Patent Publication Number: US-2023145602-A1

Title: Battery apparatus and method for predicting battery output

Description:
TECHNICAL FIELD 
     CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to and the benefit of Korean Patent Application No. 10-2020-0127981 filed in the Korean Intellectual Property Office on Oct. 5, 2020, the entire contents of which are incorporated herein by reference. 
     The described technology relates to a battery apparatus and a method for predicting a battery output. 
     BACKGROUND ART 
     An electric vehicle or a hybrid vehicle is a vehicle that obtains power by driving a motor mainly using a battery as a power source. The electric vehicles are being actively researched because they are alternatives that can solve pollution and energy problems of internal combustion vehicles. Rechargeable batteries are used in various external apparatuses other than the electric vehicles. 
     In order to use the battery in various external apparatuses, it is necessary to predict an output of the battery. A battery management system stores in advance a maximum output power (maximum discharge current or maximum charge current) for a predetermined time based on a state of charge (SOC) of the battery and a temperature of the battery, and provides an output power based on the maximum output power corresponding to a current SOC and a current temperature in response to a request from the external apparatus. 
     However, in a case of using the previously-stored values, if the external apparatus requests an output power for a time which is not stored, the output power cannot be provided. Further, even if the SOC and the temperature are in the same states, the output power for the predetermined time of the battery in a static state may be different from that of the battery in a dynamic state in which charging or discharging is repeated. Therefore, when the external apparatus requests the output power for the predetermined time, a method for predicting an output power for a requested time based on a current state of the battery is required. 
     DISCLOSURE 
     Technical Problem 
     Some embodiments may provide a battery apparatus and a method of predicting a battery output, for predicting an output during any time. 
     Technical Solution 
     According to an embodiment, a battery apparatus including a battery and a processor may be provided. The processor may estimate a surface state of charge (SOC) representing a potential at an electrode surface of the battery as a first surface SOC, and predict an output of the battery during a requested time based on the first surface SOC, a cut-off voltage, and the requested time. 
     In some embodiments, the processor may determine the surface SOC at a time when a terminal voltage of the battery becomes the cut-off voltage as a second surface SOC, estimate a current of the battery for allowing the second surface SOC to be estimated from the first surface SOC after the requested time, and predict the output based on the current. 
     In some embodiments, the processor may determine an open circuit voltage of the battery at the time when the terminal voltage of the battery becomes the cut-off voltage, and determine the second surface SOC based on the open circuit voltage. 
     In some embodiments, the processor may estimate a current of the battery for allowing a second surface SOC to be estimated from the first surface SOC after the requested time, and predict the output based on the current of the battery. In this case, a terminal voltage of the battery determined based on the second surface SOC and the current may be the cut-off voltage. 
     In some embodiments, the terminal voltage may be determined based on an open circuit voltage of the battery corresponding to the second surface SOC and a voltage corresponding to the current. 
     In some embodiments, the terminal voltage may be determined based on the open circuit voltage of the battery, the voltage corresponding to the current, and an overpotential of the battery. 
     In some embodiments, the processor may determine the cut-off voltage based on a temperature of the battery. 
     In some embodiments, the processor may decrease the predicted output in response to a voltage of the battery corresponding to the predicted output reaching a derating voltage. 
     In some embodiments, the processor may estimate the first surface SOC based on a plurality of parameters including a first parameter determined based on a measured current of the battery and a second parameter determined based on an SOC of the battery. 
     According to another embodiment, a method of predicting an output of a battery may be provided. The method may include estimating a state of the battery, and predicting an output of the battery during a requested time based on the state of the battery, a cut-off voltage, and the requested time. 
     In some embodiments, the state of the battery may include a surface SOC representing a potential at an electrode surface of the battery. 
     In some embodiments, predicting the output of the battery may include estimating a current of the battery for allowing a specific surface SOC to be estimated from the estimated surface SOC after the requested time, and predicting the output based on the current. In this case, a terminal voltage of the battery determined based on the specific surface SOC and the current may be the cut-off voltage. 
     In some embodiments, the terminal voltage may be determined based on an open circuit voltage of the battery corresponding to the specific surface SOC and a voltage corresponding to the current. 
     In some embodiments, estimating the state of the battery may include estimating the surface SOC based on a plurality of parameters including a first parameter determined based on a measured current of the battery and a second parameter determined based on an SOC of the battery. 
     According to yet another embodiment, a program configured to be executed by a processor of a battery apparatus and be stored in a recording medium may be provided. The program may cause the processor to execute estimating a state of the battery, and predicting an output of the battery during a requested time based on the state of the battery, a cut-off voltage, and the requested time. 
