GB2610420A

GB2610420A - Electrochemical pseudo-cell and method of simulating an electrochemical cell

Info

Publication number: GB2610420A
Application number: GB2112608.1A
Authority: GB
Inventors: Patel Yatish; Offer Gregory; Hales Alastair; White Gavin
Original assignee: Imperial College Innovations Ltd
Current assignee: Ip2ipo Innovations Ltd
Priority date: 2021-09-03
Filing date: 2021-09-03
Publication date: 2023-03-08
Also published as: GB202112608D0; WO2023031408A1

Abstract

A pseudo-cell 100 for simulating an electrochemical cell comprises: a casing 102, a heating element 120, a temperature sensor 124, and a controller 126. The controller controls the current to the heating element to produce a heat flux similar to that of a real electrochemical cell. The casing may be cylindrical, prismatic or of pouch form and the heater, controller and temperature sensor may all be located within the interior volume of the casing. There may also be a power source, such as a DC supply or battery, for the heater 120 within the casing. The electrochemical pseudo-cell allows battery pack testing to be carried out on the pseudo-cells without the dangers and expense of testing real electrochemical cells. Also disclosed are methods of simulating the thermal response of real cells using virtual cells, the simulations producing results that can be used to control the heater power of the pseudo-cell.

Description

Electrochemical Pseudo-Cell and Method of Simulating an Electrochemical Cell

Technical Field

The present application relates to the field of simulating electrochemical cells under conditions they may experience in real world applications. An electrochemical cell, for example a lithium ion cell, may be used to store energy for some time before it is to be generated and delivered as electrical energy for some application. Applications for electrochemical cells include, but are not limited to, delivering electrical power for a mobile device such as a telephone or portable electronic computer, delivering electrical power to an electric motor to drive some form of transport such as a car, a bike, or a scooter, or for storing electrical energy from an electrical grid or power supply to supplement electricity supply at a later time (time-shifting of electricity delivery).

In these and other applications, electrochemical cells are subjected to different cycles of charging and discharging whereby the cells will either receive electrical energy to be stored or will generate electrical energy from the previously stored energy. Over charging and discharging cycles, the state of the cells can change. For example, when charging a cell, some of the electrical energy will be converted to chemical energy and stored, but some of the electrical energy will contribute to causing the electrochemical cell to heat up. Similarly, when a cell is discharging, some of the stored energy of the cell will be converted to electrical energy, but some heat will be generated in the cell. It is important to understand this generation of heat in an electrochemical cell because it can have implications on the performance and the safety of the electrochemical cell when being used. For example, if too much heat is generated a cell might reach a threshold temperature at which a thermal runaway reaction occurs. Thermal runaway will destroy the cell, might damage or destroy other components in the vicinity of the cell, is likely to lead to a fire, and presents a risk to human safety. Even before the cell reaches a threshold temperature for thermal runaway, operating an electrochemical cell at elevated temperatures due to the operating conditions or excessive heat generation may cause damage to the cell by way of solid electrolyte interface layer breakup, anode-solvent reaction, or electrolyte decomposition.

Prior to thermal runaway, the ability of an electrochemical cell to charge, store, or discharge may also be affected by the cell temperature. As the temperature of a cell approaches the thermal runaway temperature or some other safe maximum or optimum threshold temperature, a battery management system (BMS) may need to limit or cap the current or power being received or delivered to avoid exceeding the threshold temperature. As well as temperature, there are multiple internal states of a cell which may affect the ability of the cell to charge, store, or discharge. For example, a cell which has been "cycled" many times may accumulate degradation to its state of health. This might limit the amount of energy that can be stored, the speed at which the cell can be charged, or the maximum current that the cell can deliver. It is therefore important to be able to accurately simulate the conditions that electrochemical cells may be subject to under real world conditions.

Some models exist for the simulation of a cell under different electrical conditions, for example a Thevenin model. The Thevenin model is one such example from which a heat generation output can be calculated knowing the state of charge or open circuit voltage, the internal resistance as a function of temperature, and the current flow. However, under real world conditions, such a model falls short of being able to accurately simulate the operation of an electrochemical cell. In some cases, multiple cells are arranged together in a pack so that they can be combined to collectively provide more power, more capacity, or more power and storage. When multiple cells are arranged together in a pack, each cell may affect the other cells in the pack because they affect the ability of a nearby cell to reject heat to its environment. Additionally, where the internal resistance of one cell in a pack changes, this may affect how much current must be delivered by the other cells in the pack. Some packs of cells may also include cooling to moderate the temperature of cells under more extreme loading conditions.

In order to verify that a certain design of a pack of cells, or ancillary components such as cooling systems or a BMS operate safely and effectively, a real pack of cells might be tested in a safe environment. A safe environment for testing electrochemical cells typically requires expensive extraction equipment for toxic gases and smoke, fire suppression, and significant investment. It would be useful to be able to reliably test and verify a design of a pack or ancillary component without having to rely on expensive and dangerous testing.

The current models for simulating electrochemical cells fall short of being able to provide such information about electrochemical cells or packs of electrochemical cells. Current testing methods for cells can be costly, time-consuming, and dangerous. What is needed is a method of testing an electrochemical cell or pack of cells which can safely assess the performance of a pack of cells or ancillary components under real world conditions.

Summary

In an embodiment there is provided an electrochemical pseudo-cell comprising: a casing defining an interior volume, at least one heating element disposed in the interior volume, at least one temperature sensor disposed in thermal contact with the casing, and a controller coupled to the at least one heating element and the at least one temperature sensor, and configured to control a current supplied to the at least one heating element responsive to a) a temperature reading taken from the at least one temperature sensor, and b) a calculated heat flux from a simulation of the thermal response of an electrochemical cell. An electrochemical pseudo-cell is configured to replicate the electrical and thermal response of a real electrochemical cell under real life conditions (e.g. in a pack, or with cooling) mitigating the danger of testing real electrochemical cells.

Optionally the casing is one of a cylindrical, a prismatic, or a pouch form factor. A cylindrical form factor may replicate a cylindrical cell which may be one of a number of common form factor for electrochemical cells, for example 18650 (18mm diameter, 65mm in length), 21700 (21mm diameter, 70mm in length) and 4680 (46mm diameter, 80mm in length). A prismatic form factor is another common form factor for electrochemical cells. The prismatic form factor may have a rectangular cross section. A pouch form factor is another common form factor for electrochemical cells. The casing material of a pouch form factor may be a flexible material.

Optionally the at least one heating element is a resistive heating element. By providing a resistive heating element, the heat flux or heat generation of the pseudo-cell may be directly and quickly controlled by the 30 controller and use of a power supply and/or power electronics.

