A METHOD FOR ESTIMATING CAPACITY OF A BATTERY UNIT

Abstract

A method for estimating a capacity of a battery unit in an energy storage system of a vehicle is provided. The method includes during at least a first no-load condition of the battery unit, measuring a terminal voltage of the battery unit at a number of points in time to determine a transient voltage response of the battery unit, from the transient voltage response of the battery unit during at least the first no-load condition, estimating at least a first value of an open circuit voltage of the battery unit by means of a battery model, and estimating the capacity of the battery unit based on at least the estimated at least first value of the open circuit voltage.

Claims

1. A method for estimating a capacity of a battery unit in an energy storage system of a vehicle, the method comprising: during at least a first no-load condition of the battery unit, measuring a terminal voltage of the battery unit at a number of points in time to determine a transient voltage response of the battery unit, from the transient voltage response of the battery unit during at least the first no-load condition, estimating at least a first value of an open circuit voltage of the battery unit by means of a battery model, comparing the estimated at least first value of the open circuit voltage to at least one predetermined convergence criterion, estimating the capacity of the battery unit based on at least the estimated at least first value of the open circuit voltage, wherein the estimation of the capacity of the battery unit is only carried out given that the at least one predetermined convergence criterion is fulfilled.

2. The method according to claim 1, further comprising: measuring a battery current of the battery unit during a charge process or a discharge process of the battery unit, wherein said charge process or discharge process precedes or succeeds said first no-load condition, wherein the estimation of the capacity of the battery unit is further based on the measured battery current during said charge process or said discharge process.

3. The method according to claim 2, further comprising: during a second no-load condition of the battery unit, determining a second value of the open circuit voltage of the battery unit, wherein said charge process or discharge process occurs between the first no-load condition and the second no-load condition, wherein the estimation of the capacity of the battery unit is further based on the determined second value of the open circuit voltage of the battery unit.

4. The method according to claim 1, wherein the terminal voltage used to determine the transient voltage response is measured within a predetermined period of time after a termination of an immediately preceding charge process or discharge process of the battery unit.

5. The method according to claim 1, wherein the estimation of the capacity of the battery unit based on at least the estimated at least first value of the open circuit voltage comprises using Coulomb counting.

6. The method according to claim 1, further comprising: determining a level of uncertainty of the estimated at least first value of the open circuit voltage.

7. The method according to claim 6, further comprising: based on said determined level of uncertainty of the estimated at least first value of the open circuit voltage, determining if the estimated at least first value of the open circuit voltage may be used for said estimation of the capacity of the battery unit.

8. The method according to claim 6, further comprising: based on said determined level of uncertainty of the estimated at least first value of the open circuit voltage, determining a level of uncertainty of the estimated capacity of the battery unit.

9. (canceled)

10. The method according to claim 1, wherein the battery model used in the estimation of the at least first value of the open circuit voltage is an equivalent circuit model.

11. The method according to claim 10, wherein the equivalent circuit model is a second order equivalent circuit model comprising at least two resistor-capacitor branches.

12. The method according to claim 1, wherein a recursive estimation method or a batch estimation method is used in the estimation of the at least first value of the open circuit voltage.

13. The method according to claim 1, wherein a recursive least squares estimation method is used in the estimation of the at least first value of the open circuit voltage.

14. A computer program comprising program code means for performing the method according to claim 1 when said computer program is run on a computer.

15. A computer-readable medium carrying a computer program comprising program code means for performing the method according to claim 1 when said computer program is run on a computer.

16. A control unit configured to perform the method according to claim 1.

17. A battery management system for an energy storage system comprising the control unit according to claim 16.

18. A vehicle, such as a hybrid vehicle of a fully electrified vehicle, comprising an energy storage system and a control unit according to claim 16.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] With reference to the appended drawings, below follows a more detailed description of embodiments of the invention cited as examples.

[0052] In the drawings:

[0053] FIG. 1 shows a vehicle in which a method according to the invention may be implemented,

[0054] FIG. 2 schematically illustrates parts of a battery model describing a battery unit;

[0055] FIG. 3 is a diagram showing current and voltage as functions of time after disconnection of a load from a battery unit,

[0056] FIG. 4 is a flow-chart illustrating a method according to an embodiment of the invention,

[0057] FIG. 5 is a flow-chart illustrating a method according to another embodiment of the invention, and

[0058] FIG. 6 is a flow-chart illustrating steps of a method according to yet another embodiment of the invention.