     Advantageous Effects 
     According to some embodiments, it is possible to accurately predict and provide power that the battery can provide for a time requested by the external apparatus in real time. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a drawing showing a battery apparatus according to an embodiment. 
         FIG.  2    is a diagram showing a structure of a battery according to an embodiment. 
         FIG.  3    is a diagram showing an example of a state change in a battery. 
         FIG.  4    is a diagram for explaining surface SOC estimation in a battery management system according to an embodiment. 
         FIG.  5    is a diagram showing an example of a correspondence relationship between a temperature/SOC and a kinetics coefficient in a battery according to an embodiment. 
         FIG.  6    is a diagram showing an example of a correspondence relationship between a temperature/SOC and a diffusion coefficient in a battery according to an embodiment. 
         FIG.  7    is a flowchart showing a surface SOC estimation method in a battery management system according to an embodiment. 
         FIG.  8    is a diagram for explaining battery terminal voltage estimation in a battery management system according to an embodiment. 
         FIG.  9    is a flowchart showing a battery terminal voltage estimation method in a battery management system according to an embodiment. 
         FIG.  10    is a diagram showing an example of a correspondence relationship between an SOC and an open circuit voltage in a battery according to an embodiment. 
         FIG.  11    is a diagram for explaining battery output prediction in a battery management system according to an embodiment. 
         FIG.  12    is a flowchart showing a battery output prediction method in a battery management system according to an embodiment. 
         FIG.  13    is a diagram for explaining battery output prediction in a battery management system according to another embodiment. 
         FIG.  14    is a flowchart showing a battery output prediction method in a battery management system according to another embodiment. 
     
    
    
     MODES FOR INVENTION 
     In the following detailed description, only certain embodiments have been shown and described, simply by way of illustration. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not restrictive. Like reference numerals designate like elements throughout the specification. 
     When it is described that an element is “connected” to another element, it should be understood that the element may be directly connected to the other element or connected to the other element through a third element. On the other hand, when it is described that an element is “directly connected” to another element, it should be understood that the element is connected to the other element through no third element. 
     As used herein, a singular form may be intended to include a plural form as well, unless the explicit expression such as “one” or “single” is used. 
     In flowcharts described with reference to the drawings, the order of operations or steps may be changed, several operations or steps may be merged, a certain operation or step may be divided, and a specific operation or step may not be performed. 
       FIG.  1    is a drawing showing a battery apparatus according to an embodiment, 
       FIG.  2    is a diagram showing a structure of a battery according to an embodiment, and 
       FIG.  3    is a diagram showing an example of a state change in a battery. 
     Referring to  FIG.  1   , a battery apparatus  100  has a structure that can be electrically connected to an external apparatus. When the external apparatus is a load, the battery apparatus  100  is discharged by operating as a power supply that supplies power to the load. When the external apparatus is a charger, the battery apparatus  100  is charged by receiving external power through the charger. The external apparatus operating as the load may be, for example, an electronic device, a mobility apparatus, or an energy storage system (ESS). The mobility apparatus may be, for example, a vehicle such as an electric vehicle, a hybrid vehicle, or a smart mobility. 
     The battery apparatus  100  includes a battery  110 , a voltage measuring circuit  120 , a temperature sensor  130 , a current sensor  140 , and a processor  150 . 
     The battery  110  is a rechargeable battery. The battery  100  may be, for example, a lithium battery such as a lithium ion battery or a lithium ion polymer battery, or a nickel battery such as a nickel-cadmium (NiCd) battery or a nickel-metal hydride (NiMH) battery. In some embodiments, the battery  100  may be a single battery cell, a battery module including an assembly of a plurality of battery cells or in which a plurality of assemblies are connected in series or parallel, a battery pack in which a plurality of battery modules are connected in series or parallel, or a system in which a plurality of battery packs are connected in series or parallel. 
     The voltage measuring circuit  120  measures a voltage of the battery  110 . In some embodiments, the voltage measurement circuit  120  may measure a voltage of each battery cell. 
     The temperature sensor  130  measures a temperature of the battery  110 . In some embodiments, the temperature sensor  130  may measure a temperature at a predetermined location of the battery  110 . In some embodiments, a plurality of temperature sensors  130  may be provided to measure temperatures at a plurality of locations in the battery  110 . 
     The current sensor  140  is connected to a positive output terminal or negative output terminal of the battery  110 , and measures a current of the battery  110 , i.e., a charging current or a discharging current. 
     The processor  150  estimates a state of the battery  110  based on the voltage of the battery  110  measured by the voltage measuring circuit  120 , the temperature of the battery  110  measured by the temperature sensor  130 , or the current of the battery  110  measured by the current sensor  140 . In some embodiments, the battery apparatus  100  may further include a memory  160  that stores data necessary for state estimation in the processor  150 . 
