Method and Apparatus for Operating a System for Providing an Electrochemical Battery Module for a Device Battery for a Device

Abstract

A computer-implemented method provides an electrochemical battery model and a state of health model for a device battery. The electrochemical battery model is based on a system of differential equations, models an equilibrium state, and reports a dependence between operating parameters of the device battery and a state of charge of the device battery. The state of health model includes at least one physical aging model based on a further system of differential equations, and models the state of health depending on progressions of the operating parameters of the device battery.

Claims

1. A method for providing an electrochemical battery model and a state of health model for a device battery, the method comprising: using a physical aging model of the state of health model with progressions of operating parameters configured to characterize an operation of the device battery, in order to ascertain a state of health, with establishment of an internal state of a system of differential equations of the physical aging model; adjusting at least one model parameter of the electrochemical battery model based on the operating parameters of the device battery by a calibration method; and adapting the at least one model parameter of the electrochemical battery model depending on a current internal state of the physical aging model and/or adapting the internal state of the system of differential equations of the physical aging model based on the adjusted at least model parameter of the electrochemical battery model, wherein the electrochemical battery model is based on the system of differential equations, wherein the electrochemical battery model models an equilibrium state and reports any dependence between the operating parameters of the device battery and a state of charge of the device battery, wherein the state of health model comprises the at least one physical aging model, wherein the at least one physical aging model is based on a further system of differential equations, and models the state of health depending on the progressions of the operating parameters of the device battery.

2. The method according to claim 1, wherein the current internal state of the physical aging model corresponds to a loss of cyclable lithium or a loss of active anode material.

3. The method according to claim 1, wherein the at least one model parameter comprises a parameter of cyclable lithium standardized to a cathode capacity or a proportion of an anode volume.

4. The method according to claim 1, further comprising: using the electrochemical battery model (i) to determine the state of charge of the device battery, (ii) to determine stress factors for the device battery, and/or (iii) to derive a charge strategy comprising an optimized charge curve.

5. The method according to claim 1, wherein the adapting of the at least one model parameter is conducted only when or whenever a change detected in the state of health amounts to a predetermined magnitude of change in the state of health.

6. The method according to claim 1, wherein the adapting the internal state and/or the at least one model parameter includes amalgamating the current internal state and the at least one model parameter of the battery model using a maximum likelihood estimator.

7. The method according to claim 1, further comprising: using the device battery for operation of a device such as a motor vehicle, a pedelec, a flying device including a drone, a machine tool, a consumer electronics device including a cellphone, an autonomous robot, and/or a domestic appliance.

8. A method of providing an electrochemical battery model for a device battery, comprising: using a physical aging model of a state of health model with progressions of operating parameters configured to characterize an operation of the device battery, in order to ascertain a state of health, with establishment of an internal state of a system of differential equations of the physical aging model; and adapting at least one model parameter of the electrochemical battery model depending on a current internal state of the physical aging model, wherein the electrochemical battery model is based on the system of differential equations, wherein the electrochemical battery model models an equilibrium state and reports a dependence between the operating parameters of the device battery and a state of charge of the device battery, wherein the state of health model comprises the physical aging model, wherein the physical aging model is based on a further system of differential equations, and models the state of health depending on the progressions of the operating parameters of the device battery.

9. The method according to claim 8, wherein the current internal state of the physical aging model corresponds to a loss of cyclable lithium or a loss of active anode material.

10. The method according to claim 8, wherein the at least one model parameter comprises a parameter of cyclable lithium standardized to a cathode capacity or a proportion of an anode volume.

11. The method according to claim 8, further comprising: using the electrochemical battery model (i) to determine the state of charge of the device battery, (ii) to determine stress factors for the device battery, and/or (iii) to derive a charge strategy comprising an optimized charge curve.

12. The method according to claim 8, wherein the adapting of the at least one model parameter is conducted only when or whenever a change detected in the state of health amounts to a predetermined magnitude of change in the state of health.

13. The method according to claim 8, wherein the adapting of the at least one model parameter includes amalgamating the current internal state and the at least one model parameter of the battery model using a maximum likelihood estimator.

14. The method according to claim 8, further comprising: using the device battery for operation of a device such as a motor vehicle, a pedelec, a flying device including a drone, a machine tool, a consumer electronics device including a cellphone, an autonomous robot, and/or a domestic appliance.

