A method for determining an estimated time constant of an exponential signal

Abstract

A method for determining an estimated time constant (τe) of an exponential signal. The method comprises: reading or receiving 101 discrete samples of the exponential signal which are equidistant in time, new samples being read or received as the signal evolves in time; forming 102 a plurality of consecutive subsets of the samples, each latest subset including the last read or received sample; calculating 103 subset averaged time constants (τs) for each of the subsets; continuously averaging 104 the subset averaged time constants (τs) to form an averaged time constant (τa); and determining 105 the averaged time constant (τa) to be the estimated time constant (τe) when a stop condition is present. The time constant may be related to a state change in a fault monitoring device of a DC power system.

Description

Field of the disclosure The present disclosure relates to a method for determining an estimated time constant of an exponential signal and a power system for implementing such a method. Background United States patent applications US 2022 / 0413034 A1 and US 2022 / 0413035 A1 disclose a power system which comprises a primary resistance circuit and a secondary resistance circuit arranged in parallel to a high side insulation resistance and a low side insulation resistance, wherein the secondary resistance circuit comprises additional resistors which are selectively connectable to a high voltage bus via a switching circuit. Several different states can be implemented by the switches. Voltage values associated with a state change are used to calculate the resistance values for the high side insulation resistance and the low side insulation resistance which is the relevant information to determine if the insulation of the power system is in order or if there is an insulation fault. One problem associated with such systems lies in that after a state change the measured voltages start to change exponentially, the exponential change caused by the RC circuits present in the system. Accordingly, the voltage starts to change after a state change and after an exponential ramp the voltage settles. However, it is not clear how along the voltage change takes, i.e., when the exponential voltage change has settled. This is inconvenient because a new measurement can only be started when the signal has settled, as the steady-state voltage has a to be measured in order to calculate the insulation resistance. Therefore, a fixed long response time needs to be waited before a new measurement can be initiated by implementing a further state change. There is a need for a method that allows to determine an estimated time constant of an exponential signal in a simple and efficient manner and / or for a power system for implementing such method. Summary of the disclosure In a first aspect there a method for determining an estimated time constant of an exponential signa is provided. The method comprises the steps: reading or receiving discrete samples of the exponential signal which are equidistant in time, wherein new samples are continuously read or received as the signal evolves in time; forming a plurality of consecutive subsets of the samples, wherein the subsets are consecutive in time and each latest subset includes the last read or received sample; calculating subset averaged time constants for each of the plurality of subsets, wherein for each subset a subset averaged time constant based on the samples of the respective subset is calculated; continuously averaging the subset averaged time constants to receive an averaged time constant, wherein consecutively further subset averaged time constants are considered as the signal evolves in time and new subsets are formed; and determining the averaged time constant to be the estimated time constant when a stop condition is present, the stop condition stopping further calculation of the averaged time constant. Aspects of the method and power system of the disclosure are thus based on the idea to estimate the time constant of the exponential signal based on calculations which are carried out on subsets of the samples, wherein for each subset an averaged time constant is calculated. The terminology “subset averaged time constant” is chosen to identify a time constant calculated on the basis of the samples of a particular subset. The subsets are consecutive in time and further subsets are added as the signal evolves in time and further samples of the signal are read or received. The plurality of subset averaged time constants is continuously averaged to receive an averaged time constant. At some point, if a stop condition is present, the calculation, i.e., the further averaging of the averaged time constant based on new subsets is stopped. The averaged time constant that has been calculated when the calculation is stopped is then chosen to be the desired estimated time constant. The method of the present disclosure thus allows to estimate the settled in signal value based on the exponential curve earlier than the settling time. Aspects of the present disclosure thus allow to determine the time constant of the exponential signal at an early stage of the signal development based on sample measurements of the signal. It is beneficial to know the time constant, because when knowing the time constant it is i) possible to predict the exact time when the signal has settled (which typically is 5 times the time constant), and ii) it is further possible to predict the signal level at which the signal will settle (choosing a large time in the respective equation). The present disclosure thus allows to determine the time when the signal has settled and the final signal value without having to wait until the signal has actually settled. This allows, for example, to make measurements in short repetition, as is required, e.g., in power systems as will be discussed further below. It is pointed out that in case a stop condition does not occur, the determination of an estimated time constant has not been successful. In such case, it is possible to wait until the signal has settled and determine the signal value at that time. However, in such case, it is not possible to expedite determination of the final signal value. It is further pointed out that the time constant of an exponential curve is typically referred to as tau (t) or tau value: e4 / T. In the following, time constant is also referred as tau or tau value. In some embodiments, the calculation of the averaged time constant may be stopped (such that the desired estimated time constant is chosen to be equal to the averaged time constant as averaged at the stop time) in three situations. First, further calculation may be stopped when the difference between the latest subset averaged time constant and the previously determined averaged time constant is smaller than a first predetermined value, wherein the first predetermined value defines a small deviation from the previously determined averaged time constant. This regards the situation in which the subset averaged time constant has converged towards the averaged time constant. Second, further calculation may be stopped when the difference between the latest subset averaged time constant and the previously determined averaged time constant is larger than a second predetermined value. This regards the situation that the inaccuracy in the determination of the subset averaged time constant increases such that it is better to not consider further subset averaged time constants. This may be the case when the voltage settles such that the difference between samples decreases, such that the calculated time constant is getting more inaccurate. Third, further calculation may be stopped when a defined time period has elapsed, such as at least the so far averaged time constant. The third situation considers the object to determine the time constant of the exponential signal at an early time of the signal development. In some embodiments, it is provided that each subset comprises three samples, the three samples being separated at equal distance, and that a subset averaged time constant is calculated based on these three samples. Further, the equal distance between the three samples of a subset is increased by an integer (such as by one) with each consecutive subset. Accordingly, in these embodiments, specific rules are implemented. A first rule is that each subset consists of three samples of even distance. Accordingly, a subset averaged time constant is always calculated on the basis of the three samples of the respective subset. A second rule is that the equal distance between the samples of a subset is increased with each subsequent subset. For example, if a considered subset comprises the sample numbers {0, 2, 4, ...