[0059] The drawings are schematic and not necessarily drawn to scale.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION

[0060] In the present detailed description, various embodiments of the method according to the present invention are mainly described with reference to an all-electric bus, comprising a propulsion system in the form of battery powered electric motors. However, it should be noted that various embodiments of the described invention are equally applicable for a wide range of hybrid and electric vehicles.

[0061] FIG. 1 shows a simplified perspective view of an all-electric vehicle in the form of a bus 201, which according to an embodiment is equipped with at least one electric machine (not shown) for operating the bus.

[0062] The bus 201 carries an electric energy storage system (ESS) 200 comprising a battery unit 202 in the form of a battery pack, the battery pack comprising a plurality of battery cells. The battery cells are connected in series to provide an output direct current (DC) voltage having a desired voltage level. Suitably, the battery cells are of lithium-ion type, but other types may also be used. The number of battery cells per battery pack may be in the range of 50 to 500 cells. It is to be noted that the ESS 200 may include a plurality of battery packs. The at least one electric machine forms a load, which when connected to the ESS 200 uses electric current provided from the battery pack 202. An on-board charger (not shown) also forms a load, which may be connected to an external power source and charge the battery pack with electric energy.

[0063] A sensor unit (not shown) may be arranged for collecting measurement data relating to operating conditions of the ESS 200, i.e. measuring temperature, voltage and current level of the associated battery pack 202. Measurement data from each sensor unit is transmitted to an associated battery management unit (BMU) 204, which is configured for managing the individual battery pack 202 during operation of the bus 201. The BMU 204 can also be configured for determining parameters indicating and controlling the condition or capacity of the battery pack 202, such as the state of charge (SOC), the state of health (SOH), the state of power (SOP) and the state of energy (SOE) of the battery pack 202.

[0064] The BMU 204 is connected to and configured to communicate with an ESS control unit 208, which controls the ESS 200. The ESS control unit 208 may include a microprocessor, a microcontroller, a programmable digital signal processor or another programmable device. Thus, the ESS control unit 208 comprises electronic circuits and connections (not shown) as well as processing circuitry (not shown) such that the ESS control unit 208 can communicate with different parts of the bus 201 or with different control units of the bus 201. The ESS control unit 208 may comprise modules in either hardware or software, or partially in hardware or software, and communicate using known transmission buses such as a CAN-bus and/or wireless communication capabilities. The processing circuitry may be a general purpose processor or a specific processor. The ESS control unit 208 comprises a non-transitory memory for storing computer program code and data. Thus, the skilled person realizes that the ESS control unit 208 may be embodied by many different constructions. This is also applicable to the BMU 204.

[0065] Turning now to FIG. 2, there is depicted a battery model comprising an equivalent circuit of the battery unit 202, also known as a Thevenin battery model. The exemplary equivalent circuit model comprises two RC circuits to model the battery unit, although a different number of RC circuits may be used in the model, such as one RC circuit or three RC circuits, depending on battery dynamics and application. The exemplary equivalent circuit model is used for estimation of the state of charge and capacity of the battery unit 202, and is typically implemented by the above mentioned control unit 208. The exemplified equivalent circuit model illustrated in FIG. 2 may be used for estimating the open circuit voltage V.sub.OC and capacity Q of the battery unit 202 based on direct battery measurements. The battery unit open circuit voltage estimation may for example be based on measured battery current inputs and a battery terminal voltage V.sub.b.

[0066] The equivalent circuit model described in relation to FIG. 2 consists of an active electrolyte resistance and conductive resistance of electrodes (or internal ohmic resistance) R.sub.0, connected in series with two RC branches. A first RC branch and a second RC branch comprise, respectively, capacitances C.sub.1, C.sub.2 and active charge transfer resistances R.sub.1, R.sub.2 connected in parallel. V.sub.b refers to terminal voltage output, I.sub.b refers to the current in the circuit and V.sub.OC refers to the battery open circuit voltage. For given values of the terms V.sub.OC, R.sub.0, R.sub.1, R.sub.2, C.sub.1 and C.sub.2, the terminal voltage V.sub.b can be expressed as a function of the current I.sub.b. Normally R.sub.0, R.sub.1 and R.sub.2 increase with age, while battery cell capacity (not illustrated in the figure) decreases with age. Voltages across the internal ohmic resistance R.sub.0 and the first and second RC branches, respectively, are expressed as V.sub.0, V.sub.1 and V.sub.2.