15. A method of providing a state of health model for a device battery, comprising: adjusting at least one model parameter of an electrochemical battery model based on operating parameters of the device battery by a calibration method; and adapting an internal state of a system of differential equations of a physical aging model based on the adjusted at least one model parameter of the electrochemical battery model, wherein the electrochemical battery model is based on the system of differential equations, wherein the electrochemical battery model models an equilibrium state and reports a dependence between the operating parameters of the device battery and a state of charge of the device battery, wherein the state of health model comprises the at least one physical aging model based on a further system of differential equations, and wherein the state of health model models the state of health depending on progressions of the operating parameters of the device battery.

16. The method according to claim 15, wherein a current internal state of the physical aging model corresponds to a loss of cyclable lithium or a loss of active anode material.

17. The method according to claim 15, wherein the at least one model parameter comprises a parameter of cyclable lithium standardized to a cathode capacity or a proportion of an anode volume.

18. The method according to claim 15, further comprising: using the electrochemical battery model (i) to determine a state of charge of the device battery, (ii) to determine stress factors for the device battery, and/or (iii) to derive a charge strategy comprising an optimized charge curve.

19. The method according to claim 15, wherein the adapting the internal state includes amalgamating a current internal state and the at least one model parameter of the battery model using a maximum likelihood estimator.

20. The method according to claim 15, further comprising: using the device battery for operation of a device such as a motor vehicle, a pedelec, a flying device including a drone, a machine tool, a consumer electronics device including a cellphone, an autonomous robot, and/or a domestic appliance.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The embodiments are elucidated hereinafter with reference to the appended drawings. The figures show:

[0040] FIG. 1 a schematic diagram of a system for provision of driver- and vehicle-specific operating parameters for provision of an electrochemical battery model adapted to a state of health for a vehicle battery in a central unit;

[0041] FIG. 2 a schematic block diagram of a functional construction of the functions in the central unit for implementation of a state of health model and of an electrochemical battery model; and

[0042] FIG. 3 a flow diagram for illustration of a method of adjusting the electrochemical battery model.

DETAILED DESCRIPTION

[0043] There follows a description of the method of the disclosure with reference to vehicle batteries as device batteries in a multitude of motor vehicles as equivalent “devices”. In the motor vehicles, a data-based state of health model for the respective vehicle battery may be implemented in a control unit. The state of health model may be updated or retrained continuously in a central unit on the basis of progressions of operating parameters of the vehicle batteries from the vehicle fleet. Alternatively, the state of health model may be operated purely in a cloud, and the results for calculation of the state of health and of the prediction of the state of health may be provided. The state of health model is operated in the central unit and used for calculation of aging and prediction of aging. In addition, the electrochemical battery module may be utilized in the motor vehicle and/or in the central unit. The parameterization adapted to the state of health enables improved provision of a dependence of the battery voltage, the battery current, the battery temperature and the state of charge.

[0044] The above example is representative of a multitude of stationary or mobile devices supplied with energy autonomously of the grid, for example motor vehicles (electrical vehicles, pedelecs etc.), installations, machine tools, domestic appliances, IOT devices and the like, which are connected via an appropriate communications connection (e.g. LAN, Internet) to a central unit (cloud).

[0045] FIG. 1 shows a system 1 for collecting fleet data in a central unit 2 for creation and operation and for evaluation of a state of health model and an electrochemical battery model.

[0046] The state of health model serves to determine a state of health of a vehicle battery in a motor vehicle. FIG. 1 shows a vehicle fleet 3 comprising multiple motor vehicles 4.

[0047] One of the motor vehicles 4 is shown in more detail in FIG. 1. The motor vehicles 4 each have a vehicle battery 41, an electrical drive motor 42 and a control unit 43. The control unit 43 is connected to a communications module 44 capable of transmitting data between the respective motor vehicle 4 and a central unit 2 (a “cloud”).

[0048] The motor vehicles 4 transmit to the central unit 2 the operating parameters F that at least report parameters that affect the state of health of the vehicle battery or are influenced by the state of health of the vehicle battery. The operating parameters F, in the case of a vehicle battery, may report a present battery current I(t), a present battery voltage U(t), a present battery temperature T(t) and a present state of charge SOC(t), at the pack level, at the module level and/or at the cell level. The operating parameters F are detected in a rapid timeframe according to the signal between typically between 0.1 Hz to 100 Hz and can be transmitted regularly to the central unit 2 in uncompressed and/or compressed form. For example, the time series may be transmitted in blocks to the central unit 2 at intervals of 10 min up to several hours.