     In some embodiments, the processor  150  may form a battery management system. In some embodiments, the battery management system may further include at least one of the voltage measurement circuit  120 , the temperature sensor  130 , or the current sensor  140 . 
     Referring to  FIG.  2   , the battery  110  includes a positive electrode (or cathode)  111 , a negative electrode (or anode)  112 , and an electrolyte  113 . A structure of the battery  110  shown in  FIG.  2    is a schematic example for convenience of description, and the structure of the battery  110  is not limited thereto. In  FIG.  2   , for convenience of description, it is assumed that lithium is an active material causing a chemical reaction in the battery  110 . 
     When the battery  110  is discharged in order to supply power from the battery  110  to an external apparatus, as shown in  FIG.  2   , a chemical reaction (oxidation reaction) in which a lithium ion Li+ are discharged from the negative electrode  112  may occur on a surface of the negative electrode  112 . The discharged lithium ion Li+ may pass through the electrolyte  113  and then move to a surface of the positive electrode  111 . Accordingly, a chemical reaction (reduction reaction) in which the lithium ion Li+ is absorbed into the positive electrode  111  may occur on the surface of the positive electrode  111 . 
     When the battery  110  is charged, a chemical reaction (oxidation reaction) in which a lithium ion Li+ is discharged from the positive electrode  111  may occur on a boundary surface between the positive electrode  111  and the electrolyte  113 . The discharged lithium ion Li+ may pass through the electrolyte  113  and then move to the surface of the negative electrode  112 . Accordingly, a chemical reaction (reduction reaction) in which the lithium ion Li+ is absorbed into the negative electrode  112  may occur on the surface of the negative electrode  112 . 
     A terminal voltage of the battery  110  may be appeared in a form of summing a potential at a battery electrode surface corresponding to the positive electrode  111  and the negative electrode  112 , voltage drop due to an ohmic resistance (internal resistance) formed by the electrolyte  113  and the like, and an over-potential due to electrochemical reaction. The overpotential may represent voltage drop occurred by deviation from an equilibrium potential due to polarization at each battery electrode. The overpotential is also called a polarization voltage. 
     As shown in  FIG.  3   , when the battery  110  starts discharging, the terminal voltage Vt of the battery  110  momentarily drops due to the voltage drop Vohmic by the ohmic resistance Rohmic, and then gradually decreases due to a transient change V 1  of the overpotential. In general, the transient change V 1  of the overpotential may be expressed as a change depending on a time constant defined in a parallel circuit of a resistor and a capacitor. At this time, the actual terminal voltage Vt of the battery  110  decreases with a constant slope along with the transient change V 1  of the overpotential. That is, as shown in  FIG.  3   , a decrease Vk according to the constant slope and a decrease V 1  according to the transient change of the overpotential appear together. This slope is determined by a magnitude of a current flowing through the battery  110 . As described above, the phenomenon in which the terminal voltage Vt of the battery  110  decreases with the certain slope occurs because concentration of the active material on the electrode surface due to an oxidation/reduction reaction of the active material is lower than an average concentration. That is, the voltage change Vk according to the constant slope may occur by a voltage change (change due to discharging or charging) caused by an oxidation/reduction reaction rate and a voltage change caused by a diffusion resistance (concentration difference) in a relaxation period after the current disappears. 
     In general, a state of the battery  110  is determined as a state of charge (SOC) representing an average concentration at the whole of the battery  110 , and the terminal voltage Vt of the battery  110  is estimated based on the open circuit voltage of the battery  110 , the voltage drop (Vohmic) due to the ohmic resistance (Rohmic), and the overpotential. At this time, the open circuit voltage is estimated based on the SOC of the battery  110 . However, the SOC represents the average concentration (e.g., the average concentration at the electrode) inside the battery  110  rather than the concentration on the surface of the battery electrode, and gradually decreases when the battery  110  is discharged as shown in  FIG.  3   . Therefore, when the open circuit voltage of the battery  110  is estimated based on the SOC, the terminal voltage of the battery  110  may not be accurately estimated. Accordingly, in some embodiments, a surface state of charge (SOC) capable of determining the potential at the electrode surface of the battery  110  is provided. Such a surface SOC may represent the concentration of the active material on the electrode surface of the battery  110 . 
       FIG.  4    is a diagram for explaining surface SOC estimation in a battery management system according to an embodiment,  FIG.  5    is a diagram showing an example of a correspondence relationship between a temperature/SOC and a kinetics coefficient in a battery according to an embodiment, and  FIG.  6    is a diagram showing an example of a correspondence relationship between a temperature/SOC and a diffusion coefficient in a battery according to an embodiment. 