[0067] FIG. 3 shows current I and voltage V as functions of time t during a time period Δt.sub.p after disconnection of a load from a battery unit modelled by the equivalent circuit model in FIG. 2. While the load current I changes abruptly by an amount ΔI upon disconnection of the load, the voltage drops gradually by a total amount ΔV, corresponding to the terminal voltage V.sub.b. The voltage first drops abruptly by an amount ΔV.sub.0, corresponding to the voltage across the internal resistance R.sub.0. It thereafter drops gradually over the time period Δt.sub.p.

[0068] A method for estimating a capacity Q of a battery unit in an energy storage system, such as the battery unit 202 in the ESS 200 illustrated in FIG. 1, is schematically illustrated in the flow-chart of FIG. 4. The method comprises the following steps:

[0069] S11) During at least a first no-load condition of the battery unit 202, measuring the terminal voltage V.sub.b of the battery unit 202 at a number of points in time to determine a transient voltage response of the battery unit 202. This step is performed following disconnection of a load, such as an electric machine or an on-board charger. Thus, the step S11 may be performed either after a charge process or after a discharge process of the battery unit 202. The voltage drop upon disconnection of the load is gradual, in contrast to the sudden current drop, and the measured terminal voltage V.sub.b will follow a time curve whose appearance depends on the open circuit voltage V.sub.OC of the battery unit 202.

[0070] S12) From the transient voltage response of the battery unit 202 during at least the first no-load condition, estimating at least a first value of the open circuit voltage V.sub.OC of the battery unit 202 by means of a battery model. The battery model may e.g. be the second order equivalent circuit model described with reference to FIG. 2, although other models may also be used for this purpose, such as an electrochemical model or a black box model. In order to estimate the open circuit voltage V.sub.OC using the second order equivalent circuit model, various batch estimation methods or recursive estimation methods may be used. Examples will be given below.

[0071] S13) Estimating the capacity Q of the battery unit 202 based on at least the estimated at least first value of the open circuit voltage V.sub.OC.

[0072] The method may further comprise the optional steps, marked with dashed lines:

[0073] S9) During a second no-load condition of the battery unit 202, determining a second value of the open circuit voltage V.sub.OC of the battery unit, wherein a charge process or a discharge process occurs between the first no-load condition and the second no-load condition. In this case, the estimation of the capacity Q of the battery unit 202 is further based on the determined second value of the open circuit voltage V.sub.OC of the battery unit. The second value of the of the open circuit voltage V.sub.OC does not necessarily need to be determined in the same way as the first value, although it is of course possible to determine a value of the open circuit voltage V.sub.OC according to step S12 following each charge process or discharge process of the battery unit, which values may be used for estimation of the capacity in step S13. In the flow chart in FIG. 4, the second no-load condition occurs before the first no-load condition.

[0074] S10) Measuring the battery current I.sub.b of the battery unit 202 during a charge process or a discharge process of the battery unit, wherein the charge process or discharge process precedes or succeeds the first no-load condition, during which the transient voltage response was/will be determined. The charge process or the discharge process may be the process immediately succeeding or preceding the first no-load condition. The charge process or discharge process may be the charge process or the discharge process occurring between the first no-load condition and the second no-load condition, such as illustrated in FIG. 4. The estimation of the capacity of the battery unit, performed in step S13, is in this case further based on the measured battery current I.sub.b during said charge process or said discharge process. For example, the estimation of the capacity of the battery unit may in this case be estimated using Coulomb counting, taking the first and second values of the open circuit voltage V.sub.OC and the total current during the charge or discharge process into account. Under the assumption that the battery unit is charged or discharged in a state of charge (SOC) window [z(t.sub.0), z(t.sub.f)] over a time interval t ∈ [t.sub.0, t.sub.f], the battery capacity Q can be estimated as {circumflex over (Q)} as follows, derived using Coulomb counting:

[00001]$\hat{Q}=\frac{{\int }_{t_0}^{t_f}{I}_b\left(\tau \right)d\tau }{z\left(t_f\right)-z\left(t_0\right)}$

[0075] where z(t.sub.0) and z(t.sub.f) are initial and final values of SOC during the charge or discharge process. The SOC is related to the open circuit voltage V.sub.OC, and look-up tables may be used to find the SOC value corresponding to the determined first, and if applicable second, value(s) of the open circuit voltage V.sub.OC determined in steps S12 and S9, respectively.

