METHOD

TECHNICAL FIELD The present disclosure relates to a supercapacitor for electrical power handling and to an electrical system for electrical power handling. The present disclosure relates further to a method of electrical power handling using a supercapacitor.

BACKGROUND It is known to use a capacitor for the purpose of smoothing a variable electrical power demand and/or supply profile. A capacitor stores electrical energy in an electric field generated therein. A quantity of energy stored in the electric field is related to an electric potential difference across the capacitor and a capacitance of the capacitor. Therefore, in order to store energy in or to draw energy from a capacitor, the electric potential difference across the capacitor must vary. However, for optimal power smoothing, the electric potential difference across the capacitor should not vary significantly during cyclic storing of energy therein and drawing of energy therefrom. For this reason, a capacitor which has a large power smoothing capacity must necessarily have a large capacitance. In order to have a large capacitance, an installation size of a capacitor must be disadvantageously large. Further drawbacks include an increased installation mass and/or size of such a capacitor and a requirement to use large amounts of raw material in manufacturing thereof. In addition, such capacitors are associated with large equivalent series resistances which incur significant useful energy losses in use and thereby reduce an energy efficiency of such a capacitor. An improved device for the purpose of electrical power smoothing is therefore desired.

An object of the present invention is therefore to provide a device which may be used to smooth a variable electrical power demand and/or supply profile and which may be configured to have a large power smoothing capacity without having burdensome sizing requirements, having an excessive mass and/or incurring significant useful energy losses in use. SUMMARY

According to a first aspect there is provided a supercapacitor comprising: an anodic structure including a first current collector, a second current collector and an anode; and a cathodic structure including a third current collector, a fourth current collector and a cathode, wherein the anodic structure provides an electrical conduction pathway between the first current collector and the second current collector through the anode; and the cathodic structure provides an electrical conduction pathway between the third current collector and the fourth current collector through the cathode.

It may be that a sum of: a resistance of the anodic structure between the first current collector and the second current collector, and a resistance of the cathodic structure between the third current collector and the fourth current collector is equal to or less than 2 ^c 10 ² W. Further, it may be that the sum of: the resistance of the anodic structure between the first current collector and the second current collector, and the resistance of the cathodic structure between the third current collector and the fourth current collector is equal to or less than 2x 10 ^-3 W.

The anode and/or the cathode may comprise a material having a relatively low effective electrical conductivity. Preferably, the anode and/or the cathode may comprise a material having an effective electrical conductivity less than 1 x10 ⁵ S nr ¹ .

It may also be that the anode is a first anode and the cathode is a first cathode. The anodic structure may further comprise a second anode while the cathodic structure may further comprise 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 anodic structure may provide an electrical conduction pathway between the first current collector and the second current collector through the first anode, the inter anode current conductor and the second anode. The cathodic structure may provide an electrical conduction pathway between the third current collector and the fourth current collector through the first cathode, the inter-cathode current conductor and the second cathode.

It may be that the inter-anode current conductor and/or the inter-cathode current conductor have a permeable structure or a lattice structure. It may also be that the inter anode current conductor and/or the inter-cathode current conductor comprise a material having a relatively high effective electrical conductivity. Preferably, the inter-anode current conductor and/or the inter-cathode current conductor may comprise a material having an effective electrical conductivity equal to or greater than 1 x10 ⁵ S nr 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-cathode separator.

According to a second aspect there is provided an electrical system comprising: the supercapacitor of the first aspect; a fluctuating electrical load and/or electrical source connected across the first current collector and the third current collector of the supercapacitor; and an unfluctuating electrical load and/or electrical source connected across the second current collector and the fourth current collector of the supercapacitor.

It may be that the unfluctuating electrical load and/or electrical source comprises an electrical energy storage device. The electrical energy storage device may comprise a battery. It may be that the fluctuating electrical load and/or electrical source comprises a motor-generator. The motor-generator may comprise a heat engine.