}, the subsequent subset comprises the sample numbers {1, 4, 7, ...}, and the further subsequent subset comprises the sample numbers {2, 6, 10, ...}. Such embodiments are associated with the advantage that the distances between the samples are larger with each subset tau calculation. Accordingly, the differences in the respective signal levels are bigger as well. Thereby, with every new subset tau calculation the accuracy is increased. In a refinement, the subsets of samples each include at least one N-th sample that fulfills the condition N mod M = 1, wherein mod is the modulo function and wherein M is an integer. For example, with M equal to 3 such that N mod 3 = 1, the subsets of samples comprise numbers from the sequence {4, 7, 10, 13, ...}. More particularly, in some embodiments, the samples of a subset are the three samples N, INT(N / 3)*2, and 2*(INT(N / 3)*2) - N, wherein N is one of the samples for which the condition N mod 3 = 1 is met, and wherein I NT (X) is the integer function of the fraction X that assigns the natural number to the fraction X which is equal to the natural number before the decimal point of X. To give an example, if N is equal to 13, then N / 3 is equal to 4,333, and I NT (N / 3) is equal to 4. To give a further example, the subsets that consist of samples N, INT(N / 3)*2, and 2*(INT(N / 3)*2) - N comprise the subset {16, 10, 4} when N = 16, and the subset {13, 8, 3} when N = 13. One advantage of this lies in that the distances between the samples are getting bigger with each subset and only particular samples are included in the subsets. This allows for an effective and accurate estimation of the time constant. It is pointed out that the three samples N, INT(N / 3)*2, and 2*(INT(N / 3)*2) - N which form a subset can alternatively be defined such that a first sample is taken from the sequence {4, 7, 10, 13,16 ...}, a second sample is taken from the sequence {2, 4, 6, 8, ...}, and a third sample is taken from the sequence {0, 1,2, 3, 4, 5 ...}. In some embodiments, the subset averaged time constant for the N-th sample is determined as t(N) - t(INT (y) * 2) wherein ts is the subset averaged time constant, N is the number that fulfills N mod 3 = 1, t(N) is the time (like in seconds for example) when the Nth sample was taken, I NT is the integer function, and U(t(N)) is the exponential signal value att(N) time. The values ts are calculated for each subset and averaged to receive the averaged time constant. In some embodiments, the subset averaged time constants are averaged to receive the averaged time constant until the latest subset averaged time constant deviates less than a first predetermined value from the averaged time constant, and / or the time of one time constant has elapsed. In the first alternative, the deviation of the latest subset averaged time constant from the averaged time constant is so small (i.e., smaller than the first predetermined value) that the averaging can be stopped. In the second alternative, the averaging is stopped after at least one time constant (one tau time) has elapsed (tau as determined by the averaging). The idea is that the time constant is determined at an early stage of the signal development The estimation of the time constant shall take place before the signal has settled, such as after one time constants. When the calculation has stopped and no more subsets are evaluated, the averaged time constant present after the latest added subset averaged time constant is set to be equal to the estimated time constant. In some embodiments, the calculation of the subset averaged time constant is performed in a different manner, wherein the subset also comprises three samples. However, different samples are chosen as the considered three samples. More particularly, in some embodiments, each subset comprises three samples, the three samples being the samples t, t-T and t-2*T, wherein t is the latest added sample of the signal, and T is a predetermined time which is equal to or a multiple of the sample distance; wherein for each subset the subset averaged time constant is calculated based on these three samples of the subset. Accordingly, in such embodiments, tau is calculated at every sample t. A predefined time T is used to find two earlier samples at t-T and t-2T. In a refinement, calculation of the subset averaged time constants starts after a predetermined time of 2*T has elapsed and when the difference between the sample values of two consecutive samples is bigger than a predefined limit. Further, the averaged time constant is determined to be the estimated time constant when the difference between the latest subset averaged time constant and the previously determined averaged time constant is larger than a second predetermined value. In these embodiments, as when the voltage settles the difference between samples decreases and the calculated tau is getting more inaccurate. Calculation is stopped when the inaccuracy exceeds a limit compared to the average of earlier taus. The subset averaged time constant in such embodiments may be calculated based on the formula: T TsW> = ~1nf ^(t -T)-U(t-2* ry wherein ts is the subset averaged time constant, t is the latest added sample, T is the predetermined time, and II is the signal value In some embodiments; the time constant value is calculated based on every even sample only; wherein each subset comprises three samples, the three samples being the samples to, t / 2, t, wherein to is the initial sample of the signal, t is the latest added even sample of the signal and t / 2 is the sample in the middle between to and t; and for each subset the subset averaged time constant is calculated based on these three samples of the subset. Accordingly, in such embodiments, tau is calculated at every even sample. The samples t, t / 2 and t=0 are used to consider the maximum possible voltage differences when determining the subset averaged time constants. The subset averaged time constant may be calculated based on the formula: t / 2 .V / t) - C / (t / 2). ■u(t / 2) - u(toy wherein ts is the subset averaged time constant, t is the latest added even sample, to is the initial sample of the signal, and U is the signal value. In some embodiments, after determining the estimated time constant a final predicted signal value is determined in accordance with the formula [ / (t) Vend = U(0) +--- 1 — e Te wherein Uend is the final predicted signal value, U(0) is the signal value at the beginning (sample 0) of the exponential signal, ll(t) is the signal value at the sample number t, wherein t is latest sample which has been considered for the averaged time constant Ta, and Te is the estimated time constant. In some embodiments, after determining the estimated time constant the time at which the signal has settled is estimated as five times the estimated time constant. After this time it can be assumed that the signal has settled. In some embodiments, the signal is a voltage signal for charging a capacitance. More particularly, the signal may be a voltage signal in a power system that settles exponentially after a state change in a fault monitoring device of the power system. In a second aspect a power system is provided. The power system comprises a DC battery having a DC battery positive terminal, a DC battery negative terminal and a battery voltage, a positive voltage rail connected to the DC battery positive terminal, a negative voltage rail connected to the DC battery negative terminal, a chassis, a high side insulation resistance Risoh insulating the chassis from the positive voltage rail, a low side insulation resistance Risol insulating the chassis from the negative voltage rail, and a fault monitoring device configured to assume at least two states, wherein each state is associated with a different resistance of the fault monitoring device. The power system further comprises a controller configured to determine the time constant of an exponential voltage signal associated with a state change, wherein the controller is configured to: read or receive discrete samples of the exponential voltage signal which are equidistant in time, wherein new samples are continuously read or received as the signal evolves in time; form a plurality of consecutive subsets of the samples, wherein the subsets