Classifications

• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
  • B60L58/00—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles
  • B60L58/10—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for monitoring or controlling batteries
  • B60L58/16—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for monitoring or controlling batteries responding to battery ageing, e.g. to the number of charging cycles or the state of health [SoH]
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
  • B60L3/00—Electric devices on electrically-propelled vehicles for safety purposes; Monitoring operating variables, e.g. speed, deceleration or energy consumption
  • B60L3/0023—Detecting, eliminating, remedying or compensating for drive train abnormalities, e.g. failures within the drive train
  • B60L3/0046—Detecting, eliminating, remedying or compensating for drive train abnormalities, e.g. failures within the drive train relating to electric energy storage systems, e.g. batteries or capacitors
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
  • B60L50/00—Electric propulsion with power supplied within the vehicle
  • B60L50/50—Electric propulsion with power supplied within the vehicle using propulsion power supplied by batteries or fuel cells
  • B60L50/60—Electric propulsion with power supplied within the vehicle using propulsion power supplied by batteries or fuel cells using power supplied by batteries
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
  • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
  • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
  • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
  • G01R31/374—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] with means for correcting the measurement for temperature or ageing
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
  • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
  • G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
  • G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current measurements
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
  • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
  • G01R31/389—Measuring internal impedance, internal conductance or related variables
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
  • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
  • G01R31/392—Determining battery ageing or deterioration, e.g. state of health
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60Y—INDEXING SCHEME RELATING TO ASPECTS CROSS-CUTTING VEHICLE TECHNOLOGY
  • B60Y2200/00—Type of vehicle
  • B60Y2200/90—Vehicles comprising electric prime movers
  • B60Y2200/91—Electric vehicles
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
  • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
  • G01R31/378—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] specially adapted for the type of battery or accumulator
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
  • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
  • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
  • Y02E60/10—Energy storage using batteries
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
  • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
  • Y02T10/00—Road transport of goods or passengers
  • Y02T10/60—Other road transportation technologies with climate change mitigation effect
  • Y02T10/70—Energy storage systems for electromobility, e.g. batteries

Definitions

• the present invention relates to a method for determining a status value of a traction battery of an electric vehicle, which characterizes the aging status of the traction battery, preferably a SoH value of the traction battery, the traction battery being charged or discharged by means of a test load and at least one time
• the respective pair of values of an output voltage and a charging or discharging current of the traction battery is detected, with an ohmic internal resistance of the traction battery being determined on the basis of the recorded value pair of the output voltage and the charging or discharging current, and based on the determined ohmic internal resistance the status value of the traction battery is determined.
• Electric vehicles are increasingly being used to reduce emissions of gases that are harmful to the climate, especially CO2 in the transport sector. This applies not only to passenger cars, but also to trucks. At least part of the electrical energy required to operate the electric vehicles is temporarily stored in a traction battery and made available when required.
• the mentioned traction battery is therefore a rechargeable battery or an accumulator.
• the electric vehicles mentioned do not necessarily have to be only those electric vehicles whose operating energy is provided exclusively by the traction battery. Rather, the term “electric vehicle” also includes vehicles in which an electric drive is combined with another drive, for example an internal combustion engine, ie so-called hybrid vehicles. Furthermore, the term “electric vehicle” includes not only vehicles in which the traction battery is charged from an external power source, but also those vehicles in which at least part of the electrical operating energy can also be generated on board the vehicle, for example by means of a Fuel cell system and / or by means of solar cells.
• the term "electric vehicle” also includes any other vehicles in which at least part of the drive energy is provided by the traction battery, for example bicycles with electric drive support, such as e-bikes, pedelecs, cargo bikes, e-scooters, or electrically powered small scooters ler, but also electrically powered wheelchairs.
• bicycles with electric drive support such as e-bikes, pedelecs, cargo bikes, e-scooters, or electrically powered small scooters ler, but also electrically powered wheelchairs.
• traction batteries with battery cells based on lithium-ion technology are widely used as traction batteries.
• traction batteries are also used, the battery cells of which are based on lead technology, which has long been known.
• the method described here and its advantageous refinements are in any case not restricted to a specific battery cell type, but can in principle be applied to different types of traction batteries or battery cell types.
• Traction batteries in electric vehicles like other types of rechargeable batteries, such as those used in cell phones or other electrical or electronic devices, are subject to an aging process that is caused by both aging and usage, i.e. the number the charge and discharge cycles, is determined.
• the aging process of a traction battery leads, among other things, to the fact that the storage capacity of the traction battery decreases over time.
• the storage capacity can vary significantly depending on the actual use of the traction battery. Particularly severe aging and the associated decrease in storage capacity are caused by high temperatures, high charging and / or discharging currents, deep discharging or high continuous loads.
• FIG. 1 An exemplary aging curve of a traction battery is shown in FIG. 1.
• this curve indicates the actual storage capacity or capacity Q in ampere-hours (Ah) as a function of the number of aging cycles N.
• the experiment on which the curve is based was carried out at an ambient temperature of the traction battery of 40 ° C.
• the charging current was 1 C, while the discharge current was 3 C for the determination of the aging cycles.
• the values of 1 C or 3 C mean that the variable C represents the charging or discharging current in amperes (A) with the numerical values of the nominal storage capacity QN of the traction battery.
• the actual storage capacity Q of a traction battery can therefore not only be measured by completely discharging a fully charged traction battery and continuously measuring the discharge current and discharge time, but also by means of an alternative method in which a test load is applied to the Basis of a respective value pair of an output voltage that has been determined at least at one point in time and a charging or discharging current of the traction battery, the ohmic internal resistance of the traction battery is determined.
• the relationship between the actual capacitance Q and the ohmic internal resistance Ri of a traction battery is shown as an example in FIG.
