ESTIMATE BATTERY PACK CHARGE STATE USING VIRTUAL SENSOR CELLS

Abstract

A battery monitoring system for an electric vehicle battery pack. The battery monitoring system may include a virtual cell model designed to generate a final output based on the current through the battery pack and a final equivalent circuit model (ECM) for a virtual cell, and a physical cell model designed to generate an indeterminate output based on the current and an indeterminate ECM for the battery pack. The battery monitoring system may include a state-of-charge (SOC) transformation module designed to generate a battery state of charge (SOC) for the battery pack based at least partially on the final and indeterminate outputs.

Description

INTRODUCTION

[0001] The present disclosure relates to battery monitoring systems, such as, but not necessarily limited to, a battery monitoring system that includes a virtual sensor cell model used to facilitate estimation of a state of charge (SOC) for a vehicle-based battery pack.

[0002] Document DE 10 2015 208 264 A1 discloses a battery management system for calculating the state of charge of the cells of a vehicle battery. Documents DE 10 2012 102 375 A1, DE 10 2009 046 579 A1, and DE 10 2020 215 176 A1 disclose related systems.

[0003] A vehicle may include an electric motor for converting electrical energy into mechanical energy to perform work with the mechanical energy, e.g., mechanically powering a drivetrain to propel the vehicle. Such vehicles may include a battery pack for storing and supplying electrical energy to the electric motor. Battery packs are typically formed from a plurality of battery cells arranged in one or more battery modules. The battery cells may include electrolytic or other types of materials used to store and deliver electrical energy. The materials used for the battery cells can vary greatly depending on various design considerations, performance characteristics, power parameters, etc., with one of the more favorable types of materials being lithium iron phosphate (LFP).LFP battery cells may be desirable due to their relatively high thermal stability and other desirable properties. Their use can be complicated by the fact that LFP batteries tend to exhibit a relatively flat OCV-SOC (Open Circuit Voltage State of Charge) curve compared to battery cells made of other material types with more pronounced OCV-SOC curves, such as nickel-cobalt-manganese (NCM) battery cells. These relatively flat OCV-SOC curves can make SOC estimates for the corresponding battery cells more difficult to obtain with the desired degree of accuracy compared to battery cells with more pronounced OCV-SOC curves. SUMMARY

[0004] One non-limiting aspect of the present disclosure relates to a battery monitoring system for estimating the state of charge (SOC) of a battery pack formed entirely or partially from battery cells exhibiting a relatively flat OCV-SOC curve, such as lithium iron phosphate (LFP) battery cells. The battery monitoring system may be configured with a virtual cell model for facilitating the estimation of the SOC for the battery pack based on the virtual cell model defined with respect to a battery cell material having a comparatively more pronounced OCV-SOC curve, such as a nickel-cobalt-manganese (NCM) battery cell.The virtual cell model may be used to generate a final output useful for estimating the SOC of the battery pack without requiring the battery pack to physically include an actual NCM or other battery cell formed from a material with the more pronounced OCV-SOC curve. The battery monitoring system may additionally include a physical cell model used to generate an indeterminate output to facilitate estimating the SOC based on the physical cell model defined relative to a material of the actual physical battery cells included in the battery pack, such as for the LFP battery cells with the relatively flat OCV-SOC curve.The battery monitoring system can utilize the final and indeterminate outputs of the virtual and physical cell models to generate an estimate of SOC with the desired accuracy and magnitude, thus achieving greater accuracy than would typically be possible based on a relatively flat OCV-SOC curve alone.

