GB2606707A

GB2606707A - Supercapacitor and electrical system

Info

Publication number: GB2606707A
Application number: GB2106315.1A
Authority: GB
Inventors: Jamieson Luke
Original assignee: Individual
Current assignee: Individual
Priority date: 2021-05-03
Filing date: 2021-05-03
Publication date: 2022-11-23
Anticipated expiration: 2041-05-03
Also published as: WO2022233894A1; GB202106315D0; GB2606707B

Abstract

A supercapacitor 200 comprising an anodic structure 210 and a cathodic structure 220. The anodic structure is provided with a first current collector 212 and a second current collector 213, and the cathodic structure is provided with a third current collector 222 and a fourth current collector 223.A sum of an equivalent series resistance of the anodic structure and an equivalent series resistance of the cathodic structure may be equal to or less than 2x10-3Ω. The anodic and cathodic structures may each comprise a material having a relatively low effective electrical conductivity. The anodic structure may comprise first and second anodes and the cathodic structure may comprise first and second cathodes where the first and second anodes/cathodes are separated by an inter-anode/cathode separator and connected by an inter-anode/cathode conductor which may have a permeable structure, a lattice structure and comprise a material with a relatively high effective electrical conductivity. An electrical system comprising said superconductor wherein, respectively, a fluctuating/unfluctuating electrical load and supply source is connected across the first & third/second & fourth current collectors.

Description

SUPERCAPACITOR AND ELECTRICAL SYSTEM

FIELD OF THE INVENTION

The present invention relates to a system and a method for power and energy handling in electrical systems, particularly although not exclusively relating to the 5 smoothing of a power output from an electrical motor-generator and subsequent storage of energy received therefrom.

BACKGROUND OF THE INVENTION

During an operation of a conventional heat engine, heat energy is converted to kinetic energy of a piston during a power-stroke, and kinetic energy of a piston is converted to heat energy during a compression-stroke. Kinetic energy is transferred from the piston and stored in a mechanical flywheel during the power-stroke, and kinetic energy is removed from the flywheel and transferred to the piston during the compression-stroke of the engine. As such, the mechanical flywheel functions to smooth a power output of the heat engine over a cycle of the heat engine.

Use of a mechanical flywheel requires that energy be stored in form of rotational kinetic energy. As a result, a mechanical flywheel which contains stored energy must have an angular speed. For optimum power smoothing, the angular speed of a mechanical flywheel should not very significantly throughout the cycle of the heat engine. For this reason, mechanical flywheels are typically designed to have a large mechanical inertia. Mechanical flywheels represent very efficient energy storage devices, since the only energy losses associated with use are frictional losses in any bearings and any damping due to air resistance or otherwise.

For the same reason, a linear motion of the piston connected to the flywheel through a crankshaft must have a relatively smooth geometric function with respect to time. This geometric function is often sinusoidal or near-sinusoidal. However, a sinusoidal piston motion in heat engines has been associated with efficiency losses. As a result, it is now well-known in the art to use an electrical actuator and/or an electrical alternator to transfer energy to and from a piston during the cycle of the heat engine.

This enables better control over piston motion during the cycle of the heat engine and allows the linear motion of the piston to have a non-smooth function with respect to time. This has been associated with thermal efficiency improvements.

In use, kinetic energy of the piston is converted to electrical energy by the electrical alternator during the power-stroke of the engine. Electrical energy is converted to kinetic energy of the piston during the compression-stroke of the engine. Accordingly, the electrical alternator provides a large amount of electrical energy during the power-stroke of the engine and the electrical actuator requires a large (albeit lesser) amount of electrical energy during the compression-stroke of the engine. An electrical energy storage device capable of providing and receiving electrical power to the electrical actuator and electrical alternator is therefore required. In this respect, the electrical energy storage device would function as the electrical equivalent of a mechanical flywheel.

The pre-eminent electrical energy storage device technology at present is the cell-battery. Use of a battery to serve the above function may therefore be considered. In order to fulfil this function, the battery would necessarily have to be repeatedly charged and discharged at high currents. However, repeatedly charging and discharging a battery at high currents (that is, high C-rates) is disadvantageous, since it leads to high battery degradation through, for example, lithium plating in the electrodes of the battery. In additional, charging and discharging at high currents causes a great deal of heat to be dissipated within the battery, which incurs large useful energy losses and therefore reduces an energy efficiency of the system. To overcome this issue, the size of a battery-pack connected to a motor-generator assembly in this way must be very large. This has other associated disadvantages, namely the requirement to use large amounts of raw material to produce such large battery-packs, as well as increased weight and size of the entire assembly.

An object of the present invention is therefore to provide the electrical equivalent of a 30 mechanical flywheel which would serve to smooth a power output of a motor-generator without being subject to high levels of degradation, having burdensome sizing requirements or incurring large useful energy losses in use.

STATEMENTS OF INVENTION

According to a first aspect there is provided a supercapacitor comprising an anodic structure and a cathodic structure. The anodic structure is provided with a first current collector and a second current collector, and the cathodic structure is provided with a third current collector and a fourth current collector.

It may be that a sum of an equivalent series resistance of the anodic structure and an equivalent series resistance of the cathodic structure is equal to or less than 2x10-3 0. The anodic structure and the cathodic structure may comprise a material having a relatively low effective electrical conductivity, preferably a material having an effective electrical conductivity equal to or less than 1x105 S It may be that the anodic structure comprises a first anode and second anode, while the cathodic structure comprises a first cathode and a second cathode. The first anode may be electrically connected to the second anode by an inter-anode current conductor, and the first cathode may be electrically connected to the second cathode by an inter-cathode current conductor.

