System and method for estimating electrical characteristics of an electrolytic cell

Abstract

The device for estimating the electrical properties of an electrolytic cell (103) comprises a data processing system (102) for estimating electrical values, such as the membrane resistance of the electrolytic cell based on the differential voltage, the current (I) and the initial value, and the decay time constant of the double layer capacitance voltage of the electrolytic cell during shutdown of the electrolytic cell. The differential voltage is the difference between the voltage (U) of the electrolytic cell and the total reversible voltage of the electrolytic cell. The initial value and the decay time constant of the double layer capacitance voltage are estimated based on the value of the differential voltage when the current is zero and the differential voltage is equal to the double layer capacitance voltage. The electrical values ​​can be estimated even when it is not possible to gradually shut off the current in the electrolytic cell.

Description

Technical Field

[0001] The present disclosure relates to an apparatus and a method for estimating electrical characteristics of an electrolytic cell. Further, the present disclosure relates to a computer program for estimating electrical characteristics of an electrolytic cell. Further, the present disclosure relates to an electrolysis system.

Background Art

[0002] An electrochemical process in which a material interacts with an electrode may be an electrolysis process such as water electrolysis in which electrical energy is converted into chemical energy carried by hydrogen gas and oxygen gas is produced as a by-product. A direct current is passed between two electrodes to generate hydrogen gas at the cathode, i.e., the negative electrode, and oxygen gas at the anode, i.e., the positive electrode. Faraday's law of electrolysis states that the production of hydrogen gas is proportional to the charge transferred at the electrode. For this reason, the average value of the direct current determines the production rate of hydrogen gas.

[0003] In many cases, it is necessary to estimate the electrical characteristics of an electrolytic cell. The electrical characteristics may include, for example, ohmic resistance, i.e., membrane resistance, charge transfer resistance, and double layer capacitance of the electrolytic cell of the electrolytic cell. For example, the reversible decomposition of the electrolytic cell is related to an increase in the above-mentioned membrane resistance. This makes the online estimation of membrane resistance particularly attractive. Even more information is described in publications such as Non-Patent Document 1 (I. Dedigama, P. Angeli, K. Ayers, J. Robinson, P. Shearing, D. Tsaoulidis and D. Brett, "In-situ diagnostic techniques and electrochemical impedance spectroscopy for the characterization evaluation of flow visualization of molecular electrolyte membrane water electrolytic cells", Int. J. Hydrogen Energy, 39, 9, 2014, pages 4468-4482). The estimated electrical characteristics of the electrolytic cell can be used to control the operation of the electrolytic cell to improve efficiency and / or extend the life of the electrolytic cell.

[0004] There are many known methods for estimating the electrical characteristics of an electrolytic cell. For example, identification of a polarization curve, electrochemical impedance spectroscopy "EIS", current mapping "CM", and current interruption "CI". Identification of a polarization curve shows the current-voltage behavior of an electrolytic cell or cell stack and can be used to evaluate the overall performance of the electrolytic cell. To collect polarization curve data, it is necessary to examine steady-state operation over the entire range of operating conditions, i.e., at different current densities. For this reason, it takes time and can be cumbersome to implement in combination with an industrial electrolytic cell.

[0005] In electrochemical impedance spectroscopy "EIS", a direct current with an alternating component superimposed is supplied to the electrolytic cell. In this method, although detailed small-signal level information regarding the performance of the electrolytic cell may be obtained, it is necessary to be able to add an appropriate alternating component to the direct current and measure the current and voltage with high precision at a high sampling frequency. For this reason, the application of electrochemical impedance spectroscopy to industrial megawatt-scale electrolytic cells faces significant challenges compared to the identification of a single cell by electrochemical impedance spectroscopy.

[0006] In the current mapping "CM" method, the local current density distribution is analyzed. In some current mapping methods, it is necessary to physically modify the electrolytic cell structure so that the current distribution between electrolytic cell areas can be measured. A known non-invasive current mapping method is presented in Non-Patent Document 2 (K.-H. Hauer, R. Potthast, T. Wuester, "Magnetotomography - A New Method for Analyzing Performance and Quality", J. Power Sources, 143, 1, 2005, pp. 67 - 74). This non-invasive current mapping method is based on the three-dimensional measurement of the magnetic flux induced by the flow of current in the electrolytic cell. The non-invasive current mapping method requires additional equipment and its accuracy may be insufficient for industrial electrolytic cells.

