Supercapacitor module having matched supercapacitors

Abstract

To provide a supercapacitor module and a method for manufacturing the same that are able to prevent an overvoltage without a balancing circuit.SOLUTION: A supercapacitor module may include a first supercapacitor having a first parameter value for a capacitor parameter in a first test condition. The supercapacitor module may include a second supercapacitor having a second parameter value for the capacitor parameter under approximately the first test condition. A ratio of the second parameter value to the first parameter value may be from about 0.8 to about 1.2. The supercapacitor module may prevent an overvoltage across the first and second supercapacitors, so that the supercapacitor module may satisfactorily operate without a balancing circuit.SELECTED DRAWING: None

Description

Technical Field

[0001] Cross - reference to Related Applications This application claims the benefit of U.S. Provisional Patent Application No. 62 / 555,098, filed on September 7, 2017, which is hereby incorporated by reference in its entirety.

Background Art

[0002] Electrical energy storage cells are widely used to power electronics, electromechanical, electrochemical, and other useful devices. For example, a double - layer supercapacitor can use a pair of polarized electrodes containing carbon particles (e.g., activated carbon) impregnated with a liquid electrolyte. Due to the large effective surface area of the particles and the small spacing between the electrodes, a large capacitance value can be achieved. Individual double - layer capacitors can be combined together to form a module with an increased output voltage and an increased energy capacity.

[0003] The performance and lifespan of a supercapacitor module depend on the voltage across the terminals of each supercapacitor in the module. For example, a voltage exceeding the rated voltage of a supercapacitor, called "overvoltage", can potentially reduce the performance and / or lifespan of the module. To prevent overvoltage, a supercapacitor module typically includes a balancing circuit that regulates the voltage across the terminals of the supercapacitors within the module. For example, the balancing circuit may be designed to maintain a substantially equal voltage across the terminals of each of the supercapacitors within the module.

Summary of the Invention

Problems to be Solved by the Invention

[0004] However, the use of a balancing circuit in a supercapacitor module, while undesirable, can increase the size, cost, and / or complexity of the module. The balancing circuit can further generate unwanted heat, which may require cooling of the module, adding further to the cost and / or complexity of the module and increasing the potential for heat-induced failure damage. **Means for Solving the Problem**

[0005] According to one embodiment, a capacitor module is disclosed that includes a first supercapacitor having a first parameter value for a capacitor parameter under a first test condition. The capacitor module includes a second supercapacitor having a second parameter value for the capacitor parameter under approximately the first test condition. The ratio of the second parameter value to the first parameter value may be from 0.8 to 1.2.

[0006] Other features and aspects of the present disclosure are described in more detail below. The complete and enabling disclosure of the present disclosure, including the best mode thereof, directed to one of ordinary skill in the art, is set forth in more detail in the remainder of this specification, with reference to the attached drawings. **Brief Description of the Drawings**

[0007]

Figure 1

Figure 2

Figure 3

Figure 4a

Figure 4b

Figure 4c

Figure 5

Figure 6

Figure 7a

Figure 7b

Figure 8a

Figure 8b

Best Mode for Carrying Out the Invention

[0008] The repeated use of reference numerals in this specification and the drawings is intended to represent the same or similar configurations or elements of the present disclosure. Those skilled in the art should understand that the consideration of the present invention is merely a description of exemplary embodiments and does not limit the broader aspects of the present disclosure embodied in the exemplary configurations.

[0009] As described above, the supercapacitor module typically includes a balancing circuit that controls the voltage across each supercapacitor of the module to prevent overvoltage. Some balancing circuits may be active, such as integrated circuits, for example. Other balancing circuits may be passive, such as one or more passive components connecting the terminals of the supercapacitor, such as resistors, capacitors, etc.

[0010] By matching the supercapacitors described herein, the need for a balancing circuit can be eliminated. For example, by selecting supercapacitors having similar properties as described herein, the module can operate at corresponding substantially equal voltages across the two ends of each supercapacitor. In some embodiments, overvoltage within the module can be prevented, effectively eliminating the need for a balancing circuit overall. In other embodiments, a simple passive balancing circuit may be used instead of an active balancing circuit.

[0011] Eliminating the balancing circuit from the module results in a module that is smaller, less expensive, less costly, and / or less complex. Further eliminating the need for a balancing circuit can reduce the amount of heat generated by the operating module. In other words, the need for a cooling system can be eliminated, and generally, a more robust and reliable module that is less susceptible to damage or failure due to overheating can be obtained.

[0012] I. Supercapacitor Module Configuration Referring to FIG. 1, in one embodiment, the module housing 10 may include a top surface 12, a bottom surface 14, and side surfaces 16 extending between the top surface 12 and the bottom surface 14. In this regard, the supercapacitors (shown in FIG. 2) may be housed between the top surface 14 and the bottom surface 14 of the module housing 10. Further, the module housing 30 may include external terminals or connections (not shown) for use and connections to the device.

[0013] Referring to FIG. 2, the capacitor module 100 may include a plurality of supercapacitors 102 disposed within the module housing 10. As shown herein, it should be understood that the module 100 includes more than two supercapacitors. It is. For example, the module may include two supercapacitors, and in some embodiments, may include more than two supercapacitors, such as four or more, such as six or more, such as eight or more. In some embodiments, it may include from eight to thirty individual supercapacitors. For example, in one embodiment, the module may include fifteen supercapacitors as shown in FIG. 2.

[0014] The module may include a support structure 104 configured to fix the supercapacitor within the housing 10. It should be understood that the module configurations illustrated herein are merely examples. Any suitable module configuration may be used. For example, in some embodiments, the supercapacitors may be stacked end to end. In some embodiments, instead of the housing 10 shown in FIG. 2, the housing may include, for example, a thin packaging material.

[0015] II. Supercapacitor Configuration Any of a variety of different individual supercapacitors may generally be used in the modules of the present invention. However, generally, a supercapacitor contains an electrode assembly and an electrolyte housed within a housing and optionally hermetically sealed. The electrode assembly may include, for example, a first electrode containing a first carbonaceous coating (e.g., activated carbon particles) electrically connected to a first current collector, and a second electrode containing a second carbonaceous coating (e.g., activated carbon particles) electrically connected to a second current collector. If desired, additional current collectors may be used, particularly when the supercapacitor includes a plurality of energy storage cells. The current collectors may be formed from the same or different materials. Nevertheless, each current collector is typically formed from a conductive metal such as aluminum, stainless steel, nickel, silver, palladium, etc., and a substrate including alloys thereof. Aluminum and aluminum alloys are particularly suitable for use in the present invention. The substrate may take the form of a foil, sheet, plate, mesh, etc. The substrate may have a relatively thin thickness, for example, less than about 200 micrometers, in some embodiments from about 1 to about 100 micrometers, in some embodiments from about 5 to about 80 micrometers, and in some embodiments from about 10 to about 50 micrometers. Although not required, the surface of the substrate may optionally be roughened by washing, etching, blasting, etc. When the term "about" is used in conjunction with a numerical value, it is intended to refer to within 20% of the recited amount.

