Process for the impedentiometric calculation and analysis of impedance variation of electrochemical cells by means of artificial intelligence

Abstract

A process for the impedentiometric calculation and analysis of the impedance variation of electrochemical cells under dynamic conditions with an applied load, is described. The impedance value of an electrochemical cell is obtained by means of an artificial intelligence process that is carried out by an artificial neural network.

Description

[0001] “PROCESS FOR THE IMPEDENTIOMETRIC CALCULATION AND ANALYSIS OF IMPEDANCE VARIATION OF ELECTROCHEMICAL CELLS BY MEANS OF ARTIFICIAL INTELLIGENCE”

[0002] DESCRIPTION

[0003] Field of the invention

[0004] The present invention generally refers to the calculation and analysis of the impedance of an electrochemical cell under dynamic conditions, i.e. under working conditions in which the electrochemical cell is connected to a load. A process for continuously and constantly monitoring the impedance of an electrochemical cell during its operation may be used, e.g., to obtain information useful for determining the state of charge, also known as State of Charge (SoC), and the degradation conditions, also known as State of Health (SoH), in rechargeable batteries, fuel cells or other types of electrochemical cells in general.

[0005] State of the art

[0006] An electrochemical cell, as well as any electrical / electronic system, tends to oppose the passage of current.

[0007] This opposition is defined “impedance” and its value consists of a real part Zr (resistance), always present, and an imaginary part Zi (reactance) present only when working in alternating current.

[0008] From the point of view of an electrochemical cell, there are several factors that may influence its impedance, such as resistance to transport of a charge in solution, capacitive reactance of the double diffusion layer between electrode and solution and / or overvoltage for the electronic transfer between molecule and electrode.

[0009] In general, an in-depth impedance analysis may include discriminating, within the overall impedance of an electrochemical cell, each contribution and assigning it to the corresponding stage (resistive, capacitive, inductive) of an “equivalent circuit” corresponding to the electrochemical system in question, such as to be able to provide a simulated frequency-based impedance spectrum, depending on the frequency, that corresponds to the experimental data.

[0010] Historically, the calculation of the impedance of an electrochemical cell in its two components Zr and Zi can be carried out with a conventional calculation, i.e. by evaluating the frequency response of the same cell to a sinusoidal signal because, as you know, the imaginary part Zi changes with the variation of the same frequency. This is therefore a time-consuming and laborious calculation as it must be carried out under ideal conditions and at different frequency regimes. This complexity naturally increases in cases where the impedance of each electrochemical cell has to be calculated and analysed in a group of cells electrically connected with each other, such as e.g. electrochemical cells of rechargeable batteries.

[0011] The patent application WO2023145322A1 relates to methods and equipment for the analysis of batteries consisting of multiple cells connected in series. A resistor is connected in parallel to each battery cell, whereas a circuit breaker allows to apply a damped oscillating signal to the resistor. The analysis equipment is configured to detect the real part of the impedance of each cell and to determine machine learning data in such a way as to obtain the state of degradation of the battery from this data. In this case, it appears that the determination of the state of degradation takes place in quite a long time, after many cycles of charging and discharging the battery.

[0012] The patent application JP2022080182A describes a system to balance the charge of each cell of a battery depending on the degradation conditions of each cell, in order to avoid overcharging degraded cells. Each cell includes a resistor connected in parallel to the cell and a circuit breaker which allows to discharge a possible overcharge in case the cell is degraded. A circuit measures the impedance of each cell before and after balancing. Even in this case, although theoretically expected, it is not specified how the measurement of impedance during battery use can be carried out.

[0013] Synthesis of the invention

[0014] Having said that, an object of the present invention is to provide a process for carrying out the impedentiometric calculation and analysis of the impedance variation of electrochemical cells under dynamic conditions with an applied load.

