METHOD FOR DETERMINING THE INSULATION RESISTANCE AND LEAKAGE CAPACITY OF AN UNGROUNDED POWER SUPPLY SYSTEM

Description

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

[0002] For situations requiring increased operational, fire, and contact safety, an ungrounded power supply system is used, also known as an isolated network (IT network) or IT power supply system (French: Isolé Terre - IT). In this type of power supply system, its active components are separated from earth potential. The advantage of these networks is that in the event of an insulation fault (first fault), such as a ground fault in an active conductor of the ungrounded power supply system, the function of the connected electrical loads is not affected. This is because, due to the ideally infinite impedance value between the active conductor of the network and earth, a closed circuit cannot form.An electrical resistance to earth potential (to earth) forms, as a real component (real part), in parallel with a leakage capacitance as an imaginary part, the complex-valued insulation impedance of the ungrounded power supply system.

[0003] The electrical resistance of the ungrounded power supply system to earth potential, known as insulation resistance, must therefore be monitored in accordance with regulations using a standard-compliant insulation monitoring device (IMD), since a possible further fault on another active conductor (second fault) would create a fault loop and the resulting fault current, in conjunction with an overcurrent protection device, would result in the system being shut down and operational shutdown.

[0004] In addition to passive insulation monitoring devices, which use the mains voltage of the ungrounded power supply system as the driving source for a measuring current to detect an insulation fault, actively operating insulation monitoring devices are known from the prior art. These have a measuring path running between one or more active conductor(s) of the ungrounded power supply system and earth potential, which includes an internal measuring voltage generator. A measuring voltage generated by the measuring voltage generator actively drives a measuring current that flows back into the measuring path via the active conductor(s) and through the insulation resistance and leakage impedance, causing a voltage drop across a measuring resistor connected in series with the measuring voltage generator. The voltage drop measured across the measuring resistor is used to determine the insulation resistance and the leakage impedance.

[0005] Active methods are known that superimpose a rectangular measurement voltage, consisting of successive measurement pulses, onto the ungrounded power supply system being monitored. However, a reliable calculation of the insulation resistance is only possible once the measurement voltage has stabilized, which can take up to several minutes with large leakage capacitances.

[0006] Furthermore, unwanted but unavoidable mains voltage fluctuations can interfere with the measurement. High-frequency mains voltage fluctuations (greater than a few Hz) can be removed by filters.

[0007] Low-frequency mains voltage fluctuations of just a few Hz are problematic, however, because they hinder the detection of transient responses and distort the calculated insulation resistance. Large voltage fluctuations in the low-frequency range can therefore make a measurement impossible, because the test voltage does not stabilize.

[0008] Patent EP 2 433 147 B1 discloses a method for determining the insulation resistance before the measured voltage across a measuring resistor reaches a steady state. The transient process is predicted by a mathematical model whose parameters are iteratively adjusted until the theoretical and measured voltage curves closely match. The insulation resistance can then be calculated based on the model parameters. Interfering mains voltage fluctuations are compensated for by filtering and subtracting two consecutive measurement pulses. However, eliminating low-frequency mains voltage fluctuations also appears problematic. Furthermore, the computationally intensive matrix inversion required to determine the model parameters proves to be a disadvantage.

[0009] The present invention is therefore based on the objective of being able to carry out the fastest, most accurate and robust measurement of the insulation resistance and leakage capacitance in an ungrounded power supply system, in particular the disruptive influence of low-frequency mains voltage changes in DC power supply systems should be reduced in conjunction with a computationally efficient implementation.

[0010] This problem is solved by a method having the features of claim 1.

[0011] Based on the state of the art, a measuring voltage is first coupled in series with a measuring resistor, either single-pole or double-pole, between each of the active conductors, and a voltage drop across the respective measuring resistor – caused by a measuring current driven by the measuring voltage – is measured.

