A battery exchange system for a battery powered electric vehicle, comprising: - an interchangeable battery block; - a battery dock defined at the underside of the electric vehicle and open downwards, said battery dock being adapted to receive the battery block for electrical and mechanical connection by vertical fitting when such battery is lifted from beneath the electric vehicle, said battery block being in a predetermined reference position, defined in a horizontal plane, relative to the electric vehicle when said battery block is electrically and mechanically connected to the battery dock; - a battery lift for lifting the battery block underneath the electric vehicle; wherein: - said battery block has an external casing including a peripheral wall and said peripheral wall has a pyramid shaped part (14, 15) forming at least one bevel shaped male part; - said battery dock has an internal casing including an internal peripheral wall and said internal peripheral wall has a pyramid shaped internal part (24, 25) forming at least one bevel shaped female part; - said battery block and said battery dock have guides (14, 15, 24, 25) adapted to mutually cooperate for guiding the battery block horizontally toward the reference position when the battery block is lifted for fitting with the battery dock, wherein said guides include said at least one bevel shaped male part (14, 15) and said at least one bevel shaped female part (24, 25) which is adapted to receive said bevel shaped male part; - said guides (14, 15, 24, 25) include sliding surfaces (14, 15, 24, 25; 14a, 15a; 14c, 15c) which are adapted to slide on one another freely for said guiding of said battery block horizontaly toward said reference position; and the battery lift is adapted to let the battery block move freely horizontally relative to the electric vehicle when the battery block is lifted for fitting with the battery dock and guided horizontally toward the reference position, wherein the battery lift includes a platform for supporting the battery block and a lift assembly for raising and lowering the platform; characterized in that said battery block being freely movable horizontally on the platform, wherein said battery block is horizontally slidable on the platform or rollingly supported on the platform so as to be freely movable on the platform. - an interchangeable battery block; - a battery dock defined at the underside of the electric vehicle and open downwards, said battery dock being adapted to receive the battery block for electrical and mechanical connection by vertical fitting when such battery is lifted from beneath the electric vehicle, said battery block being in a predetermined reference position, defined in a horizontal plane, relative to the electric vehicle when said battery block is electrically and mechanically connected to the battery dock; - a battery lift for lifting the battery block underneath the electric vehicle; - said battery block has an external casing including a peripheral wall and said peripheral wall has a pyramid shaped part (14, 15) forming at least one bevel shaped male part; - said battery dock has an internal casing including an internal peripheral wall and said internal peripheral wall has a pyramid shaped internal part (24, 25) forming at least one bevel shaped female part; - said battery block and said battery dock have guides (14, 15, 24, 25) adapted to mutually cooperate for guiding the battery block horizontally toward the reference position when the battery block is lifted for fitting with the battery dock, wherein said guides include said at least one bevel shaped male part (14, 15) and said at least one bevel shaped female part (24, 25) which is adapted to receive said bevel shaped male part; - said guides (14, 15, 24, 25) include sliding surfaces (14, 15, 24, 25; 14a, 15a; 14c, 15c) which are adapted to slide on one another freely for said guiding of said battery block horizontaly toward said reference position;