[0007] The current interruption "CI" method consists of two parts: 1) the natural voltage response that suddenly stops the steady-state operation of the electrolyzer and records the voltage response, and 2) the current switching technique. In the first part, the membrane resistance is estimated, and then in the second part, the charge transfer resistance and double-layer capacitance are identified. In some cases, in addition, the Warburg impedance that plays a role at high current densities is identified. More information is described, for example, in Non-Patent Document 3 (J. van der Merwe, K. Uren, G. van Schoor, D. Bessarabov, "Development of a Characterization Tool for PEM Electrolyzers", Int. J. Hydrogen Energy, 39, 26, 2014, pp. 14212-14221). Especially in industrial megawatt-scale electrolyzers, the current drop rate is limited by the safe throughput rate of the rectifier and the di / dt limitation due to the inductance of the output filter of the rectifier. Since it is impossible to perform current interruption step by step in combination with industrial electrolyzers, the conventional current interruption "CI" method cannot estimate electrical characteristics.

Prior Art Documents

Non-Patent Documents

[0008]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Summary of the Invention

[0009] In the following, a simplified summary is presented to provide a basic understanding of some aspects of various embodiments. The summary is not an extensive overview of the present invention. It is not intended to identify key or critical elements of the present invention nor to delineate the scope of the present invention. The following summary merely presents some concepts in a simplified form as a prelude to a more detailed description of exemplary and non - limiting embodiments.

[0010] According to the present invention, a new device for estimating the electrical characteristics of an electrolyzer is provided. The device according to the present invention includes current and voltage sensors for measuring the voltage applied to the electrolyzer and the current of the electrolyzer. Further, the device includes - a step of storing data indicating a value u0 of the differential voltage prevailing at the start of shutdown of the electrolyzer and a value I0 of the current of the electrolyzer prevailing at the start of shutdown, wherein the differential voltage is the difference between the voltage applied to the electrolyzer and the total reversible voltage of the electrolyzer, - in response to the situation where the current has reached zero, estimating a value τ of the time constant of the exponential decay of the double - layer capacitance voltage of the electrolyzer and an estimated value u 0C of the double - layer capacitance voltage prevailing at the start of shutdown, based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double - layer capacitance voltage, - i) estimating the membrane resistance R m of the electrolyzer as R m =(u0 - u 0C ) / I0, ii) estimating the charge - transfer resistance R ct of the electrolyzer as R ct =u 0C / I0, and iii) the double - layer capacitance C dlto C dl = τ I 0 / u 0C performing at least one of the steps of calculating: and a data processing system for performing the same is provided.

[0011] Membrane resistance R m and / or charge transfer resistance R ct and / or double layer capacitance C dl can be estimated even when it is impossible to interrupt the current in the electrolytic cell stepwise. Combining with an industrial electrolytic cell where the current drop rate is limited by the safe throughput rate of the rectifier and the di / dt limitation due to the inductance of the rectifier output filter, it is difficult or even impossible to perform stepwise current interruption.

[0012] According to the present invention, in addition, - an electrolytic cell, - a rectifier circuit for receiving one or more alternating voltages and supplying direct current to the electrodes of the electrolytic cell, - a controller for controlling the direct current supplied to the electrodes of the electrolytic cell, - an apparatus according to the present invention for estimating the electrical characteristics of the electrolytic cell, a new electrolysis system is provided.

[0013] The electrolytic cell may be, for example, an alkaline water electrolytic cell in which the electrodes operate in an alkaline liquid electrolyte that may contain, for example, aqueous potassium hydroxide "KOH" or aqueous sodium hydroxide "NaOH", but it does not necessarily have to be so.

[0014] According to the present invention, in addition, a new method for estimating the electrical characteristics of an electrolytic cell is provided. The method according to the present invention includes - a step of storing data indicating the value u0 of the differential voltage prevailing at the start of the shutdown of the electrolytic cell and the value I0 of the current of the electrolytic cell prevailing at the start of the shutdown, wherein the differential voltage is the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell, - In response to the situation where the current has reached zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage prevailing at the start of shutdown 0C are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage, and - i) estimating the membrane resistance R m of the electrolytic cell as R m =(u0 - u 0C ) / I0, ii) estimating the charge transfer resistance R ct of the electrolytic cell as R ct =u 0C / I0, and iii) estimating the double-layer capacitance C dl of the electrolytic cell as C dl =τ I 0 / u 0C , and including at least one of the steps of calculating

[0015] If the electrolysis system comprises means for, for example, electrochemical impedance spectroscopy "EIS" and / or another estimation method, the method according to the invention can be used in combination with electrochemical impedance spectroscopy and / or other estimation methods.

