METHOD AND MEASURING DEVICE FOR DETECTING A LEAKAGE CURRENT IN AN UNGROUNDED, SINGLE-PHASE ALTERNATING-CURRENT POWER SUPPLY SYSTEM

Abstract

A method and a measuring device for detecting a leakage current in an ungrounded, single-phase alternating-current power supply system. A variable test resistance is switched between one of the outer conductors and ground and starting from a minimally admissible test-resistance value, at least one of three support test-resistance values is determined as support locations. In an equivalent circuit of the modeled alternating-current power supply system, an equations system is set up for describing the dependency of currents and voltages. An extrapolation on the test-resistance value zero leads to a calculated test current which corresponds to the leakage current to be detected. Consequently, a ground fault situation may be simulated without actually causing a dangerous ground fault.

Claims

1. A method for detecting a leakage current (I.sub.d) in an ungrounded, single-phase alternating-current power supply system (2) having two outer conductors (L1, L2), the method comprising the following steps: a) switching a variable test resistance (R.sub.var) between one of the outer conductors (L1, L2) and ground (PE), a test-resistance value being supposed to be set infinitely, b) measuring an operating voltage (U.sub.0) of the alternating-current power supply system (2) between the outer conductors (L1, L2) by means of line-voltage measuring equipment (24), c) measuring an outer-conductor-to-ground voltage (U.sub.L,Pe) between one of the outer conductors (L1, L2) and ground (PE) by means of ground-voltage measuring equipment (26), d) should the condition that the outer-conductor-to-ground voltage (U.sub.L,Pe) be greater than or equal to half the operating voltage (U.sub.0) not be fulfilled, switching the variable test resistance (R.sub.var) between the other outer conductor (L1, L2) and ground (PE), e) determining a minimally admissible test-resistance value (R.sub.var,min) for the variable test resistance (R.sub.var), f) determining at least three support test-resistance values (R.sub.var,i) as support locations starting from the minimally admissible test-resistance value (R.sub.var,min), g) setting the support test-resistance value (R.sub.var,i) and measuring a correspondingly resulting, measured test current (I.sub.R, I.sub.Ri) via the variable test resistance (R.sub.var) by means of current measuring equipment (28) for detecting a functional metrological dependency of the measured test current (I.sub.Ri) of the support test-resistance value (R.sub.var,i), h) mapping the alternating-current power supply system (2) via an equivalent circuit having the test resistance (R.sub.var) and having leakage impedances (Z.sub.L1, Z.sub.L2) which have a capacitive portion of leakage capacitances (C.sub.e1, C.sub.e2) of the alternating-current power supply system (2), i) determining the leakage capacitances (C.sub.e1, C.sub.e2) from an equations system, which describes the equivalent circuit, by means of a numerical approximation method such that the deviation of a calculated test current (I.sub.R,fit, I.sub.Ri,fit) from the measured test current (I.sub.Ri) is minimized to the support test-resistance values (R.sub.var,i), j) calculating the leakage current (I.sub.d) as a calculated test current (I.sub.R,fit, I.sub.R0,fit) from the equations system having the detected leakage capacitances (C.sub.e1, C.sub.e2) and having the rest-resistance value (R.sub.var, R.sub.0) zero, k) outputting the leakage current (I.sub.d) and the leakage capacitances (C.sub.e1, C.sub.e2).

2. The method according to claim 1, wherein the numerical approximation method is executed according to the least-squares function approximation.

3. The method according to claim 1, wherein ohmic portions (R.sub.f1, R.sub.f2) of the leakage impedances (Z.sub.L1, Z.sub.L2) are neglected in the equivalent circuit in the sense of an infinitely large resistance value.

4. The method according to claim 1, wherein the method sequence is executed automatically by a computing unit (30).

5. A measuring device (20, 21) for detecting a leakage current (I.sub.d) in an ungrounded, single-phase alternating-current power supply system (2) having two outer conductors (L1, L2), comprising: a variable test resistance (R.sub.var) which is switched to one of the outer conductors (L1, L2) and ground (PE), line-voltage measuring equipment (24) for measuring an operating voltage (U.sub.0) of the alternating-current power supply system (2) between the outer conductors (L1, L2), ground-voltage measuring equipment (26) for measuring an outer-conductor-to-ground voltage (U.sub.L,Pe) between one of the outer conductor (L1, L2) and ground (PE), a current measuring device (28) for measuring a settable, measured test current (I.sub.R, I.sub.Ri) via the variable test resistance (R.sub.var), and having a computing unit (30) which is configured for controlling and executing the method sequence claimed in claim 1.