[0049] The operating parameters F, in the central unit 2 or in other embodiments, can also be used directly in the respective motor vehicles 4 to generate operating features M relating to an evaluation period. The evaluation period for the determination of the state of health may be a few hours (for example 6 hours) to several weeks (for example one month). A customary value for the evaluation period is one week.

[0050] The operating features may, for example, be features based on the evaluation period and/or features accumulated over the lifetime to date (i.e. since commencement of the lifetime) and/or statistical parameters ascertained over the entire lifetime to date. More particularly, the operating features may include, for example: histogram data versus the progression of the state of health, temperature, battery voltage, battery current, especially multidimensional histograms based on the battery temperature distribution versus the state of charge, the charging current distribution versus temperature and/or the discharging current distribution versus temperature, accumulated total charge (Ah), an average increase in capacity in a charging operation (especially for charging operations in which the increase in charge exceeds a threshold value (e.g. 20%) of the total battery capacity), an extreme value of the differential capacity during a measured charging operation with a sufficiently large amplitude in the charge state (dQ/dU: change in charge divided by change in the battery voltage) and others.

[0051] The state of health (SOH) is the key parameter for reporting of a remaining battery capacity or remaining battery charge. The state of health is a measure of the aging of the vehicle battery or a battery module or a battery cell, and can be reported as the capacity retention rate (SOH-C) or as the rise in internal resistance (SOH-R). The capacity retention rate SOH-C is reported as the ratio of the measured present capacity to an initial capacity of the fully charged battery. The relative change in internal resistance SOH-R rises with increasing aging of the battery.

[0052] A state of health model is implemented in the central unit 2, which may especially be wholly or partly data-based. The state of health model may be used regularly, i.e., for example, after the respective evaluation period has elapsed, in order to undertake ascertainment of the current state of health of the vehicle battery 41 based on the operating features and/or the operating parameters. In other words, it is possible, based on the operating parameters and/or the operating features, which result from the progressions of operating parameters of one of the motor vehicles 4 in the fleet 3, to ascertain a state of health of the relevant vehicle battery 41.

[0053] FIG. 2 shows, by way of example, in schematic form, the functional construction of a model system 10 in one embodiment. The model system 10 comprises a state of health model 11 and an electrochemical battery model 12.

[0054] The state of health model 11 may be constructed in a hybrid manner. In the embodiment shown, the state of health model 11 comprises a physical aging model 5 and a correction model 6. These receive, in an optional data cleaning block 12, filtered operating parameters F′ that can be filtered for avoidance of outliers. The operating features M of the current evaluation period are generated in a feature extraction block 8 based on the time series of the operating parameters F.

[0055] The filtered operating parameters F go directly into the physical aging model 5, which is preferably executed as an electrochemical model and describes corresponding electrochemical states, such as layer thicknesses (e.g. SEI thickness), change in cyclable lithium on account of anode/cathode side reactions, fast consumption of electrolytes, slow consumption of electrolytes, loss of active material in anode, loss of active material in cathode, etc . . . ), with the aid of nonlinear differential equations.

[0056] The physical aging model 5 corresponds to an electrochemical model of the battery cell and of the cell chemistry, which is based on differential equations. The physical aging model 9, depending on the progression of the filtered operating parameters F′ since the start of the lifetime of the vehicle battery, ascertains internal physical battery states in order to a physically based state of health SOHph of the dimension of at least one in the form of the abovementioned electrochemical states that are modeled in a linear or non-linear manner at a capacity retention rate (SOH-C) and/or a rate of rise in the internal resistance (SOH-R), in order to provide these (SOH-C and SOH-R). Model parameters of the physical aging model are assumed herein to be constant and defined. These may optionally be fitted at given junctures on the basis of labels, for example coefficients for description of the side reactions.

[0057] However, the model values provided for the physical state of health SOHph by the physical aging model 5 are inexact in particular situations, and correction of these with a correction parameter k is therefore envisaged. The correction parameter k is provided by the data-based correction model 6, which is trained with the aid of training datasets from the vehicles 4 in the vehicle fleet 3 and/or with the aid of laboratory data.