[0005] One aspect of the present disclosure relates to a battery monitoring system for a battery pack of a vehicle. The battery monitoring system comprises a sensor system configured to measure a current (I) through the battery pack and a battery voltage (U t,P) above the battery pack. The battery monitoring system includes a virtual cell model configured to generate a final output based on the current (I) and a final equivalent circuit model (ECM) for a virtual cell, wherein the final ECM defines a plurality of virtual parameters (Parameterv) for the virtual cell, and the final output comprises a virtual cell voltage (U RC,V) across one or more RC pairs of the final ECM and a virtual cell open circuit voltage (OCVv) derived based on a virtual cell state of charge (SOCv) and a final open circuit voltage-state of charge (OCV-SOC) curve for the virtual cell. The battery monitoring system includes a physical cell model configured to generate an indeterminate output based on the current (I) and an indeterminate ECM for the battery pack, wherein the indeterminate ECM includes a plurality of physical parameters (parameters P ) for the battery pack and the indeterminate output is a physical cell voltage (U RC,p ) across one or more RC pairs of the indeterminate ECM and an indeterminate open circuit voltage (OCV P) derived from an indeterminate open circuit voltage-state of charge (OCV-SOC) curve for the battery pack. The battery monitoring system comprises a voltage transformation module configured to generate a virtual voltage (Ut,v) based on the battery voltage (U t,P ) and the final and undetermined outputs, a virtual cell SOC estimator configured to determine the virtual cell SOC (SOCv) based on the virtual cell voltage (Ut,v) and the current (I), and a SOC transformation module configured to generate a battery SOC (SOC P ) for the battery pack is designed based on the virtual cell SOC (SOCv).

[0006] The virtual cell model can be designed in a time step k such that it calculates the voltage of the virtual cell (U RC,V (k)) determined in accordance with: URC,V(k)=e−ΔtR1,VC1,VURC,V(k−1)+R1,V(1−e−ΔtR1,VC1,V)I(k), where the virtual parameters (parameterv) R 1,V and C 1,V include.

[0007] The virtual cell model may be configured in time step k to determine the virtual cell OCV (OCVv(k)) based on the SOC of the virtual cell (SOCv(k-1)) in a time step k-1.

[0008] The physical cell model can be designed in time step k such that it calculates the physical cell voltage (U RC,P (k)) determined in accordance with: URC,P(k)=e−ΔtR1,PC1,PURC,P(k−1)+R1,P(1−e−ΔtR1,PC1,P)I(k), where the physical parameters (parameters P ) R 1,P and C 1,P include.

[0009] The physical model can be designed in time step k such that it calculates the physical cell OCV (OCV P (k)) based on the physical cell SOC (SOC P(k-1)) in time step k-1.

[0010] The voltage transformation module can be designed such that it converts the virtual cell voltage U t,V ) determined according to: Ut,V(k)=OCVV(k)−URC,V+R0,VR0,P(Ut,P(k)−OCVP(k)+URC,P(k)) where the virtual parameters (parameterv) R 0,V and the physical parameters (parameters P ) R 0,P include.

[0011] A Kalman filter can be designed such that in time step k it calculates the virtual cell SOC (SOCv(k)) based on the virtual cell voltage (U t,V (k)) and the current (I(k)).

[0012] The SOC transformation module can be designed in time step k such that it converts the battery SOC (SOC P (k)) determined in accordance with: SOCP(k)=QVQP[SOCV(k)−(1−QPQV)] where the physical parameters (parameters P ) Q Pand include the virtual parameters (parameterv) Qv.

[0013] A non-limiting aspect of the present disclosure relates to a non-transitory computer-readable storage medium for storing a plurality of non-transitory instructions that, when executed with one or more processors, are for monitoring a battery pack. The non-transitory instructions may be for: determining a current (I) through the battery pack and a battery voltage (U t,P ) on the battery pack; generating a final output based on the current (I) and a final equivalent circuit model (ECM) for a virtual cell, the final ECM defining a plurality of virtual parameters (Parameterv) for the virtual cell, the final output comprising a virtual cell voltage (U RC,V) across one or more RC pairs of the final ECM and a virtual cell open circuit voltage (OCVv) derived based on a virtual cell state of charge (SOCv) and a final open circuit voltage-state of charge (OCV-SOC) curve for the virtual cell; and generating an indeterminate output based on the current (I) and an indeterminate ECM for the battery pack, wherein the indeterminate ECM comprises a plurality of physical parameters (parameters P ) for the battery pack, where the indeterminate output is an indeterminate voltage (U RC,p ) across one or more RC pairs of the indeterminate ECM and an indeterminate open circuit voltage (OCV P ) derived based on an indeterminate open circuit voltage-state of charge (OCV-SOC) curve for the battery pack.