are consecutive in time and each latest subset includes the last read or received sample; calculate subset averaged time constants for each of the plurality of subsets, wherein for each subset a subset averaged time constant based on the samples of the respective subset is calculated; continuously average the subset averaged time constants to receive an averaged time constant, wherein consecutively further subset averaged time constants are considered as the signal evolves in time and new subsets are formed; and determine the averaged time constant to be the estimated time constant when a stop condition is present, the stop condition stopping further calculation of the averaged time constant. Such power system allows to determine the time constant of the exponential voltage signal at an early stage of the signal development based on sample measurements of the signal. The voltage changes associated with a state change settle with an exponential curve due to capacitances that are connected in parallel to the high side insulation resistance and the low side insulation resistance. Such capacitances represent the capacitance of the power system and may be formed, e.g., by cable insulations and filter capacitors. According to the present disclosure, the controller is configured to determine the time constant of the exponential voltage change before the voltage change has settled in. This allows to reduce the time it takes to determine the high side insulation resistance and the low side insulation resistance. This time depends on the resistance and capacitance values of RC circuits present in the system. Such RC circuit may have large RC time constants of up to tens of seconds when a high capacitive load and a high resistance are present, wherein the time constant is equal to the product of R and C (R*C). Without the inventive method / controller, the time of several time constants (such as at least five) needed to be waited until the high side insulation resistance and the low side insulation resistance can be determined which means of the presence of a long response time. The settled in value can be calculated without having to wait for the voltage settling in. In some embodiments, the controller is further configured to: determine if the estimated time constant is the first estimated time constant after startup of the power system; if so, provide the predicted voltage level at which the signal will settle on the basis of the first estimated time constant; and if not, determine whether a foreseeable wait time is less than a required response time. If the foreseeable wait time is less than a required response time, wait for the foreseeable wait time and measure the actual voltage value directly at the end of the foreseeable wait time. If the foreseeable wait time is not less than a required response time, provide the predicted voltage level at which the signal will settle on the basis of the first estimated time constant. This aspect of the disclosure considers the requirement that after startup of a power system a fast measurement is required to determine whether the insulation is in order or not. Therefore, it is determined if the estimated time constant is the first estimated time constant after startup. In such case, the settled in voltage is predicted on the basis of the first estimated time constant, and this predicted voltage provides for an insulation resistance value which is less accurate but sufficiently accurate for determining whether the insulation is in order or not. If the estimated time constant is not the first estimated time constant, there is less hurry to make a voltage measurement. It is then determined a foreseeable wait time, which is typically 5 times the time constant (5*tau). It is further considered the required response time, which is a predetermined fixed value. For example, the required response time is 50 seconds. If the foreseeable wait time is less than a required response time, the actual voltage value is measured directly at the end of the foreseeable wait time, wherein the most accurate insulation resistance value can be provided. If the foreseeable wait time is not less than a required response time, the predicted voltage level at which the signal will settle is provided on the basis of the first estimated time constant. In some embodiments, the controller is further configured to - if the conditions for determining the estimated time constant are not present - use a steady-state detector to determine the final voltage value, wherein the final voltage value is a steady value of the steady-state detector. The steady-state detector determines if the voltage signal is in or approaches a steady-state in which it does not change anymore. If a steady-state is found, then that voltage value is used. This, however, takes considerable time and, therefore, is considered as a fallback situation only in case the time constant calculation has failed (e.g., a timeout or a calculation error occurred). The skilled person will appreciate that except where mutually exclusive, a feature or parameter described in relation to any one of the above aspects may be applied to any other aspect. Furthermore, except where mutually exclusive, any feature or parameter described herein may be applied to any aspect and / or combined with any other feature or parameter described herein. Brief description of the drawings The method and power system of the present disclosure will be explained in more detail on the basis of exemplary embodiments with reference to the drawings in which: FIG. 1 is a flow chart of a method for determining an estimated time constant of an exponential signal; FIG. 2 is a first variant of how an average time constant is calculated based on subsets of the samples which each consist of three samples; FIG. 3 is a table showing samples of an exponential signal, the corresponding voltage level and particular subsets of the samples as chosen by the method of FIG. 2 from which subset averaged time constants are determined; FIG. 4 shows an example exponential signal and samples at which voltage signals are determined; FIG. 5 shows the beginning of an exponential curve on the basis of which the time constant of the exponential curve is determined; FIG. 6 is a flowchart of a method which includes the determination of an estimated time constant in accordance with FIG. 1 and considers situations in which the estimated time constant calculation fails and / or is not required; FIG. 7 is a second variant of how an average time constant is calculated based on subsets of the samples which each consist of three samples; FIG. 8 is a third variant of how an average time constant is calculated based on subsets of the samples which each consist of three samples; and FIG. 9 is an embodiment of a power system implementing the method of FIG. 1; Detailed description The disclosure relates to a method for determining an estimated time constant of an exponential signal. Such signal may be a voltage signal that occurs in a power system that implements RC circuits. In the following description, the inventive method is described in the context of a power system that comprises a fault monitoring device as shown in FIG. 9 by way of example, without the method being limited to such system. FIG. 9 shows an embodiment of a fault monitoring device 2. The fault monitoring device 2 is configured to measure a high side insulation resistance Risoh and a low side insulation resistance Risol of a power system 1 and can be considered to be part of the power system 1. The power system 1 is shown on the left-hand side of FIG. 9. It comprises a DC battery 7 that has a positive terminal 71 and a negative terminal 72. Between the positive terminal 71 and the negative terminal 72 a battery voltage Ub is present. A positive voltage rail 3 is connected to the DC battery positive terminal 71 and a negative voltage rail 4 is connected to the DC battery negative terminal 72. The positive voltage rail 3 and the negative voltage rail 4 form a high-voltage bus. The power system 1 further comprises a chassis 5. The chassis 5 is insulated from the positive voltage rail 3 by the high side insulation resistance Risoh. Further, the chassis 5 is insulated from the negative voltage rail 4 by the low side insulation resistance Risol. The voltage between the positive voltage rail 3 and the chassis 5 is the high side voltage Uhigh. The voltage between the chassis 5 and the negative voltage rail 4 is the low voltage Ulow. The sum of the high voltage and the low voltage is equal to