Method for measuring insulation resistance of electric line

A method for measuring an insulation resistance of an electric line. A low frequency signal, which has the same frequency as a signal applied to the electric line and is in phase with the line applied signal or shifted by 90 degrees therefrom, is applied with the amplitude value being varied with a period T. A leakage current sent to synchronous detector is adjusted with respect to its phase or a reference signal is adjusted with respect to its phase to minimize (make zero) or maximize one of induced effective components or induced ineffective or reactive components of the leakage current having a frequency of 1/T.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method of compensating for a measurement 
error in an apparatus which measures the insulation resistance of an 
electric power transmission line, a grounding line for lightning 
protection or the like. 
2. Description of the Related Art 
There has been so far known in electric power transmission facilities such 
a measurement apparatus which monitors the insulation resistance between 
an electric line and the ground and detects the insulation deterioration 
of the line as fast as possible, thus preventing beforehand any trouble 
from occurring for the stable transmission of electric power. An example 
of such a measurement apparatus is given by an electric circuit in FIG. 1, 
which measures an insulation resistance R.sub.0 between an electric line 
and the ground in the event where the electric power of a voltage stepped 
down by a transformer T is supplied or transmitted through electric lines 
1 and 2 on of which is connected to the earth E through a grounding 
conductor L.sub.E. 
More specifically, the aforementioned circuit of FIG. 1 is arranged so that 
a transformer OT, which is connected to a low frequency signal oscillator 
OSC generating a measuring signal of a low frequency different from a 
commercial power source frequency, is inserted in the grounding line 
L.sub.E of the power receiving transformer T to apply a measuring low 
frequency voltage to the electric lines 1 and 2; a current transformer ZCT 
having the grounding line L.sub.E passed therethrough detects a leakage 
current of the aforementioned measuring low frequency signal that is fed 
back to the grounding conductor through the insulation resistance R.sub.0 
and an earth stray capacity C.sub.0 existing between the electric lines 
and the earth; an amplifier AMP connected to the current transformer ZCT 
amplifies the detected leakage current; a filter FIL connected to the 
amplifier AMP extracts only a frequency f.sub.1 component from the 
amplified signal; and a multiplier MULT synchronously detects the 
extracted component with use of, for example, an output signal of the 
oscillator OSC to detect an effective component (OUT.sub.1) (that is, a 
component in phase with the applied low-frequency voltage) of the leakage 
current and to thereby measure the insulation resistance of the electric 
lines. 
Explanation will next be made as to the measuring theory. 
Assuming now that the measuring signal voltage applied to the grounding 
line L.sub.E is of a sine wave V sin .omega..sub.1 t (.omega..sub.1 
=2.pi.f.sub.1), then a leakage current I of a frequency f.sub.1 fed back 
to the grounding line L.sub.E through an earth point E is expressed by the 
following equation. 
EQU I=(V/R.sub.0).multidot.sin .omega..sub.1 t+.omega..sub.1 C.sub.0 V cos 
.omega..sub.1 t (1) 
The leakage current I extracted by the current transformer ZCT and passed 
through the amplifier AMP and the filter FIL is synchronously detected by 
the multiplier MULT with the signal of the oscillator OSC in phase with 
the low-frequency signal applied to the electric lines to extract its 
effective component, i.e., the first term in the right side of the above 
equation (1). The effective component, which is inversely proportional to 
the insulation resistance R.sub.0, can be used to find the insulation 
resistance of the electric lines. With such a prior art method of 
detecting at the zero-phase current transformer ZCT the leakage current 
fed back to the grounding line and extracting and outputting at the filter 
FIL the component having a frequency of f.sub.1 from the leakage current, 
however, when the leakage current component of the frequency f.sub.1 is 
shifted in phase through passage of a system comprising the zero-phase 
current transformer ZCT, the amplifier AMP and the filter FIL, it becomes 
impossible to calculate the value of the insulation resistance accurately. 
To avoid this, it has been conventional to use a phase shifter which 
adjusts with respect to phase one or both of the signal sent to the 
multiplier MULT, i.e., the signal sent from the low frequency oscillator 
OSC and the leakage current passed through the extracting filter FIL from 
the current transformer ZCT to thereby set or correct a phase difference 
between the both signals to be zero. 