[0014] The non-transitory commands can be used to generate a virtual voltage (Ut,v) based on the battery voltage (U t,P ) and the final and indefinite outputs; to determine the virtual cell SOC (SOCv) based on the virtual cell voltage (Ut,v) and current (I); and to generate a battery SOC (SOC P ) for the battery pack based on the virtual cell SOC (SOCv).

[0015] The non-transitory commands can be used to, in a time step k, the virtual cell voltage (U RC,V (k)) to be determined in accordance with: URC,V(k)=e−ΔtR1,VC1,VURC,V(k−1)+R1,V(1−e−ΔtR1,VC1,V)I(k) where the virtual parameters (parameterv) R 1,V and C 1,V include.

[0016] The non-transitory instructions can be used to determine the virtual cell OCV (OCVv(k)) in time step k based on the virtual cell SOC (SOCv(k-1)) in a time step k-1.

[0017] The non-transitory commands can be used to determine the physical cell voltage (U RC,P (k)) to be determined in accordance with: URC,P(k)=e−ΔtR1,PC1,PURC,P(k−1)+R1,P(1−e−ΔtR1,PC1,P)I(k) where the physical parameters (parameters P ) R 1,P and C 1,P include.

[0018] The non-transitory commands can be used to determine the physical cell OCV (OCV P (k)) based on the physical cell SOC (SOC P (k-1)) in a time step k-1.

[0019] The non-transitory commands can be used to determine the virtual cell voltage (Ut,v) according to: Ut,V(k)=OCVV(k)−URC,V+R0,VR0,P(Ut,P(k)−OCVP(k)+URC,P(k)) where the virtual parameters (parameterv) R 0,V and the physical parameters (parameters P ) R 0,P include.

[0020] The non-transitory commands can be used to determine the virtual cell SOC (SOCv(k)) in time step k based on the virtual cell voltage (U t,V (k)) and the current (I(k)).

[0021] The non-transitory commands can be used to determine the battery SOC (SOC P (k)) to be determined in accordance with: SOCP(k)=QVQP[SOCV(k)−(1−QPQV)] where the physical parameters (parameters P ) Q P and include the virtual parameters (parameterv) Qv.

[0022] One aspect of the present disclosure relates to a battery monitoring system for a battery pack of an electric vehicle. The battery monitoring system includes a virtual cell model configured to generate a final output based on a current (I) through the battery pack and a final equivalent circuit model (ECM) for a virtual cell, a physical cell model configured to generate an indeterminate output based on the current (I) and an indeterminate ECM for the battery pack, and a SOC transformation module configured to generate a battery SOC (SOC P ) for the battery pack is designed at least in part on the basis of the final and indefinite expenditures.

[0023] The final ECM defines a variety of virtual parameters (Parameterv) for the virtual cell, and the final output includes a virtual cell voltage (U RC,V) across one or more RC pairs of the final ECM and a virtual cell open circuit voltage (OCVv) derived based on a virtual cell state of charge (SOCv) and a final open circuit voltage-state of charge (OCV-SOC) curve for the virtual cell, the indeterminate ECM defines a variety of physical parameters (parameters P ) for the battery pack, and the indeterminate output includes an indeterminate voltage (U RC,p ) across one or more RC pairs of the indeterminate ECM and an indeterminate open circuit voltage (OCV P ), which is derived based on an indeterminate open circuit voltage-state of charge (OCV-SOC) curve for the battery pack.

[0024] The battery monitoring system may comprise a voltage transformation module configured to generate a virtual voltage (Ut,v) based on the battery voltage (U t,P) and the final and indeterminate outputs, a virtual cell SOC estimator configured to determine the virtual cell SOC (SOCv) based on the virtual cell voltage (Ut,v) and current (I), and a SOC transformation module configured to generate the battery SOC (SOC P ) for the battery pack is designed based on the virtual cell SOC (SOCv).

