Methods for determining the insulation resistance and leakage capacitance of ungrounded power supply systems

Abstract

This invention relates to a method for determining the insulation resistance (R1, R2) and leakage capacitance (C1, C2) of an ungrounded DC power supply system relative to ground (PE), wherein the method utilizes the voltage (U) as a measurement voltage. G (k) and grid voltage (U N The measured voltage (U) is a function of (k) M (k)), and uses grid parameters () to realize the linear difference equation, the grid parameters being determined by the measured resistance (R) M The insulation resistances (R1, R2) and leakage capacitances (C1, C2) to be determined are formed. For measurement time points k=1, 2 to N with sampling period T, the sampling value sequence (U... G (k),U N (k),U M The measured value equations (S5) are realized by N linear difference equations (k) and the grid parameters (k). Further method steps include: calculating (S6) the estimated grid parameters (k) as an approximate solution to the measured value equations, where the sum of squared errors between the grid parameters (I) and the estimated grid parameters (k) is minimized; minimizing the sum of squared errors by QR decomposition of the measured value matrix (k) (S7), where the QR decomposition is performed recursively; calculating (S8) the corresponding insulation resistances (R1, R2) and corresponding leakage capacitances (C1, C2) from the estimated grid parameters (I); and continuously repeating the method steps with respect to the separately calculated estimated grid parameters (I), taking into account the sampled values ​​present for the current measurement time point.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for determining the insulation resistance and the leakage capacity of an ungrounded power supply system according to the preamble of claim 1. BACKGROUND

[0002] When the requirements for operational safety, fire safety and contact safety are increasing, power grid structures are used which employ ungrounded power supply systems, which are also referred to as isolated power grids (IT power grid) or IT power supply systems (French: Isolé Terre - IT). In power supply systems of this type, the active components of the power supply system are separated from the ground potential, i.e. from "earth". The advantage of the power grid is that, in the event of an insulation fault (first fault), for example in the event of a grounding of an active conductor of the ungrounded power supply system, the functionality of the connected consumer is not impaired, since, due to the ideally infinite value of the impedance between the active conductor of the power grid and the ground, no closed loop can be formed. The resistance to the ground potential (to earth) as a real part (real component) is in parallel with the leakage capacity as an imaginary part, which forms the complex insulation impedance of the ungrounded power supply system.

[0003] Therefore, the resistance of the ungrounded power supply system, which is referred to as the insulation resistance, has to be monitored in accordance with regulations by means of a standard-compliant insulation monitoring device (IMD) with respect to the ground potential, since a further fault (second fault) which can occur at another active conductor can cause a fault loop and, in combination with an overcurrent protection device, can cause a plant shutdown including an operational interruption.

[0004] In addition to passive insulation monitoring devices which detect insulation faults using the grid voltage of the ungrounded power supply system as a driving source for the measurement current, active working insulation monitoring devices are also known from the prior art. The active working insulation monitoring devices have a measurement path which extends between one or more active conductors of the ungrounded power supply system and the ground potential, the measurement path comprising an internal measurement voltage generator. A measurement voltage generated by the measurement voltage generator actively drives a measurement current which flows back into the measurement path via the active conductor(s), via the insulation resistance and the leakage impedance and causes a voltage drop there at a measurement resistor which is connected in series with the measurement voltage generator. The voltage drop detected on the measurement resistor is used to determine the insulation resistance and the leakage impedance.

[0005] Active methods are known which superimpose a rectangular, continuous measurement voltage onto the ungrounded supply system to be monitored. However, the insulation resistance can only be reliably calculated when the measurement voltage is stable, which can last for several minutes for large leakage capacities.

[0006] In addition, undesirable but unavoidable grid voltage variations can disturb the measurement. High-frequency grid voltage variations (greater than several hertz) can be removed by a filter. However, low-frequency grid voltage variations of only a few hertz are problematic, since they prevent the identification of a steady state and distort the calculated insulation resistance. Large voltage variations in the low-frequency range can therefore also make the measurement impossible, since the measurement voltage is not stable.