[0012] In DC power supply systems, a two-pole connection proves advantageous because it effectively solves the problem of low-frequency mains voltage fluctuations. In AC and 3AC power supply systems, a single-pole connection is sufficient, as the mains frequency can be removed by filtering.

[0013] From the voltage waveforms of the measuring voltage, the mains voltage and the voltage drop across the respective measuring resistor, time- and value-discrete sample sequences of the measuring voltage, the mains voltage and a measured voltage are generated.

[0014] The continuous signal waveforms of the mains voltage (nominal voltage of the ungrounded power supply system) and the applied measurement voltage generated in a measurement signal generator, as well as the measured voltage drops across the measuring resistors, are converted into time- and value-discrete signals by sampling devices (analog-to-digital converters - ADCs) in order to make them accessible as sample value sequences for digital signal processing.

[0015] The sample sequences thus generated form the input and output variables of a functional equivalent circuit of the considered ungrounded power supply system with insulation monitoring, whose mathematical description is given by physical laws (Ohm's law) and Kirchhoff's theorems in linear networks (current-voltage relationships).

[0016] Based on these principles, a linear difference equation is implemented in which a measured voltage—corresponding to a measured voltage drop with single-pole coupling or the sum of the measured voltage drops with two-pole coupling—can be expressed as a function of the measurement voltage and the mains voltage. The mains parameters of the ungrounded power supply system to be determined represent coefficients of the linear difference equation. These mains parameters are derived from the measurement resistances, the insulation resistances to be determined, and the leakage capacitances to be determined. For computational simplification, the resistance values ​​are expressed in terms of conductances.

[0017] By including the mains voltage in the current-voltage relationships of the linear difference equation, it is not necessary to remove the mains voltage from the measurement voltage, for example by filtering or further signal processing measures. The circuit complexity is advantageously reduced, and the measurement method according to the invention becomes more resistant to interference.

[0018] Furthermore, faster and continuous measurement is possible even with slow, low-frequency changes in the grid voltage. This is particularly advantageous for PV systems, as their DC grid voltage fluctuates depending on the intensity of solar radiation.

[0019] In contrast to prior art methods which require a stable mains voltage and a steady-state measuring voltage to determine the insulation resistance, the method according to the invention allows for continuous measurement.

[0020] In a next step, for k=1, 2 to N measurement times with the sampling period T, a system of N linear difference equations is implemented from the sample sequences of the measurement voltage, the mains voltage, the measured voltage and the mains parameters.

[0021] For N > 4 measurement points, an overdetermined system of measurement equations results. For this overdetermined system of measurement equations, there is generally no solution vector, and therefore no set of network parameters (coefficient vector) that exactly solves all N linear difference equations.

[0022] Therefore, estimated network parameters are calculated as an approximate solution to the system of measured values ​​and equations, minimizing the sum of squared errors between the (actual) network parameters and the estimated network parameters.

[0023] The estimated network parameters are considered optimal in terms of the approximate solution when the sum of squared errors resulting from the remaining (residual) error between the actual network parameters and the estimated network parameters becomes minimal.

[0024] The solution to this minimization or least squares problem is achieved by minimizing the sum of squared errors using QR decomposition of a measurement matrix characterizing the measurement equation system, whereby the calculation of the QR decomposition is performed recursively.

[0025] The system of measurement equations comprising N linear difference equations can be written as a measurement matrix equation, in which the sequence of measured voltage samples (measurement vector) results from multiplying the measurement matrix by the coefficient vector (network parameter vector). The elements of the measurement matrix correspond to the samples of the measurement voltage, the network voltage, and—due to the iterative nature of difference equations—previous samples of the measured voltage.

[0026] A computationally intensive matrix inversion, required to solve the minimization problem using a gradient descent method, is avoided by a QR decomposition of the measurement matrix. Under unfavorable conditions—for example, if the measurement voltage or the mains voltage were zero—this would lead to zero columns and thus to a non-invertible matrix. In this case, matrix inversion would therefore not be possible, unlike QR decomposition.