[0058] The correction model 6 receives, on the input side, operating features M that are ascertained from the progressions of the operating parameters F and may also include one or more of the internal electrochemical states of the physical model. In addition, the correction model 6, on the input side, may receive the physical state of health SOHph obtained from the physical aging model 5. The operating features M of the current evaluation period are generated in a feature extraction block 8 based on the time series of the operating parameters F.

[0059] For the determination of a corrected state of health SOH as output, the outputs SOHph, k of the physical aging model 5 and of the correction model 6, which is preferably executed as a Gaussian process model, are processed with one another. More particularly, these are added or multiplied (not shown) in a summation block 7 in order to obtain the modeled state of health SOH as output for a current evaluation period.

[0060] The physical aging model 5 and the correction model 6 are adjusted at regular time intervals based on the progressions of operating parameters and the states of health ascertained by other methods of generating labels, such as coulomb counting and the like. New parameterization of the physical aging model 5 does not take place unless new labels from laboratory data or on the basis of field diagnosis measurements (=ground truth) are available. If new labels are available, it is possible to newly parametrize the aging model, but this is only implemented rarely (for example at intervals of 6 months). However, the adjustment of the physical aging model 5 to the actual state of the battery, with essentially constant parameters of the aging model, is achieved by the variability of the internal state (state vector) of the system of differential equations.

[0061] The physical model at the current juncture thus takes on an internal state dependent on the state of health, which corresponds to physical properties of the vehicle battery 41 or of at least one module of the vehicle battery 41 or of at least one cell of the vehicle battery 41.

[0062] For an individual device battery, it is then possible, on the basis of the underlying physical aging model 5, to ascertain an internal state by evaluating the progression of the operating parameters since commencement of operation of the vehicle battery. This internal state is characterized by one or more state parameters that can be used for derivation of one or more model parameters for the electrochemical battery model.

[0063] The system of differential equations of the physical aging model 5, with the state vector x, may, for example, have a structure as follows:

SOHC=f(x)

{dot over (x)}.sub.cLi=h(l(t), U(t), SOC(t), T(t), x)

{dot over (x)}.sub.LAM=g(l(t), U(t), SOC(t), T(t), x)

x=[. . . , x.sub.cLi, x.sub.LAM, . . . ].sup.T

[0064] For example, the internal states of the state of health model can report a loss x.sub.cLi of cyclable lithium (in Ah) and a loss x.sub.LAM of active anode material (in %) in the progression of the lifetime to date. The state vector x is calculated constantly by a time integration method from the gradient parameters {dot over (x)}.sub.cLi, {dot over (x)}.sub.LAM The model execution in the central unit 2 is typically effected 1-8 times per month.

[0065] The model system may also include an electrochemical battery model 13 that provides a dependence between the state of charge SOC, the battery current I, the terminal voltage U and the battery temperature T. This electrochemical battery model uses model parameters that characterize the battery performance. These model parameters of the electrochemical battery model characterize physical and/or chemical relationships and may include an SEI thickness, available lithium, solution concentration and others. However, these physical model parameters are not measurable directly and are initially estimated. The model parameters are subject to aging, and so regular an adjustment to the state of health of the vehicle battery is necessary.

[0066] The battery model may have the following structure, for example:

[00001]$\mathrm{SOC}=\mathrm{SOC}\left(0\right)+\int \frac{I\left(t\right)}{C\left(P\right)}\mathrm{dt}$
OCV(SOC)=OCP.sub.cathode(SOC.sub.cathode)−OCP.sub.anode(SOC.sub.anode)

where C=C(P) an electrode capacity is determined as a function of internal model parameters that may include at least one parameter of cyclable lithium c.sub.LI normalized to the anode capacity, and a proportion of anode volume ea. P is a set of parameters which is fitted regularly. OCV corresponds to the open-circuit voltage of the battery depending on the state of charge SOC, and OCP to the open-circuit potential of the anode or cathode of the battery.

[0067] It is possible to fit the electrochemical battery model with the internal states of the physical aging model to the current state of health. If the electrochemical battery model is executed as a hybrid model with a data-based correction model, the fitting of the internal states of the physical aging model may be conducted only when the data-based correction model has a sufficiently low correction value and simultaneously sufficiently high confidence (i.e. a narrow confidence interval). In this case, the electrochemical battery model has maximum certainty with regard to the electrochemical states.