[0007] From the patent document EP 2 433 147 B1 a method is known by means of which the insulation resistance can be determined before the measured voltage at the measurement resistance reaches a steady state. Here, the stabilization process is predicted by a mathematical model, the parameters of which are iteratively adjusted until the theoretical and the measured change curve of the measured voltage coincide as well as possible. The insulation resistance can then be calculated from the model parameters. Disturbing grid voltage variations are compensated by a filter and the difference of two successive measurement pulses. However, the elimination of low-frequency grid voltage variations also appears to be problematic. In addition, the computationally expensive matrix inversion for determining the model parameters proves to be disadvantageous. SUMMARY

[0008] The object underlying the present application is therefore to enable an as fast as possible, precise and robust measurement of the insulation resistance and the leakage capacity in ungrounded supply systems, in particular in DC supply systems, which should be combined with a computationally efficient implementation which reduces the disturbing influence of low-frequency grid voltage variations.

[0009] The object is achieved by a method having the features of claim 1.

[0010] Based on the prior art, the measurement voltage is first coupled in series with the measurement resistance in a unipolar or bipolar manner between the respective one of the active conductors, and the voltage drop on the measurement resistance, which is caused by the measurement current driven by the measurement voltage, is measured.

[0011] In DC supply systems, a bipolar coupling proves to be expedient, since the problem of low-frequency grid voltage variations is particularly effectively solved in this way. In single-phase AC and three-phase AC supply systems, a unipolar coupling is sufficient, since the grid frequency can be removed by filtering.

[0012] From the voltage curves of the measurement voltage, the grid voltage and the voltage drop at the corresponding measurement resistor, a sequence of sample values of the time-discrete and value-discrete measurement voltage, grid voltage and measured voltage is generated.

[0013] The continuous signal curves of the grid voltage (rated voltage of the ungrounded power supply system), the applied measurement voltage generated in the measurement signal generator and the detected voltage drop at the measurement resistor are converted by a sampling device (analog-digital converter - ADU) into time-discrete and value-discrete signals, so that the signals can be digitally signal-processed as a sequence of sample values.

[0014] The sequence of sample values thus generated forms the input and output variables of the functionally equivalent circuit diagram of the observed ungrounded power supply system with insulation monitoring, the mathematical description of which is given by the physical law (Ohm's law) and Kirchhoff's law (current-voltage relationship) in linear grids.

[0015] On the basis of the law, a linear difference equation is implemented in which the measured voltage, corresponding to the measured voltage drop in the case of a single-pole coupling or the sum of the measured voltage drops in the case of a two-pole coupling, can be expressed as a function of the measurement voltage and the grid voltage, wherein the grid parameters of the ungrounded power supply system to be determined are the coefficients of the linear difference equation. The grid parameters are formed here by the measurement resistor, the insulation resistance to be determined and the leakage capacity to be determined. For the sake of simplification in terms of calculation, the resistance values are expressed by the conductance values.

[0016] By including the grid voltage in the current-voltage relationship of the linear difference equation, it is not necessary to remove the grid voltage from the measurement voltage, for example by filtering or other signal processing measures. The circuit effort is reduced in an advantageous manner and the measurement method according to the invention becomes more resistant to interference.

[0017] In addition, faster and continuous measurements are possible in the case of slow low-frequency changes in the grid voltage. This is advantageous in particular in photovoltaic installations, since the DC grid voltage of the photovoltaic installation fluctuates depending on the intensity of the solar radiation.

[0018] In contrast to the methods prevailing in the prior art, in which a stable grid voltage and a stable measurement voltage for determining the insulation resistance are a prerequisite, further measurements can be made continuously with the aid of the method according to the invention.