the battery voltage: Ub = Uhigh + Ulow. A common mode voltage Ucm is present at the chassis 5, the common mode voltage being defined as the arithmetic mean of the high voltage and the low voltage: Ucm = % (Uhigh - Ulow). If the high voltage Uhigh and the low voltage Ulow are equal, the common mode voltage is zero. In parallel to the high side insulation resistance Risoh a capacitance Cisoh is arranged between the chassis 5 and the positive voltage rail 3. Similarly, in parallel to the low side insulation resistance Risol a capacitance Cisol is arranged between the chassis 5 and the negative voltage rail 4. The capacitances Cisoh and Cisol represent capacitive loads of the system. In a power system such as the power system 1 of FIG. 9, it is required that the insulation of the positive voltage rail 3 and of the negative voltage rail 4 from the chassis 5 is monitored. This can be done by monitoring the values of the resistances Risoh and Risol. The fault monitoring device 2 of FIG. 9 serves to provide for such monitoring. The fault monitoring device 2 comprises a first parallel circuit of resistors, the first parallel circuit comprising a first branch 21 and a second branch 23 which are both connected at one end thereof to the positive voltage rail 3 of the power system 1. The first branch 21 comprises a first resistor R_MEAS_1 and a second resistor R_MEAS_2 which are arranged in series and form a first voltage divider. The resistance of the first resistor R_MEAS_1 is substantially larger than the resistance of the second resistor R_MEAS_2. For example, the first resistor R_MEAS_1 may have a resistance in the range between 10 MQ and 50 MQ, while the second resistor R_MEAS_2 may have a resistance in the range between 10 and 100 kQ. A voltage U_H is measured by a first voltage meter 81 between a point between the first and second resistors R_MEAS_1, R_MEAS_2 and the chassis 5. By measuring the voltage U_H, the high voltage Uhigh can be calculated using the formula: Uhigh — R_MEAS_1 + R_MEAS_2 R MEAS 2 U_H The second branch 22 of the first parallel circuit comprises three electrical resistors R_INJ_1, R_INJ_2, R_INJ_3 arranged in series, wherein two of the electrical resistors R_INJ_2, R_INJ_3 can be short-circuited by a first switch SW1 and a third switch SW3. The fault monitoring device 2 further comprises a second parallel circuit of resistors, the second parallel circuit comprising a third branch 23 and a fourth branch 24 which are both connected at one end thereof to the negative voltage rail 4 of the power system 1. The third branch 21 comprises a third resistor R_MEAS_3 and a fourth resistor R_MEAS_4 which are arranged in series and form a second voltage divider. The resistance of the fourth resistor R_MEAS_4 is substantially larger than the resistance of the third resistor R_MEAS_3. For example, the fourth resistor R_MEAS_4 may have a resistance in the range between 10 MQ and 50 MQ, while the third resistor R_MEAS_3 may have a resistance in the range between 10 and 100 kQ. A voltage U_L is measured by a second voltage meter 82 between a point between the third and fourth resistors R_MEAS_3, R_MEAS_4 and the chassis 5. By measuring the voltage U_L, the low voltage Ulow can be calculated using the formula: Ulow — R, ME AS 3 + R MEAS A R_MEAS_3 U_L The voltage dividers of branches 21, 23 thus serve to measure the high voltage Uhigh and the low voltage Ulow. Other embodiments may use other methods to get or measure or determine U_HIGH and U_LOW. The voltage meters 81, 82 may be implemented as Analog-to-Digital Converters (ADCs). The fourth branch 24 of the second parallel circuit comprises three electrical resistors R_INJ_4, R_INJ_5, R_INJ_6 arranged in series, wherein two of the electrical resistors R_INJ_4, R_INJ_5 can be short-circuited by a second switch SW2 and a fourth switch SW4. The first branch 21, the second branch 22, the third branch 23 and the fourth branch 24 are each connected at the other end thereof to the chassis 5 of the power system 1. When applying the fault monitoring device 2 to the power system 1, the first parallel circuit 21, 22 with branches 21, 22 is connected in parallel to the high side insulation resistance Risoh and the second parallel circuit 23, 24 with branches 23, 24 is connected in parallel to the low side insulation resistance Risol. By switching the switches SW1 to SW4 a common mode voltage Ucm different from zero can be injected, wherein the high side voltage Uh and the low side voltage Ui_are not equal, and accordingly the voltages measured by voltage measurements devices 81 and 82 are not equal. The fault monitoring device 2 further comprises a controller 6 schematically depicted in FIG. 1. The controller 6 may be implemented in software and / or hardware. For example, the controller 6 may comprise software stored in a memory and executed by a processor. The controllers is operatively coupled to the switches SW1, SW2. SW3, SW4 and configured to selectively switch the switches SW1, SW2, SW3, SW4 of the second branch 22 and of the fourth branch 24, thereby providing for different states of the first and second parallel circuits 21,22, 23, 24. The controller 6 is further configured to determine from voltage changes associated with a state change the resistance values for the high side insulation resistance Risoh and for the low side insulation resistance Risol of the power system 1. In this respect, the controller 6 may control and / or read values of other elements of the fault monitoring device 2 as well such as of voltage meters 81, 82 measuring the voltages U_H, U_L. Further examples to determine the high side insulation resistance Risoh and the low side insulation resistance Risol are discussed in US 2022 / 0413034 A1 and US 2022 / 0413035 A1. Accordingly, by selectively switching different of the switches SW1, SW2, SW3, SW4, voltage changes can be induced which lead to a different common mode voltages which are impressed on the high-voltage bus, wherein the different voltages are associated with different states, and wherein the different states are defined by the selective switching of the switches SW1, SW2, SW3, SW4. The described fault monitoring device 2 is improved by implementing a method for estimating the end voltage reached at the end of charging the capacitances Cisoh and Cisol. A problem is based on the fact that, upon a voltage change caused by the selective switching, the capacitances Cisoh and Cisol are charged. As is well known, in such case, the voltage settles with an exponential curve, the exponential curve having a time constant t which depends on the product of resistance and capacitance. More particularly, when the state of the switches SW1, S\N2, SW3, and / or SW4 change an exponential rise / decay happens on the high side and respectively a decay / rise happens on the low side. The property of the exponential decay / rise depends on the time constant t (in the following referred to as tau). In the system of FIG. 9, tau can be expressed as: t = R ■ C = ((R JNJ_1 + R_INJ_2 + RJNJ_3') X (R_MEAS_1 + R_MEAS_2) X RJSOH ) X ((R_1N]_A + RJNJ_5 + RJNJ_6) X (R MEAS 3 + R_MEAS_A) X RJSOL) ■ (CJSOH + CJSOL). where AX B = —, and A+B the value of RJNJ_i, of course depends on the state of SWJ. Since Risoh, Risol, Cisoh and Cisol are unknown, tau is unknown during the exponential rise / decay. It is beneficial though to know tau, because with tau it is possible: to predict the exact time when the signal has settled (5*Tau); and to predict the voltage level at which the signal will settle. Predicting the exact time allows to always measure with the quickest possible response time while maintaining the full accuracy. This means that the response time is adjusted to the system parameters and not a worst case “long” wait time is selected for every new measurement. Predicting the voltage level allows to have a very quick (about 5 times quicker) predicted value of the settled in voltages, thus allowing a quicker but less accurate insulation resistance measurement. FIG. 1 shows a flowchart of a method for determining an estimated time constant, which is referred to as Te. The method may be implemented by the controller 6 of FIG. 9. However, the method may alternatively be carried out by another entity or several other entities. In step 101 discrete samples of an exponential signal (in FIG. 9: an exponential voltage signal) are received or read. Receiving the samples means that the sampling of the signal has been carried out by another entity and the respective samples are simply received. Reading