Optionally, the at least one heating element comprises a plurality of heating elements. By providing a plurality of heating elements, the cell-wide distribution of temperature of the pseudo-cell may be controlled so that hot spots may be simulated, or cooling or heating may be localised to a portion of the pseudo-cell. 35 This allows for the pseudo-cell to be heated in a more realistic manner.

Optionally, the at least one heating element is positioned in contact with an interior surface of the casing. By placing the heating element in contact with an interior surface, the heat generated bythe heating element is more quickly transferred to the casing. In this way, the temperature of the casing of the pseudo-cell may be more quickly and finely controlled by the heating element.

Optionally, the at least one heating element is adhered attached to an interior surface of the casing, further optionally wherein the at least one heating element is attached to the interior surface of the casing by one or more of: an adhesive, one or more screws, one or more fixings, and compression against the interior surface by a resilient element. By providing either adhesion to or pressure against the interior surface, the heat transfer between the heating element and the casing is improved such that the temperature of the casing of the pseudo-cell may be more quickly and finely controlled.

Optionally, the at least one heating element is an annular heating element and the casing is a cylindrical 50 form factor. By providing an annular heating element in a cylindrical casing, the heating element may provide even heating to the circumference of the casing. By providing a plurality of annular heating elements, the longitudinal profile of the temperature of the pseudo-cell casing may be more finely controlled.

Optionally, the at least one temperature sensor is disposed in the interior volume. By disposing the 55 temperature sensor in the interior volume, an indication of the temperature inside the pseudo-cell may be utilised to operate the pseudo-cell. Optionally, the at least one temperature sensor may be disposed on an outer surface of the casing. By disposing the temperature sensor on an outer surface of the casing, an indication of the outer surface temperature may be utilised to operate the pseudo-cell. An external temperature measurement may be useful in accurately replicating heat flux from the surface of the cell. 60 Optionally, the at least one temperature sensor comprises a plurality of temperature sensors. By providing a plurality of temperature sensors, the pseudo-cell may be able to account for local effects such as local cooling. In case a single temperature sensor provides a poor indication of the temperature of the bulk of the pseudo-cell, the plurality of temperature sensors will provide a more accurate indication. The plurality of temperature sensors may also allow for the cell-wide distribution of temperature to be measured.

Optionally, the at least one temperature sensor is one of a thermistor, or a thermocouple.

Optionally, the controller is disposed in the interior volume. By disposing the controller in the interior volume, the pseudo-cell may be used as one of many pseudo-cell modules together. The pseudo-cell may readily be assembled into different packs without the need for reconfiguring the controller.

Optionally the pseudo-cell further comprises a power source disposed in the interior volume. Further optionally, the power source is one of a battery, a DC power supply, or a DC-DC converter. A battery inside the pseudo-cell may provide enough power to operate the controller and the heating element for a test. Alternatively, power of the controller and/or heating element may come from an external source and either a DC power supply or a DC-DC converter is disposed in the interior volume. In this way, the heating elements which are likely to require a more significant power source may be powered externally. The external power source may provide power to the DC power supply or the DC-DC converter via the cell terminals or cell tabs. Optionally, the power source may be a connector configured to connect to an external battery cycler. In this way, a battery cycler may be used to provide the heating power for the heating element via the connector.

Optionally, the simulation of the thermal response of an electrochemical cell comprises: determining an internal state of a virtual electrochemical cell, determining an electric current flow in the virtual electrochemical cell, calculating, based on the internal state and the electric current flow, a heat generation of the virtual electrochemical cell, calculating, based on the heat generation, a heat flux of the virtual electrochemical cell, determining a heat flux response of an electrochemical pseudo-cell to an electric current, and calculating an electrical power to be supplied to the electrochemical pseudo-cell for replicating the heat flux of the virtual electrochemical cell.

Further optionally, the controller is configured to control the supply of electrical power to by one or both of controlling the resistance of the heating element, or controlling the voltage provided by the power supply.

In an embodiment, there is provided a computer-implemented method of simulating the thermal response of an electrochemical cell comprising: determining an internal state of a virtual electrochemical cell, determining an electric current flow in the virtual electrochemical cell, calculating, based on the internal state and the electric current flow, a heat generation of the virtual electrochemical cell, calculating, based on the heat generation, a heat flux of the virtual electrochemical cell, determining a heat flux response of an electrochemical pseudo-cell to an electric current, and calculating an electrical power to be supplied to the electrochemical pseudo-cell for replicating the heat flux of the virtual electrochemical cell.

Optionally, the step of calculating a heat generation of the virtual electrochemical cell includes calculating the heat generation based on one of a Thevenin model, an internal resistance battery model, a Randle model, a thermal-electrochemical model, a Newman model, or a single particle model of the virtual electrochemical cell.

Optionally, the internal state of the virtual electrochemical cell includes one or more of a temperature, internal resistance state of cell health, and state of charge, cell-wide distribution of temperature, cell-wide distribution of state of charge, cell-wide distribution of state of health, and cell-wide distribution of resistance 50 to current flow.

Optionally, the step of determining an electric current flow in the virtual electrochemical cell includes determining the electric current flow based on a drive cycle of the virtual electrochemical cell.

Optionally, the simulation of the thermal response of the electrochemical cell further comprises the step of supplying the calculated electrical power to an electrochemical pseudo-cell for replicating the heat flux from the external surfaces of the virtual electrochemical cell.

Optionally, the simulation of the thermal response of the electrochemical cell further comprises the step of 60 measuring the temperature of the electrochemical cell.

In an embodiment, there is provided a computer-implemented method of simulating the thermal response of a plurality of electrochemical cells comprising: determining a first internal state of a first virtual electrochemical cell including a first temperature of the first virtual electrochemical cell, determining a second internal state of a second virtual electrochemical cell including a second temperature of the second virtual electrochemical cell, determining a first electric current flow in the first virtual electrochemical cell, determining a second electric current flow in the second virtual electrochemical cell, calculating, based on the first internal state and the first electric current flow, a first heat generation of the first virtual electrochemical cell, calculating, based on the second internal state and the second electric current flow, a second heat generation of the second virtual electrochemical cell, calculating, based on the first heat generation and the first temperature, a first heat flux of the first virtual electrochemical cell, calculating, based on the second heat generation and the second temperature, a second heat flux of the second virtual electrochemical cell, determining a heat flux response of a first and a second electrochemical pseudo-cell to an electric current, calculating a first electrical powerto be supplied to the first electrochemical pseudo-cell for replicating the first heat flux of the first virtual electrochemical cell, calculating a second electrical power to be supplied to the second electrochemical pseudo-cell for replicating the second heat flux of the second virtual electrochemical cell.

