A power source device comprising: a first power storage element; a second power storage element that is connected in parallel to the first power storage element, the second power storage element having a lower internal resistance than an internal resistance of the first power storage element and a lower storage capacity than a storage capacity of the first power storage element; an opening and closing part that is connected between the first power storage element and the second power storage element, the opening and closing part switching between a disconnection state and a connection state; a charge circuit that is connected to an input route of the first power storage element, the charge circuit performing a step-down operation; a discharge circuit that is connected to an output route of the second power storage element, the discharge circuit performing a step-up operation; and a controller that controls operations of the opening and closing part, the charge circuit, and the discharge circuit, wherein when the opening and closing part is in the disconnection state, the first power storage element is disconnected from the second power storage element, the charge circuit performs the step-down operation to charge the first power storage element, and the discharge circuit stops operating, the discharge circuit stops operating over a predetermined time after the opening and closing part has switched from the disconnection state to the connection state, and after the predetermined time has passed since switching of the opening and closing part from the disconnection state to the connection state, the discharge circuit starts the step-up operation to discharge electric power stored in the second power storage element and the first power storage element. a first power storage element; a second power storage element that is connected in parallel to the first power storage element, the second power storage element having a lower internal resistance than an internal resistance of the first power storage element and a lower storage capacity than a storage capacity of the first power storage element; an opening and closing part that is connected between the first power storage element and the second power storage element, the opening and closing part switching between a disconnection state and a connection state; a charge circuit that is connected to an input route of the first power storage element, the charge circuit performing a step-down operation; a discharge circuit that is connected to an output route of the second power storage element, the discharge circuit performing a step-up operation; and a controller that controls operations of the opening and closing part, the charge circuit, and the discharge circuit, wherein when the opening and closing part is in the disconnection state, the first power storage element is disconnected from the second power storage element, the charge circuit performs the step-down operation to charge the first power storage element, and the discharge circuit stops operating, the discharge circuit stops operating over a predetermined time after the opening and closing part has switched from the disconnection state to the connection state, and after the predetermined time has passed since switching of the opening and closing part from the disconnection state to the connection state, the discharge circuit starts the step-up operation to discharge electric power stored in the second power storage element and the first power storage element.