Patent Publication Number: US-5830595-A

Title: Battery capacity prediction method and apparatus using natural logarithm

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a battery capacity prediction method and apparatus, and more particularly, to a method and apparatus for predicting the relationship between current and battery capacity by using natural logarithm which can be applied to any battery-powered products. 
     Generally, there are various types of methods for measuring a battery state-of-charge: i) an open circuit voltage measurement method, ii) an electrolyte specific-gravity measurement method, iii) an internal resistance measurement method, iv) a voltage measurement method at a constant-current discharging time, and v) ampere-hour (or a current accumulation) method. Among these methods, the ampere-hour method is most widely used for electric vehicles. Here, the battery state-of-charge is calculated from dividing the ampere-hours by a preset battery capacity. 
     The ampere-hour method, however, is susceptible to a high rate of error if the load varies greatly since the available capacity depends on the load condition. The capacity becomes less as the load gets heavier and vice versa. In order to rectify this shortcoming associated with the ampere-hour method, Peukert&#39;s Equation is employed as suggested in U.S. Pat. Nos. 3,886,442, 4,390,841 and 4,595,880. Peukert&#39;s Equation calculates the available capacity corresponding to the discharge current, and therefore, it can reduce the error considerably. 
     In order to use Peukert&#39;s Equation, Peukert&#39;s constants, n and K, must be obtained. The procedure for obtaining n and K is as follows: ##EQU1## where I 1  is a current value which will discharge the battery completely in 0.5 hours (i.e. 2C rate) and I 2  is a current value which will discharge the battery completely in 5 hours (i.e. C/5 rate), and t 1  and t 2  are discharge times at I 1  and I 2 , respectively. 
     Referring to FIG. 1, in step 11, the instantaneous discharge current (I(t)) of a battery is measured and read, and in step 12, the average discharge current (I d ) is calculated. In step 13, the total ampere-hour used (Ah --  Used) is calculated, and in step 14, the available capacity (Ah --  Available) is calculated by applying Peukert&#39;s Equation. Finally, in step 15, the state-of charge of the battery is calculated and the process returns to step 11. 
     This method works well if the average discharge current (I d ) is close to either I 1  or I 2 . However, if I d  is far away from either I 1  or I 2 , the accuracy is reduced as shown in TABLE A below. 
     SUMMARY OF THE INVENTION 
     To overcome the above problems, it is an object of the present invention to provide a battery capacity prediction method and apparatus for indicating the relationship between discharge current and battery capacity using an algorithm based on natural logarithm. 
     Accordingly, to achieve the above object, there is provide a battery capacity prediction method according to the discharge current using natural logarithm. 
     According to the invention, the available capacity (Ah --  Available) is calculated as 
     
         Ah.sub.-- Available=a ln(I.sub.d)!+b 
    
     wherein I d  is the average discharge current, and a and b are constants obtained from experimental results as follows: ##EQU2## where I 1  is a current value which will discharge the battery completely in 0.5 hours (i.e. 2C rate) and I 2  is a current value which will discharge the battery completely in 5 hours (i.e. C/5 rate) , and Cap 1  and Cap 2  are ampere-hour (Ah) capacities at I 1  and I 2 , respectively. 
     The method for calculating the state-of-charge according to the invention is shown in FIG. 2. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above objects and advantages of the present invention will become more apparent by describing in detail a preferred embodiment thereof with reference to the attached drawings in which: 
     FIG. 1 is a flowchart for illustrating the battery capacity prediction method using Peukert&#39;s Equation in accordance with the prior art; and 
     FIG. 2 is a flowchart for illustrating the battery capacity prediction method according to the present invention. 
     FIG. 3 is a circuit for practicing the method illustrated in FIG. 2. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 2 is a flowchart for explaining a battery capacity predicting method according to the discharge current using a natural logarithm according to the present invention. 
     In general, in using Peukert&#39;s Equation, Peukert&#39;s constants K and n are obtained by discharging a battery by more than two constant currents. However, in using a natural logarithm, the following equation (1) is obtained from the battery discharging result so as to replace the Peukert&#39;s constants K and n. 
     
         Ah.sub.-- Available=a ln(I.sub.d)!+b                       (1) 
    
     wherein a and b are constants obtained from experimental results as follows: ##EQU3## where I 1  is a current value which will discharge the battery completely in 0.5 hours (i.e. 2C rate) and I 2  is a current value which will discharge the battery completely in 5 hours (i.e. C/5 rate), and Cap 1  and Cap 2  are ampere-hour (Ah) capacities at I 1  and I 2 , respectively. 
     Referring to FIG. 2, in step 21, the instantaneous discharge current (I(t)) is measured and read. In step 22, the average discharge current (I d ) is calculated. In step 23, the total ampere-hour used capacity (Ah --  Used) is calculated. In step 24, the usable capacity (Ah --  Available) is calculated by applying natural logarithm as in expression (1). Finally, in step 25, the state-of-charge of the battery is calculated and the process returns to step 21. 
     The relationship between discharge current and capacity is shown in TABLE A below. It can be seen, by comparing the fifth and seventh columns, that natural logarithm method is superior to Peukert&#39;s Equation method. Furthermore, the procedure for obtaining the constants for natural logarithm involves much simpler calculation than the constants for Peukert&#39;s Equation. 
     
         &lt;TABLE A&gt;                                                                 
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                  Capacity using                                          
                              Capacity using                              
Discharge                                                                 
      Discharge                                                           
           Experimental                                                   
                  Peukert&#39;s Equation                                      
                           Error                                          
                              Natural                                     
                                     Error                                
Current (A)                                                               
      Time (hr)                                                           
           Capacity (Ah)                                                  
                  (Ah)     (%)                                            
                              Logarithm (Ah)                              
                                     (%)                                  
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5     10.06                                                               
           50.3   55.6     10.6                                           
                              53.1   5.6                                  
10    4.71 47.1   47.1     0.0                                            
                              47.1   0.0                                  
20    2.11 42.2   39.9     5.5                                            
                              41.1   2.7                                  
40    0.9  35.9   33.8     5.9                                            
                              35.1   2.3                                  
60    0.53 31.8   30.6     3.7                                            
                              31.5   0.8                                  
80    0.37 29.2   28.6     2.1                                            
                              29.0   0.6                                  
100   0.27 27.1   27.1     0.0                                            
                              27.1   0.0                                  
120   0.22 25.9   25.9     0.1                                            
                              25.5   1.6                                  
160   0.15 23.4   24.2     3.6                                            
                              23.0   1.5                                  
200   0.11 21.8   22.9     5.3                                            
                              21.1   3.3                                  
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     The battery capacity prediction method of the present invention can be applied to any battery-powered products from an electric vehicles to portable electric vehicle (e.g. forklift or golf cart). 
     FIG. 3 is a block diagram including a battery 31, a variable load 32, a current sensor 33, a calculation circuit, and a state of charge display 35. The calculation circuit 34 may be a microprocessor or a dedicated circuit and is programmed to calculate the state-of-charge in accordance with the flowchart of FIG. 2. 
     As described above, in the battery capacity prediction method and apparatus according to the present invention, the usable battery capacity according to the current in use is predicted by using natural logarithm. Therefore, the method is simplified and the prediction accuracy is enhanced.