instrument transformers 6.0...

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CHAPTER 6

MODELLING AND ANALYSIS OF TRANSIENTS IN

INSTRUMENT TRANSFORMERS

6.0 INTRODUCTION:

The most adopted modeling of GIS components, to simulate Very

Fast Transients by digital program, make use of electrical equivalent

circuits composed of lumped elements (of capacitances, inductances and

resistances) and distributed parameter lines derived from their surge

impedances and travel times. The disconnector spark itself has to be

taken into account by a transient spark resistance and a subsequent arc

resistance of a few ohms. Dielectric losses in some components such as

bushing need to be taken into account because of very high frequencies.

From the point of view of the overall integrity of the GIS, it is

important to assess the over voltages set up not only locally but also at

various other points remote from the disconnector. In view of the

electrical and physical complexity of the substation layout, it is essential

to verify that the over voltages are unlikely to overstress the dielectric

medium. Therefore the entire mesh of the substation and the various

installations involved such as generator transformers, inter bus

transformers, SF6/Oil bushings, isolators, cable/overhead line

connections etc., and should be considered for analysis. Generally a

disconnector is provided in each arm of a circuit breaker. Enclosures are

arranged in several levels in a complex layout resulting in a large number

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reflections and a model of study should take care of the physical

arrangements as closely as possible. Calculation of over voltages is by no

means easy because of the number of busbar sections and cables having

distributed parameters where as generators, transformers and capacitors

are considered as lumped elements. The method employed to calculate

must satisfactorily represent both lumped and distributed parameter, the

popular method used being the Bewley lattice method.

6.1 MODELLING CONCEPT

In the present work, modelling and analysis are confined to a

section of the GIS bay illustrated in Figure 6.4. The section chosen

consists of an air/SF6 bushing (through which an external circuit such

as a transmission line is connected), insulating spacers, disconnector

switch module and a busbar of 10 meters length. Fast transient

overvoltage wave forms generated during a closing operation of

disconnector have been considered for calculation.

All the distributed parameter lines are considered in the internal

mode (conductor-enclosure) only and the external enclosure is

considered to be perfectly earthed. At high frequencies earth connections

assume significant impedance values and this mode has not been

considered.

The insulating spacers used in this GIS are cone type insulators

supporting the inner conductor against the outer enclosure. These are

assumed to be disc type for approximate calculations of spacer

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capacitance which comes out to a value of 3.07pF. Three spacers per

meter length have been considered.

The coaxial bus duct used is modeled as a series of pi – networks.

The inductance of bus duct is calculated from the diameters of the

conductor and enclosure. Capacitances are calculated on the basis of

actual diameters of inner and outer cylinder of central copper conductor

and outer enclosure.

The schematic diagram of the GIS section considered is shown in Figure

6.1.

Fig 6.1 The schematic diagram of the GIS section

The capacitance on the source side (sum of the capacitances of SF6

– air bushing and capacitance of the transformer) is assumed as 2000

Pico Farads and used in the calculation. Spark resistance is simulated

by a constant value of 2 ohms.

Any desired configuration is represented by an equivalent circuit of

the main components of the GIS after calculation of the parameters. A

trapped charge is assumed to be left on the floating section of the

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switchgear due to a previous opening operation of the disconnector or

circuit breaker. This is simulated by a voltage of certain value on the

bus on one side of the switch. This is the most severe situation during

switching with a voltage collapse of 2 p.u. This pessimistic condition will

result in the maximum overvoltage for a particular configuration.

Therefore this simulation will ascertain the maximum value of the over

voltages in the particular GIS section due to the closing of a

disconnector. For a specific GIS section, in the parameters such as the

load side capacitance, length of load side busbar, source side

capacitance and length of source side busbar etc. decide the peak value

of over voltages.

6.2 CALCULATION OF R, L AND C:6.2.1 Calculation of Resistance:

When DC current flows through conductor, there will be uniform

distribution of current. Burt when AC current flows through it, a non-

uniform distribution occurs, i.e., more current concentrates on the

surface. Due to this there is a slight increase in resistance.

R = x L

A

The average value of resistance = 238.46 μΩ/ m

= 0.238 mΩ/m

The calculated value of specific resistances is 1.3189 X 10–8 Ω–m

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6.2.2 Calculation of Inductance

The coaxial inner and outer conductors of a coaxial GIS are shown in

Figure 6.2.and the corresponding values are 260 mm and 80 mm

respectively.

