スーパーキャパシタにおける急速充電モデル - Fujikura

1 Mathematical Models of Flash Charging Method for supercapacitors N. Misaki, M. Inaguma, K. Akashi, and T. Yamamoto .. Idle time .. Flash Charging .. Recently, a lot of mobile equipment has installed Electrical energy storage devices that are available in various markets. It is preferable that all kinds of mobile equipment should be used in the condition of high efficiency. However, the idle time relating with moving to charging stations and recharging the devices is inevitable. To save time, supercapacitors , such as Electrical Double Layer Capacitor (EDLC) or Lithium - Ion Capacitor (LIC) with huge capacitance, can be employed because of their excellent rapid charging abilities. In order to charge them, a power supply that can provide a supercapacitor with enough electricity, is required. Although supercapacitors have such great benefit, it is very difficult to find the power supply whose cost or weight is satisfactory. With this in mind, a simple rapid charging system while using a supercapacitor is strongly advised.

2 Flash Charging Method is a solution that enable charging supercapacitors rapidly. This paper presents Mathematical Models which can implement to calculate the charging time when Flash Charging Method is applied to charge supercapacitors , even though both of required State of Charge (SOC) and required charging time are settled prior to the system design. Results of experiments to demonstrate the models are also presented. CC - CV . 1 . 2 . EDLC . LIC . 1 . Constant Current Mode SW1 SW2. Load Constant Voltage Mode . CONSTANT CURRENT - CONSTANT VOLTAGE. CC-CV. Supercapacitor CC - CV Power Supply 1 .. 2 1 CC - CV Charging . 3 Fig. 1. Basic Configuration Diagram of CC - CV Method. 1. 2018 131 .. EDLC Electrical Double Layer . Capacitor LIC Lithium - Ion Capacitor . Li Lithium . CC - CV CONSTANT CURRENT - . CONSTANT VOLTAGE . Jf Faradaic Current . Jnf Non - Faradaic Current . Lithium pre - doping . SOC State of Charge 100 0 . OCV Open Circuit Voltage . CCV Closed Circuit Voltage.

3 As Ampere Second SI Coulomb C 1 C 1 A 1 sec . As . As Ah Ampere Hour mAh Milliampere - Hour .. Supply Voltage Y . Charging Current Charging Current Y . SOC Y . Voltage V . Current A . Voltage V . Current A . SOC X . SOC % . Supply Voltage Charging Current X . Supply Voltage X . Charging Time min Fully charged Fully charged X . Fully charged Y . 2 CC - CV Charging Time sec . Fig. 2. Charging profile of CC - CV. 3 . Fig. 3. Charging profile of Constant Voltage Control from Power Supply.. 10 .. CC - CV .. EDLC LIC CC - CV .. 3 .. 2.. 2 . CC - CV . EDLC 5 . EDLC . 2 CC - CV J f . 2 . CCV Closed Circuit Voltage J nf J J f J nf . OCV J f J J nf . Open Circuit Voltage J nf . J nf . CCV .. OCV CCV Activated Carbon . 2 CC - CV . 1000 F . OCV 5 SW1 SW2 . OCV SW2 J nf . SW2 .. J J f J nf . 4 Flash Charging . 1 . Flash Charging SW1 SW2 SW3. Load . Flash Charging 4 CC-CV Supercapacitor Power Supply SC1 . CC - CV SC1 . Supercapacitor SC2 SC2 .. 4 Flash Charging . Fig. 4. Basic Configuration Diagram of Flash Charging SC2 Method.

4 CC - CV .. SW1. SC2 Load Vc SW2. SC1 SC1. SC2 SC2 .. Separator Electrolyte .. OCV CCV. Cation CC - CV . Anion . Negative charge SC2 CCV Positive charge . Electrical Double Layer . 4 SC1 SC2 .. Negative electrode . SC2 Current Collector . Positive electrode . SOC Flash Current Collector . Charging 5 EDLC . Fig. 5. EDLC Schematic Diagram Fully Charged . 3. 2018 131 .. EDLC . Q =C V LIC . Q C V .. EDLC 3 V .. 3 Flash Charging .. 3 1 . LIC 6 LIC Flash Charging . EDLC . 3 . LIC EDLC . 7 . 3 2 . LIC Q C . 3 V V Q C V Q. LIC 4 V V EDLC . EDLC LIC 6 Q V LIC . SW2 SW1 3 V .. Q C V . LIC Emax CCV 2 V Emin . SW1 OCV Vx SOCx % .. LIC LIC . Vx Emin SOCx = 100 1 . Emax Emin EDLC . 1 SOC 100 Vx Emax SOC. Vx Emin . Li ion 4 SC1 SC2 . Anion 7 SC1 . Negative charge Positive charge C1 R1 SC2 C2 . SW1 R2 4 SC1 SOC . Load Vc SW2 100 SC2 SOC SW1 . SW2 SW3 . 8 SC1. Separator Electrolyte . SC2 Emax Emin . Li Li Li . Li Li Li Li Li Li Li Li Li . Li Li Li Capacitor . Li Li Li . Internal Resistance.