According to a third aspect there is provided a method of electrical power handling using the supercapacitor of the first aspect, the method comprising: transmitting a first electrical power through the first current collector and the third current collector of the supercapacitor; and transmitting a second electrical power through the second current collector and the fourth current collector of the supercapacitor.

BREIF DESCIRPTION OF THE DRAWINGS

Embodiments of the disclosure will now be described by way of example only with reference to the accompanying drawings, which are purely schematic and not to scale, and in which:

FIG. 1 shows a cross-sectional view of a conventional supercapacitor;

FIG. 2 shows a cross-sectional view of a first example supercapacitor;

FIG. 3 shows a cross-sectional view of a second example supercapacitor;

FIG. 4 is a diagram showing a first example electrical system;

FIG. 5 is a diagram showing a second example electrical system;

FIG. 6 is a flowchart which shows a method of electrical power handling using a supercapacitor; and

FIGs. 7A-7B are graphs which show idealised profiles of electrical power being transmitted through different pairs of current collectors of a supercapacitor during execution of the method shown in FIG. 6. 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 i _d r = ^s E (1a) where i _dr is an electrical drift current density, s is an effective electrical conductivity and E is an electric field strength. In addition, an electrical diffusion current density, i _di , may be defined according to Fick’s law. This may be stated as i _di = DVq (1b) where q is an electric charge density and D is a solid-state diffusivity. Further, Einstein’s relationship for charged particles mandates that s k _B T

D (1c) q e where k _B is the Boltzmann constant, T is a temperature and e is the elementary charge. A conservation of charge condition requires that where t represents a time. If the effective electrical conductivity can be considered to be a constant, Eq. 2 becomes dq

= a(V · E) + V · (DVq) (3)

A reasonable assumption provides that E = v<p, where f is a solid phase electrical potential. This permits Eq. 3 to be expressed as

In one dimension, this can be written as where x is a spatial coordinate. By inspection, it may be seen that where and when dq/dt is non-zero and if s is very large, then d ² <p/dx ² is very small. This is the case for most electrical conductors, such as copper for example, which has an effective electrical conductivity of approximately 6x 10 ⁷ S nr ¹ . Most common electrical conductors have electrical conductivities of a similar order of magnitude.

For the above reasons, a significant electrical potential gradient will not develop in a typical solid medium used for electrical conduction, 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, dq/dt 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 composed of both an inductor and a group of small capacitors connected in parallel.

However, where the effective electrical conductivity of a solid medium is not large, then d ² <p/dx ² 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 heat dissipation when an electrical current is passed therethrough, which represents a conduction efficiency reduction.

II. Description of a conventional supercapacitor

FIG. 1 is a cross-sectional schematic view of a conventional supercapacitor 100. 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 electrode structures such that the separator 130 may be referred to as an inter electrode structure separator 130.

The anodic structure 110 includes a current collector 112 and an anode 114, wherein the anode comprises a plurality of pores 116 such that the anode 114 has a substantially porous structure. The cathodic structure 120 includes a second current collector 122 and a cathode 124, wherein the cathode comprises a plurality of pores 126 such that the cathode 124 has a substantially porous structure. The anode 114 and the cathode 124 may be referred to as a pair of electrodes.

The anode 114, the cathode 124 and the separator 130 are immersed in an electrolyte. The electrolyte comprises a plurality of anions and a plurality of cations in solution. Each anion and each cation may pass across the separator 130 but may not pass from the electrolyte into either the anode 114 or the cathode 124. A geometry of the anode 114 defines an interfacial area between the anode 114 and the electrolyte, while a geometry of the cathode 124 defines an interfacial area between the cathode 124 and the electrolyte. 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.