[0027] In contrast, QR decomposition is numerically much more stable and enables the calculation of estimated network parameters even with a poorly conditioned measurement matrix. The calculation of estimated network parameters according to the invention is less sensitive to erroneous measurement data and rounding errors, and is therefore more accurate.

[0028] Starting from a geometric interpretation of the minimization problem, the squared errors are considered as the square of the Euclidean norm. Using a QR decomposition of the measurement matrix, the minimization problem can then be reduced to a QR matrix equation. In contrast to the measurement matrix equation, which represents the system of measurement equations consisting of the difference equations, the (matrix) equation that solves the minimization problem—which represents a result vector as the matrix product of an upper triangular matrix and an estimated network parameter vector—is here referred to as the QR matrix equation.

[0029] A solution for the estimated network parameter vector is then determined by back-substitution using the previously (recursively) calculated upper triangular matrix R of the QR decomposition and the (recursively) determined result vector of the QR matrix equation.

[0030] According to the invention, the QR decomposition is calculated recursively. The results of the QR decomposition calculated in each iteration – the upper triangular matrix R and the result vector of the QR matrix equation – are updated in the subsequent iteration by incorporating currently available measured values, thus achieving a stepwise approximation of the actual network parameters.

[0031] Recursive calculation significantly reduces memory requirements and computational effort, as only the currently available set of measurements is processed. This enables efficient implementation on a microcontroller.

[0032] Besides the advantage that recursive QR decomposition requires little memory and processing time, it allows for rapid adaptation to changing (actual) network parameters. If the currently effective insulation resistance or leakage capacitance changes, the measurements and calculations can easily continue due to the continuous adaptation.

[0033] The respective conductor-related insulation resistance and leakage capacitance are calculated from the estimated network parameters.

[0034] The insulation resistances and leakage capacitances are not calculated directly from the voltage drops measured across the measuring resistors, as is customary in the prior art, but rather from the estimated network parameters. Therefore, it is not a prerequisite that the measured voltage has reached a steady state in order to perform reliable calculations.

[0035] Firstly, the method according to the invention enables the rapid determination of the insulation resistance and the leakage capacitance, and secondly, it provides greater freedom in the choice of the signal waveform of the measuring voltage. For example, it is possible to select a sinusoidal measuring voltage or a mixture of sinusoidal voltage waveforms of different frequencies as the measuring signal.

[0036] The process steps are continuously repeated with the respective calculated, estimated network parameters, taking into account the sampled values ​​available for the current measurement time.

[0037] Thus, continuous adjustment to the current insulation state of the ungrounded power supply system takes place, whereby the recursive calculation ensures a resource-saving and fast determination of the insulation resistance and leakage capacitance.

[0038] In a further development, the linear difference equation is derived by transforming a linear algebraic equation describing the current-voltage relationships in the frequency domain into a time-continuous differential equation and its time-discrete implementation.

[0039] The starting point for implementing the linear difference equation is a description of the current-voltage relationships in the frequency domain (image domain) derived from the equivalent circuit diagram of the considered ungrounded power supply system with insulation monitoring, using a linear algebraic equation. Preferably, the Laplace transform is used to describe the relationships in the frequency domain. Converting this to the time domain results in a continuous-time differential equation, and the subsequent time discretization yields the linear difference equation. Applying this equation to successive measurement points (sample values) results in the system of measured value equations, which can be represented as a measured value matrix equation, with the measured value matrix used to determine the network parameters.

[0040] Preferably, the recursive QR decomposition is performed on the basis of a recursion matrix.

[0041] In an initialization phase of the procedure, 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 extended to a recursion matrix using the current set of measurements. In each subsequent iteration, this set of measurements is replaced by the then-current set of measurements. Thus, in each iteration, the upper triangular matrix R and the result vector are recalculated, taking into account the current measurements.

[0042] The QR decomposition is then carried out using Givens rotation.