The inter-anode current conductor and/or the inter-cathode current conductor may have a permeable structure. Additionally or alternatively, the inter-anode current conductor and/or the inter-cathode current conductor may have a lattice structure. Further, the inter-anode current conductor and the inter-cathode current conductor may comprise a material having a relatively high effective electrical conductivity. Preferably, the inter-anode current conductor and the inter-cathode current conductor may comprise a material having an effective electrical conductivity equal to or greater than 1x105S m-1.

It may be that the first anode is separated from the second anode by an inter-anode separator, and the first cathode is separated from the second cathode by an inter-30 cathode separator.

According to a second aspect there is provided an electrical system comprising a supercapacitor in accordance with the first aspect. The electrical system further comprises a fluctuating electrical load and supply source connected across the first current collector and the third current collector, as well as an unfluctuating electrical load and supply source connected across the second current collector and the fourth current collector.

The unfluctuating electrical load and supply source may comprise an electrical energy storage device. The electrical energy storage device may comprise a battery.

It may be that the fluctuating electrical load and supply source comprises a motor-generator. The motor-generator may comprise a closed-cycle heat engine.

Additionally or alternatively, the motor-generator may comprise an open-cycle heat engine.

According to a third aspect there is provided a method for smoothing a power output of a fluctuating electrical load and supply source using an electrical system. The electrical system comprises a supercapacitor in accordance with the first aspect. The method comprises: connecting the power output of the fluctuating electrical load and supply source across the first current collector and the third current collector of the supercapacitor; and receiving a smoothed power output of the fluctuating electrical load and supply source across the second current collector and the fourth current collector of the supercapacitor.

INTRODUCTION TO THE DRAWINGS

FIG. 1 shows a cross-sectional view of an example supercapacitor as known from

the prior art.

FIG. 2 shows a cross-sectional view of a first example supercapacitor according to the invention.

FIG. 3 shows a cross-sectional view of a second example supercapacitor according to the invention.

FIG. 4 shows a first example electrical system according to the invention.

FIG. 5 shows a second example electrical system according to the invention.

FIG. 6 shows a method for smoothing a power output of a fluctuating electrical load and supply source according to the invention.

DETAILED DESCRIPTION

I. General description of electrical conduction in solid media Electrical conduction in solid media is widely held in the art as being governed by Ohm's law. Kirchhoff's formulation of Ohm's law is idr = GE (la) where is an electrical drift current density, a is an effective electrical conductivity and E is an electric field strength. In addition, an electrical diffusion current density, 'di, may be defined according to Fick's law. This may be stated as di = DI'q (lb) where q is an electric charge density and D is a solid-state diffusivity. Further, Einstein's relationship for charged particles mandates that a kBT D= q e Where Icn is the Boltzmann constant, T is a temperature and e is the elementary charge. A conservation of charge condition requires that Oq where t represents a time. If the effective electrical conductivity can be considered to be a constant, Eq. 2 becomes dq = o-(V * E) + V * (DVq) (3) A reasonable assumption provides that E = Vq, where yo is a solid phase electrical potential. This permits Eq. 3 to be expressed as dq -at = 0-(v * vf,o) + VD * Vq + D(V * Vq) = a Vq) + VDVq + DV2q (4a) In one dimension, this can be written as dq d2y9 OD dq 02.7 -= -+ + D (4b) Ot dx2 Ox Ox dx2 where x is a spatial coordinate. By inspection, it may be seen that where and when dq/dt is non-zero, then if o-is very large, 0246i/0x2 is very small. This is the case for most electrical conductors, such as copper for example, which has an effective electrical conductivity of approximately 6x107S m-1. Most common conductors have electrical conductivities of a similar order of magnitude. (1c)

= V * (idr + idi) = V * (o-E) + V * (DVq) at (2) In practice, this means that an electrical potential gradient will not develop in a solid medium, except when dq/dt is very large. An example of when this is not the case is when an inductor is driven with a high-frequency alternating current. Under these circumstances, dig/at becomes large, and a local electric potential gradient develops inside the inductor, forming an equivalent of a small capacitor between respective loops of the inductor. The inductor then begins to behave as if it were both an inductor and a small capacitor connected in parallel.

However, where the effective electrical conductivity of a solid medium is not large, then ä2w/äx2 is not small under ordinary conditions. Therefore, a solid medium with a relatively small effective conductivity will exhibit significant electric potential gradients therein when an electric current is passed therethrough. However, such a solid medium will also exhibit significant heat dissipation when an electrical current is passed therethrough, which represents a significant conduction efficiency reduction.

Description of a supercapacitor as known from the prior art Supercapacitors, also known as ultracapacitors or electric-double layer capacitors (EDLCs), are electrical energy storage devices known for typically having a relatively high power density and for being capable of "fast-charging". However, a variety of factors such as low typical energy density and the exhibition of self-discharge effects have hindered widespread adoption of supercapacitors for the purpose of energy storage, especially following recent advances in cell-battery technology.

Supercapacitors store energy in an electric field formed at the interface of a solid electrode and an electrolyte. In contrast, batteries store energy in the form of chemical potential achieved after chemical reactions occur in the presence of a driving electric field. Chemical reactions play no role in an energy storage process of a supercapacitor, and any chemical reactions which are present are generally considered to be undesirable. However, relying on electric fields for energy storage rather than chemical potential means that supercapacitors are not prone to high levels of degradation in use, in contrast to batteries.

FIG. 1 shows a cross-sectional view of an example supercapacitor 100 as known from the prior art. The supercapacitor 100 comprises an anodic structure 110, a cathodic structure 120 and a separator 130. The anodic structure 110 and the cathodic structure 120 together form a pair of electrodes. The anodic structure 110, the cathodic structure 120 and the separator 130 are immersed in an electrolyte.

The anodic structure is provided with a first current collector 112. The anodic structure comprises an anode 114, wherein the anode comprises a plurality of pores 116 such that the anode has a substantially porous structure. A geometry of the anode 114 defines an interfacial area between the anode 114 and the electrolyte.

