Patent Publication Number: US-2021167616-A1

Title: Battery management apparatus, battery management method and battery pack

Description:
TECHNICAL FIELD 
     The present disclosure relates to battery state of charge (SOC) estimation. 
     The present application claims priority to Korean Patent Application No. 10-2019-0014609 filed in the Republic of Korea on Feb. 7, 2019, the disclosure of which is incorporated herein by reference. 
     BACKGROUND ART 
     Recently, there has been dramatically growing demand for portable electronic products such as laptop computers, video cameras and mobile phones, and with the extensive development of electric vehicles, accumulators for energy storage, robots and satellites, many studies are being made on batteries that can be recharged repeatedly. 
     Currently, commercially available batteries include nickel-cadmium batteries, nickel-hydrogen batteries, nickel-zinc batteries, lithium batteries and the like, and among them, lithium batteries have little or no memory effect, and thus they are gaining more attention than nickel-based batteries for their advantages that recharging can be done whenever it is convenient, the self-discharge rate is very low and the energy density is high. 
     One of important parameters required to control the charge/discharge of a battery is State of Charge (SOC). The SOC is a parameter indicating a relative ratio of the remaining capacity to the maximum capacity indicating electrical energy stored in the battery when the battery is fully charged, and may be expressed as 0˜1 or 0%˜100%. For example, when the maximum capacity of the battery is 1000 Ah (ampere-hour) and the remaining capacity of the battery is 750 Ah, the SOC of the battery is 0.75 (or 75%). 
     Ampere counting and an equivalent circuit model are typically used to estimate the SOC of the battery. According to ampere counting, the SOC of the battery is estimated based on a cumulative current value corresponding to the current flowing through the battery accumulated over time. However, due to a measurement error of a current sensor and/or external noise, there may be a discrepancy between the SOC estimated by ampere counting and the actual SOC. The equivalent circuit model is designed to simulate the electrochemical properties of the battery. However, the battery has the nonlinear feature according to the operational state, and it is very difficult to design the equivalent circuit model for perfectly simulating the nonlinear feature of the battery. 
     To overcome the above-described drawbacks of each of the ampere counting and the equivalent circuit model, battery SOC estimation using the extended Kalman filter has been suggested. The extended Kalman filter using the ampere counting with the equivalent circuit model in combination achieves more accurate SOC estimation than when the ampere counting or the equivalent circuit model is used alone. 
     To estimate the SOC of the battery using the extended Kalman filter, it is necessary to set two process noise each associated with at least one state variable (e.g., SOC, overpotential). 
     However, since fixed values are allocated to each process noise, it is difficult to adjust the reliability of each of the ampere counting and the equivalent circuit model appropriately for the operational state of the battery and environment in which the battery is used. 
     DISCLOSURE 
     Technical Problem 
     The present disclosure is designed to solve the above-described problem, and therefore the present disclosure is directed to providing a battery management apparatus, a battery management method and a battery pack, in which a plurality of candidate values for the state of charge (SOC) of the battery is determined in each cycle, and the SOC of the battery is determined based on the relationship between the plurality of candidate values. 
     The present disclosure is further directed to providing a battery management apparatus, a battery management method and a battery pack, in which reliability of each of the ampere counting and the equivalent circuit model in the extended Kalman filter is adjusted based on each value of two components included in the Kalman gain of the extended Kalman filter determined in each cycle. 
     These and other objects and advantages of the present disclosure may be understood by the following description and will be apparent from the embodiments of the present disclosure. In addition, it will be readily understood that the objects and advantages of the present disclosure may be realized by the means set forth in the appended claims and a combination thereof. 
     Technical Solution 
     A battery management apparatus according to an aspect of the present disclosure includes a sensing unit configured to detect a current, a voltage and a temperature of a battery, and a control unit. The control unit is configured to generate a data set including a current value indicating the detected current, a voltage value indicating the detected voltage and a temperature value indicating the detected temperature. The control unit is configured to determine a first candidate value for a state of charge (SOC) of the battery based on the current value using ampere counting. The control unit is configured to determine a Kalman gain and a second candidate value for the SOC based on the data set using an extended Kalman filter. The control unit is configured to determine the SOC to be equal to the first candidate value when a difference value between the first candidate value and the second candidate value is larger than a threshold value. The control unit is configured to set a ratio of a second process noise to a first process noise in the extended Kalman filter to be equal to a predetermined reference ratio when a first component of the Kalman gain is equal to or higher than a predetermined first lower limit and a second component of the Kalman gain is equal to or higher than a predetermined second lower limit. The first process noise is associated with reliability of the ampere counting. The second process noise is associated with reliability of an equivalent circuit model of the battery. 
     The control unit may be configured to set the first process noise to be equal to a predetermined first reference value and the second process noise to be equal to a predetermined second reference value when the first component of the Kalman gain is equal to or higher than the first lower limit and the second component of the Kalman gain is equal to or higher than the second lower limit. The reference ratio may be a value obtained by dividing the second reference value by the first reference value. 
     The control unit may be configured to reduce the radio of the second process noise to the first process noise below the reference ratio when the first component is lower than the first lower limit and the second component is equal to or higher than the second lower limit. 
     The control unit may be configured to determine the first process noise to be equal to a value that is larger than the first reference value or determine the second process noise to be equal to a value that is smaller than the second reference value when the first component is lower than the first lower limit and the second component is equal to or higher than the second lower limit. 
     The control unit may be configured to increase the ratio of the second process noise to the first process noise above the reference ratio when the first component is equal to or higher than the first lower limit and the second component is lower than the second lower limit. 
     The control unit may be configured to determine the first process noise to be equal to a value that is smaller than the first reference value or determine the second process noise to be equal to a value that is larger than the second reference value when the first component is equal to or higher than the first lower limit and the second component is lower than the second lower limit. 
     The control unit may be configured to determine the first process noise and the second process noise using the following Equations 1 and 2 when the first component is lower than the first lower limit or the second component is lower than the second lower limit: 
         W 1 k =( M   1   D   1   −M   2   D   2 )+ M   W1    &lt;Equation 1&gt;
 