• a test load can be designed as a load resistor, ie an energy sink or current consumer, which effects a discharge current, or as a charger, ie an energy source or current generator, which effects a charging current.
• a load current can accordingly be a discharge current or a charging current.
• a status value of the traction battery can then be determined, which characterizes the aging status of the traction battery.
• the actual storage capacity of the traction battery for example, can be determined as a status value.
• SoFI value is used synonymously for the term "health value” (SoFI stands for "State of Health”).
• SoH value describes the ratio of the current, aging-related reduced storage capacity of the traction battery to its original, ideal or nominal storage capacity and is usually given as a percentage.
• the above-mentioned determination of the ohmic internal resistance of the traction battery on the basis of a recorded pair of values of the output voltage and the charging or discharging current when applying a known test load is based on an electrical model or an equivalent circuit diagram for a battery or a battery cell.
• Such an exemplary equivalent circuit diagram which characterizes the structure of a battery cell consisting of a voltage source, various resistors Ri to R4 and various capacitors C2 to C4, is shown in FIG. 3. It is also possible to use different equivalent circuit diagrams, for example with only one serial ohmic internal resistance R1 and one RC element R2, C2.
• SoC battery state of charge
• SoFI state of charge of the battery
• Li ohmic resistance
• SoC state of charge
• the SoC describes the current state of charge of accumulators and is usually given in percentages, with 100% representing a fully charged accumulator. 100% minus the value of the state of charge gives the degree of discharge (DoD or DOD - depth of discharge).
• the ohmic resistance Ri decreases significantly with increasing temperature. It was also found that the ohmic resistance Ri remains almost constant in a large SoC range of generally 10 to 90%, in particular from 30 to 90%. Only when the battery is more than 90% discharged can a sharp increase in the ohmic resistance Ri be observed.
• the investigations carried out on individual cells have shown that essentially only the temperature and aging have a significant influence on the values of the resistances and the capacities of the replacement model, whereas the state of charge of the cells has hardly any influence on the ohmic resistance.
• FIG. 10 shows a tendency for the internal resistance Ri to increase when a traction battery is continuously discharged, with the influence of other RC elements over time, see the battery equivalent circuit diagram in FIG , ie with long-term loading, a clearly non-linear internal resistance develops, which can be a multiple of the internal resistance Ri in the idle state.
• An alternative diagnostic method is impedance spectroscopy. This determines an impedance, i.e. the alternating current resistance, of a traction battery as a function of the frequency of an alternating voltage or alternating current. Impedance spectroscopy is usually carried out by impressing an alternating voltage, i.e. the potential of the working electrode is sinusoidally modulated and the current and its phase are measured. However, this requires direct galvanic access to the battery and a complex interpretation of the results. For the technical investigation and / or evaluation of electric vehicles, in particular a mercantile evaluation of used vehicles, it is desirable to know the condition of the traction battery regardless of environmental influences or specific measurement conditions.
• At least one normalization variable characterizing the traction battery is determined, that on the basis of the determined ohmic internal resistance and the at least one normalization variable, a normalized internal resistance related to a reference value of the normalization variable is determined, with the determination of the status value of the traction battery on the Based on the standardized internal resistance.
• the ohmic internal resistance of the traction battery can be normalized to one or more normalization variables.
• These normalization variables are, in particular, parameters which each characterize a property or a state of the traction battery and which can have an influence on the value of the internal resistance determined.
• An example of a normalization variable is the temperature of the traction battery, which will be explained in more detail below.
• the normalized internal resistance can also be determined in several iterations, with the respective normalized internal resistance being determined in a subsequent normalization step on the basis of the normalized internal resistance determined in the previous normalization step and the at least one normalization variable of the subsequent one In the normalization step, a further normalized internal resistance related to a reference value of this normalization variable is determined.
• the measured ohmic internal resistance is therefore converted into an internal resistance standardized to one or more normalization variables, which enables internal resistance measurements to be compared that were carried out on different traction batteries and under different conditions by eliminating the boundary conditions for determining internal resistance as a result of normalization.
• the state value for example the SoH value of the traction battery, can then finally be determined from the normalized internal resistance, with a mathematical function or a table, both for example a lookup table can be used as a basis.
• the charge or discharge is designed using a test load in such a way that the charge current or discharge current changes according to a step function.
• the charge current or discharge current changes according to a step function.
• provision can be made for several pairs of values to be recorded before and after the load jump, with the time interval being able to be equidistant or also variant.
• the measured value density is preferably increased directly in the area of the load current.
• the determination of a standardized internal resistance for determining the state value can be carried out in a simple manner.
• An exemplary determination using a characteristic curve function can be carried out with little technical signal processing effort.
• a conceivable alternative solution, in which a reference characteristic diagram is used as the basis, which must take into account a large number of relevant parameters, is significantly more complex than the solution according to the invention.
• the standardization method according to the invention enables a significant reduction in the cost of an initial characterization of a respective battery cell type to determine the relationship between the stated state value and the ohmic internal resistance. This makes it possible to quickly and economically assess different types of traction batteries, which can also have different states of aging, with regard to their state, in particular their SoH.
• the condition of the traction battery can be determined very quickly in a few minutes with low fault tolerance and inexpensively and without dismantling.
• the method according to the invention is characterized by a low energy load on the traction battery. Furthermore, only compact, inexpensive test equipment is required as a diagnostic device. There are only relatively few errors due to the standardization methodology and independence from energy buffers provided by the manufacturer is achieved. Direct galvanic access to the traction battery or to measuring points for current / voltage measurements is not necessary.
• the measured values can be picked up indirectly via a diagnostic interface of the vehicle, ie the OBD interface (on-board diagnosis). Measured values can be picked up via a standardized connector via a serial interface with standardized protocol such as K-line or via the CAN bus. This can usually be done using a plug dongle with, if necessary, a wireless connection to a diagnostic device, for example in the form of a mobile data terminal such as a smartphone, tablet or notebook.
