A method for determining an insulation resistance in a power system

Abstract

A method for determining an insulation resistance in a power system that comprises: a DC power source 7, positive and negative voltage rails 3,4, a chassis 5, high and low side insulation resistances RISOH, RISOL, first and second capacitances CISOH, CISOL, and a fault monitoring device 2. The fault monitoring device can assume at least two states. The method comprises: determining a first time constant of a first exponential voltage signal after a first state change, wherein the fault monitoring device assumes a first resistance after the change; determining a second time constant of a second exponential voltage after a second state change, wherein the fault monitoring device assumes a second resistance after the change; inserting the first time constant and resistance in a formula in which the time constant is equal to the product of the total resistance and capacitance; inserting the second time constant and resistance in the same formula; and reorganizing the two equations to arrive at an insulation resistance as a function of the first and second time constants and the first and second resistances.

Description

Field of the disclosure The present disclosure relates to a method for determining an insulation resistance in a power system and a power system for implementing such a method. Background Unites 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. There is a desire to be able to determine the insulation resistance of the power system in a simple and fast manner. There is a need for a method that allows to determine the insulation resistance of a power system in a simple and fast manner, and / or to further provide for a power system implementing such a method. Summary of the disclosure In a first aspect, a method for determining an insulation resistance in a power system is provided. The power system in which the method is carried out is of the kind that comprises a DC power source having a positive terminal, a negative terminal and a DC voltage, a positive voltage rail connected to the positive terminal, a negative voltage rail connected to the negative terminal, a chassis, a high side insulation resistance insulating the chassis from the positive voltage rail and a low side insulation resistance insulating the chassis from the negative voltage rail, a first capacitance connected between the positive voltage rail and the chassis in parallel to the high side insulation resistance and a second capacitance connected between the chassis and the negative voltage rail in parallel to the low side insulation resistance, and a fault monitoring device arranged between the positive voltage rail and the negative voltage rail, wherein the fault monitoring device comprises resistors and is configured to assume at least two states, wherein each state is associated with a different resistance of the fault monitoring device that can be calculated from the resistors of the fault monitoring device present in the respective state. In such system, the method comprises the steps of: determining a first time constant of a first exponential voltage signal after a first state change, wherein the fault monitoring device assumes a first resistance after the first state change; determining a second time constant of a second exponential voltage signal after a second state change, wherein the fault monitoring device assumes a second resistance after the second state change; inserting the first time constant and the first resistance in a formula in which the time constant of the voltage signal is equal to the product of the total resistance of the system and the total capacitance of the system, wherein the total resistance comprises as variables the high side insulation resistance, the low side insulation resistance and the resistance of the fault monitoring device, and wherein the total capacitance of the system comprises as variables the first capacitance and the second capacitance; inserting the second time constant and the second resistance in the same formula, thereby arriving at two equations having as variables the high side insulation resistance, the low side insulation resistance, the first capacitance and the second capacitance; and reorganizing the two equations to arrive at an insulation resistance as a function of the first time constant, the first resistance of the fault monitoring device, the second time constant, and the second resistance of the fault monitoring device, wherein the insulation resistance is the product of the high side insulation resistance and low side insulation resistance divided by the sum of the high side insulation resistance and low side insulation resistance. Aspects of the disclosure are first based on the realization that, in order to check the insulation resistance of a power system, it is not necessary to determine the high side insulation resistance and the low side insulation resistance separately, but that it is sufficient to determine the product of the high side insulation resistance and low side insulation resistance divided by the sum of the high side insulation resistance and low side insulation resistance. Expressed in formulas, it is determined (Risoh * Risol) / (Risoh + Risol) which can be abbreviated as Risoh X Risol and which is termed insulation resistance Riso, wherein Risoh is the high side insulation resistance and Risol is the low side insulation resistance. Determination of the insulation resistance Riso is sufficient to determine if there is a fault with the high side insulation resistance and / or the low side insulation resistance. Aspects of the