Method and device for measuring, in real time and in situ, thermodynamic data of a battery (enthalpy and entropy)

12123,915

17/280011

September 26, 2019

The invention relates to a method and a device for measuring, in real time and in situ, thermodynamic data of a battery (enthalpy and entropy). The object of the invention is to provide a reliable method for measuring, in situ, online and in real time, the variation in entropy (ΔS) of a battery. To this end, the method is characterized in that it consists primarily in: (phase I) producing a prior model of the battery: (a) charging the battery; (b) and/or discharging the battery; (c) measuring actual variables; (d) modeling the electrical behavior of the battery during charging (a) and/or discharging (b) in order to estimate the electrical parameters of the battery; (e) estimating electrical parameters of the battery; (f) modeling the thermal behavior of the battery during charging (a) and/or discharging (b) in order to estimate ΔS in situ, online and in real time; (g) estimating ΔS, by using at least one of the electrical parameters estimated in step (d); (phase II) measuring ΔS of the battery during use in any application and with any state of charge by carrying out step (d) and step (f) of phase I, step (c) and step (g); (phase III) optionally storing the data measured/calculated in phase II and/or in phase I. The invention also relates to a method for determining the state of charge and the state of health of a battery on the basis of these thermodynamic data. Another subject of the invention is a device for implementing this method.

INSTITUT POLYTECHNIQUE DE GRENOBLE (Grenoble, FR)

INSTITUT POLYTECHNIQUE DE GRENOBLE (Grenoble, FR)

1. A method for measuring, in situ, online and in real time, thermodynamic data including a variation in entropy ΔS, of at least one battery, the method comprising: a modelling phase: producing a prior model of the battery of which a state of charge (SOC) is comprised between 0 and 100% by implementing: step (a) charging the battery at least partially with a charge current signal Sc, wherein the step (a) is optionally followed by a step (b) discharging the battery at least partially with a discharge current signal Sd; step (c) measuring actual variables useful in the following steps; step (d)modelling electrical behaviour of the battery during the charging step (a) with the charge current signal Sc and/or the discharging step (b) with the discharge current signal Sd, in order to estimate electrical parameters of the battery; step (e) estimating periodically, at a first alternating current frequency Fe, the electrical parameters of the battery; step (f) modelling thermal behaviour of the battery during charging in the step (a) with the charge current signal Sc and/or discharging in the step (b) with the discharge current signal Sd, in order to estimate in situ, online and in real time, at least one of parameters of a thermal model, namely ΔS; step (g)estimating periodically, at a second alternating current frequency Fg, the at least one of the parameters of the thermal model ΔS, by using at least one of the electrical parameters estimated in the step (e); and an estimating phase: estimating thermodynamic data including ΔS of the battery during use in an application and with any state of charge, by implementing an electrical model in the step (d) and the thermal model in the step (f) of the modelling phase, estimating electrical parameters in the step (e), and estimating at least one of the parameters of the thermal model ΔS in the step (g), wherein the modelling in the step (d) consists in considering that the battery is an electrical circuit or the electrical model comprising a resistor R 0 , an open circuit voltage OCV, and a circuit R 1 C 1 in series, the electrical behaviour of the battery being described, in this electrical model, by the following equations: [mathematical expression included] where U 1 is a voltage at terminals of the circuit R 1 C 1 , I is a current passing through the battery and V bat a voltage at terminals of the battery, the equation (2) being discretised as follows: V bat,k =I k b 0,k +I k-1 b 1,k +a 1,k (OCV k-1 −V bat,k-1)+ OCV k   (2′) and thus rewritten: [mathematical expression included] T s is a sampling period of a periodic input electrical signal S e , and Θ k T is a parameter vector, the modelling in the step (f) comprises considering the battery as the thermal model, wherein the battery is subjected to a charge current Sc able to be subjected to a sampling or to a discharge current Sd able to be subjected to a sampling, and the battery is a heat exchanger with its environment, the thermal behaviour of the battery is described by the following equation: [mathematical expression included] where: m is a mass of the battery, C p is a heat capacity of the battery, T bat is a temperature of the battery, t is a time variable, I is the current passing through the battery, V bat is the voltage at the terminals of the battery, OCV is the open circuit voltage of the battery, ΔS is the variation in entropy of the battery, F is the Faraday constant, h is the thermal exchange coefficient with the exterior, A is the area of the battery in contact with the exterior, T amb is the temperature of the outside environment, the equation (3) being discretised as follows: T bat,k −T bat,k-1 =a 0,k [I k (V bat,k −OCV k)]+ a 1,k I k T bat,k +a 2,k (T bat,k −T amb,k)  (4) and thus rewritten: [mathematical expression included] T s is the measurement sampling period, the variation in entropy ΔS of the battery is measured, in situ, online and in real time, and used as an input of a battery management system associated at least with said battery, in order to provide feedback to the battery management system thus allowing this latter for controlling the battery in situ, online and in real time at least in function of the measured variation in entropy ΔS of the battery, in the charging step (a), the charge current signal Sc is repetitively applied, of which a frequency range is comprised between 0 and 1 Hz, the charge current signal being chosen in such a way that a capacity ratio of the battery is comprised between 0.01C and 3C, and in the discharging step (b), the discharge current signal Sd is repetitively applied which is an input current Se, of which a frequency range is comprised between 0 and 1 Hz.