However, the prior art method has been defective in that the phase 
characteristics of the current transformer ZCT, filter FIL, phase shifter 
and so on vary with temperature variations, the deterioration of 
characteristics of used parts with age and so on, which results in that a 
phase error from the initial adjustment value takes place, thus making it 
impossible to provide a correct measurement result. To cope with the 
defect, there has been so far employed such a high quality of zero-phase 
current transformer, filter and the like that are very small in their 
characteristic variations to thereby minimize the influence due to the 
phase error. Even so, it has been impossible to completely eliminate the 
influence. 
More in detail, if the leakage current component I of the frequency f.sub.1 
shown in the equation (1) is assumed to have a phase shift .theta. when 
passed through the system of the zero-phase current transformer ZCT, 
amplifier AMP and filter FIL, then the filter FIL produces such an output 
I.sub.1 as follows. 
EQU I.sub.1 =(V/R.sub.0) sin (.omega..sub.1 t+.theta.)+.omega..sub.1 C.sub.0 V 
cos (.omega..sub.1 t+.theta.) (2) 
And the output I.sub.1 is applied to a first input terminal of the 
multiplier MULT. 
Assuming a voltage applied to a second input terminal of the synchronous 
detector is, for example, a.sub.0 sin (.omega..sub.1 t+.theta..sub.1) of a 
constant amplitude, then an output or an effective component D of the 
synchronous detector is expressed as follows. 
##EQU1## 
where -- means to eliminate components of D above angular frequency 
.omega..sub.1. 
Hence, an output D.sub.0 when .theta.=.theta..sub.1 is given as follows. 
EQU D.sub.0 =Va.sub.0 /2R.sub.0 ( 5) 
Since V and a.sub.0 are constant, the output D.sub.0 can be measured as a 
value inversely proportional to the insulation resistance R.sub.0. 
Accordingly, an error E for the effective component D with respect to the 
output D.sub.0 when the phase shift (.theta.-.theta..sub.1) is not zero 
becomes: 
##EQU2## 
For example, when .theta.-.theta..sub.1 =1 degree, R.sub.0 =20 K.OMEGA. 
and C.sub.0 =5 .mu.F, f.sub.1 =25 Hz and .omega..sub.1 C.sub.0 R.sub.0 
.apprxeq.15.7. This yields 27.4% of an error .epsilon. with a remarkably 
large measurement error. 
It is an object of the present invention to provide a phase correcting 
method in an insulation resistance measuring apparatus, which eliminates 
the above defects in the prior art insulation resistance measuring method, 
and which can automatically correct a phase shift in a measurement signal 
inexpensively without the need for any expensive parts and can produce 
always a correct measurement result. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, the above object is attained by 
providing the following arrangement. That is, the present invention is 
arranged so that a low frequency signal, which has the same frequency as a 
signal applied to electric lines and is in phase with the line applied 
signal or shifted by 90 degrees therefrom, is applied with the amplitude 
value being varied with a period T, and so that a leakage current sent to 
synchronous detecting means is adjusted with respect to its phase or a 
reference signal is adjusted with respect to its phase to minimize (make 
zero) or maximize one of induced effective components or induced 
ineffective or reactive components of the leakage current having a 
frequency of 1/T.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to FIG. 2, there is shown a circuit diagram of a first embodiment 
of the insulation resistance measuring apparatus in accordance with the 
present invention. In the drawing, reference symbol T denotes a voltage 
transformer and reference numerals 1 and 2 denote lower voltage electric 
lines. Connected to one electric line 2 is a grounding conductor L.sub.E 
to satisfy the Japanese Second Kind Grounding Work Regulations, which 
conductor in turn is connected with a low-impedance transformer OT and a 
current transformer ZCT. The transformer OT is further coupled to a low 
frequency oscillator OSC. After a low frequency signal of a frequency 
f.sub.1 is applied to the electric lines 1 and 2, a signal fed back to the 
grounding conductor L.sub.E is extracted through the current transformer 
ZCT, amplified at an amplifier AMP and then passed through a filter FIL 
where only the low frequency signal is extracted from the fed back signal. 