[0025] These features and advantages, as well as other features and advantages of the present teachings, will be readily apparent from the following detailed description of modes for carrying out the present teachings, taken in conjunction with the accompanying drawings. It should be understood that, although the following figures and embodiments may be described individually, individual features thereof may be combined to form additional embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The accompanying drawings, which may be incorporated in and constitute a part of this specification, illustrate embodiments of the disclosure and, together with the description, serve to explain the principles of the disclosure. Fig. 1 illustrates a schematic view of a vehicle according to one non-limiting aspect of the present disclosure. Fig. 2 illustrates a schematic diagram of a battery monitoring system according to one non-limiting aspect of the present disclosure. Fig. 3 shows a flowchart of a method for monitoring a battery pack according to a non-limiting aspect of the present disclosure. Fig. 4 illustrates a distinct OCV-SOC curve according to one non-limiting aspect of the present disclosure. Fig. Figure 5 illustrates an example of such a relatively flat OCV-SOC curve, with a vertical axis indicating the OCV (V) and the horizontal axis indicating the SOC (%). DETAILED DESCRIPTION

[0027] Where appropriate, detailed embodiments of the present disclosure may be disclosed herein; however, it should be understood that the disclosed embodiments are merely exemplary of the disclosure that may be embodied in various and alternative forms. The figures are not necessarily to scale; some features may be exaggerated or reduced in size to show details of particular components. Therefore, the specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for showing one skilled in the art how to variously employ the present disclosure.

[0028] Fig. 1 illustrates a schematic view of a vehicle 10 according to one non-limiting aspect of the present disclosure. The vehicle 10, which may also be interchangeably referred to as an electric or hybrid vehicle 10, may include an electric motor 12 operable to convert electrical energy into mechanical energy to use the mechanical energy to perform work, e.g., to mechanically power a drivetrain and propel the vehicle. The vehicle 10 is depicted as a hybrid vehicle because the drivetrain 16 optionally includes an internal combustion engine (ICE) 18 for generating mechanical energy. The drivetrain 16 may include a transmission, a driveshaft, a differential, shafts, and / or other components to facilitate transferring rotational power from a rotor shaft coupled to a rotor to one or more of the wheels 20, 22, 24, 26.The vehicle 10 may include a battery pack 30 that serves to store electrical energy for the electric motor 12 and / or other systems, buses, etc. onboard the vehicle, and to supply electrical energy to the electric motor 12 and / or other systems, buses, etc. onboard the vehicle. Particularly when the vehicle 10 is powered solely by the electric motor 12, the battery pack 30 may be formed from a plurality of battery cells arranged in a plurality of battery modules. The vehicle 10 may include a battery monitoring system 32 that facilitates monitoring, controlling, measuring, and otherwise controlling the operation, performance, etc. of the battery pack 30.

[0029] The battery pack 30 may include battery cells formed from a variety of materials designed to facilitate the storage and delivery of electrical energy, so the present disclosure is not limited to any particular battery material, chemistry, etc. The types of materials used for the battery cells can vary widely depending on various design considerations, performance characteristics, power parameters, etc., with one of the more advantageous types of materials being lithium iron phosphate (LFP) because LFP batteries tend to have comparatively high thermal stability and have other desirable characteristics. The present disclosure will be described primarily with respect to the battery pack 30 being of the homogeneous type, wherein the battery cells may each have the same material type and / or chemistry.This is provided for exemplary and non-limiting purposes, as the present disclosure fully contemplates that the battery pack may be of a heterogeneous type, where the battery cells may have mixed chemistries and / or different battery cells with different material types. The use of LFP battery cells or other battery cells can be complicated because the materials tend to have a relatively flat open circuit voltage-state of charge (OCV-SOC) curve compared to battery cells with other material types with more pronounced OCV-SOC curves, such as nickel-cobalt-manganese (NCM) battery cells. The relatively flat OCV-SOC curves may tend to make SOC or other estimates, calculations, etc., for the corresponding battery cells and / or battery pack more difficult to obtain with the desired degree of accuracy than for those with more pronounced OCV-SOC curves.

