir, designed to store hydrogen or, reversibly, to supply hydrogen to the converter or, if appropriate, to a methanation reactor upstream of the converter; - an air compressor; - an air storage reservoir, designed to store air that comes from the compressor in electricity storage mode and to supply air to the converter in electricity extraction mode; - a supply line for supplying liquid water to the converter; - a heat exchanger designed to exchange heat between the supply line and the air compressor; • when the system operates in electricity storage mode and the converter operates in electrolysis mode, the compressor introduces the heat produced during the air compression to the liquid water via the exchanger in order to vaporize the water before it enters the H 2 electrode of the converter, while the air compressed by the compressor is stored in the air reservoir and the hydrogen produced is stored in the hydrogen reservoir; • when the system operates in electricity extraction mode and the converter operates reversibly as a fuel cell, the hydrogen reservoir supplies hydrogen to the H 2 electrode of the converter or, if appropriate, the methanation reactor which itself supplies a mixture of methane and water to the H 2 electrode of the converter, while the air reservoir supplies air to the O 2 electrode of the converter.