• the discharging takes place as part of an evaluation drive of the electric vehicle, the test load being formed by an assembly of the electric vehicle, preferably by a drive motor of the electric vehicle.
• the test load can be switched on to initiate the charging or discharging process, for example, by briefly strong acceleration and subsequent braking. Braking for the determination of the internal resistance can also be omitted and is primarily for test drive-specific reasons. This results in a significant load on the traction battery. A distance of less than 100 m, preferably up to 50 m, for example, can be sufficient for such an evaluation drive. If necessary, the evaluation run can be repeated one or more times.
• boundary conditions of this evaluation run which are suitable for influencing the load current (for example the The type of electric vehicle, the prevailing weather conditions, the conditions, the condition of the road, the inclination of the road, a load on the electric vehicle or the influences of a control of the drive motor) are taken into account, for example, by specifying respective areas for the boundary conditions that are not under - or may be exceeded.
• the boundary conditions can also be taken into account by including them in the process in the form of one or more further characterizing nomination variables.
• the exposure time of the test load can be very short in the range of 10-100 ms up to 10 seconds. However, test loads can last from 1 second to 30 seconds, even up to 2 minutes, in particular between 5 to 15 minutes.
• the load current can regularly be a discharge current, but it can also be an impressed charging current.
• a first normalization variable is a temperature of the traction battery while the values of the output voltage and the load current are being recorded, and the reference value of the first nomination variable is a reference temperature.
• the internal resistance determined at a specific battery temperature can be converted to a standardized internal resistance based on the reference temperature.
• a second normalization variable preferably characterizes a type of traction battery
• the reference value of the second normalization variable is a normalization factor which relates different types of traction batteries to one another, the normalization factor being specified on the basis of at least one battery type parameter.
• the battery type parameter can, for example, characterize the cell type of the traction battery, for example lithium-ion or lead technology, and / or also represent the type of arrangement of the cells of the traction battery, for example a respective number of battery cells connected in series and / or in parallel.
• the normalization factor is preferably obtained empirically, for example by reference measurements on new batteries of the respective type.
• mathematical or statistical methods can also be used in addition to the determination of the normalization factor, for example an interpolation or extrapolation, i.e. the battery type parameter or the associated second normalization factor for a battery with a specific number of rows connected in parallel and a specific one Number of batteries per row has been determined can be converted to batteries for which the specified number of cells deviates from this.
• the normalization factor is usually dimensionless.
• other normalization variables such as the degree of charge (SoC) of the traction battery, can also be taken into account.
• the state value is determined on the basis of the normalized internal resistance using a mathematical model or a table, preferably a lookup table or a characteristic field, with preferably parameters or values that the mathematical model or the table describe to be retrieved from a database.
• the database is preferably stored on a server, the parameters or values being called up via a wireless and / or wired data connection, for example a mobile data connection or an Internet connection.
• the status value can thus be normalized, i.e. converted into a comparable value by using reference values.
• a first normalization variable is a temperature of the traction battery during the acquisition of the values of the output voltage and the load current and the reference value of the first normalization variable is a reference temperature.
• the temperature of the traction battery is determined in that, in a first measuring step, a first ambient temperature at a first point in time and a first ohmic internal resistance of the traction battery is determined, and a second ambient temperature and a second ohmic resistance of the traction battery are determined in a second measuring step after a predetermined period of time has elapsed at a second point in time.
• An internal resistance change rate is determined on the basis of the difference between the first and the second ohmic internal resistance and the predetermined time period. On the basis of the internal resistance change rate, a temperature difference between the ambient temperature and the temperature of the traction battery is determined. The temperature of the traction battery is determined by adding a reference ambient temperature determined from the first and / or the second ambient temperature and the determined difference temperature.
• the ohmic internal resistance of the traction battery depends to a considerable extent on the temperature of the traction battery.
• direct access to the traction battery to determine the battery voltage and the charging or discharging current is not possible.
• These parameters, as well as current and voltage values are regularly provided at an interface of a vehicle diagnostic system (OBD for on-board diagnosis), for example in the form of value pairs that are generated with a specific fixed or variable sampling rate.
• OBD vehicle diagnostic system
• the battery temperature which can possibly be determined by the vehicle diagnostic system at one or more points, is not provided or is only provided in encrypted form. Under certain circumstances, reading out the battery temperature is only possible with considerable additional expenditure in terms of time or processing technology, with additional manufacturer-specific peculiarities often having to be taken into account.
• the aforementioned embodiment of the method provides a possibility of determining the battery temperature in an indirect way. This makes use of the fact that a battery temperature deviating from the ambient temperature adjusts itself to the ambient temperature over time, at least if The battery temperature is not influenced by longer charging and / or discharging processes.
• the adaptation of the battery temperature to the ambient temperature follows a so-called acclimatization gradient, which is characteristic of the type of battery used and depends, among other things, on the design of the traction battery, in particular on the number and arrangement of the battery cells contained in the traction battery.
• the traction battery has a rate of change in its internal resistance, ie a resistance difference per unit of time, which depends on the difference between the battery temperature and the ambient temperature, ie on the temperature difference mentioned.
• the temperature difference present at the time of measurement can be determined.
• the temperature of the traction battery then results from the reference ambient temperature and the determined difference temperature, the reference ambient temperature can be determined for example by forming the mean value of the first and the second ambient temperature. Assuming that the ambient temperature has not changed or has not changed significantly between the two times mentioned, the reference ambient temperature can also be set equal to the first or the second ambient temperature.
• the above-mentioned predetermined period of time between the two measuring steps is preferably between five and fifteen minutes. During this period, a sufficiently large change in the traction battery temperature can be expected, which results in a corresponding change in the ohmic internal resistance of the traction battery.