Fig 6.2 Cross section of a typical GIS system

The calculated value of inductance is 0.2295 μH per meter of bus length.

6.2.3 Calculation of Capacitance6.2.3.1 Capacitance of Bus Duct

The capacitance is calculated with the assumption that the

conductors are cylindrical and calculated.

The calculated value of capacitance is 51.22 Pico Farads per meter.

6.2.3.2 Spacer Capacitance CalculationSpacers are used for supporting the inner conductor with reference

to the outer enclosure. They are made with Alumina filled epoxy material

whose relative permittivity is 4. The thickness of the space is assumed to

be the length of the capacitance for calculation.

By using the above formula the spacer capacitance calculation is as

follows.

Capacitance of each spacer = 51.22x0.015x4=3.073pF

Assume three spacers per meter length.

Total capacitance of GIS bus per meter length is calculated as follows

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= 51.22+3x3.073=60.44pF/meter.

The completed 123KV GIS configuration is shown in figure 6.3,

in which the experiments were carried out the analyzed GIS, enables the

realization of triple busbar system with corresponding bypass.

Fig 6.3 The completed 123 KV GIS configuration

Each bus bar system consists of three phases in one encapsulation.

The basic electric circuit of this substation is shown in figure 6.4. The

analysis of the transients generated during disconnector switch

operations are performed for the line feeder bay = E15.The line feeder

E15 bay and its geometrical structure is shown in figure 6.4.

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Fig 6.4 Figure of the analyzed line feeder bay = E15.

Z1 : Source Impedance

Q8, Q51, Q52 : Earth Switch

Q9 : Outgoing Disconnector

T5 : Potential Transformer

T1 : Current Transformer

Q0 : Switch Gear

Q1, Q2, Q3, Q70 : Busbar Disconnector

In order to predict the transient electromagnetic phenomena

in the secondary circuits of voltage (T5) and current (T1) transformers,

several network models of GIS – components and physical effects in the

GIS have been developed the help of the models available. The

simulations of transients in GIS due to disconnector operation have been

carried out.

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6.2.3.3 The Arc – Model of the Disconnector Operations:

In view of the generation of transients in GIS, the disconnector

operation has been modeled with the help of the modified Kopplin model,

which describes the disconnector arc resistance. The resistance of the

arc-discharge represents a substantial part of the damping of the whole

GIS-system. Normally the resistance is a frequency dependent parameter

due to the skin effect. In the case of arc-discharge there exists a strong

time-dependency according to temperature, diameter and losses of the

discharge. Thus the time behaviour of the spark’s resistivity has to be

evaluated correctly. The time behaviour of the conductivity g(t) is mainly

influenced by the time dependent temperature function T(t) of the arc-

discharge. Both the functions are displayed below.

1/g. dg/dt = 1/g(t) (ui/p (g)-1) -----------6.1

T (g) = T0 (1-e-(g/g0)) ---------------------6.2

Where u = voltage and i = current

p = the power of the arc

T0= initial temperature of the arc

g0= initial conductivity of the arc

This description of the physical arc-discharge process is valid from the

beginning of the discharge up to its end.

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6.3 MODELING OF GIS COMPONENTS

Due to the traveling nature of the transients the modeling of

GIS makes use of electrical equivalent circuits composed by lumped

elements and especially by distributed parameter lines defines by surge

impedances and traveling times. The equivalent circuits can be derived

from the manufacturer’s drawings and from the internal physical

arrangement.

The inner system, which consists of the high voltage bus duct

and the Inner surface of the encapsulation, has been represented

thoroughly by line sections modeled as transmission lines with

distributed parameters. The phases and their inter phase coupling have

been investigated by applying the cable constants subroutine and the

method of modal components. This method permits the Calculation of

each phase and its coupling to the other phases separately.

More complex detailed models of the current and voltage transformers,

adopted particularly due to the accuracy to be reached and the

frequencies of interest, have been shown below. The transients are

transmitted to the secondary lines of the GIS by stray capacitances

which result of the construction of the protection electrodes in the

transformers.