The porous structure of the anode 114 provides an enlarged interfacial area between the anode 114 and the electrolyte.

The cathodic structure is provided with a second current collector 122. The cathodic structure comprises a cathode 124, wherein the cathode comprises a plurality of pores 126 such that the cathode has a substantially porous structure. A geometry of the cathode 124 defines an interfacial area between the cathode 124 and the electrolyte. The porous structure of the cathode 124 provides an enlarged interfacial area between the cathode 124 and the electrolyte.

The anodic structure 110 and the cathodic structure 120 are immersed in an ion-containing liquid, also known as an electrolyte. The electrolyte comprises a plurality of anions and a plurality of cations in solution (not shown). Each anion and each cation may pass freely across the separator 130 but may not pass from the electrolyte into either the anode 114 or the cathode 124. The porous structure of the anode 114 and the cathode 124 provides a large interfacial surface area between the anode 114 and the electrolyte and the cathode 124 and the electrolyte.

In use, during a charging process, a positive conventional electric current comprising a flow of holes is provided to the anode 114 through the first current collector 112 The holes are transported across the anode 114 from the current collector 112 toward the separator 130. A negative conventional electric current comprising a flow of electrons is provided to the cathode 124 through the second current collector 122.

The electrons are transported across the cathode 124 from the current collector 122 toward the separator 130 Over time, the anode becomes relatively positively charged and the cathode becomes relatively negatively charged. As a result, anions are drawn toward the holes in the anode due to electrostatic attraction. Energy is stored in the electric field formed between the anions and the holes at the interface between the anode and the electrolyte. At the same time, cations are drawn toward electrons in the cathode due to electrostatic attraction. Energy is stored in the electric field formed between the cations and the electrons at the interface between the cathode and the electrolyte.

The transportation of charge carriers (that is, holes and electrons) in a solid conductor, such as the anodic structure and the cathodic structure, is governed by the set of principles of electrical conduction in solid media described in the previous section. Accordingly, a speed at which holes are transported across the anode from the current collector 112 toward the separator 130 is dictated by an effective conductivity of the anode 114. Likewise, a speed at which electrons are transported across the cathode from the current collector 122 toward the separator 130 is dictated by an effective conductivity of the cathode 124.

Many commercially available supercapacitors comprise electrodes (that is, anodic structures and cathodic structures) having an effective electrical conductivity of around 5x10-2 S m1 to 5 S m-1. This represents an eight-to ten-order of magnitude difference between such a medium and a copper medium, for example. As a result, the speed at which holes are transported across the anode 114 from the current collector 112 toward the separator 130 and the speed at which electrons are transported across the cathode 124 from the current collector 122 toward the separator 130 is much lower than it would be if the pair of electrodes were comprised of a non-porous copper structure.

In such a case, because the speed at which holes and electrons are transported across the anode and cathode respectively is limited by the low effective electrical conductivity of the pair of electrodes, an electric potential at a point within the anode 114 near the separator 130 does not immediately rise to correspond with a rise in an electric potential at a point within the anode 114 near the current collector 112 in response to a positive conventional electric current being provided to the anode 114 via the current collector 112. Likewise, an electric potential at a point within the cathode 124 near the separator 130 does not immediately fall to correspond with a fall in an electric potential at a point within the cathode 124 near the current collector 122 in response to a negative conventional electric current being provided to the cathode 124 via the current collector 122.

For the same reason, the point within the anode 114 near the separator 130 does not experience a local electric current density until enough time has passed for holes to be transported across the anode 114 from the point within the anode 114 near the current collector 112. In the same way, the point within the cathode 124 near the separator 130 does not experience a local electric current density until enough time has passed for electrons to be transported across the cathode 124 from the point within the cathode 124 near the current collector 122.

Description of a supercapacitor according to the invention FIG. 2 shows a cross-sectional view of a first example supercapacitor 200 according to the invention. The supercapacitor 200 comprises an anodic structure 210, a cathodic structure 220 and a separator 230. The anodic structure 210 and the cathodic structure 220 together form a pair of electrodes. The anodic structure 210, the cathodic structure 220 and the separator 230 are immersed in an electrolyte.

The anodic structure 210 is provided with a first current collector 212 and a second current collector 213. The anodic structure comprises an anode 214, which provides a convoluted electrical conduction pathway between the first current collector 212 and the second current collector 213. A geometry of the anode 214 defines an interfacial area between the anode 214 and the electrolyte. The anode may comprise a plurality of pores such that the anode has a substantially porous structure. The anodic structure 210 has a distance between the first current collector 212 and the second current collector 213 and a projected area between the first current collector 212 and the second current collector 213.

The cathodic structure 220 is provided with a third current collector 222 and a fourth current collector 223. The cathodic structure comprises a cathode 224, which provides a convoluted electrical conduction pathway between the third current collector 222 and the fourth current collector 224. A geometry of the cathode 224 defines an interfacial area between the cathode 224 and the electrolyte. The cathode may comprise a plurality of pores such that the cathode has a substantially porous structure. The cathodic structure 220 has a distance between the third current collector 222 and the fourth current collector 223 and a projected area between the third current collector 222 and the fourth current collector 223.

In use, when an electrical current is applied to either the first current collector 212 or the second current collector 213, energy is stored in an electric field formed between anions and holes at the interface between the anode 214 and the electrolyte. At the same time, energy is transmitted through the anode 214 in the form of the electrical current flowing between respective current collectors. Similarly, when an electrical current is applied to either the third current collector 222 or the fourth current collector 223, energy is stored in an electric field formed between cations and electrons at the interface between the cathode 224 and the electrolyte. At the same time, energy is transmitted through the cathode 224 in the form of the electrical current flowing between respective current collectors.