• the first ohmic internal resistance can be used to determine the status value of the traction battery.
• the state value of the traction battery is determined on the basis of the second ohmic internal resistance. For this is assumed that the battery temperature at the time the second ohmic internal resistance was determined has approached the ambient temperature more than it was at the first time. It follows from this that, due to the lower differential temperature, the rate of internal resistance change also decreases, which improves the measurement accuracy. In addition, there is no need to measure the ohmic internal resistance again, since the ohmic internal resistance actually measured for determining the temperature at the second point in time can also be used to determine the state value.
• the current curve of the load current changes.
• This can be designed, for example, as a current ramp, i.e. a linear rise or fall in a charging or discharging current.
• the loading or unloading takes place by means of the test load in such a way that when the test load is applied, the load current has a current jump.
• the load current can thus be measured in the form of a step response.
• a measuring sequence of pairs of values for the output voltage and the load current is recorded, the measuring sequence comprising a plurality of pairs of values for the output voltage and the load current recorded at quickly successive points in time.
• An impedance consists of an imaginary part, i.e. a reactance, and a real part, i.e. an ohmic resistance. The reactance is usually negligibly small, so that the impedance estimates the ohmic resistance quite precisely.
• the measurement sequence thus represents the step response to the load or current jump generated when the test load is applied.
• the time intervals between the Points in time at which the respective pairs of values are recorded can be constant (ie a fixed sampling frequency or rate is provided) or also vary, with the time density preferably being increased at the point in time of the load jump. If necessary, the time intervals between the points in time can also be specified by the OBD and cannot be influenced.
• the measurement sequence can be recorded in such a way that a first pair of values is recorded at the latest immediately at the time the test load is applied, although the recording of the measurement sequence is preferably also a few milliseconds before the Current jump can take place. This case is therefore also included in the expression "beginning with the application of the test load".
• the ohmic internal resistance can be determined as the quotient of the difference between the recorded output voltage and the open-circuit voltage Uo and the difference between the recorded load current and the closed-circuit current for a respective further value pair of the measurement sequence.
• parameters of a logarithmic function can be determined for the measurement sequence by means of a mathematical compensation calculation, which models the course of the measurement sequence, with the ohmic internal resistance at a desired point in time, preferably at the time of the current jump, or on the basis of the logarithmic function can be determined at least approximately at a corresponding frequency.
• the idle voltage Uo or idle current low is understood to mean the output voltage or load current which is present when the traction battery is loaded with a base load, the base load having a substantial higher ohmic resistance than the test load. Investigations have shown that the course of the internal resistance over time shows the course of a logarithmic function immediately after the test load is applied.
• the ohmic internal resistance can be determined particularly precisely, since the actually measured internal resistance can be determined at a desired point in time, in particular in relation to the point in time of the current jump.
• the internal resistance Ri can take place at a point in time which is very close to the switch-on point in time of the load to, or at another point in time ti with relatively high accuracy, even if no or only imprecise data is available for this point in time stand.
• Recourse to a compensation function is also particularly advantageous if the time relationship between the times at which a respective pair of values was recorded and the time at which the current jump occurred (switching on of the test load) cannot be precisely logged.
• the temporal relationship can then be determined subsequently from the course of the logarithmic function, for example by introducing a temporal shift constant t 0 y set , whereby by maximizing a coefficient of determination R 2 with variation of the shift constant to / fset between the function curve and the measured values is possible. lent an exact estimate of the jump time can be determined.
• the degree of certainty R 2 describes a goodness of fit of a regression, in particular a regression function of the internal resistance behavior, in order to evaluate how well the measured values fit the assumed model of the internal resistance.
• the compensation function By evaluating the compensation function, the fact that the internal resistance of the traction battery has a complex value is also taken into account, ie it includes a frequency-independent real part and a frequency-dependent imaginary part.
• the real part of the complex internal resistance corresponds to the ohmic internal resistance, depending on the test conditions, this is usually not directly measurable. Even if the imaginary part of the internal resistance is significantly, ie approximately one order of magnitude, smaller than the real part, the consideration of the imaginary part in the determination of the internal resistance can improve the accuracy. As a rule, the influence of the imaginary part on the total impedance is negligible.
• the internal resistance can be determined not only in the form of a step response, but also through periodic load changes, the period or frequency of these load changes being varied.
• This method is called impedance spectroscopy.
• the result of such an impedance spectroscopy is shown for an exemplary traction battery in FIG. 13, the determination of the real and imaginary parts Re (Z) and Im (Z) being able to be determined with relatively great technical effort.
• Fig. 13 shows a so-called Nyquist plot, i.e. each point of the imaginary part Im (Z) and the real part Re (Z) of the complex internal resistance Z is shown at a certain frequency.
• the position of the switch-on time of the load can be determined relatively precisely with the aid of the fitted logarithmic function.
• this switch-on time can be estimated by varying the assumed position of this time and maximizing it to the degree of certainty R 2 .
• the Ri is determined using the measurement curve for the battery using the least squares method described.
• b corresponds to the internal resistance Ri at an examination frequency of 1 Hz or the internal resistance after 1 s when a step function is applied.
• the factor a describes approximately the influence of the RC elements in the substitute model described at the beginning (FIG. 3) on the time behavior.
• t 0 ⁇ set is the time between the actual switch-on time and an assumed switch-on time.
• optimization can be used to make a good estimate of t g ffset using a maximum coefficient of determination R 2 , the coefficient of determination R 2 being used to assess the goodness of fit of the regression, ie how well the measured values fit the underlying battery model.
• t offset can initially be set to zero.
• the quality of the curve can be determined with the measure of certainty R 2.
• toffset it is possible to optimize to a maximum R 2 and thus the switch-on time can be estimated relatively precisely.