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Table 6.1 Equivalent Circuit of Current Transformer

L1, L2, L3: The conductors of theCT inner system

Table 6.2 Equivalent Circuit of Potential Transformer

DFK: The Pressure Spring Contact.CK: Coupling CapacitorLM1, LM2: Conductors of theSecondary Circuit

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Table 6.3 Equivalent Circuits Of the GIS Components

6.4 RESULTS AND DISCUSSIONS:

The simulations have been made for the analyzed bay = E15, the

busbar disconnectors Q1, Q2, Q3 and Q70, as well as the switchgear Q0

were switched off. The transients caused by closing operation of the

outgoing disconnector Q9 of the line feeder bay E15, have been

determined by applying the SIMULINK module of the MATLAB software

with the basic circuit of the line feeder bay E15, AC voltage source

applied 123kV, 50 Hz, with a source impedance (z1) of 10 micro henrys

considered. To make on/off the breaker with a specified timing, here the

timer is on at 2 micro Seconds and switched off at 4 micro Seconds. The

breaker (Q9) Resistance at on is 0.001ohm. The values of Q0, Q1 Q51

and open disconnector in the circuit considered as 50 Pico Farads. With

this basic circuit due to switching operation of Q9 breaker the transient

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voltages at the secondary circuit of CT across the load terminals around

16 kV and across the PT was about 26kV.

By adding series line impedance (Z) 0.212 micro Henry and shunt

capacitance of Q2=Q3=50 Pico Farads in between the breaker Q9 and

Potential transformer and the length of the cable of the secondary circuitry

of CT/PT considered as 1meter only. Due to switching operation of Q9

breaker the transient voltages at the secondary circuit of CT across the

load terminals around 0.67 kV and across the PT was about 4.53 kV.

The transient voltages across the secondary circuit of C.T and P.T are

measured for the following cases

Fig 6.5 Basic circuit of the line feeder bay

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6.5 Case 1: Analysis of VFTO’s across CT and PT for different ofthe Control circuit Cable:

In the basic circuit shown in figure 6.5, the length of control circuit

cable is varied to 1m, 5m and 10m respectively by keeping all other

values are fixed.

The source impedance =Z1=10 micro henrys.

Earth switch Q8 =Q51=Q52=1nano farads

Series impedance =Z=0.212 micro Henry

Shunt capacitance =Q2=Q3= 50 Pico Farads

6.5.1 Case (i) Analysis of VFTOs across CT and PT for Length ofthe control circuit Cable is 1 meters

For length of the cable 1 meter andLm1=Lm2=Lm3=Lm4=0.5

μH/1metre, the transient voltages across the load terminals of secondary

circuit of current transformer (CT) and the potential transformer (PT) is

0.69kV and 4.53 kV respectively as shown in figures 6.6 and 6.7

Fig 6.6 VFTO’s across secondary circuit of current transformer

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Fig 6.7 VFTO’s across secondary circuit of potential transformer

6.5.2 Case (ii) Analysis of VFTOs across CT and PT for Length ofthe control circuit Cable is 5 meters

For the length of cable 5metres and the values of

Lm1=Lm2=Lm3=Lm4= 2.5 micro Henry /5 meters, then the transient

voltages across the load terminals of secondary circuit of current

transformer (CT) and the potential transformer (PT) is 2.84kV and 29.6

kV respectively as shown in figures 6.8 and 6.9.


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Fig 6.9 VFTOs across secondary circuit of potential transformer

6.5.3 Case (iii) Analysis of VFTOs across CT and PT for Length of theCable is 10 meters

For the length of cable 10 meters and the values of

Lm1=Lm2=Lm3=Lm4= 5 micro Henry /10 meters, then the transient

voltages across the load terminals of secondary circuit of current

transformer (CT) and the potential transformer (PT) is 5.90kV and 118.9

kV respectively as shown in figures 6.10 and 6.11


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As the length of the cable of the secondary circuitry of

CT/PT increases the transient voltages induced across the load terminals

of CT/PT also increased abnormally.

The VFTO’S across secondary circuit of CT & PT are estimated for

different lengths of control circuit cable and are shown in table 6.5

Table 6.4 Transient voltages across CT & PT for different cable lengths

S.No DescriptionTransient

voltages acrossCT

Transientvoltages across

PT1 Length of the control cable

=1 meter 0.67 kV 004.53 kV

2 Length of the control cable= 5 meters 2.84 kV 029.66 kV

3 Length of the control cable= 10 meters 5.90 kV 118.90 kV

6.6 CASE (2) Case (i): Analysis of VFTOs across CT and PT for fixedValue of high voltage capacitance (C1) and differentvalues of Winding Capacitance (C2) of the currenttransformer (CT).