         W 2 k =( M   4   D   2   −M   3   D   1 )+ M   W2    &lt;Equation 2&gt;
 
     wherein D 1  denotes an absolute value of a difference between the first component and the first lower limit, D 2  denotes an absolute value of a difference between the second component and the second lower limit, M W1  denotes the first reference value, M W2  denotes the second reference value, M 1  denotes a first weight, M 2  denotes a second weight, M 3  denotes a third weight, M 4  denotes a fourth weight, W 1   k  denotes the first process noise, and W 2   k  denotes the second process noise. 
     The control unit may be configured to determine the SOC to be equal to the second candidate value rather than the first candidate value when the difference value is equal to or smaller than the threshold value. 
     The control unit may be configured to selectively output a switching signal for controlling a switch installed on a current path of the battery. The control unit may be configured to regulate a duty cycle of the switching signal to be equal to or smaller than a reference duty cycle when the first component is lower than the first lower limit or the second component is lower than the second lower limit. 
     A battery pack according to another aspect of the present disclosure includes the battery management apparatus. 
     A battery management method according to still another aspect of the present disclosure includes detecting a current, a voltage and a temperature of a battery, generating a data set including a current value indicating the detected current, a voltage value indicating the detected voltage and a temperature value indicating the detected temperature, determining a first candidate value for an SOC of the battery based on the current value using ampere counting, determining a Kalman gain and a second candidate value for the SOC based on the data set using an extended Kalman filter, determining the SOC to be equal to the first candidate value when a difference value between the first candidate value and the second candidate value is larger than a threshold value, and setting a ratio of a second process noise to a first process noise in the extended Kalman filter to be equal to a predetermined reference ratio when a first component of the Kalman gain is equal to or higher than a predetermined first lower limit and a second component of the Kalman gain is equal to or higher than a predetermined second lower limit. The first process noise is associated with reliability of the ampere counting. The second process noise is associated with reliability of an equivalent circuit model of the battery. 
     The battery management method may further include reducing the ratio of the second process noise to the first process noise below the reference ratio when the first component is lower than the first lower limit and the second component is equal to or higher than the second lower limit. 
     The battery management method may further include increasing the ratio of the second process noise to the first process noise above the reference ratio when the first component is equal to or higher than the first lower limit and the second component is lower than the second lower limit. 
     Advantageous Effects 
     According to at least one of the embodiments of the present disclosure, it is possible to determine the state of charge (SOC) of the battery more accurately based on the relationship between a plurality of candidate values determined for the SOC of the battery in each cycle. 
     In addition, according to at least one of the embodiments of the present disclosure, it is possible to adjust the reliability of each of the ampere counting and the equivalent circuit model in the extended Kalman filter based on each value of two components included in the Kalman gain of the extended Kalman filter determined in each cycle. 
     The effects of the present disclosure are not limited to the effects mentioned above, and these and other effects will be clearly understood by those skilled in the art from the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is an exemplary diagram of a configuration of a battery pack according to an embodiment of the present disclosure. 
         FIG. 2  is an exemplary diagram of a circuit configuration of an equivalent circuit model of a battery. 
         FIG. 3  is an exemplary diagram of an open circuit voltage (OCV)-state of charge (SOC) curve of a battery. 
         FIGS. 4 and 5  are exemplary flowcharts of a battery management method performed by a battery management apparatus of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, the preferred embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. Prior to the description, it should be understood that the terms or words used in the specification and the appended claims should not be construed as being limited to general and dictionary meanings, but rather interpreted based on the meanings and concepts corresponding to the technical aspects of the present disclosure on the basis of the principle that the inventor is allowed to define the terms appropriately for the best explanation. 
     Therefore, the embodiments described herein and illustrations shown in the drawings are just a most preferred embodiment of the present disclosure, but not intended to fully describe the technical aspects of the present disclosure, so it should be understood that a variety of other equivalents and modifications could have been made thereto at the time that the application was filed. 
     The terms including the ordinal number such as “first”, “second” and the like, are used to distinguish one element from another among various elements, but not intended to limit the elements by the terms. 
     Unless the context clearly indicates otherwise, it will be understood that the term “comprises” when used in this specification, specifies the presence of stated elements, but does not preclude the presence or addition of one or more other elements. Additionally, the term “control unit” as used herein refers to a processing unit of at least one function or operation, and this may be implemented by either hardware or software or a combination of hardware and software. 
     In addition, throughout the specification, it will be further understood that when an element is referred to as being “connected to” another element, it can be directly connected to the other element or intervening elements may be present. 
       FIG. 1  is an exemplary diagram of a configuration of a battery pack according to an embodiment of the present disclosure,  FIG. 2  is an exemplary diagram of a circuit configuration of an equivalent circuit model of a battery, and  FIG. 3  is an exemplary diagram of an open circuit voltage (OCV)-state of charge (SOC) curve of the battery. 
     Referring to  FIG. 1 , the battery pack  10  is configured to supply electrical energy required for an electricity powered device such as an electric vehicle  1 , and includes a battery  20 , a switch  30  and a battery management apparatus  100 . 
     The battery  20  includes at least one battery cell. Each battery cell may be, for example, a lithium ion cell. Of course, the type of the battery cell is not limited to the lithium ion cell, and may include, without limitation, any type that can be recharged repeatedly. Each battery cell included in the battery  20  is electrically connected to other battery cell in series or in parallel. 
     The switch  30  is installed on a current path for charging and discharging the battery  20 . A control terminal of the switch  30  is provided to be electrically connected to a control unit  120 . The switch  30  is controlled to be turned on and off according to the duty cycle of a switching signal SS outputted by the control unit  120 , in response to the switching signal SS being applied to the control terminal. When the switching signal SS is high-level, the switch  30  may be turned on, and when the switching signal SS is low-level, the switch  30  may be turned off. 
     The battery management apparatus  100  is provided to be electrically connected to the battery  20  to periodically determine the SOC of the battery  20 . The battery management apparatus  100  includes a sensing unit  110 , the control unit  120 , a memory unit  130  and a communication unit  140 . 
     The sensing unit  110  is configured to detect the voltage, current and temperature of the battery  20 . The sensing unit  110  includes a current sensor  111 , a voltage sensor  112  and a temperature sensor  113 . 
     The current sensor  111  is provided to be electrically connected to the charge/discharge path of the battery  20 . The current sensor  111  is configured to detect the current flowing through the battery  20 , and output a signal SI indicating the detected current to the control unit  120 . 
     The voltage sensor  112  is provided to be electrically connected to positive and negative terminals of the battery  20 . The voltage sensor  112  is configured to detect the voltage across the positive and negative terminals of the battery  20 , and output a signal SV indicating the detected voltage to the control unit  120 . 
     The temperature sensor  113  is configured to detect the temperature of an area within a predetermined distance from the battery  20 , and output a signal ST indicating the detected temperature to the control unit  120 . 
     The control unit  120  is operably coupled to the sensing unit  110 , the memory unit  130 , the communication unit  140  and the switch  30 . The control unit  120  may be implemented in hardware using at least one of application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), microprocessors and electrical units for performing other functions. 
     The control unit  120  is configured to periodically receive the signal SI, the signal SV and the signal ST outputted by the sensing unit  110 . The control unit  120  is configured to determine a current value, a voltage value and a temperature value from the signal SI, the signal SV and the signal ST respectively using an analog-to-digital converter (ADC) included in the control unit  120 , and store a data set including the current value, the voltage value and the temperature value in the memory unit  130 . 
     The memory unit  130  is operably coupled to the control unit  120 . The memory unit  130  may store programs and data necessary to perform the steps described below. The memory unit  130  may include, for example, at least one type of storage medium of flash memory type, hard disk type, Solid State Disk (SSD) type, Silicon Disk Drive (SDD) type, multimedia card micro type, random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM) and programmable read-only memory (PROM). 
     The communication unit  140  may be coupled to communicate with an external device  2  such as an Electronic Control Unit (ECU) of the electric vehicle  1 . The communication unit  140  may receive a command message from the external device  2 , and provide the received command message to the control unit  120 . The command message may be a message requesting the activation of a specific function (e.g., SOC estimation, control of ON/OFF of the switch  30 ) of the battery management apparatus  100 . The communication unit  140  may send a notification message from the control unit  120  to the external device  2 . The notification message may be a message for notifying the result (e.g., the estimated SOC) of the function performed by the control unit  120  to the external device  2 . For example, the communication unit  140  may communicate with the external device  2  via a wired network such as a local area network (LAN), a controller area network (CAN) and a daisy chain and/or a short range wireless network, for example, Bluetooth, Zigbee and WiFi. 
     The control unit  120  is configured to determine the state of health (SOH) or the maximum capacity of the battery  20 . The maximum capacity indicates the maximum amount of charges that can be currently stored in the battery  20 , and may be referred to as ‘full charge capacity’. That is, the maximum capacity is equal to the cumulative value of currents flowing during discharging of the battery  20  at SOC of 1 (=100%) until the SOC is 0 (=0%). In an example, the control unit  120  may calculate the internal resistance of the battery  20 , and determine the SOH or the maximum capacity of the battery  20  based on a difference between the calculated internal resistance and the reference resistance. In another example, the control unit  120  may determine the SOH or the maximum capacity of the battery  20 , based on the SOC at each of different time points at which the battery  20  is charged and discharged and the cumulative current value for a period of time between the two time points, using the following Equation 1. Assume that the earlier time point of the two time points is ti, and the later time point is t 2 . 
     
