A controller for a power supply system comprising z power supplies connected in parallel, z being a natural number equal to or larger than 2, wherein the controller is configured to determine the number of the power supplies in operation based on values of intersection currents i 1 to i (z-1) which the controller is configured to determine by: identifying loss characteristics with respect to load currents of the z power supplies by use of respective convex functions fl to fz; obtaining a function η n expressing a conversion efficiency of a total load current at the time of operating the n power supplies based on the convex functions f1 to fz, n being a natural number equal to or smaller than z; and obtaining an intersection current i q which is a current of an intersection point between a function η q and a function η (q+1) , q being a natural number equal to or smaller than (z-1), wherein all of the convex functions f1 to fz are equal to a single quadratic polynomial with respect to the load current, characterised in that the controller further comprises: a number storage element which stores the number n of the power supplies in operation; a current detection element which detects a load current of one of the power supplies in operation and outputs a voltage signal corresponding to the load current; a square element which squares the output signal of the current detection element; and threshold generation elements which respectively give a threshold V thL =K ∗ ((n-l)/n) for decreasing the number of power supplies in operation, K being a positive constant, and a threshold V thH =K ∗ ((n+1)/n) for increasing the number of power supplies in operation, and the controller decreases or increases the number n of the power supplies in operation by comparing the output of the square element with the threshold V thL or the threshold VthH. identifying loss characteristics with respect to load currents of the z power supplies by use of respective convex functions fl to fz; obtaining a function η n expressing a conversion efficiency of a total load current at the time of operating the n power supplies based on the convex functions f1 to fz, n being a natural number equal to or smaller than z; and obtaining an intersection current i q which is a current of an intersection point between a function η q and a function η (q+1) , q being a natural number equal to or smaller than (z-1), wherein all of the convex functions f1 to fz are equal to a single quadratic polynomial with respect to the load current, characterised in that the controller further comprises: a number storage element which stores the number n of the power supplies in operation; a current detection element which detects a load current of one of the power supplies in operation and outputs a voltage signal corresponding to the load current; a square element which squares the output signal of the current detection element; and threshold generation elements which respectively give a threshold V thL =K ∗ ((n-l)/n) for decreasing the number of power supplies in operation, K being a positive constant, and a threshold V thH =K ∗ ((n+1)/n) for increasing the number of power supplies in operation, and a number storage element which stores the number n of the power supplies in operation; a current detection element which detects a load current of one of the power supplies in operation and outputs a voltage signal corresponding to the load current; a square element which squares the output signal of the current detection element; and threshold generation elements which respectively give a threshold V thL =K ∗ ((n-l)/n) for decreasing the number of power supplies in operation, K being a positive constant, and a threshold V thH =K ∗ ((n+1)/n) for increasing the number of power supplies in operation, and the controller decreases or increases the number n of the power supplies in operation by comparing the output of the square element with the threshold V thL or the threshold VthH. <EOS>