[0016] According to the invention, moreover, a new computer program for estimating the electrical characteristics of an electrolytic cell is provided. In the computer program according to the invention, a programmable processor - receives data indicating the voltage applied to the electrolytic cell and the current of the electrolytic cell from voltage and current sensors, and - stores data indicating a value u0 of the differential voltage prevailing at the start of shutdown of the electrolytic cell and a value I0 of the current of the electrolytic cell prevailing at the start of shutdown, the differential voltage being the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell, - In response to the situation where the current has reached zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage prevailing at the start of shutdown 0Ccalculating based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage; - i) the membrane resistance R of the electrolytic cell m is estimated as R m =(u0 - u 0C ) / I0, ii) the charge transfer resistance R ct of the electrolytic cell is estimated as R ct = u 0C / I0, and iii) the double-layer capacitance C dl of the electrolytic cell is estimated as C dl = τ I 0 / u 0C ; and performing at least one of the steps of calculating; and computer-executable instructions for controlling to perform the same are included.

[0017] According to the present invention, additionally, a new computer program product is provided. The computer program product includes a non-volatile computer-readable medium encoding the computer program according to the present invention, for example, a compact disc "CD".

[0018] Exemplary and non-limiting embodiments are described in the accompanying dependent claims.

[0019] Various exemplary and non-limiting embodiments related to both the structure and the operation method will be best understood from the following description of specific exemplary and non-limiting embodiments when read in conjunction with the accompanying drawings, together with their additional objectives and advantages.

[0020] The verbs "comprise" and "include" are used in this document as open limitations that do not exclude or require the presence of features not recited. The features described in the dependent claims can be freely combined with each other unless otherwise specified. Further, it should be understood that the use of "a" or "an" throughout this document, i.e., the singular form, does not exclude the plural.

[0021] Exemplary and non - limiting embodiments and their advantages will be described in more detail below, by way of example, with reference to the accompanying drawings.

Brief Description of the Drawings

[0022]

Fig. 1a

Fig. 1b

Fig. 1c

Fig. 2

Modes for Carrying Out the Invention

[0023] The specific examples provided in the description below should not be construed as limiting the scope of the appended claims and / or their applicability. The lists and groups of examples provided in the description below are not exhaustive unless otherwise specifically stated.

[0024] Figure 1a shows an electrolysis system according to an exemplary and non-limiting embodiment. The electrolysis system includes an electrolytic cell 103 having one or more electrolytic cells each including an anode, a cathode, and an electrolyte. In this exemplary case, the electrolytic cell 103 is a water electrolytic cell in which electrical energy is converted into chemical energy carried by hydrogen gas H2. Oxygen gas O2 is produced as a byproduct. The electrolytic cell 103 may be, for example, an alkaline water electrolytic cell including an alkaline liquid electrolyte, a porous diaphragm that divides the electrolytic cell into a cathode compartment including a cathode and an anode compartment including an anode, but it is not necessarily so. The alkaline liquid electrolyte may include, for example, aqueous potassium hydroxide "KOH" or aqueous sodium hydroxide "NaOH". The electrolytic cell 103 may include, for example, dozens or hundreds of electrolytic cells. However, alternatively, the electrolytic cell 103 can include from 1 to 10 electrolytic cells. The electrolytic cells can be electrically connected in series or electrically connected in parallel. However, alternatively, the electrolytic cells can be arranged such that they form a series-connected group of parallel-connected electrolytic cells, or a parallel-connected group of series-connected electrolytic cells, or the electrolytic cells can be electrically connected to each other in other ways.

[0025] The electrolysis system includes a rectifier circuit 104 for receiving an alternating voltage and supplying a direct current I to the electrodes of the electrolytic cell 103. In this exemplary case, the rectifier circuit 104 includes forced commutation converter bridges 106, 108, and 109 and a supply inductor 107 on the alternating voltage side of the forced commutation converter bridges. Further, the rectifier circuit 104 includes a DC filter 113 for smoothing the current I of the electrolytic cell 103. The forced commutation converter bridges 106, 108, and 109 are connected to each other such that the current supplied to the DC filter 113 is the sum of the direct currents generated by the forced commutation converter bridges. Each of the forced commutation converter bridges 106, 108, and 109 includes an alternating voltage terminal and a converter leg connected between the DC voltage terminals of the converter bridge under consideration. Each converter leg includes a bidirectional upper branch controllable switch between the alternating voltage terminal of the converter leg under consideration and the positive terminal of the DC voltage terminal, and a bidirectional lower branch controllable switch between the alternating voltage terminal of the converter leg under consideration and the negative terminal of the DC voltage terminal. In the exemplary case shown in FIG. 1a, each bidirectional controllable switch includes an insulated gate bipolar transistor "IGBT" and an antiparallel diode. However, alternatively, each bidirectional controllable switch can include, for example, a gate turn-off thyristor "GTO" or a metal oxide field effect transistor "MOSFET" or some other suitable semiconductor switch in place of the IGBT.