As such, the supercapacitor 200 functions as both an electrical energy storage device and an electrical energy transmission device. As detailed in the following description, the supercapacitor 200 functions an electrical equivalent of a mechanical flywheel in that it serves to smooth a substantially variable power demand and supply profile provided to a current collector of each of the anodic structure 210 and the cathodic structure 220.

As previously described, if an effective electrical conductivity of the anode 214 and cathode 224 is relatively low, a speed at which holes and electrons are transported across the anode and cathode respectively is limited. As a result, an electric potential at a point within the anode 214 near the second current collector 213 does not immediately rise to correspond with a rise in an electric potential at a point within the anode 214 near the first current collector 212 in response to a positive conventional electric current being provided to the anode 214 via the first current collector 212. Likewise, an electric potential at a point within the cathode 224 near the fourth current collector 223 does not immediately fall to correspond with a fall in an electric potential at a point within the cathode 224 near the third current collector 222 in response to a negative conventional electric current being provided to the cathode 224 via the third current collector 222.

For the same reason, the point within the anode 214 near the second current collector 213 does not experience a local electric current density until enough time has passed for holes to be transported across the anode 214 from the point within the anode 114 near the first current collector 212. In the same way, the point within the cathode 224 near the fourth current collector 223 does not experience a local electric current density until enough time has passed for electrons to be transported across the cathode 224 from the point within the cathode 224 near the third current collector 222.

It follows that when a large positive conventional current is applied to the first current collector 212, an appreciable period of time must elapse before holes are transported across the anode 214 and a large positive conventional current is observed at the second current collector 213. Likewise, when a large negative conventional current is applied to the third current collector 222, an appreciable period of time must elapse before electrons are transported across the cathode 224 and a large negative current is observed at the fourth current collector 223.

In an example scenario, a very large positive conventional current and a large negative conventional current are alternately applied to the first current collector 212. The very large positive conventional current is applied to the first current collector 212 for a first period of time, before the large negative conventional current is applied to the first current collector 212 for a second period of time. Simultaneously, a very large negative conventional current and a large positive conventional current are alternately applied to the third current collector 222. The very large negative conventional current is applied to the third current collector 222 for the first period of time, before the large positive conventional current is applied to the third current collector 222 for the second period of time. This process is then cyclically repeated for a number of cycles. This corresponds to a substantially variable power demand and supply profile provided to the supercapacitor 200 via a current collector of each of the anodic structure 210 and the cathodic structure 220.

If the first period of time and the second period of time are sufficiently short, the supercapacitor 200 will reach a steady state after a sufficient number of cycles in which a small positive conventional current is received from the second current collector 213 and a small negative conventional current is received from the fourth current collector 223.

Since the first period of time is sufficiently short, there is insufficient time for a flow of holes corresponding to the very large positive conventional current to be transported from the first current collector 212 to the second current collector 213. Likewise, because the second period of time is sufficiently short, there is insufficient time for a flow of electrons corresponding to the large negative conventional current to be transported from the first current collector 212 to the second current collector 213.

Nevertheless, conservation of charge requires that in the steady state, a flow of charge into the anode 214 must equal a flow of charge out of the anode 214. Accordingly, the small positive conventional current received from the second current collector 213 corresponds to a time average of the current applied to the first current collector 212, after a throughput energy loss associated with electrical conduction through the anode 214 is accounted for.

The same reasoning applies, mutatis mutandis, to a process undergone in the cathodic structure 220 between the third current collector 222 and the fourth current collector 223 through the cathode 224. The small negative conventional current received from the fourth current collector 223 corresponds to a time average of the current applied to the third current collector 222, after a throughput energy loss associated with electrical conduction through the cathode 224 is accounted for.

Accordingly, the supercapacitor 200 smooths a substantially variable power demand and supply profile provided to a current collector of each of the anodic structure 210 and the cathodic structure 220 to provide a substantially invariable power demand and supply profile received from another current collector of each of the anodic structure 210 and the cathodic structure 220.

The throughput energy loss associated with the anode 224 and the throughput energy loss associated with the cathode 224 may be analysed by considering a throughput energy efficiency of the supercapacitor. The throughput energy efficiency of the supercapacitor is related to a combined equivalent series resistance (ESR) of supercapacitor. The combined ESR of the supercapacitor, REs, is simply a sum of an equivalent series resistance of the anodic structure, Ran, and an equivalent series resistance of the cathodic structure, R"th. That is RES = Ran ± Reath (5) The anodic structure and the cathodic structure comprise may materials with an effective electrical resistivity denoted by pa, and pcath respectively, which is defined as the mathematical reciprocal of an effective electrical conductivity thereof, the equivalent series resistance of the anodic structure and cathodic structure may be calculated using Pouillet's law, as given in Eqs. 6a and 6b Ian lcath Ran -Pan(6a) n (6a) Reath Pcath A ca (6b) th where /a, is the distance between the first current collector and the second current collector, Icath is the distance between the third current collector and the fourth current collector, Aan is the projected area between the first current collector and the second current collector and Achth is the projected area between the third current collector and the fourth current collector.