The transient voltages across CT & PT are estimated for different

Values of winding capacitance (C2=300pF, 500pF and 700pF) and fixed

value of high voltage capacitance (C1=1pF) for 1meter length of control

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circuit cable by keeping the other values remain constant in the modelled

circuit shown in figure 6.5.



From the above figures 6.12 and 6.13, it has been observed that the

transient voltages across the load terminals of the CT and PT are 0.67 kV

and 4.50 kV respectively for 1meter control circuit cable length. It means

by keeping the high voltage capacitance (C1) constant and changing the

value of winding capacitance (C2) will not affect the transient voltages in

the secondary circuit of the CT/PT across the load terminals.

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6.6.1 Case (ii) Analysis of VFTO’s across CT and PT for differentValues of high voltage capacitance (C1) and fixedvalue of Winding Capacitance (C2) of the currenttransformer (CT).

The transient voltages across CT & PT are estimated for fixed

value of winding capacitance (C2=300pF ) and different values of high

voltage capacitance (C1=1pF,5pF and 10pF) for 1meter length of control

circuit cable by keeping the other values remain constant in the

modeling circuit shown in figure 6.5.

Fig 6.14 VFTOs across secondary circuit of Current transformer(c1=1pF, c2=300pF)

Fig 6.15 VFTOs across secondary circuit of Potential transformer(c1=1pF, c2=300pF)

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Fig 6.16 VFTO’s across secondary circuit of Current transformer(c1=5pF, c2=300pF)

Fig 6.17 VFTO’s across secondary circuit of potential transformer(c1=5pF, c2=300pF)

Fig 6.18 VFTO’s across secondary circuit of Current transformer(c1=10pF, c2=300pF)

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Fig 6.19 VFTO’s across secondary circuit of Potential transformer(c1=10pF, c2=300pF)

From the figures 6.14 to 6.19, it has been observed that the

transient voltages across the load terminals of the CT are 0.67 kV, 2.78

kV and 5.73 kV and the transient voltages across the load terminals of

the PT are 4.53 kV, 4.51 kV and 4.53 kV respectively for fixed value of

winding capacitance (C2=300pF) and different values of high voltage

capacitance (C1=1pF, 5pF and 10pF) for 1meter length of control circuit

cable.

That means by keeping the value of winding capacitance (C2)

constant and changing the high voltage capacitance (C1) will affect the

transient voltages in the secondary circuit of the CT across the load

terminals only.

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Fig 6.21 VFTOs across secondary circuit of Potential transformer(c1=1pF, c2=500pF)


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Fig 6.23 VFTOs across secondary circuit of potential transformer(c1=1pF, c2=700pF)

From the figures 6.20 to 6.23, it has been observed that the transient

voltages across the load terminals of the CT are 0.67 kV, and the

transient voltages across the load terminals of the PT are 4.54 kV

respectively for different values of winding capacitance (C2=300pF,

500pF and 700pF) and fixed value of high voltage capacitance (C1=1pF)

for 1meter length of control circuit cable.The transient voltages across

load terminals of CT and PT are calculated for fixed values of C1 by

varying C2 and vice –versa. The results are tabulated in table 6.6.

Table 6.5 Transient voltages across CT & PT for different values ofC1 and C2

S. No. Value of highvoltages cap. (C1)

Value ofwindingcap. (C2)

Transientvoltages

across (CT)

Transientvoltages

across (PT)1 1pF 300 pF 0.67 kV 4.53 kV2 1pF 500 PF 0.67 kV 4.54 kV3 1pF 700 PF 0.67 kV 4.54 kV4 1pF 300 PF 0.67 kV 4.53 kV5 5 pF 300 PF 2.78 kV 4.50 kV6 10 pF 300 PF 5.73 kV 4.53 kV

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6.7 CASE (3): EFFECT OF BURDEN CT/PT

The transient voltages across CT & PT are estimated by varying

burden on secondary circuit of CT and for fixed value of burden on PT

and vice -versa in the modeling circuit shown in figure 6.5.