[0026] The electrolysis system includes a controller 105 for controlling the operation of the controllable switches, such that a desired current is supplied to the electrolytic cell 103 and a desired alternating voltage is generated at the alternating voltage terminals of the forced commutation converter bridges 106, 108, and 109. The forced commutation of the bidirectional switches of the converter bridges 106, 108, and 109 enables reduction of the current ripple of the current I supplied to the electrolytic cell 103. Further, by the forced commutation of the bidirectional switches, the power factor of the alternating voltage supply of the electrolysis system and the current harmonics injected into the alternating voltage supply can be controlled.

[0027] FIG. 1b shows an equivalent circuit of the electrolytic cell of the electrolytic cell 103. The impedance of the electrolytic cell is the membrane resistance Rm and charge transfer resistance R ct and double layer capacitance C dl It is composed of. To explain the mass transfer loss, it is necessary to include the Warburg impedance Z wbg in the equivalent circuit. However, Z wbg is only relevant at high current densities and low frequencies. Further considering, the Warburg impedance Z wbg is assumed to be zero. U rev is the reversible voltage of the electrolytic cell. The reversible voltage U rev is the minimum cell voltage for the electrochemical reaction to occur. The reversible voltage U rev can be estimated based on the operating temperature and pressure of the electrolytic cell. For example, the estimated value of the reversible voltage of alkaline water electrolysis can be obtained from the following equation. U rev =ΔG0 / (2F)-ln(P / P0)RT / (2F), where ΔG0 is the increment of Gibbs free energy, F is the Faraday constant, R is the gas constant, T is the absolute temperature, and P0 and P are the vapor pressures of pure water and electrolyte, respectively. ΔG0 / (2F) is 1.226 volts at 298K and 1 atmosphere.

[0028] The equivalent circuit shown in Fig. 1b can be used for the series connection of electrolytic cells. As a result, the membrane resistance R m corresponds to the membrane resistance of the series-connected electrolytic cells, and the charge transfer resistance R ct is considered to correspond to the charge transfer resistance of the series-connected electrolytic cells, and the double layer capacitance C dl is considered to correspond to the double layer capacitance of the series-connected electrolytic cells, and U rev is considered to correspond to the total reversible voltage of the series-connected electrolytic cells, and U is the voltage of the series-connected electrolytic cells. Accordingly, the equivalent circuit shown in Fig. 1b can be used for the parallel connection of electrolytic cells.

[0029] Fig. 1c shows an exemplary time trend of the differential voltage u and current I of the electrolytic cell 103 during shutdown of the electrolytic cell. The differential voltage u is the difference between the voltage U applied to the electrolytic cell and the total reversible voltage of the electrolytic cell. That is, u = U - Urev It is as follows.

[0030] The electrolysis system shown in Fig. 1a comprises an apparatus according to an exemplary and non - limiting embodiment for estimating the electrical characteristics of the electrolytic cell 103. This apparatus comprises a current and voltage sensor 101 for measuring the voltage U applied to the electrolytic cell 103 and the current I of the electrolytic cell 103. Further, the apparatus comprises a data processing system 102 configured to store in a memory circuit data indicating the value u0 of the differential voltage prevailing before and at the start of the shutdown of the electrolytic cell 103 and the value I0 of the current I of the electrolytic cell prevailing before and at the start of the shutdown. In the exemplary case shown in Fig. 1c, the shutdown starts at time t0. The data processing system 102 estimates the estimated value τ of the time constant of the exponential decay of the double - layer capacitance voltage u of the electrolytic cell and the estimated value u of the double - layer capacitance voltage prevailing at the start of the shutdown. C Since the current I is zero, it is configured to calculate based on two or more values of the differential voltage u equal to the double - layer capacitance voltage u. 0C When the current I is zero, the above - mentioned differential voltage u can be estimated using the following formula. C u = u

[0031] u = u u = u 0C e -(t-t0) / τ , where u 0C is the estimated value of the double - layer capacitance voltage of the electrolytic cell prevailing at the start of the shutdown, and e is Napier's constant ≈ 2.71828. The double - layer capacitance voltage u C can be estimated as u 0C e -(t-t0) / τ when starting and after starting the shutdown of the electrolytic cell, i.e., when the time ≥ t0.