     Referring to  FIG.  4   , a processor (e.g.,  150  in  FIG.  1   ) of a battery management system may estimate a surface SOC of a battery (e.g.,  110  in  FIG.  1   ) based on measured information of the battery  110  including a current of the battery  110 , using a surface SOC estimation model  410 . In some embodiments, the surface SOC may be estimated as a percentage. In some embodiments, the processor  150  may estimate an SOC of the battery  110  representing an average concentration based on the measured information of the battery including the current of the battery  110 , using the surface SOC estimation model  410 . 
     As described with reference to  FIG.  3   , when the battery  110  is discharged, a terminal voltage of the battery  110  may decrease with a certain slope. Since the phenomenon in which the terminal voltage of the battery  110  decrease with the certain slope occurs because concentration of an active material on an electrode surface decreases by an oxidation/reduction reaction of the active material, the certain slope is proportional to the current of the battery  110 . Accordingly, the surface SOC estimation model  410  may estimate the surface SOC based on the reaction rate determined by the current of the battery  110 . In some embodiments, a reaction rate (kinetics) may be determined based on a value obtained by reflecting a specific coefficient to the current of the battery  110 . Hereinafter, such a specific factor is referred to as a “kinetics coefficient”. In one embodiment, the reaction rate may be determined based on a product of the current of the battery  110  and the kinetics coefficient. 
     The reaction rate of the oxidation/reduction reaction may be determined by the temperature of the battery  110  and the average concentration inside the battery  110 . Thus, in some embodiments, the kinetics coefficient may vary depending on the temperature of the battery  110  and the SOC of the battery  110 . In one embodiment, the SOC of the battery  110  may include the SOC of the battery  110  representing the average concentration. In another embodiment, the SOC of the battery  110  may include the surface SOC of the battery  110 . In yet another embodiment, the SOC of the battery  110  may include the SOC of the battery  110  representing the average concentration and the surface SOC of the battery  110 . That is, the surface SOC estimation model  410  may determine the kinetics coefficient based on the temperature of the battery  110  and the SOC of the battery  110 . In some embodiments, as shown in  FIG.  5   , a correspondence relationship between the temperature/SOC of the battery  110  and the kinetics coefficient may be predefined through experiments. In some embodiments, a memory of the battery management system may store such correspondence relationship, for example, in the form of a lookup table. In some embodiments, the surface SOC estimation model  410  may determine the kinetics coefficient based on either the temperature of the battery  110  or the SOC of the battery  110 . 
     When the concentration on the electrode surface is lower than the average concentration by the oxidation/reduction reaction on the electrode surface, a resistance component in which the reaction on the electrode surface is lowered by a diffusion rate caused by a concentration difference between the concentration on the electrode surface and the average concentration may appear. Such a resistance caused by the diffusion (hereinafter referred to as a “diffusion resistance”) may be expressed as a force that suppresses the oxidation/reduction reaction in a reverse direction. Therefore, the surface SOC estimation model  410  additionally reflects the diffusion resistance when estimating the surface SOC. In some embodiments, the diffusion resistance may be determined based on a difference between the SOC representing the average concentration and the surface SOC representing the concentration on the electrode surface. In some embodiments, the surface SOC estimation model  410  may estimate the surface SOC based on a value obtained by reflecting a specific coefficient to the difference between the SOC and the surface SOC. Hereinafter, such a specific coefficient is referred to as a “diffusion coefficient”. In one embodiment, the surface SOC estimation model  410  may estimate the surface SOC based on a product of the diffusion coefficient and the difference between the SOC and the surface SOC. 
     The reaction rate of the oxidation/reduction reaction may be determined based on the temperature of the battery  110  and the average concentration inside the battery  110 . Thus, in some embodiments, the diffusion coefficient that suppresses the oxidation/reduction reaction may vary depending on the temperature of the battery  110  and the SOC of the battery  110 . In one embodiment, the SOC of the battery  110  may include the SOC of the battery  110  representing an average concentration. In another embodiment, the SOC of the battery  110  may include the surface SOC of the battery  110 . In yet another embodiment, the SOC of the battery  110  may include the SOC of the battery  110  representing the average concentration and the surface SOC of the battery  110 . That is, the surface SOC estimation model  410  may determine the diffusion coefficient based on the temperature of the battery  110  and the SOC of the battery  110 . In some embodiments, as shown in  FIG.  6   , a correspondence relationship between the temperature/SOC of the battery  110  and the diffusion coefficient may be predefined through experiments. In some embodiments, the memory of the battery management system may store the correspondence relationship, for example, in the form of a lookup table. In some embodiments, the surface SOC estimation model  410  may determine the diffusion coefficient based on either the temperature of the battery  110  or the SOC of the battery  110 . 