the samples means that the sampling is implemented by the entity which performs the method (such as the controller 6). The sampling can be implemented by a conventional sampler that extracts samples from the continuous signal. The samples are equidistant in time and continuously read or received as the signal progresses in time. In step 102, a plurality of consecutive subsets of the samples are formed. The subsets are consecutive in time and each latest subset includes the last read or received sample. For example, the subsets each consist of three samples or another number of samples. In the considered embodiments, the subsets each consist of three samples, wherein different embodiments of how the three samples are chosen will be discussed with reference to FIGS. 2, 7 and 8. In step 103, subset averaged time constants are calculated for each of the plurality of subsets. A subset averaged time constant is the time constant which is received when averaging the samples of the respective subset. The average that is determined as the arithmetic mean in an embodiment. Alternatively, a weighted arithmetic mean may be chosen. In step 104, the subset averaged time constants are continuously averaged to receive an averaged time constant. The averaged time constant is thus the result of the averaging of the subset averaged time constant. Again, the average may be determined as the arithmetic mean or as a weighted arithmetic mean. In step 104, further subset averaged time constants are consecutively further considered in the averaged time constant is the signal progresses in time and as new subsets are formed. Accordingly, the averaged time constant is constantly further improved by the consideration of further subset averaged time constants. In step 105, the averaged time constant is determined to represent the desired estimated time constant when a stop condition is present. With the presence of a stop condition, calculation of the averaged time constant stops and the averaged time constant is not further calculated by the consideration of further subset averaged time constants. The desired estimated time constant is then set to be equal to the averaged time constant as present when the stop condition occurs. In embodiments, a stop condition is present if one of three conditions is met. The first condition is that the difference between the latest subset averaged time constant and the previously determined averaged time constant is smaller than a first predetermined value. In such case, adding further subset averaged time constants does not substantially improve the so far determined averaged time constant. The second condition is that the difference between the latest subset averaged time constant and the previously determined averaged time constant is larger than a second predetermined value. In other words, further calculation of the averaged time constant is stopped when further values of the subset averaged time constants start to become inaccurate. This is typically the case when changes in the signal value from sample to sample becomes small. The third condition is that a defined time period has elapsed. For example, the defined time period is the time of one time constant (one tau) as determined so far. As the time constant tau shall be determined at an early stage of the signal development, at some point the time constant needs to be determined which is set by the defined time period. In an embodiment, the third condition needs to be present in addition to the first and / or second condition, i.e., if the first condition and / or the second condition is not met at the end of the defined time period, the calculation of the time constant has not been successful. FIG. 2 depicts a first variant of how an average time constant is calculated based on subsets of the samples which each consist of three samples. There are considered three samples for each subset, wherein the three samples are separated and at equal distance, and wherein a subset averaged time constant is calculated based on these three samples, step 201. Further, in accordance with step 202, the equal distance between the three samples of a subset is increased by an integer with each consecutive subset. Accordingly, as the signal evolves, the distance between the three samples of a considered subset is becoming larger and larger. In step 203, which is similar to step 104, the subset averaged time constants are averaged to receive the averaged time constant. In an embodiment, the subsets of samples each include at least one N-th sample that fulfills the condition N mod 3=1, wherein mod is the modulo function. Accordingly, each subset comprises at least one sample from the sequence {4, 7, 10, 13, ...}. More particularly, the three samples of a subset are built based on N-th sample that fulfills the condition N mod 3 = 1 as follows: sample N, sample INT(N / 3)*2, and sample 2*(INT(N / 3)*2) - N, wherein N is one of the samples for which the condition N mod 3 = 1 is met, and wherein I NT (X) is the integer function of the fraction X that assigns the natural number to the fraction X which is equal to the natural number before the decimal point of X. For example, INT(4 / 3) is equal to 1 and INT(5 / 3) is equal to 1. To give an example, the subsets that consist of samples N, INT(N / 3)*2, and 2*(INT(N / 3)*2) - N comprises the subset {16, 10, 4} when N = 16, the subset {13, 8, 3} when N = 13, and the subset {10, 6, 2} when N = 10. Respective subsets of three samples N, INT(N / 3)*2, and 2*(INT(N / 3)*2) are shown in the table of FIG. 3. The table of FIG. 3 indicates in the first column the sample number, in the second column the corresponding real-time, in the fourth column the signal value (voltage value U) of the respective sample, and in the fourth to seventh columns the sample numbers which form a subset and from which a subset averaged time constant is calculated. The first subset averaged time constant is calculated at the fourth sample, the second subset averaged time constant is calculated at the seventh sample, etc. It can be seen from FIG. 3 that the distance between the samples of a subset increases by the integer 1 from subset to subset. Based on the three samples N, INT(N / 3)*2, and 2*(INT(N / 3)*2), the subset averaged time constant ts for the N-th sample is determined as t(N) - t (iNT * 2) TSW =------------------------------- (1) C7(t(JV)) - U (t (iNT (y) * 2) j wherein ts is the subset averaged time constant, N is the number that fulfills N mod 3 = 1, t(N) is the time (like in seconds for example) when the Nth sample was taken, INT is the integer function, and U(t(N)) is the exponential signal value att(N) time. This formula (1) can be explained such that the numerator is the time difference of two samples t(N) and t(N-T), wherein T increases from subset to subset by the integer 1. The denominator is the logarithm of the ratio of the voltage change between the last two signal samples (dU2) and the previous two sample (dill). This is illustrated in FIG. 4, which depicts an exponential voltage signal 10 for charging a capacitor and indicates three samples N, N-T, N-2T of a subset and respective voltage changes dU1 and dU2 between the samples. Again, it is pointed out that T increases by 1 with the next subset. In accordance with step 104 and 105 of FIG. 1, the subset averaged time constants ts calculated in accordance with formula (1) are averaged to form the averaged time constant Ta until a stop criterium is present. In the embodiment of FIGS. 2 to 4, the stop criterium is that the latest subset averaged time constant ts deviates less than the first predetermined value from the averaged time constant Ta, and / or that the time of at least one time constant has elapsed (the time constant as calculated so far). Once the calculation of the average time constant has been stopped, the averaged time constant Ta present after the latest added subset averaged time constant is set to be equal to the estimated time constant Te which is the desired value. This is illustrated in FIG. 5 which shows the beginning of an exponential signal 10 the time constant of which shall be determined. The calculation of subset averaged time constants ts is already stopped at sample 23 in the depicted example, and, accordingly, the estimated time constant Te is found at sample 23 and thus much earlier than when the signal 10 settles. After having determined the estimated time constant Te, a final predicted signal value can be determined in accordance with the formula: U(t) UEND = UW+--(2) Uend is the