Definition of complex admittance of electric isolation without disconnection of electrical equipment

Nikolay Grebchenko1, Igor Koval 2, Aleksey Sidorenko1, Mariya Smirnova1

1Donetsk National Technical University (Donetsk, Ukraine), 2PLC "PES-Energougol"(Donetsk, Ukraine) gvn@dgtu.donetsk.ua, offise@pes.dn.ua, sid@mirtes.donbass.com, mary_sm@mail.ru

Abstract-The method of uninterrupted measuring of complex admittance of the electric equipment isolation is proposed.

I. INTRODUCTION

In order to control periodically the isolation quality various ways of measuring isolation active admittance by means of meggers or indirect methods are widely applied. These ways are based on measuring the current flowing through isolation when applied voltage is constant. Reactive admittance is not defined in this case.

Various methods of control tests of isolation may also be related to the periodic control of isolation [1]:

- tests by high voltage application allowing to check a level of short-term breakdown strength of isolation;

- measurements of partial discharges intensity and value of tg δ and tests by the increased voltage, allowing to estimate long breakdown strength of isolation;

- the preventive tests allowing to estimate a condition of isolation and its suitability to long operation.

However, efficiency of the periodic control of isolation essentially decreases at increase of time interval between tests, and reduction of these time intervals is limited by possibilities to shut down the equipment and by growth of labour costs to carry out the tests. Only the continuous control of isolation parameters can provide the timely detection of isolation damages. Lately years the big attention has been given to working out the methods and equipments for automatic continuous control of isolation at operating voltage on the basis of measuring dielectric characteristics and registration of partial discharges [1]. Methods of measuring an isolation resistance and absorption factor are most widely applied to control the condition of isolation of electric machines in operation.

The isolation condition is most fully characterized by its complex admittance [2]. The known methods of definition of isolation complex admittance have disadvantages, which do not allow to apply them for the continuous control. Besides, they are not suitable for such feeders as a cable-engine and a cable-transformer. For example, the ways of definition of network phase isolation parameters relatively the ground [3] are based

on creation of temporary asymmetry which is created artificially by connection a capacity between one of the phases and the ground. To realize this it is necessary to switch-off the feeder for the period of taking the measurements. For the networks with compensation of capacity currents there are the methods expounded in [4].

II. THE PROBLEM SOLUTION

Changing of isolation complex admittance of a feeder leads to changing the parameters of its mode. Therefore to define the parameters of isolation it is necessary to solve the task of synthesis of the electric circuit parameters, when the scheme and the values of currents and voltages characterizing the mode of this circuit operation are known [5]. The isolation is represented by the corresponding shunt admittance in an equivalent circuit of electric equipment. Then the analysis of the received values of the scheme parameters is made. The decision whether it is possible to use the feeder further is made on the basis of comparison with admissible values of the shunt admittances of the feeder phases.

A. Equations of electric equipment state Elements of electric systems can be represented by an

equivalent circuit, which is shown in Fig.1. Most simply it is carried out for loading feeders.

Electric motors feeders are of the utmost interest.

Fig. 1. The equivalent circuit of a loading feeder in a network with the insulated neutral

CHY

BHY

АНY

СIY ВIY АIY CII ВII AII

CI

А

В

С

AI

BI

AU BU CU NU

AНI

ВНI

СНI

POWER QUALITY, ALTERNATIVE ENERGY AND DISTRIBUTED SYSTEMS 61

978-1-4244-2856-4/09/$25.00 ©2009 IEEE

According to the equivalent circuit of connection (Fig.1) the correlation for vectors of phase currents of a feeder AI , BI and CI in a normal mode of operation in the matrix form is as follows [5]:

( )NHHI UUYUYIII I −+=+=DD

(1)

or

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−

⋅⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⋅⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

NC

NB

NA

CH

BH

AH

C

B

A

CI

BI

AI

CH

BH

AH

CI

BI

AI

C

B

A

UUUUUU

YY

Y

UUU

YY

Y

III

III

III

(2)

where AHI , BHI , CHI - the vectors of phase currents of loading of a feeder;

AII , BII , CII - the vectors of currents flowing through insulation of phases of a feeder;

AIY , BIY , CIY - shunt complex admittances of phases isolation in relation to the ground (diagonal matrix

DIY ); AU , BU , CU - the vectors of phases voltages in relation to the ground;

AHY , BHY , CHY - longitudinal phase complex admittances of loading of a feeder (diagonal matrix

DHY );

NU - voltage of a neutral of connection in relation to the ground, which can be found by the method of two potentials,

CHBHAH

CHCBHBAHAN YYY

YUYUYUU

++⋅+⋅+⋅

=.