The extracted low frequency signal is then sent to a multiplier MULT as a 
synchronous detector to be synchronously detected with a signal sent from 
the low frequency oscillator OSC. The multiplier MULT and the other 
multipliers described hereafter are used as synchronous detectors for 
synchronous detection. As a result, the multiplier MULT produces at its 
output terminal OUT.sub.1 such an output voltage that is inversely 
proportional to the insulation resistance existing between the electric 
lines and the earth, as mentioned earlier. In the present embodiment, 
however, for the purpose of correcting a phase shift due to the zero-phase 
current transformer ZCT, amplifier AMP and filter FIL, a series circuit of 
a capacitor C and a switch SW is provided in parallel to the grounding 
conductor L.sub.E, the switch SW is opened and closed at a period of T, 
and a part of an output of the multiplier MULT is applied through a 
band-pass filter BP for extraction of a frequency 1/T and a rectifying 
circuit DET to a phase shifter (controller) PC wired between the 
oscillator OSC and the multiplier MULT. 
Explanation will next be directed to the operation of the above arrangement 
and how to control the same. 
When the switch SW is now turned ON (closed), a current .omega..sub.1 CV 
cos .omega..sub.1 t (shifted by a phase of 90 degrees) flowing through the 
capacitor C is added to the grounding conductor L.sub.E and thus a total 
leakage current I.sub.0 flowing through the grounding conductor L.sub.E is 
as follows. 
EQU I.sub.0 =(V/R.sub.0) sin .omega..sub.1 t+.omega..sub.1 C.sub.0 V cos 
.omega..sub.1 t+.omega..sub.1 CV cos .omega..sub.1 t (7) 
Accordingly, an output I.sub.2 of the filter FIL becomes as follows, from 
the equation (2). 
EQU I.sub.2 =(V/R.sub.0 sin (.omega..sub.1 t+.theta.)+(C.sub.0 +C).omega..sub.1 
V cos (.omega..sub.1 t+.theta.) (8) 
The then output D of the multiplier MULT is as follows, from the equation 
(4) 
EQU D=(Va.sub.0 /2R.sub.0) cos (.theta.-.theta..sub.1)-{(C.sub.0 
+C).omega..sub.1 Va.sub.0 }/2.multidot.{sin (.theta.-.theta..sub.1)}(9) 
When the switch SW is turned ON and OFF at a period of T (in this 
embodiment, T&gt;&gt;2.pi./.omega..sub.1), the value of the capacitor C included 
in the second term of the equation (9) varies also with the period T and 
thus the output D of the multiplier contains a component of a frequency 
1/T. When the synchronous detector output OUT.sub.1 is applied to the 
filter BP for extraction of only the frequency 1/T component, the filter 
produces such an output A as follows. 
EQU A=-kC.omega..sub.1 Va.sub.0 sin (2.pi.t/T+.phi.) sin 
(.theta.-.theta..sub.1) (10) 
where k is a constant and .phi. is a phase determined by the filter 
characteristics and so on. Hence, when the output of the filter BP is 
rectified at, for example, the rectifying circuit DET, an output B of the 
rectifier DET is: 
EQU B=KC.omega..sub.1 Va.sub.0 .vertline.sin 
(.theta.-.theta..sub.1).vertline.(11) 
When there is not present any phase shift in the measurement system (when 
.theta.=.theta..sub.1), the second term in the equation (9) becomes zero 
and thus it will be seen that the component of the frequency 1/T becomes 
zero. 
Therefore, if the phase .theta..sub.1 of the voltage a.sub.0 sin 
(.omega..sub.1 t+.theta..sub.1) of a constant amplitude applied to the 
second input terminal of the multiplier MULT is adjusted so that the 
output of the rectifying circuit DET becomes zero, i.e., 
.theta.-.theta..sub.1 becomes zero, the phase shift can be made to 
approach to zero. 
The present invention is basd on such principle, that is, the switch SW is 
repetitively turned ON and OFF at intervals of the predetermined period T 
and the phase .theta..sub.1 is automatically adjusted so that the 
component of the frequency 1/T becomes always zero, and the output 
OUT.sub.1 of the multiplier MULT at this time is used to measure the 
insulation resistance always without any phase error, i.e., accurately. In 
this connection, the necessary automatic phase control circuit can be 
easily realized using existing techniques by those skilled in the art and 
thus explanation thereof is omitted. 
A means for causing a current (which is sometimes referred to merely a 
phase-shifted ON/OFF current) shifted by a phase of 90 degrees and turned 
ON and OFF at intervals of T to flow through the grounding conductor 
L.sub.E is not limited to the above particular example and may be varied 
in various manners. For example, the means can be modified as shown in 
FIGS. 3(a), 3(b) and 3(c). 