[0016] The first and second carbonaceous coatings may be electrically connected to the first and second current collectors, respectively. They may be formed of the same or different types of materials and may include one or more layers, but each of the carbonaceous coatings generally includes at least one layer containing activated particles. In certain embodiments, for example, an activated carbon layer may be positioned directly on the current collector and may optionally be the only layer of the carbonaceous coating. Examples of suitable activated carbon particles include, for example, activated carbon based on coconut shells, activated carbon based on petroleum coke, activated carbon based on pitch, activated carbon based on polyvinylidene chloride, activated carbon based on phenolic resin, activated carbon based on polyacrylonitrile, and activated carbon obtained from natural sources such as coal, charcoal, or other natural organic sources.

[0017] In certain embodiments, after being subjected to one or more charge-discharge cycles, it is considered desirable to selectively control certain aspects of the activated carbon particles, such as their particle size distribution, surface area, and pore size distribution, in order to assist in improving the ionic mobility with respect to a certain type of electrolyte. For example, at least 50 volume% (D50 size) of the particles may have a size in the range of about 0.01 to about 30 micrometers, in some embodiments about 0.1 to about 20 micrometers, and in some embodiments about 0.5 to about 10 micrometers. The size of at least 90 volume% (D90 size) of the particles may similarly have a size in the range of about 2 to about 40 micrometers, in some embodiments about 5 to about 30 micrometers, and in some embodiments about 6 to about 15 micrometers. The BET surface may range from about 900 m 2 / g to about 3,000 m 2 / g, in some embodiments from about 1,000 m 2 / g to about 2,500 m 2 / g, and in some embodiments from about 1,100 m 2 / g to about 1,800 m 2 / g.

[0018] In addition to having a particular size and surface area, the activated carbon particles may include pores having a particular size distribution. For example, the amount of pores having a size of less than about 2 nanometers (i.e., "micropores") may be about 50 volume % or less of the total pore volume, in some embodiments about 30 volume % or less, and in some embodiments may provide a pore volume of from 0.1 volume % to 15 volume %. Similarly, the amount of pores having a size between about 2 nanometers and about 50 nanometers (i.e., "mesopores") may range from about 20 volume % to about 80 volume %, in some embodiments from about 25 volume % to about 75 volume %, and in some embodiments from about 35 volume % to about 65 volume %. Finally, the amount of pores having a size greater than about 50 nanometers (i.e., "macropores") may be from about 1 volume % to about 50 volume %, in some embodiments from about 5 volume % to about 40 volume %, and in some embodiments from about 10 volume % to about 35 volume %. The total pore volume of the carbon particles is from about 0.2 cm 3 / g to about 1.5 cm 3 / g, in some embodiments from about 0.4 cm 3 / g to about 1.0 cm 3 / g, and the median pore width may be about 8 nanometers or less, in some embodiments from about 1 to about 5 nanometers, and in some embodiments from about 2 to 4 nanometers. The pore diameter and total pore volume may be measured using nitrogen adsorption, as is well known in the art, and may be analyzed by the Barrett-Joyner-Halenda ("BJH") technique.

[0019] If desired, the binder may be present in an amount of about 60 parts or less, in some embodiments 40 parts or less, and in some embodiments about 1 to about 25 parts per 100 parts of carbon in the first and / or second carbonaceous coating. The binder may, for example, constitute about 15 wt% or less, in some embodiments about 10 wt% or less, and in some embodiments about 0.5 wt% to about 5 wt% of the total weight of the carbonaceous coating. Any of various suitable binders can be used for the electrodes. For example, water-insoluble organic binders may include styrene-butadiene copolymers, polyvinyl acetate homopolymers, vinyl-acetate ethylene copolymers, vinyl-acetate acrylic copolymers, ethylene-vinyl chloride copolymers, ethylene-vinyl chloride-vinyl acetate terpolymers, acrylic polyvinyl chloride polymers, acrylic polymers, nitrile polymers, fluoropolymers such as polytetrafluoroethylene or polyvinylidene fluoride, polyolefins, etc., as well as mixtures thereof, and may be used in certain embodiments. For water-soluble organic binders, polysaccharides and their derivatives may be used. In certain embodiments, the polysaccharide is a non-ionic cellulose ether, such as an alkyl cellulose ether (e.g., methyl cellulose and ethyl cellulose); a hydroxyalkyl cellulose ether (e.g., hydroxyethyl cellulose, hydroxypropyl cellulose, hydroxypropyl hydroxybutyl cellulose, hydroxyethyl hydroxypropyl cellulose, hydroxyethyl hydroxybutyl cellulose, hydroxyethyl hydroxypropyl hydroxybutyl cellulose, etc.); an alkyl hydroxyalkyl cellulose ether (e.g., methyl hydroxyethyl cellulose, methyl hydroxypropyl cellulose, ethyl hydroxyethyl cellulose, ethyl hydroxypropyl cellulose, methyl ethyl hydroxyethyl cellulose, and methyl ethyl hydroxypropyl cellulose); a carboxyalkyl cellulose ether (e.g., carboxymethyl cellulose); and the like, as well as any of the aforementioned protonated salts, such as sodium car It may be carboxymethyl cellulose.

[0020] Other materials may be used within the activated carbon layer of the first and / or second carbonaceous coating and / or within other layers of the first and / or second carbonaceous coating. For example, in certain embodiments, a conductivity promoter may be used to further increase the conductivity. Exemplary conductivity promoters include, for example, carbon black, graphite (natural or artificial), graphene, carbon nanotubes, nanowires or nanotubes, metal fibers, and mixtures thereof. Carbon black is particularly preferred. When used, the conductivity promoter typically constitutes about 60 parts or less per 100 parts of the activated carbon particles of the carbonaceous coating, in some embodiments 40 parts or less, and in some embodiments about 1 to about 25 parts. The conductivity promoter may, for example, constitute about 15 wt% or less of the total weight of the carbonaceous coating, in some embodiments about 10 wt% or less, and in some embodiments about 0.5 wt% to about 5 wt%. The activated carbon particles typically similarly constitute 85 wt% or more of the carbonaceous coating, in some embodiments about 90 wt% or more, and in some embodiments about 95 wt% to about 99.5 wt%.

[0021] Specific techniques for applying the carbonaceous coating to the current collector may vary, such as printing (e.g., rotogravure), spraying, slot-die coating, drop coating, dip coating, etc., as is well known to those skilled in the art. Regardless of the application technique, the resulting electrode is typically dried at a temperature of, for example, about 100 °C or higher, in some embodiments about 200 °C or higher, and in some embodiments from about 300 °C to about 500 °C so that moisture is removed from the coating. The electrode may be compressed (e.g., calendared) to optimize the volumetric efficiency of the supercapacitor. After any optional compression, the thickness of each carbonaceous coating may generally vary based on the desired electrical performance and operating range of the supercapacitor. However, typically, the coating thickness is from about 20 to about 200 micrometers, from 30 to about 150 micrometers, and in some embodiments from about 40 to about 100 micrometers. The coating may be present on one or both sides of the current collector. Nevertheless, the thickness of the entire electrode (including the current collector and the optional carbonaceous coating(s) after compression) is typically in the range of about 20 to about 350 micrometers, in some embodiments in the range of about 30 to about 300 micrometers, and in some embodiments in the range of about 50 to about 250 micrometers.

