A traction energy storage system for a vehicle, comprising: multiple electrical energy stores, wherein each of the energy stores comprises multiple cell modules electrically connected via busbars, one or more contactors and an energy store controller for controlling the cell modules and the contactor or contactors, and each of the cell modules comprises multiple storage cells and a cell module controller, wherein the contactor or contactors in each energy store are designed to connect the busbars of the energy store to an energy store high-voltage interface of the respective energy store, as specified by the energy store controller, in a closed position of the contactor or contactors and to isolate said busbars in an open position of the contactor or contactors, and wherein the energy store high-voltage interfaces of the energy stores are connected in parallel in the traction energy storage system; and a system controller operatively connected to the energy store controllers, which is designed to produce the closed position of the contactors of all the energy stores in an operating state of the traction energy storage system, to receive signals indicating an energy storage state (612; 614) of the energy stores from the respective energy store controllers; to produce the open position of the contactors of the energy stores for a measurement phase of a run-on state, wherein the received energy storage states (612; 614) are based on an open-circuit voltage of the respective energy store measured in the measurement phase, and to produce the closed position of the contactors of at least two of the energy stores, which are a genuine subset of all the energy stores, in the run-on state of the traction energy storage system, wherein, in the run-on state, the closed contactors connect the at least two energy stores via their parallel-connected energy store high-voltage interfaces for the purpose of charge exchange in order to equalize an inequality of the energy storage states (612; 614) that has arisen in the operating state, and to terminate the run-on state and to begin an idle state if there is less than a prescribed difference between the energy storage states (612; 614), wherein the system controller is designed to produce the open position of the contactors of all the energy stores in the idle state of the traction energy storage system. multiple electrical energy stores, wherein each of the energy stores comprises multiple cell modules electrically connected via busbars, one or more contactors and an energy store controller for controlling the cell modules and the contactor or contactors, and each of the cell modules comprises multiple storage cells and a cell module controller, wherein the contactor or contactors in each energy store are designed to connect the busbars of the energy store to an energy store high-voltage interface of the respective energy store, as specified by the energy store controller, in a closed position of the contactor or contactors and to isolate said busbars in an open position of the contactor or contactors, and wherein the energy store high-voltage interfaces of the energy stores are connected in parallel in the traction energy storage system; and a system controller operatively connected to the energy store controllers, which is designed to produce the closed position of the contactors of all the energy stores in an operating state of the traction energy storage system, to receive signals indicating an energy storage state (612; 614) of the energy stores from the respective energy store controllers; to produce the open position of the contactors of the energy stores for a measurement phase of a run-on state, wherein the received energy storage states (612; 614) are based on an open-circuit voltage of the respective energy store measured in the measurement phase, and to produce the closed position of the contactors of at least two of the energy stores, which are a genuine subset of all the energy stores, in the run-on state of the traction energy storage system, wherein, in the run-on state, the closed contactors connect the at least two energy stores via their parallel-connected energy store high-voltage interfaces for the purpose of charge exchange in order to equalize an inequality of the energy storage states (612; 614) that has arisen in the operating state, and to terminate the run-on state and to begin an idle state if there is less than a prescribed difference between the energy storage states (612; 614), wherein the system controller is designed to produce the open position of the contactors of all the energy stores in the idle state of the traction energy storage system.