6. The measuring device (20, 21) according to claim 5, wherein the variable test resistance (R.sub.var), the ground-voltage measuring equipment (26), the current measuring equipment (28) and the computing unit (30) are realized as a structural unit (20), or in that the variable test resistance (R.sub.var), the ground-voltage measuring equipment (26), the current measuring equipment (28), the computing unit (30) and the line-voltage measuring equipment (24) are realized as an enhanced structural unit (21).

7. The measuring device (20, 21) according to claim 5, wherein the variable test resistance (R.sub.var) is configured as a resistance network having discretely switchable resistance values or as an electronic resistance having semiconductor structural elements.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Further advantageous embodiment features are derived from the following description and drawings which describe an embodiment of the invention by means of examples.

[0049] FIG. 1 shows a leakage-current measurement according to the state of the art,

[0050] FIG. 2 shows a measuring device according to the invention for detecting a leakage current, and

[0051] FIG. 3 shows an equivalent circuit for detecting the leakage current.

DETAILED DESCRIPTION

[0052] In a functional circuit diagram, FIG. 1 shows a method known from the state of the art for measuring leakage current I.sub.d in a single-phase alternating-current power supply system 2 having outer conductors L1, L1 and an operational voltage U.sub.0.

[0053] Per definition, all active parts of ungrounded power supply system 2 are separate from ground PE; however, ungrounded alternating-current power supply system 2 comprises unpreventable leakage impedances Z.sub.L1, Z.sub.L2 of outer conductors L1, L2 with respect to ground PE. Leakage impedances Z.sub.L1, Z.sub.L2 are made up of an ohmic portion R.sub.f1, R.sub.f2 (insulation resistance) and a capacitive portion C.sub.e1, C.sub.e2 (leakage capacitances). A grounding resistance R.sub.A consists of the sum of the resistances of ground electrode R.sub.AE and ground conductor R.sub.PE-L.

[0054] For insulation monitoring as mandated by standards, an insulation monitoring device IMD having coupling resistances R.sub.a1, R.sub.a2 is switched between each one of outer conductors L1, L2 and ground PE.

[0055] According to the state of the art, leakage current I.sub.d is measured by an ammeter 4 having inner resistance zero being switched between outer conductor L1 and ground PE. However, the thus consciously caused ground fault poses a risk to the handler and to the electric installation because a possible second fault (ground fault at the other outer conductor L2) could be the cause for high capacitive discharge current to flow or electric arcs to arise.

[0056] FIG. 2 illustrates a measuring device 20, 21 according to the invention for detecting leakage current I.sub.d in an ungrounded, single-phase alternating-current power supply system 2.

[0057] Measuring device 20, 21 according to the invention comprises a variable test resistance R.sub.var which is switched between one of outer conductors L1, L2—outer conductor L1 presently. In the following, the designation R.sub.var is used both for the electric resistance as a physical object (test resistance) and for the (continuous) physical factor (test-resistance value) assigned to this test resistance.

[0058] Measuring device 20, 21 according to the invention further comprises current measuring equipment 28 by means of which a measured test current I.sub.R settable for a pre-specified test-resistance value R.sub.var is registered via variable test resistance R.sub.var.

[0059] Ground-voltage measuring equipment 26 of measuring device 20, 21 according to the invention measures an outer-conductor-to-ground voltage U.sub.L,Pe between outer conductor L1 and ground PE, it holding true for outer conductor L1 that U.sub.L,Pe≥U.sub.0/2.

[0060] A computing unit 30 of measuring device 20, 21 according to the invention is configured for controlling the method sequence and for executing the calculations and can comprise a remote control.

[0061] Variable test resistance R.sub.var, ground-voltage measuring equipment 26, current measuring equipment 28 and computing unit 30 can be realized as a structural unit 20.

[0062] Line-voltage measuring equipment 24 serves for measuring an operational voltage U.sub.0 of alternating-current power supply system 2 between outer conductors L1, L2.

[0063] Line-voltage measuring equipment 24 can be integrated with variable test resistance R.sub.var, ground-voltage measuring equipment 26, current measuring equipment 28 and computing unit 30 to form an enhanced structural unit (21).

