Method and devices for determining the elements of a dielectric equivalent circuit diagram for an insulation of an electric system

Abstract

A method and a test apparatus for determining the elements of a dielectric equivalent circuit diagram for an insulation of an electric system and to an insulation monitoring device. All data points of the system's step response are stored for a measuring period T.sub.m, and fault resistance R.sub.f and an initial value C.sub.e0 of leakage capacitance C.sub.e are calculated. After this determination of fault resistance R.sub.f and initial value C.sub.e0, the elements of absorption element R.sub.a and C.sub.a and leakage capacitance C.sub.e are determined by numeric signal processing by using an approximation algorithm which continuously simulates the recorded step response. For simulating the step response, a transfer function G(s) modelled by the equivalent circuit diagram having equivalent circuit diagram elements R.sub.f, C.sub.e, R.sub.a, C.sub.a and measurement resistance R.sub.m is formed analytically and the output signal is calculated, which is described using transfer function G(s), by means of the step function.

Claims

1. A method for determining the elements of a dielectric equivalent circuit diagram for an insulation of an electric system, the equivalent circuit diagram being a parallel connection made up of a fault resistance (R.sub.f), a leakage capacitance (C.sub.e) and an absorption element which is made up of a series connection of an absorption resistance (R.sub.a) and an absorption capacitance (C.sub.a), comprising the method steps: applying a voltage step to the electric system as a test voltage (u.sub.0 (t)) of a voltage source having a known measurement resistance (R.sub.m) in series to the voltage source; measuring a voltage dropping at the measurement resistance (R.sub.m) as a step response (u.sub.a(t)) of the electric system; wherein recording the step response (u.sub.a(t)) over a measuring period (T.sub.m) whose duration approximately corresponds to a twofold settling phase of the step response (u.sub.a(t)); calculating the fault resistance (R.sub.f) from the progression of the step response (u.sub.a(t)) in the settled state; determining the time constant (τ) from the progression of the step response (u.sub.a(t)) in the settling phase; calculating an initial value (C.sub.e0) of the leakage capacitance (C.sub.e) from the time constant (τ), the fault resistance (R.sub.f) and the measurement resistance (R.sub.m); forming a transfer function (G(s)) of the electric system, which was modelled by the equivalent circuit diagram using the equivalent circuit diagram elements (R.sub.f, C.sub.e, R.sub.a, C.sub.a) and the measurement resistance (R.sub.m), as a ratio between an output signal (U′.sub.a(s)) at the measurement resistance (R.sub.m) and a test signal (U.sub.0(s)) of the voltage source as an input signal; calculating the output signal (U′.sub.a(s)) from the transfer function (G(s)) using a step function as a test signal (U.sub.0(s)) while incorporating the calculated fault resistance (R.sub.f), the calculated initial value (C.sub.e0) of the leakage capacitance (C.sub.e) and the known measurement resistance (R.sub.m), the absorption resistance (R.sub.a), the absorption capacitance (C.sub.a) and the leakage capacitance (C.sub.e) each being iteratively determined in such a manner via approximate values (R′.sub.a, C′.sub.a, C′.sub.e) by means of an approximation algorithm that the deviation between the calculated output signal (u′.sub.a(t)) transformed in the time range and the measured recorded step function (u.sub.a(t)) is minimized.

2. The method according to claim 1, wherein the approximation algorithm minimizes the deviation in a temporal section between the four- to fivefold time constant (τ) and the metrological end of the settling phase at approximately ⅗ of the measuring period (T.sub.m).

3. The method according to claim 1, wherein the approximation algorithm functions according to the least squares method.

4. The method according to claim 1, wherein an application determines the dielectric characteristics of an insulation in an ungrounded power supply system in conjunction with insulation monitoring.

5. A test apparatus for determining the elements of a dielectric equivalent circuit diagram for an insulation of an electric system, wherein a signal processing device is configured for executing the method according to the invention for determining the elements of a dielectric equivalent circuit diagram for an insulation of an electric system according to claim 1.

6. An insulation monitoring device for identifying an insulation resistance of an ungrounded power supply system, wherein a signal processing device is configured for executing the method according to the invention for determining the elements of a dielectric equivalent circuit diagram for insulating an ungrounded power supply system according to claim 1.

7. The insulation monitoring device according to claim 6, a variable measurement resistance (R.sub.m) and/or a variable coupling impedance for low-noise detection for a test voltage (u.sub.0(t)) having variable amplitude.

Description

BRIEF DESCRIPTION OF THE DRAWING FIGURES

(1) Further advantageous embodiment features can be derived from the following description and the drawings which show a preferred embodiment of the invention by means of examples.

(2) FIG. 1 shows a dielectric equivalent circuit diagram for an insulation,

(3) FIG. 2 shows a progression of the voltage via the measurement resistance R.sub.m (step response u.sub.a(t)),

(4) FIG. 3 shows steps of the numerical signal processing by means of approximation algorithms,

(5) FIG. 4 shows a test device according to the invention in an ungrounded power supply system, and

(6) FIG. 5 shows an insulation monitoring device having a signal processing device according to the invention.