The throughput energy efficiency, q, of the supercapacitor 200 may be calculated using Eq. 7a Pout Pin -Pdiss Pdiss

-D

=1 (7a) in Pin Pin where Pin is a net average electrical power supplied to the supercapacitor, R"t is a net average electrical power delivered by the supercapacitor and Pai" is a power dissipated as heat in the supercapacitor. Making use of Ohm's law and the definition of electric power, the above reduces to 12 RES 1 RES = 1 - =1 iv where / is an electric current passed through the supercapacitor in use and V is an electric potential difference across the supercapacitor. Further, by rearrangement V V2 REs = -1(1 -n) = n(1 - (8a) r tit and RES' -Pa Pcath A n nan cath n = (in)-0, (1 -11) (8b) Ian icath V2

-A

Conventional supercapacitors have a maximum voltage requirement known as a breakdown voltage. A breakdown voltage in the region of 2.5 V between respective electrodes (that is, between the anodic structure and the cathodic structure) is common among commercially available supercapacitors. Hence a reasonable assumption would be to choose an operating voltage of approximately 2 V between respective electrodes. In addition, a minimum efficiency requirement may be chosen. A figure of merit for the throughput energy efficiency of the supercapacitor may be, for example, 95%. This may be chosen as the minimum efficiency requirement. Finally, if the average power supplied to the supercapacitor is chosen, the maximum combined ESR may be defined. The maximum average power supplied to the supercapacitor should ideally be high, since a low maximum average power supplied to the supercapacitor would require many supercapacitors to smooth a power output from a fluctuating load and supply source having a reasonably high average power output. The maximum average power supplied to the supercapacitor may be, for example, 100W. In such a case, Eq. 8b becomes n 1-A" n 5 -(1-0.95) <2 x io-3 (8c) cath (-4 S' RE 5 Pa -Pcath-Alcath Ian, which provides an upper bound for the combined ESR of the supercapacitor if the figure of merit for the throughput energy efficiency of the supercapacitor is to be 20 achieved.

This also provides a criterion for a geometrical construction of the anodic structure 210 and the cathodic structure 220 so as to constrain a combined equivalent series resistance of the supercapacitor 200 and thereby limit throughput energy losses in use thereof. (7b)

FIG. 3 shows a cross-sectional view of a second example supercapacitor 300 according to the invention. The supercapacitor 300 comprises an anodic structure 310, a cathodic structure 320 and an inter-electrode separator 330. The anodic structure 310 and the cathodic structure 320 together form a pair of electrodes. The anodic structure 310, the cathodic structure 320 and the inter-electrode separator 330 are immersed in an electrolyte.

The anodic structure 310 is provided with a first current collector 312, a second current collector 313 and an inter-anode current conductor 311. The anodic structure 310 comprises a first anode 314, which provides a convoluted electrical conduction pathway between the first current collector 312 and the inter-anode current conductor 311. The anodic structure further comprises a second anode 315, which provides a convoluted electrical conduction pathway between the inter-anode current conductor 311 and the second current collector 313.

A geometry of the first anode 314 defines an interfacial area between the first anode 314 and the electrolyte. The first anode 314 may comprise a plurality of pores such that the first anode 314 has a substantially porous structure. A geometry of the second anode 315 defines an interfacial area between the second anode 315 and the electrolyte. The second anode 315 may comprise a plurality of pores such that the second anode 315 has a substantially porous structure.

The cathodic structure 320 is provided with a third current collector 322, a fourth current collector 323 and an inter-cathode current conductor 321. The cathodic structure 320 comprises a first cathode 324, which provides a convoluted electrical conduction pathway between the third current collector 322 and the inter-cathode current conductor 321. The cathodic structure 320 further comprises a second cathode 325, which provides a convoluted electrical conduction pathway between the inter-cathode current conductor 321 and the fourth current collector 323.

A geometry of the first cathode 324 defines an interfacial area between the first cathode 324 and the electrolyte. The first cathode 324 may comprise a plurality of pores such that the first cathode 324 has a substantially porous structure. A geometry of the second cathode 325 defines an interfacial area between the second cathode 325 and the electrolyte. The second cathode 325 may comprise a plurality of pores such that the second cathode 325 has a substantially porous structure.

The anodic structure 310 has a distance between the first current collector 312 and the second current collector 313, which is a mathematical sum of: a distance between the first current collector 312 and the inter-anode current conductor 311; and a distance between the inter-anode current conductor 311 and the second current collector 313. The anodic structure 310 also has a projected area between the first current collector 312 and the second current collector 313, which is the lesser of: a projected area between the first current collector 312 and the inter-anode current conductor 311; and a distance between the inter-anode current conductor 311 and the second current collector 313.

The cathodic structure 320 has a distance between the third current collector 322 and the fourth current collector 323, which is a mathematical sum of: a distance between the third current collector 322 and the inter-cathode current conductor 321; and a distance between the inter-cathode current conductor 321 and the fourth current collector 323. The cathodic structure 320 also has a projected area between the first current collector 312 and the second current collector 313, which is the lesser of: a projected area between the third current collector 322 and the inter-cathode current conductor 321; and a distance between the inter-cathode current conductor 321 and the fourth current collector 323.

The anodic structure 310 and the cathodic structure 320 may be geometrically constructed in accordance with the criterion described in relation to the previous example so as constrain a combined equivalent series resistance of the supercapacitor 300 and limit throughput energy losses in use thereof.

The electrolyte comprises a plurality of anions and a plurality of cations in solution 30 (not shown). Each anion and each cation may pass freely across the inter-electrode separator 330 but may not pass from the electrolyte into the first anode 314, the second anode 315, the first cathode 324 or the second cathode 325.

In use, during a charging process, a plurality of anions are drawn toward a plurality of holes in the first anode 314 and the second anode 315 due to electrostatic attraction. Energy is stored in the electric field formed between the anions and the holes at the interface between the first anode 314 and the electrolyte and the second anode 315 and the electrolyte. In order for this process to be effective, individual anions must be able to pass across the inter-electrode separator 330 and the inter-anode current conductor 311. For the same reasoning, individual cations must be able to pass across the inter-electrode separator 330 and the inter-cathode current conductor 321. Preferably, both individual anions and individual cations of the electrolyte should be able to pass across the inter-electrode separator 330, the inter-anode current conductor 311 and the inter-cathode current conductor 321.