     In some embodiments, the surface SOC estimation model  410  may estimate the surface SOC at a current time point by reflecting at least a change due to the reaction rate from a previous time point to the current time point and a change due to the diffusion resistance from the previous time point to the current time point to the surface SOC estimated at the previous time point. In some embodiments, the processor  150  may predefine an initial value SSOC[ 0 ] of the surface SOC for estimating the surface SOC. 
       FIG.  7    is a flowchart showing a surface SOC estimation method in a battery management system according to an embodiment. 
     Referring to  FIG.  7   , a processor (e.g.,  150  in  FIG.  1   ) inputs measured information of a battery (e.g.,  110  in  FIG.  1   ) to a surface SOC estimation model at S 710 . The measured information of the battery  110  may include a current of the battery  110 . 
     In some embodiments, the current of the battery  110  may be a charging or discharging current of the battery  110  measured by a current sensor (e.g.,  140  in  FIG.  1   ). In some embodiments, the measured information of the battery  110  may further include a measured voltage of the battery  110 . In some embodiments, the measured voltage of the battery  110  may be an average cell voltage, and the average cell voltage may be an average value of voltages of a plurality of battery cells. In some embodiments, the measured voltage of the battery  110  may be a sum of voltages of the plurality of battery cells. In some embodiments, the measured information of the battery  110  may further include a temperature of the battery  110 . In some embodiments, the temperature of the battery  110  may be a temperature measured by a temperature sensor (e.g.,  130  in  FIG.  1   ) 
     The processor  150  determines a plurality of parameters at time point t using the surface SOC estimation model at S 720  and S 730 . The plurality of parameters may include a parameter corresponding to a reaction rate and a parameter corresponding to a diffusion resistance. 
     The processor  150  determines the reaction rate K[t] of the battery  110  at time point t using the surface SOC estimation model at S 720 . The processor  150  may calculate the reaction rate K[t] as a product Kc*I[t] of a kinetics coefficient Kc and the temperature of the battery  110  at time point t. In some embodiments, the processor  110  may extract the kinetics coefficient Kc corresponding to the temperature of the battery  110  and the SOC of the battery  110  from a memory. In some embodiments, the memory may be a memory (e.g.,  160  in  FIG.  1   ) of a battery management system. In some embodiments, the processor  150  may estimate the SOC of the battery  110  based on the measured information of the battery  110 . In some embodiments, the processor  150  may estimate the SOC using any one of various known methods, and the present invention is not limited to the method of estimating the SOC. 
     In addition, the processor  150  determines the diffusion resistance D[t] of the battery  110  at time point t using the surface SOC estimation model at S 730 . The processor  150  may calculate the diffusion resistance D[t] as a product Dc*ΔSOC[t] of a difference ΔSOC[t] between the SOC and the surface SOC at time point t and the diffusion coefficient Dc. In some embodiments, the processor  110  may extract the diffusion coefficient Dc corresponding to the temperature of the battery  110  and the SOC of the battery  110  from the memory. In some embodiments, the memory may be the memory  160  of the battery management system. 
     Next, at S 740 , the processor  150  estimates the surface SOC SSOC[t+1] at the time point (t+1) based on the surface SOC SSOC[t], the reaction rate K[t], and the diffusion resistance D[t] estimated at time point t, using the surface SOC estimation model. In some embodiments, the processor  150  may estimate the surface SOC SSOC[t+1] as in Equation 1 or 2. 
       SSOC[ t +1]=SSOC[ t ]+( K[t]+D [ t ])·Δ t    Equation 1
 
       SSOC[ t +1]=SSOC[ t ]+( Kc·I [ t ]+ Dc ·ΔSOC[ t ]) Δ t    Equation 2
 
     In Equations 1 and 2, Δt denotes a time change (time difference) between time point (t+1) and time point t. 
     In some embodiments, the surface SOC estimation model may accurately estimate the surface SOC by repeatedly performing the estimation of the surface SOC. In some embodiments, an adaptive filter may be used as the surface SOC estimation model. 
     According to above-described embodiments, the state of the battery  110  can be accurately estimated by using the surface SOC that can accurately represent the potential of the electrode surface of the battery  110 . 
     Next, embodiments of estimating a terminal voltage of the battery  110  using a surface SOC are described with reference to  FIG.  8   ,  FIG.  9   , and  FIG.  10   . 