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. At the same time, 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 114 becomes relatively positively charged and the cathode 124 becomes relatively negatively charged. As a result, anions within the electrolyte are drawn toward the holes in the anode 114 due to electrostatic attraction. Energy is stored in an electric field formed between the anions and the holes at the interface between the anode 114 and the electrolyte. At the same time, cations are drawn toward electrons in the cathode 124 due to electrostatic attraction. Energy is stored in the electric field formed between the cations and the electrons at the interface between the cathode 124 and the electrolyte.

The transportation of charge carriers (that is, holes and electrons) in a solid conductor, such as the anodic structure 110 or the cathodic structure 120, is governed by the set of principles of electrical conduction in solid media described in the preceding section. Accordingly, a speed at which holes are transported across the anode 114 from the current collector 112 toward the separator 130 is dictated by an effective electrical conductivity of the anode 114. Likewise, a speed at which electrons are transported across the cathode 124 from the current collector 122 toward the separator 130 is dictated by an effective electrical conductivity of the cathode 124.

Many commercially available supercapacitors comprise electrodes (that is, anodes and cathodes) having an effective electrical conductivity of around 5x10 ² S nr ¹ to 5 S nr 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 may be much lower than it would be than if the pair of electrodes comprised a non-porous copper structure, for instance.

In such a case, because the speed at which holes and electrons are transported across the anode 114 and cathode 124 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.

III. Description of a supercapacitor according to the present disclosure

FIG. 2 is a cross-sectional schematic view of a first example supercapacitor 200 according to the present disclosure. 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 electrode structures such that the separator 230 may be referred to as an inter-electrode structure separator 230. It will be understood that the general physical principles described above in respect of the conventional supercapacitor 100 and with reference to FIG. 1 apply, mutatis mutandis, to the first example supercapacitor 200.

Unlike the conventional supercapacitor 100, 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 such that the anodic structure 210 provides an electrical conduction pathway between the first current collector 212 and the second current collector 213 through the anode 214. The anodic structure 210 has a distance between the first current collector 212 and the second current collector 213, l _an , as well as a projected area between the first current collector 212 and the second current collector 213, A _an .

Similarly, 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 223 such that the cathodic structure 220 provides an electrical conduction pathway between the third current collector 222 and the fourth current collector 223 through the cathode 224. The cathodic structure 220 has a distance between the third current collector 222 and the fourth current collector 223, h _ath , as well as a projected area between the third current collector 222 and the fourth current collector 223, A _cath .

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 explained in further detail below, the supercapacitor 200 may therefore be used as a type of electrical power buffer (i.e. an electrobuffer).

As previously described with respect to the conventional supercapacitor 100, 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. A similar process occurs in the cathodic structure 220 between the third current collector 222 and the fourth current collector 223. 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.

Accordingly, the supercapacitor 200 may be used to smoothen and flatten a substantially variable power demand and/or supply profile provided to a current collector of each of the anodic structure 210 and the cathodic structure 220 and to provide a substantially invariable power demand and/or supply profile received from another current collector of each of the anodic structure 210 and the cathodic structure 220. Use of the supercapacitor 200 in this way is described in further detail with respect to FIG. 6 and FIGs. 7A-7B.

A throughput energy loss associated with the anode 214 and a throughput energy loss associated with the cathode 224 may be analysed by considering a throughput energy efficiency of the supercapacitor 200. The throughput energy efficiency of the supercapacitor 200 is related to a combined resistance of the supercapacitor 200. The combined resistance of the supercapacitor, R, is simply a sum of a resistance of the anodic structure 210 between the first current collector 212 and the second current collector 213, R _an , and a resistance of the cathodic structure between the third current collector 222 and the fourth current collector 223, R _cat h That is

R ⁼ Ran T Rcath (5)

The anodic structure 210 and the cathodic structure 220 may comprise materials with an effective electrical resistivity denoted by p _an and p _cath respectively, which is defined as the mathematical reciprocal of an effective electrical conductivity thereof, the resistance of the anodic structure and cathodic structure may be calculated using Pouillet's law, as given in Eqs. 6a and 6b

The throughput energy efficiency, h, of the supercapacitor 200 may be calculated using Eq. 7a where P _in is a net average electrical power supplied to the supercapacitor, P _out is a net average electrical power delivered by the supercapacitor and P _diss is a power dissipated as heat within the supercapacitor 200. Making use of Ohm’s law and the definition of electric power, the above reduces to where / is an electric current passed through the supercapacitor in use and V is an electric potential difference across the supercapacitor. Further, by rearrangement

Typical 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 electrode structures.