[0043] Using the Givens rotation method to calculate the upper triangular matrix, rotation matrices are calculated in each iteration to selectively generate zero entries in the recursion matrix. This results in an updated upper triangular matrix R and an updated result vector at the end of each iteration. These vectors can then be used to solve the QR matrix equation by back-substitution, thus determining the estimated network parameter vector.

[0044] Advantageously, in recursive QR decomposition, an upper triangular matrix and a result vector are weighted with a forgetting factor.

[0045] The upper triangular matrix R and the result vector of the QR matrix equation are multiplied by a factor - the Forgetting Factor - to introduce a weighting of the measured values.

[0046] The forgetting factor causes current measurements to be weighted more heavily than those from the past. It typically has a value between 0.95 and 1. The larger this factor, the more older measurements are considered in the calculation. This results in slower detection of parameter changes, but also better filtering of short-term disturbances. Conversely, a smaller factor allows for faster detection of parameter changes, but makes the measurement more susceptible to interference. Such changes can be tracked through recursive calculations using the forgetting factor.

[0047] Further advantageous design features will become apparent from the following description and the drawings, which illustrate a preferred embodiment of the invention by means of examples. They show Fig. 1: a functional equivalent circuit diagram of an ungrounded DC power supply system with insulation monitoring, Fig. 2: a flowchart of the inventive method, Fig. 3: a rectangular pulse measuring voltage, Fig. 4: a voltage drop measured across a measuring resistor during a change in mains voltage, Fig. 5: a time history of a calculated insulation resistance and Fig. 6: a time course of a calculated discharge capacity.

[0048] Fig. 1 shows a functional equivalent circuit diagram of an ungrounded power supply system 2 to be monitored with the mains voltage UN .

[0049] The method according to the invention is applicable both in a DC power supply system and in a single- or multi-phase AC power supply system, wherein the coupling of the measuring voltage UG is here exemplified in a DC power supply system in a two-pole manner to two active conductors L1, L2.

[0050] An insulation impedance effective between active conductors L1, L2 and earth PE is represented by an insulation resistance R1, R2 (real part of the insulation impedance) in parallel with a leakage capacitance C1, C2 (imaginary part of the insulation impedance).

[0051] For insulation monitoring, a measuring voltage generator produces a measuring voltage UG, which drives a measuring current that flows via the active conductors L 1 , L 2 , via the insulation resistances R 1 , R 2 and via the leakage capacitances C 1 , C 2 and causes a voltage drop U M1 , U M2 across measuring resistances RM, which is measured and evaluated to determine the insulation resistance R 1 , R 2 and the leakage capacitance C 1 , C 2.

[0052] In practice, the measuring voltage UG is coupled via a series circuit with a high-resistance coupling resistor and a low-resistance measuring resistor. For computational simplification, both resistors have been combined into the respective measuring resistor RM.

[0053] Fig. 2 describes a flowchart of the method according to the invention.

[0054] After an initialization phase of the procedure, in which initial values ​​of the parameters for the upper triangular matrix of the QR decomposition and for the result vector of the QR matrix equation are set, in steps S1 and S2 the measuring voltage UG is switched and the respective voltage drop U M1 , U M2 across the measuring resistors RM due to the measuring current is measured.

[0055] In step S3, time- and value-discrete sample sequences UG (k), UN (k), UM (k) of the measurement voltage UG , the mains voltage UN and the voltage drops U M1 , U M2 are generated by sampling and quantizing.

[0056] In step S4, a linear difference equation is implemented using the current-voltage relationships derived from the functional equivalent circuit.