[0015] Another object of the present invention is to provide a process which allows to carry out the impedentiometric calculation and analysis of the impedance variation of each electrochemical cell in a group of electrochemical cells electrically connected with each other.

[0016] A further object of the present invention is to provide a process which allows to carry out the impedentiometric calculation and analysis of the impedance variation of each electrochemical cell connected to a load continuously and instantaneously, within intervals of a few milliseconds.

[0017] Additionally, another object of the present invention is to provide a process which allows to carry out the impedentiometric calculation and analysis of the impedance variation of each electrochemical cell while limiting the computational calculation time necessary to provide meaningful and accurate real-time measurements of the state of charge and / or degradation of each electrochemical cell under dynamic conditions or, in other words, during the use of each electrochemical cell connected to a load.

[0018] These objects are achieved by means of a process according to claim 1. Further characteristics and advantages of the present invention are set forth in the dependent claims.

[0019] A process for the impedentiometric calculation and analysis of the impedance variation of electrochemical cells under dynamic conditions with a load applied is therefore proposed, wherein the dynamic conditions provide for an operating electric voltage at the ends of each electrochemical cell and an operating electric current which flows through each electrochemical cell, and wherein a preliminary step of static impedance calculation is carried out on each of said cells, under different temperature and state of charge conditions, under open circuit conditions, or anyway free of load, for the training of an artificial neural network which performs an artificial intelligence process.

[0020] According to a possible embodiment, the process comprises the steps of: a) providing a group of electrochemical cells electrically connected in series with each other, wherein each electrochemical cell is electrically connected in parallel to a drain resistor and at least one control-actuated circuit-breaker device is connected in series to the drain resistor to enable and disable the connection of the drain resistor to the respective electrochemical cell; b) detecting at least the voltage at the ends of each electrochemical cell and at least the current which flows through each electrochemical cell under dynamic conditions; c) controlling the opening and closing of the circuit-breaker device of each electrochemical cell with opening and closing cycles at the pre-set at least four frequencies for a pre-set time interval (At) in order to distribute a fraction of the current which flows through the respective electrochemical cell and supply it to the respective drain resistor, wherein the opening and closing cycles of the circuitbreaker device are controlled by digital signals of constant amplitude and frequency; d) detecting the variation in the current value which flows in each electrochemical cell during the pre-set time interval (At); e) obtaining the impedance value of each electrochemical cell, by calculating at least its value of the real part of the impedance for each of the at least four pre-set frequencies during the opening and closing cycles of the circuit-breaker device, wherein the artificial intelligence process obtains the impedance value of each electrochemical cell by an artificial neural network that receives as input at least the value of the current entering each electrochemical cell, the value of the current drained by each electrochemical cell, the variation of the value of the current which passes through each electrochemical cell, the duration of the pre-set time interval in which each opening and closing cycle of the circuit-breaker device is performed, and wherein the artificial intelligence process results in new values of the at least four pre-set frequencies of opening and closing of the circuit-breaker device to estimate the impedance of each cell as if it were under an open-circuit condition or free of load.

[0021] In order to obtain significant results in an impedentiometric analysis, certain basic conditions are necessary, namely:

[0022] • Linearity: this condition is only achievable when the amplitude of the input wave signal is small enough to allow the system to remain unchanged;

[0023] • Stationarity: measurements must be independent of the time at which they are performed;

[0024] Finiteness: o The real Zr and imaginary Zi parts of the impedance must assume finite values in the frequency range under investigation; o a single set of input data must correspond to a single output result; o memory effect phenomena must not occur;

[0025] • Observability: phenomena that want to be observed must be visible in the frequency range used.