Accordingly, at least one of the inter-anode current conductor 311 and the inter-cathode current conductor 321 may be permeable to individual ions of the electrolyte. To this end, the inter-anode current conductor 311 and/or the inter- cathode current conductor 321 may have a permeable structure. Additionally or alternatively, at least one of the inter-anode current conductor 311 and the inter-cathode current conductor 321 may have a lattice structure. The lattice structure may be constructed such that the inter-anode current conductor 311 and/or of the inter-cathode current conductor 321 are permeable to individual ions of the electrolyte.

Notwithstanding the permeable or lattice structure of the inter-anode current conductor 311 and/or the inter-cathode current conductor 321, at least one of the inter-anode current conductor 311 and/or the inter-cathode current conductor 321 may comprise a material having a relatively high electrical conductivity. A relatively high electrical conductivity may generally be considered to be an electrical conductivity equal to or greater than 1x105S m-1. An equivalent series resistance of the anodic structure and cathodic structure may therefore be reduced compared to an example in which at least one of the inter-anode current conductor 311 and/or the inter-cathode current conductor 321 may comprise a material having a relatively low electrical conductivity. In turn, this ensures that an equivalent series resistance of the supercapacitor 300 is sufficiently low so as not to incur significant throughput energy losses in use.

The supercapacitor 300 may further comprise an inter-anode separator 331. The inter-anode separator 331 separates the first anode 314 from the second anode 315. A separation provided by the inter-anode separator 331 ensures that there is no electrical conduction pathway for electrons and/or holes between the first anode 314 and the second anode 315 except through the inter-anode current conductor 311. However, each anion and each cation of the electrolyte may pass freely across the inter-anode current separator 331, such that the inter-anode separator 331 provides an electrical conduction pathway for anions and/or cations of the electrolyte between the first anode 314 and the second anode 315. This may improve an ease at which an electric field is formed between the anions and the holes at an interface between the respective anodes and the electrolyte. In turn, this increases an effectiveness at which the anodic structure 310 can store energy through the formation of the electric field. In turn, this improves an energy storage efficiency of the supercapacitor 300.

The supercapacitor 300 may further comprise an inter-cathode separator 332. The inter-cathode separator 332 separates the first cathode 324 from the second cathode 325. A separation provided by the inter-cathode separator 332 ensures that there is no electrical conduction pathway for electrons and/or holes between the first cathode 324 and the second cathode 325 except through the inter-cathode current conductor 332. However, each anion and each cation of the electrolyte may pass freely across the inter-cathode current separator 332, such that the inter-cathode separator 332 provides an electrical conduction pathway for anions and/or cations of the electrolyte between the first cathode 324 and the second cathode 325. This may improve an ease at which an electric field is formed between the cations and the elections at an interface between the respective cathodes and the electrolyte. In turn, this increases an effectiveness at which the cathodic structure 320 can store energy through the formation of the electric field. In turn, this improves an energy storage efficiency of the supercapacitor 300.

In order to minimise a volume occupied by a supercapacitor, the supercapacitor may be wound in a spiral or formed into another shape during an assembly process. The second example supercapacitor 300 described above may be more suitable to such a process during a later assembly stage than the first example supercapacitor 200 described prior. The second example supercapacitor 300 may then be able to occupy a smaller volume than the first example supercapacitor 200 when fully assembled.

However, the inclusion of the inter-anode current conductor 311 and the inter-cathode current conductor 321 in the second example supercapacitor 300, among other features thereof, may mean that an initial manufacturing process required to produce the second example supercapacitor 300 may be more involved than an initial manufacturing process required to produce the first example supercapacitor 200. As such, the first example supercapacitor 200 may only require a simple 10 manufacturing process in comparison to a manufacturing process required to produce the second example supercapacitor 300.

IV. Description of an electrical system according to the invention FIG. 4 shows a first example electrical system 400 according to the invention. The electrical system 400 comprises a supercapacitor 401 according to a previously described example. The supercapacitor 401 is provided with a first current collector 412, a second current collector 413, a third current collector 422 and a fourth current collector 423. The first current collector 412 and the second current collector 413 are provided to an anodic structure of the supercapacitor 401. The third current collector 422 and the fourth current collector 423 are provided to a cathodic structure of the supercapacitor 401.

A fluctuating electrical load and supply source 440 is connected to a current collector provided to the anodic structure of the supercapacitor and a current collector provided to the cathodic structure of the supercapacitor 401. In the example shown in FIG. 4, the fluctuating electrical load and supply source 440 is connected to the first current collector 412 and the third current collector 422. It will be understood that it that the order of connection may be varied, and that the fluctuating load and supply source 440 may be connected to the first current collector 412 and the fourth current collector 423, the second current collector 413 and the third current collector 422, or the second current collector 413 and the fourth current collector 423.

The fluctuating electrical load and supply source 440 is a device or system which, in use, has a substantially variable power demand and supply profile in time. At a given moment in time, the fluctuating electrical load and supply source 440 may either require an electrical power to be supplied to it (that is, draws an electrical power from the supercapacitor 401) or deliver an electrical power from it (that is, provides an electrical power to the supercapacitor 401). Over a given period of time, an average of the power demand and supply profile thereof with time may render the fluctuating electrical load and supply source 440 to function as a net electrical load source, a net electrical supply source or neither.

An unfluctuating electrical load and supply source 450 is connected to a current collector provided to the anodic structure of the supercapacitor and a current collector provided to the cathodic structure of the supercapacitor 401. In the example shown in FIG. 4, the unfluctuating electrical load and supply source 450 is connected to the second current collector 413 and the fourth current collector 423. It will be understood that it that the order of connection may be varied, and that the unfluctuating electrical load and supply source 450 may be connected to the second current collector 413 and the third current collector 422, the first current collector 412 and the third current collector 422, or the first current collector 412 and the fourth current collector 423.

The unfluctuating electrical load and supply source 450 is a device or system which, in use, has a substantially constant power demand and supply profile in time. Over a given period of time, an average of the power demand and supply profile thereof with time may render the unfluctuating electrical load and supply source 450 to function as a net electrical load source, a net electrical supply source or neither.