(3)

Longitudinal and shunt complex admittances of a

cable or an air-line feeder are taken into account in corresponding admittances of loading of the feeder.

From the correlation (2) the vectors of feeder phase currents are the following:

( ) AHNAAIAA YUUYUI −+⋅= , (4)

( ) BHNBBIBB YUUYUI −+⋅= , (5)

( ) CHNCCICC YUUYUI −+⋅= . (6)

As it seen from the received simultaneous equations (4) - (6) complex admittances of phases isolation can be defined without disconnecting equipment. For this purpose it is necessary to define vectors of phase currents AI , BI and CI , vectors of phase voltages in

relation to ground AU , BU , CU and a vector of voltage

of the feeder neutral in relation to ground NU . However, in the equations (4) - (6) both shunt complex admittances of phases isolation in relation to ground

AIY , BIY , CIY and longitudinal phase complex

admittances of loading of a feeder AHY , BHY , CHY are unknown. Thus, six unknowns are in three equations, therefore the simultaneous equations like this can not be solved. Solution of this system can be found if the parameters of load phases are known or when the symmetry of loading is assumed.

If longitudinal phase complex admittances of loading of connection AHY , BHY , CHY are known, parameters of phases isolation are defined from (4) - (6) as follows:

( )[ ]AHNAAA

AI YUUIU1Y −−= , (7)

( )[ ]BHNBBB

BI YUUIU1Y −−= , (8)

( )[ ]CHNCCC

CI YUUIU

1Y −−= . (9)

In phase admittances of loading are equal

CHBHAH YYY == the definition of admittances of isolation becomes a little simpler since measuring neutral-point displacement voltage NU becomes unnecessary. It follows from the fact that expression (3) takes the following form:

( )CBAN UUU31U ++= , (10)

i.e. neutral-point displacement voltage NU is rated using known phase voltages in relation to the ground. However it is necessary to bear in mind that in expression (10) the vectors of voltages AU , BU , CU depend not only on value of complex admittances of phase isolation of a feeder AIY , BIY , CIY , but they also depend on a mode and parameters of elements of all electrically connected network.

62 2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP

B. Symmetrical load If complex longitudinal phase admittances of loading

are equal to each other CHBHAH YYY == then expression (4) - (6) can be transformed taking into account this fact. For this purpose from expression (4) we find longitudinal admittance of a phase A as:

NA

AIAAAH UU

YUIY−

⋅−= .

As it is accepted that BHAH YY = , we substitute

received expression in (5) instead of longitudinal admittance of a phase B, and as result we will have:

( )NA

AIAANBBIBB UU

YUIUUYUI−

⋅−−+⋅= .

After fulfilling similar substitutions from (5) to (6)

and from (6) to (4) we have received:

( ) ( )( ) ( )NABNBA

BINABAINBA

UUIUUI

YUUUYUUU

−−−=

=⋅−−⋅−, (12)

( ) ( )( ) ( )NBCNCB

CINBCBINCB

UUIUUI

YUUUYUUU

−−−=

=⋅−−⋅−, (13)

( ) ( )( ) ( )NAСNСA

CINAСAINСA

UUIUUI

YUUUYUUU

−−−=

=⋅−−⋅−. (14)

We have received non-uniform system of three linear

equations in relative to three unknown complex admittances of phase isolation. In the simultaneous equations (12) - (14) there are no longitudinal phase admittances of loading.

In a general view in the matrix form simultaneous equations (12) - (14) look like:

BYA I =⋅ , (15)

where A - a square matrix of factors at unknown admittances of isolation:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

3331

2322

1211

a0aaa00aa

A ; (16)

IY - a matrix-column of required complex admittances of phase isolation;

B - matrix-column of the absolute terms of the equation.

The solution of the received system of the algebraic equations (12) - (14) by exact methods, for example by Gauss method, if entrance parameters change in real ranges, is unacceptable because of very low accuracy. Results of calculations of isolation admittances with application of these methods differ from the real values by several times and even can differ by more than ten times. It is caused basically by an unfavorable correlation of parameters of equivalent circuit values, which influence the coefficients of unknowns in equations (12) - (14). The feature of the parameters values is that longitudinal admittances of phases of loading can be by 103 – 106 times more, than a shunt admittance of phase isolation. Besides, the isolation capacity admittance is approximately 100 times more than its active component.