[0026] In addition, if the cell has some particular electrochemical characteristics:

[0027] • additivity of the Faraday current and the double-layer loading current;

[0028] • electroneutrality of the electrolyte solution;

[0029] • lack of convective and migration phenomena, i.e. no changes in local concentrations other than those due to diffusion and charge transfer phenomena; then it can be deemed to be dealing with a “causal” system, i.e. any change in the “cell system” is caused solely and exclusively by the input signal. Therefore, the complete description of the “cell system” can take place even if only one (real or imaginary) part of the impedance is known, as these, in a causal system, are related to each other (Kramers-Kronig Relation). This aspect is a fundamental element in the calculation of impedance and the analysis of its variation over time and space, i.e. under different conditions of use.

[0030] The analysis of the impedance variation of an electrochemical cell over time and space (environmental conditions, time of use, stress, mechanical and geometric stability, etc.) allows the deviation of the impedance of the electrochemical cell from the initial value to be verified and thus to provide, for example, an indication of the state of health and / or to predict its state of health by simulating a certain dynamic condition with an applied load. The comparison of the piece of data obtained with the initial data of the electrochemical cell (initial characterisation) leading to the identification of the degradation state of the same is a further step that can be performed at a later step.

[0031] The process according to the invention requires steps a) to e) to be repeated a pre-set number of times at different at least four pre-set opening and closing frequencies of the circuit-breaker device, which are obtained by the artificial neural network.

[0032] In an embodiment, the step c) of the process is performed in a pre-set period of time in which the operating electric current which flows through each electrochemical cell is constant.

[0033] The step e) of the process may further provide for calculating the value of the imaginary part of the impedance for each of the at least four pre-set frequencies in the opening and closing cycles of the circuit-breaker device.

[0034] The artificial neural network can also receive other information as input, e.g. the value of the pressure in each of the electrochemical cells in case they are certain types of electrochemical cells not previously pressurised, and the value of the temperature in each of the electrochemical cells.

[0035] In an embodiment of the process according to the present invention, at least during the preliminary step of static impedentiometric calculation on each of the cells, the at least four frequencies are in the range between 1 Hz and 100 Hz.

[0036] The limitation to only four frequencies allows an accurate calculation of the impedance of each cell to be obtained in a very short time, in the order of milliseconds, with a very little margin of error, around 5%, and an estimate of the degradation of each cell comparable with the initial value, i.e. that calculated one under open circuit conditions or, in any case, without load. A higher number of frequencies could provide greater accuracy but would significantly burden the computational calculation necessary to determine the impedance, and thus the calculation times of the values determined substantially in real-time.

[0037] For each of the at least four frequencies, the corresponding points on the resultant curve in a Bode plot in terms of frequency and phase and / or on the resultant curve of a Nyquist plot in terms of real and imaginary parts of the impedance may be determined.

[0038] For each of the points identified, the first derivative of the curve resulting on the Bode plot and / or the curve resulting on the Nyquist plot is determined to determine the characteristics of each tangent passing through the points of inflection on each of the curves. This may allow the margin of error, and thus the accuracy of the impedentiometric calculation, to be further limited without making computational calculation too heavy.

[0039] Neural networks are mathematical models inspired by the structure of the human brain, which are composed of a series of nodes called artificial neurons that are connected with each other through connections called synapses. These connections, in turn, are equipped with a weight, which is modified during the training of the artificial neural network on the basis of input data. The ability of neural networks to learn patterns and make decisions on the basis of these patterns makes them a very powerful tool in different technology applications. An artificial neural network is easily implemented with the programming languages normally used for microprocessors and has the characteristic of being able to continue learning even after the preliminary learning step.

[0040] Brief description of the drawings

[0041] Further details, characteristics and benefits of the present invention will be more evident from the following description of some embodiments illustrated by way of non-limiting example, in the accompanying drawings, wherein:

[0042] - Figure 1 is a schematic view of an electrochemical cell that can be subjected to the process of the present invention;

[0043] - Figure 2 is a schematic view of a group of electrochemical cells, such as those in Figure 1, electrically connected in series with each other;

[0044] - Figure 3 is a schematic view depicting an example of an artificial neural network and the respective inputs / outputs according to the process of the present invention.

