A method for the continuous monitoring of partial discharges in three-phase high voltage cables (5.2), the method comprising: - synchronously measuring the electric signals of the three-phase high voltage cables for a time interval of at least one grid voltage period (4.1) with a plurality of partial discharge sensors (6.2.1) positioned at accessories as sensing points distributed along each cable; - filtering the noise (4.2) of the measured signals (4.1) and discriminating pulses by means of calculating the Wavelet transform with complementary statistical processing for a time interval of at least one grid voltage period regardless of background noise and identifying a partial discharge as a function of the statistical dispersion of the components of said transform; - determining (4.3) in the filtered signals (4.2) for each discriminated pulse a start time of the pulse t i and the following parameters: phase angle over time in relation to the zero-crossing of the grid voltage, amplitude A i and the integral of the pulse of the partial discharge at the sensing point (4.11); - identifying (4.4) the cable where the partial discharge is originated as a function of the highest amplitude A i of the signals detected by the sensors located in the accessories of the three phases, and determining the parameter associated with the location of the partial discharge x i, taking into account the differences of arrival times t i to the different sensors that have detected it; - determining (4.8) the location map of partial discharges as a function of the parameter of the location x i of each partial discharge; - automatically generating (4.9) patterns of partial discharges as a function of the phase angle with the grid voltage wave applied for each group of partial discharges positioned at the same location x i of the cable; - establishing a correlation (4.10) between each group of partial discharges and partial discharge producing defects by means of automatically recognising using a neural network the patterns of partial discharges as a function of the phase angle with the grid voltage wave applied to the cable. - synchronously measuring the electric signals of the three-phase high voltage cables for a time interval of at least one grid voltage period (4.1) with a plurality of partial discharge sensors (6.2.1) positioned at accessories as sensing points distributed along each cable; - filtering the noise (4.2) of the measured signals (4.1) and discriminating pulses by means of calculating the Wavelet transform with complementary statistical processing for a time interval of at least one grid voltage period regardless of background noise and identifying a partial discharge as a function of the statistical dispersion of the components of said transform; - determining (4.3) in the filtered signals (4.2) for each discriminated pulse a start time of the pulse t i and the following parameters: phase angle over time in relation to the zero-crossing of the grid voltage, amplitude A i and the integral of the pulse of the partial discharge at the sensing point (4.11); - identifying (4.4) the cable where the partial discharge is originated as a function of the highest amplitude A i of the signals detected by the sensors located in the accessories of the three phases, and determining the parameter associated with the location of the partial discharge x i, taking into account the differences of arrival times t i to the different sensors that have detected it; - determining (4.8) the location map of partial discharges as a function of the parameter of the location x i of each partial discharge; - automatically generating (4.9) patterns of partial discharges as a function of the phase angle with the grid voltage wave applied for each group of partial discharges positioned at the same location x i of the cable; - establishing a correlation (4.10) between each group of partial discharges and partial discharge producing defects by means of automatically recognising using a neural network the patterns of partial discharges as a function of the phase angle with the grid voltage wave applied to the cable.