SCIENCE REVIEW. – 2012. -№2 (10). – P.17-21
DETERMINING CAPACITIVE SUSCEPTANCE OF NETWORK WITH
INSULATED NEUTRAL OF UNDER 1000 V VOLTAGE
Utegulov В.B.,Utegulov A.B.,
Uakhitova A.B.
________________________________________________________________
Abstract
The present work develops the method of determining capacitive
susceptance of an electrical network with insulated neutral of under 1000 V
voltage for delfts, based on the measurement of values of phase-to-ground
voltage, line-to-line voltage and the measurement of the phase shift angle between
the vectors of line-to-line voltage and phase-to-ground voltage, as well as
consideration of the length of air-cable lines and coefficients that characterize the
capacitive susceptance of the line.
Keywords: state of insulation, capacitive susceptance, insulated neutral,
reliability, security, electrical network.
1. Introduction
Delfts pay great attention to the state of electrical installation insulation
during their exploitation, because the state of insulation is a most important aspect
that characterizes the electrical safety of delfts.
Deterioration of the state of insulation may be caused by hard usage of
electrical installations: the unfavorable effect of the environment (in underground
operations – aggressive and dangerously explosive), the uneven regime of using
machines and mechanisms, presence of current-conducting dust and so on, which,
in its turn, leads to the aggravation of the level of electrical safety, as well as the
reduction of electrical supply systems reliability [1].
As a result of this, to raise the electrical safety of delfts, it is necessary to
pay still greater attention to the study of the state of insulation at the exploiting
electrical installations.
2. Capacitive susceptance characteristics
When considering the parameters of insulation, it is necessary to analyze
the overall, active, capacitance and ohmic resistance of the insulation. The value
of the overall resistance of insulation Z ins characterizes the value of total leakage
current, the value of the active R ins and ohmic R ohm resistances of insulation are
used in constructing protection devices against the leakage current, and the value
of the capacitance resistance X ins is necessary for the solution of the problem of
compensating the electrical networks in relation to the ground [2].
To the parameters, characterizing the electrical safety of electrical
networks also belong the admittance, conductance, and capacitive susceptance of
insulation. The conductance is in direct dependence on the insulation properties of
the materials, of which it is composed, and the capacitive susceptance
corresponds to the quantitative indices of the connected electrical installations
and the length of air-cable lines.
The electrical installations exploitation practice at delfts shows that as
different from open-cast mine electrical networks, in underground electrical
networks the value of insulation conductance is determined mainly by the
capacitive susceptance constituent [2]:
y  b.
(1)
In this case the value of the current in single-phase ground short circuit is
described by the capacitive susceptance, because the conductance constituent is
very small:
I 0  I 0C  U ph b .
(2)
3. Method of determining capacitive susceptance
To determine the capacitive susceptance in a three-phase electrical network
with insulated neutral under a damage of one of the phases of the network they use
the value of the current of single-phase ground short circuit, which is expressed
through the mathematical dependence [3]:
I0 
U l U ph0
U0
g0 ,
(3)
where U l is the line voltage, V; U ph 0 is the phase-to-ground voltage under
the phase-to-ground connection of additional conductance, V; U 0 is the zero
string voltage, V; g 0 is the additional conductance.
The value of single phase ground short circuit current, which takes into
consideration the extent of air-cable lines, is established through the expression
[2]:
L
L 
I 0  U l  A  C  ,
 KA KC 
(4)
where L A , L C are extent of the air and cable lines, km; K A , K C are
coefficients for the air and cable line, kOhmkm.
Handling the equations (3) and (4) together, let’s establish the value of the
additional conductance:
g0 
U 0 L A K C  L C K A 
.
K C K A U ph0
(5)
The value of the voltage in a zero string is expressed through the
mathematical dependence:
U0 
1,73U ph0 (U l2 + 3U 2ph0 - 3,46U l U ph0Sin α)
U l (U l - 1,73U ph0Sin α)
,
(6)
where α is the phase-shift angle between the vectors of line voltage and
phase-to-ground voltage.
The value of capacitive susceptance of the network insulation is established
on the basis of the expression [3]:
b
Ul
g 0 Cosα .
U0
(7)
Solving the equations (5), (6) and (7) together, we find the value of
capacitive susceptance of the network:
b
U l (L A K C  L C K A )Cos
.
K A K C U ph0
(8)
When inserting expression (8) in the equation (2), the value of the current
of single-phase ground short circuit will have the following form:
U l2 (L A K C  L C K A )Cos
I0 
.
1,73K A K C U ph0
(9)
The expression (8) is a random relative root-mean-square error of
determining the network insulation capacitive susceptance, where the values U l ,
U ph0 , Cosα have been obtained by direct measurement.
The relative root-mean-square error of the method in the determination of
capacitive susceptance of the electrical network phase-to-ground insulation is
found through the expression [4]:
1 b 2
b 2
b 2
2
2
b  
U l 
U ph 0 
Cos 2  ,
2
2
2
b U l
U ph 0
Cos 
(10)
b
b
b
,
,
are partial derivative functions of
U l U ph 0 Cos
b  f U l , U ph 0 , Cos .
where


Here U l , U ph 0 , Cos are absolute errors of direct measurement of
the values U l , U ph0 , Cosα , which are established through the following
expressions:
U l  U l U l ;
U ph 0  U ph 0 U ph 0 ;
(11)
Cos  CosCos  .
To establish the errors of measuring instruments, let’s assume that:
U l  U ph 0  U  ,
where U  is the relative error of the metering circuits of voltage;
Cos  is the relative error of the instrument for measuring the phase-shift
between the vector of phase-to-ground voltage and the vector of the line voltage
[4].
We determine the partial derivative functions b  f U l , U ph 0 , Cos by the


variables U l , U ph0 , Cosα :
L K  L C K A Cosα
b
 A C
;
U l
K A K C U ph0
 U l L A K C  L C K A Cos
b

;
U ph 0
K A K C U 2ph 0
(12)
U L K  L C K A 
b
 l A C
.
Cos
K A K C U ph 0
We solve the equation (10), substituting in it the values of partial of
equation (12) and the values of partial absolute errors (11), assuming here that
U   Cos     , then we obtain [5]:
b 
3 U l CosL A K C  L C K A 

.

b
K A K C U ph 0
(13)
To establish the root-mean-square relative error of capacitive susceptance
of the network insulation, we divide equation (13) by equation (8), and after the
transformation we obtain:
b 
b 
 3.

(14)
The value of relative root-mean-square error of establishing b does not
exceed 1,73 %, under the use of a measuring instrument of 0,1 precision.
The developed method of determining capacitive susceptance of insulation
in electrical networks with insulated neutral of under 1000 V voltage is based on
the measurement of phase-to-ground voltage modules values, the line voltage,
and the measurement of the phase-shift angle between the vectors of the line
voltage and the phase-to-ground voltage, as well as considers the extent of
air-cable lines and coefficients, characterizing the line capacitive susceptance.
4. Conclusion
On the basis of the above-stated, it follows that the developed method
makes it possible to determine the capacitive susceptance in an electrical network
with insulated neutral under the damage of one of net phases in relation to the
ground with adequate accuracy and ease. The developed method provides for the
reliability of the determination of capacitive susceptance, on the basis of which
the technical-organizational measures are proposed, to raise the reliability of the
internal electrical power supply system of delft, as well as to ensure the rise of
electrical safety under the exploitation of electrical installations of the voltage of
under 1000 V.
References
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