       
         
           
             
               
                 
                   
                     SOH 
                     new 
                   
                   = 
                   
                     
                       
                         
                           
                             ∫ 
                             
                               t 
                               1 
                             
                             
                               t 
                               2 
                             
                           
                            
                           
                             
                               i 
                               t 
                             
                              
                             dt 
                           
                         
                         
                           
                             SOC 
                             2 
                           
                           - 
                           
                             SOC 
                             1 
                           
                         
                       
                       
                         Q 
                         ref 
                       
                     
                     = 
                     
                       
                         
                           
                             Δ 
                              
                             C 
                           
                           
                             Δ 
                              
                             SO 
                              
                             C 
                           
                         
                         
                           Q 
                           ref 
                         
                       
                       = 
                       
                         
                           Q 
                           est 
                         
                         
                           Q 
                           ref 
                         
                       
                     
                   
                 
               
               
                 
                   &lt; 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   &gt; 
                 
               
             
           
         
       
     
     In Equation 1, Q ref  denotes reference capacity, SOC 1  denotes SOC estimated at the time point t 1 , SOC 2  denotes SOC estimated at the time point t 2 , ΔSOC denotes a difference between SOC 1  and SOC 2 , i t  denotes a current value indicating the current detected at a time point t between the time point t 1  and the time point t 2 , ΔC denotes the cumulative current value for a period of time from the time point t 1  to the time point t 2 , Q est  denotes an estimate of maximum capacity at the time point t 2 , and SOH new  denotes an estimate of SOH at the time point t 2 . Q ref  is a preset value indicating the maximum capacity when the SOH of the battery  20  is 1, and may be pre-stored in the memory unit  130 . 
     In relation to Equation 1, when ΔSOC is too small, Q est  may be greatly different from the actual one. Accordingly, the control unit  120  may be configured to determine the SOH or the maximum capacity of the battery  20  using Equation 1 only when ΔSOC is equal to or larger than a predetermined value (e.g., 0.5). 
     Hereinafter, the operation for estimating the SOC of the battery  20 , performed by the control unit  120 , will be described in more detail. 
     The control unit  120  determines a first candidate value based on the current value using ampere counting. The first candidate value indicates an estimate of SOC of the battery  20  in the current cycle. The following Equation 2 may be used to determine the first candidate value. 
     