Optionally, the method comprises the steps of arranging the first and second electrochemical pseudo-cells in a pack, supplying the first calculated electrical power to the first electrochemical pseudo-cell and supplying the second calculated electrical power to the second electrochemical pseudo-cell for replicating the first and second heat fluxes.

Optionally, the method comprises the step of measuring the thermal response of at least one of the first and second electrochemical pseudo-cells in the pack.

Brief Description of the Drawings

Figure 1 shows an exemplary power based drive cycle. The vertical axis indicates the power required from a battery pack in Watts, the horizontal axis indicates time in seconds.

Figure 2 shows an exemplary modelled voltage response to a drive cycle as shown in figure 1. The vertical axis indicates the voltage response taken from a model in Volts, the horizontal axis indicates time in seconds.

Figure 3 shows an exemplary current derived to meet the drive cycle of figure 1. The vertical axis indicates the cell current in Amps, the horizontal axis indicates time in seconds.

Figure 4 shows an exemplary modelled cell resistance during the drive cycle of figure 1. The vertical axis indicates cell resistance in milli Ohms, the horizontal axis indicates time in seconds.

Figure 5 shows an exemplary modelled cell heat generation during the drive cycle of figure 1. The vertical axis indicates heat generation in Watts, the horizontal axis indicates time in seconds.

Figure 6 shows an exemplary modelled cell surface temperature during the drive cycle of figure 1. The vertical axis indicates cell surface temperature in degrees Celsius, the horizontal axis indicates time in seconds.

Figure 7 shows an electrochemical pseudo-cell from an isometric view.

Figure 8 shows the electrochemical pseudo-cell of figure 7 in a cross-sectional view.

Figure 9 shows the cross-sectional view of the pseudo-cell of figure 7 in an exploded view.

Figure 10 shows a block diagram of a pseudo-cell operating with a cell model built in to the cell controller.

Figure 11 shows a diagram of the power electronics to control a heating element.

Figure 12 shows a block diagram of a pseudo-cell operating with a cell model built in to a master controller.

Figure 13 shows a block diagram of a plurality of cell models each representing a single pseudo-cell operating in tandem.

Detailed Description

Figure 1 depicts an exemplary power based drive cycle that a battery pack might typically experience. The cycle shown in figure 1 is by no means exhaustive and could take many forms depending on what is being demanded from a battery pack used in any application. The vertical axis indicates the power required from the battery pack in Watts. A negative value as indicated between roughly 10 seconds and 30 second on the horizontal axis indicates that electrical power is being drawn from the battery pack. This might occur in an automotive battery pack when a vehicle is accelerating and the motors require an electric current supplied by the battery pack to provide power. A positive value as indicated between roughly 30 and 50 seconds indicates that electrical power is being delivered to the battery pack. This might occur where a vehicle is using regenerative braking to store energy from the motion of the car to be used later.

Figure 2 depicts a modelled cell voltage response to the drive cycle that is depicted in figure 1. The vertical axis indicates in Volts the voltage response of a cell which is part of the battery pack. As can be seen for the time that the vehicle would be accelerating or driving between roughly 10 and 30 seconds, the cell voltage drops from the normal value of 3.65W. When the vehicle is carrying out regenerative braking and charging the battery pack, the cell experiences an increase in cell voltage to above 3.65W.

Figure 3 depicts a derived current requirement to meet the drive cycle as shown in figure 1. The vertical axis indicates in Amps the current which is require from a cell of the battery pack to meet the power requirement of the drive cycle depicted in figure 1. As can be seen for the time that the vehicle would be accelerating or driving between roughly 10 and 30 seconds, the cell current required to be delivered to meet the power requirements is positive. When the vehicle is carrying out regenerative braking and charging the battery pack, the current is negative. The current requirements of the cell can be derived as the power requirement divided by the cell voltage since current I = Power(P)/Voltage(V) Figure 4 depicts a modelled cell resistance of a cell of the battery pack during the drive cycle depicted in figure 1. The vertical axis indicates cell resistance in milli Ohms, the horizontal axis indicates time in seconds. As can be seen, the cell resistance fluctuates over the course of the cycle, but is generally dropping as the drive cycle progresses. This change in resistance may affect the current flow in the battery pack as the current passes through a lower resistance path preferentially.

Figure 5 depicts a modelled cell heat generation of a cell of the battery pack during the drive cycle depicted in figure 1. The vertical axis indicates heat generation in Watts, the horizontal axis indicates time in seconds. When the cell either charges or discharges, heat is generated in the cell. When the cell is neither charging nor discharging, the heat generation is negligible or zero. The heat generation may be calculated as 0 = PR where I is the current flow and R is the cell resistance as depicted in figure 4.

Figure 6 depicts a modelled cell surface temperature of a cell during the drive cycle depicted in figure 1. The vertical axis indicates the cell surface temperature in degrees Celsius, the horizontal axis indicates time in seconds. The modelled cell surface temperature is calculated from accumulation of the heat generated as shown in figure 5. As will be appreciated, the cell surface temperature during a cycle is important as an indicator of the state that a cell is in and whether there is a risk of a thermal runaway reaction or other damage to the cell.

The cell surface temperature calculated and shown in figure 6 is an idealised situation in which the cell is not affected by changes in other cells in the same battery pack. In a typical real-life situation, a plurality of cells would be arrange in a battery pack in close proximity and encased in a battery housing. By being located in close proximity to one another, the heat generation and the cell surface temperature of one cell will affect the cell surface temperature of the adjacent cells. For example, where one cell increases in cell surface temperature to a temperature significantly above ambient temperature, an adjacent cell which is generating heat will be less capable of rejecting that heat to its environment because the temperature gradient between the cell surface and the surrounding environment is reduced. A smaller temperature gradient results in less heat rejection. However, the situation is more complex in a typical battery pack due to the interrelated effects of cell temperature, internal resistance, and which cells will generate the most heat. For example, as a cell generates heat and the temperature increases, the cell resistance may drop and the cell voltage may drop. If multiple cells are electrically connected together in the pack, the relative cell resistances and cell voltages will affect which cells provide the power and therefore which cells then generate more heat. Since each cell may affect the heat generation and heat rejection of the adjacent cells in the pack both due to thermal effects and due to electrical effects, a small variation in some cell conditions could lead to a large difference in the response of the cell in a battery pack.

In order to ensure reliable safe operation of a battery pack it is desirable to do physical testing. In "normal" physical testing, a real battery pack might be assembled, containing the actual electrochemical cells in the pack. The battery pack would then be subjected to a power drive cycle, such as that depicted in figure 1. The battery pack would be instrumented so that individual temperature measurements and measurements of current and voltage of cells within the battery pack is recorded during the power cycle. In this way, it can be verified that a battery pack subjected to an exemplary power drive cycle performs acceptably within limits of temperature and cell safety. It can be dangerous to test electrochemical cells in this way because of the risks of thermal runaway. Once a cell reaches a thermal runaway, toxic gases and smoke may be released as well as heat which can damage other cells and equipment.