[0057] Starting from a description in the frequency domain by the algebraic equation for the measured voltage UM (this is composed of the sum of the voltage drops U M1 , U M2 due to the two-pole coupling considered here as an example, and would only correspond to the voltage drop U M1 or U M2 in the case of a single-pole coupling) U M 1 s + U M 2 s = U M s = − 2 s + G 1 + G 2 C 1 + C 2 s + G 1 + G 2 + 2 G M C 1 + C 2 U G s + C 2 − C 1 C 1 + C 2 ⋅ s + G 2 − G 1 C 2 − C 1 s + G 1 + G 2 + 2 G M C 1 + C 2 U N s From their transformation into the time domain, the continuous-time differential equation follows, and from the subsequent time discretization with the index k of the sample sequences and the sampling period T, the linear difference equation is obtained, in which the measured voltage UM (k) can be expressed as a function of the measurement voltage UG (k) and the mains voltage UN (k) as U M k = − 2 G 1 + G 2 + 1 T C 1 + C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 U G k − G 1 − G 2 + 1 T C 1 − C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 U N k + 1 T C 1 − C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 U N k − 1 + 1 T C 1 + C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 U M k − 1 + 2 U G k − 1

[0058] In matrix notation, this results in: U M k = U G k U N k U N k − 1 U M k − 1 + 2 U G k − 1 ⋅ − 2 G 1 + G 2 + 1 T C 1 + C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 − G 1 − G 2 + 1 T C 1 − C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 1 T C 1 − C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 1 T C 1 + C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2

[0059] For k=1, 2 to N measurement times, the implementation of an overdetermined measurement equation system takes place in step S5: U M 1 ⋮ U M N = U G 1 U N 1 U N 0 U M 0 + 2 U G 0 ⋮ ⋮ ⋮ ⋮ U G N U N N U N N − 1 U M N − 1 + 2 U G N − 1 ⋅ − 2 G 1 + G 2 + 1 T C 1 + C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 − G 1 − G 2 + 1 T C 1 − C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 1 T C 1 − C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 1 T C 1 + C 2 G 1 + G 2 + 2 G M + 1 T C 1 + C 2 which is expressed as a measurement matrix equation with the measurement vector y, the measurement matrix Ψ and the network parameter vector (coefficient vector) θ can be written: y = Ψ ⋅ θ

[0060] The network parameter vector θ consists of the elements θ i (Network parameters) which are formed from the network parameters to be determined G 1 =1 / R 1 , G 2 =1 / R 2 , C 1 and C 2 as well as from the measuring resistances RM.

[0061] Since overdetermined systems of equations generally have no solution, an approximate solution is calculated in step S6, which leaves a (residual) error e that ideally only represents the measurement noise. From the network parameter vector θ In equations (4) and (5) an estimated network parameter vector is thus obtained. θ̂ with estimated network parameters θ̂ i : y = Ψ ⋅ θ ^ + e

[0062] The estimated network parameters θ̂ i (Elements of the network parameter vector θ̂ are considered optimal if the sum of squares of the error e minimal is: min θ ^ ∑ k = 1 N e k 2 = min θ ^ e T e

[0063] Solving this minimization problem using a gradient descent method requires a matrix inversion, the computation of which can become numerically unstable. To avoid the matrix inversion, equation (7) is interpreted geometrically and considered as the square of the Euclidean norm: min θ ^ e T e = min θ ^ Ψ θ ^ − y 2 2

[0064] On the measurement matrix Ψ In step S7, the (full) QR decomposition is applied using the orthonormal matrix. Q and an upper triangular matrix R , where 0 The zero matrix is: Ψ = Q R 0

[0065] Left-hand multiplication with Q T< This results from orthonormality Q T< Q = 1: Q T Ψ = R 0

[0066] The multiplication of the measured value vector y can be divided equally into: Q T y = c c ˜ where here c is referred to as the result vector and the vector c̃ depicts the remaining error.

[0067] Because Q The orthonormal state changes upon left-hand multiplication with Q T< The Euclidean norm does not apply – multiplication conserves length – and the expression to be minimized in equation (8) becomes Ψ θ ^ − y 2 2 = Q T Ψ θ ^ − y 2 2 = Q T Ψ θ ^ − Q T y 2 2 = R 0 θ ^ − c c ˜ 2 2 = R θ ^ − c 0 − c ˜ 2 2 = R θ ^ − c 2 2 ︸ = 0 + c ˜ 2 2

[0068] The expression R θ ^ − c 2 2 ︸ = 0 + c ˜ 2 2 Equation (12) has a minimum when the QR matrix equation R θ ^ = c is fulfilled. The estimated network parameter vector θ̂ can then, with knowledge of the upper triangular matrix R and the result vector c can be determined simply by reverse substitution.