       
         
           
             
               
                 
                   
                     SOC 
                      
                     
                       [ 
                       
                         k 
                         + 
                         1 
                       
                       ] 
                     
                   
                   = 
                   
                     
                       
                         SOC 
                         e 
                       
                        
                       
                         [ 
                         k 
                         ] 
                       
                     
                     + 
                     
                       
                         
                           i 
                            
                           
                             [ 
                             
                               k 
                               + 
                               1 
                             
                             ] 
                           
                         
                          
                         
                           Δ 
                            
                           t 
                         
                       
                       
                         Q 
                         
                           e 
                            
                           s 
                            
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   &lt; 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   &gt; 
                 
               
             
           
         
       
     
     Below is the description of the symbols used in Equation 2. Δt denotes the time length per cycle. K is a time index that increases by 1 each time Δt passes away, and indicates the number of cycles from the time point at which a predetermined event occurred to the current time point. The event may be, for example, a starting event of the charging and discharging of the battery  20  of which voltage is stabilized. The battery  20  of which voltage is stabilized may be the battery  20  on no-load condition in which the current does not flow through the battery  20  and the voltage of the battery  20  is uniformly maintained. In this case, SOC e [0] may be determined from an OCV-SOC curve defining a correspondence relationship between OCV and SOC of the battery  20  using the OCV of the battery  20  at the time point when the event occurred as an index. The OCV-SOC curve is stored in the memory unit  130 . 
     In Equation 2, i[k+1] denotes the current detected in the current cycle, and SOC e [k] denotes the SOC determined in the previous cycle by the ampere counting or the extended Kalman filter. SOC[k+1] is the first candidate value. In Equation 2, i[k+1] may be replaced with i[k]. 
     The control unit  120  determines a second candidate value using the extended Kalman filter. The second candidate value indicates an estimate of SOC of the battery  20  in the current cycle. Hereinafter, the extended Kalman filter will be described. 
     The extended Kalman filter is an algorithm for periodically updating the SOC of the battery  20 , by additionally using the equivalent circuit model  200  of the battery  20  together with the ampere counting represented by Equation 2. 
     Referring to  FIG. 2 , the equivalent circuit model  200  includes an OCV source  210 , an ohm resistor R 1  and a resistor-capacitor (RC) pair  220 . 
     The OCV source  210  simulates the OCV that is the voltage between the positive and negative electrodes of the battery  20  electrochemically stabilized for a long term. The OCV outputted by the OCV source  210  is in a nonlinear functional relationship with the SOC of the battery  20 . That is, OCV=f 1 (SOC), SOC=f 2 (OCV), and f 1  and f 2  are inverse functions of each other. For example, referring to  FIG. 3 , 3.3 V=f 1 (0.5), and 0.7=f 2 (3.47 V). 
     The OCV outputted by the OCV source  210  may be preset by SOC and temperature through experimentation. 
     The ohm resistor R 1  is associated with IR drop V 1  of the battery  20 . The IR drop refers to an instantaneous change in voltage across the battery  20  when the battery  20  is switched from the no-load condition to the charging/discharging condition or from the charging/discharging condition to the no-load condition. In an example, the voltage of the battery  20  measured at the time point when the battery  20  on no-load condition starts charging is higher than the OCV. In another example, the voltage of the battery  20  measured at the time point when the battery  20  on no-load condition starts discharging is lower than the OCV. The resistance value of the ohm resistor R 1  may be also preset by SOC and temperature through experimentation. 
     The RC pair  220  outputs overpotential (also known as ‘polarization voltage’) V 2  induced by an electric double layer of the battery  20 , and includes a resistor R 2  and a capacitor C 2  connected in parallel. The overpotential V 2  may be referred to as ‘polarization voltage’. The time constant of the RC pair  220  is the multiplication of the resistance value of the resistor R 2  by the capacitance of the capacitor C 2 , and may be preset by SOC and temperature through experimentation. 
     V ecm  is an output voltage of the equivalent circuit model  200 , and equals the sum of the OCV from the OCV source  210 , the IR drop V 1  across the ohm resistor R 1  and the overpotential V 2  across the RC pair  220 . 
     In the equivalent circuit model  200 , the overpotential in the current cycle may be defined as the following Equation 3. 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       2 
                     
                      
                     
                       [ 
                       
                         k 
                         + 
                         1 
                       
                       ] 
                     
                   
                   = 
                   
                     
                       
                         
                           V 
                           2 
                         
                          
                         
                           [ 
                           k 
                           ] 
                         
                       
                        
                       
                         e 
                         
                           - 
                           
                             
                               Δ 
                                
                               t 
                             
                             
                               τ 
                                
                               
                                 ⌈ 
                                 
                                   k 
                                   + 
                                   1 
                                 
                                 ⌉ 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         
                           R 
                           2 
                         
                          
                         
                           [ 
                           
                             k 
                             + 
                             1 
                           
                           ] 
                         
                       
                        
                       
                         i 
                          
                         
                           [ 
                           
                             k 
                             + 
                             1 
                           
                           ] 
                         
                       
                        
                       
                         ( 
                         
                           1 
                           - 
                           
                             e 
                             
                               - 
                               
                                 
                                   Δ 
                                    
                                   t 
                                 
                                 
                                   τ 
                                    
                                   
                                     ⌈ 
                                     
                                       k 
                                       + 
                                       1 
                                     
                                     ⌉ 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   &lt; 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   &gt; 
                 
               
             
           
         
       
     
     In Equation 3, R 2 [k+1] denotes the resistance value of the resistor R 2  in the current cycle, τ[k+1] denotes the time constant of the RC pair  220  in the current cycle, V 2 [k] denotes the overpotential in the previous cycle, and V 2 [k+1] denotes the overpotential in the current cycle. In Equation 3, i[k+1] may be replaced with i[k]. The overpotential V 2 [0] at the time point when the event occurred may be 0 V (volt). 
     The following Equation 4 is a first state equation associated with the time update process of the extended Kalman filter, and is derived from a combination of Equation 2 and Equation 3. 
     