As electrochemical cells are subjected to many drive cycles over their lifetime, the cells can degrade. This might limit their ability to store charge, deliver electrical power, or to maintain low temperatures. For example, when charging an "aged" cell, the heat generation in the cell may be greater than if a new cell were subjected to the same charging current. The state of health of a cell is a parameter which can be assigned to a cell to provide an indication of this "aging" process of the cell. A cell may lose health faster if it is charged or discharged too quickly or kept at high temperatures. In order to assess the performance of a battery pack once the health of the cells has degraded (for example at a point where the battery pack is nearing the end of its useful lifetime), a battery pack of pre-aged cells might be required. In order to age the cells, these would need to be cycled in charging and discharging many times. To prepare such aged cells requires a long time in orderto cycle the cells a sufficient number of times to lower their state of health. It would be advantageous to have a reliable method of simulating the performance of an electrochemical cell under real conditions, avoiding the costs and safety implications of testing real electrochemical cells which can be dangerous.

Figure 7 shows an isometric view of an electrochemical pseudo-cell 100 according to a first aspect of the disclosure. The electrochemical pseudo-cell 100 comprises a casing 102 which defines an interior volume 104 of the cell 100 (see figure 8 for a cross-sectional view). In the example shown in figure 7, the cell 100 is in a cylindrical form factor wherein the casing 102 comprises a can 105 and a cap 110. The can 105 comprises a cylindrical wall 106 and a base 108 at one end of the cylindrical wall 106. At the opposite end of the base 108, the cylindrical wall 106 defines an opening into which the contents of the cell 100 may be assembled. The cap 110 may be positioned over the opening of the cylindrical wall 106 to close off the opening and seal the cell 100. The cap 110 may be held in place over the opening by any means of fixing such as adhesive, interference fit, screw thread, or crimping to the cylindrical wall 106.

The cap 110 may be shaped so as to mimic the shape of an end terminal of a real cell. For example, the cylindrical cell cap 110 shown in figure 7 includes a terminal 112 in the form of a protrusion, and a recess 40 114 around the terminal 112. The outer edge 116 of the cap 110 may include a recess to receive an edge of the can 105 and seal the opening of the cylindrical wall 106.

Whilst a cylindrical type pseudo-cell has been depicted as an example, other cell form factors may be used. For example, the cell casing 102 may be prismatic. In such an instance, the wall of the pseudo-cell may include one or more substantially flat sides. A prismatic pseudo-cell may have a rectangular base and cap, as well as four vertical walls, forming a cuboid shape. Alternatively, the pseudo-cell may be in a pouch form factor. When the pseudo cell is formed as a pouch, the casing 102 may be formed from a flexible material. The casing of a pouch cell may be formed from two sheets of flexible material which are sealed to each other around their perimeters.

Turning now to figure 8, a cross section of the casing 102 in the pseudo-cell 100 of figure 7 is shown to more readily depict the contents. Disposed in the interior volume 104 is at least one heating element 120. The heating element 120 is disposed around an outer edge of the interior volume 104 such that it is in physical contact with an inner surface of the cell casing 102. The heating element 120 may be shaped such that it conforms to the shape of a portion of the cell casing 102. In this way, the heating element 120 is in physical contact with a substantial portion of the inner surface of the casing 102. Because of the physical contact of the heating element 120 with an inner surface of the cell casing 102, the heating element 120 may heat the casing 102 to a predictable degree. To explain further, if the heating element were disposed in the centre of the interior volume 104, or away from the inner surface of the cylindrical wall 106, then the transfer of heat energy from the heating element 120 to the cell casing 102 might be affected by the thermal properties of whatever sits between the heating element 120 and the casing 102. For example, where the heating element 120 may deliver a certain heating power to its surroundings, a layer of air between the heating element 120 and the cell casing 102 would slow the rate of temperature increase that can be applied to the cell casing 102. By providing the heating element 120 in physical contact with the cell casing 102, the maximum rate of temperature increase of the cell casing 102 provided by the heating element 120 is increased.

The heating element 120 may be a resistive heating element. When the heating element 120 is resistive, the heat generated by the heating element 120 may be controlled by supplying electrical power to the heating element 120 which then heats up by Ohmic heating. The heat power is directly proportional to the square of the current supplied to the heating element and the resistance of the heating element.

Alternatively, the heating element 120 may include a Peltier element to control the temperature of the cell casing 102 by the thermoelectric cooling effect.

In some embodiments, and as shown in figure 8, the electrochemical pseudo-cell 100 may include a plurality of heating elements 120. The plurality of heating elements 120 may be disposed in the interior volume such that they each cover a different portion of the inner surface of the cell casing 102. In the embodiment depicted in figure 8, the plurality of heating elements 120 are annular in shape, such that they conform to the cylindrical shape of the cylindrical wall 106. The plurality of heating elements 120 may be stacked such that together they cover the whole length of an inner surface of the casing 102.

By providing a plurality of heating elements 120, it is possible to vary the temperature of different portions of the cell casing 102 according to what is predicted by a cell model. For example, where the cell model predicts that the bottom of a cell will heat more than the top of the cell, the heating element at the relevant part of the cell may be supplied with more electrical power to locally increase the temperature at that part of the cell 100. By controlling the pseudo-cell 100 in this way, the build up of hot spots in a cell may be simulated and/or predicted.

The heating element 120 may comprise a spot heating element 122. In the case of a spot heating element, heating power is delivered to a particular point rather than distributed over a portion of the inner surface of the cell casing 102. In the example depicted in figure 8, a spot heating element 122 is located at the base 108 of the can 105, such that the temperature of the base 108 can be independently controlled. Additionally or alternatively, a spot heating element 122 may be located on the cap 110 such that the temperature of the cap can be independently controlled. Where a spot heating element 122 is located on one or both of the cap 110 and the base 108, this can be useful in simulating the heating effects of a cell which is cooled through the electrodes. This is of particular interest in the case of pouch cells which might be cooled directly through their tabs (terminals). A spot heating element 122 would be located in physical contact with each tab to independently heat the tabs.