[0022] The electrode assembly typically also includes a separator positioned between the first and second electrodes. If desired, other separators may be used in the electrode assembly. For example, one or more separators may be positioned on the first electrode, on the second electrode, or on both. The separator can electrically isolate one electrode from another and help prevent electrical short circuits, while still allowing ion transport between the two electrodes. In certain embodiments, for example, a separator including a cellulose-based fiber material (such as an airlaid paper web, a wet-laid paper web, etc.), a nonwoven material (such as a polyolefin nonwoven), a woven fabric, a film (such as a polyolefin film), etc. may be used. The cellulose-based fiber material is particularly suitable for use in supercapacitors containing natural fibers, synthetic fibers, etc. Specific examples of cellulose fibers suitable for use as a separator include, for example, hardwood pulp fibers, softwood pulp fibers, rayon fibers, regenerated cellulose fibers, etc. Regardless of the specific material used, the separator typically has a thickness of from about 5 to about 150 micrometers, in some embodiments from about 10 to about 100 micrometers, and in some embodiments from about 20 to about 80 micrometers.

[0023] The manner in which the components of the electrode assembly are combined together can be various as is known in the art. For example, the electrodes and separator may first be folded, wound, or otherwise brought into contact together to form the electrode assembly. In certain embodiments, the electrodes, separator, and optional electrolyte may be wound into an electrode assembly having a "jelly roll" configuration.

[0024] To form a supercapacitor, an electrolyte is disposed to be in ionic contact with a first electrode and a second electrode before, during, and / or after the electrodes and a separator are combined together to form an electrode assembly. The electrolyte generally has a nature that is originally non-aqueous and thus contains at least one non-aqueous solvent. To help extend the operating temperature range of the supercapacitor, typically the non-aqueous solvent desirably has a relatively high boiling temperature, such as about 150 °C or higher, in some embodiments about 200 °C or higher, and in some embodiments from about 220 °C to about 300 °C. Particularly suitable high-boiling solvents include, for example, cyclic carbonate solvents such as ethylene carbonate, propylene carbonate, butylene carbonate, vinylene carbonate, and the like. Of course, other non-aqueous solvents may be used alone or in combination with cyclic carbonate solvents. Examples of such solvents include, for example, open-chain carbonates (such as dimethyl carbonate, ethyl methyl carbonate, diethyl carbonate, etc.), aliphatic monocarboxylates (such as methyl acetate, ethyl propionate, etc.), lactone solvents (such as butyrolactone, valerolactone, etc.), nitriles (such as acetonitrile, glutaronitrile, adiponitrile, methoxyacetonitrile, 3-methoxypropionitrile, etc.), amides (such as N,N-dimethylformamide, N,N-dimethylacetamide, N-methylpyrrolidinone), alkanes (such as nitromethane, nitroethane, etc.), sulfur compounds (such as sulfolane, dimethyl sulfoxide, etc.); and the like.

[0025] The electrolyte may contain at least one ionic liquid dissolved in the non-aqueous solvent. The concentration of the ionic liquid can be varied, but typically it is desirable for the ionic liquid to be present at a relatively high concentration. For example, the ionic liquid may be present in an amount of about 0.8 mole (M) or more per liter of electrolyte, in some embodiments about 1.0 M or more, in some embodiments about 1.2 M or more, and in some embodiments from about 1.3 to about 1.8 M.

[0026] Ionic liquids are generally salts that have a relatively low melting temperature, such as about 400 °C or lower, in some embodiments about 350 °C or lower, in some embodiments about 1 °C to about 100 °C, and in some embodiments about 5 °C to about 50 °C. The salt contains a cationic species and a counter ion. The cationic species contains a compound having at least one heteroatom (e.g., nitrogen or phosphorus) as a "cationic center". Examples of such heteroatom compounds include, for example, unsubstituted or substituted organic quaternary ammonium compounds such as ammonium (e.g., trimethylammonium, tetramethylammonium, etc.), pyridinium, pyridazinium, pyrimidinium, pyrazinium, imidazolium, pyrazolium, oxazolium, triazolium, thiazolium, quinolinium, piperazinium, pyrrolidinium, a quaternary ammonium spiro compound in which two or more rings are connected together by a spiro atom (e.g., carbon, heteroatom, etc.), a quaternary ammonium condensed ring structure (e.g., quinolinium, isoquinolinium, etc.), and the like. In certain embodiments, for example, the cationic species may be an N-spiro bicyclic compound, such as a symmetric or asymmetric N-spiro bicyclic compound having a cyclic ring. An example of such a compound has the following structure:

[0027] [Chemical formula]

[0028] [wherein m and n are independently numbers from 3 to 7, and in some embodiments are 4 to 5 (e.g., pyrrolidinium or piperidinium)] and has.

[0029] Similarly, suitable counterions for cationic species include halogens (e.g., chloride, bromide, iodide, etc.); sulfates or sulfonates (e.g., methyl sulfate, ethyl sulfate, butyl sulfate, hexyl sulfate, octyl sulfate, hydrogen sulfate, methane sulfonate, dodecylbenzene sulfonate, dodecyl sulfate, trifluoromethane sulfonate, heptadecafluorooctane sulfonate, sodium dodecylethoxysulfate, etc.); sulfosuccinates; amides (e.g., dicyanamide); imides (e.g., bis(pentafluoroethylsulfonyl)imide, bis(trifluoromethylsulfonyl)imide, bis(trifluoromethyl)imide, etc.); borates (e.g., tetrafluoroborate, tetracyano borate, bis[oxalato]borate, bis[salicylato]borate, etc.); phosphates or phosphinates (e.g., hexafluorophosphate, diethyl phosphate, bis(pentafluoroethyl)phosphinate, tris(pentafluoroethyl)-trifluorophosphate, tris(nonafluorobutyl)trifluorophosphate, etc.); antimonates (e.g., hexafluoroantimonate); aluminates (e.g., tetrachloroaluminate); fatty acid carboxylates (e.g., oleate, isostearate, pentadecafluorooctanoate, etc.); cyanates; acetates; and the like, as well as combinations of any of the foregoing can be mentioned.

[0030] Some examples of suitable ionic liquids include, for example, spiro-(1,1’)-bipyrrolidinium tetrafluoroborate, triethylmethylammonium tetrafluoroborate, tetraethylammonium tetrafluoroborate, spiro-(1,1’)-bipyrrolidinium iodide, triethylmethylammonium iodide, tetraethylammonium iodide, methyltriethylammonium tetrafluoroborate, tetrabutylammonium tetrafluoroborate, tetraethylammonium hexafluorophosphate, and the like.

[0031] As described above, the supercapacitor also includes a housing that holds an electrode assembly and an electrolyte therein and is optionally hermetically sealed. The properties of the housing may be varied as desired. In one embodiment, for example, the housing may include a metal container (a "can") formed from tantalum, niobium, aluminum, nickel, hafnium, titanium, copper, silver, steel (e.g., stainless), alloys thereof, composites thereof (e.g., a metal coated with a conductive oxide), and the like. Aluminum is particularly suitable for use in the present invention. The metal container may have any of a variety of different shapes, such as cylindrical, D-shaped, etc. A cylindrical container is particularly suitable.