       
         
           
             
               
                 
                   
                     
                       
                         x 
                         ^ 
                       
                       
                         k 
                         + 
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                       - 
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 SOC 
                                  
                                 
                                   [ 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                   ] 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   V 
                                   2 
                                 
                                  
                                 
                                   [ 
                                   
                                     k 
                                     + 
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                                   ] 
                                 
                               
                             
                           
                         
                         ) 
                       
                       = 
                       
                         
                           A 
                            
                           
                             
                               x 
                               ^ 
                             
                             k 
                           
                         
                         + 
                         
                           Bi 
                            
                           
                             [ 
                             
                               k 
                               + 
                               1 
                             
                             ] 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         x 
                         ^ 
                       
                       k 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 SOC 
                                 e 
                               
                                
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                           
                         
                         
                           
                             
                               
                                 V 
                                 2 
                               
                                
                               
                                 [ 
                                 k 
                                 ] 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                    
                   
                     
 
                   
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                     A 
                     = 
                     
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                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               e 
                               
                                 - 
                                 
                                   
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                                       [ 
                                       
                                         k 
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                                       ] 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                    
                   
                     
 
                   
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                     B 
                     = 
                     
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                                 Δ 
                                  
                                 t 
                               
                               
                                 Q 
                                 est 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   R 
                                   2 
                                 
                                  
                                 
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                                     k 
                                     + 
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                                               1 
                                             
                                             ] 
                                           
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   &lt; 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   &gt; 
                 
               
             
           
         
       
     
     In Equation 4 and the following Equations 5 to 8, the superscripted symbol {circumflex over ( )} indicates a value estimated by time updates. Additionally, the superscripted symbol − indicates a value before correction by measurement updates described below. 
     The following Equation 5 is a second state equation associated with the time update process of the extended Kalman filter. 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       
                         k 
                         + 
                         1 
                       
                       - 
                     
                     = 
                     
                       
                         
                           AP 
                           k 
                         
                          
                         
                           A 
                           T 
                         
                       
                       + 
                       
                         Q 
                         k 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Q 
                       k 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 W 
                                  
                                 1 
                               
                               k 
                             
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             
                               
                                 W 
                                  
                                 2 
                               
                               k 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   &lt; 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   &gt; 
                 
               
             
           
         
       
     
     In Equation 5, P k  denotes an error covariance matrix corrected in the previous cycle, Q k  denotes a process noise covariance matrix in the previous cycle, T denotes a transpose operator, and P −   k+1  denotes an error covariance matrix in the current cycle. In k=0, P 0  may be equal to [1 0 ; 0 1]. W 1   k  is first process noise set in the previous cycle, and is associated with reliability of the ampere counting. That is, W 1   k  is a positive number indicating inaccuracy of the cumulative current value calculated using the ampere counting. W 2   k  is second process noise set in the previous cycle, and is associated with reliability of the equivalent circuit model  200 . That is, W 2   k  is a positive number indicating inaccuracy of the parameters associated with the equivalent circuit model  200 . 
     Accordingly, the control unit  120  may increase the first process noise as the inaccuracy of the ampere counting increases. The control unit  120  may increase the second process noise as the inaccuracy of the equivalent circuit model  200  increases. 
     When the time update process using Equation 4 and Equation 5 is completed, the control unit  120  performs a measurement update process. 
     The following Equation 6 is a first observation equation associated with the measurement update process of the extended Kalman filter. 
     
       
         
           
             
               
                 
                   
                     
                       K 
                       
                         k 
                         + 
                         1 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 K 
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         , 
                                         1 
                                       
                                       ) 
                                     
                                      
                                     k 
                                   
                                   + 
                                   1 
                                 
                               
                             
                           
                           
                             
                               
                                 K 
                                 
                                   
                                     
                                       ( 
                                       
                                         2 
                                         , 
                                         1 
                                       
                                       ) 
                                     
                                      
                                     k 
                                   
                                   + 
                                   1 
                                 
                               
                             
                           
                         
                         ) 
                       
                       = 
                       
                         
                           P 
                           
                             k 
                             + 
                             1 
                           
                           - 
                         
                          
                         
                           
                             
                               H 
                               
                                 k 
                                 + 
                                 1 
                               
                               T 
                             
                              
                             
                               ( 
                               
                                 
                                   
                                     H 
                                     
                                       k 
                                       + 
                                       1 
                                     
                                   
                                    
                                   
                                     P 
                                     
                                       k 
                                       + 
                                       1 
                                     
                                     - 
                                   
                                    
                                   
                                     H 
                                     
                                       k 
                                       + 
                                       1 
                                     
                                     T 
                                   
                                 
                                 + 
                                 R 
                               
                               ) 
                             
                           
                           
                             - 
                             1 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     
                       H 
                       
                         k 
                         + 
                         1 
                       
                       T 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 
                                   
                                     f 
                                     1 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         SOC 
                                          
                                         
                                           [ 
                                           
                                             k 
                                             + 
                                             1 
                                           
                                           ] 
                                         
                                       
                                       + 
                                       
                                         0.01 
                                          
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                               
                             
                           
                           
                             
                               
                                 
                                   f 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       SOC 
                                        
                                       
                                         [ 
                                         
                                           k 
                                           + 
                                           1 
                                         
                                         ] 
                                       
                                     
                                     - 
                                     
                                       0.01 
                                        
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 2 
                                  
                                 n 
                               
                             
                           
                           
                             
                               1 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   &lt; 
                   
                     Equation 
                      
                     
                         
                     
                      