The at least one heating element 120 may be attached to the interior surface of the casing 102. In this way, the at least one heating element 120 may be held in physical contact with the interior surface of the casing 102. The at least one heating element 120 may be attached to the interior surface of the casing by means of an adhesive. The adhesive may adhere and hold the heating element 120 in physical contact with the casing 102 as well as acting as a thermal conductor, transferring heat from the heating element 120 to the casing 102. Alternatively or additionally, the at least one heating element 120 may be attached to the interior surface of the casing 102 by one or more screws or one or more fixings. The one or more screws or one or more fixings may be arranged to hold the at least one heating element 120 against the interior surface of the casing 102. Alternatively or additionally, the at least one heating element 120 may be attached to the interior surface of the casing 102 by means of a resilient element disposed to compress the at least one heating element 120 against the interior surface of the casing 102. The resilient element may comprise a spring, a wedge, a bung, or some other mechanically resilient component which is located inside the heating element 120 and compresses the heating element 120 outwards into contact with the interior surface of the casing 102. In the case where an adhesive is not used, the heating element 120 may be directly applied to the interior surface of the casing 102, or a layer of thermally conductive compound may be applied to improve the thermal contact between the heating element 120 and the casing 102.

The electrochemical pseudo-cell 100 may comprise at least one temperature sensor 124 disposed in the interior volume 104. The temperature sensor 124 may be disposed in the interior volume 104 and in contact with the interior surface of the casing 102, such that a reading from the temperature sensor 124 may provide an indication of the temperature of the casing 102 at that point.

In some embodiments, there may be a plurality of temperature sensors 124 provided in the interior volume 104. A plurality of temperature sensors 124 may be distributed over the interior surface of the casing 102 such that readings from each of the temperature sensors 124 provide an indication of the distribution of temperature over the casing 102.

In some embodiments, there are a combination of a plurality of temperature sensors 124 and a plurality of heating elements 120. In combination, the plurality of temperature sensors 124 allow for the control of the temperature distribution over the whole casing 102 of the cell 100 by adjusting each heating element 120 individually.

The temperature sensor 124 may comprise a thermistor which changes resistance in response to a 10 temperature change. Alternatively or additionally, the temperature sensor 124 may comprise a thermocouple which produces a voltage which is dependent on the temperature by means of the Seebeck effect.

The pseudo-cell may include a controller 126. The controller is coupled to the at least one heating element 120 and the at least one temperature sensor 124. The controller is configured to control a current supplied to the at least one heating element 120 in response to a temperature recorded by the at least one temperature sensor 124 and a calculated heat flux from a simulation of the thermal response of an electrochemical cell. By taking a reading of the temperature of the at least one temperature sensor 124, the controller can read or record the temperature of the casing 102 of the pseudo cell 100. In the case where there are a plurality of temperature sensors 124 the controller 126 can read and record the temperature distribution over the casing 102 of the pseudo-cell 100.

In response to a simulation of the thermal response of an electrochemical cell, the controller may also adjust the electrical power being delivered to the at least one heating element 120 such that the heat flux from the external surfaces of the pseudo-cell 100 matches that of a simulated electrochemical cell. The heat flux from an electrochemical cell is the heat energy that would flow out of or into the external surfaces of the electrochemical cell. By matching the heat flux from the external surfaces of the pseudo-cell 100 to the external surfaces of the simulated electrochemical cell the thermal response of the electrochemical cell is accurately replicated.

The controller 126 may be disposed in the interior volume 104 of the pseudo-cell 100. The controller 126 may be electrically connected to the at least one heating element 120 and the at least one temperature sensor 124.

The pseudo-cell 100 may comprise a power source 128 disposed in the interior volume 104 of the pseudo-cell 100. The power source 128 may include a battery to provide electrical power for the controller 126 and/or the at least one heating element 120. Alternatively or additionally, the power source 128 may comprise a power supply (for example a DC power supply or a DC-DC converter) to provide electrical power for the controller 126 and/or the at least one heating element 120. When the power source 128 comprises a power supply, electrical energy may be provided from an external source. The power supply may be electrically connected to the external source by one or more electric wires. Alternatively, the power supply may be electrically connected to the external source via electrical contacts at the base 108 of the can 105 and the cap 110. Where the pseudo-cell is in a prismatic or a pouch form-factor, the power supply may be electrically connected to the external source via the positive and negative contacts or tabs of the pseudo-cell.

Figure 10 shows a schematic view of an arrangement of a pseudo-cell 200 in operation with at least one other pseudo-cell in a pack. The pseudo-cell 200 may include one or more heating elements 220, one or more temperature sensors 224, and a controller 226. The pseudo-cell 200 may include power electronics 230 which are configured to allow the controller 226 to control power supplied by a power supply 232 to the one or more heating elements 220. The power supply 232 may be onboard the pseudo-cell 200 or it may be disposed external to the pseudo-cell 200 and electrically connected to the one or more heating elements 220. The power supply 232 for the one or more heating elements 220 may be the same power supply used to power the controller 226, or it may be a separate power supply wherein the controller has its own power supply 234.

In operation, the controller 226 may be configured to simulate the thermal response of an electrochemical cell by determining an internal state of a virtual electrochemical cell, determining an electric current flow in the virtual electrochemical cell, calculating, based on the internal state and the electric current flow, a heat generation of the virtual electrochemical cell, calculating, based on the heat generation, a heat flux of the virtual electrochemical cell, determining a heat flux response of an electrochemical pseudo-cell to an electric current, and calculating an electrical power to be supplied to the electrochemical pseudo-cell for replicating the heat flux of the virtual electrochemical cell.

The virtual electrochemical cell may include a set of parameters which define the current internal state of a virtual electrochemical cell and a set of parameters which determine how that virtual electrochemical cell should respond to an external stimulus. The internal state of the virtual electrochemical cell may include one or more of temperature, internal resistance, state of health, state of charge, cell-wide distribution of temperature, cell-wide distribution of state of charge, cell-wide distribution of state of health, and cell-wide distribution of resistance to current flow.

The temperature may provide an indication of a temperature representative of the average temperature of the whole virtual electrochemical cell. The internal resistance may provide a value in milli Ohms representative of the internal resistance of the virtual electrochemical cell, as would be determined for a real cell by measuring the open circuit voltage and the voltage under load. The state of health of the virtual electrochemical cell may provide a value indicative of the ability of the virtual electrochemical cell to charge, store energy, and discharge. The state of health fraction of the virtual electrochemical cell may be a value between 0 and 1 which indicates whether the virtual electrochemical cell can operate at its full capacity (a state of health fraction of 1), at no capacity (a state of health fraction of 0), or at a diminished capacity (between 0 and 1). The state of charge of the virtual electrochemical cell may provide a value indicative of the total energy stored in the virtual electrochemical cell. The state of charge fraction of the virtual electrochemical cell may be a value between 0 and 1 which indicates whether the virtual electrochemical cell is holding the maximum amount of energy for that particular type of electrochemical cell (a state of charge fraction of 1), no energy (a state of charge fraction of 0), or some amount of energy less than the maximum for that particular type of cell (between 0 and 1).