[0045] Detailed description

[0046] Figure 1 shows the schematic diagram of an electrochemical cell C subjected to a continuous voltage Vdc, which is electrically connected in parallel to a drain resistor Rd. A circuit-breaker device 15 is connected in series to the drain resistor 12 and can be operated to enable and disable the connection of drain resistor Rd, of known resistance, to the respective electrochemical cell 10. The circuit-breaker device 15 can, for example, be implemented by a MOSFET-type device controlled by a sinusoidal signal S of pre-set frequency. This way, when the circuit-breaker device 15 is enabled to close the circuit, a fraction Id of the current I which flows in electrochemical cell C is drawn through the drain resistor Rd.

[0047] The basic idea of the process of the present invention is to create frequency perturbations during those fractions of time in which the current I, which flows in the electrochemical cell C, is “stationary”, i.e. substantially constant. In this condition, a controlled perturbation can therefore be introduced by means of a discharge circuit consisting for example of the frequency-controlled MOSFET 15 and a resistive load consisting of the resistor Rd. In this condition, even if I»0, the drained current fraction Id can be easily measured through specific sensors (e.g. Hall sensors), thus allowing at least different values of Zr and Zi at different frequencies to be acquired.

[0048] Figure 2 shows a group 10 of a certain number “n” of electrochemical cells Ci, C2...Ck. ..Cn electrically connected in series with each other. Each electrochemical cell Ck of the group 10 is the same as the one shown in Figure 1 and is therefore equipped with a respective drain resistor Rdk (with k between 1 and n, unless otherwise specified herein and below) and a respective circuit-breaker device 15. Each circuit-breaker device 15, combined with each electrochemical cell Ck, is controlled simultaneously by the same sinusoidal signal S.

[0049] When the group 10 of electrochemical cells Ck is under dynamic conditions with an applied load, the group 10 has an operating electric voltage V given by the sum of the voltages Vk at the ends of each electrochemical cell Ck, and an operating electric current I which flows through each electrochemical cell Ck, from which the respective currents Idk will be drawn through the respective drain resistor Rdk.

[0050] The operating electric voltage V, the operating electric current I, the voltage Vk on each electrochemical cell Ck, and the current Ik which flows through each electrochemical cell are detected continuously, or at least during the periods of time when the impedance of each electrochemical cell Ck has to be measured.

[0051] The process provides for controlling the opening and closing of the circuitbreaker device 15 of each electrochemical cell Ck with opening and closing cycles at pre-set frequencies, e.g. for at least four pre-set frequencies, for a pre-set time interval At in order to distribute a fraction Idk(t) of the current Ik(t) which flows through the respective electrochemical cell Ck and supply it to the respective drain resistor Rdk. The variation in the current value Ik which flows in each electrochemical cell Ck during the pre-set time interval At is therefore detected. This cycle is repeated two or more times, by applying a sinusoidal signal S to the different at least four frequencies in order to control the circuit-breaker device 15 during the opening and closing.

[0052] It is thus possible to obtain the value of the impedance of each electrochemical cell Ck by calculating at least the value of the real part Zr thereof for each of the pre-set frequencies during the opening and closing cycles of the circuitbreaker device. The value of the imaginary part Zi for each of the applied frequencies is in any case related to the value of the part Zr and can be obtained directly or indirectly during the calculation.

[0053] Figure 3 schematically depicts an artificial neural network 100 that can be used to perform the process according to the present invention. The circles in the diagram correspond to the “neurons” of a biological neural network, whereas the connection lines between neurons are the equivalent of biological synaptic connections. The “neurons” are organised into several layers among which an input layer 110, that receives input data and may consist of one or more neurons, one or more intermediate layers 115 that process the data received from the input layer 110 or from an intermediate layer 115 immediately preceding it and, finally, an output layer 120 that is the last layer of the artificial neural network and is configured to return results, can be identified. The latter may also consist of one or more neurons, depending on the objective and the results intended to be achieved by the artificial neural network. The elements that make up the layers 110, 115 and 120 are implemented by means of a mathematical algorithm.