[0032] The electrode assembly may be sealed within the cylindrical housing using a variety of techniques. Referring to FIG. 3, an embodiment of a supercapacitor 2000 is shown that includes an electrode assembly 2108 that includes layers 2106 wound together in a jelly roll configuration. In this particular embodiment, the supercapacitor includes a first collector disc 2114 that includes a disc-shaped portion 2134, a stud portion 2136, and a fastener 2138 (e.g., a screw). The collector disc 2114 is aligned with a first end of a hollow core 2160 formed in the center of the electrode assembly, and then the stud portion 2136 is inserted into the opening of the core such that the disc-shaped portion 2134 is positioned against the first end of the electrode assembly 2108 at a first contact edge 2110. A lid 2118 is welded (e.g., laser welded) to the first terminal 2116, and a socket, which may be threaded, for example, is coupled to the fastener 2138. The supercapacitor also includes a second collector disc 2120 that includes a disc-shaped portion 2142, a stud portion 2140, and a second terminal 2144. The second collector disc 2120 is aligned with a second end of the hollow core 2160, and then the stud portion 2140 is inserted into the opening of the core such that the collector disc portion 2142 is positioned against the second end of the electrode assembly 2108.

[0033] Thereafter, the metal container 2122 (e.g., a cylindrical can) is slid onto the electrode assembly 2108 such that the second collector disk 2120 first enters the container 2122, passes through the first insulating washer 2124, through the axial hole at the end of the container 2122, and then through the second insulating washer 2126. The second collector disk 2120 also passes through the flat washer 2128 and the spring washer 2130. The lock nut 2132 is tightened on the spring washer 2130 to press the spring washer 2130 against the flat washer 2128, which in turn presses against the second insulating washer 2126. The second insulating washer 2126 is pressed against the outer periphery of the axial hole of the metal container 2122, and as the second collector disk 2120 is drawn out by this compressive force towards the axial hole, the first insulating washer 2124 is pressed between the second collector disk 2120 and the inner periphery of the axial hole of the container 2122. The flange on the first insulating washer 2124 prevents electrical contact between the second collector disk 2120 and the rim of the axial hole. At the same time, the lid 2118 is inserted into the opening of the container 2122 such that the rim of the lid 2118 is positioned just inside the lip of the opening of the container 2122. The rim of the lid 2118 is then welded to the lip of the opening of the container 2122.

[0034] When the lock nut 2132 is tightened against the spring washer 2130, a hermetic seal can be formed between the shaft hole, the first insulating washer 2124, the second insulating washer 2126, and the second collector disk 2120. Similarly, the welding of the lid 2118 to the lip of the container 2122 and the welding of the lid 2118 to the first terminal 2116 can form another hermetic seal. The hole 2146 in the lid 2118 can be left open to serve as the inlet for the above-mentioned electrolyte. When the electrolyte enters the can (i.e., is drawn into the can in a vacuum as described above), the bushing 2148 is inserted into the hole 2146 and seated against the flange 2150 at the inner edge of the hole 2146. The bushing 2148 may be a hollow cylinder whose shape is adapted to receive, for example, the plug 2152. The plug 2152 having a cylindrical shape is pressed into the center of the bushing 2148, thereby pressing the bushing 2148 inside the hole 2146 and forming a hermetic seal between the hole 2146, the bushing 2148, and the plug 2152. The plug 2152 and the bushing 2148 may be selected to be removed when a specified level of pressure is reached within the supercapacitor, thereby forming an overpressure safety mechanism.

[0035] The above embodiments generally refer to the use of a single electrochemical cell within a capacitor. However, it should be understood that the capacitor of the present invention may also include two or more electrochemical cells. In one such embodiment, for example, the capacitor may include a stack of two or more electrochemical cells that may be the same or different. And may include a stack of two or more electrochemical cells that may be the same or different.

[0036] The resulting supercapacitor can exhibit excellent electrical properties. For example, the supercapacitor has a capacitance of about 6 farads per cubic centimeter (\"F / cm 3 \") or more when measured at a temperature of 23 °C, a frequency of 120 Hz, and without an applied voltage. In some embodiments, it is about 8 F / cm 3 or more. In some embodiments, it is about 9 to about 100 F / cm 3 and in some embodiments, it is about 10 to about 80 F / cm 3The capacitance may be shown. The supercapacitor may have a low equivalent series resistance (ESR), such as less than about 150 milliohms, in some embodiments less than about 125 milliohms, in some embodiments from about 0.01 to about 100 milliohms, and in some embodiments from about 0.05 to about 70 milliohms, as determined at a temperature of 23° C., a frequency of 100 kHz, and without an applied voltage.

[0037] In particular, the supercapacitor can exhibit excellent electrical properties when exposed to high temperatures. For example, the supercapacitor may be disposed in contact with an atmosphere having a temperature of about 80° C. or higher, in some embodiments from about 100° C. to about 150° C., and in some embodiments from about 105° C. to about 130° C. (e.g., 85° C. or 105° C.). The capacitance and ESR values can remain stable for a significant period of time, such as for about 100 hours or more, in some embodiments from about 300 hours to about 5000 hours, and in some embodiments from about 600 hours to about 4500 hours (e.g., 168, 336, 504, 672, 840, 1008, 1512, 2040, 3024, or 4032 hours) at such temperatures.

[0038] In one embodiment, for example, the ratio of the capacitance value of the supercapacitor after being exposed to a high-temperature atmosphere (e.g., 85°C or 105°C) for 1008 hours to the capacitance value of the supercapacitor when first exposed to the high-temperature atmosphere is about 0.75 or more, in some embodiments about 0.8 to 1.0, and in some embodiments about 0.85 to 1.0. Such a high capacitance value can also be maintained under various extreme conditions, such as when a voltage is applied and / or when in a high-humidity atmosphere. For example, the ratio of the capacitance value of the supercapacitor after being exposed to a high-temperature atmosphere (e.g., 85°C or 105°C) and an applied voltage to the initial capacitance value of the supercapacitor when it was exposed to the high-temperature atmosphere but before the voltage was applied may be about 0.60 or more, in some embodiments about 0.65 to 1.0, and in some embodiments about 0.7 to 1.0. The voltage may be, for example, about 1 volt or more, in some embodiments about 1.5 volts or more, and in some embodiments about 2 to about 10 volts (e.g., 2.1 volts). In one embodiment, for example, the above ratio may be maintained for 1008 hours or more. The supercapacitor may maintain the above capacitance value when exposed to a high-humidity level, for example, when placed in contact with an atmosphere having a relative humidity of about 40% or more, in some embodiments about 45% or more, in some embodiments about 50% or more, and in some embodiments about 70% or more (e.g., about 85% to 100%). The relative humidity may be determined, for example, in accordance with ASTM E337-02, Method A (2007). For example, the ratio of the capacitance value of the supercapacitor after being exposed to a high-temperature atmosphere (e.g., 85°C or 105°C) and high humidity (e.g., 85%) to the initial capacitance value of the supercapacitor when it was exposed to the high-temperature atmosphere but before being exposed to the high humidity may be about 0.7 or more, in some embodiments about 0.75 to 1.0, and in some embodiments about 0.80 to 1.0. In one embodiment, for example, this ratio may be maintained for 1008 hours or more.