       FIG.  8    is a diagram for explaining battery terminal voltage estimation in a battery management system according to an embodiment,  FIG.  9    is a flowchart showing a battery terminal voltage estimation method in a battery management system according to an embodiment, and  FIG.  10    is a diagram showing an example of a correspondence relationship between an SOC and an open circuit voltage in a battery according to an embodiment. 
     Referring to  FIG.  8    and  FIG.  9   , a processor (e.g.,  150  of  FIG.  1   ) estimates a surface SOC using a surface SOC estimation model (e.g.,  410  of  FIG.  4   ). That is, as described with reference to  FIG.  7   , the processor inputs measured information of the battery ( 110  in  FIG.  1   ) to the surface SOC estimation model  410  at S 910 , calculates a reaction rate K[t] and a diffusion resistance D[t] of the battery  110  at S 920  and S 930 , and estimate the surface SOC SSOC[t+ 1 ] based on the reaction rate K[t] and the diffusion resistance D[t] at S 940 . 
     Next, the processor  150  inputs the SOC, the surface SOC, and a current of the battery  110  to a terminal voltage estimation model  810 , and estimates a terminal voltage of the battery  110  using the terminal voltage estimation model  810 . 
     To this end, the processor  150  estimates an open circuit voltage of the battery  110  based on the surface SOC at S 950 . The processor  150  may estimate the open circuit voltage Voc based on a non-linear functional relationship Voc=f(SSOC) between the surface SOC SSOC and the open circuit voltage Voc. In general, a memory (e.g.,  160  in  FIG.  1   ) of the battery management system stores a correspondence relationship between the open circuit voltage Voc of the battery  110  and the SOC of the battery  110  in advance. For example, the correspondence relationship between the open circuit voltage Voc and the SOC may be defined as shown in  FIG.  10   . In this case, the processor  150  determines the open circuit voltage Voc by inputting the surface SOC instead of the SOC. For example, when the surface SOC is 70%, the processor  150  may extract an open circuit voltage corresponding to the SOC of 70% from the memory. In some embodiments, the correspondence relationship between the open circuit voltage and the SOC may be stored per temperature. In this case, the processor  150  may determine the open circuit voltage based on the correspondence relationship between the SOC and the open circuit voltage, corresponding to the temperature of the battery  110 , among various correspondence relationships. 
     Further, the processor  150  estimates an overpotential due to polarization at S 960 . Since the overpotential is caused by deviation of a potential at an electrode surface from an equilibrium potential, the processor  150  estimates the overpotential based on the surface SOC representing the potential at the electrode surface and the SOC representing the equilibrium potential. In some embodiments, the processor  150  may estimate the overpotential based on a value obtained by comparing the SOC and the surface SOC. In one embodiment, the value obtained by comparing the SOC and the surface SOC may be a ratio of the SOC and the surface SOC. In another embodiment, the value obtained by comparing the SOC and the surface SOC may be a difference between the SOC and the surface SOC. In some embodiments, the processor  150  may estimate the overpotential V 1 [t+1] at time point (t+1) based on the overpotential V 1 [t], the SOC SOC[t], and the surface SOC SSOC[t] at time point t, using the terminal voltage estimation model  810 . In some embodiments, the processor  150  may estimate the overpotential V 1 [t+1], for example, as in Equation 3. 
         V 1[ t +1]= V 1[ t ]+α(SOC[ t ]/SSOC[ t ])   Equation 3
 
     In Equation 3, a denotes an overpotential coefficient. 
     In some embodiments, the overpotential coefficient a may be determined by experiments. In some embodiments, the overpotential coefficient a may be determined by repeatedly performing overpotential estimation using an adaptive filter. In some embodiments, the processor  150  may predefine an initial value B 1 [0] of the overpotential for estimating the overpotential. 
     In addition, the processor  150  estimates a voltage due to an ohmic resistance of the battery  110  at S 970 . The processor  150  estimates the voltage Vohmic due to the ohmic resistance as a product of the ohmic resistance of the battery  110  and the current of the battery  110 . In some embodiments, the processor  150  may estimate the ohmic resistance using any one of various known methods, and the present invention is not limited to the method for estimating the ohmic resistance. 
     Next, the processor  150  determines the terminal voltage of the battery  110  based on the open circuit voltage Voc, the overpotential V 1 , and the voltage Vohmic due to the ohmic resistance at S 980 . In some embodiments, as shown in Equation 4, the processor  150  may determine a sum of the open circuit voltage Voc, the overpotential V 1 , and the voltage Vohmic by the ohmic resistance as the terminal voltage Vt of the battery  110 . 