[0054] An artificial neural network 100, such as that depicted in Figure 3 as an example, is defined as “fully connected multi-level” and is the most significant model for data processing according to the Hecht-Nielsen Theorem because the fact that a piece of data (information) is processed in a distributed manner by a multitude of units leads to two significant consequences: resistance to noise and resistance to degradation. Noise resistance means that the network is capable of providing satisfactory results even under uncertain, incomplete or slightly incorrect input information conditions. Resistance to degradation means that the network is capable of ‘resolving’ the input piece of information even in the event of failure or malfunctioning (this is only the case if the artificial neural network is of the hardware type and not exclusively of the software type). The impedance value of each electrochemical cell is obtained by means of an artificial intelligence process carried out by an artificial neural network 100 which receives as input, for each electrochemical cell Ck, an information set of Dk(t) which may comprise the following data:

[0055] • Idk(t): Current value drained from the cell Ck at the instant t;

[0056] • Ik(to): Total input current value to the cell Ck at the time to;

[0057] • Ik(ti) : Total input current value to the cell Ck at the time ti;

[0058] • to: Instant to;

[0059] • ti: Instant ti (where ti - to = At);

[0060] • co: Sinusoidal signal pulse S (given by 2TTV):

[0061] • v: Frequency of the sinusoidal signal S.

[0062] The artificial neural network can also receive further information as input, e.g. the value of the pressure in each of the electrochemical cells Ck, in case they are certain types of electrochemical cells not previously pressurised, and the value of the temperature in each of the electrochemical cells Ck.

[0063] By varying the frequency of the sinusoidal signal S over a pre-set number of calculation cycles, the artificial neural network 100 therefore constantly updates the impedance value thus obtained under operating conditions. In particular, the artificial neural network 100 can therefore output, at each calculation cycle, the values of the real part Zrk(t) and Zik(t) of each cell Ck. These values can therefore be stored in one or more memory units to be then used in the impedentiometric analysis and the assessment of the conditions of each electrochemical cell Ck over time. The artificial neural network receives input values of the at least four frequencies and can calculate a set of at least four other frequencies to be used in the subsequent impedentiometric calculation steps of each cell.

[0064] The learning step of the artificial neural network 100 is a real path that is carried out in several steps which allow the artificial neural network 100 to learn to calculate Zr and Zi under certain conditions that, as mentioned above, are considered of substantial stability. The learning step is performed by comparing the result of the artificial neural network 100 with the values of Zr and Zi obtained according to the conventional calculation, all this on a sufficient number of examples prepared beforehand and under laboratory conditions, e.g. by carrying out the calculation under open circuit conditions.

[0065] In practice, the (multi-level) artificial neural network 100 is prepared with suitable input values and as output values Zr and Zi. A series of examples are submitted to the artificial neural network 100 by providing inputs and comparing the output result values with the values of Zr and Zi obtained by means of the conventional calculation. Whenever the network fails, Back-Propagation process is performed, i.e. the values, or “weights”, of the artificial synaptic connections are adjusted so as to bring the result provided by the network closer to the actual result calculated in the conventional way. This process is performed cyclically until the artificial neural network 100 reaches a pre-set degree of “capability1”, understood as the capability to provide satisfactory results, e.g. allowing the artificial neural network 100 a margin of error between 0.2% and 0.8% under open circuit conditions.

[0066] It is clear and evident that the greater the number and type of examples used in the learning step, the greater the capability of the artificial neural network to carry out the calculation under any dynamic condition and whatever inputs are provided.