disclosure are second based on the idea to make measurements of the time constant of two exponential voltage signals, wherein each exponential voltage signal is triggered by a state change that leads to a specific total resistance of the fault monitoring device. It is important to note that the total resistance of the fault monitoring device associated with a respective state of the fault monitoring device is a number that can be calculated using Ohm’s law and Kirchhoffs circuit laws, without the need for any measurements. Accordingly, two time constants are measured and two resistances (the total resistances of the fault monitoring device in two different states) are calculated and thus known values. It is mentioned 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. As is well known, the time constant tau is equal to the product of the total resistance with the total capacitance: t = R ■ C, wherein R is the total resistance of the system and C is the total capacitance of the system. When considering that the total resistance R depends on the high side insulation resistance Risoh, the low side insulation resistance Risol and further on the resistance of the fault monitoring device, it is clear that using the formula t = R ■ C for two known time constants and for two known values of the resistance of the fault monitoring device a system of two equations is formed which each include Riso = (Risoh * Risol) / (Risoh + Risol), such that they can be reorganized to find a value for Riso = (Risoh * Risol) / (Risoh + Risol) based on the known values of the first time constant, the first resistance of the fault monitoring device, the second time constant, and the second resistance of the fault monitoring device. Accordingly, simply making two measurements of the time constant in two states / configurations of the fault monitoring device allows to determine the actual value for the insulation resistance Riso. In some embodiments, the two equations are further reorganized to arrive at the capacitance Csys of the system as a function of the first time constant, the first resistance, the second time constant, and the second resistance, wherein the capacitance Csys of the system is the sum of the first capacitance Cisoh and the second capacitance Cisol. Accordingly, reorganization of the two equations also allows to determine the capacitance of the system. Therefore, in addition to the insulation resistance, the capacitance of the system can be determined by simply making two measurements of the time constant in two states / configurations of the fault monitoring device In some embodiments, the first time constant is measured based on voltage measurements of the first exponential signal and the second time constant is measured based on voltage measurements of the second exponential signal. By making several measurements of the voltage at different times, the time constant of the exponential voltage signal can be estimated. In some embodiments, the first and second time constants are estimated before the respective first and second exponential voltage signals have settled. This represents a particular useful aspect of the disclosure. In this respect, it is to be noted that to have an estimate of the insulation resistance Riso it is not necessary to have the exact values of the time constant. Rather, it is sufficient that the time constants are estimated. Accordingly, time constants may be estimated without waiting for the voltage signals to settle, thereby allowing very fast measurements of the time constants and, accordingly, a quick determination of the insulation resistance Riso. The approach to estimate the first and second time constants before the respective first and second exponential voltage signals have settled addresses the problem that after a state change the measured voltages start to change exponentially, wherein the exponential change is caused by 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 in principle to be waited before a new measurement can be initiated by implementing a further state change. By estimating the time constant, however, this is not necessary and a quicker measurement of the insulation resistance Riso is a possible. In some embodiments, the fault monitoring device further comprises at least one switch, wherein the switch is configured to switch on or off at least one resistor of the fault monitoring device, and wherein a state change of the fault monitoring device is initiated by switching the switch. Accordingly, the different states of the fault monitoring device associated with a different total resistance of the fault monitoring device are provided for by the use of one or several switches. In some embodiments, the two equations that have as variables the high side insulation resistance, the low side insulation resistance, the first capacitance and the second capacitance are the equations: Ti = (Riso X Rimdi) * Csys> and T2 = (^ / so X R1MD2) * ^SYS’ wherein Ti is the first time constant, T2 is the second time constant, Riso = Risoh X Risol = (Risoh * Risol) / (Risoh + Risol) CsYS = ClSOH + ClSOL, Rimdi is the first resistance, and Rimd2 is the second resistance. Reorganizing these two equations leads to the insulation resistance as follows: _ Rimdi * Rimd2(ti ~ T2) Rimdi * t2 — Rimd2 * Ti In a similar manner, the two equations may be reorganized to arrive at the capacitance of the system as follows: _ Rimdi * ^ * t2 ~ Rimd2 * ^ * t2 Rimdi * Rim02(^1 — T2) wherein CsYS = ClSOH + ClSOL, Ti is the first time constant, T2 is the second time constant, Rimdi is the first resistance, and Rimd2 is the second resistance. In a second aspect, a power