final predicted signal value U(0) is the signal value at the beginning of the exponential signal ll(t) is the signal value at the sample number t, wherein t is latest sample which has been considered for the averaged time constant (Ta), and Te is the estimated time constant. Further, after having determined the estimated time constant Te, the time at which the signal has settled can be estimated as five times the estimated time constant as it can be assumed that after five times the time constant the voltage is settled in. FIG. 6 illustrates a method of how and when the described expedited calculation of the time constant is implemented in a fault monitoring device. In step 601 the time constant tau is calculated in accordance with the method of FIG. 1 when a state change occurs (e.g., the configuration of the switches SW_i in FIG. 9 changes). It is determined if a tau value of the exponential voltage signal has been successfully calculated. For example, the difference between the latest subset averaged time constant ts and the previously determined averaged time constant Ta is smaller than a first predetermined value when a defined time period has elapsed, wherein the first predetermined value may be 2 percent of the so far calculated averaged time constant and the defined time period may be 13 seconds. If the tau value has been successfully calculated, it is then determined in step 602 if the time constant estimated in step 601 is the first estimated time constant after startup of the power system. The background is that an insulation monitoring device may have a requirement that after startup a fast measurement is needed to determine whether the insulation is OK / NOT OK. If the estimated time constant is the first estimated time constant after startup, the predicted voltage level at which the signal will settle is provided on the basis of the first estimated time constant in step 603. The tau value calculated in step 601 is thus used to predict the settled in voltage. This predicted value can then be used to provide the insulation resistance. The insulation resistance determined in this way is less accurate compared to waiting until the exponential signal has settled, but is sufficient for the OK / NOT OK decision. If the estimated time constant is not the first estimated time constant after startup, it is then determined in step 604 whether a foreseeable wait time (such as 5 times the estimated time constant) is less than a required preset response time (such as 50 seconds). If the foreseeable wait time is not less (i.e., is more) than the required response time, the predicted voltage level at which the signal will settle is provided on the basis of the estimated time constant in step 603. Accordingly, if the foreseeable wait time exceeds the required response time, then the predicted voltage value can be used to fit in the required response time-period. This usually happens if the Riso is high. The reduced accuracy in determining this resistance (as determined based on the predicted voltage) is not a safety concern in such case. If the foreseeable wait time is less than the required response time, the actual voltage value is measured directly at the end of the foreseeable wait time (such as 5*tau) in step 605, wherein the most accurate insulation resistance value can be provided (as the resistance value is not based on a predicted voltage but on the voltage measured at the end of the foreseeable wait time). If the tau value has not been successfully calculated in step 601, e.g., because of a timeout or a calculation error, then as a fallback method a simple steady detector is used in step 606. The steady-state detector is used to determine the final voltage value, wherein the final voltage value is a steady value of the steady-state detector. Once a steady state has been detected, the voltage ll(t) is returned in step 607 and the insulation resistance value is provided on the basis of this returned voltage. The steady-state detector, e.g., could determine if the signal value stays in a “window”. If the signal value does not exit of this window, then the signal is deemed settled in. FIG. 7 regards a method alternative to the method of FIG. 2 to choose a subset of samples and determine subset averaged time constants. According to step 701 of FIG. 7, the time constant value is calculated (701) based on every even sample only, wherein, according to step 702, each subset comprises three samples, namely, the samples to, t / 2, t, wherein to is the initial sample of the signal (such as sample number 0 at real time 0,00 s in FIG. 3), t is the latest added even sample of the signal and t / 2 is the sample in the middle between to and t. In step 703, for each subset the subset averaged time constant ts is calculated based on the three samples of the subset. The method then continues with steps 104 and 105 of FIG. 1. In the method of FIG. 7, the maximum possible voltage differences are considered for each subset of three samples. The subset averaged time constant ts for each such subset is calculated based on the formula: t_ =--7----—7KV (3) I / t\            I (2) — ^(^0) y ts is the subset averaged time constant, t is the latest added even sample, to is the initial sample of the signal, and II is the signal value. FIG. 8 regards a further method that is alternative to the method of FIG. 2 to choose a subset of samples and determine subset averaged time constants. Again, each subset comprises three samples. Tau is calculated at every sample t. According to step 801, the three samples are the samples t, t-T and t-2T, wherein t is the latest added sample of the signal, and T is a predetermined time which is equal to or a multiple of the sample distance. For example, T may be equal to the distance of three samples, wherein, e.g., a subset consists of samples 10, 7, 4 and the subsequent subset consists of samples 11, 8, 5. The subsets thus kind of provide for a moving average. In step 802, for each subset the subset averaged time constant ts is calculated based on these three samples of the subset. According to step 803, calculation of subset averaged time constants ts starts after a predetermined time of 2*T has elapsed (otherwise this method will not be possible yet) and when the difference between the sample values of two consecutive samples is bigger than the predefined limit (indicating that the signal values are starting to rise or fall). In step 804, the averaged time constant Ta is determined to be the estimated time constant Te (i.e., the averaging of the averaged time constant is stopped) when the difference between the latest subset averaged time constant ts and the previously determined averaged time constant Ta is larger than a second predetermined value. This takes into consideration the fact that, as the voltage settles, the difference between the samples decreases such that the calculated time constant tau is getting more inaccurate. Calculation is stopped when the inaccuracy exceeds a limited compared to the average of earlier taus. In addition, a time period such as one tau may be defined at the end of which further averaging of the averaged time constant is stopped. The subset averaged time constant ts for each such subset is calculated based on the formula: T TsW> = -, / U(t)-U(t-T) \ (4) \U(t - T) - U(t - 2 * T)) wherein ts is the subset averaged time constant, t is the latest added sample, T is the predetermined time, and II is the signal value It should be understood that the above description is intended for illustrative purposes only, and is not intended to limit the scope of the present disclosure in any way. In 5 particular, the described method may be implemented anywhere where an exponential signal is present and the settled value is needed. For example, another application is the prediction of a settled in temperature after a temperature change has occurred. Also, those skilled in the art will appreciate that other aspects of the disclosure can be obtained from a study of the drawings, the disclosure and the appended claims. All 10 methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. Various features of the various embodiments disclosed herein can be combined in different combinations to create new embodiments within the scope of the present disclosure. In particular, the disclosure extends to and includes all combinations and sub-combinations of one or more 15 features described herein. Any ranges given herein include any and all specific values within the range and any and all sub-ranges within the given range.