More specifically, a secondary winding is added to the application 
transformer OT to obtain such a phase-shifted ON/OFF current in FIG. 3(a), 
the phase-shifted ON/OFF current is obtained from the output terminals of 
the primary winding of the same transformer in FIG. 3(b), and the same 
ON/OFF current is obtained directly from the low frequency oscillator OSC 
in FIG. 3(c), respectively. 
These means may be applied commonly to second and third embodiments of the 
present invention which will be detailed later. 
For the purpose of the automatic adjustment of the phase shifter PC, if the 
output A of the filter BP is further synchronously detected by another 
synchronous detector (not shown) with a signal used to turn ON and OFF the 
capacitor C for example, then an output S.sub.0 of the synchronous 
detector is expressed by the following equation. 
EQU S.sub.0 =-k.sub.0 C.omega..sub.1 Va.sub.0 cos .phi..multidot.sin 
(.theta.-.theta..sub.1) (12) 
(where k.sub.0 is a constant.) 
Accordingly, in the case where .vertline..phi..vertline.&lt;.pi./2 and 
.vertline..theta.-.theta..sub.1 .vertline.&lt;.pi./2, if 
.theta.&gt;.theta..sub.1 then S.sub.0 &lt;0, if .theta.&lt;.theta..sub.1 then 
S.sub.0 &gt;0, and if .theta.=.theta..sub.1 then S.sub.0 =0. Thus it will be 
appreciated that the discrimination of the phase adjustment direction 
(phase advance or retard direction) can be achieved with use of S.sub.0 
and the automatic phase control can be realized by utilizing the 
discrimination result. 
The present invention may be modified further as shown in FIG. 4. That is, 
FIG. 4 is a block diagram showing a second embodiment of the present 
invention. The second embodiment is featured in that a current in phase 
with the leakage current is added to the grounding conductor, reactive 
components are extracted from the leakage current and one of the reactive 
components having a frequency of 1/T is controlled to be minimized (zero); 
through, in the foregoing embodiment, effective components of the leakage 
have been synchronously detected, and the phase of the signal applied to 
the synchronous detecting means (synchronous detector) has been adjusted 
so that one of the effective components having a frequency of 1/T becomes 
minimized (zero). 
More specifically, in FIG. 4, a resistor R is used in place of the 
capacitor C shown in FIG. 2; the output of the filter FIL, whose input is 
sent from the output of the zero-phase current transformer via an 
amplifier AMP, is partly applied, in addition to a first multiplier 
MULT.sub.1, to a series circuit of a second multiplier MULT.sub.2, a 
bandpass filter BP and a rectifying circuit DET; and an output of the 
rectifying circuit DET is used to control a phase control circuit PC. 
Further, the first and second multipliers MULT.sub.1 and MULT.sub.2 receive 
at the other input terminals directly an output of the phase control 
circuit PC and the same PC output through a 90.degree. phase shifter PSS, 
respectively. In addition, a subtractor SUB eliminates another output of 
the phase control circuit PC from the output of the first multiplier 
MULT.sub.1. 
Such an apparatus arranged as mentioned above will be detailed as to the 
operation of the apparatus and the functions of the respective component 
elements therein by using mathematical equations. 
That is, when the switch SW inserted between the earthing point of the 
electric line 2 and the grounding point E is turned ON, a current 
(V/R).multidot.sin .omega..sub.1 t is added to the aforementioned low 
frequency signal so that the total currents flow through the grounding 
conductor L.sub.E. Thus, a leakage current I.sub.0 of application low 
frequency components flowing through the grounding conductor L.sub.E is 
expressed as follows. 
EQU I.sub.0 (1/R.sub.0 +1/R)V sin .omega..sub.1 t+.omega..sub.1 C.sub.0 V cos 
.omega..sub.1 t (13) 
Hence, the filter FIL produces, from the equation (2), an output I.sub.2 
which follows. 
EQU I.sub.2 =(1/R.sub.0 +1/R)V sin (.omega..sub.1 t+.theta.)+.omega..sub.1 
C.sub.0 V cos (.omega..sub.t t+.theta.) (14) 
Assuming a voltage a.sub.0 sin (.omega..sub.1 t+.theta..sub.1) is applied 
to the second input terminal of the first multiplier MULT.sub.1, then the 
application of the same voltage to the 90.degree. phase shifter PSS causes 
the shifter PSS to output a voltage a.sub.0 cos (.omega..sub.1 
t+.theta..sub.1). When the output voltage of the shifter PSS is applied to 
the second multiplier MULT.sub.2, the multiplier MULT.sub.2 produces an 
output D.sub.1. 