[0069] To calculate R and c A recursive procedure is used. The starting values ​​are for R the identity matrix and for c suitable initial network parameters θ̂ i (0) selected. For example, with four network parameter values ​​to be estimated, the following matrix results as the starting matrix: Q T Ψ y = R c = 1 0 0 0 θ ^ 1 0 0 1 0 0 θ ^ 2 0 0 0 1 0 θ ^ 3 0 0 0 0 1 θ ^ 4 0

[0070] This initial matrix is ​​now supplemented by a first set of measured values ​​( ψ T< y' ) extends and leads to the recursion matrix R c ψ T y ′ = 1 0 0 0 θ ^ 1 0 0 1 0 0 θ ^ 2 0 0 0 1 0 θ ^ 3 0 0 0 0 1 θ ^ 4 0 ψ 1 ψ 2 ψ 3 ψ 4 y ′

[0071] Givens rotation allows for repeated left-hand multiplication with rotation matrices. G i,j Zero entries are deliberately created. If the element ( i,j If the rows are to be zeroed, then the rotation only applies to those rows. i and j Influence. This allows the recursion matrix from equation (15) to be transformed into the form R c ψ T y ′ → R ′ c ′ 0 T c ˜ be transformed: G 5 , 1 1 0 0 0 θ ^ 1 0 0 1 0 0 θ ^ 2 0 0 0 1 0 θ ^ 3 0 0 0 0 1 θ ^ 4 0 ψ 1 ψ 2 ψ 3 ψ 4 y ′ → G 5 , 2 * * * * * 0 1 0 0 θ ^ 2 0 0 0 1 0 θ ^ 3 0 0 0 0 1 θ ^ 4 0 0 * * * * → G 5 , 3 * * * * * 0 * * * * 0 0 1 0 θ ^ 3 0 0 0 0 1 θ ^ 4 0 0 0 * * * → G 5 , 4 * * * * * 0 * * * * 0 0 * * * 0 0 0 1 θ ^ 4 0 0 0 0 * * → * * * * * 0 * * * * 0 0 * * * 0 0 0 * * 0 0 0 0 c ˜

[0072] The initial starting values ​​are iteratively replaced by a newly calculated upper triangular matrix. R ' and a newly calculated result vector c' replaced. With the newly calculated upper triangular matrix R' and the newly calculated result vector c' can the estimated network parameter vector θ̂ can be determined according to the QR matrix equation (13) by back substitution.

[0073] At the end of each process run, in step S8, the respective insulation resistance R1, R2 and the respective leakage capacitance C1, C2 are calculated from the estimated network parameters. θ̂ i .

[0074] Including the mains voltage in the description of the current-voltage relationships (derived from the equivalent circuit diagram) thus makes it possible to determine the insulation resistance and leakage capacitance conductor-selectively, i.e., separately for each active conductor. Distributing the values ​​across the individual active conductors simplifies troubleshooting in the ungrounded DC power supply system.

[0075] Based on the recursion matrix represented in equations (15) and (16), the procedure sequence is carried out with the next set of measured values ​​available at the current measurement time ( ψ T< y' ), with the newly calculated upper triangular matrix R' and with the newly calculated result vector c' repeated continuously.

[0076] In this process, the newly calculated upper triangular matrix can be used before the next procedure run. R' and the newly calculated result vector c' with a forgetting factor λ They are multiplied to achieve a time-weighted analysis of the measured values.