[0032] Fig. 1c shows exemplary values u1 and u2 of the differential voltage u corresponding to time points t1 and t2 when the current I is zero. In an apparatus according to an exemplary and non - limiting embodiment, the data processing system 102 is configured to calculate the estimated values τ and u 0C using the following formula. τ=(t2 - t1) / ln(u1 / u2) and u 0C = u1e (t1-t0) / τ = u2e (t2-t0) / τ 。

[0033] Since u1 and u2 are the values of the differential voltage u corresponding to the time points t1 and t2 when the current I is zero, u1 = u 0C e -(t1-t0) / τ and u2 = u 0C e -(t2-t0) / τ is obtained. Thus, u1 / u2 = e (t2-t1) / τ , τ = (t2 - t1) / ln(u1 / u2) is obtained. The value u2 is preferably u1 / e, in which case ln(u1 / u2) = ln(e) = 1, and τ is simply t2 - t1.

[0034] In an apparatus according to another exemplary and non - limiting embodiment, in the data processing system 102 shown in FIG. 1a, the curve u 0C e -(t-t0) / τ is adapted, for example, using a curve fitting such as the least - mean - square "LMS" fitting that uses u 0C and τ as fitting parameters to estimate the values of τ and u 0C such that it fits the curve of the differential voltage u over a time interval during which the current I is zero, for example, from t1 to t2.

[0035] The data processing system 102 shown in FIG. 1a is configured to calculate at least one of: i) estimating the membrane resistance R m of the electrolytic cell as R m = (u0 - u 0C ) / I0, ii) estimating the charge - transfer resistance R ct of the electrolytic cell as R ct = u 0C / I0, and iii) estimating the double - layer capacitance C dl of the electrolytic cell as C dl = τ I 0 / u 0C .

[0036] The reversible decomposition in the electrolytic cell of the electrolytic cell 103 is related to the increase in the above - mentioned membrane resistance R m . For this reason, the membrane resistance R mshows the state of the electrolytic cell 103.

[0037] In an apparatus according to an illustrative and non - limiting embodiment, the data processing system 102 calculates an estimated value of the membrane resistance R of the electrolytic cell 103 during successive shutdowns of the electrolytic cell 103, m and is configured to detect an increase in the calculated estimated value of the membrane resistance R. m

[0038] In an apparatus according to an illustrative and non - limiting embodiment, the data processing system 102 is configured to enable a procedure to improve the life of the electrolytic cell 103 by recovering from reversible decomposition in response to a detected increase in the calculated estimated value of the membrane resistance R. The procedure may include, for example, successive shutdowns and startups of the electrolytic cell 103 to recover from reversible decomposition. m

[0039] The data processing system 102 can be implemented using one or more processor circuits. Each processor circuit can be a programmable processor circuit with appropriate software, a dedicated hardware processor such as an application - specific integrated circuit "ASIC", or a configurable hardware processor such as a field - programmable gate array "FPGA", for example. Further, the data processing system 102 may include one or more memory elements. Each memory element may be, for example, a random - access memory "RAM" circuit.

[0040] FIG. 2 shows a flowchart of a method according to an illustrative and non - limiting embodiment for estimating the electrical characteristics of an electrolytic cell. This method includes the following operations: - Operation 201: Saving data indicating the value u0 of the dominant differential voltage at the start of shutdown of the electrolytic cell and the value I0 of the current of the electrolytic cell dominant at the start of shutdown, where the differential voltage is the difference between the voltage U applied to the electrolytic cell and the total reversible voltage U rev of the electrolytic cell, the step; - In response to the situation where the current I reaches zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage dominant at the start of shutdown 0C are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage. - Action 203: i) The membrane resistance R of the electrolytic cell m is estimated as R m =(u0 - u 0C ) / I0, ii) the charge transfer resistance R of the electrolytic cell ct is estimated as R ct =u 0C / I0, and iii) the double-layer capacitance C of the electrolytic cell dl is estimated as C dl =τ I 0 / u 0C . At least one of the calculation steps is included.

[0041] In combination with the above method, the above value I0 of the current is required, and only the detection of the zero-current situation is required after the start of shutdown. This brings advantages to an electrolysis system on an industrial scale where it may be difficult to measure the large-current trend accurately enough.