##EQU3## 
(-- has the same meaning as in the equation (3).) 
When the switch SW is turned ON and OFF at intervals of a period T 
(T&gt;&gt;2.pi./.omega..sub.1). the value of R in the first term of the equation 
(15) varies with the period T and thus the second amplifier MULT.sub.2 
produces the output D.sub.1 containing a component of the frequency 1/T. 
When the output D.sub.1 is applied to the filter BP which functions to 
extract only the component of the frequency 1/T, the filter BP produces 
such an output A as given below. 
EQU A=(kVa.sub.0 /R) sin (2.pi.t/T+.phi.).multidot.sin (.theta.-.theta..sub.1) 
(16) 
where k represents a constant and .phi. represents the phase determined by 
the phase characteristics of the filter BP and so on. Accordingly, when 
the output A of the filter BP is applied to the rectifying circuit DET to 
be rectified, the circuit DET produces such an output B as expressed by 
the following equation. 
EQU B=(kVa.sub.0 /R).multidot..vertline.sin 
(.theta.-.theta..sub.1).vertline.(17) 
Hence, if the phase .theta..sub.1 in the voltage a.sub.0 sin (.omega..sub.1 
t+.theta..sub.1) applied to the second input terminal of the multiplier 
MULT.sub.1 is adjusted by the phase control circuit PC so that the output 
B of the rectifying circuit DET becomes zero, then (.theta.-.theta..sub.1) 
becomes zero and therefore a phase shift can be made to approach to zero. 
Since (.theta.-.theta..sub.1) becomes zero under the correction or 
compensation of the phase shift in accordance with the above method, the 
output D of the first multiplier MULT.sub.1, as seen from the equation 
(4), is expressed as follows during turning ON of the switch means SW. 
EQU D=(Va.sub.0 /2).multidot.(1/R.sub.0 +1/R) 
During turning OFF of the switch SW, the output D becomes: 
EQU D=(Va.sub.0 /2).multidot.(1/R.sub.0) 
Thus, when the subtraction circuit SUB subtracts only (Va.sub.0 
/2).multidot.(1/R) (constant value) from the output D of the first 
multiplier MULT.sub.1 during turning ON of the switch SW, the subtraction 
circuit SUB can produces an output OUT.sub.2 of (Va.sub.0 
/2).multidot.(1/R.sub.0) and thus the insulation resistance of the 
electric lines can be measured correctly. 
For example, when the output A of the filter BP is further subjected to a 
synchronous detection by another multiplier (not shown) with a signal 
turning ON and OFF the switch means SW, this multiplier produces such an 
outptut S.sub.0 as follows. 
EQU S.sub.0 =(k.sub.0 Va.sub.0 /R) cos .phi..multidot.sin 
(.theta.-.theta..sub.1) (18) 
(where, k.sub.0 is a constant.) 
Accordingly, in the case where .vertline..phi..vertline.&lt;(.pi./2) and 
.vertline..theta.-.theta..sub.1 .vertline.&lt;(.pi./2), if 
.theta.&gt;.theta..sub.1 then S.sub.0 &gt;0, if .theta.&lt;.theta..sub.1 then 
S.sub.0 &lt;0 and if .theta.=.theta..sub.1 then S.sub.0 =0. In this way, the 
discrimination of the phase adjustment direction (phase advance or retard 
direction) can be achieved on the basis of S.sub.0 and thus automatic 
phase control can be effectively achieved on the basis of the 
discrimination ressult. 
It goes without saying that even the present embodiment may be subjected to 
such modifications as shown in FIGS. 3(a), 3(b) and 3(c). 
Although the mere resistor R has been turned ON and OFF at the period T in 
the foregoing embodiment, a variable resistor may be used to be varied in 
value continously (for example, sinusoidally) with the period T or a 
combination circuit of a coil and a capacitor may be used in carrying out 
the above phase control method. 