[0030] Fig. 2 illustrates a schematic diagram of the battery monitoring system 32 according to one non-limiting aspect of the present disclosure. The battery monitoring system 32 may include a virtual cell model 40 and a physical cell model 42. The physical cell model 42 may be based on measurements physically taken on the battery pack 30, for example, with one or more cell monitoring units (CMUs) 44 of a sensor system 46. The physical cell model 42 may be used to generate an indeterminate output based on a battery control unit (BCU) 48 or other function that receives measurements taken with the sensor system 46 to determine a current (I) through the battery pack 30 and a battery voltage (U t,P) across the battery pack 30. The virtual model 40 may be defined with respect to a battery cell material having a comparatively more pronounced OCV-SOC curve, such as a nickel-cobalt-manganese (NCM) battery cell. The virtual cell model 40 may be used to generate a final output useful for estimating the SOC of the battery pack 30 without the battery pack 30 physically having to include an actual NCM or other battery cell made of a material with a more pronounced OCV-SOC curve. The battery pack 30 may be configured such that the battery modules and the battery cells are connected in series, however, the present disclosure also contemplates other series and / or parallel connections of the battery modules and / or cells. The use of the battery monitoring system 32 is primarily discussed with respect to calculating a battery SOC (SOC P) for the battery pack 30 based on the current (I) and the battery voltage (U t,P ) are described for non-limiting purposes, since the corresponding calculations and estimates may be similarly used at a more detailed level, for example for the individual battery modules and / or the individual battery cells.

[0031] Fig. 3 illustrates a flowchart 50 of a method for monitoring the battery pack 30 according to a non-limiting aspect of the present disclosure. The method is described primarily with respect to the operation of the battery monitoring system 32 to facilitate estimating the battery SOC (SOC P) for the battery pack 30. The method may be embodied or facilitated in / with a controller or other features of the battery monitoring system 32, each operating on-board and / or off-board the vehicle 10, and having one or more non-transitory computer-readable storage media for storing a plurality of non-transitory instructions that, when executed with one or more processors of the controller or additional controllers, may be used to monitor the battery pack in the manner described.The method may include a virtual sensor cell or process 52, wherein the virtual cell model 40 and the physical cell model 42 may cooperate with a voltage transformation module 54 to facilitate generating values ​​for use with a SOC estimator 54 for the physical cell, whereupon a SOC transformation module 56 and optionally a SOC estimator 60 for the virtual cell may calculate the battery SOC (SOC. P ) accordingly. The method considered for estimating the battery SOC (SOC P ) is considered advantageous for enhancing the physical battery pack 30 with a virtual model observer, whereby using this method can improve SOC accuracy, reduce hardware complexity, increase robustness to power management drift and noise, and provide the desired accuracy levels.

[0032] Block 64 refers to a virtual cell model process for generating a final output based on the current (I) and a final equivalent circuit model (ECM) for a virtual cell. The virtual cell may be a mathematical, logical, or other modeling construct suitable for modeling the characteristics of an NCM battery cell or another type of battery cell with a more pronounced OCV-SOC curve. Fig. Figure 4 illustrates an example of a graph 68 for such a distinct OCV-SOC curve 70, where a vertical axis 72 indicates the OCV (V) and a horizontal axis 74 indicates the SOC (%). The final ECM may define a plurality of virtual parameters (Parameterv) for the virtual cell. The final output may be a virtual cell voltage (U RC,V) across one or more RC pairs of the final ECM and a virtual cell open circuit voltage (OCVv) derived based on a virtual cell state of charge (SOCv) and a final and relatively flat OCV-SOC curve for the physical cell. Fig. Figure 5 illustrates an example of a graph 78 for such a relatively flat OCV-SOC curve 80, where a vertical axis 82 indicates the OCV (V) and a horizontal axis 84 indicates the SOC (%). Block 90 refers to a physical cell model process for generating an indeterminate output based on the current (I) and an indeterminate ECM for the battery pack. The indeterminate ECM may include a variety of physical parameters (parameters P ) for the battery pack 30. The indeterminate output can be a physical cell voltage (U RC,p ) across one or more RC pairs of the indeterminate ECM and an indeterminate open circuit voltage (OCPP ) derived based on an indeterminate OCV-SOC curve for the battery pack 30.