The solution of the simultaneous equations of state is carried out by iterative Seidel method. When applying it a convergence of calculation is reached, if the matrix of coefficients (16) has a dominating diagonal, i.e. the sum of diagonal elements of a matrix of coefficients A exceeds the sum of other coefficients.

In case of equality of shunt complex admittances of isolation in all three phases the system of equations has no solution, and therefore it is impossible to define the admittances of isolation. If the difference in isolation resistances in phases differ is not less than on 0.05 Ohm the system of equations has the solution.

C. Influence of loading asymmetry The accuracy of definition of phase isolation

admittance in relation to the earth by solving simultaneous equations (12) - (14) depends in a great measure on a correlation of values of longitudinal phase admittances of loading of a controllable feeder. It comes from the fact that the simultaneous equations (12) - (14) are received at an assumption about equality of admittances of three phases of loading. Taking into account real parities of phase admittances of loading the equations (12) - (14) look like:

( ) ( )( ) ( ) HANABНBNBA

BIHANABAIHBNBA

kUUIkUUI

YkUUUYkUUU

⋅−−⋅−=

=⋅⋅−−⋅⋅− (17)

( ) ( )( ) ( ) HBNBCНСNCB

CIНBNBCBIНСNCB

kUUIkUUI

YkUUUYkUUU

⋅−−⋅−=

=⋅⋅−−⋅⋅−

( ) ( )( ) ( ) НАNACНСNCA

CIНАNACAIНСNCA

kUUIkUUI

YkUUUYkUUU

⋅−−⋅−=

=⋅⋅−−⋅⋅−

where HHAAH YkY ⋅= , HHBBH YkY ⋅= ,

HHCCH YkY ⋅= - longitudinal complex phase

POWER QUALITY, ALTERNATIVE ENERGY AND DISTRIBUTED SYSTEMS 63

admittances of loading of a feeder;

HCHBHA k,k,k - the complex coefficients of asymmetry, considering difference between longitudinal phase admittances of loading and average (nominal) value of admittance of a phase of loading HY ;

NU - voltage of a neutral of a feeder in relation to the earth:

HCHBHA

HCCHBBHAA

CHBHAH

CHCBHBAHAN

kkkkUkUkU

YYYYUYUYUU

++⋅+⋅+⋅

=

=++

⋅+⋅+⋅=.

As a result of the realized transformations the

magnitude of average longitudinal admittance of phases

of loading HY is excluded from the equations of system (17). The values of the asymmetry coefficients

HCHBHA k,k,k are defined as a result of corresponding measurements when a feeder is off. The coefficients of asymmetry HCHBHA k,k,k allow us to take into account automatically static and dynamic asymmetry which can take place on feeder in operation.

Dependence of an error at definition of an active admittance component of isolation on the value of this component at presence of turn-to-turn short circuit is shown in Fig.2. An estimation of the calculation error of phase B admittance, appearing as the result of asymmetry at turn-to-turn short circuit, is made by comparison of exact and calculated values of isolation admittance. The exact value BIY is received taking into account real values of asymmetry coefficients. The

approximate value *BIY , is received with the

coefficients of asymmetry 1kkk НСНВНА === . The fractional error at definition of isolation admittance

BIYΔ , appearing because of the load phase admittance asymmetry, is equal to:

НА

НАНВ

B

B*BI

BI

BI

*BIBI

BI

BI

kkk

UIY

Y1

YYY

YY

−⎟⎟⎠

⎞⎜⎜⎝

⎛−=

=−=Δ

(18)

It is visible from (18), that asymmetry of longitudinal

admittance in the phase C does not influence

BIY calculation. Ideally longitudinal admittances of all three phases of loading of a feeder are equal to each other. Practically these admittances always differ from

each other. Depending on the reasons correlation of the admittances can be time-constant that is static asymmetry takes place, or the correlation varies with time i.e. there is a dynamic asymmetry.

-100

-50

0

50

100

150

0 4000 8000 12000 16000 20000

Defect of isolation Rdef, Ом

Fig.2. An error of definition of active admittance component GΔ of the phase B when: 1 - 1 % of turns in the phase A are short-circuited; 2 - 1 % of turns in the phase B are short-circuited.

