A cooling system for cooling a power transmission system comprising a cable (C 1, C 2, C 3) carrying a current corresponding to a transported electric power, the cooling system comprising: - a cooling device arranged to remove heat from the power transmission system; - a power supply system (T 1, T 2, T 3, JB) comprising at least one transformer (T 1, T 2, T 3), arranged to extract a fraction (P max, P x) of said transported electric power from the cable (C 1, C 2, C 3) and to supply the cooling device with said fraction of the power (P max, P x), said at least one transformer (T 1, T 2, T 3) comprising a first terminal (E 1, E 2, E 3), a second terminal (E 1, E 2, E 3) and an intermediate terminal (E i (x)) placed at an intermediate position between said first terminal (E 1, E 2, E 3) and said second terminal (E 1, E 2, E 3); - a sensor configured to detect a parameter of the power transported in the cable; - a control unit configured to control the amount of the extracted fraction of the power (P max, P x) responsive to said parameter of the power transported in the cable, so that - when the parameter is higher than a threshold (I th), the extracted fraction of the power (P max, P x) is equal to a first value (P max) depending on the power carried in the cable through a first function; and - when the parameter is lower than the threshold (I th), the extracted fraction of the power is equal to a second value (P x) depending on the power carried in the cable through a second function, the second function corresponding to the first function multiplied by a factor k, k being higher than 0 and lower than 1. - a cooling device arranged to remove heat from the power transmission system; - a power supply system (T 1, T 2, T 3, JB) comprising at least one transformer (T 1, T 2, T 3), arranged to extract a fraction (P max, P x) of said transported electric power from the cable (C 1, C 2, C 3) and to supply the cooling device with said fraction of the power (P max, P x), said at least one transformer (T 1, T 2, T 3) comprising a first terminal (E 1, E 2, E 3), a second terminal (E 1, E 2, E 3) and an intermediate terminal (E i (x)) placed at an intermediate position between said first terminal (E 1, E 2, E 3) and said second terminal (E 1, E 2, E 3); - a sensor configured to detect a parameter of the power transported in the cable; - a control unit configured to control the amount of the extracted fraction of the power (P max, P x) responsive to said parameter of the power transported in the cable, so that - when the parameter is higher than a threshold (I th), the extracted fraction of the power (P max, P x) is equal to a first value (P max) depending on the power carried in the cable through a first function; and - when the parameter is lower than the threshold (I th), the extracted fraction of the power is equal to a second value (P x) depending on the power carried in the cable through a second function, the second function corresponding to the first function multiplied by a factor k, k being higher than 0 and lower than 1. - when the parameter is higher than a threshold (I th), the extracted fraction of the power (P max, P x) is equal to a first value (P max) depending on the power carried in the cable through a first function; and - when the parameter is lower than the threshold (I th), the extracted fraction of the power is equal to a second value (P x) depending on the power carried in the cable through a second function, the second function corresponding to the first function multiplied by a factor k, k being higher than 0 and lower than 1.