                     6 
                   
                   &gt; 
                 
               
             
           
         
       
     
     In Equation 6, K k+1  denotes a Kalman gain in the current cycle. K (1,1)k+1  is a first component of the Kalman gain, and K (2,1)k+1  is a second component of the Kalman gain. Additionally, R is a measurement noise covariance matrix, and has preset components. H k+1  is a system matrix, and is used to reflect changes in OCV of the battery  20  according to the OCV-SOC curve when estimating the SOC of the battery  20 . n is a preset positive integer (e.g., 1). 
     The following Equation 7 is a second observation equation associated with the measurement update process of the extended Kalman filter. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             x 
                             ^ 
                           
                           
                             k 
                             + 
                             1 
                           
                         
                         = 
                         
                           
                             
                               x 
                               ^ 
                             
                             
                               k 
                               + 
                               1 
                             
                             - 
                           
                           + 
                           
                             
                               K 
                               
                                 k 
                                 + 
                                 1 
                               
                             
                              
                             
                               { 
                               
                                 
                                   z 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                 
                                 - 
                                 
                                   
                                     V 
                                     ecm 
                                   
                                    
                                   
                                     [ 
                                     
                                       k 
                                       + 
                                       1 
                                     
                                     ] 
                                   
                                 
                               
                               } 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               x 
                               ^ 
                             
                             
                               k 
                               + 
                               1 
                             
                             - 
                           
                           + 
                           
                             
                               K 
                               
                                 k 
                                 + 
                                 1 
                               
                             
                              
                             
                               { 
                               
                                 
                                   z 
                                   
                                     k 
                                     + 
                                     1 
                                   
                                 
                                 - 
                                 
                                   ( 
                                   
                                     
                                       
                                         f 
                                         1 
                                       
                                        
                                       
                                         ( 
                                         
                                           SOC 
                                            
                                           
                                             [ 
                                             
                                               k 
                                               + 
                                               1 
                                             
                                             ] 
                                           
                                         
                                         ) 
                                       
                                     
                                     + 
                                     
                                       
                                         V 
                                         1 
                                       
                                        
                                       
                                         [ 
                                         
                                           k 
                                           + 
                                           1 
                                         
                                         ] 
                                       
                                     
                                     + 
                                     
                                       
                                         V 
                                         2 
                                       
                                        
                                       
                                         [ 
                                         
                                           k 
                                           + 
                                           1 
                                         
                                         ] 
                                       
                                     
                                   
                                   ) 
                                 
                               
                               } 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   &lt; 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   &gt; 
                 
               
             
           
         
       
     
     In Equation 7, z k+1  denotes the voltage of the battery  20  measured in the current cycle, and V ecm [k+1] denotes the output voltage of the equivalent circuit model  200  in the current cycle. f 1 (SOC[k+1]) denotes the OCV in the current cycle (see the description of  FIG. 2 ). V 1 [k+1] denotes the voltage across the ohm resistor R 1  in the current cycle, and may equal the multiplication of any one of i[k+1] and i[k] by R 1 [k+1]. R 1 [k+1] is the resistance value of the ohm resistor R 1  in the current cycle. The control unit  120  may determine R 1 [k+1] based on the temperature value. To this end, the memory unit  130  records a first lookup table defining a correspondence relationship between the temperature value and the resistance value of the ohm resistor R 1 . The control unit  120  may obtain a resistance value mapped to a specific temperature value (e.g., the temperature value of the data set) from the first lookup table using the specific temperature value as an index. Each of SOC[k+1] and V 2 [k+1] obtained from Equation 4 is corrected by Equation 7. 
     Referring to Equations 6 and 7, in correcting SOC[k+1] obtained from Equation 4, as the value of k (1,1)k+1  is closer to 0, the influence of a difference between z k+1  and V ecm [k+1] decreases. One of the causes of decrease in K (1,1)k+1  is incompleteness of the ampere counting (see Equation 2). The decrease in K (1,1)k+1  results in reduced learning capability of the extended Kalman filter based on the difference between z k+1  and V ecm [k+1]. 
     Additionally, referring to Equations 6 and 7, in correcting V 2 [k+1] obtained from Equation 4, as the value of K (2,1)k+1  is closer to 0, the influence of a difference between z k+1  and V ecm [k+1] decreases. One of the causes of decrease in K (2,1)k+1  is unstability of the equivalent circuit model  200 . The decrease in K (2,1)k+1  results in reduced learning capability of the extended Kalman filter based on the difference between z k+1  and V ecm [k+1]. 
     The control unit  120  may regulate a ratio between the first process noise and the second process noise to prevent estimation accuracy reduction due to the significant decrease in at least one of K (1,1)k+1  and K (2,1)k+1  in estimating the SOC of the battery  20  using the extended Kalman filter. 
     The following Equation 8 is a third observation equation associated with the measurement update process of the extended Kalman filter. 
         P   k+1 =( E−K   k+1   H   k+1 ) P   k+1   −   &lt;Equation 8&gt;
 