5 Electrical Double Layer . Negative electrode Current Collector .. Current Collector Positive electrode . 7 . 6 LIC Fig. 7. Equivalent Circuit Diagram of a supercapacitor Fig. 6. LIC Schematic Diagram. cell. 4.. 3 3 2 . Flash Charging SC2 9 SW . SC2 CCV SOC CCV . C1 Emax . CCV CCV . 8 SW C2 Emin . 2 3 . SW . I s C 1 Emax I s C 2 E. 9 9 SW R 1 I s =. +. C 1 S C 1 S C 2 S C 2 . 9 . I s C 1 Emax I s C 2 Emin . R 1 I s = + + R 2 I S . C 1 S C 1 S C 2 S C 2 S. 1 1 .. i t dt R 1 i t = i t i t . dt + R 2 . C1 C2. 2 . 1 1 Emax Emin 1. i t . dt R 1 i t = i t dt + R 2 i t I S = . C1 C2 R1 + R 2 C1 + C 2 3 . S +. C 1 C 2 . R 1 + R 2 . 2 i t . 3 . SC1 SC2. Emax Emin C 1 + C 2 . t i t =. e C 1 C 2 R 1 + R 2 4 . R1 Internal Resistance of R1 + R 2. SW. SC1-capacitor-cell R2 Internal Resistance of SC2-capacitor-cell 4 Flash Charging . C1 C2. C1 Capacitance of SC1- V open . capacitor-cell R2. C2 Capacitance of SC2- 4 SC2 . R1 V2open capacitor-cell . V1open Emax OCV of SC1 3 4.

6 V2open Emin Flash Charging . OCV of SC2 .. 8 1 SC1 C1 SC2 C2 . Fig. 8. Equivalent Circuit Diagram of Flash Charging C1 C2. Method. SC1 SC2.. i t . SW. R1 Internal Resistance of SC1-capacitor-cell R2 Internal Resistance of SC2 -capacitor-cell C2 C1 Capacitance of SC1-capacitor-cell C1 C2 Capacitance of SC2-capacitor-cell V2c t . V c t . V2cls( ). V1cls SC1- Closed Circuit Voltage V2cls SC2- Closed Circuit Voltage R1 R2. V1cls( ). V R t V1c Theoretical Capacitor Voltage V2c Theoretical Capacitor Voltage V2R t .. i t .. i t V1R Voltage Drop across R1. V2R Voltage Drop across R2.. i t . 9 Flash Charging . Fig. 9. Current Vector and Voltage Vector in Charging of Flash Charging Method. 5. 2018 131 . 2 SC1 SOC SC2 SOC SOC1 SOC2 SOC CCV . SW SW . 2 SC1 OCV Emax SC2 OCV Emin 2 . V t . 1 SC1 SC2 SOC . SC2 SC1 V t 9 . N V2cls t . V t . 1 . M. t . t . V Emin . SC1 SC2 / Emax Emin SC2 SOC M . N 100 0 M 1 T SC2. SC1 CCV M M T =M . 10 10 SC1 V T 6 . R2. N C2 . N V T1 M Emax Emin Emin 6.

7 4 . 10 T SC2 2 . N Emax Emin C 2 t i t =. e R 2 5 Emin 7 . N + 1 . R 2. V T 1 = Emin +. 1.. N Emax Emin .. T1 t e C 2 R 2 dt + R 2 . N Emax Emin C T 1. e 2 R 2. C2 N + 1 R 2 N + 1 R2. 3 5 . O. Emax Emin . N T 1. Emax Emin C . N T 1. = Emin e C 2 R 2 1 + e 2 R 2. Flash Charging SC2 SOC N +1 N +1. N . Emax Emin . 10 SW = Emin +. N +1 7 .. SC2 11 V 6 V T . V R2 i T 7 . SOC . SOC . CCV N Emax Emin C 2 TR 2 1. Emax Emin + Emin + R2 . M e = Em N + 1 R 2.. Emax Emin C . N T 1. N Emax Emin . Emax 10 Emin M . R2 + . Emin +R2. R2 e 2 R 2 = Emin +. N + 1 R 2 N +1. i t V T. N N 1. M+ e C 2 R 2 = 8 . N +1 N +1. SC1 SC2 8 . N +1. SW T1 = C2 R2 log . e 1 M 9 . N. N C2. C2. Closed Circuit Voltage Voltage V . R2 SC1 . R2 SC1 OCV . V1open N. V2. SC2 . SC2 OCV . V2open R2 Internal Resistance of SC2 -capacitor cell Time sec . C2 Capacitance of SC2-capacitor cell Charging Start Stop 10 SC1 N . Fig. 10. Equivalent Circuit Diagram in case of SC1with 11 vs . in parallel of N cells. Fig.