[0068] For example, the resultant state parameters for the internal state of the physical model may be the loss of cyclable lithium X.sub.C,LI (in Ah) and the loss of active anode material X.sub.LAM (scalar parameter).

[0069] These may be used, for example, for adjustment of the model parameters of the electrochemical battery model. As illustrative model parameter, it is possible to determine a parameter of cyclable lithium c.sub.LI normalized to the cathode capacity and a proportion of anode volume ea as follows:

cLi=cLi(0)−k1.Math.x.sub.cLi

ea=ea(0)−k2.Math.x.sub.LAM

where cLi(0) and ea(0) correspond to a scalar figure for the amount cLi of cyclable lithium at the start of the lifetime or a proportion by volume of the anode at the start of the lifetime of the vehicle battery 41, and k1, k2 are defined physical constants.

[0070] Alternatively, the internal state of the physical aging model 5 may also be adjusted depending on a new determination or adjustment of the model parameters of the battery model.

[0071] The adjustments of the internal state and of the model parameters may be implemented in an adaptation block 15, in each case depending on a change in the model parameters by a model adjustment undertaken or on a change in the internal state by a significant change in battery aging, for example after a change in the state of aging by a predetermined magnitude.

[0072] In addition, amalgamation of the internal state of the aging model 15 with the model parameters of the battery model 13 is also possible in the adaptation block 15, in order, for example, to determine the most likely internal state of the aging model and optimized model parameters of the battery model on the basis of the maximum likelihood method or control technology-related observation approaches.

[0073] The amalgamation takes account of the uncertainties in the determination of the internal state and the model parameters. The uncertainties may be quantified and combined in order to obtain a lower uncertainty overall in the adaptation of the aging model and the battery model.

[0074] For example, when a hybrid state of health model with a correction model based on a Gaussian process is used, the uncertainty of the internal state can be stated/quantified by the measure of the correction parameter of the correction model and the confidence thereof. The uncertainty of the at least one model parameter can be derived, for example, via a residual error between the data basis for adjustment of the model parameters of the battery model and the fitted model curve.

[0075] In a prediction block 16, based on the adapted state of health model 10, it is possible to ascertain and signal a current state of health. More particularly, by prediction of a progression of the state of health, it is possible to make a statement as to a residual lifetime of the vehicle battery 41.

[0076] In a charging strategy block 17, the electrochemical battery model 13 is utilized in order to precisely determine a current state of charge and/or to determine the stress factors. In the charging strategy block 17, it is possible to derive a charging strategy in order to obtain an optimized charging curve that minimizes stress factors for aging of the vehicle battery and hence contributes to extension of the lifetime of the vehicle battery 41. This firstly includes the updating of the charging curve, which can be derived from the electrochemical battery model in such a way as to minimize aging stress for the battery during charging. The charging curve, which shows a progression of the charging current versus a state of charge, is found by solving an optimization problem based on the anode potential. The optimization problem is solved here in such a way that the charging curve derived is Pareto-optimal for the assessment criteria of charging time (to be minimized) and, on the other hand, lifetime (to be maximized). In the maximization of lifetime within the optimization problem, critical battery states associated with high stress factors are avoided.

[0077] FIG. 3 shows a flow diagram for illustration of a method of adapting an electrochemical battery model for monitoring of individual device batteries.

[0078] For this purpose, in step S1, the state of health model is evaluated on the basis of progressions of operating parameters F that have been detected continuously or provided in some other way, in order to obtain a current state of health SOH.

[0079] In step S2 as well, the progressions of operating parameters are evaluated in order to provide, with the aid of the electrochemical battery model 13, dependences between the state of charge, the battery current, the terminal voltage and the battery temperature. This enables the calculating of dynamic responses of voltage with battery current, and the calculation of internal states, for example an anode overpotential, which is used to derive charging curves. The electrochemical battery model is utilized in order to ascertain charging curves, which enables a precise statement of the present state of charge based on present operating parameters. It is also possible to utilize the electrochemical battery model in order to analyze the operating performance of the device or the charging and running performance of the vehicle battery, and to derive operating recommendations.