In use, if the fluctuating electrical load and supply source 440 is functioning as a net electrical load source, the supercapacitor 401 provides an electrical power to the fluctuating electrical load and supply source 440 when momentarily required and receives an electrical power from the same when momentarily available, all the while drawing a net average electrical power required to operate the fluctuating electrical load and supply source 440 from the unfluctuating electrical load and supply source 450. In this case, the unfluctuating electrical load and supply source 450 functions as a net electrical supply source.

In use, if the fluctuating electrical load and supply source 440 is functioning as a net electrical supply source, the supercapacitor 401 receives an electrical power from the fluctuating electrical load and supply source 440 when momentarily available and provides an electrical power to the same when momentarily required, all the while providing a net average electrical power generated by the fluctuating electrical load and supply source 440 to the unfluctuating electrical load and supply source 450. In this case, the unfluctuating electrical load and supply source 450 functions as a net electrical load source.

Therefore in use the supercapacitor 401 serves as a buffer between the fluctuating electrical load and supply source 440 and the unfluctuating electrical load and supply source 450. Accordingly, the supercapacitor 401 functions as an electrical equivalent of a mechanical flywheel in that it serves to smooth the substantially variable power demand and supply profile of the fluctuating electrical load and supply source 440.

Further, the supercapacitor 401 is able to rapidly and/or cyclically receive an electrical power from the fluctuating electrical load and supply source 440 when momentarily available and provide an electrical power to the same when momentarily required without suffering from high levels of degradation. As a result, the size of the supercapacitor 401 may be relatively small. This brings other advantages, namely a reduction in an amount of raw material required to produce the electrical system 400, as well as a decreased weight and size of the electrical system 400.

FIG. 5 shows a second example electrical system 500 according to the invention. The electrical system 500 comprises a supercapacitor 501 according to a previously described example. The supercapacitor 501 is provided with a first current collector 512, a second current collector 513, a third current collector 522 and a fourth current collector 523. The first current collector 512 and the second current collector 513 are provided to an anodic structure of the supercapacitor 501. The third current collector 522 and the fourth current collector 523 are provided to a cathodic structure of the supercapacitor 501.

A motor-generator 540 is connected to a current collector provided to the anodic structure of the supercapacitor and a current collector provided to the cathodic structure of the supercapacitor 501. In the example shown in FIG. 5, the motor-generator 540 is connected to the first current collector 511 and the third current collector 513. It will be understood that it that the order of connection may be varied, and that the motor-generator may be connected to the first current collector 512 and the fourth current collector 523, the second current collector 513 and the third current collector 522, or the second current collector 513 and the fourth current collector 523.

The motor-generator 540 may be considered to be an example of a fluctuating electrical load and supply source as previously described. At a given moment in time, the motor-generator 540 may either require an electrical power to be supplied to it (that is, draws an electrical power from the supercapacitor 501) or deliver an electrical power from it (that is, provides an electrical power to the supercapacitor 501). Over a given period of time, an average of the power demand and supply profile thereof with time may render the motor-generator 540 to function as a net electrical load source, a net electrical supply source or neither.

An electrical energy storage device 550 is connected to a current collector provided to the anodic structure of the supercapacitor and a current collector provided to the cathodic structure of the supercapacitor 501. The electrical energy storage device 550 may be considered to be an example of an unfluctuating electrical load and supply source as previously described. In the example shown in FIG. 5, the electrical energy storage device 550 is connected to the second current collector 513 and the fourth current collector 523. It will be understood that it that the order of connection may be varied, and that the electrical energy storage device 550 may be connected to the second current collector 513 and the third current collector 522, the first current collector 512 and the third current collector 522, or the first current collector 512 and the fourth current collector 523. Further, in the example shown in FIG. 5, the electrical energy storage device is shown as a battery, although it will be appreciated that an alternative electrical energy storage device may be used.

In use, if the motor-generator 540 is functioning as a net electrical load source, the supercapacitor 501 provides an electrical power to the motor-generator 540 when momentarily required or receives an electrical power from the same when momentarily available, all the while drawing a net average electrical power required to operate the motor-generator 540 from the electrical energy storage device 550. In this case, the electrical energy storage device 550 functions as a net electrical supply source. On the other hand, if the motor-generator 540 is functioning as a net electrical supply source, the supercapacitor 501 receives an electrical power from the motor-generator 540 when momentarily available and provides an electrical power to the same when momentarily required, all the while providing a net average electrical power generated by the motor-generator 540 to the electrical energy storage device 550. In this case, the electrical energy storage device 550 functions as a net electrical load source.

In general, batteries have a relatively high energy density and supercapacitors have a relatively high power density. Energy storage and power storage are often considered to be conflicting objectives in an electrical system. If the electrical energy storage device 550 is a battery, the electrical system 500 is able to both effectively store energy produced or consumed by the motor-generator 540 and effectively store power produced or consumed by the motor-generator 540, which is highly advantageous.

The motor-generator 540 may comprise a closed-cycle heat engine. The closed-cycle heat engine has an operating cycle and an operating cycle direction. The operating cycle may be, for example, based on a Stirling cycle, a Brayton cycle or a combination thereof. The operating cycle direction of the closed-cycle heat engine may be a forward operating cycle direction or a reverse operating cycle direction.

The motor-generator 540 may further comprise an electrical actuator and an electrical alternator. The electrical actuator is configured to convert electrical energy to kinetic energy of, for example, a piston during a first phase of the operating cycle.

In use, the closed-cycle heat engine draws an electrical power from the supercapacitor 501 via the electrical actuator during the first phase of the operating cycle. The electrical alternator is configured to convert kinetic energy of, for example, a piston to electrical energy during a second phase of the operating cycle. In use, the closed-cycle heat engine provides an electrical power to the supercapacitor 501 during the second phase of the operating cycle.