[0039] The ESR can remain stable for a significant period of time as described above at such temperatures. In one embodiment, for example, the ratio of the ESR of the supercapacitor after being exposed to a high-temperature atmosphere (e.g., 85 °C or 105 °C) for 1008 hours to the ESR of the supercapacitor when first exposed to the high-temperature atmosphere is about 1.5 or less, in some embodiments about 1.2 or less, and in some embodiments about 0.2 to about 1. In particular, such low ESR values can also be maintained under various extreme conditions, such as when a high voltage is applied as described above and / or when in a high-humidity atmosphere. For example, the ratio of the ESR of the supercapacitor after being exposed to a high-temperature atmosphere (e.g., 85 °C or 105 °C) and an applied voltage to the initial ESR of the supercapacitor when it was exposed to the high-temperature atmosphere but before the voltage was applied can be about 1.8 or less, in some embodiments about 1.7 or less, and in some embodiments about 0.2 to about 1.6. In one embodiment, for example, the above ratio may be maintained for 1008 hours or more. The supercapacitor may maintain the above ESR value when exposed to a high humidity level. For example, the ratio of the ESR of the supercapacitor after being exposed to a high-temperature atmosphere (e.g., 85 °C or 105 °C) and high humidity (e.g., 85%) to the initial capacitance value of the supercapacitor when it was exposed to the high-temperature atmosphere but before being exposed to the high humidity can be about 1.5 or less, in some embodiments about 1.4 or less, and in some embodiments about 0.2 to about 1.2. In one embodiment, for example, this ratio may be maintained for 1008 hours or more.

[0040] III. Supercapacitor Matching In some embodiments, the supercapacitor module may include a plurality of supercapacitors. The supercapacitors may be matched such that a balancing circuit is not required to control the respective voltages across each of the supercapacitors. In some embodiments, the supercapacitors may be matched based on one or more characteristics, such as direct current leakage (DCL), equivalent series resistance (ESL), capacitance, and / or any other suitable characteristic, as described in more detail below.

[0041] In one embodiment, the capacitor module may include a first supercapacitor having a first parameter value for a capacitor parameter under a first test condition. The capacitor may include a second supercapacitor having a second parameter value for the capacitor parameter under approximately the first test condition. The first test condition may include various test condition parameters, such as temperature, humidity, direct current (DC) voltage, alternating current (AC) voltage, time before use, and / or the like, as described in more detail below. As described above, the capacitor parameters may include direct current leakage, equivalent series resistance, and / or capacitance, and the direct current leakage, also referred to as "leakage current", is the amount of current flowing through the capacitor at a given DC voltage, e.g., the rated DC voltage of the supercapacitor. Further, any suitable characteristic of the capacitor may be a capacitor parameter.

[0042] In some embodiments, the ratio of the second parameter value to the first parameter value may be from about 0.8 to about 1.2. In some embodiments, the ratio may be from about 0.85 to about 1.15, and in some embodiments from about 0.9 to about 1.1, and in some embodiments from about 0.95 to about 1.05, and in some embodiments from about 0.975 to about 1.025, and in some embodiments from 0.99 to 1.01, and in some embodiments from 0.995 to 1.005.

[0043] In some embodiments, the matching of the supercapacitors can eliminate the need for a voltage balancing circuit. As described above, the balancing circuit can control the respective voltages across each supercapacitor to prevent overvoltage. The balancing circuit may be active, such as an integrated circuit, or passive, such as one or more passive components (e.g., resistors) connected to the terminals of the supercapacitor. By matching the supercapacitors described herein, the module can operate at a substantially equal voltage across each supercapacitor. This can prevent overvoltage from occurring , thus eliminating the need for a balancing circuit in some embodiments.

[0044] In some embodiments, the first capacitor may be connected in series with the second supercapacitor without an active or passive balancing circuit. In some embodiments, a simple passive balancing circuit may be used, while an active balancing circuit may be eliminated. In other embodiments, the first supercapacitor may be connected in series with the second supercapacitor using a simplified active balancing circuit. For example, a simplified active balancing circuit may include fewer components than a standard active balancing circuit, consume less energy, cost less to produce, and / or generate less heat.

[0045] Although the above has been described with reference to two supercapacitors, as noted above, the module may include any suitable number of supercapacitors. In some embodiments, additional supercapacitors beyond the first and second supercapacitors may be selected based on a comparison with the first supercapacitor using the methods described herein. For example, each of the additional supercapacitors may have respective parameter values for capacitor parameters under approximately the first test conditions. Each of the additional supercapacitors may be selected based on the ratio of the capacitor parameter values for each additional supercapacitor under the first test conditions to the first capacitor parameter value of the capacitor parameters under the first test conditions, which is from about 0.8 to about 1.2 times. In other embodiments, the ratio is included in any of the other ratio ranges discussed herein.

[0046] In some embodiments, each supercapacitor may be compared only to the supercapacitor to which it is directly connected. For example, each nth supercapacitor may be compared to the n-1, n+1, or both supercapacitors. In some embodiments, each supercapacitor may be selected such that the module is assembled based on the last supercapacitor added to the module, i.e., supercapacitor n-1). In some embodiments, the capacitor parameters for each nth supercapacitor may be compared to a nominal target capacitor parameter. In other embodiments, the supercapacitors may be selected using any statistical analysis technique, machine learning algorithm, and / or optimization algorithm. For example, in one embodiment, the supercapacitors may be selected such that the standard deviation(s) of one or more capacitor parameters is within one or more respective predetermined standard deviation ranges.

[0047] In some embodiments, empirical analysis may be combined with other methods described herein to match supercapacitors. For example, a test voltage may be applied across the terminals of a first supercapacitor. Next, several supercapacitors may be “auditioned” to determine which supercapacitor should be added to the module as a second supercapacitor. This may include connecting each of the supercapacitors to be “auditioned” one by one in series to the first supercapacitor. The voltage is applied across the terminals of the series supercapacitors, and the voltage across the terminals of the first supercapacitor and the voltage across the terminals of the supercapacitor being auditioned can be measured and a mathematical difference calculated. Then, the supercapacitor that results in the smallest mathematical difference between the voltage across the terminals of the first supercapacitor and the voltage across the terminals of the supercapacitor being “auditioned” may be selected as the second supercapacitor. The process may then be repeated to select a third supercapacitor, a fourth supercapacitor, and so on. Further, the above process can assist in determining the optimal order for connecting the supercapacitors within the module.

[0048] In other embodiments, any suitable optimization algorithm may be used to theoretically determine the selection and / or connection order of potential supercapacitors for the module. For example, the empirical selection procedure described above may be theoretically simulated using known characteristics of potential supercapacitors, as well as theoretical or empirical relationships between the characteristics of the supercapacitors, the associated test conditions, and the voltage obtained across the terminals of the supercapacitor when connected to the module. In other embodiments, given a pool of potential supercapacitors, each possible combination and / or order of the supercapacitors can be theoretically modeled to determine the combination and connection order that is most suitable for minimizing voltage differences and / or overvoltages in the module.

[0049] ​In other embodiments, when selecting a plurality of supercapacitors for a module, several capacitor parameters may be measured for each supercapacitor. The supercapacitors may then be ranked based on the capacitor parameters. For example, in some embodiments, the supercapacitors may first be ranked by the capacitor parameters determined to be the most predictable of the interactions of the supercapacitors within the module. The supercapacitors may then be ranked second by the next most predictable capacitor parameters, and so on. In other embodiments, each capacitor parameter may be weighted, and the supercapacitors may then be ranked according to the weighted average of the capacitor parameters. The weights may be based on how decisive each capacitor parameter is as to the voltage across the supercapacitors once connected within the module. The selection and / or connection order of the supercapacitors may be selected based on the resulting ranking.