8 11. Terminal Voltage in Charging Profile. 6.. 9 4 1 80 Farads SC1 SC2 LIC . M. N 10 SC2 80 F SC1 . 1 M. N 10 . 9 SC2 SC2 SOC 90 Tx 10 .. SC2 N 1 SC1 10 . SC1 SOC= 100 2 . SOC SC2 Flash Charging M N N . 10 =9. T 1 N= 10 . 1 SC2 M 100 Tx 11 . M. 2 M SC1 N N . 1 M. SC1 SW SC2 SC1 SC2. N . SW. 3 SC2 C2 . C2 C2 C2 C2. R2 C2 R2 . R2 R2 R2 R2. 4 SC2 M Cy Cz T . L L. 3 6 . Ry Rz SOC M Tx C2 C2 C2 C2. 9 R2 R2 R2 R2. Tx Cy C2 n p L. Ry R2 L n P .. 10 9 n P P Cz C2 P L. P P Rz R2 L P.. : The number of capacitor cells connected in parallel . L . N +1 : The number of capacitor cells connected in series . Tx C2 R2 log . e 1 M . N 12 . N +1 Fig. 12. Single Equivalent - cell from Capacitor Banks. C2 R2 Tx/log . e 1 M 11 . N. Tx SC2 . 1 . C2 R2 11 Table 1. Experimental Condition. 11 N . M Tx Item Rate/Calculation Specimens . SC2 . A 80 Capacitance of SC 2 F . SC2 SC2 Internal B 12 SC1 SC2 Resistance of SC2 m . Time Constant A B . 12 SC2 Cz P /L C 2 C 0 95. F or Sec . Rz L /P R 2.

9 Cz Rz Cz Rz P /L C 2 L /P R 2 C 2 R 2 D Maximum Termination Voltage . of Charging V . C2 R2 . Cz Rz E Minimum Termination Voltage . Cy Cz of Discharging V . SC2 . L Emax L Emin F. Configuration of SC2 . Capacitor - cell . SC1 10 Capacitor - cells G . Configuration of SC1 in parallel 4 H. 11 Maximum . Time Constant of equation 11 . Flash Charging 9 T . I Minimum Charging Time T . of equation 9 sec .. J . Ambient temperature Room Temperature 7. 2018 131 . 2 SC1 80F/ SC2 Compensated SOC. Table 2. Cells Data of SC1. SC1 1 2 3 4 5 6 7 8 9 10. Capacitor Average SOC % . Cell NO.. Capacitance F . Internal Resistance m . Time sec . 80 F/Charging Time vs Current & Voltage SC1 Closed Circuit SC2 Closed Circuit 14 SC2/80F SOC. Voltage Voltage Fig. 14. Compensated SOC from Closed Circuit Voltage SC2 Open Circuit Charging Current Voltage of SC2/80F. 150. 140. 130 SC1. Rw1 SC2. 120. 110. SW. 100. Voltage V . Current A . 90. 80. 70 N C2. C2. 60. 50. 40. 30 R2. R2. 20. N. 10. 0.

10 Time sec . 13 SC2 80F, SC1 10 . Fig. 13. SC2 80F SC1 80F 10 Experimental Result. Rw . R1:wiring resistance of supply lines R2:wiring resistance of ground lines 15 . 11 . Fig. 15. Equivalent Charging Circuit Diagram in case of 10 including wiring resistance. SOC 90 . SC2 . 13 A 13 . SC1 SC2 CCV 98 A 2 . SC2 V . SC2 SC2 OCV Rw 15 . SC2 OCV 5 12 Rw Rw1 Rw2. SOC 14 14 . SOC 90 . 10 N Emax Emin N + 1 . t i t =. e C 2 N + 1 R 2 + NRw 12 . SOC 90 1 N + 1 R 2 + NRw . 7 98 A . LIC Q=C V. 98 Emax Emin / R 2/N . R 2 Rw . R= m 5 . 8.. Rw= m 10 m N= 10 . Tx 11 . m 11 . 14 2 SOC 75 SOC 10 SOC 90 . 75 C V . As As Ampere Second CC - CV 16 SC2 SOC . 2 16 10 SOC 72 90 . DC 49 A . SC2 SOC 75 SC1 SOC 90 . 4 SW2 SW1 SC1 16 40 . 10 SC1 1 SOC 90 . 10 = A . 1 / 5 . SC2 C2 39 F SC1 . 10 390 F . 4 2 40 Farads SC1 . 80 F 4 SC1 F. N= 10 N Np . Np = 10 = . SC1 SC2 LIC SC2 390. 40 F SC1 . 5 N . N= 10 4 . SC2 SOC 90 Tx 10 5 N. 3 Np T 2 3 . SC1 10 Flash Charging . 4 . M N N . 10 =9. 1 4 SC1.