DETAILED DESCRIPTION

(7) In FIG. 1 a dielectric equivalent circuit diagram is shown for an insulation in a test circuit. Between a conductor L, e.g., of an ungrounded power supply system, and ground PE, fault resistance R.sub.f and leakage capacitance C.sub.e are effective which together form the complex-valued insulation resistance (insulation impedance) of the ungrounded power supply system. In order to describe the dielectric absorption behavior of the insulation between conductor L and ground PE, the equivalent circuit diagram is enhanced with an absorption element which is switched parallel to the insulation impedance and consists of the series connection of an absorption resistance R.sub.a and an absorption capacitance C.sub.a.

(8) For determining the equivalent circuit diagram quantities R.sub.f, C.sub.e, R.sub.a and C.sub.a, the dielectric equivalent circuit diagram is integrated in a test circuit which has a test voltage u.sub.0 (t) and a measurement resistance R.sub.m at which a step response u.sub.a(t) can be measured in the event that a step function is applied as a test voltage u.sub.0(t).

(9) In FIG. 2, the progression of the voltage at measurement resistance R.sub.m is shown. The voltage progression coincides with step response u.sub.a(t) when applying a step function as test voltage u.sub.0(t). Step response u.sub.a(t) is recorded over a measuring period T.sub.m which can be divided into three partial sections A, B and C which in turn can also overlap.

(10) Temporal section A extends from a point in time t=0, at which the voltage amplitude has the value of the height of step function U.sub.0, to approximately the point in time 5*τ, τ forming the time constant of the exponential voltage progression. A second temporal section B extends from approximately from the four- to fivefold of the time constant to approximately ⅗ of measuring period T.sub.m. A third temporal section C encompasses the duration from approximately one half of measuring period T.sub.m to the end of measuring period T.sub.m. From this temporal section C, which represents the settled state and in which leakage capacitance C.sub.e and absorption capacitance C.sub.a can be seen as open-circuited, fault resistance R.sub.f is preferably calculated by determining an average when measurement resistance R.sub.m is known. Assuming the settling process is nearly terminated at five times time constant Ω, an initial value C.sub.e0 is determined for leakage capacitance C.sub.e from thus identified time constant τ and with the knowledge of measurement resistance R.sub.m and previously determined fault resistance R.sub.f.

(11) After analytically calculating fault resistance R.sub.f from temporal section C and analytically determining initial value C.sub.e0 of leakage capacitance C.sub.e from temporal section A, absorption resistance R.sub.a and absorption capacitance C.sub.a are numerically determined in middle temporal section B of step function U.sub.a(t), and leakage capacitance C.sub.e is more precisely determined via an approximation algorithm.

(12) In FIG. 3, the steps for digital signal processing are shown which iteratively identify approximated values R′.sub.a, C′.sub.a, C′.sub.e for absorption resistance R.sub.a, absorption capacitance C.sub.a and leakage capacitance C.sub.e via the approximation method in a numeric manner.

(13) Assuming broad value fields for absorption resistance R.sub.a (1 kΩ . . . 100 GΩ), for absorption capacitance C.sub.a (1 pF . . . 100 mF) and leakage capacitance C.sub.e=(0.8 . . . 1.2)*C.sub.e0, initial values are first established for these three quantities. Naturally empirical values from specific installations can be resorted to as well.

(14) Transfer function G(s) is calculated by further incorporating the known value for measurement resistance R.sub.m and identified fault resistance R.sub.f. The transfer function is multiplied by the Laplace-transformed step function U.sub.0(s) (step height U.sub.0) and yields signal output U′.sub.a(s). This output signal U′.sub.a(s) leads to output signal u′.sub.a(t) which was transformed in the time domain and is compared to the real captured step response u.sub.a(t) according to the least squares method. By continuously varying approximated values R′.sub.a, C′.sub.a, C′.sub.e for absorption resistance R.sub.a, for absorption capacitance C.sub.a and for leakage capacitance C.sub.e, a new transfer function G(s) is iteratively calculated until the sum of the error squares falls below a set threshold value when comparing output signal u′.sub.a(t) transformed in the time range to recorded step response u.sub.a(t). Consequently the values of absorption value R.sub.a, absorption capacitance C.sub.a and leakage capacitance C.sub.e are determined precisely enough.

(15) FIG. 4 shows a test device 10 according to the invention in an ungrounded power supply system 2. Test device 10 is connected between active conductor L of power supply system 2 and ground PE and comprises a signal processing device 12 according to the invention configured for executing the method according to the invention.

(16) In FIG. 5, an insulation monitoring device 20 is shown in ungrounded power supply system 2. Standardized insulation monitoring device 20 is connected between active conductor L of power supply system 2 and ground PE and additionally comprises signal processing device 12 according to the invention for executing the method according to the invention for determining the elements of the dielectric equivalent circuit diagram for an insulation.