[0019] In a next step, from the sequence of sample values of the measured voltage, the grid voltage, the measurement voltage and the grid parameters, for k = 1, 2 to N sampling time points with a sampling period T, a system of measurement equations consisting of N linear difference equations is implemented.

[0020] For N > 4 sampling time points, the overdetermined measurement equation system is generated. For the overdetermined measurement equation system, there is generally no solution vector, so there is currently no set of grid parameters (coefficient vector) that exactly solves all N linear difference equations.

[0021] Therefore, the estimated grid parameters are calculated as an approximate solution of the measurement equation system, wherein the sum of squares of errors between the (actual) grid parameters and the estimated grid parameters is minimized.

[0022] The estimated grid parameters are considered optimal in the sense of an approximate solution when the sum of squares of errors resulting from the residual errors between the actual grid parameters and the estimated grid parameters is minimized.

[0023] The solution of the minimization problem or compensation problem is achieved by minimizing the sum of squares of errors by means of a QR decomposition of the measurement matrix characterizing the measurement equation system, wherein the calculation of the QR decomposition is carried out recursively.

[0024] The measurement equation system comprising N linear difference equations can be written as a measurement matrix equation, in which the sequence of sampled values of the measured voltage (measurement vector) results as a result of the multiplication of a measurement matrix with a coefficient vector (grid parameter vector). The elements of the measurement matrix correspond to the sampled values of the measured voltage, the grid voltage, and, due to the iterative nature of the difference equations, also to previous sampled values of the measured voltage.

[0025] By means of the QR decomposition of the measurement matrix, the computationally intensive matrix inversion required for solving the minimization problem by means of a gradient method is circumvented. In unfavorable conditions, for example when the measured voltage or the grid voltage is equal to zero, this leads to a zero column, thus to an irreversible matrix. Therefore, in the case, the matrix inversion is not feasible contrary to the QR decomposition.

[0026] In contrast thereto, the QR decomposition is numerically significantly more stable and enables the calculation of the estimated grid parameters even in the case of poor conditions of the measurement matrix. The calculation of the estimated grid parameters according to the present invention is less sensitive to false measurement data and rounding errors, thus more accurate.

[0027] Starting from the geometric interpretation of the minimization problem, the sum of squares of errors is considered as the square of the Euclidean norm. By applying the QR decomposition of the measurement matrix, the minimization problem can be attributed to a QR matrix equation. In contrast to the measurement matrix equation representing the measurement equation system consisting of difference equations, the (matrix) equation solving the minimization problem is referred to here as QR matrix equation, which represents the result vector as a matrix product of an upper triangular matrix and the estimated grid parameter vector.

[0028] The solution of the estimated grid parameter vector is then determined by back substitution using the upper triangular matrix R of the previously (recursively) calculated QR decomposition and the result vector of the QR matrix equation determined (recursively) in each case.

[0029] According to the application, the calculation of the QR decomposition is carried out recursively. Here, the result of the QR decomposition calculated in each case in the method cycle - the upper triangular matrix R and the result vector of the QR matrix equation - is updated in the subsequent cycle by taking into account the currently existing measurement values, so that the actual grid parameters are approximated step by step.

[0030] By means of the recursive calculation, the storage requirement and the calculation effort are significantly reduced, since only the currently existing measurement set is processed. By this, an efficient implementation on a microcontroller is possible.

[0031] In addition to the advantages of the recursive QR decomposition in terms of less storage space and calculation time, it is also possible to quickly adapt to changing (actual) grid parameters. If the currently valid insulation resistance or leakage capacity changes, the measurement and calculation can simply continue due to the continuous adaptability.

[0032] From the estimated grid parameters, the corresponding conductor-dependent insulation resistance and the corresponding leakage capacity are calculated.

[0033] The insulation resistance and the leakage capacity are not calculated directly from the voltage drop measured on the measuring resistor, as is common in the prior art, but from the estimated grid parameters. Therefore, there is no mandatory prerequisite that the measured voltage must reach a steady state in order that a reliable calculation can be carried out.