[0050] IV. Selection Based on Direct Current Leakage (DCL) In some embodiments, the supercapacitors may be selected based on DCL. For example, a first supercapacitor may have a DCL of 25 microamps (μA) under a first test condition. In some embodiments, the first test condition may include a constant frequency of temperature, relative humidity, applied DC voltage, and / or applied AC voltage. For example, the first test condition may include an applied DC voltage of 5 volts (no AC voltage component) at a temperature of 25°C. A second supercapacitor may be selected based on having a DCL of approximately 0.9 to approximately 1.1 times the DCL of the first supercapacitor under approximately the first test condition. Thus, in this example, the second supercapacitor may have a DCL of 22.5 μA to 27.5 μA at an applied DC voltage of 5 volts (no AC voltage component) and a temperature of 25°C. For example, the supercapacitors may be selected based on a DCL test using one of the test methods described in the following sections.

[0051] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having a DCL that is about 0.95 to about 1.05 times the DCL of the first supercapacitor at approximately the same voltage and at approximately the same temperature. Thus, in this example, the second supercapacitor may have a DC of about 23.75 μA to about 26.25 μA at about 5 volts and about 25 °C.

[0052] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having a DCL that is about 0.975 to about 1.025 times the DCL of the first supercapacitor at approximately the same voltage and at approximately the same temperature. Thus, in this example, the second supercapacitor may have a DCL between about 24.375 μA and about 25.625 μA at about 5 volts and about 25 °C.

[0053] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having a DCL that is about 0.99 to about 1.01 times the DCL of the first supercapacitor at approximately the same voltage and at approximately the same temperature. Thus, in this example, the second supercapacitor may have from about 24.75 μA to about 25.25 μA at about 5 volts and about 25 °C.

[0054] V. Selection Based on Equivalent Series Resistance (ESR) In some embodiments, the supercapacitor may be selected based on ESR. In some embodiments, the ESR may be related to alternating current (ESR AC ), and in other embodiments, the ESR may be related to direct current (ESR DC ). For example, the supercapacitor may be selected based on an ESR test using the test methods described in the following sections.

[0055] For example, the first supercapacitor may have an ESR of 65 milliohms under the first test conditions. AC In some embodiments, the first test conditions may include a constant frequency of temperature, relative humidity, applied DC voltage, and / or applied AC voltage. For example, the first test conditions may include an AC voltage of 10 millivolts (mV) at a temperature of 1 kHz (DC bias voltage is 0.0 volts) and 25°C. In other embodiments, the DC bias voltage may be, for example, 1.1 volts or 2.1 volts. The second supercapacitor may be selected based on having an ESR that is approximately 0.9 to approximately 1.1 times the ESR of the first supercapacitor under the first test conditions. Thus, in this example, the second supercapacitor may have an ESR of approximately 58.5 milliohms to approximately 71.5 milliohms at approximately 10 mV, approximately 1 kHz (DC bias is 0.0 volts), and a temperature of approximately 25°C. AC ESR that is about 0.9 to about 1.1 times AC In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having an ESR that is approximately 0.95 to approximately 1.05 times the ESR of the first supercapacitor under the first test conditions. Thus, in this example, the second supercapacitor may have an ESR of approximately 61.75 milliohms to approximately 68.25 milliohms at approximately 10 mA (DC bias is 0.0 volts), approximately 1000 Hz, and approximately 25°C. AC ESR that is about 0.95 to about 1.05 times

[0056] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having an ESR that is approximately 0.975 to approximately 1.025 times the ESR of the first supercapacitor under the first test conditions. AC ESR that is about 0.975 to about 1.025 times AC ESR that is about 0.975 to about 1.025 times AC In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having an ESR that is approximately 0.975 to approximately 1.025 times the ESR of the first supercapacitor under the first test conditions.

[0057] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having an ESR that is approximately 0.975 to approximately 1.025 times the ESR of the first supercapacitor under the first test conditions. AC ESR that is about 0.975 to about 1.025 times ACIt may be selected based on having. Thus, in this embodiment, the second supercapacitor has an ESR of approximately 63.375 milliohms to approximately 66.625 milliohms at about 10 mV (DC bias is 0.0 volts), about 1000 Hz, and about 25°C AC It may have.

[0058] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor has an ESR that is approximately 0.99 to approximately 1.01 times the ESR of the first supercapacitor under approximately the first test conditions AC It may be selected based on having an ESR that is approximately 0.99 to approximately 1.01 times that of the first supercapacitor. AC Thus, in this embodiment, the second supercapacitor may have from approximately 64.350 milliohms to approximately 65.650 milliohms at about 10 mV (DC bias is 0.0 volts), about 1000 Hz, and about 25°C.

[0059] VI. Selection Based on Capacitance In some embodiments, the supercapacitor may be selected based on capacitance. For example, the first supercapacitor may have a capacitance of 5 farads (F) under the first test conditions. In some embodiments, the first test conditions may include temperature, relative humidity, applied DC voltage, and / or applied AC voltage at a constant frequency . For example, the first test conditions may include a temperature of about 25°C. The second supercapacitor may be selected based on having a capacitance that is approximately 0.9 to approximately 1.1 times the capacitance of the first supercapacitor under approximately the first test conditions. Thus, in this embodiment, the second supercapacitor may have a capacitance of from about 4.5 F to about 5.5 F at a temperature of about 25°C. The supercapacitor may be selected based on a capacitance test using the test method described in the following section.

[0060] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having a capacitance that is approximately from about 0.95 to about 1.05 times the capacitance of the first supercapacitor under approximately the first test conditions. Thus, in this example, the second supercapacitor may have a capacitance of from about 4.75 F to about 5.25 F at about 25°C.

[0061] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be based on having a capacitance that is approximately from about 0.975 to about 1.025 times the capacitance of the first supercapacitor under approximately the first test conditions. Thus, in this example, the second supercapacitor may have a capacitance of from about 4.875 F to about 5.125 F at about 25°C.

[0062] In another embodiment, the first supercapacitor may be selected as described above, and the second supercapacitor may be selected based on having a capacitance that is approximately from about 0.99 to about 1.01 times the capacitance of the first supercapacitor under approximately the first test conditions. Thus, in this example, the second supercapacitor may have a capacitance of from about 4.95 F to about 5.05 F at about 25°C.

[0063] VII. Selection Based on Multiple Parameters In some embodiments, the supercapacitor may be selected based on two or more combinations of the above parameters. For example, in one embodiment, the first supercapacitor may have a DCL of 25 microamps (μA) at an applied voltage of 5 volts (DC) (no AC voltage component) and a temperature of 25 °C, and an ESR of 65 milliohms at 10 millivolts (mV), 1000 Hz (no DC voltage bias), and a temperature of 25 °C. The second supercapacitor may be selected based on (1) a ratio within a range of a first ratio of the DCL of the second supercapacitor under the first test conditions to the DCL of the first supercapacitor (e.g., from about 0.8 to about 1.2), and (2) a second ratio within a range of a second ratio of the ESR of the second supercapacitor under the second test conditions to the ESR of the first supercapacitor under the second test conditions (e.g., from about 0.95 to about 1.05). In some embodiments, the range of the first ratio may be equal to the range of the second ratio. For example, in one embodiment, each of the first and second ranges may be from about 0.99 to about 1.01. In other embodiments, the range of the first ratio regarding DCL may be different from the range of the second ratio regarding ESR. For example, in one embodiment, the range of the first ratio regarding DCL may be from about 0.99 to about 1.01, and the range of the second ratio regarding ESR may be from about 0.95 to about 1.05.

