Method and device for operating an energy store

Abstract

An energy store has at least one energy storage module with a plurality of energy storage cells. The energy storage cells are each electrically coupled to a monitoring unit. Each monitoring unit is designed to discharge the respective energy storage cell by use of a specified symmetry current in an active operating state. The method operates the energy store by performing the acts of: detecting an open-circuit voltage of each energy store cell and determining a discharge duration for each energy storage cell as a function of the open-circuit voltage of the energy storage cell and a specified target discharge voltage value; and controlling each monitoring unit in order to discharge the respective energy storage cell by use of the specified symmetry current for the discharge duration associated with the respective energy storage cell.

Claims

1. A method for operating an energy store comprising at least one energy storage module having a plurality of energy storage cells, which are each electrically coupled to a respective different monitoring unit that discharges the coupled energy storage cell by use of a specified symmetry current in an active operating state, the method comprises the acts of: detecting an open-circuit voltage of each energy storage cell; drawing, by each monitoring unit, a specified operating current from the coupled energy storage cell that enables the respective monitoring unit to discharge the coupled energy storage cell by use of the specified symmetry current; determining a discharge duration for each energy storage cell as a function of the detected open-circuit voltage of the energy storage cell, a specified target discharge voltage value, and the specified operating current, such that: ${t\_\mathrm{aktiv}}_{m,z}=\frac{\mathrm{U\_global}\mathrm{\_min}-{\mathrm{OCV}}_{m,z}}{C.Math.I_S}+\frac{I_{\mathrm{SG}}}{I_S}.Math.\frac{\mathrm{U\_modul}\mathrm{\_max}-\mathrm{U\_global}\mathrm{\_min}}{C.Math.I_S+I_{\mathrm{SG}}}$ where t_aktiv.sub.m,z is the discharge duration, U_global_min is the target discharge voltage value, U_modul_max is the maximum cell voltage for the energy storage module, OCV.sub.m,z is the open-circuit voltage of the energy storage cell, C is a specified increase of an open-circuit voltage characteristic curve, I.sub.SG is operating current, and I.sub.S is the symmetry current; and controlling each monitoring unit in order to discharge the respective energy storage cell coupled to each such monitoring unit by use of the specified symmetry current for the discharge duration associated with the respective energy storage cell, wherein the specified symmetry current used by each monitoring unit to discharge each respectively coupled energy storage cell is equal for each monitoring unit.

2. The method according to claim 1, wherein the maximum cell voltage for the energy storage module is respectively determined as a function of the open-circuit voltages of each energy storage cell of the energy storage module.

3. The method according to claim 1, wherein the specified increase is determined as a function of a state of charge detected for the energy storage cell.

4. The method according to claim 1, wherein the target discharge voltage value is determined as a function of the open-circuit voltages detected for a specified first number of energy storage cells.

5. The method according to claim 1, further comprising the acts of: respectively determining a minimum open-circuit voltage for each energy storage module as a function of the open-circuit voltages of the respective energy storage cells of said energy storage module; determining a cell discharge voltage for the respective energy storage module as a function of the minimum open-circuit voltage of the respective energy storage module; and determining the target discharge voltage value as a function of the cell discharge voltages determined for a second number of energy storage modules.

6. The method according to claim 5, wherein the cell discharge voltage for each energy storage module is determined as a function of the maximum cell voltage of the energy storage module.

7. The method according to claim 5, wherein the cell discharge voltage for each energy storage module is determined as a function of a ratio of the symmetry current to the operating current of the monitoring unit.

8. The method according to claim 6, wherein the cell discharge voltage for each energy storage module is determined as a function of a ratio of the symmetry current to the operating current of the monitoring unit.

9. The method according to claim 1, wherein the respective monitoring unit has an active operating state and a passive operating state, wherein in the active operating state the monitoring unit discharges the energy storage cell by way of the specified symmetry current and the operating current drawn from the energy storage cell, and wherein in the passive operating state the monitoring unit discharges the energy storage cell by way of the operating current and draws the specified operating current from the energy storage cell but does not discharge the energy storage cell by way of the specified symmetry current.