For each internal state parameter, the virtual electrochemical cell may include a single parameter defining the bulk state of the cell, or the virtual electrochemical cell may include multiple parameters defining the cell-wide distribution of the state of the cell. For example, the internal state of the virtual electrochemical cell may include a cell-wide distribution of temperature. In this instance, the internal state may comprise a plurality of temperature values which indicate the temperature at different physical locations in the virtual electrochemical cell. For example, a first temperature may correspond to one end of the virtual electrochemical cell, a second temperature may correspond to another end of the virtual electrochemical cell, a third temperature may correspond to the centre of the virtual electrochemical cell, and so on.

The internal state of the virtual electrochemical cell may include a cell-wide distribution of state of charge, wherein the state of charge of multiple portions of the virtual electrochemical cell may be individually defined. In this way, one portion of the virtual electrochemical cell may charge or discharge faster than another portion of the virtual electrochemical cell. The cell-wide distribution of charge may reflect a real electrochemical cell wherein certain portions of the cell may charge or discharge faster or earlier than other portions of the cell.

The internal state of the virtual electrochemical cell may include a cell-wide distribution of state of health, wherein the state of health of multiple portions of the virtual electrochemical cell may be individually defined. In this way, one portion of the virtual electrochemical cell may have a diminished capacity to store, charge, or discharge relative to another portion of the virtual electrochemical cell. The cell-wide state of health of the virtual electrochemical cell may reflect a real electrochemical cell wherein certain portions of the cell may accumulate damage or age faster or earlier than other portions of the cell due to uneven charging/discharging or uneven temperature distribution.

The internal state of the virtual electrochemical cell may include a cell-wide distribution of resistance to current flow, wherein the resistance to current flow of multiple portions of the virtual electrochemical cell may be individually defined. In this way, one portion of the virtual electrochemical cell may have a different resistance to current flow than other portions. This difference may result in a variation in current flow in different portions of the virtual cell and subsequently different heat generation profiles.

The step of determining the current internal state of the virtual electrochemical cell may include, for a first time step, setting the initial conditions for the virtual electrochemical cell. The initial conditions may include an initial state of health, state of charge, and resistance to current flow (per cell or cell-wide distribution). The initial conditions may be set to full charge, and 100% health in order to simulate new, charged cells.

Alternatively, the initial conditions may be set so that the state of health of the virtual electrochemical cells are diminished (for example 85% health). In this way, the virtual electrochemical cell may simulate the operation of a real electrochemical cell which has degraded through use.

The step of determining the internal state of the virtual electrochemical cell may include detecting the temperature of an electrochemical pseudo-cell 200 from one or more temperature sensors 224 of the pseudo-cell 200 and updating the internal state of the virtual electrochemical cell to reflect the temperature of the pseudo-cell.

The step of determining the internal state of the virtual electrochemical cell may include updating a previous internal state of the virtual electrochemical cell from a previous value to a new value. The new value of the internal state may be determined based on the previous value of the internal state and the drive cycle applied to the virtual electrochemical cell. For example, the step of determining the state of charge of the virtual electrochemical cell may be based on the previous state of charge and a determination of the electric current flow in the virtual electrochemical cell.

The step of determining the internal state of the virtual electrochemical cell may include determining the virtual electrochemical cell resistance. The cell resistance of the virtual electrochemical cell may be determined from the parameters which define the virtual electrochemical cell, as is known to those skilled in the art. These parameters are determined through parameterisafion experiments and are themselves a function of the electrochemical cell's state of charge, state of health, and temperature.

The step of determining the electric current flow in the virtual electrochemical cell may include calculating the current flow based on a cell voltage of the virtual electrochemical cell and the power to be delivered by the cell or the battery pack according to a drive cycle.

Based on an internal state of the virtual electrochemical cell and the electric current flow in the virtual electrochemical cell, a heat generation of the virtual electrochemical cell is calculated. The heat generation may be derived from the square of the current flow in the cell multiplied by the internal resistance of the virtual electrochemical cell. The heat generation of the virtual electrochemical cell may be indicative of the heat generation that would occur in a real electrochemical cell subjected to the same conditions.

Based on the calculated heat generation of the virtual electrochemical cell, a heat flux of the virtual electrochemical cell is calculated. The heat flux from the external surfaces (boundaries) of the virtual electrochemical cell represents the heat energy per unit time that passes out of or into the electrochemical cell, not just the heat energy per unit time that is generated in the electrochemical cell. For example, where there is lOW of heat generation in a virtual electrochemical cell at 45 degrees Celsius in an ambient temperature of 20 degrees Celsius, 5W of the generated heat might be stored within the volume of the cell (thus contributing towards increasing the temperature of the cell) and 5W of the generated heat might be rejected to the environment, thus contributing to the heat flux from the external surfaces of the cell. Furthermore, the materials and structure of an electrochemical cell may affect the relationship between heat generation and heat flux from the external surfaces of the cell, for example where thicker or more thermally insulating materials are used to manufacture the cell, the heat flux from the external surfaces of the cell would lag more significantly behind the heat generation. Furthermore, the material and structure of the materials surrounding the electrochemical cell will affect the heat flux from the external surfaces of the cell. For example, more insulating material surrounding the cell would reduce the heat flux from the external surfaces of the cell, and a greater amount of the heat generation in the cell would be stored as heat energy, thus contributing to a sharper rise in temperature.

Based on the calculated heat flux, an electrical power to be supplied to the electrochemical pseudo-cell 200 for replicating the heat flux of the virtual electrochemical cell may be calculated. The electrochemical pseudo-cell 200 may have a particular response to electrical power to produce a desired heat flux from the external surfaces of the cell. The response of the pseudo-cell 200 to electrical power may be predetermined or may be calibrated through testing the heat flux output response of the pseudo-cell 200 to an electric current input. For example, a pseudo-cell 200 may be subjected to a range of electrical currents at a range of temperatures and the change in temperature measured. This profile may be used to replicate the heat flux of the virtual electrochemical cell. The materials chosen to manufacture the pseudo-cell 200 as well as the structure and layout of components such as the heating elements 226 may affect how the pseudo-cell 200 heats or cools in response to electrical power. The materials and structure used to make the casing of the pseudo-cell 200 may be chosen to closely match the materials used to make the casing of an equivalent real electrochemical cell.

The calculated electrical power may be supplied to the electrochemical pseudo-cell 200. By supplying the electrical powerto the pseudo-cell 200, the heat flux from the external surfaces of the virtual electrochemical cell is matched in the pseudo-cell 200. The controller 226 may control the power delivered to the at least one heating element 220 via the power electronics and the power supply 232 for heating elements.