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 resistance 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, 100 W. In such a case, Eq. 8a becomes which provides an upper bound for the combined resistance of the supercapacitor if the figure of merit for the throughput energy efficiency of the supercapacitor is to be achieved. If the maximum average power suppled to the supercapacitor were 10 W, for example, the maximum combined resistance would instead be only 2 ^c 10 ² W. These example calculations provide respective criteria for a geometrical construction of the anodic structure 210 and the cathodic structure 220 so as to constrain a combined resistance of the supercapacitor 200 and thereby limit throughput energy losses in use thereof.

FIG. 3 is a cross-sectional schematic view of a second example supercapacitor 300 according to the present disclosure. The second example supercapacitor 300 is generally similar to the first example supercapacitor 200 with like reference numerals indicating common or similar features.

In the example of FIG. 3, the anode 214 is a first anode 214 and the cathode 224 is a first cathode 224. The anodic structure 210 further comprises a second anode 315 and the cathodic structure 220 further comprises a second cathode 325. The first anode 214 is electrically connected to the second anode 315 by an inter-anode current conductor 311 while the first cathode 224 is electrically connected to the second cathode 325 by an inter-cathode current conductor 321 . The anodic structure 210 provides a convoluted electrical conduction pathway between the first current collector 212 and the second current collector 213 through the first anode 214, the inter-anode current conductor 311 and the second anode 315. Similarly, the cathodic structure 220 provides a convoluted electrical conduction pathway between the third current collector 222 and the fourth current collector 223 through the first cathode 224, the inter-cathode current conductor 321 and the second cathode 325.

A geometry of the first anode 214 defines an interfacial area between the first anode 214 and the electrolyte. The first anode 214 may comprise a plurality of pores such that the first anode 214 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. Likewise, a geometry of the first cathode 224 defines an interfacial area between the first cathode 224 and the electrolyte. The first cathode 224 may comprise a plurality of pores such that the first cathode 224 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 210 has a distance between the first current collector 212 and the second current collector 213, which is a mathematical sum of: a distance between the first current collector 212 and the inter-anode current conductor 311 ; and a distance between the inter-anode current conductor 311 and the second current collector 213. The anodic structure 210 also has a projected area between the first current collector 212 and the second current collector 213, which is the lesser of: a projected area between the first current collector 212 and the inter-anode current conductor 311 ; and a distance between the inter-anode current conductor 311 and the second current collector 213.

The cathodic structure 220 has a distance between the third current collector 222 and the fourth current collector 223, which is a mathematical sum of: a distance between the third current collector 222 and the inter-cathode current conductor 321 ; and a distance between the inter-cathode current conductor 321 and the fourth current collector 223. The cathodic structure 220 also has a projected area between the first current collector 212 and the second current collector 213, which is the lesser of: a projected area between the third current collector 222 and the inter-cathode current conductor 321 ; and a distance between the inter-cathode current conductor 321 and the fourth current collector 223.

The anodic structure 210 and the cathodic structure 220 may be geometrically constructed in accordance with the criterion described in relation to the previous example so as constrain a combined resistance of the supercapacitor 300 and limit throughput energy losses in use thereof.

Each anion and each cation in solution within the electrolyte may pass freely across the inter-electrode separator 330 but may not pass from the electrolyte into the first anode 214, the second anode 315, the first cathode 224 or the second cathode 325.