[0064] It should be understood that any suitable combination of ratio ranges and parameters may be used. In some embodiments, the supercapacitor may be selected based on all three parameters (DCL, ESR, and capacitance). In other embodiments, additional parameters such as peak current, maximum energy, energy density, etc. may be used. Further, as described above, any suitable statistical analysis technique, machine learning algorithm, and / or optimization algorithm may be used. Although described as having two supercapacitors, the module may have any suitable number of super It should be understood that it may have a capacitor. Further, the above description of selecting the second supercapacitor based on the first supercapacitor can be similarly applied to selecting the third supercapacitor based on the second supercapacitor, and so on hereinafter.

[0065] Referring to FIGS. 4a to 4c, the leakage current and the equivalent series resistance may each change with temperature. The relationship between each capacitor parameter and temperature can be determined empirically or theoretically. These relationships may be used to select a supercapacitor, as will be described in more detail below.

[0066] For example, FIG. 5 shows an exemplary implementation of testing and matching supercapacitors. In this example, a target range of from about 0.8 to about 1.2 is used for the ratio of the capacitor parameter values. FIG. 5 shows the leakage current versus temperature for five supercapacitors 4002, 4004, 4006, 4008, 4010. The leakage current of each supercapacitor may be measured at 25° C. (indicated by the vertical dotted line at 25° C.). The ratio of the leakage current for each supercapacitor may be formed with respect to one of the supercapacitors. For example, the ratio may be calculated with respect to supercapacitor 4010 since supercapacitor 4010 has the lowest leakage current at 25° C. The ratio of the leakage current at 25° C. for supercapacitor 4008 to the leakage current at 25° C. for supercapacitor 4010 is about 1.1, which is within the target range of 0.8 to 1.2. Thus, in this hypothetical example, supercapacitors 4008 and 4010 can be matched to form a module. FIG. 5 shows that it is predicted that the ratio of the leakage currents for these supercapacitors 4008, 4010 will remain within the above range for all temperatures in the range from -40° C. to 80° C. This matching can provide a module in which the leakage currents of the supercapacitors are approximately equal regardless of temperature changes. In other words, this can automatically control the respective voltages across each supercapacitor so that no overvoltage occurs. FIG. 5 can also show that another module can be formed using supercapacitors 4004, 4006. It should be understood that this hypothetical example is applicable to the formation of modules having more than just supercapacitors.

[0067] In some embodiments, the relationship between capacitor parameters (e.g., leakage current) and test conditions (e.g., temperature) is used to match supercapacitors. For example, in some embodiments, supercapacitors may be matched based on measured values obtained under various test conditions. For example, the leakage current of a second supercapacitor may be tested at a temperature different from that of a first supercapacitor that is tested under a first test condition. The known relationship between the capacitor parameter and temperature can be used to estimate a second parameter value for the second supercapacitor at approximately the first test condition so that the second supercapacitor can be matched to the first supercapacitor based on the available data.

[0068] For example, referring to FIG. 5, the leakage current of supercapacitor 4008 is known to be 80° C., and the leakage current of supercapacitor 4010 may be known at 25° C. Using the relationship between the leakage current and temperature shown in FIG. 5, the leakage current for supercapacitor 4008 can be estimated at 25° C. This estimated value can then be used to determine whether the second supercapacitor is a suitable match for the first supercapacitor.

[0069] Similarly, in some embodiments, the relationship between different capacitor parameters can be determined so that supercapacitors can be matched based on capacitor parameter values for different capacitor parameters. For example, leakage current may be correlated empirically or theoretically to equivalent series resistance. This correlation can be used to match a first supercapacitor with a known leakage current under a first condition to a second supercapacitor with a known ESR under a second condition.

[0070] In some embodiments, the supercapacitors may be matched using two or more capacitor parameters using statistical analysis and / or machine learning. For example, referring to FIG. 6, in one embodiment, data regarding a plurality of supercapacitors, any suitable clustering algorithm, or machine learning model may be used to locate groups of supercapacitors having similar capacitor parameters. For example, in FIG. 6, "capacitor parameter 1" may be capacitance measured under a first test condition, and "capacitor parameter 2" may be leakage current measured under approximately the first test condition. The algorithm may be able to group the supercapacitors into several groups including similar supercapacitors. Although illustrated with respect to two capacitor parameters, in some embodiments, the clustering algorithm may be configured to create clusters of supercapacitors based on three or more capacitor parameters. Examples of inputs regarding the clustering algorithm include ratios of capacitor parameter values discussed herein, the desired number of supercapacitors per module, and the desired overall properties of the module (e.g., total capacitance, ESR, and DCL).

[0071] As described above, in some embodiments, a machine learning model may be used to match supercapacitors. For example, the model may be trained using the exemplary data shown in FIG. 6 and configured to predict and optimize each voltage obtained across the individual supercapacitors of the theoretical module. For example, a training set of data may be created by monitoring each voltage across the individual supercapacitors in various modules of different sizes, capacitances, etc. These monitored voltages, combined with known capacitor parameter values for each supercapacitor within the module, may be used as a training data set to minimize voltage differences and / or overvoltages when clustering or grouping supercapacitors based on the capacitor parameter values, such that a machine learning model may be configured.

[0072] The present invention will be better understood by reference to the following examples. Test Method In the following sections, an exemplary method is provided for testing supercapacitors such that various capacitor parameters are determined. However, the capacitor parameters may be tested using any suitable method. Further, some capacitor parameters may change from when the supercapacitor is first formed. Thus, the capacitor parameters may be measured after an initial test time. For example, in some embodiments, the test may be performed after an initial test period of 20 to 150 hours, in some embodiments 40 to 130 hours, in some embodiments 50 to 110 hours, such as 72 hours.

[0073] Furthermore, the test may be performed at various temperature and relative humidity levels. For example, the temperature may be room temperature (about 23° C.), 25° C., 85° C., or 105° C., and the relative humidity may be 25% or 85%.

[0074] I. Direct Current Leakage (DCL) DC current leakage may be measured across the resistor using a Keithley 2400, 2602, or 3330 precision LCZ meter. The DC current leakage of the supercapacitor is measured by charging the supercapacitor to 5 volts for 72 hours at 25 °C and 25% humidity. Next, the supercapacitor may be connected in series to a resistor with a known resistance of 1000 ohms. The current flowing from the supercapacitor through the resistor may be stabilized for 10 minutes, and then the voltage across the resistor may be measured. Then, using Ohm's law, the DCL may be calculated as the value obtained by dividing the voltage across the resistor by the known resistance of the resistor.

[0075] II. Equivalent Series Resistance (ESR) The equivalent series resistance (ESR AC ) with respect to alternating current may be measured using a Keithley 2400, 2602, or 3330 precision LCZ meter with a DC bias of 0.0 volts, 1.1 volts, or 2.1 volts (sinusoidal signal between 0.5 volts peak). The operating frequency is 1 kHz.