Once the heat flux has been replicated in the pseudo-cell 200, the temperature of the pseudo-cell 200 will 5 change. The degree to which the temperature of the pseudo-cell will change will depend on a number of factors, including the effects of any cooling in a battery pack, the thermal insulation around the cells, the temperature of the battery pack, and the temperature of the adjacent pseudo-cells in the battery pack. In a subsequent timestep, the new temperature of the pseudo-cell 200 or pseudo-cells, or the cell-wide distribution of temperature in the pseudo-cell 200 or pseudo-cells may be measured using the temperature 10 sensor 224 or temperature sensors. The internal state of the virtual electrochemical cell may be updated based on the measurements of temperature from the pseudo-cell 200 and the determined current flow over the previous timestep.

An updated current flow in the virtual electrochemical cell may then be determined based on the power drive cycle, as well as a new heat generation of the virtual electrochemical cell, and a new heat flux of the virtual electrochemical cell. An updated electrical power to be supplied to the electrochemical pseudo-cell for replicating the updated heat flux of the virtual electrochemical cell may then be determined. The updated electrical power may be supplied to the electrochemical pseudo-cell 200. In this way, the electrochemical pseudo-cell simulates the thermal response of a real electrochemical cell under the conditions of the battery pack over multiple timesteps. As the drive cycle is followed, the temperature conditions of the pseudo-cells as well as the other internal states, such as cell-wide temperature distribution, state of health, cell-wide state of health, state of charge and cell-wide state of charge may be monitored. Should the simulation of the pseudo-cells result in a critical temperature being reached in any of the pseudo-cells, the method may generate a warning that thermal runaway or cell damage may occur in a real electrochemical cell pack.

Figure 11 shows a block diagram of the power electronics which may be used to control the heating element or heating elements. A transistor controls the flow of current from a power supply to ground through a resistance heater. The control input of the transistor may be controlled by the controller 226 of a pseudo-cell 200. In this way, large power requirements of the heating element or heating elements may be controlled by a low power component such as the controller 226.

The method of simulating the thermal response of an electrochemical cell may be carried out using a plurality of electrochemical pseudo-cells 200, such as would be found in a battery pack. To coordinate the operation of the plurality of pseudo-cells 200, there is provided a master controller 240 which monitors the conditions of the pack of pseudo cells 200 and coordinates the pack response to the drive cycle. The master controller 240 may be a separate controller located outside of the plurality of pseudo-cells 200, as shown in figure 10. Alternatively, the master controller 240 may be the onboard controller 226 of one of the plurality of pseudo-cells 200, as shown in figure 12. In either case, the master controller determines the power requirements of each pseudo-cell 200 in the pack based on the drive cycle and the voltage of the pack.

The master controller 240 then updates the controller 220 of each pseudo-cell 200 with the required current.

Figure 13 shows a flow diagram of a plurality of pseudo-cells operating in parallel in a pseudo-cell pack 300. The pseudo-cell pack 300 includes first, second, third, and fourth pseudo-cells (310, 320, 330, 340 respectively) connected in the pack in parallel. Each pseudo-cell (310, 320, 330, 340) measures a temperature from at least one temperature sensor as an input to a respective first, second, third and fourth virtual electrochemical cell model. Each pseudo-cell (310, 320, 330, 340) additionally determines a state of charge of the respective virtual electrochemical cell.

The state of charge of each virtual electrochemical cell may be updated based on the previous state of charge of the virtual electrochemical cell and the simulated current flow in the virtual electrochemical cell.

This method is known as coulomb counting, i.e. the passing of current (amps) multiplied by the time over which the current is passing (seconds) produces the unit of charge, from which state of charge is directly calculated by dividing by the electrochemical cell's nominal capacity. The current flow in the pack is determined by previous pack voltage and the power requirement of the drive cycle. The first pseudo-cell 310 may then determine a pseudo-voltage output of the first virtual electrochemical cell based on the current flow in the pack, the state of charge of the first virtual electrochemical cell, and the temperature of the first virtual electrochemical cell. The first pseudo-cell 310 may also determine the heat generation output of the first virtual electrochemical cell based on the current flow in the pack, the state of charge of the first virtual electrochemical cell, and the temperature of the first virtual electrochemical cell. Each of the second 320, third 330, and fourth 340 pseudo-cells may determine the respective outputs of pseudo-voltage and heat generation in the same way.

The first pseudo-cell 310 may then power a heating element to provide a heat flux which matches the heat flux from the heat generation output of the first virtual electrochemical cell. The second 320, third 330, and fourth 340 pseudo-cells may also power their respective heating elements.

In this way, the first 310, second 320, third 330, and fourth 340 pseudo-cells may together simulate the thermal response of a pack of real cells including their response within the pack thermally and electrically.

As shown in figure 13, the first 310, second 320, third 330, and fourth 340 pseudo-cells may each include a virtual electrochemical cell model. As depicted in figure 13, the virtual electrochemical cell model is an internal resistance battery model. Specifically, the internal resistance battery model simulates the cell as a voltage source and a resistor connected across an output. The internal resistance battery model represents the cell open circuit voltage as a function of the state of charge of the cell and the resistance as a function of temperature. Based on the current input or output from the cell, the internal resistance battery model provides an out put of cell voltage and a heat generation rate. The skilled person will appreciate that any suitable cell model may be used which uses the inputs of current, temperature, and cell state of charge to provide the outputs of cell voltage and heat generation rate. For example, the virtual electrochemical cell model may comprise a Thevenin model, a Randle model, a Thermal-electrochemical model, a Newman model, or a Single particle model.

Whilst four pseudo-cells are shown in figure 13, any number of a plurality of pseudo-cells may be assembled into a battery pack.