[0034] On the one hand, the method according to the application enables a fast determination of the insulation resistance and the leakage capacity, and on the other hand, more degrees of freedom are obtained in the selection of the signal shape of the measurement voltage. Therefore, for example, it is possible to select a sinusoidal measurement voltage or a mixture of sinusoidal voltage curves of different frequencies as a measurement signal.

[0035] The method steps are continuously repeated with the estimated grid parameters calculated in each case by taking into account the sample values existing for the current measurement point in time.

[0036] Thus, a continuous adaptation of the currently existing insulation condition of the ungrounded power supply system is carried out, in which a resource-saving and fast determination of the insulation resistance and the leakage capacity is ensured by the recursive calculation.

[0037] In another design, the linear difference equation is derived by converting the linear algebraic equation describing the current-voltage relationship in the frequency domain into a time-continuous difference equation and a time-discrete implementation of the difference equation.

[0038] The starting point of the implementation scheme of the linear difference equation is the description of the current-voltage relationship in the frequency domain (image domain) by means of linear algebraic equations, which is derived from the equivalent circuit diagram of the observed ungrounded power supply system with insulation monitoring. Preferably, the Laplace transformation is used to describe the relationship in the frequency domain. Conversion into the time domain results in time-continuous differential equations, and from the subsequent time discretization a linear difference equation results. The application of the linear difference equation at successive measurement time points (sample values) results in a system of measurement value equations which can be represented as a measurement value matrix equation with a measurement value matrix for determining the grid parameters.

[0039] Preferably, the recursive QR decomposition is based on a recursion matrix.

[0040] In the initialization phase of the method, a starting matrix with suitable initial parameters for the upper triangular matrix of the QR decomposition and for the result vector of the QR matrix equation is expanded into a recursion matrix by means of the current measurement set. In each subsequent method cycle, the measurement set is then replaced by the respective current measurement set. Thus, in each method cycle, the upper triangular matrix R and the result vector are iteratively recalculated taking into account the respective current measurement.

[0041] Furthermore, the QR decomposition is carried out by means of Givens rotations.

[0042] The method with Givens rotations to calculate the upper triangular matrix calculates a rotation matrix in each method cycle in order to purposefully generate zero terms in the recursion matrix. Thus, at the end of each method cycle, an updated upper triangular matrix R and an updated result vector are provided, by means of which the QR matrix equation can be solved by back substitution in order to determine the estimated grid parameter vector.

[0043] Advantageously, in the recursive QR decomposition, the upper triangular matrix and the result vector are weighted by means of a forgetting factor.

[0044] The upper triangular matrix R as well as the result vector of the QR matrix equation are multiplied by a factor, namely a forgetting factor, in order to introduce a weighting of the measurement values.

[0045] The forgetting factor causes the current measurement values to be weighted more strongly than the measurement values located in the past. The forgetting factor has a typical value in the range between 0.95 and 1. The larger the factor, the more strongly older measurement values are taken into account in the calculation. With this parameter, changes are recognized more slowly, however, short-term disturbances are better filtered. Conversely, a smaller factor enables faster recognition of parameter changes, at the disadvantage that the measurements are more susceptible to disturbances. With the recursive calculation with a forgetting factor, such changes can be tracked. BRIEF DESCRIPTION OF DRAWINGS

[0046] Further advantageous design features result from the following description and the figures, which illustrate the preferred embodiments of the application according to examples. The figures show:

[0047] Figure 1 a functionally equivalent circuit diagram of an ungrounded DC power supply system with insulation monitoring,

[0048] Figure 2 a flow chart of the method according to the application,

[0049] Figure 3 a measurement voltage of rectangular pulse shape,

[0050] Figure 4 a voltage drop measured over a measurement resistor in the event of a change in the network voltage,

[0051] Figure 5 a time curve of the calculated insulation resistance, and

[0052] Figure 6 a time curve of the calculated leakage capacity. DETAILED DESCRIPTION

[0053] Figure 1 a functionally equivalent circuit diagram of an ungrounded power supply system 2 to be monitored, which has a network voltage U N .