[0033] Block 92 refers to a voltage transformation module process for generating a virtual voltage (Ut,v) based on the battery voltage (U t,P ) and the final and indeterminate outputs. Block 94 refers to a virtual cell SOC estimation process configured to determine the virtual cell SOC (SOCv) based on the virtual cell voltage (Ut,v) and current (I). Block 96 refers to a SOC transformation module process for generating a battery SOC (SOC P ) for the battery pack based on the virtual cell SOC (SOCv). In a time step k, the virtual cell model can be designed such that it calculates the virtual cell voltage (U RC,V (k)) determined in accordance with: URC,V(k)=e−ΔtR1,VC1,VURC,V(k−1)+R1,V(1−e−ΔtR1,VC1,V)I(k). where the virtual parameters (parameterv) R 1,V and C 1,V include.

[0034] In time step k, the virtual cell model may be configured to determine the virtual cell OCV (OCVv(k)) based on the virtual cell SOC (SOCv(k-1)) in a time step k-1.

[0035] In time step k, the physical cell model can be designed in such a way that it calculates the physical cell voltage (U RC,P (k)) determined in accordance with: URC,P(k)=e−ΔtR1,PC1,PURC,P(k−1)+R1,P(1−e−ΔtR1,PC1,P)I(k). where the physical parameters (parameters P ) R 1,P and C 1,P include.

[0036] In time step k, the physical model can be designed in such a way that it calculates the physical cell OCV (OCV P (k)) based on the physical cell SOC (SOC P(k-1)) in a time step k-1.

[0037] The voltage transformation module can be designed such that it determines the virtual cell voltage (Ut,v) according to: Ut,V(k)=OCVV(k)−URC,V+R0,VR0,P(Ut,P(k)−OCVP(k)+URC,P(k)). where the virtual parameters (parameterv) R 0,V and the physical parameters (parameters P ) R 0,P include.

[0038] At time step k, a Kalman filter can be used to determine the virtual cell SOC (SOCv(k)) based on the virtual cell voltage (U t,V (k)) and the current (I(k)).

[0039] In time step k, the SOC transformation module can be designed such that it converts the battery SOC (SOC P (k)) determined in accordance with: SOCP(k)=QVQP[SOCV(k)−(1−QPQV)] where the physical parameters (parameters P ) Q P and include the virtual parameters (parameterv) Qv.

[0040] The combination of virtual NCM and Kalman filter can be used to correct the SOC estimation according to the final OCV-SOC curve of the NCM in real time, thus mitigating the accumulation error caused by Coulomb counting.

[0041] Coulomb counting accumulation error: CC error=ηQ⋅ΔI⋅t

[0042] Error in the virtual sensor model: VS error=1K⋅ΔI⋅(R0+R1) OCV=K⋅SOC; URC(∞)=IR1 Ut=OCV−URC−IR0=K⋅SOC−IR1−IR0 SOC=1K⋅I⋅(R0+R1)+1K⋅Ut VS error=1K⋅ΔI⋅(R0+R1)

[0043] For example, for the Coulomb count (assuming η=1, Q = 100Ah = 100*3600As): CC error = 2.7×10 -6 . ΔI · t and for the virtual sensor model (assuming K = 1, R0=1mOhm and R1=2mOhm): VS error = 5×10 -3· ΔI with VS error < CC error when t > 1080 s, even if the Coulomb count has an accurate initial SOC.