The present can also be modified as shown in FIG. 5. That is, FIG. 5 shows 
a third embodiment of the present invention, which corresponds to a 
combination of the first and second embodiments. More specifically, the 
circuit of FIG. 5 is different from that of FIG. 4 in that a capacitor C 
is provided as a reactance element inserted between the electric line 2 
and the earth E in series with the switch SW as in FIG. 2, the subtractor 
SUB of FIG. 4 is removed, and phase control is made so that one of 
reactive components (synchronously detected with the use of a signal 
obtained by shifting the leakage signal by a phase of 90 degrees) of the 
second multiplier MULT.sub.2 becomes maximum. Even in this circuit, when 
the switch SW is turned ON, the first synchronous detection output becomes 
as shown by the equation (9), whereas when the switch SW is turned ON and 
OFF at the period T (even in the present embodiment, 
T&gt;&gt;2.pi./.omega..sub.1), the value of the capacitor C contained in the 
second term of the equation (9) varies similarly with the period T (that 
is, becomes C or zero) and the output D.sub.1 of the first multiplier 
MULT.sub.1 contains a component having a frequency of 1/T, as in FIG. 2. 
In the present embodiment, a part of the leakage current is subjected at 
the second multiplier MULT.sub.2 to a synchronous detection with the use 
of a signal a.sub.0 cos (.omega..sub.1 t+.theta..sub.1) corresponding to 
the low frequency signal a.sub.0 sin (.omega..sub.1 t+.theta..sub.1) 
subjected by the 90.degree. phase shifter PSS to a 90.degree. phase shift, 
so that the second multiplier MULT.sub.2 can produce as its output a 
reactive component signal D' of the leakage signal. 
The component of the frequency 1/T in the reactive component signal D' is 
obtained as the output A of the filter BP, which is expressed by the 
following equation. 
EQU A=kC.omega..sub.1 Va.sub.0 sin (2.pi.t/T+.theta.) cos 
(.theta.-.theta..sub.1) (19) 
where k is a constant and .phi. is the phase determined by the phase 
characteristics of the filter BP and so on. Therefore, the rectifying 
circuit DET, when receiving the output A of the filter BP, produces such 
an output B as given below. 
EQU B=kC.omega..sub.1 Va.sub.0 .vertline.cos 
(.theta.-.theta..sub.1).vertline.(20) 
Hence, when the phase .theta..sub.1 in the voltage a.sub.0 sin 
(.omega..sub.1 t+.theta..sub.1) applied to the second input terminal of 
the first multiplier MULT.sub.1 so that the output B of the rectifying 
circuit becomes maximum, (.theta.-.theta..sub.1) becomes zero and thus the 
phase shift can be made to approach to zero. 
If the filter BP is subjected to a further synchronous detection by another 
multiplier (not shown) with the signal turning ON and OFF of the switch, 
the output S.sub.0 of this synchronous detector is: 
EQU S.sub.0 =k.sub.0 C.omega..sub.1 Va.sub.0 cos .phi..multidot.cos 
(.theta.-.theta..sub.1) (21) 
where k.sub.0 is a constant. 
Thus it will be appreciated also from the equation (12) that the output 
S.sub.0 becomes maximum when (.theta.-.theta..sub.1) is zero and thus the 
phase .theta..sub.1 may also be controlled so that the output S.sub.0 
becomes maximum. 
Further, the present invention can be modified as shown in FIG. 6. That is, 
FIG. 6 shows a fourth embodiment, in a block diagram form, of the present 
invention. The present embodiment is featured in that, as shown in FIG. 6, 
currents act on the leakage current inducing means as alternately 
phase-shifted by .+-.90 degrees with a period of T/2 by means of, for 
example, a capacitor C and two switches SW.sub.1 and SW.sub.2. The aim of 
the present embodiment is to increase the detection sensitivity by passing 
the alternately 90.degree. phase-shifted currents through the leak current 
inducing means and thus making large the amplitude of the output of the 
band pass filter BP and also to relax the severe low-frequency (DC) pass 
characteristics demanded for the band pass filter BP when the period T is 
large (that is, when the frequency 1/T is as low as about 1 Hz). 
FIG. 6 is different from the other foregoing embodiments in that a 
reactance circuit additionally inserted betwen the electric line 2 and the 
earth E comprises the capacitor C and the two switches SW.sub.1 and 
SW.sub.2 and these switches are turned ON and OFF at a period of T/2 so 
that the above alternate currents flow through the capacitor C in mutually 
opposite directions (the alternate currents are shifted by a phase of 
.+-.90 degrees with respect to the low frequency signal applied to the 
electric line). 