[0064] FIG. 3 shows an equivalent circuit for detecting leakage current I.sub.d. For this purpose, alternating-current power supply system 2 is modelled in an impedance network having overall impedances Z.sub.1, Z.sub.2 and variable test resistance R.sub.var and operating voltage U.sub.0.

[0065] Overall impedances Z.sub.1 and Z.sub.2 summarize the individual electric components between outer conductors L1, L2 and ground PE to each overall impedance Z.sub.1, Z.sub.2 according to equation (1).

[00001]$\begin{array}{cc}\left[\begin{array}{c}{Z}_1\\ Z_2\end{array}\right]=\left[\begin{array}{c}{R}_{a1}.Math.R_{f1}.Math.X_{\mathrm{Ce}1}\\ R_{a2}.Math.R_{f2}.Math.X_{\mathrm{Ce}2}\end{array}\right]& \left(1\right)\end{array}$

[0066] Overall impedance Z.sub.1 therefore results from the parallel circuit of ohmic resistance R.sub.a1 (coupling resistance of insulation monitoring device IMD) and leakage impedance Z.sub.L1 which consists of ohmic portion R.sub.f1 (insulation resistance) and reactance X.sub.Ce1 (according to leakage capacitance C.sub.e1). The same applies to overall impedance Z.sub.2 accordingly.

[0067] From Kirchhoff's second law MI, MII and Kirchhoff's first law, the equations system is yielded from the equivalent circuit diagram according to equation (2).

[00002]$\begin{array}{cc}\left[\begin{array}{cc}{Z}_1+Z_2& -Z_1\\ -Z_1& Z_1+R_{var}\end{array}\right].Math.\left[\begin{array}{c}{I}_{\mathrm{MI}}\\ I_{\mathrm{MII}}\end{array}\right]=\left[\begin{array}{c}{U}_0\\ 0\end{array}\right]& \left(2\right)\end{array}$$\mathrm{with}$$\begin{array}{cc}{I}_R=I_{\mathrm{MII}}& \left(3\right)\end{array}$

[0068] The equations system describes the analytic correlation between measured test current I.sub.R as a function of variable test-resistance value R.sub.var.

[0069] From the measurements, accordingly set, measured test currents I.sub.Ri are known for known support test-resistance values R.sub.var,i.

[0070] Hence, an equivalent circuit diagram model of the measuring order is available—parameters R.sub.a1, R.sub.a2, R.sub.f1, R.sub.f2, X.sub.Ce1, X.sub.Ce2, however, are unknown at first (gray box model). For this reason, assumptions are made for ohmic portions R.sub.a1, R.sub.a2, R.sub.f1, R.sub.f2. Insulation resistances R.sub.f1 and R.sub.f2 are assumed to be infinite because of the prerequisite of an intact insulation. Coupling resistances R.sub.a1, R.sub.a2 of insulation monitoring device IMD can be set to common values in practice or be implemented as precise values when known. Consequently, leakage capacitances C.sub.e1 and C.sub.e2 as unknown variables are significantly relevant parameters for measured test current I.sub.R.

[0071] By means of a numerical approximation method, leakage capacitances C.sub.e1 and C.sub.e2 are determined such that the deviation of a calculated approximated test current I.sub.R,fit, I.sub.Ri,fit from measured test current I.sub.Ri is minimized to support test-resistance values R.sub.var,i (support locations) in support points I.sub.Ri (R.sub.var,i).

[0072] This becomes possible by applying the method least-squares function approximation according to equation (4).

[00003]$\begin{array}{cc}{.Math.}_{i=1}^n{\left(\frac{I_{Ri}\left(R_{v\mathrm{ar},i}\right)-I_{\mathrm{Ri},\mathrm{fit}}\left(R_{\mathrm{var},i},C_{e1},C_{e2}\right)}{I_{\mathrm{Ri},\mathrm{fit}}\left(R_{\mathrm{var},i},C_{e1},C_{e2}\right)}\right)}^2.fwdarw.\min & \left(4\right)\end{array}$

[0073] Using thus detected leakage capacitances C.sub.e1, C.sub.e2, leakage current I.sub.d can now be determined using equations (2), (3) and I.sub.R=I.sub.d as calculated test current I.sub.R0,fit, and the zero setting of test-resistance value R.sub.var can be determined.