     In Equation 8, E denotes the unit matrix. P k+1   −  obtained from Equation 5 is corrected to P k+1  by Equation 8. 
     The control unit  120  periodically updates the SOC of the battery  20  by performing each calculation step of Equations 4 to 8 at least once each time the time index k increases by 1. 
     Hereinafter, the operation of determining the second candidate value will be described with reference to the above description of the extended Kalman filter. 
     The control unit  120  determines the second candidate value based on the data set. As described previously, the data set includes the current value, the voltage value and the temperature value. The control unit  120  determines R 2 [k+1] and τ[k+1] of Equation 4 based on the temperature value and the SOC determined in the previous cycle. To this end, the memory unit  130  may record a second lookup table defining a correspondence relationship between the SOC, the temperature value and the resistance value of the resistor R 2 . The control unit  120  may obtain the resistance value mapped to the temperature value of the data set and the SOC determined in the previous cycle as R 2 [k+1] of Equation 4 from the second lookup table using the temperature value of the data set and the SOC determined in the previous cycle as an index. Additionally, the memory unit  130  may record a third lookup table defining a correspondence relationship between the SOC, the temperature value and the time constant. The control unit  120  may obtain the time constant mapped to the temperature value of the data set and the SOC determined in the previous cycle as τ[k+1] of Equation 4 from the third lookup table using the temperature value of the data set and the SOC determined in the previous cycle as an index. 
     The control unit  120  may set i[k+1] (or i[k]) of Equation 4 to be equal to the current value of the data set, and may set z k+1  of Equation 7 to be equal to the voltage value of the data set. Accordingly, the control unit  120  may determine the second candidate value to be equal to SOC[k+1] corrected by Equation 7. 
     When the determination of the first candidate value and the second candidate value for the SOC of the battery  20  is completed in the current cycle, the control unit  120  is configured to determine one of the first candidate value and the second candidate value as the SOC of the battery  20  in the current cycle through a process described below. 
     The control unit  120  determines a difference value that is an absolute value of a difference between the first candidate value and the second candidate value. In an example, when the first candidate value is 0.51 and the second candidate value is 0.52, the difference value is 0.01. In another example, when the first candidate value is 0.77 and the second candidate value is 0.75, the difference value is 0.02. 
     The control unit  120  may compare the first difference value with a predetermined threshold value. The threshold value is stored in the memory unit  130 , and may be, for example, 0.03. 
     When the difference value is larger than the threshold value, the control unit  120  may determine the SOC of the battery  20  to be equal to the first candidate value. 
     When the difference value is equal to or smaller than the threshold value, the control unit  120  may determine the SOC of the battery  20  to be equal to the second candidate value rather than the first candidate value. 
     When the first component K (1,1)k+1  of the Kalman gain K k+1  is equal to or higher than a predetermined first lower limit (e.g., 0.01), and the second component K (2,1)k+1  of the Kalman gain K k+1  is equal to or higher than a predetermined second lower limit (e.g., 0.001), the control unit  120  may set a ratio of the second process noise to the first process noise to be equal to a predetermined reference ratio (e.g., 0.1). For example, the first process noise may be set to be equal to a predetermined first reference value (e.g., 0.1), and the second process noise may be set to be equal to a predetermined second reference value (e.g., 0.01). That is, the reference ratio may be equal to a value obtained by dividing the second reference value by the first reference value. 
     When the first component K (1,1)k+1  of the Kalman gain K k+1  is lower than the first lower limit and the second component K (2,1)k+1  of the Kalman gain K k+1  is equal to or higher than the second lower limit, the control unit  120  may reduce the ratio of the second process noise to the first process noise below the reference ratio. In an example, the first process noise may be set to be equal to the first reference value, and the second process noise may be set as a value that is smaller than the second reference value. In another example, the first process noise may be set as a value that is larger than the first reference value, and the second process noise may be set to be equal to the second reference value. In still another example, the first process noise may be set as a value that is larger than the first reference value, and the second process noise may be set as a value that is smaller than the second reference value. 
     When the first component K (1,1)k+1  of the Kalman gain K k+1  is lower than the first lower limit and the second component K (2,1)k+1  of the Kalman gain K k+1  is equal to or higher than the second lower limit, the control unit  120  may determine the ratio of the second process noise to the first process noise such that a difference between the ratio of the second process noise to the first process noise and the reference ratio is proportional to a difference between the first component K (1,1)k+1  and the first lower limit. For example, when the difference between the first component K (1,1)k+1  and the first lower limit is 0.002, the ratio of the second process noise to the first process noise may be determined as 0.09, and when the difference between the first component k (1,1)k+1  and the first lower limit is 0.003, the ratio of the second process noise to the first process noise may be determined as 0.085. 
     When the first component K (1,1)k+1  of the Kalman gain K k+1  is equal to or higher than the first lower limit and the second component K (2,1)k+1  of the Kalman gain K k+1  is lower than the second lower limit, the control unit  120  may increase the ratio of the second process noise to the first process noise above the reference ratio. In an example, the first process noise may be set to be equal to the first reference value, and the second process noise may be set as a value that is larger than the second reference value. In another example, the first process noise may be set as a value that is smaller than the first reference value, and the second process noise may be set to be equal to the second reference value. In still another example, the first process noise may be set as a value that is smaller than the first reference value, and the second process noise may be set as a value that is larger than the second reference value. 
     When the first component K (1,1)k+1  of the Kalman gain K k+1  is equal to or higher than the first lower limit and the second component K (2,1)k+1  of the Kalman gain K k+1  is lower than the second lower limit, the control unit  120  may determine the ratio of the second process noise to the first process noise such that the difference between the ratio of the second process noise to the first process noise and the reference ratio is proportional to a difference between the second component K (2,1)k+1  and the second lower limit. For example, the difference between the second component K (2,1)k+1  and the second lower limit is 0.002, the ratio of the second process noise to the first process noise may be determined as 0.115, and when the difference between the second component K (2,1)k+1  and the second lower limit is 0.003, the ratio of the second process noise to the first process noise may be determined as 0.121. 
     When the first component K (1,1)k+1  of the Kalman gain K k+1  is lower than the first lower limit, the control unit  120  may determine the first process noise using the following Equation 9. When the second component K (2,1)k+1  of the Kalman gain K k+1  is lower than the second lower limit, the control unit  120  may determine the second process noise using the following Equation 10. 
         W 1 k =( M   1   D   1   −M   2   D   2 )+ M   W1    &lt;Equation 9&gt;
 
         W 2 k =( M   4   D   2   −M   3   D   1 )+ M   W2    &lt;Equation 10&gt;
 