[0042] The method according to an exemplary and non-limiting embodiment includes a step of calculating an estimated value of the membrane resistance R of the electrolytic cell at the continuous shutdown of the electrolytic cell and a step of detecting an increase in the calculated estimated value. m

[0043] The method according to an exemplary and non-limiting embodiment includes a step of enabling a procedure for recovering from the reversible decomposition of the electrolytic cell of the electrolytic cell to improve the life of the electrolytic cell in response to the detected increase in the calculated estimated value of the membrane resistance R. In the method according to an exemplary and non-limiting embodiment, the procedure includes continuous shutdown and startup of the electrolytic cell to recover from the reversible decomposition. m

[0044] A computer program according to an illustrative and non - limiting embodiment includes computer - executable instructions for controlling a programmable processor to perform operations associated with the method according to any of the above - mentioned illustrative and non - limiting embodiments.

[0045] A computer program according to an illustrative and non - limiting embodiment includes a software module for estimating the electrical characteristics of an electrolytic cell. The software module causes a programmable processor to - save data indicating a value u0 of the differential voltage prevailing at the start of the shutdown of the electrolytic cell and a value I0 of the current of the electrolytic cell prevailing at the start of the shutdown, wherein the differential voltage is the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell; - in response to the situation where the current has reached zero, estimate a value τ of the time constant of the exponential decay of the double - layer capacitance voltage of the electrolytic cell and an estimated value u 0C of the double - layer capacitance voltage prevailing at the start of the shutdown, based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double - layer capacitance voltage; - (i) estimate the membrane resistance R m of the electrolytic cell as R m =(u0 - u 0C ) / I0, (ii) estimate the charge - transfer resistance R ct of the electrolytic cell as R ct =u 0C / I0, and (iii) estimate the double - layer capacitance C dl of the electrolytic cell as C dl =τ I 0 / u 0C , and include computer - executable instructions for controlling the programmable processor to perform at least one of the above - mentioned calculation steps.

[0046] The software module may be, for example, a sub - routine or function implemented using an appropriate programming language.

[0047] A computer program product according to an illustrative and non-limiting embodiment includes a computer-readable medium encoded with a computer program according to an embodiment of the present invention, for example, a compact disc "CD".

[0048] Encode a signal according to an illustrative and non-limiting embodiment to carry information defining a computer program according to an embodiment of the present invention. In this illustrative case, the computer program may be downloadable, for example, from a server that may form part of a cloud service.