• the switch-on time is then t 1 sec - t offset - 1 sec. This only applies to step excitations and is only useful to a limited extent for ramp-shaped excitations.
• an expected load current is predetermined by the test load, preferably by an ohmic resistance of the test load, and by the output voltage (e.g. a nominal output voltage or a quiescent output voltage) of the traction battery, with those pairs of values when determining the ohmic resistance stand of the traction battery are not taken into account, in which a difference between the expected load current and the recorded load current exceeds a predetermined tolerance value.
• Said tolerance value can be, for example, 20%, preferably 10%, particularly preferably 5% of the expected load current.
• the detection of the at least one value pair of an output voltage and a load current of the traction battery takes place in several passes, with the test load being switched on in each pass and removed again at the end of the pass, at at least one point in time of a pass a respective pair of values is recorded and a respective ohmic resistance of the traction battery is determined on the basis of the recorded value pair, and a mean value for the ohmic internal resistance is determined from the respective ohmic internal resistance determined in the several runs, with the determination of the state value of the Traction battery based on the mean value of the ohmic internal resistance.
• the determination of the ohmic internal resistance of the traction battery further comprises at least one of the following steps: a) a respective valid measurement range is defined for at least one value of a value pair, a value pair not being taken into account if one or Both values lie outside the respective measuring range, the measuring range preferably being defined on the basis of an absolute value or a rate of change of the associated value.
• a measurement sequence of pairs of values for the output voltage and the load current is recorded, with the test load being continuously switched on for the duration of the measurement sequence, the measurement sequence comprising several pairs of values for the output voltage and the load current recorded at briefly successive points in time, one pair of values is not taken into account if one or both values of this value pair are equal to the corresponding value of at least one value pair that was recorded at a previous point in time.
• so-called hanging measured values can be sorted out, in which, due to errors, one or both values of a value pair do not change over one or more successive measurements.
• the low-pass filtering can improve the accuracy of the state value determination, in particular if a repetition of the measurement in several runs cannot be carried out.
• a measurement sequence of pairs of values for the output voltage and the load current is recorded, the test load being continuously applied for the duration of the measurement sequence, the measurement sequence comprising several pairs of values for the output voltage and the load current recorded at briefly successive points in time, with d1)
• a sliding mean value of the ohmic internal resistance is determined from the pairs of values for the output voltage and the load current of the measurement sequence, with the respective ohmic internal resistance from the difference between the two output voltages divided by the difference between the two loads, preferably for two respective pairs of values recorded immediately one after the other flow currents are determined and the moving average of the ohmic see internal resistance is formed by the mean value of the respective ohmic resistances determined in this way, or d2) the ohmic internal resistance is determined from the respective value pairs of the output voltage and the load current on the basis of a mathematical compensation calculation, preferably
• the evaluation ie the determination of the ohmic resistance
• the ohmic internal resistance can be carried out from the multiple value pairs on the basis of a mathematical compensation calculation, preferably using the least squares method. Seen clearly, the voltage is plotted against the current (or vice versa) for each pair of values and a compensation burr is determined according to the principle of least squares ("Least Square Fit").
• Least Square Fit least square Fit
• Both methods for d can be further improved through the use of further statistical methods, such as the determination of a range, an interquartile range, a variance, a scatter or a standard deviation and, if necessary, can be discarded if the data quality is too low.
• statistical methods can be applied to the result as well as to the raw measurement data, ie to the original current and voltage values. Two or more of the above-mentioned methods can also be combined with one another in order to achieve a further improvement in the data quality.
• a voltage, in particular an open circuit voltage of the traction battery can be determined approximately in a voltage-current diagram if no direct pair of measured values with a current, in particular idle current Io and a voltage, in particular idle voltage Uo, is available.
• a current in particular idle current Io
• a voltage in particular idle voltage Uo
• at least two, in particular a plurality of measured value pairs from current and voltage are to be compared and a straight line through the measured value pairs to be determined using the least squares method.For example, it enables the determination of an intersection of this straight line with the current axis I, i.e. for the quiescent current Io an estimate of the open-circuit voltage Io of the battery at a current state of charge.
• the traction battery is excited by a load current in the form of a charging or discharging current.
• the type of excitation can take place as a ramp-shaped excitation or as a jump-like excitation. If there is a sudden excitation, the previous determination of an open-circuit voltage Uo and a closed-circuit current Io can be used as a reference to determine the internal resistance Ri.
• Improved identification of the point in time of the jump can be achieved by optimizing the coefficient of determination R 2 of a curve fit. Furthermore, an improved identification of the time-dependent internal resistance Ri (ti) can take place.
• the present invention also relates to a diagnostic device for determining a status value of a traction battery of an electric vehicle, the diagnostic device having an evaluation unit which can be coupled directly or indirectly to the traction battery and which is set up to carry out the method according to one of the preferred embodiments according to the invention described above.
• a direct coupling of the diagnostic device with the traction battery is understood in particular to be a coupling in which the diagnostic device can be coupled to voltage or current measuring points of the traction battery.
• An indirect coupling consists in particular in that the diagnostic device is coupled to a diagnostic device, in particular an on-board diagnostic system (OBD) of the electric vehicle, this diagnostic device of the electric vehicle at least the values of the output voltage and the load current, preferably also the temperature of the traction battery , transmitted to the evaluation unit.
• OBD on-board diagnostic system
• the diagnostic device can preferably fall back on a central data storage with regard to the battery data, such as vehicle type, battery type, historical measured values, cross-fleet comparison values.
• the data storage can in particular be implemented as a central cloud storage on the Internet.
• both the diagnostic device can be regularly and independently supplied with new software updates, and the central data storage can also be regularly supplemented with measured values and diagnostic results from various temporally and spatially distributed diagnostic processes. Analyzes based on this can also enable type-specific or fleet-related evaluations with regard to the SoFI behavior of the traction battery in relation to an individual vehicle.