[0054] The method according to the application can be used not only in DC power supply systems, but also in single- or multi-phase AC power supply systems, in which a measurement voltage U G is coupled to two active conductors L1, L2 in a bipolar manner.

[0055] The insulation impedance effective between the active conductors L1, L2 and the ground PE is represented in parallel by the insulation resistance R1, R2 (real part of the insulation impedance) and the leakage capacity C1, C2 (imaginary part of the insulation impedance).

[0056] For the insulation monitoring, a measurement voltage generator generates a measurement voltage U G , which drives a measurement current, which flows through the active conductors L1, L2, the insulation resistances R1, R2 and the leakage capacities C1, C2 and causes voltage drops U M , U M1 , respectively, at the measurement resistors R M2 , which are measured and evaluated for determining the insulation resistances R1, R2 and the leakage capacities C1, C2.

[0057] In practice, the measurement voltage U GThe coupling is achieved via a series connection of a high-resistance coupling resistor and a low-resistance measuring resistor. For computational simplification, the two resistors have been combined into a single measuring resistor R. M .

[0058] Figure 2 A flowchart describing the method according to the present invention.

[0059] After the initialization phase of the method, the resistance R is measured by means of the measured current. M The corresponding voltage drop U appears on M1 U M2 The voltage U is measured in steps S1 and S2. G The switching is performed by setting the initial values ​​of the parameters for the upper triangular matrix used for QR decomposition and the result vector used for the QR matrix equation during the initialization phase.

[0060] The measurement voltage U is generated in step S3 through sampling and quantization. G Grid voltage U N and voltage drop U M1 U M2 Time-discrete and value-discrete sampled value sequence U G (k), U N (k), U M (k).

[0061] Using the current-voltage relationship derived from the functional equivalent circuit diagram, the linear difference equation is realized in step S4.

[0062] From the measured voltage U M The algebraic equations begin with a description in the frequency domain (due to the bipolar coupling observed exemplarily here, the measured voltage is determined by a voltage drop U). M1 U M2 The sum of these components, and in the case of only unipolar coupling, corresponds only to the voltage drop U. M1 or U M2 ),

[0063]

[0064] (Equation 1)

[0065] The time-continuous differential equation is derived from the measured voltage transformed into the time domain, and the linear difference equation is obtained from the subsequent time discretization of the sequence of sampled values, with index k and sampling period T, in which the measured voltage U... M (k) can be expressed as the measured voltage U G (k) and grid voltage U N The function of (k), such as

[0066]

[0067] (Equation 2)

[0068] In matrix notation this results in:

[0069]

[0070] (Equation 3)

[0071] For k = 1, 2 to N measurement time points, in step S5 an overdetermined measurement equation system is thus realized:

[0072]

[0073] (Equation 4)

[0074] The overdetermined measurement equation system can be written as a measurement matrix equation with measurement vector , measurement matrix and grid parameter vector (coefficient vector) :

[0075]

[0076] (Equation 5)

[0077] The grid parameter vector is composed of the elements (grid parameters) which are formed by the grid variables G1 = 1 / R1, G2 = 1 / R2, C1 and C2 to be determined and by the measurement resistances R M .