Claims

1. A method for determining an estimated time constant (Te) of an exponential signal, the method comprising the steps of:reading or receiving (101) discrete samples of the exponential signal (10) which are equidistant in time, wherein new samples are continuously read or received as the signal evolves in time;forming (102) a plurality of consecutive subsets of the samples, wherein the subsets are consecutive in time and each latest subset includes the last read or received sample;calculating (103) subset averaged time constants (ts) for each of the plurality of subsets, wherein for each subset a subset averaged time constant (ts) based on the samples of the respective subset is calculated;continuously averaging the subset averaged time constants (ts) to receive an averaged time constant (Ta), wherein consecutively further subset averaged time constants (ts) are considered as the signal evolves in time and new subsets are formed; anddetermining the averaged time constant (Ta) to be the estimated time constant (Te) when a stop condition is present, the stop condition stopping further calculation of the averaged time constant (Ta).

2. The method of claim 1, wherein a stop condition is present when the difference between the latest subset averaged time constant (ts) and the previously determined averaged time constant (Ta) is smaller than a first predetermined value or is larger than a second predetermined value and / or when a defined time period has elapsed.

3. The method of claim 1 or 2, wherein each subset comprises (201) three samples, the three samples being separated at equal distance, and a subset averaged time constant (ts) is calculated based on these three samples; and the equal distance between the three samples of a subset is increased (202) by an integer with each consecutive subset.

4. The method of claim 3, wherein the subsets of samples each include at least one N-th sample that fulfills the condition N mod M = 1, wherein mod is the modulo function and M is an integer.

5. The method of claim 4, wherein the samples of a subset are the three samples:N, INT(N / 3)*2, and 2*(INT(N / 3)*2) - N;wherein N is one of the samples for which the condition N mod 3 = 1 is met; andI NT (X) is the integer function of the fraction X that assigns the natural number to the fraction X which is equal to the natural number before the decimal point of X.

6. The method of claim 5, wherein the subset averaged time constant (ts) for the N-thsample is determined as:whereints is the subset averaged time constant,N is the number that fulfills N mod 3=1, t(N) is the time when the Nth sample was taken, I NT is the integer function, andU(t(N)) is the exponential signal value at t(N) time.