[0076] As illustrated in the flow chart of FIG. 5, the method may also comprise the optional step:

[0077] S14) Comparing the estimated at least first value of the open circuit voltage V.sub.OC to a predetermined convergence criterion, wherein the step S13 of the estimation of the capacity Q of the battery unit 202, based on the estimated at least first value of the open circuit voltage V.sub.OC, is only carried out given that the predetermined convergence criterion is fulfilled. The convergence criterion may for example be set so that the obtained first value of the open circuit voltage is estimated repeatedly following disconnection of the load until two subsequently estimated first values of the open circuit voltage V.sub.OC differ from each other by less than a predetermined amount. If the predetermined convergence criterion is not fulfilled, steps S11 and S12 are resumed. Thus, step S14 is carried out after step S12 and is decisive of whether the method should proceed to step S13 or not.

[0078] As illustrated in the flow-chart of FIG. 6, the method may also comprise the optional steps:

[0079] S15) Determining a level of uncertainty of the estimated at least first value of the open circuit voltage V.sub.OC as estimated in step S12. The open circuit voltage V.sub.OC is herein determined as a stochastic variable. The determined level of uncertainty may be used in step S16 and/or step S17 as explained below.

[0080] S16) Based on the determined level of uncertainty of the estimated at least first value of the open circuit voltage V.sub.OC, determining if the estimated at least first value of the open circuit voltage V.sub.OC may be used for the estimation of the capacity Q of the battery unit. For example, if the estimated level is above a predetermined threshold, it may be determined that the value may not be used for capacity estimation in step S13. In this case, the method may be aborted and resumed at a later occasion, such as during a subsequent no-load condition of the battery unit 202. Alternatively, step S11 may be resumed to attempt to get a more accurate value of the open circuit voltage V.sub.OC.

[0081] S17) Based on the determined level of uncertainty of the estimated at least first value of the open circuit voltage V.sub.OC, determining a level of uncertainty of the estimated capacity Q of the battery unit 202. Thus, in this case, the capacity Q is also determined as a stochastic variable whose estimated uncertainty level is dependent on the uncertainty of the open circuit voltage V.sub.OC. Step S17 may of course be carried out in close connection with step S13.

[0082] Although illustrated in three different flow charts, the steps S9-S17 may of course be combined in different ways. For example, the steps S9-S10 may be included also in the embodiments illustrated in FIGS. 5 and 6.

[0083] In step S12, the first value of the open circuit voltage V.sub.OC of the battery unit 202 may e.g. be estimated using the second order equivalent circuit model described with reference to FIG. 2. The equivalent circuit model illustrated in FIG. 2 can be described by the following equations:

V.sub.1(k+1)=a.sub.1(k).Math.V.sub.1(k)+b.sub.1(k).Math.I.sub.b(k),

V.sub.2(k+1)=a.sub.2(k).Math.V.sub.2(k)+b.sub.2(k).Math.I.sub.b(k),

SoC(k+1)=SoC(k)+b.sub.3(k).Math.I.sub.b(k),

V.sub.b(k)=V.sub.oc(k)+V.sub.1(k)+V.sub.2(k)+R.sub.0(k).Math.I.sub.b(k),

[0084] where V.sub.OC, a.sub.1, a.sub.2, b.sub.1, b.sub.2, and b.sub.3 are constants.

[0085] Under a no load condition, when I.sub.b=0, the model is reduced to

V.sub.1(k)=a.sub.1.Math.V.sub.1(k−1),

V.sub.2(k)=a.sub.2.Math.V.sub.2(k−1),

V.sub.b(k)=V.sub.oc+V.sub.1(k)+V.sub.2(k),

[0086] where V.sub.OC, a.sub.1 and a.sub.2 are constants.

[0087] Depending on the type of battery unit, two different cases apply, which may be treated separately.

EXAMPLE CASE 1

[0088] In a first case, a fast decay of activation polarization of the battery unit 202 is assumed, corresponding to a fast voltage drop ΔV.sub.1 across the first RC branch of the equivalent circuit model as the load is removed. In this case, the voltage V.sub.1 across the first RC branch may be neglected and the model is further simplified to

V.sub.2(k)=a.sub.2.Math.V.sub.2(k−1),

V.sub.b(k)=V.sub.oc+V.sub.2(k),

[0089] which can be rewritten on a one step ahead predictor form as

V.sub.b(k)=V.sub.oc+a.sub.2.Math.(V.sub.b(k−1)−V.sub.oc),

y(k)=φ(k).Math.θ,

[0090] where

[00002]$y=V_b,$$\phi =\left[\begin{array}{cc}{\phi }_1& {\phi }_2\end{array}\right]=\left[\begin{array}{cc}y\left(k-1\right)& 1\end{array}\right],$$\theta =\left[\begin{array}{c}{\theta }_1\\ {\theta }_2\end{array}\right]=\left[\begin{array}{c}{a}_2\\ \begin{array}{cc}(1-& a_2)V_{oc}\end{array}\end{array}\right].$