[0080] In step S3, it is examined whether a change in the state of health by more than a predetermined change in the state of health has occurred since a last adjustment of the electrochemical battery model, for example of more than 1%, or an adjustment of the model parameters has been undertaken by evaluating the data basis in the central unit. If this is the case (alternative: yes), the method is continued with step S4; otherwise (alternative: no), the process jumps back to step S1.

[0081] In step S4, in the manner described above, the internal state and/or the model parameters are adapted depending on the internal state obtained in the aging model 5 and the present model parameters of the battery model 13.

[0082] More particularly, by an amalgamation of the internal state of the aging model and the model parameters of the battery model, for example on the basis of the maximum likelihood method or control technology-related observation approaches, it is possible to determine a most likely internal state of the aging model and a most likely parameterization of the battery model. It is also possible in each case to adapt only the internal state of the aging model 5 or the model parameters of the battery model.

[0083] In principle, the progressions of the raw data and operating parameters can be stored in a suitable manner and can be utilized for analysis, assessment and improvement of the data-based correction model when a state of health is ascertained in some other way, for example in the case of complete charging or complete discharging of the device battery, such that the total battery capacity remaining can be ascertained. By determining the ratio to the nominal battery capacity, it is possible to determine an empirical state of health SOH-C. There are also other known means of determining the state of aging, for example the SOH-R by an evaluation of dU/dI operations with the aid of an assignment function. The training data can then assign the progressions of operating parameters to an empirical state of health for an individual vehicle battery.

[0084] The physical aging model can be parametrized at regular time intervals depending on the training data, especially by parameterization with the aid of the least-squares method or the like. The parameterization of the physical state of health model can be conducted at regular time intervals, but especially when a measurement of the empirical state of health has been conducted or when the modulated state of health is a variance from the measured state of health of the last measurement of more than a given threshold, for example 1%, or when the global optimum has been attained with sufficient accuracy in numerical terms. The physical state of health of the SOHPH as output from the physical aging model 5 is assumed here to be the state of health of the respective training dataset.

[0085] When a hybrid state of health model is used, the data-based correction model 6 can be trained with the training data in order to ascertain a correction parameter that serves to compensate for the residual error of the physical aging model. In this way, the correction model 6 can learn the weaknesses of the physical aging model 5, in order thus to be able to undertake a correction of the physical state of health SOH.sub.ph in the correction block 7.

[0086] The training of the date-based correction model 6 can be conducted with cross-validation and sequential bagging (bootstrap aggregating) in order to improve robustness and accuracy.

[0087] After parameterization of the physical aging model by adjusting the model parameters of the physical model based on labels from laboratory data or on fleet data from a multitude of vehicles, it is then possible to undertake a new calculation of the actual state of health based on vehicle-specific progressions of operating parameters since commencement of operation of the vehicle battery. On the basis of the differential equations of the physical model, an internal state is established, which may comprise, for example, as described above, the loss of cyclable lithium or the loss of active anode material. After amalgamation, it is possible to ascertain the model parameters of the electrochemical battery model therefrom. These can then be updated correspondingly, such that the adjustment of the state of health model based on training data from a multitude of vehicle batteries of the same battery type can automatically also result in an improvement in the electrochemical battery model, the model parameters of which can otherwise be ascertained only in a very complex manner, especially by intrusion into the respective vehicle battery. In this way, it is possible to adapt the electrochemical battery model in a vehicle-specific manner without having to undertake complex analysis of the individual vehicle battery.

[0088] In step S5, based on the adapted state of health model 10, it is possible to ascertain and signal a current state of health. More particularly, by predicting a progression of the state of health, it is possible to make a statement as to a residual lifetime of the vehicle battery 41. For this purpose, there can be constant monitoring of the optimization of lifetime in the field. This can be updated and optimized in a model-predictive manner on the basis of the assessment of efficacy, in order, for example, to maximize the lifetime of a vehicle battery under the constraint of a sufficiently rapid charging operation.

[0089] In step S6, it is alternatively or additionally possible, based on the electrochemical battery model, especially one that has been adapted, to derive a charging strategy in order to obtain an optimized charging curve that minimizes stress factors for aging of the vehicle battery. In this case, the electrochemical battery model may also be implemented in the vehicle.

[0090] Subsequently, the method is continued with step S1.