• the diagnostic device advantageously comprises a mobile, portable, independently and wirelessly connectable display and / or input device that can be used in the context of a test inspection inside or outside the vehicle in order to control a diagnostic process and to display diagnostic data.
• the diagnostic device can be designed as a customary mobile terminal such as a smartphone, tablet or notebook.
• 1 is a diagram showing the storage capacity Q of a traction battery as a function of the number of aging cycles N;
• Fig. 2 is a diagram showing the capacity Q and the internal resistance Ri of a traction battery as a function of the number of aging cycles N indicates;
• FIG. 3 shows an equivalent circuit diagram of a battery cell or a traction battery
• FIG. 4 shows a block diagram which shows the determination of a state value of a traction battery in accordance with an embodiment of the method according to the invention
• Fig. 5 is a diagram showing the adjustment of a temperature T of a traction battery to an ambient temperature as a function of the time t;
• FIG. 6 is a diagram showing an internal resistance change rate of a traction battery as a function of a temperature difference between a battery temperature and an ambient temperature exemplarily for a specific battery type; 7 shows a block diagram which indicates a determination of a state value of a traction battery according to a further embodiment of the method according to the invention;
• Fig. 8 is a diagram which indicates the output voltage and the load current of a traction battery as a function of the time when a sudden connection of a test load indicates;
• Fig. 9 is a diagram showing the output voltage and the load current of a traction battery as a function of time in a ramp-shaped connection of a test load indicates;
• FIG. 14 shows a diagram which indicates a coefficient of determination R 2 for a determined internal resistance of a traction battery as a function of a variation of a point in time t offset for the application of a test load.
• Fig. 4 shows a block diagram which illustrates the determination of a status value of a traction battery of an electric vehicle 20 by means of a diagnostic device 10 which is set up to carry out a method according to an embodiment of the present invention.
• the diagnostic device 10 has an evaluation unit which comprises at least one determination module 12 and a normalization module 14.
• the diagnostic device 10 is indirectly coupled to the traction battery (not shown) of the electric vehicle 20 so that the values of an output voltage U, a load current I and a temperature T of the traction battery can be transmitted to the evaluation unit.
• the coupling to the traction battery can either take place directly at corresponding measuring points or sensors or indirectly via an interface of an on-board diagnostic device (OBD) of the electric vehicle 20.
• OBD on-board diagnostic device
• the traction battery of the electric vehicle 20 can be coupled to a test load, for example a drive motor of the electric vehicle 20, in order to cause the traction battery to be discharged.
• the output voltage U and the load current I are transmitted to the diagnostic device 10 in the form of respective pairs of values, whereby both a single pair of values and a measurement sequence of several pairs of values determined at certain time intervals can be recorded by the diagnostic device 10.
• the determination module 12 is set up to determine an ohmic internal resistance of the traction battery. In addition to the actual calculation of the ohmic internal resistance from the output voltage U and the load current I, further data processing steps can be carried out in the determination module 12, which is explained in more detail below, in particular with reference to further embodiments of the method according to the invention and the diagnostic device according to the invention.
• the determined ohmic internal resistance is transmitted to a normalization module 14.
• the temperature T of the traction battery is also transmitted to the standardization module 14.
• the detection of the temperature T of the traction battery hereinafter also abbreviated as battery temperature, is determined in the exemplary embodiment according to FIG. 4 by means of a sensor system that can be arranged within the traction battery and transmitted to the normalization module 14.
• a standardized internal resistance is determined in the standardization module, which converts the ohmic internal resistance measured at the current battery temperature to a standardized internal resistance.
• the battery temperature thus forms a normalization variable, whereby when determining the normalized internal resistance, the currently determined ohmic internal resistance is related to a reference internal resistance using a normalization function or a normalization table, which is structurally identical or also identical at a reference temperature within the framework of the previous other traction batteries has been determined.
• a normalization factor can be taken into account as an additional normalization variable.
• the normalization factor can be provided on the basis of at least one battery type parameter, wherein the battery type parameter can represent, for example, a cell type (lithium ions, lead, etc.), a number of battery cells connected in series and / or parallel, or the like.
• the normalization factor can be obtained empirically, for example by measurements on batteries that are as good as new, and is usually dimensionless.
• the degree of charge (SoC) of the traction battery can be taken into account as a further standardization variable.
• the test load can be applied, for example, by performing an evaluation drive over a relatively short distance of for example up to 100 m, preferably up to 50 m, with the electric vehicle 20, with the highest possible acceleration being advantageously set here.
• the short evaluation run consists, for example, of a short, powerful acceleration.
• the load depends on various test boundary conditions (driving style of the tester, vehicle, weather conditions, road conditions such as pavement surface or inclination, payload of the vehicle, functionality of a vehicle approach control, etc.). If necessary, relevant test boundary conditions can be taken into account in the form of further standardization variables.
• the normalization can be carried out, for example, on the basis of a table, for example a lookup table or a characteristic diagram, or also on the basis of a mathematical model. If several normalization parameters are to be taken into account, the normalization, i.e. the determination of the normalized internal resistance, can also be carried out in several sub-steps.
• the parameters required for normalization i.e. characteristic map tables or characteristic field values or parameters of a mathematical model or a mathematical normalization function, can be stored in the diagnostic device 10 and / or can also be called up by the diagnostic device 10 from an external database.
• the diagnostic device 10 can optionally also feed correction values for these parameters back into the database.
• the normalization module 14 is also set up to determine a status value of the traction battery on the basis of the normalized internal resistance.
• the health status (SoFI) of the traction battery is output as the status value.
• the SoH can be calculated, for example, on the basis of a SoH assignment function or table that was previously determined empirically in tests. From- The SoH is provided, for example, in the form of a log printout 16.