In the forward operating cycle direction, the electrical power provided to the supercapacitor 501 during the second phase of the operating cycle exceeds the electrical power drawn from the supercapacitor 501 during the first phase of the operating cycle. As such, the closed-cycle heat engine functions as a net electrical generator (that is, a net electrical supply source). Operating the closed-cycle heat engine in the forward cycle direction causes the closed-cycle heat engine to operate as a net electrical supply source and may form part of a heat energy recovery system and/or an electrical energy generation system.

In the reverse operating cycle direction, the electrical power drawn from the supercapacitor 501 during the first phase of the operating cycle exceeds the electrical power provided to the supercapacitor 501 during the second phase of the operating cycle. As such, the closed-cycle heat engine functions as a net electrical motor (that is, a net electrical load source). Operating the closed-cycle heat engine in the reverse cycle direction causes the closed-cycle heat engine to operate as a net electrical load source, and may form part of a heat pump system, a refrigeration system, an air conditioning system and/or a chiller system.

Alternatively or additionally, the motor-generator 540 may comprise an open-cycle heat engine. The closed-cycle heat engine has an operating cycle. The operating cycle may be, for example, based on an Atkinson cycle, an Otto cycle, a Brayton cycle, a Diesel cycle or a combination thereof.

The motor-generator 540 may further comprise an electrical actuator and an electrical alternator. The electrical actuator is configured to convert electrical energy to kinetic energy of, for example, a piston during a first phase of the operating cycle. In use, the open-cycle heat engine draws an electrical power from the supercapacitor 501 via the electrical actuator during the first phase of the operating cycle. The electrical alternator is configured to convert kinetic energy of, for example, a piston to electrical energy during a second phase of the operating cycle. In use, the open-cycle heat engine provides an electrical power to the supercapacitor 501 during the second phase of the operating cycle.

The electrical actuator and electrical alternator enable better control over, for example, a piston motion during the operating cycle of the open-cycle heat engine and allows, for example, a linear motion of the piston to have a non-smooth function with respect to a time. This is associated an increased thermal efficiency of an open-cycle heat engine.

In use the supercapacitor 501 functions as an electrical equivalent of a mechanical flywheel in that it serves to smooth the substantially variable power demand and supply profile of the motor-generator 540. The technical advantages associated with the first example electrical system 400 are also associated with the electrical system 500, namely a reduction in an amount of raw material required to produce the electrical system 500, as well as a decreased weight and size of the electrical system 500.

V. Description of method according to the invention FIG. 6 shows a method 600 for smoothing a power output of a fluctuating electrical load and supply source using an electrical system. The electrical system comprises 25 a supercapacitor 401 in accordance with any of the previously described examples.

The method comprises connecting, at block 602, the power output of the fluctuating electrical load and supply source across a first current collector 412 and a third current collector 422 of the supercapacitor 401.

The method further comprises receiving, at block 604, a smoothed power output of the fluctuating electrical load and supply source across the second current collector 413 and the fourth current collector 423 of the supercapacitor 401.

Claims

CLAIMSWhat is claimed is: 1. A supercapacitor comprising an anodic structure and a cathodic structure, 5 wherein the anodic structure is provided with a first current collector and a second current collector; and the cathodic structure is provided with a third current collector and a fourth current collector.
2. A supercapacitor according to claim 1, wherein a sum of: an equivalent series resistance of the anodic structure; and an equivalent series resistance of the cathodic structure is equal to or less than 2x1030.
3. A supercapacitor according to claim 1 or 2, wherein the anodic structure and the cathodic structure comprise a material having a relatively low effective electrical conductivity.
4. A supercapacitor according to any preceding claim, wherein the anodic structure comprises a first anode and a second anode; the cathodic structure comprises a first cathode and a second cathode; the first anode is electrically connected to the second anode by an inter-anode current conductor; and the first cathode is electrically connected to the second cathode by an inter-cathode current conductor.
5. A supercapacitor according to claim 4, wherein the inter-anode current conductor and/or the inter-cathode current conductor have a permeable structure.
6. A supercapacitor according to claim 4 or 5, wherein the inter-anode current conductor and/or the inter-cathode current conductor have a lattice structure.
7. A supercapacitor according to any of claims 4 to 6, wherein the inter-anode current conductor and the inter-cathode current conductor comprise a material having a relatively high effective electrical conductivity.
A supercapacitor according to any preceding claim, wherein the first anode is separated from the second anode by an inter-anode separator; and the first cathode is separated from the second cathode by an inter-cathode separator.
9. An electrical system, comprising: a supercapacitor in accordance with any preceding claim; a fluctuating electrical load and supply source connected across the first current collector and the third current collector; an unfluctuating electrical load and supply source connected across the second current collector and the fourth current collector.
10. An electrical system according to claim 9, wherein the unfluctuating electrical load and supply source comprises an electrical energy storage device. 20
11. An electrical system according to claim 10, wherein the electrical energy storage device comprises a battery.
12. An electrical system according to any of claims 9 to 11, wherein the fluctuating electrical load and supply source comprises a motor-generator.
13. An electrical system according to claim 12, wherein the motor-generator comprises a closed-cycle heat engine.
14. An electrical system according to claim 12 or 13, wherein the motor-generator comprises an open-cycle heat engine.
15. A method for smoothing a power output of a fluctuating electrical load and supply source using an electrical system, the electrical system comprising: a supercapacitor in accordance with any of claims 1 to 8; the method comprising: connecting the power output of the fluctuating electrical load and supply source across the first current collector and the third current collector of the supercapacitor; and receiving a smoothed power output of the fluctuating electrical load and supply source across the second current collector and the fourth current collector of the supercapacitor.