[0049] The specific examples described in the above description should not be construed as limiting the applicability and / or interpretation of the appended claims. The lists and groups of examples provided in the above description are not exhaustive unless otherwise specifically stated. The invention disclosed in this specification includes the following. [Aspect 1] An apparatus for estimating the electrical characteristics of an electrolytic cell, the apparatus comprising a current and voltage sensor (101) for measuring the voltage (U) applied to the electrolytic cell and the current (I) of the electrolytic cell, wherein the apparatus is a data processing system (102), - a step of storing data indicating the value u of the differential voltage prevailing at the start of the shutdown of the electrolytic cell 0 and the value I of the current of the electrolytic cell prevailing at the start of the shutdown, 0 wherein the differential voltage is the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell, - in response to the situation where the current has reached zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage prevailing at the start of the shutdown 0C are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage, - i) estimating the membrane resistance R of the electrolytic cell as R, m ii) estimating the charge transfer resistance R of the electrolytic cell as R, m =(u 0 -u 0C ) / I 0 and iii) estimating the double-layer capacitance C of the electrolytic cell as C = τI, ct characterized in that it comprises a data processing system (102) for performing at least one of the steps of calculating. ct =u 0C / I 0 [Aspect 2] dl The data processing system is configured to calculate the estimated value of the membrane resistance R of the electrolytic cell during successive shutdowns of the electrolytic cell and to detect an increase in the calculated estimated value, according to the apparatus of Aspect 1. dl [Aspect 3] 0 / u 0C The data processing system is configured to enable a procedure for recovering from the reversible decomposition of the electrolytic cell in response to the detected increase in the calculated estimated value of the membrane resistance, according to the apparatus of Aspect 2. [Aspect 4] The procedure includes successive shutdowns and startups of the electrolytic cell, according to the apparatus of Aspect 3. m [Aspect 5] - an electrolytic cell (103), - a rectifier circuit (104) for receiving one or more alternating voltages and supplying direct current to the electrodes of the electrolytic cell, - a controller (105) for controlling the direct current supplied to the electrodes of the electrolytic cell, - an apparatus according to any one of Aspects 1 to 4 for estimating the electrical characteristics of the electrolytic cell. [Aspect 6] ​ ​ ​ ​ ​ The electrolysis system according to aspect 5, wherein the rectifier circuit includes a forced commutation converter bridge (106) and a supply inductor (107) on the AC voltage side of the forced commutation converter bridge. [Aspect 7] The electrolysis system according to aspect 6, wherein the rectifier circuit includes at least one other forced commutation converter bridge (108, 109), and as a result, the DC power supplied to the electrodes of the electrolytic cell is the sum of the DC powers of the forced commutation converter bridges (106, 108, 109) of the rectifier circuit. [Aspect 8] The electrolysis system according to any one of aspects 5 to 7, wherein the electrolytic cell (103) is configured to decompose water into hydrogen gas and oxygen gas. [Aspect 9] A method for estimating the electrical characteristics of an electrolytic cell, the method comprising: - A step (201) of storing data indicating a value u of the dominant differential voltage and a value I of the current of the electrolytic cell dominant at the start of the shutdown of the electrolytic cell, wherein the differential voltage is the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell. 0 - In response to the situation where the current reaches zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage dominant at the start of the shutdown are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage. Step (202). 0 - i) Estimating the membrane resistance R of the electrolytic cell as R, ii) estimating the charge transfer resistance R of the electrolytic cell as R, and iii) estimating the double-layer capacitance C of the electrolytic cell as C = τI. A method characterized by including at least one of the steps (203) of calculating. [Aspect 10] 0C The method according to aspect 9, including a step of calculating the estimated value of the membrane resistance R of the electrolytic cell at the continuous shutdown of the electrolytic cell and a step of detecting an increase in the calculated estimated value. [Aspect 11] m The method according to aspect 10, including a step of enabling a procedure for the electrolytic cell to recover from the reversible decomposition of the electrolytic cell in response to the detected increase in the calculated estimated value of the membrane resistance. m =(u 0 -u 0C ) / I 0 [Aspect 12] ct The method according to aspect 11, wherein the procedure includes continuous shutdown and startup of the electrolytic cell. ct =u 0C / I 0 [Aspect 13] dl ​ dl ​ 0 / u 0C ​ ​ ​ m ​ ​ ​ ​ ​ ​ A computer program for estimating the electrical characteristics of an electrolytic cell, the computer program causing a programmable processor to - receive data indicating a voltage applied to the electrolytic cell and a current of the electrolytic cell from a voltage and current sensor; - save data indicating a value u of a differential voltage prevailing at the start of shutdown of the electrolytic cell 0 and a value I of the current of the electrolytic cell prevailing at the start of shutdown, 0 wherein the differential voltage is a difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell; - in response to a situation where the current has reached zero, an estimated value τ of a time constant of an exponential decay of a double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage prevailing at the start of shutdown 0C are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage; - calculating at least one of i) estimating a membrane resistance R of the electrolytic cell as R, ii) estimating a charge transfer resistance R of the electrolytic cell as R, and iii) estimating a double-layer capacitance C of the electrolytic cell as C = τI. m A computer program comprising computer-executable instructions for causing the above to be performed. m =(u 0 -u 0C ) / I 0 [Aspect 14] ct A computer program product comprising a non-transitory computer-readable medium encoded with the computer program according to Aspect 13. ct =u 0C / I 0 ​ dl ​ dl ​ 0 / u 0C ​ ​ ​

Claims

1. An apparatus for estimating the electrical characteristics of an electrolytic cell, the apparatus comprising a current and voltage sensor (101) for measuring the voltage (U) applied to the electrolytic cell and the current (I) of the electrolytic cell, wherein the apparatus is a data processing system (102), - The value u of the differential voltage dominant at the start of the shutdown of the electrolytic cell 0 and the value I of the current of the electrolytic cell dominant at the start of the shutdown 0 and storing data indicating the same, wherein the differential voltage is the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell - In response to the situation where the current has reached zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage that was dominant at the start of the shutdown 0C are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage. - i) Membrane resistance R of the electrolytic cell m R m = (u 0 -u 0C ) / I 0 ii) the charge transfer resistance of the electrolytic cell, R ct R ct =u 0C / I 0 and iii) the double layer capacitance of the electrolytic cell, C dl C dl = τI 0 / u 0C and estimating the same as:

2. The data processing system calculates the estimated value of the membrane resistance R of the electrolytic cell during continuous shutdown of the electrolytic cell m The apparatus according to claim 1, wherein the apparatus is configured to detect an increase in the calculated estimated value

3. The data processing system is configured to execute a procedure for recovering from the reversible decomposition of the electrolytic cell of the electrolytic cell in response to the detected increase in the calculated estimated value of the membrane resistance, The apparatus according to claim 2, wherein the procedure is a continuous shutdown and startup of the electrolytic cell.