• Other output options are also possible, for example by a display or by wireless or wired transmission to corresponding display, acquisition or data processing devices.
• the SoH value along with other recorded parameters, for example the input parameters U, I and T and possibly vehicle identification data, can be transmitted to a central server, from where a paper or electronic transmission, for example to users of the electric vehicle or to a workshop.
• a central data storage is that different traction batteries or electric vehicles that have not been tested at first can be analyzed.
• a type of standard can be defined for several traction batteries or electric vehicles of the same type, which is composed of empirical values from several batteries or electric vehicles. Compared to a reference to a single reference battery, the influence of any manufacturing tolerances can thus be reduced and, even with a correspondingly large database, the respective aging status of the traction battery can also be taken into account.
• the measured values of the output voltage U and the load current I required to determine the internal battery resistance are usually provided by an OBD of the electric vehicle or another interface, since access to components with high voltage within the battery is usually not possible for safety reasons .
• the battery temperature T is not provided at all or is only provided in encrypted form.
• an alternative method for determining the battery temperature is specified in accordance with this advantageous embodiment. This takes advantage of the fact that when determining the status value, the battery temperature differs from the temperature of the environment in which the test of the traction battery is to be carried out.
• the curve directly gives the Temperature difference between the ambient temperature and the battery temperature.
• the rate of temperature change can be determined from the rate of internal resistance change and from the rate of temperature change, which, as explained above, can be determined from FIG If the gradient DT / t corresponds to the curve in FIG. 5, the associated temperature difference can in turn be derived by appropriate calculation steps. Since the ambient temperature is known or can easily be measured, conclusions can be drawn directly about the battery temperature on the basis of the ambient temperature and the differential temperature.
• the relationship between the rate of internal resistance change over time AHL and the temperature difference DT between the environment and the battery can also be represented in a simplified manner directly by a corresponding curve AHL to DT, see FIG. 6 with regard to a battery-specific temperature behavior.
• this curve which can be represented by a mathematical model or a table, the temperature difference can be read off directly for a respective rate of internal resistance change.
• a first ohmic internal resistance and a second ohmic internal resistance of the traction battery are determined at intervals of, for example, 5 to 15 minutes. The difference between the first and second ohmic internal resistance divided by the time interval between the two measurements then gives the internal resistance change rate ARi / t.
• the ambient temperature T can also be recorded, from which the battery temperature can then be determined by adding the differential temperature. If the ambient temperature T should change slightly during the measurement, one of the two ambient temperatures or an average of the ambient temperatures T determined at the various points in time can be used as the reference ambient temperature. More than two internal resistances Ri can advantageously be determined in order to achieve greater accuracy for determining the rate of change in resistance.
• a diagnostic device 110 designed to carry out this modification of the method according to the invention is shown in FIG. 7. Since the Diagnostic device 110 is a modification of the diagnostic device 10 shown in FIG. 4, only the essential differences are described below. Identical or similar elements are therefore provided with the same reference numerals.
• the diagnostic device 110 also has a buffer module 18 in which an internal resistance value Ri determined by the determination module 12 can be temporarily stored. A transmission of the battery temperature T from the electric vehicle 20 to the diagnostic device 110 is not provided. Instead, the normalization module 14 has an additional input via which an ambient temperature Tu of an environment in which the electric vehicle 20 is at the time of the measurements can be recorded.
• an internal resistance value Ri is determined and transmitted to the buffer module 18, where it is temporarily stored as the internal resistance value Rn.
• the output voltage U and the load current I are measured again at a second point in time and converted in the determination module 12 into a further internal resistance value R i .
• This second internal resistance value is transmitted to the normalization module 14.
• the temporarily stored first internal resistance value Rn is transmitted from the buffer module 18 to the normalization module 14.
• the normalization module now determines the difference between the two internal resistance values Rn, Ri2 and divides this by the time between the two measurement times.
• an associated temperature difference is determined on the basis of the battery-specific curve from FIG. 6, which can be stored in the diagnostic device 110, for example in the form of a table or a mathematical function.
• the normalization module 14 On the basis of this differential temperature and the ambient temperature temperature T u, the normalization module 14 now determines the battery temperature, which can then be used as the basis for the normalization described with reference to FIG. 4.
• FIG. 8 the curves of the output voltage U and the load current I, which reflects a jump in a charging current, an exemplary traction battery is shown.
• the diagram of FIG. 8 shows the measured values for U and I at a respective point in time t.
• the origin of the time scale is chosen arbitrarily.
• a regression function for example an exponential function
• U and I a description function of U and I can be found. If a time offset t 0 set is provided in this regression function, the coefficient of determination R 2 can be maximized by shifting the time base by changing t 0 ff Se t and thus the switch-on time to of the jump S can be determined, this is for example in 14 for different values of t offset .
• Corresponding internal resistance values can be determined from the pairs of measured values determined at a particular point in time.
• some of these internal resistance values Ri are plotted over time t, the internal resistance values Ri1 to Ri3 determined during the jump being marked accordingly.
• the straight line shown in dashed lines in FIG. 10 represents an equilibrium line for the internal resistance measured values Ri.
• FIG. 10 and also in FIG Plausibility check. This is also shown by the minimized value of the coefficient of determination R 2 .
• the current and voltage difference during an acceleration process is used to calculate the internal resistance Ri.
• the internal resistance Ri is calculated according to the equation:
• charging of the battery can also be provided as system excitation. It is often not possible to synchronize the time scale of the system excitation, ie the application of the test load or the charging current, with the time scale of the system response, ie the acquisition of the measured values.
• the resistance Ri in the equivalent circuit diagram of FIG. 3, it is necessary to determine the internal resistance immediately after switching on the test load or at a defined, timely point in time. Due to the large rate of change of current and voltage, the corresponding pairs of measured values are often highly error-prone at this moment or are not determined at the right time due to the discrete sampling. Interpolation or extrapolation of the measurement data is therefore preferred for a correct determination of Ri. A suitable interpretation of the measurement data is therefore essential.