[0077] Fig. 3 Figure 1 shows a rectangular pulse measuring voltage UG generated by the measuring voltage generator, which is superimposed on the ungrounded DC power supply system 2. Since the maximum output range is 1.2V, the measuring voltage UG has an amplitude of approximately 1V. The pulse width is 8s.

[0078] In Fig. 4 The figure shows a voltage drop U M1 measured across a measuring resistor RM when the mains voltage UN has a low-frequency mains voltage change of 0.1Hz.

[0079] The voltage drop UM1 is composed of the superposition of the changing mains voltage UN and the rectangular pulse-shaped measurement voltage UG. It is clearly evident that the low-frequency mains voltage change dominates and thus has a disruptive influence on the measurement. According to the prior art, interference suppression, for example by filtering, is therefore necessary. Such a measure for suppressing interference effects, which is particularly complex in terms of circuitry when dealing with low-frequency mains voltage changes, can be dispensed with when using the method according to the invention. Advantageously, according to the invention, it is still possible to obtain usable measured values ​​even under these difficult conditions, i.e., with distorted measurement signals.

[0080] Fig. 5 shows a time course of a calculated insulation resistance R f (here as the total resistance of the parallel connection of the insulation resistances R 1 and R 2 ) during a sudden (test) change in the true insulation resistance after 40s under the conditions of the mains voltage UN characterized by the mains voltage change. Fig. 4 .

[0081] It initially takes about 20 seconds for the calculated insulation resistance Rf to roughly correspond to the true value. After the abrupt change in the true insulation resistance at time 40 seconds, it takes about 30 seconds for the measurement method to again deliver the true value of the insulation resistance.

[0082] Fig. 6 shows in an analogous way to Fig. 5 a time course of a calculated discharge capacitance C e (here as the sum of the discharge capacitances C 1 and C 2 ) during a sudden change in the true discharge capacitance after 40s.

Claims

1. A method for determining an insulation resistance (R1, R2) and a leakage capacitance (C1, C2) against ground (PE) of an ungrounded DC power supply system, which has a line voltage (UN) and active conductors (L1, L2), the method comprising the following method steps: coupling (S1) a measuring voltage (UG) in series to a measured resistance (RM) in a unipolar or bipolar manner between one of the active conductors (L1, L2) and ground (PE) in each instance, measuring (S2) a voltage drop (UM1, UM2) via the corresponding measured resistance (RM), generating (S3) time and value-discrete sample sequences (UG(k), UN(k), UM(k)) of the measuring voltage (UG), the line voltage (UN) and the corresponding voltage drop (UM1, UM2), implementing (S4) a linear difference equation having a measuring voltage (UM(k)) as a function of the measuring voltage (UG(k)) and the line voltage (UN(k)) and having network parameters (θi), which are formed from the measured resistances (RM), from the insulation resistances to be determined (R1, R2) and from the leakage capacitances to be determined (C1, C2), implementing (S5) a measured-value equation system from N linear difference equations using the sample sequences (UG(k), UN(k), UM(k)) and the network parameters (θi) for k = 1, 2 to N measuring points in time having the sampling period T, computing (S6) estimated network parameters (θi) as an approximate solution of the measured-value equation system, a sum of squared residuals between the network parameters (θi) and the estimated network parameters (θi) being minimized, minimizing (S7) the sum of squared residuals via QR decomposition of a measured-value matrix (Ψ), the QR decomposition being computed recursively, computing (S8) the corresponding insulation resistance (R1, R2) and the corresponding leakage capacitance (C1, C2) from the estimated network parameters (θ̂i), continuously repeating the method steps having the correspondingly computed, estimated network parameters (θ̂i) while taking into consideration the samples available for the current measuring point in time.

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

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

4. The method according to any one of the claims 1 to 3, characterized in that the QR decomposition is carried out by means of Givens rotation.

5. The method according to any one of the claims 1 to 4, characterized in that an upper triangular matrix (R) and a result vector (c) are weighted using a Forgetting Factor ( λ ) in the recursive QR decomposition.