10. An energy store, comprising: at least one energy storage module having a plurality of energy storage cells; at least one monitoring unit, each of the plurality of energy storage cells being electrically coupled to a respective different monitoring unit, wherein each respective monitoring unit is operatively configured to discharge the respective electrically coupled energy storage cell via a specified symmetry current in an active operating state of the respective monitoring unit, and wherein each monitoring unit draws a specified operating current from the coupled energy storage cell to enable the respective monitoring unit to discharge the coupled energy storage cell by use of the specified symmetry current; a control unit operatively configured to operate the energy store, the control unit comprising a memory having program code stored therein that: detects an open-circuit voltage of each energy storage cell; determines a discharge duration of each energy storage cell as a function of the detected open-circuit voltage of the energy storage cell, a specified target discharge value, and the specified operating current, such that: ${t\_\mathrm{aktiv}}_{m,z}=\frac{\mathrm{U\_global}\mathrm{\_min}-{\mathrm{OCV}}_{m,z}}{C.Math.I_S}+\frac{I_{\mathrm{SG}}}{I_S}.Math.\frac{\mathrm{U\_modul}\mathrm{\_max}-\mathrm{U\_global}\mathrm{\_min}}{C.Math.I_S+I_{\mathrm{SG}}}$ where t_aktiv.sub.m,z is the discharge duration, U_global_min is the target discharge voltage value, U_modul_max is the maximum cell voltage for the energy storage module, OCV.sub.m,z is the open-circuit voltage of the energy storage cell, C is a specified increase of an open-circuit voltage characteristic curve, I.sub.SG is operating current, and I.sub.S is the symmetry current; and controls each monitoring unit in order to discharge the respective energy storage cell coupled to each such monitoring unit by use of the specified symmetry current for the discharge duration associated with the respective energy storage cell, wherein the specified symmetry current used by each monitoring unit to discharge each respectively coupled energy storage cell is equal for each monitoring unit.

11. The energy store according to claim 10, wherein the memory of the control unit further has program code stored therein that operates the respective monitoring unit in an active operating state and in a passive operating state, wherein in the active operating state the monitoring unit discharges the energy storage cell by way of the specified symmetry current and the operating current drawn from the energy storage cell, and wherein in the passive operating state the monitoring unit discharges the energy storage cell by way of the operating current and draws the specified operating current from the energy storage cell but does not discharge the energy storage cell by way of the specified symmetry current.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a first model depiction of an energy store;

(2) FIGS. 2a and 2b provide a second model depiction of an energy store;

(3) FIGS. 3a-3c provide a model depiction for a symmetrization of the energy storage cells;

(4) FIG. 4 is a time diagram;

(5) FIG. 5 is a flow chart for a program for operating the energy store;

(6) FIG. 6 is a diagram showing progression of the state of charge of a plurality of energy storage cells during the symmetrization phase;

(7) FIG. 7 is a diagram showing the state of charge of a plurality of energy storage cells at the end of the symmetrization phase; and

(8) FIG. 8 is a diagram showing an additional progression of the state of charge of a plurality of energy storage cells after the symmetrization phase.

DETAILED DESCRIPTION OF THE DRAWINGS

(9) FIG. 1 shows a model depiction of an energy store. The energy store has a plurality of energy storage modules EM.sub.m, for example four energy storage modules EM.sub.m. Each energy storage module EM.sub.m includes a plurality of energy storage cells for example three energy storage cells EZ.sub.m,z. Each energy storage module EM.sub.m preferably has an identical number of energy storage cells EZ.sub.m,z, which are designed similarly with respect to materials and construction technology. The energy storage cells EZ.sub.m,z have at least, in part, different states of charge (SOC).

(10) Each energy storage cell EZ.sub.m,z is respectively coupled to a monitoring unit, which is designed to discharge the respective energy storage cell EZ.sub.m,z by way of a specified symmetry current I.sub.S. The symmetry current I.sub.S is preferably approximately equal, in particularly identically equal for all monitoring units. The symmetry current I.sub.S is, for example, approximately 60 mA.

(11) The monitoring unit has, for example, a switchable resistor. If, for example, the switchable resistor has a first switch position, the associated energy storage cell EZ.sub.m,z can be discharged via said resistor. If the switchable resistor has, for example, a second switch position, the associated energy storage cell EZ.sub.m,z cannot be discharged via said resistor.

(12) The monitoring unit can require a specified operating current I.sub.SG in an active and in a passive operating state, which current is preferably drawn from the associated energy storage cell EZ.sub.m,z. The operating current I.sub.SG is, for example, approximately 25 mA. The active operating state of the monitoring unit can be characterized in that the monitoring unit draws the specified operating current I.sub.SG from the associated energy storage cell EZ.sub.m,z and the switchable resistor is in the first switch position, so that the monitoring unit actively discharges the energy storage cell EZ.sub.m,z by use of the specified symmetry current I.sub.S. The passive operating state of the monitoring unit can be characterized in that the monitoring unit draws the specified operating current I.sub.SG from the associated energy storage cell EZ.sub.m,z, however, the switchable resistor is in the second switch position, so that the energy storage cell EZ.sub.m,z is not actively discharged by use of the symmetry current I.sub.S.

(13) In an active operating state, the monitoring unit discharges the energy storage cell EZ.sub.m,z by way of the symmetry current I.sub.S and the operating current I.sub.SG (FIG. 2a). While the monitoring unit is in an active operating state, the associated energy storage cell EZ.sub.m,z is actively discharged. In a passive operating state, the monitoring unit discharges the energy storage cell EZ.sub.m,z by way of the operating current I.sub.SG (FIG. 2b). While the monitoring unit is in a passive operating state, the associated energy storage cell EZ.sub.m,z is passively discharged. A duration, during which the monitoring unit is in an active and/or in a passive operating state, can be designated as awake time T_wach,m of the monitoring unit.

(14) The respective monitoring units can be designed in such a way that a discharge of at least one of the energy storage cells EZ.sub.m,z of the energy storage module EM.sub.m requires that all monitoring units are in the active operating state and/or the passive operating state during a duration of the discharge of at least one energy storage cell EZ.sub.m,z.

(15) FIG. 3 illustrates a discharge of the energy storage cell EZ.sub.m,z during a symmetrization phase. Prior to the symmetrization phase (FIG. 3a), the energy storage cells EZ.sub.m,z have at least in part different states of charge as illustrated.

(16) During the symmetrization phase (FIG. 3b), insofar as not all energy storage cells EZ.sub.m,z of each energy storage module EM.sub.m have a minimum state of charge, all energy storage cells EZ.sub.m,z of the energy storage module EM.sub.m are each actively and/or passively discharged.

(17) After completion of the symmetrization phase (FIG. 3c), all energy storage cells EZ.sub.m,z of the energy store have approximately the identical state of charge, in particular the identical state of charge.

(18) The discharge of the energy storage cell EZ.sub.m,z having a highest state of charge requires a certain time duration. During this time duration, the energy storage cell EZ.sub.m,z of the energy storage module EM.sub.m having a lowest state of charge is also passively or actively discharged.

(19) FIG. 4 shows, respectively, a time diagram for a first and a second energy storage module EM.sub.m. The monitoring units of the first energy storage module EM.sub.m have a first awake time T_wach,1, and the monitoring units of the second energy storage module EM.sub.m have a second awake time T_wach,2. The first awake time T_wach,1 and the second awake time T_wach,2 are different in size. For example, during the first awake time T_wach,1, the monitoring units of the first energy storage module EM.sub.1 are respectively in the active or in the passive operating state for different lengths of time.

(20) FIG. 5 shows a flow chart for a program for operating the energy store. After a start of the program, an open-circuit voltage OCV.sub.m,z of the respective energy storage cell EZ.sub.m,z is detected in a first step S10.

(21) In a step S20, for example a cell discharge voltage U_modul_min,m is determined. For this purpose, for example in a subroutine step 21, a minimum open-circuit voltage OCV_modul_min,m is determined for the respective energy storage module EM.sub.m as a function of the open-circuit voltage OCV.sub.m,z of the respective energy storage cell EZ.sub.m,z of said energy storage module EM.sub.m. For example, the minimum open-circuit voltage OCV_modul_min,m of the energy storage module EM.sub.m can be determined according to Equation 1:
OCV_modul_min,m=min(OCV.sub.1,m, . . . ,OCV.sub.z,m, . . . ,OCV.sub.Z,m)  (Equation 1)

(22) where z=1 to Z, wherein Z represents for example the total number of energy storage cells EZ.sub.m,z of the energy storage module EM.sub.m.

(23) Furthermore, in a subroutine step 23, a maximum open-circuit voltage U_modul_max,m is determined for the energy storage module EM.sub.m as a function of the open-circuit voltage OCV.sub.m,z of the respective energy storage cell EZ.sub.m,z of said energy storage module EM.sub.m. For example the maximum open-circuit voltage U_modul_max,m in of the energy storage module EM.sub.m can be determined according to Equation 2:
U_modul_max,m=max(OCV.sub.1,m, . . . ,OCV.sub.z,m, . . . ,OCV.sub.Z,m)  (Equation 2)

(24) where z=1 to Z, wherein Z represents for example the total number of energy storage cells EZ.sub.m,z of the energy storage module EM.sub.m.

(25) In a subroutine step 25, the cell discharge voltage U_modul_min,m is determined for the respective energy storage module EM.sub.m as a function of the minimum open-circuit voltage OCV_modul_min,m and of the maximum cell voltage U_modul_max,m of the respective energy storage module EM.sub.m, as well as a function of the ratio of the symmetry current I.sub.S to the operating current I.sub.SG. For example, the cell discharge voltage U_modul_min,m of the energy storage module EM.sub.m can be determined according to Equation 3:

(26) $\begin{array}{cc}\mathrm{U\_modul}\mathrm{\_min},m-=\min \left[\begin{array}{c}-\frac{I_{\mathrm{SG}}}{I_S}*\left(\begin{array}{c}\mathrm{U\_modul}\mathrm{\_max},\\ m-\mathrm{OCV\_modul}\mathrm{\_min},m\end{array}\right)+\\ \mathrm{OCV\_modul}\mathrm{\_min},m\end{array}\right]& \left(\mathrm{Equation}3\right)\end{array}$

(27) In a step S30, for example, the target discharge voltage value U_global_min is determined as a function of the determined cell discharge voltage U_modul_min,m of a second number M of energy storage modules EM.sub.m. For example, the target discharge voltage value U_global_min of the energy storage module EM.sub.m can be determined according to Equation 4:
U_global_min=min(U_modul_min,1; . . . ;U_modul_min,m; . . . ; U_modul_min,M)  (Equation 4)

(28) where m=1 to M, wherein M represents for example the total number of energy storage modules EM.sub.m of the energy store.

(29) In a step S40, for example, an active discharge time t_aktiv.sub.m,z is determined for the respective energy storage cell EZ.sub.m,z as a function of the specified symmetry current I.sub.S, the specified operating current I.sub.SG, a specified increase C of an open-circuit voltage characteristic OCV_SOC of the energy storage cell EZ.sub.m,z, the target discharge voltage value U_global_min, and the maximum cell voltage U_modul_max,m of the energy storage module EM.sub.m, which includes the energy storage cell EZ.sub.m,z. For example, the discharge duration t_aktiv.sub.m,z for the respective energy storage cell EZ.sub.m,z can be determined according to Equation 5:

(30) $\begin{array}{cc}{\mathrm{t\_aktiv}}_{m,z}=\frac{\mathrm{U\_global}\mathrm{\_min}-{\mathrm{OCV}}_{m,z}}{C*I_S}+\frac{I_{\mathrm{SG}}}{I_S}*\frac{\mathrm{U\_modul}\mathrm{\_max},-\mathrm{U\_global}\mathrm{\_min}}{C*\left(I_S+I_{\mathrm{SG}}\right)}& \left(\mathrm{Equation}5\right)\end{array}$

(31) In a step S50, for example, the respective monitoring unit for discharging the respective energy storage cell EZ.sub.m,z is controlled by use of the specified symmetry current I.sub.S for the discharge duration t_aktiv.sub.m,z associated with the respective energy storage cell EZ.sub.m,z.

(32) A device for operating the energy store can, for example, have a processing unit such as a central processing unit, with a program and data memory, and can be designed to execute the program for operating the energy store described in FIG. 5. The device for the operation can, for example, be part of a central energy store management system.

(33) FIGS. 6 to 8 show the progression of the state of charge SOC.sub.m,z of a plurality of energy storage cells EZ.sub.m,z for example for 96 energy storage cells EZ.sub.m,z during the symmetrization phase. The energy storage cells EZ.sub.m,z have, respectively, the open-circuit voltage characteristic OCV_SOC shown in FIG. 6. A maximum open-circuit voltage range of an energy storage cell EZ.sub.m,z can be limited by a specified lower limit open-circuit voltage Umin_grenz and a specified upper limit open-circuit voltage Umax_grenz. The upper limit open-circuit voltage Umax_grenz can, for example, be specified by a manufacturer.

(34) The open-circuit voltage characteristic OCV_SOC has, for example, a hysteresis with a charge curve LK and a discharge curve EK. The charge curve LK characterizes the open-circuit voltage OCV.sub.m,z of the energy storage cells EZ.sub.m,z as a function of the respective state of charge SOC.sub.m,z, which the energy storage cell EZ.sub.m,z has after a longer charging phase. The discharge curve EK characterizes the open-circuit voltage OCV.sub.m,z of the energy storage cells EZ.sub.m,z as a function of the state of charge SOC.sub.m,z, which the energy storage cell EZ.sub.m,z has after a longer discharge phase. For example, the energy storage cells EZ.sub.m,z all respectively have an operating point at the beginning of the symmetrization phase, which operating point is characterized by the respective open-circuit voltage OCV.sub.m,z and the respective state of charge SOC.sub.m,z of the energy storage cell EZ.sub.m,z, which operating point can be associated with the charge curve LK. The energy storage cells EZ.sub.m,z can have different states of charge and thus also different open-circuit voltages.

(35) The energy storage cells EZ.sub.m,z are, respectively, discharged for the discharge duration t_aktiv.sub.m,z associated with the respective energy storage cell EZ.sub.m,z by means of the specified symmetry current I.sub.S. After the discharge of the respective energy storage cells EZ.sub.m,z, at the end of the symmetrization phase, the energy storage cells EZ.sub.m,z each have the identical state of charge (see FIG. 7). The symmetrization can thus take place independently from the hysteresis of the open-circuit voltage characteristic OCV_SOC. The respective open-circuit voltages OCV.sub.m,z can, however, be different after the symmetrization. The open-circuit voltage OCV.sub.m,z of the respective energy storage cell EZ.sub.m,z does not follow the charge curve LK during discharging, but instead an intermediate curve specific to the respective energy storage cell EZ.sub.m,z, which curve runs in the direction of the discharge curve EK. After completion of the symmetrization phase (see FIG. 8), the open-circuit voltage OCV.sub.m,z of the respective energy storage cell EZ.sub.m,z follows the respective intermediate curve ZK of the energy storage cell EZ.sub.m,z as a function of a specified operating mode of the energy store, for example a specified discharge of the energy store to supply electrical consumers in a vehicle or a specified charging of the energy store.

(36) The following specifies a derivation of the equation for the discharge duration t_aktiv.sub.m,z. For a current voltage of the energy storage cell EZ.sub.m,z, equation (a1) applies:
U(t)=−C*(I.sub.SG+I.sub.S)*t+OCV.sub.m,z  (a1)

(37) Where

(38) U: current voltage of the energy storage cell EZ.sub.m,z [V]

(39) OCV.sub.m,z: open-circuit voltage of the energy storage cell EZ.sub.m,z [V]

(40) C: increase of the open-circuit voltage characteristic OCV_SOC [V/(A*min)]. The increase of the open-circuit voltage characteristic OCV_SOC is not constant, but instead is a function of the state of charge SOC. To increase the precision of the symmetrization, the increase C can also be determined as a function of the state of charge SOC.

(41) I.sub.SG=operating current [A] of the monitoring unit

(42) I.sub.S=symmetry current [A]

(43) It is initially assumed that the energy storage cell EZ.sub.m,z having the lowest cell voltage in the energy storage module EM.sub.m is not actively discharged. In order to determine the cell discharge voltage U_modul_min,m within an energy storage module EM.sub.m, initially only the discharge is considered by the operating current I.sub.SG. Equation (a1) becomes:
U′.sub.min(T′.sub.wach)=−C*I.sub.SG*T′.sub.wach+U.sub.min  (a2)

(44) Where

(45) Umin=OCV_modul_min,m

(46) T′wach=equalization time to equalize all energy storage cells EZ.sub.m,z in the one energy storage module EM.sub.m; this equalization time is a mathematical intermediate variable, since the symmetrization must be implemented within all energy storage modules EM.sub.m.

(47) U′min=U_modul_min,m; cell discharge voltage within an energy storage module EM.sub.m, which represents a minimum cell voltage in the energy storage module EM.sub.m after the passive discharge due to the operating current of the monitoring unit.

(48) The energy storage cell EZ.sub.m,z, having the largest cell voltage is actively discharged in the energy storage module EM.sub.m for the entire equalization time. In addition to equation (a1), (a3) applies:
U_modul_min,m(T′.sub.wach)=−C*(I.sub.SG+I.sub.S)*T′.sub.wach+U.sub.max  (a3)

(49) where U.sub.max=U_modul_max,m: maximum cell voltage of the energy storage module EM.sub.m.

(50) After the equalization time T′.sub.wach, all energy storage cells EZ.sub.m,z in the energy storage module EM.sub.m have mathematically the same voltage. For this reason, the two previous equations correspond to the identical value. The cell discharge voltage U_modul_min,m can be determined by means of equation (a2) and (a3):

(51) $\begin{array}{cc}\mathrm{U\_modul}\mathrm{\_min},m=-\frac{I_{\mathrm{SG}}}{I_S}*\left(U_{\mathrm{ma}x}-U_{min}\right)+U_{min}& \left(\mathrm{a4}\right)\end{array}$

(52) In the following, a global minimum, i.e. the target discharge voltage value U_global_min, is determined. For the target discharge voltage value U_global_min, equation (a5) applies:
U_global_min=min(U_modul_min,1; . . . ;U_modul_min,M,)  (a5)

(53) Furthermore, the awake time T_wach,m can be determined for each monitoring unit:
ΔU.sub.SG(T_wach,m)=−C*I.sub.SG*T_wach,m  (a6)

(54) Equation (a6) defines a calculated voltage drop for each energy storage cell EZ.sub.m,z after the symmetrization due to the operating current I.sub.SG. A calculated total voltage drop for each energy storage cell EZ.sub.m,z is a function of the sum of the voltage drops due to the active discharge and the passive discharge.
U(T.sub.Ende)−U(T.sub.0)=ΔU.sub.SG+ΔU.sub.aktiveEntl.  (a7)

(55) The voltage at the end of the symmetrization (T.sub.Ende) is identical to the target discharge voltage value U_global_min.
U_global_min−OCV.sub.m,z=ΔU.sub.SG+ΔU.sub.aktiveEntl.  (a8)
ΔU.sub.aktiveEntl.=U_global_min−OCV.sub.m,z−ΔU.sub.SG  (a9)

(56) For the calculated voltage drop due to the active discharge by the symmetry current I.sub.S, equation (a10) applies:
ΔU.sub.aktiveEntl.=−C*I.sub.S*t.sub.aktiveEntl.  (a10)

(57) By this means, a first equation for the discharge duration t_aktive.sub.m,z can be specified for each energy storage cell EZ.sub.m,z:

(58) $\begin{array}{cc}{\mathrm{t\_aktive}}_{m,k}=-\frac{\Delta U_{\mathrm{aktiveEntl}.}}{C*I_S}& \left(\mathrm{a11}\right)\end{array}$

(59) Furthermore, the awake time T_wach,m can be determined for each monitoring unit. The awake time T_wach,m of the associated monitoring unit can be determined for each energy storage module EM.sub.m as a function of the largest discharge duration t_aktiv.sub.m,z in the energy storage module EM.sub.m:
T_wach,m=max(t_akvive.sub.m,1,t_akvive.sub.m,2, . . . ,t_akvive.sub.m,Z)  (a12)

(60) i.e., from the energy storage cell EZ.sub.m,z having the maximum open-circuit voltage of the energy storage module EM.sub.m.

(61) Applying (a6) and (a9) results in:
ΔU.sub.aktiveEntl.=U_global_min−U_modul_max,m+C*I.sub.SG*T_wach,m  (a13)

(62) Applying (a13), (a10), and (a12) results in:

(63) $\begin{array}{cc}\max \left(t_{\mathrm{aktiveEntl}.}\right)=\mathrm{T\_wach},m=-\frac{\begin{array}{c}\mathrm{U\_global}\mathrm{\_min}-\mathrm{U\_modul}\mathrm{\_max},\\ m+C*I_{\mathrm{SG}}*\mathrm{T\_wach},m\end{array}}{C*I_S}& \left(\mathrm{a14}\right)\\ \mathrm{T\_wach},m=\frac{\mathrm{U\_modul}\mathrm{\_max},m-\mathrm{U\_global}\mathrm{\_min}}{C*\left(I_S+I_{\mathrm{SG}}\right)}& \left(a15\right)\end{array}$

(64) Applying equations (a11), (a13), and (a15), the discharge duration t_aktive.sub.m,z can be determined according to equation (a16):

(65) $\begin{array}{cc}{\mathrm{t\_active}}_{m,z}=-\frac{\mathrm{U\_global}\mathrm{\_min}-{\mathrm{OCV}}_{m,z}+C*I_{\mathrm{SG}}*\mathrm{T\_wach},m}{C*I_S}& \left(\mathrm{a16}\right)\end{array}$

LIST OF REFERENCE NUMERALS

(66) EM.sub.m Energy storage module EZ.sub.m,z Energy storage cell SOC.sub.m,z State of charge of an energy storage cell I.sub.S Symmetry current I.sub.SG Operating current OCV Open-circuit voltage SOC State of charge OCV.sub.m,z Open-circuit voltage of an energy storage cell T_wach,m Awake time EM.sub.1 First energy storage module EM.sub.2 Second energy storage module EZ.sub.1 . . . 2, 1 . . . 3 Energy storage cells of the first and the second energy storage module T_wach,1; First awake time T_wach,2 Second awake time OCV_SOC Open-circuit voltage characteristic LK Charge curve EK Discharge curve Umin_grenz Lower limit open-circuit voltage Umax_grenz Upper limit open-circuit voltage SOC_min Lower limit state of charge SOC_max Upper limit state of charge SOC_Nutzhub Usable state of charge amount t_aktiv.sub.m,z Discharge duration of an energy storage cell U_global_min Target discharge voltage value U_modul_max,m Maximum cell voltage of an energy storage module OCV_modul_min,m Minimum open-circuit voltage of an energy storage module U_modul_min,m Cell discharge voltage

(67) The foregoing disclosure has been set forth merely to illustrate the invention and is not intended to be limiting. Since modifications of the disclosed embodiments incorporating the spirit and substance of the invention may occur to persons skilled in the art, the invention should be construed to include everything within the scope of the appended claims and equivalents thereof.