• FIG. 11a essentially corresponds to FIG. 10 and shows a relatively low coefficient of determination R 2 , ie a relatively imprecise determination of the internal resistance profile.
• the measured value Ri1 is discarded due to its strong deviation from the best-fit straight line or a predetermined expected value.
• FIG. 11a shows that the training Equal function of FIG. 11b, the slope has increased somewhat and the value of the coefficient of determination R 2 has improved from 0.9249 (FIG. 11a) to 0.9665 (FIG. 11b).
• FIG. 11d corresponds to FIG. 11c, the time axis (x-axis) having been scaled logarithmically.
• Fig. 12 shows a diagram of a linear current and voltage curve l / U of a traction battery with a ramp-shaped load R.
• Ri To determine the internal resistance Ri, a regression line using a least square approach, ie the method of small- th error squares determined.
• the coefficient of determination R 2 that can be determined here provides information as to whether the compensation function considered for this purpose, in this case a straight line, matches the measured values determined.
• the method is ideal for determining an open-circuit voltage Uo when the current fluctuates.
• a further significant improvement in the data evaluation can be achieved in that those value pairs when determining the ohmic component internal resistance are not taken into account, in which a difference between the expected load current and the recorded load current exceeds a predetermined tolerance value, as was done in the present example for the pair of values on which the internal resistance Ri1 was based.
• the internal resistance can be determined in several runs, whereby the test load is applied in each run and removed again at the end of the run. At least one value pair, preferably a measurement sequence, is recorded in each run. Then a respective ohmic internal resistance of the traction battery is determined for each run. Finally, an average value for the ohmic internal resistance is determined from the ohmic internal resistances determined in several runs. This mean value is then used to determine the status value of the traction battery.
• a respective valid measuring range is defined for at least one value of a value pair, a value pair not being taken into account if one or both values are outside the respective measuring range, where the measuring range is preferably defined on the basis of an absolute value or a rate of change of the associated value is.
• the measuring ranges can be absolute, for example by absolute limit values for the
• a measurement sequence of pairs of values for the output voltage and the load current is recorded, with the test load being applied continuously for the duration of the measurement sequence, the measurement sequence comprising several pairs of values for the output voltage and the load current recorded at briefly successive points in time. A value pair is not taken into account if one or both values of this value pair are equal to the corresponding value of at least one value pair which was recorded at a previous point in time.
• hanging measured values can be eliminated, which result in particular from the fact that transmission errors and, in particular, delays occur during data transmission from the traction battery or the OBD.
• This data can lead to errors in the evaluation result, which are difficult or even impossible to identify in retrospect.
• Such “hanging measured values” can, however, be sorted out according to fixed criteria, since this erroneous data is primarily characterized by the fact that the measured values do not change over a certain period of time. Due to the peculiarity of the method according to the invention, according to which a system response to an abrupt system excitation is to be determined, all measured values that do not differ from the previous measured value can be sorted out.
• At least one value ie voltage or current
• the relevant value pair recorded at a later point in time can be deleted from the evaluating data record. If the error of a hanging measured value only affects one value of a value pair, it can also be replaced with the help of an interpolation from the remaining corresponding values.
• a measurement sequence of pairs of values for the output voltage and the load current is recorded, with the test load being continuously applied for the duration of the measurement sequence.
• the measurement sequence comprises several pairs of values for the output voltage and the load current that are recorded at times in quick succession.
• the measurement sequence is subjected to low-pass filtering. With such a simple filtering it is often possible to achieve surprisingly good improvements in the accuracy of the determination of the internal resistance.
• Low-pass filtering is particularly useful if it is not possible to carry out several measurement runs repeatedly (see method 1.).
• the low-pass filter can be used as if several repeated measurements had been carried out at a similar point in time, but taking into account the inadequate measurement resolution and thus forming a virtual mean value.
• This method can preferably be used for test arrangements which have no jumps but are continuous.
• a measurement sequence of pairs of values for the output voltage and the load current is recorded, with the test load being continuously applied for the duration of the measurement sequence.
• the measurement sequence records several pairs of values for the output voltage and the load current recorded at briefly successive points in time.
• a sliding mean value of the ohmic internal resistance is determined from the pairs of values for the output voltage and the load current of the measurement sequence.
• This method is particularly suitable for a ramp-shaped excitation, ie more continuous Load increase or decrease. This is preferably done by determining the respective ohmic internal resistance from the difference between the two output voltages divided by the difference between the two load currents and the moving average of the ohmic internal resistance by the mean value of the respective ohmic resistances determined in this way for two respective pairs of values recorded immediately one after the other is formed.
• the associated internal resistance is determined from two adjacent pairs of values in the measurement sequence, and an average value of these internal resistances is then calculated according to the following equation: where n is the number of value pairs, and a respective ohmic resistance Rim is determined from two pairs of values recorded immediately one after the other according to the equation n _ Um + l - Um im - - l j ⁇ J m + 1 l m, where Um, Um + i are the respective output voltages and Im, Im + i are the respective load currents of two pairs of values m, m + 1 of the measurement sequence that are recorded immediately one after the other. If the open-circuit voltage Uo and the closed-circuit current Io are selected instead of Um and Im, this method can also be used for sudden excitations.
• the number n does not necessarily have to represent the number of all measured value pairs of the measurement sequence, but can also be a number of measured value pairs to be taken into account, for example if one or Several pairs of measured values have been removed from the measurement sequence or are not to be taken into account.
• the ohmic internal resistance can be determined from the respective value pairs of the output voltage and the load current on the basis of a mathematical compensation calculation, preferably using the least squares method. This approach has already been described above with reference to FIGS. 8 to 14.

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