[0091] Based on the above model, the parameter vector θ is estimated, for example using a batch estimation method or a recursive estimation method, such as a recursive least squares method. The open circuit voltage V.sub.OC is thereafter estimated as:

[00003]$V_{oc}=\frac{{\theta }_2}{1-{\theta }_1}.$

EXAMPLE CASE 2

[0092] In a second and more general case, a fast decay of activation polarization of the battery unit 202 cannot be assumed. In this case, the voltage drops more slowly across the first RC branch of the equivalent circuit model as the load is removed. Thus, the voltage V.sub.1 across the first RC branch may not be neglected. This case can be handled by re-parameterizing the output equation on a 2.sup.nd order autoregressive form that leads to a 2.sup.nd order output predictor equation:

y=(a.sub.1+a.sub.2).Math.y(k−1)−a.sub.1a.sub.2.Math.y(k−2)−(a.sub.1+a.sub.2−a.sub.1a.sub.2).Math.V.sub.oc,

y=φ.Math.θ.

[0093] where

[00004]$\phi =\left[\begin{array}{ccc}{\phi }_1& {\phi }_2& {\phi }_3\end{array}\right]=\left[\begin{array}{ccc}y\left(k-1\right)& y\left(k-2\right)& 1\end{array}\right],$$\theta =\left[\begin{array}{c}{\theta }_1\\ {\theta }_2\\ {\theta }_3\end{array}\right]=\left[\begin{array}{c}{a}_1+a_2\\ a_1{a}_2\\ \left(1-{\theta }_1+{\theta }_2\right)V_{\mathrm{oc}}\end{array}\right].$

[0094] The equation may be solved for the parameter vector e using recursive or batch optimization approaches. The open circuit voltage V.sub.OC may thereafter be estimated as follows:

[00005]$V_{oc}=\frac{{\theta }_3}{1-{\theta }_1+{\theta }_2}$

[0095] One particular approach to find the parameter vector θ and the open circuit voltage V.sub.OC based on a recursive least-squares is given below:

[00006]$K_k=\frac{P_{k-1}{\phi }_k}{\lambda +{\phi }_k^T{P}_{k-1}{\phi }_k},$$P_k=\frac{\left(1-K_k{\phi }_k^T\right)P_{k-1}}{\lambda },$$e\left(k\right)=V_b\left(k\right)-{\phi }_k^T\hat{\theta }\left(k-1\right),$$\hat{\theta }\left(k\right)=\hat{\theta }\left(k-1\right)+K_{k}e\left(k\right),$

[0096] where λ and the initialization of P are tuning parameters, representing a forgetting factor and a covariance matrix, respectively, and wherein k represents a time sample. When the parameters have converged, the open circuit voltage may be estimated as defined above.

[0097] It is to be noted that the same solution may be found using various recursive and batch estimation and filtering techniques. For example, a batch least squares (RLS) technique can be used, which however requires more memory.

[0098] A convergence criterion that may be used is

[00007]$y\left(k\right)=\underset{k=k_0}{\overset{k_0-m}{.Math.}}.Math.e\left(k\right).Math.<\epsilon ,$

[0099] where e(k) is defined above, k.sub.0 is the current time step, and m and ε are tuning parameters.

[0100] Although the figures may show a sequence, the order of the steps may differ from what is depicted. Also two or more steps may be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps. Additionally, even though the invention has been described with reference to specific exemplifying embodiments thereof, many different alterations, modifications and the like will become apparent for those skilled in the art.

[0101] The estimated capacity of the battery unit may e.g. be communicated to an electronic control unit of the vehicle, such as an engine control unit (ECU). The estimated operating parameter may be communicated at time intervals depending on e.g. operating conditions of the ESS 200, or in real time.

[0102] The control functionality of the example embodiments may be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwire system. Embodiments within the scope of the present disclosure include program products comprising machine-readable medium for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the machine properly views the connection as a machine-readable medium. Thus, any such connection is properly termed a machine-readable medium. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions.

[0103] It is to be understood that the present invention is not limited to the embodiments described above and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the appended claims. For example, although the present invention has mainly been described in relation to an electrical bus, the invention should be understood to be equally applicable for any type of electric vehicle, in particular an electric truck or the like.