The main reasons of static asymmetry occurrence are the following:

- Deviations from the procedures while manufacturing or design changes after an electric motor repair (technological asymmetry);

- Short circuit of several turns of one phase of a motor stator winding (turn-to-turn short circuit);

- Defect of phase-to-phase insulation (it is most probable on a motor stator leads).

As a result of static asymmetry when a feeder is in operation there appears a current of negative sequence, amplitude and phase of which do not depend on an electric motor mode of operation. This current frequency is equal to a power network frequency.

Dynamic asymmetry shows up in a periodic change of longitudinal admittances of each phase of a feeder and happens, basically, for these reasons:

- Infringement of the air-gap symmetry in an electric motor;

- Runout of electric motor bearings; - Breakages of cores of a short-circuited winding of

an asynchronous motor rotor. As a result of dynamic asymmetry there is also a

negative sequence current. However, its amplitude and phase periodically change. The change period depends on asynchronous motor slip. Frequency of a negative sequence current differs from a network frequency on value of an electric motor slip [6].

Asymmetry in the form of phase-to-phase shirt circuits or phase breakages is short-term as these damages are revealed and quickly disconnected by relay protection. Therefore influence of a short-term asymmetry on the method of definition of isolation parameters is not taken into account.

2 1

Erro

r at d

efin

ition

ΔG

, %

64 2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP

Generally, the account of a load asymmetry at solving of simultaneous equations (17) consists in defining and specifying of asymmetry coefficients НСНВНА k,k,k .

In the case of technological asymmetry numerical values of coefficients are defined by measuring on the working or disconnected feeder and they are entered together with nominal parameters into the equipment database. Further, in the process of a motor application asymmetry level can change at any moment, even on a running electric motor, for example because of turn-to-turn short circuit occurrence, breakage of winding cores of an asynchronous motor rotor etc. In these cases in order to exclude the mistakes in definition of isolation admittances the appeared asymmetry is automatically revealed and taken into account. The method how it is taken into account depends on the kind of an asymmetry. When dynamic asymmetry is taken into account it is necessary to provide the conformity of asymmetry coefficients values to the moment of definition of instantaneous values of parameters of a current mode. The development of the defects which have caused asymmetry is automatically synchronously taken into account by definition and change of asymmetry coefficients.

D. Estimation of the method accuracy With really probable ranges of admittance changes the

maximum error of the method does not exceed 12 % (Fig.3, curve 1). The principal cause of an error occurrence in this case is the algorithm used to define current and voltage vectors by measuring their instantaneous values. Practically the same values of an error as shown in Fig.3 (curves 2, 3) are received as a result of admittance calculations in a running motor when the error of the current measuring channel is 0.01%.

-60

-40

-20

0

20

40

60

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Fig.3. An error of definition of an isolation complex admittance of phase A by solving simultaneous equations (12) - (14): 1 - if there is no error of the current measuring channels; 2 - if an error of the current measuring channel of phase A is 0.05 %; 3 - if an error of the current measuring channel of phase B is 0.05 %.

The error of the current measuring channel shown in Fig.3 is accepted 0.05 % as namely this error is provided in an ideal case by the calibrated shunt in accordance with national standard.

To carry out the experimental researches applying the offered method we have a pump drive motor with the capacity of 500 kW which is connected to 6 кV section with a cable with cross section 95 mm2 and 70 m long. The isolation defect of phase A was made by active resistance connected between a phase A lead of the stator winding of the electric motor and the earth. Current and voltage vectors are defined on the basis of the results of digital oscillography of process of supplying voltage to a section.

Using the values of vectors received according to the method of definition of isolation complex admittances the calculations of isolation parameters of a feeder were carried out. The calculation results showed that active resistance of phase A isolation is equal to 147.8 kOhm (active resistance 110 kOhm was connected to phase A, i.e. the mistake of definition of resistance was 34.4 %), and active resistances of isolation of phases B and C are equal to 2.44 megOhm.

For the automatic account of load asymmetry of a feeder which appears in the process of electric equipment application, the special algorithm is used in the offered method. This algorithm is shown in Fig.4. Asymmetry occurrence is defined when negative sequence current I2 appears. If the frequency of current I2 differs from the frequency of feeding voltage it means there appears a dynamic asymmetry.