system is provided. The power system comprises a DC power source having a positive terminal, a negative terminal and a DC voltage, a positive voltage rail connected to the positive terminal, a negative voltage rail connected to the negative terminal, a chassis, a high side insulation resistance insulating the chassis from the positive voltage rail and a low side insulation resistance insulating the chassis from the negative voltage rail, a first capacitance connected between the positive voltage rail and the chassis in parallel to the high side insulation resistance and a second capacitance connected between the chassis and the negative voltage rail in parallel to the low side insulation resistance, and a fault monitoring device arranged between the positive voltage rail and the negative voltage rail, wherein the fault monitoring device comprises resistors and is configured to assume at least two states, wherein each state is associated with a different resistance of the fault monitoring device that can be calculated from the resistors of the fault monitoring device present in the respective state. The power system further comprises a controller configured to determine an insulation resistance of the power system, wherein the controller is configured to: determine a first time constant of a first exponential voltage signal after a first state change, wherein the fault monitoring device assumes a first resistance after the first state change; determine a second time constant of a second exponential voltage signal after a second state change, wherein the fault monitoring device assumes a second resistance after the second state change; insert the first time constant and the first resistance in a formula in which the time constant of the voltage signal is equal to the product of the total resistance of the system and the total capacitance of the system, wherein the total resistance comprises as variables the high side insulation resistance, the low side insulation resistance and the resistance of the fault monitoring device, and wherein the total capacitance of the system comprises as variables the first capacitance and the second capacitance; insert the second time constant and the second resistance in the same formula, thereby arriving at two equations having as variables the high side insulation resistance, the low side insulation resistance, the first capacitance and the second capacitance; and reorganize the two equations to arrive at an insulation resistance as a function of the first time constant, the first resistance of the fault monitoring device, the second time constant, and the second resistance of the fault monitoring device, wherein the insulation resistance is the product of the high side insulation resistance and low side insulation resistance divided by the sum of the high side insulation resistance and low side insulation resistance. Such power system allows to determine the insulation resistance simply by making two measurements of the time constant in two states / configurations of the fault monitoring device. In some embodiments, the controller is further configured to implement the embodiments as stated above with respect to the method of the present disclosure. The fault monitoring device may generally be configured to define two different states of the fault monitoring device by selectively switching on an off resistors arranged in parallel to the first and second voltage dividers, wherein the controller determines from the voltage changes associated with the two different states the insulation resistance. In some embodiments, the fault monitoring device comprises: a first voltage divider arranged between the positive voltage rail and the chassis, the first voltage divider comprising a first resistor and a second resistor, wherein a first voltage measurement device is arranged in parallel to the second resistor and configured to measure the voltage of the second resistor; a second voltage divider arranged between the chassis and the negative voltage rail, the second voltage divider comprising a third resistor and a fourth resistor, wherein a second voltage measurement device is arranged in parallel to the third resistor and configured to measure the voltage of the third resistor; a first additional branch arranged between the positive voltage rail and the chassis parallel to the first voltage divider, wherein the first additional branch comprises at least one electrical resistor, wherein the at least one electrical resistor can be activated or deactivated by at least one switch; and / or a second additional branch arranged between the chassis and the negative voltage rail parallel to the second voltage divider, wherein the second additional branch comprises at least one electrical resistor, wherein the at least one electrical resistor can be activated or deactivated by at least one switch; wherein the controller is configured to selectively switch the at least one switch of the first additional branch and / or of the second additional branch to provide for different states of the fault monitoring circuit. The switches thus serve to define different states of resistance of the fault monitoring device, wherein a switch can deactivate a corresponding switch (by short-circuiting the resistor when arranged in parallel to the resistor or by being switched off when arranged in series with the resistor). In some embodiments, the first resistance Rimdi of the fault monitoring device after the first state change and the second resistance Rimd2 of the fault monitoring device after the second state change are calculated as ~ (^+^)^3 + ^4)^(^7, R8, R9 series resulting in state] )X(R}IJ,Rn, R12 series resulting in statel) and RIMD2 = (R1 + R2W3 + R3)X(R7,R8iR9 series resulting in state2)X(Rw,R11,R12 series resulting in state2) wherein Ri, R2 are the resistors of the first voltage divider, R3, R4 are the resistors of the second voltage divider, R7-R9 are the resistors of the first additional branch, R10-R12 are the resistors of the second additional branch, “series resulting in state 1 / state2” depends on the switching status of the switches of the first / second additional branch, and wherein generally a X b = These formulars follow from Ohm’s law and Kirchhoffs circuit laws. It is pointed out that the first resistance Rimdi and the second resistance Rimd2 are both determined solely by the resistance values of the resistors and can thus be simply calculated without the need for any measurement. 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 invention will be explained in more detail on the basis of exemplary embodiments with reference to the accompanying drawings in which: FIG. 1 is an embodiment of a power system of the present disclosure; FIG. 2 is a flow chart of a method for determining an insulation resistance in a power system such as the power system of FIG. 1; FIG. 3 shows an example exponential signal and samples at which voltage signals are determined; and FIG. 4 is a further embodiment of a power system of the present disclosure. Detailed description The disclosure relates to a method for determining an insulation resistance in a power system. An embodiment of such power system is shown in FIG. 1. The power system 1 is shown on the left-hand side of FIG. 1. It comprises a DC power source 7 such as a battery that has a positive terminal 71 and a negative terminal 72. Between the positive terminal 71 and the negative terminal 72 a DC voltage Ub is present. A positive voltage rail 3 is connected to the positive terminal 71 and a negative voltage rail 4 is connected to the 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. The chassis 5 is further 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 Uh. The voltage between the chassis 5 and the negative voltage rail 4 is the low side voltage Ul. The sum of the high side voltage and the low side voltage is equal to the DC power source / battery voltage: Ub = Uh + Ul. 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. 1, 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 or by monitoring an insulation resistance Riso which is defined as the product of the high side insulation resistance Risoh and the low side insulation resistance Risol divided by the sum of the high side insulation resistance Risoh and the low side insulation resistance Risol. A fault monitoring device 2 (also referred to as insulation monitoring device) 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 22 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 R1 and a second resistor R2 which are arranged in series and form a first voltage divider. The resistance of the first resistor R1 is typically substantially larger than the resistance of the second resistor R2. A voltage Uadch is measured by a first voltage measurement device 81 between a point between the first and second resistors R1, R2 and the chassis 5. The voltage measurement device 81 may be implemented as an analog-to-digital converter (ADC) which provides the measured voltage as a digital signal which is convenient for further processing of the signal. By measuring the voltage Uadch, the high side voltage Uh can be calculated. The second branch 22 of the first parallel circuit comprises three electrical resistors R7, R8, R9 arranged in series, wherein two of the electrical resistors R8, R9 can be short-circuited by a first switch S1 and a second switch S2. 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 R3 and a fourth resistor R4 which are arranged in series and form a second voltage divider. The resistance of the fourth resistor R4 is typically substantially larger than the resistance of the third resistor R3. A voltage Uadcl is measured by a second voltage measurement device 82 between a point between the third and fourth resistors R3, R4 and the chassis 5. the second voltage measurement device 82 may also be implemented by an ADC. By measuring the voltage Uadcl, the low voltage Ul can be calculated. The voltage dividers of branches 21, 23 thus serve to measure the high voltage Uh and the low voltage Ul. The fourth branch 24 of the second parallel circuit comprises three electrical resistors R10, R11, R12 arranged in series, wherein two of the electrical resistors R10, R11 can be short-circuited by a second switch S3 and a fourth switch S4. 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 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 S1 to S4 a common mode voltage Ucm different from zero can be injected. The fault monitoring device 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 controller 6 is operatively coupled to the switches S1, S2, S3, S4 and configured to selectively switch the switches S1, S2, S3, S4 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 the different states 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 measurement devices 81, 82. The voltage changes associated with a state change settle with an exponential curve due to the capacitances Cisoh and Cisol that are connected in parallel to the high side insulation resistance Risoh and the low side insulation resistance Risol. Such capacitances represent the capacitance of the power system and may be formed, e.g., by cable insulations and filter capacitors. More particularly, when the state of the switches S1, S2, S3 and / or S4 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). The described fault monitoring device 2 is improved by implementing a method to determine in a fast and efficient manner the insulation resistance Riso which is defined as the product of the high side insulation resistance Risoh and the low side insulation resistance Risol divided by the sum of the high side insulation resistance Risoh and the low side insulation resistance Risol. To this end, the controller 6 or alternatively any other controlling device or computer program is configured to carry out the method described in FIG. 2. In step 201, the time constant ti of a first exponential voltage signal after a first state change is determined, wherein the fault monitoring device assumes a first resistance Rimdi after the first state change. The time constant Ti is a measured value that can be determined from measured values of the exponential voltage signal. An example for such measurement is discussed with respect to FIG. 3. The first resistance Rimdi of the fault monitoring device after the first state change is defined by the resistors which are present or activated (i.e., not deactivated by a respective switch). The first resistance Rimdi of the fault monitoring device in the example of FIG. 1 is: Rimdi = (^i + ^2)^3 + / ?4)X( / ?7, / ?8, / ?9 series resulting in state!)X (R10, Rllt R12 series resulting in state!) wherein “R7, Rs, R9 series resulting in statel” depends on the switching status of the switches S1, S2 and “R10, R11, R12 series resulting in statel” depends on the switching status of the switches S3, S4. The first resistance Rimdi is thus solely calculated from the “active” resistors active in state 1 of the fault monitoring device 2. Accordingly, the result of the first step 201 are two numbers, one number for the time constant T1 and one number for the first resistance Rimdi. In step 202, the time constant t2 of a second exponential voltage signal after a second state change is determined, wherein the fault monitoring device assumes a second resistance Rimd2 after the second state change. Again, the time constant T2 is a measured value that can be determined from measured values of the exponential voltage signal. The second resistance Rimd2 of the fault monitoring device after the second state change is defined by the resistors which are present or activated. The second resistance Rimd2 of the fault monitoring device in the example of FIG. 1 is: ^IMD2 = (^1 + ^2)^(^3 + R3)X(R7,R8,R9 series resulting in state2)X (Rw, Rllt R12 series resulting in state2) wherein “R7, Rs, R9 series resulting in state2” depends on the switching status of the switches S1, S2 and “R10, R11, R12 series resulting in state2” depends on the switching status of the switches S3, S4. The second resistance Rimd2 is thus solely calculated from the “active” resistors active in state 2 of the fault monitoring device 2. Accordingly, the result of the second step 202 are two numbers, one number for the time constant T2 and one number for the second resistance Rimd2. In step 203, the first time constant T1 and the first resistance Rimdi are inserted in a formula in which the time constant of the voltage signal 10 is equal to the product of the total resistance of the system and the total capacitance of the system. As is generally known, t = R ■ C, wherein the total resistance R comprises as variables the high side insulation resistance Risoh, the low side insulation resistance Risol, and the resistance Rimd of the fault monitoring device 2, and wherein the total capacitance C of the system comprises as variables the first capacitance Cisoh and the second capacitance Cisol. More particularly, the relevant equation is: T = (^ / SO % Md) * ^SYS (1) wherein Riso = Risoh X Risol = (Risoh * Risol) / (Risoh + Risol) is the insulation resistance, Rimd is the resistance of the fault monitoring device, and Csys = Cisoh + Cisol is the system capacitance. In step 203, the first time constant ti and the first resistance Rimdi are inserted in this equation, thereby arriving at: Ti = (Riso % Rimdi) * ^sys (2) In a similar manner, in step 204, the second time constant T2 and the second resistance Rimd2 determined in step 202 is inserted in formula (1): t2 = (RlSO X R1MD2) * ^SYS (3) Accordingly, by inserting the two time constants T1 and T2 and the two resistances Rimdi, Rimdz into formula (1), two equations are provided having as variables the high side insulation resistance Risoh, the low side insulation resistance Risol, the first capacitance Cisoh and the second capacitance Cisoh (as Riso = Risoh X Risol = (Risoh * Risol) / (Risoh + Risol) and as Csys = Cisoh + Cisol). In step 205, the two equations are reorganized to arrive at an insulation resistance Riso as a function of the first time constant T1, the first resistance Rimdi of the fault monitoring device, the second time constant T2, and the second resistance Rimdz of the fault monitoring device. More particularly, the two equations are reorganized to arrive at the insulation resistance Riso as follows: _ RIMD1*RIMD2Ct1~t2) z^x IS0 RIMD1*t2~RIMD2*t1 It is pointed out that the values on the right hand side of equation (4) are all numbers previously determined. The insulation resistance Riso can thus be determined simply from measuring the time constant of the exponential voltage signal in two states of the fault monitoring device and by determining the resistance of the fault monitoring device in the two states. In addition, the two equations (2) and (3) may be reorganized to arrive at the capacitance Csys of the system: „ _ Rimdi *t2 - Rjmd2 * ti * t2 lsys — B To TT v5) Rimdi * Rimd2\Ji tz) In some embodiments of the present disclosure, but not necessarily, the time constant of the exponential voltage change is measured before the voltage change has settled in. By determining the time constant in a fast manner, the insulation resistance Riso can also be determined fast. This may be important, e.g., after startup of the system when a fast measurement is needed to determine whether the insulation is OK / NOT OK. FIG. 3 shows an exponential voltage signal 10 in an RC circuit of the general form: [ / (t) = 1 — e~r (6) wherein t is the time constant which is equal to R times C. The signal 10 is sampled, wherein the samples may be equidistant in time and continuously formed as the signal progresses in time. The time constant can be determined from the samples. For example, the whole curve may be measured from the start to the settled state. The time constant tau is the time where the rise reaches 63.21 % of the final value (which is 1 - 1 / e, e being the Euler’s number). In other embodiments, the time constant may be determined in other manners. FIG. 4 shows an alternative embodiment of a power system and fault monitoring device that differs from the embodiment of FIG. 1 in that the fault monitoring device comprises a single additional branch 22 only, wherein the additional branch 22 comprises a single resistor R7 only which is arranged in series with a switch D5. By switching switch S5 on or off, the resistor R7 is activated / deactivated. Accordingly, the embodiment of FIG. 4 provides for two different states, one state when S5 is switched on and one state when S5 is switched off. FIG. 4 is an example of a fault monitoring device that comprises two resistance states only. Another difference to the embodiment of FIG. 1 lies in that a third voltage measurement device 83 is provided which measures the voltage between a point between the first and second resistors R1, R2 and a point between the third and fourth resistors R3, R4. The voltage it measures can be used to calculate the DC voltage of the power source. Such third voltage measurement device 83 provides for redundancy and a validity check in the measurements. It may similarly be implemented in the embodiment of FIG. 1. 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. 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 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 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 insulation resistance (Riso) in a power system that comprises:a DC power source (7) having a positive terminal (71), a negative terminal (72) and a DC voltage (Ub);a positive voltage rail (3) connected to the positive terminal (71);a negative voltage rail (4) connected to the negative terminal (72);a chassis (5);a high side insulation resistance (Risoh) insulating the chassis (5) from the positive voltage rail (3) and a low side insulation resistance (Risol) insulating the chassis (5) from the negative voltage rail (4);a first capacitance (Cisoh) connected between the positive voltage rail (3) and the chassis (5) in parallel to the high side insulation resistance (Risoh) and a second capacitance (Cisol) connected between the chassis (5) and the negative voltage rail (4) in parallel to the low side insulation resistance (Risol), anda fault monitoring device (2) arranged between the positive voltage rail (3) and the negative voltage rail (4), wherein the fault monitoring device (2) comprises resistors (R1-R12) and is configured to assume at least two states, wherein each state is associated with a different resistance of the fault monitoring device (2) that can be calculated from the resistors (R1-R12) of the fault monitoring device (2) present in the respective state;wherein the method comprises the steps of:determining (201) a first time constant (ti) of a first exponential voltage signal (10) after a first state change, wherein the fault monitoring device (2) assumes a first resistance (Rimdi) after the first state change;determining (202) a second time constant (T2) of a second exponential voltage signal (10) after a second state change, wherein the fault monitoring device (2) assumes a second resistance (R1MD2) after the second state change;inserting (203) the first time constant (ti) and the first resistance (Rimdi) in a formula in which the time constant of the voltage signal (10) is equal to the product of the total resistance of the system and the total capacitance of the system, wherein the total resistance comprises as variables the high side insulation resistance (Risoh), thelow side insulation resistance (Risol), and the resistance (Rimd) of the fault monitoring device (2), and wherein the total capacitance of the system comprises as variables the first capacitance (Cisoh) and the second capacitance (Cisoh);inserting (204) the second time constant (t2) and the second resistance (Rimd?) in the same formula, thereby arriving at two equations having as variables the high side insulation resistance (Risoh), the low side insulation resistance (Risol), the first capacitance (Cisoh) and the second capacitance (Cisoh); andreorganizing (205) the two equations to arrive at an insulation resistance (Riso) as a function of the first time constant (ti), the first resistance (Rimdi) of the fault monitoring device (2), the second time constant (t2), and the second resistance (Rimd2) of the fault monitoring device (2), wherein the insulation resistance (Riso) is the product of the high side insulation resistance (Risoh) and the low side insulation resistance (Risol) divided by the sum of the high side insulation resistance (Risoh) and the low side insulation resistance (Risol).

2. The method of claim 1, wherein the two equations are further reorganized to arrive at the capacitance (Csys) of the system as a function of the first time constant (ti), the first resistance (Rimdi), the second time constant (t2), and the second resistance (R1MD2), wherein the capacitance (Csys) of the system is the sum of the first capacitance (Cisoh) and the second capacitance (Cisoh).

3. The method of claim 1 or 2, wherein the first time constant (t-i) is measured based on voltage measurements of the first exponential voltage signal and that the second time constant (t2) is measured based on voltage measurements of the second exponential voltage signal.

4. The method of any preceding claim, wherein the first and second time constants (ti, t2) are estimated before the respective first and second exponential voltage signals (10) have settled.

5. The method of any preceding claim, wherein the fault monitoring device (2) further comprises at least one switch (S1-S5), wherein the switch (S1-S5) is configured to switch on or off at least one resistor (R7, R8-R11) of the fault monitoring device (2), and wherein a state change of the fault monitoring device (2) is initiated by switching the switch (S1-S5).

6. The method of any preceding claim, wherein the two equations that have as variables the high side insulation resistance (Risoh), the low side insulation resistance (Risol), the first capacitance (Cisoh) and the second capacitance (Cisoh) are the equations:T1 — ISO RiMDi) * ^SYS’ andT2 = (RlSO % R]MDz) * ^SYS’whereinTi is the first time constant,T2 is the second time constant,Riso = Risoh X Risol = (Risoh * Risol) / (Risoh + Risol) is the insulation resistanceCsys = Cisoh + Cisol is the system capacitanceRimdi is the first resistance, andRimd2 is the second resistance; andthe two equations are reorganized to arrive at the insulation resistance (Riso) as follows:„ _ Rimdi * Rimd2(ti ~ ^2)iso p * t — R * T ‘ kIMD1 * t2 kIMD2 * T17. The method of any preceding claim, when dependent on claim 2, wherein the two equations are reorganized to arrive at the capacitance (Csys) of the system as follows:_ Rimdi * * t2 ~ Rimdz * ti * t2Rimdi * Rimd2(Ji — T2)whereinCsys = Cisoh + Cisol,ti is the first time constant,T2 is the second time constant,Rimdi is the first resistance, andRimd2 is the second resistance.

8. A power system comprising:a DC power source (7) having a positive terminal (71), a negative terminal (72) and a DC voltage (Ub);a positive voltage rail (3) connected to the positive terminal (71);a negative voltage rail (4) connected to the negative terminal (72);a chassis (5);a high side insulation resistance (Risoh) insulating the chassis (5) from the positive voltage rail (3) and a low side insulation resistance (Risol) insulating the chassis (5) from the negative voltage rail (4);a first capacitance (Cisoh) connected between the positive voltage rail (3) and the chassis (5) in parallel to the high side insulation resistance (Risoh) and a second capacitance (Cisol) connected between the chassis (5) and the negative voltage rail (4) in parallel to the low side insulation resistance (Risol);a fault monitoring device (2) arranged between the positive voltage rail (3) and the negative voltage rail (4), wherein the fault monitoring device (2) comprises resistors (R1-R12) and is configured to assume at least two states, wherein each state is associated with a different resistance of the fault monitoring device (2) that can be calculated from the resistors (R1-R12) of the fault monitoring device (2) present in the respective state; anda controller (6) configured to determine an insulation resistance (Riso) of the power system, wherein the controller (6) is configured to:determine (201) a first time constant (ti) of a first exponential voltage signal (10) after a first state change, wherein the fault monitoring device (2) assumes a first resistance (Rimdi) after the first state change;determine (202) a second time constant (T2) of a second exponential voltage signal (10) after a second state change, wherein the fault monitoring device (2) assumes a second resistance (Rimdz) after the second state change;insert (203) the first time constant (ti) and the first resistance (Rimdi) in a formula in which the time constant of the voltage signal (10) is equal to the product of the total resistance of the system and the total capacitance of the system, wherein the total resistance comprises as variables the high side insulation resistance (Risoh), the low side insulation resistance (Risol), and the resistance (Rimd) of the fault monitoring device (2), and wherein the total capacitance of the system comprises as variables the first capacitance (Cisoh) and the second capacitance (Cisoh);insert (204) the second time constant (T2) and the second resistance (R1MD2) in the same formula, thereby arriving at two equations having as variables the high side insulation resistance (Risoh), the low side insulation resistance (Risol), the first capacitance (Cisoh) and the second capacitance (Cisoh); andreorganize (205) the two equations to arrive at an insulation resistance (Riso) as a function of the first time constant (t-i), the first resistance (Rimdi) of the faultmonitoring device (2), the second time constant (T2), and the second resistance (Rimd?) of the fault monitoring device (2), wherein the insulation resistance (Riso) is the product of the high side insulation resistance (Risoh) and the low side insulation resistance (Risol) divided by the sum of the high side insulation resistance (Risoh) and the low side insulation resistance (Risol).

9. The power system of claim 8, wherein the controller is further configured to reorganize the two equations to arrive at the capacitance (Csys) of the system as a function of the first time constant (ti), the first resistance (Rimdi), the second time constant (T2), and the second resistance (R1MD2), wherein the capacitance (Csys) of the system is the sum of the first capacitance (Cisoh) and the second capacitance (Cisoh).

10. The power system of claim 8 or 9, wherein the controller is further configured to measure the first time constant (ti) based on voltage measurements of the first exponential voltage signal and to measure the second time constant (T2) based on voltage measurements of the second exponential voltage signal.

11. The power system of any one of claims 8 to 10, wherein the controller is further configured to estimate the first and second time constants (ti, T2) before the respective first and second exponential voltage signals (10) have settled.

12. The power system of any one of claims 8 to 11, wherein the fault monitoring device (2) further comprises at least one switch (S1-S5), wherein the switch (S1-S5) is configured to switch on or off at least one resistor (R7, R8-R11) of the fault monitoring device (2), and wherein a state change of the fault monitoring device (2) is initiated by switching the switch (S1-S5).

13. The power system of any one of claims 8 to 12, wherein the two equations that have as variables the high side insulation resistance (Risoh), the low side insulation resistance (Risol), the first capacitance (Cisoh) and the second capacitance (Cisoh) are:Ti = (RISo * Rimdi) * CSyS, andT2 = (filSO % Rimdz) * CSys,whereinTi is the first time constant,T2 is the second time constant,Riso = Risoh X Risol = (Risoh * Risol) / (Risoh + Risol) is the insulation resistance Csys = Cisoh + Cisol is the system capacitanceRimdi is the first resistance, andRimd2 is the second resistance;and the controller is configured to reorganize the two equations to arrive at the insulation resistance (Riso) as follows:„ _ ^IMDl * ^ / MD2(T1 — T2)" / SO — "5 ~ n ~~T-RiMDI * T2 — RlMD2 * T114. The power system of any one of claims 8 to 13, wherein the controller is configured to reorganize the two equations to arrive at the capacitance of the system as follows:_ Rjmdi * T1 * T2 ~ RlMD2 * Ti * T2 RiMDI * RlMD2(Tl — t2)whereinCsYS = ClSOH + ClSOL,Ti is the first time constant,T2 is the second time constant,Rimdi is the first resistance, andRimd2 is the second resistance.

15. The power system of any one of claims 8 to 14, wherein the fault monitoring device (2) comprises:a first voltage divider (21) arranged between the positive voltage rail (3) and the chassis (5), the first voltage divider (21) comprising a first resistor (R1) and a second resistor (R2), wherein a first voltage measurement device (81) is arranged in parallel to the second resistor (R2) and configured to measure the voltage (Uadch) of the second resistor (R2);a second voltage divider (23) arranged between the chassis (5) and the negative voltage rail, the second voltage divider (23) comprising a third resistor (R3) and a fourth resistor (R4), wherein a second voltage measurement device (82) is arranged in parallel to the third resistor (R3) and configured to measure the voltage (Uadch) of the third resistor (R3);a first additional branch (22) arranged between the positive voltage rail (3) and the chassis (5) parallel to the first voltage divider, wherein the first additional branch (22) comprises at least one electrical resistor (R7, R8, R9), wherein the at least one electrical resistor can be activated or deactivated by at least one switch (S1, S2, S5); and / ora second additional branch (24) arranged between the chassis (5) and the negative voltage rail (4) parallel to the second voltage divider, wherein the second additional branch (24) comprises at least one electrical resistor (R10, R11, R12), wherein the at least one electrical resistor (R10, R11, R12) can be activated or deactivated by at least one switch (S3, S4);wherein the controller (6) is configured to selectively switch the at least one switch (S1-S5) of the first additional branch (22) and / or of the second additional branch (24) to provide for different states of the fault monitoring circuit (2).

16. The power system of claim 14, wherein the first resistance (Rimdi) of the fault monitoring device (2) after the first state change and the second resistance (Rimd2) of the fault monitoring device (2) after the second state change are calculated asRlMDl = (^i + +R4)X(R7,Re,R9 series resulting in statel)X(Rw,R11,R12 series resulting in statel)Rimd2 = (^1 + ^2)-^(^3 +R2)X(R7, RB, R9 series resulting in state2yx(Rw, Ru, R12 series resulting in slale2)whereinRi, R2 are the resistors of the first voltage divider,R3, R4 are the resistors of the second voltage divider,R7-R9 are the resistors of the first additional branch,R10-R12 are the resistors of the second additional branch, and“series resulting in state 1 / state2” depends on the switching status of the switches of the first / second additional branch.

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