2. The method according to claim 1 , wherein the products mC p and hA are constant and are estimated in a step (a 0) prior to the step (a), and the step (a 0) comprises: implementing a relaxation of the battery so that the parameter OCV of the equation (2′) of the electrical model, has a precise given value; applying the periodic input electrical signal S e of which the period is chosen in such a way that the average of the heat generated by ΔS over a period is about 0; estimating the products mC p and hA, using a recursive least-squares algorithm, thanks to the equation (3) that has become the following equation (3′): [mathematical expression included] and by measuring actual variables that correspond to the parameters V Bat , I, T bat , T amb ; integrating this estimate of products mC p and hA into the thermal model for the steps (f) and (g).

3. The method according to claim 1 , wherein the actual variables measured in the step (c) correspond to the parameters V Bat , I, T bat , T amb of the electrical and thermal models.

4. The method according to claim 2 , wherein the periodic input electrical signal S e is a signal with a period comprised between 10 and 30 seconds.

5. The method according to claim 2 , wherein the periodic input electrical signal S e is a zero average.

6. The method according to claim 1 , wherein the estimating according to the step (e) is carried out using a recursive least-squares algorithm and the estimating according to the step (g) is carried out using a recursive least-squares algorithm.

7. The method according to claim 1 , wherein the variation in enthalpy ΔH is estimated from OCV and ΔS using the following equation: Δ H=−F·OCV−T bat ΔS   (6).

8. A method for determining the state of charge and/or the state of health of the battery from ΔS and/or from ΔH measured or estimated by the method according to claim 7 .

9. The method according to claim 1 , further comprising: storing data estimated in the estimation phase and/or data measured in the modelling phase.

10. The method according to claim 1 , wherein the charge current signal Sc is a signal corresponding to a Pseudo Random Binary Sequence (PRBS).

11. The method according to claim 1 , wherein the discharge current signal Sd is a signal corresponding to a Pseudo Random Binary Sequence (PRBS).

12. A device for measuring, in situ, online and in real time, thermodynamic data including a variation in entropy ΔS, of at least one battery, the device comprising: at least one programmable charger/discharger; at least one sensor configured to detect at least one of actual variables that corresponds to the following parameters: V Bat , I, T bat , T amb ; at least one data recorder; at least one charge current signal generator; and at least one central control and calculation unit configured to control at least one of the at least one programmable charger/discharger, the at least one sensor, the at least one data recorder, or the at least one charge current signal generator, to produce a prior model of the battery of which a state of charge (SOC) is comprised between 0 and 100% by implementing: step (a) charging the battery at least partially with a charge current signal Sc, wherein the step (a) is optionally followed by a step (b) discharging the battery at least partially with a discharge current signal Sd; step (c) measuring the actual variables useful in the following steps; step (d)modelling electrical behaviour of the battery during the charging step (a) with the charge current signal Sc and/or the discharging step (b) with the discharge current signal Sd, in order to estimate electrical parameters of the battery; step (e) estimating periodically, at a first alternating current frequency Fe, the electrical parameters of the battery; step (f) modelling thermal behaviour of the battery during charging in the step (a) with the charge current signal Sc and/or discharging in the step (b) with the discharge current signal Sd, in order to estimate in situ, online and in real time, at least one of parameters of a thermal model, namely ΔS; step (g)estimating periodically, at a second alternating current frequency Fg, the at least one of the parameters of the thermal model ΔS, by using at least one of the electrical parameters estimated in the step (e); estimate thermodynamic data including ΔS of the battery during use in an application and with any state of charge, by implementing an electrical model in the step (d) and the thermal model in the step (f) of the modelling phase, estimate electrical parameters in the step (e), and estimate at least one of the parameters of the thermal model ΔS in the step (g), wherein the modelling in the step (d) consists in considering that the battery is an electrical circuit or the electrical model comprising a resistor R 0 , an open circuit voltage OCV, and a circuit R 1 C 1 in series, the electrical behaviour of the battery being described, in this electrical model, by the following equations: [mathematical expression included] where U 1 is a voltage at terminals of the circuit R 1 C 1 , I is a current passing through the battery and V bat a voltage at terminals of the battery, the equation (2) being discretised as follows: V bat,k =I k b 0,k +I k-1 b 1,k +a 1,k (OCV k-1 −V bat,k-1)+ OCV k   (2′) and thus rewritten: [mathematical expression included] [mathematical expression included] [mathematical expression included] [mathematical expression included] [mathematical expression included] T z is a sampling period of a periodic input electrical signal S e , and Θ k T is a parameter vector, the modelling in the step (f) comprises considering the battery as the thermal model, wherein the battery is subjected to a charge current Sc able to be subjected to a sampling or to a discharge current Sd able to be subjected to a sampling, and the battery is a heat exchanger with its environment, the thermal behaviour of the battery is described by the following equation: [mathematical expression included] where: m is a mass of the battery, C p is a heat capacity of the battery, T bat is a temperature of the battery, t is a time variable, I is the current passing through the battery, V bat is the voltage at the terminals of the battery, OCV is the open circuit voltage of the battery, ΔS is the variation in entropy of the battery, F is the Faraday constant, h is the thermal exchange coefficient with the exterior, A is the area of the battery in contact with the exterior, T amb is the temperature of the outside environment, the equation (3) being discretised as follows: T bat,k −T bat,k-1 =a 0,k [I k (V bat,k −OCV k)]+ a 1,k I k T bat,k +a 2,k (T bat,k −T amb,k)  (4) and thus rewritten: [mathematical expression included] [mathematical expression included] [mathematical expression included] [mathematical expression included] [mathematical expression included] T s is the measurement sampling period, the at least one central control and calculation unit is configured to estimate the products mC p and hA in a step (a 0) prior to the step (a), the products mC p and hA being constant, the at least one central control and calculation unit is configured to perform the step (a 0) by implementing a relaxation of the battery so that the parameter OCV of the equation (2′) of the electrical model, has a precise given value; applying the periodic input electrical signal S e of which the period is chosen in such a way that the average of the heat generated by ΔS over a period is about 0; estimating the products mC p and hA, using a recursive least-squares algorithm, thanks to the equation (3) that has become the following equation (3′): [mathematical expression included] and by measuring the actual variables that correspond to the parameters V Bat , I, T bat , T amb ; and integrating this estimate of products mC p and hA into the thermal model for the steps (f) and (g), the at least one central control and calculation unit is configured to control at least one of the at least one programmable charger/discharger, the at least one sensor, the at least one data recorder, or the at least one charge current signal generator, to collect and to process data for the estimations of the steps (a 0), (e), and (g), by implementing recursive least-squares algorithms, the device is configured to measure the variation in entropy ΔS of the battery, in situ, online and in real time, the variation being used as an input of a battery management system associated at least with said battery, in order to provide feedback to the battery management system thus allowing this latter for controlling the battery in situ, online and in real time at least in function of the measured variation in entropy ΔS of the battery, the at least one programmable charger/discharger is configured to repetitively apply, in the charging step (a), the charge current signal Sc, of which a frequency range is comprised between 0 and 1 Hz, the charge current signal being chosen in such a way that a capacity ratio of the battery is comprised between 0.01C and 3C, and the at least one programmable charger/discharger is configured to repetitively apply, in the discharging step (b), the discharge current signal Sd which is an input current Se, of which a frequency range is comprised between 0 and 1 Hz.

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