During a charging process, a plurality of anions are drawn toward a plurality of holes in the first anode 214 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 214 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 1 x10 ⁵ S nr ¹ . A 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 a combined 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 214 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 214 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 214 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 210 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 224 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 224 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 224 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 220 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 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 a manufacturing process required to produce the second example supercapacitor 300 is more involved than a manufacturing process required to produce the first example supercapacitor 200. As such, the first example supercapacitor 200 may only require a relatively simple 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 present disclosure

FIG. 4 is a diagram showing a first example electrical system 400 according to the present disclosure. The electrical system 400 comprises a supercapacitor 200 in accordance with the first example supercapacitor 200 described above with reference to FIG. 2 or the second example supercapacitor 300 described above with reference to FIG. 3. The supercapacitor 200 is shown symbolically in FIGs. 4 and 5.

A fluctuating electrical load and/or electrical source 440 is connected to a first pair of current collectors of the supercapacitor 200. The first pair of current collectors includes a current collector which forms part of the anodic structure 210 of the supercapacitor 200 and a current collector which forms part of the cathodic structure 220 of the supercapacitor 200. In the example shown in FIG. 4, the first pair of current collectors includes the first current collector 212 and the third current collector 222. However, it will be understood that the first pair of current collectors may otherwise include the first current collector 212 and the fourth current collector 223, the second current collector 213 and the third current collector 222, or the second current collector 213 and the fourth current collector 223.

The fluctuating electrical load and/or electrical source 440 is a device or system which, in use, has a substantially variable power demand and/or supply profile in time. At a given moment in time, the fluctuating electrical load and/or electrical source 440 may either require an electrical power to be supplied to it (i.e. draws an electrical power from the supercapacitor 200) or deliver an electrical power from it (i.e. provides an electrical power to the supercapacitor 200). Over a given period of time, an average of the power demand and/or supply profile of the fluctuating electrical load and/or electrical source 440 determines whether the fluctuating electrical load and/or electrical source 440 functions as a net electrical load, a net electrical source or neither. An unfluctuating electrical load and/or electrical source 450 is connected to a second pair of current collectors of the supercapacitor 200. The second pair of current collectors of the supercapacitor 200 includes two current collectors which are not included within the first pair of the current collectors of the supercapacitor 200. However, like the first pair of current collectors, the second pair of current collectors includes a current collector which forms part of the anodic structure 210 of the supercapacitor 200 and a current collector which forms part of the cathodic structure 220 of the supercapacitor 200 such that each pair of current collectors includes a current collector which forms part of the anodic structure 210 of the supercapacitor 200 and a current collector which forms part of the cathodic structure 220 of the supercapacitor 200. In the example shown in FIG. 4, the second pair of current collectors includes the second current collector 213 and the fourth current collector 223. Nevertheless, it will be understood that the second pair of current collectors may otherwise include the second current collector 213 and the third current collector 222, the first current collector 212 and the third current collector 222, or the first current collector 212 and the fourth current collector 223 as applicable.

The unfluctuating electrical load and/or electrical source 450 is a device or system which, in use, has a substantially constant power demand and/or supply profile in time. Over a given period of time, an average of the power demand and/or supply profile of the unfluctuating electrical load and/or electrical source 450 determines whether the unfluctuating electrical load and/or electrical source 450 functions as a net electrical load, a net electrical source or neither.

As an example, if the fluctuating electrical load and/or electrical source 440 is functioning as a net electrical load in use, the supercapacitor 200 provides an electrical power to the fluctuating electrical load and/or electrical source 440 when momentarily required and receives an electrical power from the same when momentarily available, while simultaneously drawing a net average electrical power required to operate the fluctuating electrical load and/or electrical source 440 from the unfluctuating electrical load and/or electrical source 450. In this example, the unfluctuating electrical load and/or electrical source 450 functions as a net electrical source.