7. The method of any one of claims 3 to 6, when dependent on claim 2, wherein subset averaged time constants (ts) of the subsets are averaged to receive the averaged time constant (Ta) untilthe latest subset averaged time constant (ts) deviates less than the first predetermined value from the averaged time constant (Ta); and / orthe time of at least one time constant has elapsed;wherein the averaged time constant (Ta) present after the latest added subset averaged time constant is set to be equal to the estimated time constant (Te).

8. The method of claim 1 or 2, wherein each subset comprises (801) three samples, the three samples being the samples t, t-T and t-2T, wherein t is the latest added sample of the signal, and T is a predetermined time which is equal to or a multiple of the sample distance; wherein for each subset the subset averaged time constant (ts) is calculated (802) based on these three samples of the subset.

9. The method of claim 8, as far as referring to claim 2, wherein the calculation of subset averaged time constants (ts) starts (803) after a predetermined time of 2*T has elapsed and when the difference between the sample values of two consecutive samples is bigger than the predefined limit; wherein the averaged time constant (Ta) is determined (804) to be the estimated time constant (t6) when the difference betweenthe latest subset averaged time constant (ts) and the previously determined averaged time constant (Ta) is larger than the second predetermined value.

10. The method of claim 8 or 9, wherein the subset averaged time constant (ts) is calculated based on the formula:U(t) - U(t - T) U(t-T)-U(t-2* T)whereints is the subset averaged time constant, t is the latest added sample, T is the predetermined time, and II is the signal value.

11. The method of claim 1 or 2, wherein the time constant value is calculated (701) based on every even sample only; each subset comprises (702) three samples, the three samples being the samples to, t / 2, t, wherein to is the initial sample of the signal, t is the latest added even sample of the signal and t / 2 is the sample in the middle between to and t; and for each subset the subset averaged time constant (ts) is calculated (703) based on these three samples of the subset.

12. The method of claim 11, wherein the subset averaged time constant (ts) is calculated based on the formula:t / 2Ts(t) = -In.[ / (t) - [ / (t / 2).[ / (t / 2) - u(toywhereints is the subset averaged time constant, t is the latest added even sample, to is the initial sample of the signal, andII is the signal value.

13. The method of any of preceding claim, wherein after determining the estimated time constant (Te) a final predicted signal value is determined in accordance with the formulaUEND = uw +--1 — e TewhereinUend is the final predicted signal value,U(0) is the signal value at the beginning of the exponential signal,U(t) is the signal value at the sample number t, wherein t is latest sample which has been considered for the averaged time constant (Ta), and Te is the estimated time constant.

14. The method of any preceding claim, wherein after determining the estimated time constant (Te) the time at which the signal has settled is estimated as five times the estimated time constant.

15. A power system comprising:a DC battery (7) having a DC battery positive terminal (71), a DC battery negative terminal (72) and a battery voltage (Ub);a positive voltage rail (3) connected to the DC battery positive terminal (71);a negative voltage rail (4) connected to the DC battery negative terminal (72);a chassis (5);a high side insulation resistance (Risoh) insulating the chassis (5) from the positive voltage rail (3);a low side insulation resistance (Risol) insulating the chassis (5) from the negative voltage rail (4);a fault monitoring device (2) configured to assume at least two states, wherein each state is associated with a different resistance of the fault monitoring device; anda controller (6) configured to determine an estimated time constant (Te) of an exponential voltage signal associated with a state change, wherein the controller (6) is configured to:read or receive discrete samples of the exponential voltage signal which are equidistant in time, wherein new samples are continuously read or received as the signal evolves in time;form a plurality of consecutive subsets of the samples, wherein the subsets are consecutive in time and each latest subset includes the last read or received sample;calculate subset averaged time constants (ts) for each of the plurality of subsets, wherein for each subset a subset averaged time constant (ts) based on the samples of the respective subset is calculated;continuously average the subset averaged time constants (ts) to receive an averaged time constant (Ta), wherein consecutively further subset averaged time constants (ts) are considered as the signal evolves in time and new subsets are formed; anddetermine the averaged time constant (Ta) to be the estimated time constant (Te) when a stop condition is present, the stop condition stopping further calculation of the averaged time constant (Ta).

16. The power system of claim 15, wherein the controller is further configured to:determine (602) if the estimated time constant is the first estimated time constant after startup of the power system;if so, provide (603) the predicted voltage level at which the signal will settle on the basis of the first estimated time constant; andif not, determine (604) whether a foreseeable wait time is less than a required response time:if so, wait (605) for the foreseeable wait time and measure the actual voltage value directly at the end of the foreseeable wait time, andif not, provide (603) the predicted voltage level at which the signal will settle on the basis of the estimated time constant.

17. The power system of claim 15 or 16, wherein the controller is further configured to, if the conditions for determining the estimated time constant are not present, use (606) a steady-state detector to determine the final voltage value, wherein the final voltage value is a steady value of the steady-state detector.

18. The power system of any one of claims 15 to 17, wherein the controller is further configured to: choose the subsets such that each subset comprises three samples, the three samples being separated at equal distance, and calculate (201) a subset averaged time constant (ts) based on these three samples; and increase (202) the equal distance between the three samples of a subset by an integer with each consecutive subset.

19. The power system of any one of claims 15 to 17, wherein the controller is further configured to: choose the subsets such that each subset comprises three samples,the three samples being the samples t, t-T and t-2T, wherein t is the latest added sample of the signal, and T is a predetermined time which is equal to or a multiple of the sample distance; and calculate (802) for each subset the subset averaged time constant (ts) based on these three samples of the subset.5 20. The power system of any one of claims 15 to 17, wherein the controller is furtherconfigured to:calculate (701) the time constant value based on every even sample only; andchoose (702) the subsets such that each subset comprises three samples, the three samples being the samples to, t / 2, t, wherein to is the initial sample of the signal, t is 10 the latest added even sample of the signal and t / 2 is the sample in the middle between to and t, wherein for each subset the subset averaged time constant (ts) is calculated (703) based on these three samples of the subset.

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