[0078] Since the overdetermined equation system generally has no solution, in step S6 an approximate solution is calculated in which a (remaining) error is retained which in the ideal case only reflects the measurement noise. As a result, the grid parameter vector in equations (4) and (5) becomes an estimated grid parameter vector with the estimated grid parameters :

[0079]

[0080] (Equation 6)

[0081] The estimated grid parameters (estimates of the elements of the grid parameter vector ) are considered to be optimal when the sum of the squares of the errors is smallest:

[0082]

[0083] (Equation 7)

[0084] Solving the minimization problem by means of a gradient method requires matrix inversion, the computation of which can become numerically unstable. To circumvent matrix inversion, equation (7) is geometrically interpreted and considered as the square of the Euclidean norm:

[0085]

[0086] (Equation 8)

[0087] In step S7, a (complete) QR decomposition is applied to the measurement matrix by means of an orthogonal matrix and an upper triangular matrix R:

[0088]

[0089] (Equation 9)

[0090] Due to the orthogonality , left multiplication by yields:

[0091]

[0092] (Equation 10)

[0093] The multiplication of the measurement vector can likewise be divided into:

[0094]

[0095] (Equation 11)

[0096] where here is called the result vector and the vector reflects the remaining error.

[0097] Since is orthogonal, left multiplication by does not change the Euclidean norm, the multiplication is length preserving, and the expression to be minimized in equation (8) is transformed into:

[0098]

[0099] (Equation 12)

[0100] The expression in equation (12) has a minimum when the following QR matrix equation is satisfied:

[0101] ​

[0102] (Equation 13)

[0103] In case the upper triangular matrix and the result vector are known, the estimated grid parameter vector can be easily determined by back substitution.

[0104] For the calculation of and a recursive method is used. As starting values the identity matrix is chosen for and a suitable initial grid parameter (0) is chosen for . In case of four grid parameter values to be estimated, the following matrix is obtained from them as starting matrix:

[0105]

[0106] (Equation 14)

[0107] The starting matrix is now extended with the first measurement set and the recursive matrix is obtained:

[0108]

[0109] (Equation 15)

[0110] With the help of Givens rotations, the zero entries can be generated purposefully by repeated left multiplication with the rotation matrix . If the element (i, j) shall be zero, then the rotation affects only the i-th and j-th row. By this, the recursive matrix in equation (15) can be transformed into the following form:

[0111]

[0112] (Equation 16)

[0113] It is obtained:

[0114]

[0115] (Equation 17)

[0116] The initial starting values are iteratively replaced by the recalculated upper triangular matrix and the recalculated result vector . With the help of the recalculated upper triangular matrix and the recalculated result vector , the estimated grid parameter vector can be determined by back substitution according to the QR matrix equation (13).

[0117] At the end of each method cycle, the respective insulation resistances R1, R2 and the respective leakage capacitances C1, C2 are calculated in step S8 from the estimated grid parameters .

[0118] Thus, the inclusion of the grid voltage into the description of the current-voltage relationship (derived from the equivalent circuit diagram) enables the selective, i.e. individual determination of the insulation resistance and the leakage capacitance for each active conductor. The division of the individual active conductors simplifies the fault finding in the ungrounded DC power supply system.

[0119] Based on the recursive matrix shown in equations (15) and (16), the method flow is continuously repeated with the next, at the current measurement time point existing, measurement value set (Y ), with the re-calculated upper triangular matrix (A ) and the re-calculated result vector (b ).

[0120] Here, before the next method cycle, the re-calculated upper triangular matrix (A ) and the re-calculated result vector (b ) can be multiplied by a forgetting factor (0 in order to achieve a time weighting of the measurement values.

[0121] Figure 3 The measurement voltage U G generated by the measurement voltage generator is shown in a rectangular pulse shape, which is superimposed on the ungrounded DC power supply system 2. Since the maximum modulation range is 1.2 V, the measurement voltage U G has an amplitude of approximately 1 V. The pulse width is 8 s.

[0122] Figure 4 The voltage drop U M1 measured on the measurement resistance R M is shown when the grid voltage U N has a low-frequency grid voltage variation of 0.1 Hz.