[0067] It is also evident that during the learning step, it is also necessary to introduce examples of “impossible” or wrong calculations a priori, so that the network can not only perform the calculation (when possible) but also reject the request if the input parameters do not correspond to values that can lead to results

[0068] Several changes may be made to the above description set forth by way of example without departing from the scope of the present invention. For example, the direction of voltages and currents may also be opposite the direction depicted in the figures.

Claims

CLAIMS1. A process for the impedentiometric calculation and analysis of the impedance variation of electrochemical cells under dynamic conditions with a load applied, said dynamic conditions providing for an operating electric voltage at the ends of each electrochemical cell and an operating electric current which flows through each electrochemical cell, wherein a preliminary step of static impedentiometric calculation is carried out on each of said cells under different temperature conditions and state of charge under open circuit conditions, or anyway free of load, for the training of an artificial neural network which performs an artificial intelligence process, the process being characterised by the steps of: a) providing a group of electrochemical cells electrically connected in series with each other, wherein each electrochemical cell is electrically connected in parallel to a drain resistor and at least one control-actuated circuit-breaker device is connected in series to the drain resistor to enable and disable the connection of the drain resistor to the respective electrochemical cell; b) detecting at least the voltage at the ends of each electrochemical cell and at least the current which flows through each electrochemical cell under dynamic conditions; c) controlling the opening and closing of said circuit-breaker device of each electrochemical cell with opening and closing cycles at pre-set at least four frequencies for a pre-set time interval (At) in order to distribute a fraction of the current which flows through the respective electrochemical cell and supply it to the respective drain resistor, wherein said opening and closing cycles of said circuitbreaker device are controlled by digital signals of constant amplitude and frequency; d) detecting the variation in the current value which flows in each electrochemical cell during said pre-set time interval (At); e) obtaining the impedance value of each electrochemical cell, by calculating at least its value of the real part of the impedance for each of said at least four pre-set frequencies during the opening and closing cycles of said circuit-breaker device, wherein said artificial intelligence process obtains the impedance value of each electrochemical cell by an artificial neural network that receives as input at leastthe value of the current entering each electrochemical cell, the value of the current drained by each electrochemical cell, the variation of the value of the current which passes through each electrochemical cell, the duration of the pre-set time interval in which each opening and closing cycle of said circuit-breaker device is performed, and wherein said artificial intelligence process results in new values of said at least four pre-set frequencies of opening and closing of said circuit-breaker device to estimate the impedance of each cell as if it were under an open-circuit condition or free of load.

2. The process according to claim 1, wherein said steps a) to e) are repeated a pre-set number of times at the different at least four pre-set frequencies for the opening and closing of said circuit-breaker device, which are obtained by said artificial neural network.

3. The process according to claim 1, wherein said step c) is carried out in a pre-set period of time (At) in which the operating electric current which flows through each electrochemical cell is constant.

4. The process according to claim 1, wherein said step e) further provides for calculating the value of the imaginary part of the impedance for each of said at least four pre-set frequencies in the opening and closing cycles of said circuit-breaker device.

5. The process according to claim 1, wherein said artificial neural network further receives as input the pressure value in each of said electrochemical cells.

6. The process according to claim 1, wherein said artificial neural network further receives as input the temperature value in each of said electrochemical cells.

7. The process according to claim 1, wherein said circuit-breaker device of each electrochemical cell consists of a frequency-controlled MOSFET-type device.

8. The process according to claim 1 wherein, at least in the preliminary step of static impedentiometric calculation on each of said cells, said at least four frequencies are in a range between 1 Hz and 100 Hz.

9. The process according to claim 1 wherein, for each of said at least four frequencies, the corresponding points on the resultant curve in a Bode plot in terms of frequency and phase and / or on the resultant curve of a Nyquist plot in terms of thereal and imaginary parts of the impedance are determined.

10. The process according to claim 9 wherein, for each of said points, the first derivative of the resultant curve on the Bode plot and / or the resultant curve on the Nyquist plot is also determined to determine the characteristics of each tangent passing through the points of inflection on each of said curves.

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