As another example, if the fluctuating electrical load and/or electrical source 440 is functioning as a net electrical source in use, the supercapacitor 200 receives an electrical power from the fluctuating electrical load and/or electrical source 440 when momentarily available and provides an electrical power to the same when momentarily required, while simultaneously providing a net average electrical power generated by the fluctuating electrical load and/or electrical source 440 to the unfluctuating electrical load and/or electrical source 450. In this example, the unfluctuating electrical load and/or electrical source 450 functions as a net electrical load.

In both of the above examples, the supercapacitor 200 functions as an electrical power buffer between the fluctuating electrical load and/or electrical source 440 and the unfluctuating electrical load and/or electrical source 450. In a previously-considered electrical system, at least one conventional supercapacitor having a large capacitance was considered for use as a filtering buffer between the fluctuating electrical load and/or electrical source 440 and the unfluctuating electrical load and/or electrical source 450. In contrast to such an electrical system, the first example electrical system 400 enables a reduction in an amount of raw material required to produce the electrical system as well as a decreased installation size and mass of the electrical system.

FIG. 5 is a diagram showing a second example electrical system 500 according to the present disclosure. The second example electrical system 500 is generally similar to the first example electrical system 400, with like reference numerals indicating common or similar features. In the more specific example of FIG. 5, the fluctuating electrical load and/or electrical source 440 comprises a motor generator 540, while the unfluctuating electrical load and/or electrical source 450 comprises an electrical energy storage device 550. Further, in the example shown in FIG. 5, the electrical energy storage device is a battery, although it will be appreciated that a suitable alternative electrical energy storage device may be used in other examples, as will be known to those skilled in the art.

In general, batteries have a relatively high energy density and supercapacitors have a relatively high power density. For this reason, energy storage and power storage are often considered to be conflicting objectives in a design process for 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 include a heat engine. The heat engine may be, for example, a closed-cycle heat engine or an open-cycle heat engine. The 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 heat engine may be a forward operating cycle direction or a reverse operating cycle direction.

The motor-generator 540 may include an electrical actuator and an electrical alternator. The electrical actuator is configured to convert electrical energy to kinetic energy of, for example, a piston of the heat engine during a first phase of the operating cycle. In use, the heat engine draws an electrical power from the supercapacitor 200 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 heat engine provides an electrical power to the supercapacitor 200 during the second phase of the operating cycle.

In the forward operating cycle direction, the electrical energy provided to the supercapacitor 200 during the second phase of the operating cycle exceeds the electrical energy drawn from the supercapacitor 200 during the first phase of the operating cycle. As such, operating the heat engine in the forward cycle direction causes the heat engine to operate as a net electrical supply source. When operated in the forward cycle direction, the heat engine may be suitable for use as part of a heat energy recovery system and/or an electrical energy generation system.

In the reverse operating cycle direction, the electrical energy drawn from the supercapacitor 200 during the first phase of the operating cycle exceeds the electrical energy provided to the supercapacitor 200 during the second phase of the operating cycle. As such, operating the heat engine in the reverse cycle direction causes the heat engine to function as a net electrical load source. When operated in the reverse cycle direction, the heat engine may be suitable for use as part of a heat pump system, a refrigeration system, an air conditioning system and/or a chiller system.

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

FIG. 6 is a flowchart which shows a method 600 of electrical power handling using a supercapacitor in accordance with the first example supercapacitor 200 described above with reference to FIG. 2 or the second example supercapacitor 300 described above with reference to FIG. 3. The method 600 comprises transmitting, at block 602, a first electrical power through the first current collector 212 and the third current collector 222 of the supercapacitor 200, 300. The method further comprises transmitting, at block 604, a second electrical power through the second current collector 213 and the fourth current collector 223 of the supercapacitor 200, 300. The first electrical power is transmitted through the first pair of current collectors of the supercapacitor 200, 300 whereas the second electrical power is transmitted through the second pair of current collectors of the supercapacitor 200, 300. As described above with reference to FIG. 4, each pair of current collectors includes a current collector which forms part of the anodic structure 210 of the supercapacitor 200, 300 and a current collector which forms part of the cathodic structure 220 of the supercapacitor 200, 300.