[0076] The equivalent series resistance (ESR DC ) with respect to direct current may be measured by periodically charging and discharging the supercapacitor with a constant current between (1) the rated voltage of the supercapacitor and (2) half of the rated voltage of the supercapacitor. The equivalent series resistance value may be calculated for each of these charge and discharge steps based on the respective current flow and voltage associated with each step. Then the ESR DC value may be calculated by averaging the resistance values calculated in the previous steps.

[0077] III. Capacitance The capacitance of the supercapacitor may be measured using a Keithley 2400, 2602, or 3330 precision LCZ meter with a DC bias of 0.0 volts, 1.1 volts, or 2.1 volts (sinusoidal wave signal between 0.5 volts peak). The operating frequency is 120 Hz. The temperature is room temperature (about 23 °C), and the relative humidity is 25%.

[0078] Alternatively, the supercapacitor may be charged to the rated voltage of the supercapacitor at a known temperature and humidity using a power supply. For example, the supercapacitor may be charged to the rated voltage at room temperature and 25% relative humidity. The supercapacitor may then be removed from the power supply and discharged at a constant current while measuring the time required to discharge the supercapacitor from a first voltage to a second voltage. The capacitance may then be calculated based on the first voltage, the second voltage, and the elapsed time.

[0079] Examples The ability to form a matched supercapacitor module that operates in a satisfactory state without using a balancing circuit was demonstrated. Pairs of supercapacitors were matched based on similar DCL values and connected in series to form a module.

[0080] The resulting module had a rated voltage of 5.0 volts, a rated capacitance of 5 F at room temperature, and a rated ESR of AC 65 milliohms at 1000 hz and 10 mV (0.0 DC bias voltage). The module was tested at 100%, 90%, 80%, and 70% of the rated voltage of the module corresponding to 5.0 volts, 4.5 volts, 4.0 volts, and 3.5 volts, respectively. The tests were performed at an operating temperature of 85 °C. Each group of modules was cycled between the respective test voltage and half of the respective test voltage at a constant current at 85 °C as described above.

[0081] Satisfactory operating limits were defined with respect to both capacitance and ESR. Specifically, the satisfactory operating limits required that (1) the capacitance remain at 70% or more of the rated capacitance at 85°C and (2) the ESR remain at 300% or less of the rated ESR at 85°C.

[0082] The test results showed that the module remained within the above operating limits for over 3,000 hours at 4 volts and for over 4,000 hours at 3.5 volts without using any balancing circuit in a satisfactory state.

[0083] Figures 7a and 7b show that the module tested at 4 volts and 85°C satisfied the operating limits for over 3,000 hours without using a balancing circuit. Specifically, referring to Figure 7a, the average capacitance of the module remained above 70% of the rated capacitance (CAP SPEC ) for over 3,000 hours. However, at about 3,500 hours, the capacitance dropped below the 70% threshold. Referring to Figure 7b, the average ESR of the module remained well below 300% of the rated ESR (ESR0) throughout the test period.

[0084] Figures 8a and 8b show that the module tested at 3.5 volts and 85°C was within the satisfactory operating limits for 4,000 hours without using a balancing circuit. In particular, referring to Figure 8a, the average capacitance of the module remained higher than 70% of the rated capacitance for 4,000 hours. Further referring to Figure 8b, the average ESR of the module remained well below 300% of the rated ESR for 4,000 hours.

[0085] These and other modifications and variations of the present invention can be implemented by those skilled in the art without departing from the spirit and scope of the present invention. Furthermore, it should be understood that aspects of various embodiments may be exchanged both wholly and partially. Additionally, those skilled in the art will understand that the foregoing description is merely an example and does not limit the present invention as further described in such appended claims.

Claims

1. a first supercapacitor having a first parameter value for a capacitor parameter at a first test condition; a second supercapacitor having a second parameter value for the capacitor parameter at approximately the first test condition; and wherein the ratio of the second parameter value to the first parameter value is from about 0.8 to about 1.

2. Supercapacitor module.

2. 10. The supercapacitor module of claim 1, wherein the ratio of the second parameter value to the first parameter value is from about 0.85 to about 1.

15.

3. 10. The supercapacitor module of claim 1, wherein the ratio of the second parameter value to the first parameter value is from about 0.9 to about 1.

1.

4. The supercapacitor module of claim 1 , wherein the supercapacitor module does not include a voltage balancing circuit.

5. The supercapacitor module of claim 1 , wherein the capacitor parameter is leakage current.

6. 6. The supercapacitor module of claim 5, wherein the leakage current is greater than about 23.75 microamps and less than about 26.25 microamps at an applied DC voltage of about 5 volts and a temperature of about 25°C.

7. The supercapacitor module of claim 1 , wherein the capacitor parameter is an equivalent series resistance.

8. 8. The supercapacitor module of claim 7, wherein the equivalent series resistance is greater than about 61.75 milliohms and less than about 68.25 milliohms at an applied AC voltage of about 10 mV at a frequency of about 1000 Hz and a temperature of about 25° C.

9. The supercapacitor module of claim 1 , wherein the capacitor parameter is capacitance.

10. 10. The supercapacitor module of claim 9, wherein the capacitance is greater than about 4.75F and less than about 5.25F at a temperature of about 25°C.

11. The supercapacitor module of claim 1 , wherein the first test condition comprises a test voltage.

12. The supercapacitor module of claim 1 , wherein the first test conditions include a test temperature.

13. The supercapacitor module of claim 1 , wherein the first supercapacitor is connected in series with the second supercapacitor.

14. the first supercapacitor having a third parameter value for a second capacitor parameter at a second test condition; the second supercapacitor having a fourth parameter approximately related to the second capacitor parameter at the second test condition; a second ratio of the fourth parameter value to the third parameter value is from about 0.8 to about 1.2; The supercapacitor module of claim 1 .

15. 1. A method for manufacturing a supercapacitor module from a first supercapacitor having a first parameter value for a capacitor parameter at a first test condition and a second supercapacitor, the method comprising: selecting the second supercapacitor based on the second capacitor having a second parameter value for the capacitor parameter at about the first test condition, wherein a ratio of the second parameter value to the first parameter value is from about 0.8 to about 1.

2.

16. The method of claim 15 , wherein the capacitor parameter is leakage current.

17. The method of claim 15 , wherein the capacitor parameter is an equivalent series resistance.

18. The method of claim 15 , wherein the capacitor parameter is a capacitance.

19. 16. The method of claim 15, further comprising enclosing the first and second supercapacitors in a housing without a balancing circuit.

20. 16. The method of claim 15, wherein the voltage across the first capacitor is not regulated using a balancing circuit.

21. 16. The method of claim 15, further comprising connecting the first supercapacitor in series with the second supercapacitor without a balancing circuit.

22. 16. The method of claim 15, wherein the second ratio of the second parameter value to the first parameter value is from about 0.9 to about 1.

1.

23. 16. The method of claim 15, wherein the second ratio of the second parameter value to the first parameter value is from about 0.95 to about 1.

05.

24. the first supercapacitor having a third parameter value for a second capacitor parameter at a second test condition; the second supercapacitor having a fourth parameter value for the second capacitor parameter at about the second test condition; selecting the second supercapacitor is further based on a second ratio of the fourth parameter value to the third parameter value being from about 0.8 to about 1.2; The method of claim 15.

Images