With the circuit of FIG. 6, when switches SW.sub.1 and SW.sub.2 are wired 
as shown by solid lines, the low frequency signal flowing through the 
grounding conductor L.sub.E is expressed by the equation (7), since the 
current flowing through the capacitor C and the current flowing through 
the grounding conductor are the same in their flowing direction. Hence, 
the the output I.sub.2 of the filter BP is given by the earlier-mentioned 
equation (8), while the output D of the multiplier MULT is by the equation 
(9). 
On the other hand, when the switches SW.sub.1 and SW.sub.2 are switched as 
shown by dotted lines in FIG. 6 and the above capacitor current and the 
grounding line current are opposite in their flowing directions, the 
current -.omega..sub.1 CV cos .omega..sub.1 t is added to the grounding 
conductor L.sub.E in the opposite direction to the above, so that the then 
output I.sub.3 of the filter FIL and the then output D of the multiplier 
MULT are given as follows, respectively. 
EQU I.sub.3 =(V/R.sub.0) sin (.omega..sub.1 t+.theta.)+(C.sub.0 
-C).omega..sub.1 V cos (.omega..sub.1 t+.theta.) (22) 
EQU D.sub.2 =(Va.sub.0 /2R.sub.0) cos (.theta.-.theta..sub.1)-{(C.sub.0 
-C).omega..sub.1 Va.sub.0 }/2.times.sin (.theta.-.theta..sub.1) (23) 
Therefore, when the switches SW.sub.1 and SW.sub.2 operatively connected 
with each other are changed over at intervals of a time T/2 to satisfy the 
above-mentioned relationship, the synchronous detector produces such an 
output that contains a component having a frequency 1/T. (As seen from the 
equation (9), the second term becomes zero when .theta.=.theta..sub.1 and 
thus the frequency 1/T component will not be generated.) When the output D 
of the multiplier is applied to the filter BP acting to extract only the 
frequency 1/T component, the filter BP produces the output A expressed by 
the equation (10). When the output A of the filter BP is further applied 
to the rectifying circuit DET, the rectifier produces the rectified output 
B expressed by the equation (11). Thus, when the switches SW.sub.1 and 
SW.sub.2 are controlled so that the value B becomes zero as in the first 
embodiment, the phase shift can be made zero. 
Even in the present embodiment, the method of obtaining the current flowing 
through the capacitor may be arranged so that the current is obtained from 
the secondary winding of the transformer OT as shown in FIGS. 7(a) and 
7(b) or from the primary winding of the same transformer as that in FIG. 
6, like the first embodiment of the present invention. 
For example, when the output A of the filter BP is subjected at another 
multiplier (not shown) to a further synchronous detection with the use of 
a signal acting to turning ON and OFF the capacitor C, this multiplier 
produces such an output S.sub.0 as given below. 
EQU S.sub.0 =-k.sub.0 C.omega..sub.1 Va.sub.0 cos .phi..multidot.sin 
(.theta.-.theta..sub.1) (24) 
(where k.sub.0 is a constant.) 
Accordingly, in the case where .vertline..phi..vertline.&lt;(.pi./2) and 
.vertline..theta.-.theta..sub.1 .vertline.&lt;(.pi./2), if 
.theta.&gt;.theta..sub.1 then S.sub.0 &gt;0, if .theta.&lt;.theta..sub.1 then 
S.sub.0 &lt;0 and if .theta.=.theta..sub.1 then S.sub.0 =0. In this way, the 
discrimination of the phase adjustment direction (phase advance or retard 
direction) can be achieved on the basis of S.sub.0 and thus automatic 
phase control can be effectively achieved on the basis of the 
discrimination ressult. 
The amount of phase adjustment may also be varied depending on the 
magnitude of the output S.sub.0. That is, if the output S.sub.0 is large 
then the phase is varied by a large step, while if the S.sub.0 is small 
then the phase is varied by a small step, whereby the phase adjustment can 
be quickly and accurately effected. 
There may also be employed such an arrangement that the phase adjustment is 
intermittently carried out as by effecting the phase adjustment for a 
certain constant, fixing .theta..sub.1 when .theta.-.theta..sub.1 
.congruent.0 and again effecting the phase adjustment after the passage of 
a certain constant time. Such a modification may be similarly applied to 
the foregoing other embodiments. 