List of reference numerals 100, 200 Electrochemical pseudo-cell 102 Casing 104 Interior volume (defined by the casing) can 106 cylindrical wall 108 base cap 112 terminal 114 recess around the terminal 116 outer edge of cap 118 recess 120, 220 heating element 122 spot heating element 124, 224 temperature sensor 126, 226 controller 128 power source 230 power electronics 232 power supply for heating elements 234 power supply for controller 240 master controller 310 first pseudo-cell 320 second pseudo-cell 330 third pseudo-cell 340 fourth pseudo-cell

Claims

Claims 1 An electrochemical pseudo-cell comprising: a casing defining an interior volume, at least one heating element disposed in the interior volume, at least one temperature sensor disposed in thermal contact with the casing, and a controller coupled to the at least one heating element and the at least one temperature sensor, and configured to control a current supplied to the at least one heating element responsive to a) a temperature reading taken from the at least one temperature sensor, and b) a calculated heat flux from a simulation of the thermal response of an electrochemical cell.
2 The electrochemical pseudo-cell according to claim 1, wherein the casing is one of a cylindrical, a prismatic, or a pouch form factor
3 The electrochemical pseudo-cell of any preceding claim, wherein the at least one heating element is a resistive heating element.
4 The electrochemical pseudo-cell of any preceding claim, wherein the at least one heating element comprises a plurality of heating elements.
5. The electrochemical pseudo-cell of any preceding claim, wherein the at least one heating element is positioned in contact with an interior surface of the casing.
6 The electrochemical pseudo-cell of any preceding claim, wherein the at least one heating element is attached to an interior surface of the casing, optionally wherein the at least one heating element is attached to the interior surface of the casing by one or more of: an adhesive, one or more screws, one or more fixings, and compression against the interior surface by a resilient element.
7. The electrochemical pseudo-cell of any preceding claim, wherein the at least one heating element is an annular heating element and the casing is a cylindrical form factor.
8 The electrochemical pseudo-cell of any preceding claim, wherein the at least one temperature sensor is disposed in the interior volume, or wherein the at least one temperature sensor is disposed on an outer surface of the casing.
9 The electrochemical pseudo-cell of any preceding claim, wherein the at least one temperature sensor is disposed in thermal contact with the casing via a thermally conductive layer, and optionally wherein the thermally conductive layer is one or more of an adhesive layer, an air gap, or an epoxy layer.
10. The electrochemical pseudo-cell of any preceding claim, wherein the at least one temperature sensor comprises a plurality of temperature sensors.
11. The electrochemical pseudo-cell of any preceding claim, wherein the at least one temperature sensor is one of a thermistor, or a thermocouple.
12. The electrochemical pseudo-cell of any preceding claim, wherein the controller is disposed in the interior volume.
13. The electrochemical pseudo-cell of any preceding claim, further comprising a power source disposed in the interior volume.
14. The electrochemical pseudo-cell of claim 13, wherein the power source is one of a battery, a DC power supply, a DC-DC converter, a connector configured to connect to an external power supply, or a connector configured to connect to an external battery cycler.
The electrochemical pseudo-cell of any preceding claim, wherein the simulation of the thermal response of an electrochemical cell comprises: determining an internal state of a virtual electrochemical cell, determining an electric current flow in the virtual electrochemical cell, calculating, based on the internal state and the electric current flow, a heat generation of the virtual electrochemical cell, calculating, based on the heat generation, a heat flux of the virtual electrochemical cell, determining a heat flux response of an electrochemical pseudo-cell to an electric current, and calculating an electrical power to be supplied to the electrochemical pseudo-cell for replicating the heat flux of the virtual electrochemical cell.
16 The electrochemical pseudo-cell of any preceding claim, wherein the controller is configured to control the supply of electrical power to by one or both of controlling the resistance of the heating element, or controlling the voltage provided by the power supply.
17 A computer-implemented method of simulating the thermal response of an electrochemical cell comprising: determining an internal state of a virtual electrochemical cell, determining an electric current flow in the virtual electrochemical cell, calculating, based on the internal state and the electric current flow, a heat generation of the virtual electrochemical cell, calculating, based on the heat generation, a heat flux of the virtual electrochemical cell, determining a heat flux response of an electrochemical pseudo-cell to an electric current, and calculating an electrical power to be supplied to the electrochemical pseudo-cell for replicating the heat flux of the virtual electrochemical cell.
18 The electrochemical pseudo-cell of claim 14 or the method of claim 17, wherein the step of calculating a heat generation of the virtual electrochemical cell includes calculating the heat generation based on one of a Thevenin model, an internal resistance battery model, a Randle model, a thermal-electrochemical model, a Newman model, a single particle model, or a model which replicates the operation of the virtual electrochemical cell.
19 The electrochemical pseudo-cell of claims 15 or 18 or the method of claims 17 or 18, wherein the internal state of the virtual electrochemical cell includes one or more of a temperature, internal resistance state of health, state of charge, cell-wide distribution of temperature, cell-wide distribution of state of charge, cell-wide distribution of state of health, and cell-wide distribution of resistance to current flow.
The electrochemical pseudo-cell of claims 15 or 18 or the method of any one of claims 17 or 18, wherein the step of determining an electric current flow in the virtual electrochemical cell includes determining the electric current flow based on a drive cycle of the virtual electrochemical cell.
21. The electrochemical pseudo-cell of claims 15, 18, or 19 or the method of any one of claims 17 to 19, wherein the simulation of the thermal response of the electrochemical cell further comprises the step of supplying the calculated electrical power to an electrochemical pseudo-cell for replicating the heat flux of the virtual electrochemical cell.
22 The electrochemical pseudo-cell of claim 20, or the method of claim 20, wherein the simulation of the thermal response of the electrochemical cell further comprises the step of measuring the temperature of the electrochemical cell.
23 The method of any one of claims 17 to 21, wherein the electrochemical pseudo-cell is an electrochemical pseudo-cell according to any one of claims 1 to 16.
24. An electrochemical pseudo-cell pack comprising two or more electrochemical pseudo-cells according to any one of claims 1 to 16, or 18 to 20.
A computer-implemented method of simulating the thermal response of a plurality of electrochemical cells comprising: determining a first internal state of a first virtual electrochemical cell including a first temperature of the first virtual electrochemical cell, determining a second internal state of a second virtual electrochemical cell including a second temperature of the second virtual electrochemical cell, determining a first electric current flow in the first virtual electrochemical cell, determining a second electric current flow in the second virtual electrochemical cell, calculating, based on the first internal state and the first electric current flow, a first heat generation of the first virtual electrochemical cell, calculating, based on the second internal state and the second electric current flow, a second heat generation of the second virtual electrochemical cell, calculating, based on the first heat generation and the first temperature, a first heat flux of the first virtual electrochemical cell, calculating, based on the second heat generation and the second temperature, a second heat flux of the second virtual electrochemical cell, determining a heat flux response of a first and a second electrochemical pseudo-cell to an electric current, calculating a first electrical power to be supplied to the first electrochemical pseudo-cell for replicating the first heat flux of the first virtual electrochemical cell, calculating a second electrical power to be supplied to the second electrochemical pseudo-cell for replicating the second heat flux of the second virtual electrochemical cell.
26 The method of claim 25, further comprising the steps of arranging the first and second electrochemical pseudo-cells in a pack, supplying the first calculated electrical power to the first electrochemical pseudo-cell and supplying the second calculated electrical power to the second electrochemical pseudo-cell for replicating the first and second heat fluxes.
27. The method of claim 26, further comprising the step of measuring the thermal response of at least one of the first and second electrochemical pseudo-cells in the pack.