       Vt=Voc+ V 1+Vohmic   Equation 4
 
     While the surface SOC estimating method or the terminal voltage estimating method has been described in a case of discharging the battery, the surface SOC estimating method or the terminal voltage estimating method according to above-described embodiments may be applied to a case of charging the battery. As shown in  FIG.  3   , in the discharging, the surface SOC representing the surface concentration appears lower than the SOC representing the average concentration, whereas in the charging, the surface SOC may appear higher than the SOC. 
     According to the above-described embodiments, by estimating the surface SOC representing the potential at the electrode surface based on the current of the battery and the oxidation/reduction reaction of the active material, it is possible to accurately estimate the state of the battery not only in a static state of the battery but also in a dynamic state in which charging or discharging is repeated. 
     Next, a method for predicting a battery output in a battery management system according to an embodiment is described with reference to  FIG.  11    and  FIG.  12   . 
       FIG.  11    is a diagram for explaining battery output prediction in a battery management system according to an embodiment, and  FIG.  12    is a flowchart showing a battery output prediction method in a battery management system according to an embodiment. 
     Referring to  FIG.  11    and  FIG.  12   , a processor (e.g.,  150  in  FIG.  1   ) predicts a battery output using an output prediction model  1110 . The processor  150  receives a desired requested time from an external apparatus (e.g., a vehicle) at S 1210 . Accordingly, the processor  150  may predict the battery output (e.g., power) for the requested time and provide the battery output to the vehicle. 
     In order to predict the battery output, the processor  150  inputs a state of a battery estimated at a current time point to the output prediction model  1110  at S 1220 . In some embodiments, the state of the battery may include a surface SOC described above. In some embodiments, the processor  150  may additionally input an SOC calculated at the current time point to the output prediction model  1110  at S 1220 . 
     Further, the processor  150  inputs a cut-off voltage and the requested time received from the vehicle to the output prediction model  1110  at S 1220 . In some embodiments, the cut-off voltage may be a lower-limit voltage upon discharging of the battery  110 . In some embodiments, the processor  150  may determine the cut-off voltage based on a temperature of the battery  110 . In some embodiments, a correspondence relationship between the temperature of the battery  110  and the cut-off voltage may be predefined. In some embodiments, a memory (e.g.,  160  in  FIG.  1   ) of a battery management system may store the correspondence relationship. In some embodiments, the processor  150  may determine the cut-off voltage in response to a request from the external apparatus. 
     The output prediction model  1110  predicts the battery output based on the surface SOC, the cut-off voltage, and the request time at S 1230 , S 1240 , and S 1250 . In some embodiments, the output prediction model  1110  may determine the surface SOC at a time when the terminal voltage of the battery becomes the cut-off voltage at S 1230 , and estimate, based on the inputted surface SOC, a current for allowing the surface SOC at the time when the terminal voltage becomes the cut-off voltage to be estimated after the requested time at S 1240 . 
     In some embodiments, as described with reference to  FIG.  8    and  FIG.  9   , the terminal voltage of the battery may be determined based on an open circuit voltage Voc of the battery, an overpotential VI, and a voltage due to an ohmic resistance, and the voltage due to the ohmic resistance may be determined as a product of a magnitude of the ohmic resistance RO and a magnitude of the current of the battery. As described above, since the overpotential VI and the ohmic resistance RO can be estimated and converge to specific values after a certain time elapses, the output prediction model  1110  may estimate the open circuit voltage Voc and the current I of the battery at the time when the terminal voltage of the battery reaches the cut-off voltage Vc. In one embodiment, the output prediction model  1110  may estimate the open circuit voltage Voc and the current I of the battery based on Equation  5 . In this case, the open circuit voltages Voc corresponding to various magnitudes I of the current may be estimated, respectively. 
       Vc=Voc+ V 1 +R 0· I    Equation 5
 
     In Equation 5, the cut-off voltage Vc, the overpotential VI, and the magnitude RO of the ohmic resistance have predetermined values. 
     As described with reference to  FIG.  4    to  FIG.  7   , since the open circuit voltage of the battery is determined by the surface SOC, the output prediction model  1110  may determine, based on the estimated open circuit voltage Voc the surface SOC SSOC[k+1] at the time when the terminal voltage reaches the cut-off voltage. In some embodiments, the output prediction model  1110  may determine, based on the inputted surface SOC SSOC[k], the current I[k] for allowing the determined surface SOC SSOC[k+1] corresponding to the cut-off voltage to be estimated after the requested time Lt. In one embodiment, the output prediction model  1110  may predict the current I[k] of the battery based on Equation 6. 
       SSOC[ k +1]=SSOC[ k ]+( Kc·I [ k ]+ D [ k ])·Δ t    Equation 6
 
     In Equation 6, SSOC[k+1] is the surface SOC at the time when the terminal voltage reaches the cut-off voltage, SSOC[k] is the surface SOC that is inputted to the output prediction model  1110  and is estimated at a current time, and D[k] is a diffusion resistance, and Δt is the requested time. In some embodiments, D[k] may be determined based on the difference between the inputted surface SOC SSOC[k] and SOC SOC[k]. 