The method 600 is now explained in further detail with reference to FIGs. 7A-7B, which are example graphs showing idealised profiles of first and second electrical powers being transmitted through each pair of current collectors of the supercapacitor 200, 300 with respect to time during execution of the method 600. These idealised profiles are provided for the purpose of illustrating the principles and the effects of the method 600, and it will be understood that they are not intended to closely resemble real- world conditions. A profile of the first electrical power being transmitted through the first pair of current collectors of the supercapacitor 200, 300 is denoted by reference numeral 710. A profile of the second electrical power being transmitted through the second pair of current collectors of the supercapacitor 200, 300 is denoted by reference numeral 720.

For the purposes of FIGs. 7A-7B, a positive electrical power is defined as a rate of electrical energy flowing into the supercapacitor 200, 300 in accordance with the passive sign convention. Conversely, a negative electrical power is defined a rate of electrical energy flowing out of the supercapacitor 200, 300. A positive electrical power as shown on FIGs. 7A-7B corresponds to an electrical power being provided to the supercapacitor 200, 300 whereas a negative electrical power as shown on FIGs. 7A-7B corresponds to an electrical power being received from the supercapacitor 200, 300.

In the example of FIG. 7A, the profile of the first electrical power 710 transmitted through the first pair of current collectors of the supercapacitor is a triangular wave, whereas the profile of the second electrical power 720 transmitted through the second pair of current collectors is a flat straight line. The profile of the first electrical power 710 may be described as a substantially variable power demand and supply profile, whereas the profile of the second electrical power 720 may be described as a substantially invariable power demand and supply profile. The second electrical power profile 720 is therefore both smoother and flatter than the first electrical power profile 710. Conversely, in the example of FIG. 7B, the first electrical power profile 710 transmitted through the first pair of current collectors of the supercapacitor is a flat straight line, whereas the second electrical power 720 profile transmitted through the second pair of current collectors is a triangular wave. The profile of the first electrical power 710 may be described as a substantially invariable power demand and supply profile, whereas the profile of the second electrical power 720 may be described as a substantially variable power demand and supply profile. Accordingly, the first electrical power profile 710 is both smoother and flatter than the second electrical power profile 720.

Further, in the example of FIG. 7A, there are a plurality of points in time at which the power flowing through the first pair of collectors is positive and a plurality of points time at which the power transmitted through the first pair of current collectors is negative while the power flowing through the second pair of current collectors is always positive. On the other hand, in the example of FIG. 7B, there are a plurality of points in time at which the power flowing through the second pair of collectors is positive and a plurality of points time at which the power transmitted through the second pair of current collectors is negative while the power flowing through the first pair of current collectors is always negative.

It follows that the method 600 is able to handle electrical power using the supercapacitor 200, 300 such that a gradient of the first electrical power profile is not dictated by a gradient of the second electrical power profile at a given point in time. Further, the method 600 is able to handle electrical power using the supercapacitor 200, 300 such that a sign of the electrical power profile is not dictated by a sign of the second electrical power profile at a given point in time. In general terms, the method 600 is able to handle electrical power using the supercapacitor 200, 300 such that a property of a first electrical power transmitted through a first pair of current collectors of the supercapacitor 200, 300 is not dictated by and/or does not dictate a corresponding property of a second electrical power transmitted through a second pair of current collectors of the supercapacitor 200, 300. In this way, the method 600 uses the supercapacitor 200, 300 as a type of electrical power buffer (i.e. an electrobuffer).

It will be understood that the disclosure is not limited to the embodiments above- described and various modifications and improvements can be made without departing from the concepts described herein. Except where mutually exclusive, any of the features may be employed separately or in combination with any other features and the disclosure extends to and includes all combinations and sub-combinations of one or more features described herein. The present invention is defined by the attached claims, to which reference should now be made.