     In Equations 9 and 10, D 1  denotes the absolute value of the difference between the first component K (1,1)k+1  and the first lower limit, D 2  denotes the absolute value of the difference between the second component K (2,1)k+1  and the second lower limit, M W1  denotes the first reference value, M W2  denotes the second reference value, M 1  denotes a first weight, M 2  denotes a second weight, M 3  denotes a third weight, M 4  denotes a fourth weight, W 1   k  denotes the first process noise, and W 2   k  denotes the second process noise. M 1 , M 2  M 3  and M 4  may be positive numbers that are preset to be identical or different from one another. 
     When the first component K (1,1)k+1  of the Kalman gain K k+1  is lower than the first lower limit and the second component K (2,1)k+1  of the Kalman gain K k+1  is lower than the second lower limit, the control unit  120  may set the first process noise and the second process noise to be equal to W 1   k  by Equation 9 and W 2   k  by Equation 10, respectively. 
     The first process noise and the second process noise set as described above may be respectively allocated to W 1   k  and W 2   k  of Equation 5 in the process of estimating the SOC for the next cycle. 
     The control unit  120  may selectively output the switching signal SS to control the switch  30 . When the first component K (1,1)k+1  is lower than the first lower limit or the second component K (2,1)k+1  is lower than the second lower limit, the control unit  120  may regulate the duty cycle of the switching signal SS to be equal to or smaller than a predetermined reference duty cycle (e.g., 0.2). When the duty cycle of the switching signal SS is regulated below the reference duty cycle, the maximum amount of currents that can flow through the battery  20  reduces, thereby avoiding rapid changes in voltage and temperature of the battery  20 . 
       FIGS. 4 and 5  are exemplary flowcharts of a battery management method performed by the battery management apparatus of  FIG. 1 . The method of  FIGS. 4 and 5  may be periodically performed from the time point at which the event occurred. The method of  FIGS. 4 and 5  may end when charging/discharging of the battery  20  is stopped. 
     Referring to  FIGS. 1 to 5 , in step S 400 , the control unit  120  determines the maximum capacity (or SOH) of the battery  20  (see Equation 1). 
     In step S 405 , the control unit  120  detects the current, voltage and temperature of the battery  20  using the sensing unit  110 . The sensing unit  110  outputs a signal SI indicating the detected current, a signal SV indicating the detected voltage and a signal ST indicating the detected temperature to the control unit  120 . 
     In step S 410 , the control unit  120  receives the signal SI, the signal SV and the signal ST, and generates a data set including a current value indicating the current of the battery  20 , a voltage value indicating the voltage of the battery  20  and a temperature value indicating the temperature of the battery  20 . 
     In step S 420 , the control unit  120  determines a first candidate value for the SOC of the battery  20  based on the current value using ampere counting (see Equation 2). 
     In step S 430 , the control unit  120  determines a Kalman gain K k+1  and a second candidate value for the SOC of the battery  20  based on the data set using the extended Kalman filter (see Equations 3 to 8). 
     As opposed to that of  FIG. 4 , the steps S 420  and S 430  may be performed at the same time, or the step S 430  may precede the step S 420 . 
     In step S 440 , the control unit  120  determines a difference value between the first candidate value and the second candidate value. 
     In step S 500 , the control unit  120  determines if the difference value is larger than the threshold value. When a value of the step S 500  is “YES”, step S 510  is performed. When the value of the step S 500  is “NO”, step S 520  is performed. 
     In step S 510 , the control unit  120  determines the SOC of the battery  20  to be equal to the first candidate value. 
     In step S 520 , the control unit  120  determines the SOC of the battery  20  to be equal to the second candidate value. 
     In step S 530 , the control unit  120  determines whether the first component K (1,1)k+1  of the Kalman gain K k+1  is lower than the first lower limit, or the second component K (2,1)k+1  of the Kalman gain K k+1  is lower than the second lower limit. A value of the step S 530  being “NO” represents that the first component K (1,1)k+1  is equal to or higher than the first lower limit, and the second component K (2,1)k+1  is equal to or higher than the second lower limit. When the value of the step S 530  is “NO”, step S 540  is performed. When the value of the step S 530  is “YES”, at least one of steps S 550  and S 560  is performed. 
     In step S 540 , the control unit  120  sets a ratio of a second process noise to a first process noise to be equal to the reference ratio. For example, the first process noise may be set to be equal to the first reference value, and the second process noise may be set to be equal to the second reference value. The reference ratio is a value obtained by dividing the second reference value by the first reference value. 
     In step S 550 , the control unit  120  decreases or increases the ratio of the second process noise to the first process noise with respect to the reference ratio (see Equations 9 and 10). 
     In step S 560 , the control unit  120  regulates the duty cycle of the switching signal SS outputted to the switch  30  to be equal to or smaller than the reference duty cycle. A difference between the regulated duty cycle and the reference duty cycle may be proportional to any one (e.g., a larger one) of the absolute value of the difference between the first component K (1,1)k+1  and the first lower limit and the absolute value of the difference between the second component K (2,1)k+1  and the second lower limit. As opposed to that of  FIG. 5 , the steps S 550  and S 560  may be performed at the same, or the step S 560  may precede the step S 550 , or only one of the step S 550  and the step S 560  may be performed. 
     The embodiments of the present disclosure described hereinabove are not implemented only through the apparatus and method, and may be implemented through programs that perform functions corresponding to the configurations of the embodiments of the present disclosure or recording media having the programs recorded thereon, and such implementation may be easily achieved by those skilled in the art from the disclosure of the embodiments previously described. 
     While the present disclosure has been hereinabove described with regard to a limited number of embodiments and drawings, the present disclosure is not limited thereto and it is obvious to those skilled in the art that various modifications and changes may be made thereto within the technical aspects of the present disclosure and the equivalent scope of the appended claims. 
     Additionally, as many substitutions, modifications and changes may be made to the present disclosure described hereinabove by those skilled in the art without departing from the technical aspects of the present disclosure, the present disclosure is not limited by the above-described embodiments and the accompanying drawings, and some or all of the embodiments may be selectively combined to allow various modifications.