Although the current flowing through the fixed capacitor or the fixed 
resistor has been turned ON and OFF at a period of T by means of the 
switch(es) in all the foregoing embodiments to act on the leakage current 
extracting means, a variable capacitor and a variable resistor may be used 
in place of the switch(es) and the fixed capacitor and resitor and be 
controlled in their values depending on the period T, providing 
substantially the same function as that in the foregoing embodiments. 
Further, the variable capacitor and the variable resitor may comprise each 
such an active element as a transistor, a pin diode, a vari-cap diode or 
the like. 
The leakage current extracting means may comprise not only the current 
transformer coupled to the grounding conductor but also the current 
transformer coupled to the electric line 1 or 2. 
Furthermore, the capacitor C or the resistor R has been connected to the 
side of the grounding electric line, but it may be inserted between the 
non-grounding electric line and the earth. In this connection, since the 
capacitor C or the resistor R is applied with the voltage of a commercial 
power source, a current flowing through the capacitor or resistor becomes 
remarkably large and thus such elements must be capable of withstanding 
such a large current. 
The voltage V has been applied to the resistor or capacitor as shown in the 
equation (7), but it is clear that the voltage is not limited to the 
specific example and another voltage may be used without any trouble in 
the operation. 
When the phase, which is outputted from the phase control circuit and 
applied to the second input terminal of the phase synchronous circuit, is 
previously adjusted for in-phase control and only the phase shift due to 
the temperature and so on is compensated for through the aforementioned 
automatic phase control, the phase synchronization time can be shortened. 
Although the capacitor element has been used to provide the current having 
a phase difference of 90 degrees with respect to the measuring 
low-frequency voltage in the foregoing embodiments, it will be obvious 
that the present invention is not limited to the particular example and 
may employ another circuit network (for example, a combination circuit of 
an inductance and a capacitor). 
The phase of the reference input signal applied to the second input 
terminals of the multipliers MULT.sub.1 and MULT.sub.2 has been adjusted 
for the purpose of the phase adjustment in the foregoing embodiments, but 
it is clear that the phase of the comparison input signal or signals 
applied to each or both of the both multipliers may be adjusted with 
substantially the same effect as in the embodiments. 
Though the explanation has been made as to the single-phase, 2-wire 
electric line in the foregoing embodiments, the invention may be applied 
to a single-phase, 3-wire electric line or to a three-phase, 3-wire line. 
The low frequency signal voltage has been of a sine wave in the foregoing 
explanation, but the present invention is not restricted to the particular 
example and the fundamental wave component or harmonic component of, for 
example, a rectangular wave may be used as the low frequency signal 
voltage. 
Although the phase of the signal applied to the second input terminal of 
the multiplier has been adjusted for phase adjustment in the foregoing 
explanation, the phase of the output signal of the filter FIL applied to 
the first input terminal of the multiplier may be obviously adjusted to 
obtain the same effect. 
The resistor R has been connected and disconnected at intervals of the 
period T in the foregoing explanation, but the present invention is not 
intended to limit to the particular example and it may be randomly 
connected and disconnected with a predetermined interval T to obtain the 
same effect. 
The foregoing measuring method is not restricted to the electric line for 
electric power transmission and may be applied widely to such an electric 
line at its one end connected to the earth as an electric line for a 
lightning protector apparatus, a communication line and so on. 
For the purpose of applying to the electric line the low frequency signal 
and the same signal subjected to a variation with the period T or of 
extracting the leakage component of these signals, the electric lines 1 
and 2 may be passed through the current transformer ZCT as coupled thereto 
as shown in FIGS. 8(a) and 8(b), in addition to coupling the transformer 
to the grounding conductor as in the foregoing embodiments. 
As has been disclosed in the foregoing, in accordance with the present 
invention, the leakage current as the measurement signal. after subjected 
to a variation with the period T, acts on the means for extracting the 
measurement signal or leakage current, and the phase of the extracted 
leakage current or the phase of the sigalused to synchronously detect the 
leakage current is adjusted so that the component of the leakage current 
having a frequency of 1/T becomes minimum or maximum, thereby correcting a 
measurement error resulting from variations in the characteristics of the 
measurement circuit. As a result, automatic correction can be facilitated 
and the insulation resistance can be obtained always accurately.