[0123] The voltage drop U M1 is caused by the varying grid voltage U N and the measurement voltage U GThe superposition of the components. It is clear that low-frequency grid voltage variations dominate and thereby exert an interfering effect on the measurement. Therefore, according to the prior art, interference suppression, such as interference suppression through filtering, is necessary. When applying the method according to the invention, especially in the case of low-frequency grid voltage variations, such circuitry-intensive measures for suppressing interference effects can be omitted. According to the invention, even under the aforementioned difficult conditions, i.e., in the case of distorted measurement signals, it is still possible to obtain usable measurement values ​​in an advantageous manner.

[0124] Figure 5 Shown in Figure 4 In the context of grid voltage U, characterized by grid voltage variations N Under the given conditions, when the actual insulation resistance undergoes a step change (test test) after 40 seconds, the calculated insulation resistance R... f The time variation curve of (here, the total resistance of the parallel connection of insulation resistances R1 and R2).

[0125] First, continue for approximately 20 seconds until the calculated insulation resistance R is reached. f This roughly corresponds to the true value. After the step change in the true insulation resistance at time point 40s, it persists for approximately 30s until the measurement method again provides the true value of the insulation resistance.

[0126] Figure 6 With Figure 5 A similar approach is used to show the calculated leakage capacitance C when the actual leakage capacitance undergoes a step change after 40 seconds. e The time variation curve (here, the sum of leakage capacitances C1 and C2).

Claims

1. A method for determining an insulation resistance (Rl, R2) and a leakage capacitance (Cl, C2) of an ungrounded DC power supply system with respect to ground (PE), the DC power supply system having a system voltage (U N ) and an active conductor (LI, L2), the method comprising the following method steps: between each one of the active conductors (L1, L2) and ground (PE), in a unipolar or bipolar manner, a measurement voltage (U G ) is coupled (S1) in series with a measurement resistance (R M ). measuring (S2) the voltage drop (U M1 , U M2 ) over the respective measurement resistor (R M ) characterized in that generating (S3) a time-discrete and value-discrete sequence of sample values (U G (k), U N (k), U M1 (k)) of the measured voltage (U M2 ), the grid voltage (U G ) and the corresponding voltage drop (U N , U M ), by means of the measured voltage (U G (k) ) as a function of the measurement voltage (U N (k) ) and of the network voltage (U M (k) ), and by means of network parameters (p ), which are formed from the measurement resistance (R M ), the insulation resistances (R1, R2) to be determined and the leakage capacitances (C1, C2) to be determined, For k = 1, 2 to N sampling time points with a sampling period T, by means of the sampling value sequence (U G (k), U N (k), U M (k) and the grid parameter (P ), a measurement equation system consisting of N linear difference equations is realized (S5), Calculate (S6) the estimated power grid parameters ( ) as an approximate solution to the system of equations for the measured values, wherein the power grid parameters ( ) and the estimated power grid parameters ( Minimize the sum of squared errors between ) Through the measurement matrix ( The QR decomposition of the error is performed to minimize the sum of squared errors (S7), wherein the calculation of the QR decomposition is performed recursively. from the estimated grid parameters (R1, R2, C1, C2) corresponding insulation resistances (R1, R2) and corresponding leakage capacities (C1, C2) are calculated (S8) from the estimated grid parameters (R1, R2, C1, C2), Incorporating the sample values existing at the current point of time of measurement, the estimated grid parameters (Pest, Qest) are calculated The method steps are repeated continuously.

2. The method according to claim 1, characterized in that The linear difference equation is derived by converting a linear algebraic equation describing the current-voltage relationship in the frequency domain into a time-continuous difference equation and a time-discrete implementation of the difference equation.

3. The method according to claim 1 or 2, characterized in that The recursive QR decomposition is based on a recursion matrix.

4. The method according to claim 1 or 2, characterized in that The QR decomposition is performed by means of Givens rotations.

5. The method according to claim 1 or 2, characterized in that In the recursive QR decomposition, the upper triangular matrix (R) and the result vector (c) are weighted by means of a forgetting factor (λ ).

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