Claims

[1] Battery monitoring system (32) for a battery pack (30) of a vehicle (10), comprising: a sensor system (46) designed to measure a current (I) through the battery pack (30) and a battery voltage (U t,P ) on the battery pack (30); a virtual cell model (40) configured to generate a final output based on the current (I) and a final equivalent circuit model (ECM) for a virtual cell, the final ECM defining a plurality of virtual parameters (Parameterv) for the virtual cell, the final output comprising a virtual cell voltage (U RC, V ) across one or more RC pairs of the final ECM and a virtual cell open circuit voltage (OCVv) calculated based on a virtual cell state of charge (SOC V ) and a final open circuit voltage-state of charge (OCV-SOC) curve for the virtual cell; a physical cell model (42) configured to generate an indeterminate output based on the current (I) and an indeterminate ECM for the battery pack (30), wherein the indeterminate ECM comprises a plurality of physical parameters (parameters P ) for the battery pack (30), wherein the indeterminate output is a physical cell voltage (U RC,p ) across one or more RC pairs of the indeterminate ECM and an indeterminate open circuit voltage (OCV P ) derived from an indeterminate open circuit voltage-state of charge (OCV-SOC) curve for the battery pack (30); and a voltage transformation module (54) configured to generate a virtual voltage (Ut,v) based on the battery voltage (U t,P ) and the final and indeterminate outcomes; a virtual cell SOC estimator (60) configured to determine the virtual cell SOC (SOCv) based on the virtual cell voltage (Ut,v) and the current (I); and a SOC transformation module (56) configured to convert a battery SOC (SOC P ) for the battery pack (30) based on the SOC of the virtual cell (SOCv). [2] Battery monitoring system (32) according to claim 1, wherein: in a time step k, the virtual cell model (40) is designed such that it calculates the voltage of the virtual cell (U RC,V (k)) determined in accordance with: URC,V(k)=e−ΔtR1,VC1,VURC,V(k−1)+R1,V(1−e−ΔtR1,VC1,V)I(k) where the virtual parameters (parameterv) R 1,V and C 1,V include. [3] Battery monitoring system (32) according to claim 2, wherein: in time step k, the virtual cell model (40) is designed such that it determines the OCV of the virtual cell (OCVv(k)) on the basis of the SOC of the virtual cell (SOCv(k-1)) in a time step k-1. [4] Battery monitoring system (32) according to claim 3, wherein: in time step k, the physical cell model (42) is designed such that it calculates the physical cell voltage (U RC,P (k)) determined in accordance with: URC,P(k)=e−ΔtR1,PC1,PURC,P(k−1)+R1,P(1−e−ΔtR1,PC1,P)I(k) where the physical parameters (parameters P ) R 1,P and C 1,P include. [5] Battery monitoring system (32) according to claim 4, wherein: in the time step k the physical model (42) is designed such that it calculates the OCV of the physical cell (OCV P (k)) based on the SOC of the physical cell (SOC P (k-1)) in a time step k-1. [6] Battery monitoring system (32) according to claim 5, wherein: the voltage transformation module (54) for determining the voltage of the virtual cell (Ut,v) is designed according to: Ut,V(k)=OCVV(k)−URC,V(k)+R0,VR0,P(Ut,P(k)−OCVP(k)+URC,P(k)) where the virtual parameters (parameterv) R 0,V and the physical parameters (parameters P ) R 0,P include. [7] Battery monitoring system (32) according to claim 6, wherein: in time step k, a Kalman filter is designed to calculate the SOC of the virtual cell (SOCv(k)) based on the voltage of the virtual cell (U t,V (k)) and the current (I(k)). [8] Battery monitoring system (32) according to claim 7, wherein: in time step k, the SOC transformation module (56) is designed such that it converts the battery SOC (SOC P (k)) determined in accordance with: SOCP(k)=QVQP[SOCV(k)−(1−QPQV)] where the physical parameters (parameters P ) Q P and include the virtual parameters (parameterv) Qv. [9] Battery monitoring system (32) for a battery pack (30) of an electric vehicle (10), comprising: a virtual cell model (40) configured to generate a final output based on a current (I) through the battery pack (30) and a final equivalent circuit model (ECM) for a virtual cell; and a physical cell model (42) configured to generate an indeterminate output based on the current (I) and an indeterminate ECM for the battery pack (30); and a state of charge (SOC) transformation module (56) configured to convert a battery SOC (SOC P ) for the battery pack (30) is generated at least in part based on the final and indefinite outputs, wherein: the final ECM defines a plurality of virtual parameters (Parameterv) for the virtual cell; the final output is a virtual cell voltage (U RC,V ) across one or more RC pairs of the final ECM and a virtual cell open circuit voltage (OCVv) derived based on a virtual cell state of charge (SOCv) and a final open circuit voltage-state of charge (OCV-SOC) curve for the virtual cell; the indeterminate ECM a variety of physical parameters (parameters P ) for the battery pack (30); and the indeterminate output an indeterminate voltage (U RC,p ) across one or more RC pairs of the indeterminate ECM and an indeterminate open circuit voltage (OCV P ) derived based on an indeterminate open circuit voltage-state of charge (OCV-SOC) curve for the battery pack (30).

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