The estimation of accuracy of the method at load asymmetry is carried out with the help of a mathematical model of an electric system node. Mathematical modeling has shown, that the introduction of automatic definition of asymmetry coefficients (Fig.5) at the static asymmetry at the rate of ± 0.3 % leads to the error decrease from ± 44 % (a curve 1) to - (1.16÷0.16) % (curve 2). Curve 3 reflects dependence of an error at active resistance of isolation defect RDEF = 100 kOhm. If there are any isolation defects in phase A and longitudinal load asymmetry in phase C (curve 4), the error increases a little.

The research of the relationship between an error in definition of isolation active resistance ΔR in phase A and a level of dynamic longitudinal asymmetry has shown that automatic definition of asymmetry coefficients allows us to exclude an error practically completely. An obligatory condition for this is the correct choice of the moment of the calculation which is defined by a motor rotor position and its slipping.

At present to increase accuracy of considered method of complex admittance of the electric equipment isolation the authors are working on way of using as input data the average values of basic harmonic of currents and voltages.

1

2

3

Erro

r at d

efin

ition

ΔR A

I ,%

Defect of isolation of a phase A RAI,megOhm

POWER QUALITY, ALTERNATIVE ENERGY AND DISTRIBUTED SYSTEMS 65

Fig. 4. Algorithm of the automatic account of asymmetry

-50

-40

-30

-20

-10

0

10

20

30

40

50

0,985 0,99 0,995 1 1,005 1,01 1,015

Fig.5. An error of definition of an isolation admittance active component if a load has static asymmetry

III. CONCLUSIONS

1. The considered method of definition of isolation complex admittance allows us to estimate continuously the state of electric equipment isolation. Thanks to it the probability to prevent electric equipment damages rises.

2. The automatic accounting the static and dynamic asymmetry, arising in running electric motors, provides sufficient accuracy of the method of complex admittances definition at its application on feeders with electric motors.

REFERENCES [1] Kuchinskiy G.S., Kiziwetter V.E., Pintal J.S. Izolajcia ustanowok

wisokogo naprjazhenija. - M.: Energoatomizdat, 1987. - 368 s. [2] Swi P.M. Kontrol izoljacii oborudowanija wisokogo

naprjazhenija. - M.: Energoatomizdat , 1988. - 128 s. [3] Capenko E.F. Zamikanija na zemlj w setjakh 6-35 kV.-M.:

Energoatomizdat , 1986.-128 s. [4] Welfonder T., Leitloff V., Feuillet R., Vitet S. Location

Strategies and Evaluation of Detection Algorithms for Earth Faults in Compensated MV Distribution Systems. – IEEE Transactions on Power Delivery, 2000, vol. 15, No. 4, Oct.

[5] Grebchenko N.V. Н.В. Metod nepreriwnogo opredelenija kompleksnikh prowodimostei izoljacii w rabochikh rezhimakh electricheskikh prisoedinenii 6-10 kV // Electrichestwo .- 2003. - № 12. – S.24-29.

[6] Grebchenko N.V. Sistema zashhitno-diagnostirujshheii awtomatiki lokalnich obektow elektricheskikh sistem // Naukowi prazi Donezkogo nazionalnogo technicheskogo uniwersitetu. Serija: Elektrotekhnika i energetika, wipusk 112: Donetsk: DonDTU. – 2006. – S. 81- 87.

Input of the instantane- ous values of the phase currents and voltages

in relation to the earth

I2 > I2 DOP

Accounting the frequency of negative sequence

current f2

f2 = f0

1HCk

1HBk

1I2I3

1HAk

=

=

+=

1HCk

1HBk

1HAk

=

=

=

Solving the simultaneous equations of current state

Dynamic asymmetry. Definition of the calculation

moment of time

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

π−π+=

π+π+=

π+=

3

2t2f2sin

1I

2I

2

231HCk

3

2t2f2sin

1I

2I

2

231HBk

t2f2sin1I

2I

2

231HAk

Yes

Yes

No

No

Complex admittances of the phase isolations

CIBIAI YYY ,,

Static asymmetry. Definition the feeder phase, where asymmetry has appeared

Accounting the vector of negative current sequence

2I

1

2

3

4

Coefficients of asymmetry kH, p.u.

Erro

r at d

efin

ition

ΔR,

%

66 2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP