Electrical supply system of an aircraft, said system comprising at least a first electrical source and a second electrical source, which are coupled together in order to electrically supply a group of electrical loads (Z1, Z2, Z3... Zn) of the aircraft, as well as a controller configured to control the first electrical source and the second electrical source, the first electrical source being mechanically coupled to a primary energy source, to which at least one energy consumer other than the first electrical source is also coupled, wherein the controller is configured to: - determine an instantaneous electrical consumption consumed by said group of electrical loads; the controller furthermore being configured to: - determine an instantaneous nominal power (P 12) capable of being delivered by the primary energy source; - determine an instantaneous power (P 16) drawn by the at least one energy consumer from the primary energy source; and - control the first electrical source and the second electrical source so that: - on the one hand the power (PP S1) drawn by the first electrical source from the primary energy source corresponds to a difference between the instantaneous nominal power (P 12) capable of being delivered by the primary energy source and the instantaneous power (P 16) drawn by the at least one energy consumer, so as to ensure that the mechanical power drawn by the first electrical source and by the at least one energy consumer is never greater than the instantaneous nominal power capable of being delivered by the primary energy source, and - on the other hand an electrical power (P S2) delivered by the second electrical source is such that the sum of an electrical power (P S1) delivered by the first electrical source and the electrical power delivered by the second electrical source corresponds to the instantaneous electrical consumption. wherein the controller is configured to: - determine an instantaneous electrical consumption consumed by said group of electrical loads; - determine an instantaneous electrical consumption consumed by said group of electrical loads; the controller furthermore being configured to: - determine an instantaneous nominal power (P 12) capable of being delivered by the primary energy source; - determine an instantaneous power (P 16) drawn by the at least one energy consumer from the primary energy source; and - control the first electrical source and the second electrical source so that: - on the one hand the power (PP S1) drawn by the first electrical source from the primary energy source corresponds to a difference between the instantaneous nominal power (P 12) capable of being delivered by the primary energy source and the instantaneous power (P 16) drawn by the at least one energy consumer, so as to ensure that the mechanical power drawn by the first electrical source and by the at least one energy consumer is never greater than the instantaneous nominal power capable of being delivered by the primary energy source, and - on the other hand an electrical power (P S2) delivered by the second electrical source is such that the sum of an electrical power (P S1) delivered by the first electrical source and the electrical power delivered by the second electrical source corresponds to the instantaneous electrical consumption. - determine an instantaneous nominal power (P 12) capable of being delivered by the primary energy source; - determine an instantaneous power (P 16) drawn by the at least one energy consumer from the primary energy source; and - control the first electrical source and the second electrical source so that: - on the one hand the power (PP S1) drawn by the first electrical source from the primary energy source corresponds to a difference between the instantaneous nominal power (P 12) capable of being delivered by the primary energy source and the instantaneous power (P 16) drawn by the at least one energy consumer, so as to ensure that the mechanical power drawn by the first electrical source and by the at least one energy consumer is never greater than the instantaneous nominal power capable of being delivered by the primary energy source, and - on the other hand an electrical power (P S2) delivered by the second electrical source is such that the sum of an electrical power (P S1) delivered by the first electrical source and the electrical power delivered by the second electrical source corresponds to the instantaneous electrical consumption. - on the one hand the power (PP S1) drawn by the first electrical source from the primary energy source corresponds to a difference between the instantaneous nominal power (P 12) capable of being delivered by the primary energy source and the instantaneous power (P 16) drawn by the at least one energy consumer, so as to ensure that the mechanical power drawn by the first electrical source and by the at least one energy consumer is never greater than the instantaneous nominal power capable of being delivered by the primary energy source, and - on the other hand an electrical power (P S2) delivered by the second electrical source is such that the sum of an electrical power (P S1) delivered by the first electrical source and the electrical power delivered by the second electrical source corresponds to the instantaneous electrical consumption.