     The output prediction model  1110  may determine the current of the battery that can satisfy Equations 5 and 6 at the same time. For example, the output prediction model  1110  may determine a combination, i.e., i.e., a current that can satisfy Equation 6 from among various combinations of the open circuit voltage Voc and the current that can satisfy Equation 5. 
     The processor  150  may predict a battery output during the requested time based on the current estimated through the output prediction model  1110  and provide the predicted battery output to a vehicle at S 1250 . In some embodiments, the output prediction model  1110  may predict the estimated current of the battery as a current that the battery can provide during the requested time. In some embodiments, the output prediction model  1110  may calculate battery power based on the estimated current of the battery, and predict the calculated battery power as power that the battery can provide during the requested time. 
     According to the above-described embodiments, it is possible to accurately predict and provide power that the battery can provide during a time requested by the external apparatus (e.g., the vehicle) in real time. In some embodiments, the battery management system may predict the output based on the periodically estimated surface SSOC, so that the output can be predicted in consideration of the battery usage history. In some embodiments, the battery management system may predict the output by taking the cut-off voltage into account, thereby preventing the terminal voltage of the battery from falling below the cut-off voltage. 
       FIG.  13    is a diagram for explaining battery output prediction in a battery management system according to another embodiment, and  FIG.  14    is a flowchart showing a battery output prediction method in a battery management system according to another embodiment. 
     Referring to  FIG.  13    and  FIG.  14   , a processor (e.g.,  150  in  FIG.  1   ) predicts a battery output using an output prediction model  1310 . The processor  150  receives a desired requested time from an external apparatus (e.g., a vehicle) at S 1410 . In order to predict the battery output, the processor  150  inputs a battery state estimated at a current time to the output prediction model  1310  at S 1420 . In some embodiments, the state of the battery may include a surface SOC. Further, the processor  150  inputs a cut-off voltage and the requested time received from the vehicle to the output prediction model  1310  at S 1420 . Furthermore, the processor  150  inputs a derating voltage to the output prediction model  1310  at S 1420 . In some embodiments, the processor  150  may determine the derating voltage based on a temperature of the battery  110 . In some embodiments, a correspondence relationship between the temperature of the battery  110  and the derating voltage may be predefined. In some embodiments, a memory (e.g.,  160  in  FIG.  1   ) of a battery management system may store the correspondence relationship. 
     As described with reference to S 1230 , S 1240  and S 1250  in  FIG.  12   , the output prediction model  1310  estimates a current of the battery based on the surface SOC, the cut-off voltage and the requested time at S 1430  and S 1440 ), and predicts a battery output during the requested time based on the estimated current at S 1450 . 
     Next, the processor  150  determines whether a voltage of the battery (e.g., a terminal voltage of the battery) reaches the derating voltage at S 1460 . In some embodiments, the terminal voltage of the battery may be estimated as described with reference to  FIG.  8    to  FIG.  10   . When the voltage of the battery reaches the derating voltage, the processor  150  decrease the predicted battery output by a predetermined ratio and provides the decreased battery output as the predicted battery output at S 1470 . In some embodiments, the processor  150  may decrease the battery power predicted by the output prediction model  1310  by the predetermined ratio and provide the decreased battery power as the predicted battery output. In some embodiments, the predetermined ratio may be a ratio that is defined in advance. 
     According to the above-described embodiments, when the battery output is predicted and provided, the battery output may be predicted in consideration of the derating voltage, so that the under-voltage diagnosis can be prevented from occurring due to the lowering of the battery voltage. 
     In some embodiments, the processor (e.g.,  150  in  FIG.  1   ) may perform computation on a program for executing the surface SOC estimation method, the terminal voltage estimation method, or the battery output prediction method described above. A program for executing the surface SOC estimation method, the terminal voltage estimation method, or the battery output prediction method may be loaded into a memory. The memory may be the same memory as a memory (e.g.,  160  in  FIG.  1   ) for storing a table or a separate memory. The program may include instructions for causing the processor  150  to perform the surface SOC estimation method, the terminal voltage estimation method, or the battery output prediction method when loaded into a memory. That is, the processor may perform an operation for the surface SOC estimation method, the terminal voltage estimation method, or the battery output prediction method by executing the instructions of the program. 
     While this invention has been described in connection with what is presently considered to be practical embodiments, it is to be understood that the invention is not limited to the disclosed embodiments. On the contrary, it is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.