4. - An electrolytic cell (103); - A rectifier circuit (104) for receiving one or more alternating voltages and supplying direct current to the electrodes of the electrolytic cell; - A controller (105) for controlling the direct current supplied to the electrodes of the electrolytic cell; - An electrolysis system comprising the apparatus according to any one of claims 1 to 3 for estimating the electrical characteristics of the electrolytic cell.

5. The electrolysis system according to claim 4, wherein the rectifier circuit comprises a forced commutation converter bridge (106) and a supply inductor (107) on the alternating voltage side of the forced commutation converter bridge.

6. The electrolysis system according to claim 5, wherein the rectifier circuit comprises at least one other forced commutation converter bridge (108, 109), such that the direct current supplied to the electrodes of the electrolytic cell is the sum of the direct currents of the forced commutation converter bridges (106, 108, 109) of the rectifier circuit.

7. The electrolysis system according to claim 4, wherein the electrolytic cell (103) is configured to decompose water into hydrogen gas and oxygen gas.

8. A method for estimating the electrical characteristics of an electrolytic cell, the method comprising: - The value u of the differential voltage dominant at the start of the shutdown of the electrolytic cell 0 and the value I of the current of the electrolytic cell dominant at the start of the shutdown 0 A step (201) of storing data indicating the above, wherein the differential voltage is the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell, step (201); - In response to the situation where the current has reached zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage that was dominant at the start of the shutdown 0C are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage (step 202); - i) estimating the membrane resistance R of the electrolytic cell as R = (u - u) / I; ii) estimating the charge transfer resistance R of the electrolytic cell as R = u / I; and iii) estimating the double layer capacitance C of the electrolytic cell as C = τI0 / u, and including at least one of the steps of calculating (203). m as R m = (u 0 - u 0C ) / I 0 and ii) estimating the charge transfer resistance R of the electrolytic cell as R ct as R ct = u 0C / I 0 and iii) estimating the double layer capacitance C of the electrolytic cell as C dl as C dl = τI0 / u 0C and a method characterized by including the step (203).

9. The method includes a step of calculating an estimated value of the membrane resistance R of the electrolytic cell at the time of continuous shutdown of the electrolytic cell m and a step of detecting an increase in the calculated estimated value, the method according to claim 8.

10. The method includes a step of executing a procedure for recovering from the reversible decomposition of the electrolytic cell of the electrolytic cell in response to the detected increase in the calculated estimated value of the membrane resistance, The method according to claim 9, wherein the procedure is a continuous shutdown and startup of the electrolytic cell.

11. A non-transitory computer-readable medium encoded with a computer program for estimating the electrical characteristics of an electrolytic cell, the computer program causing a programmable processor to, - receiving data indicating the voltage applied to the electrolytic cell and the current of the electrolytic cell from a voltage and current sensor; - The value u of the differential voltage that is dominant at the start of the shutdown of the electrolytic cell 0 and the value I of the current of the electrolytic cell that is dominant at the start of the shutdown 0 and storing data indicating the same, wherein the differential voltage is the difference between the voltage applied to the electrolytic cell and the total reversible voltage of the electrolytic cell, the step - In response to the situation where the current has reached zero, an estimated value τ of the time constant of the exponential decay of the double-layer capacitance voltage of the electrolytic cell and an estimated value u of the double-layer capacitance voltage that was dominant at the start of the shutdown 0C are calculated based on two or more values of the differential voltage when the current is zero and the differential voltage is equal to the double-layer capacitance voltage. - i) estimating the membrane resistance R of the electrolytic cell as R = (u - u) / I; ii) estimating the charge transfer resistance R of the electrolytic cell as R = u / I; and iii) estimating the double layer capacitance C of the electrolytic cell as C = τI0 / u, and including a step of calculating at least one of them, and computer-executable instructions for causing the steps to be performed. A computer-readable medium characterized by this is provided. m as R m = (u 0 - u 0C ) / I 0 and ii) estimating the charge transfer resistance R of the electrolytic cell as R ct as R ct = u 0C / I 0 and iii) estimating the double layer capacitance C of the electrolytic cell as C dl as C dl = τI0 / u 0C and a computer-readable medium including computer-executable instructions for causing at least one of the above steps to be performed.

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