The length of the control cable is considered as 1 meter and the other

Values are Lm1=Lm2=Lm3=Lm4=0.5 micro Henry/meter, and

C1=1PF and C2=300 PF.

Fig 6.24 VFTOs across secondary circuit of current transformer


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Fig 6.26 VFTOs across secondary circuit of current transformer




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From the figures 6.24 to 6.29, it has been observed that the transient

voltages across the load terminals of CT and PT are 0.67 kV and 4.53 kV

and are constant by changing CT secondary burden of load inductance

and load capacitance for fixed burden on PT.

Further, it is observed that the transient voltages across the load

terminals of CT and PT are 0.67 kV and 4.53 kV and are constant by

changing PT secondary burden of load inductance and load capacitance

for fixed burden on CT. All simulation results obtained for change of

burden on CT and PT are tabulated in table 6.6

So, the transient voltages across the load terminals of CT/PT are

constant even though the burden on CT/PT is increased.

6.6 Transient voltages across CT & PT for change in burden:

Table 6.6 Transient voltages across CT & PT for change in burden

S.No Burden ofCT

Burden ofPT

Transientvoltages across

CT

Transientvoltages

across PT1 LB=2.8μH

CB=20pFLB=170mHCB=600pF

0.67 kV 4.5 kV

2 LB=4 μHCB=30pF

LB=170mHCB=600pF

0.67 kV 4.5 kV

3 LB= μHCB=40pF

LB=170 mHCB=600pF

0.67 kV 4.5 kV

4 LB= μHCB=80pF

LB=170 mHCB=600pF

0.67 kV 4.5 kV

5 LB=15 μHCB=80pF

LB=300 mHCB=800pF

0.67 kV 4.5 kV

6 LB=15 μHCB= 80pF

LB=600 mHCB=1000pF

0.67 kV 4.5 kV

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6.8 Case (4): Effect of length of the GIS Section between CurrentTransformer (CT) and potential Transformer (PT):

As the length of the GIS Section increases the series impedance also

increases and the shunt capacitance also considered accordingly

6.8.1 By adding one Pi-section as shown in figure 6.30 i.e. shuntcapacitance, and series inductance values are 50 pF, 0.212µHenry, respectively in between CT and PT.

The transient voltages across the load terminals of CT and PT are

observed as 0.62kV and 4.08kV from figures 6.31 and 6.32 respectively

due to switching operation of circuit breaker.

Fig 6.30 Simulink modeled circuit for addition of one pi-section

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Fig 6.31 VFTO’s across secondary circuit of current transformerFor adding one pi-section

Fig 6.32 VFTOs across secondary circuit of potential transformer for

adding one pi-section

6.8.2 By adding two Pi-sections i.e. a shunt capacitance and a seriesInductance of each pi- section values are 50pF and 0.212μHrespectively in between CT and PT as shown in figure 6.33.

The transient voltages across the load terminals of CT and PT are

observed as 0.80kV and 4.54 kV from figures 6.34 and 6.35 respectively

due to switching operation of circuit breaker

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Fig 3.33 Simulink modeled circuit for addition of two pi-sections

Fig 6.34 VFTO’s across secondary circuit of current transformerFor adding two pi-sections

Fig 6.35 VFTO’s across secondary circuit of potential transformers

For adding two pi-sections

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6.8.3 By adding three Pi-sections i.e. a shunt capacitance and aseries inductances of each pi- section value are 50pF and0.212μH respectively in between CT and PT as shown in figure6.36.The transient voltages across the load terminals of CT and PT are

observed as 1.02kV and 4.2 kV from figures 6.37 and 6.38 respectively

due to switching operation of circuit breaker

Fig 6.36 Simulink modeled circuit for addition of three pi-sections

Fig 6.37 VFTOs across secondary circuit of current transformersFor adding three pi-sections

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Fig 6.38 VFTO’s across secondary circuit of potential transformersFor adding three pi-sections

As the length of the GIS section increases in between CT and PT,

due to switching operations the transient voltages across the load

terminals of CT and PT are also increased. The transient voltages across

the load terminals of CT and PT are estimated for addition of pi- sections

(length of GIS) in between CT and PT and are tabulated in table 6.7

Table 6.7 Transient voltages across CT & PT for change in length of GISsection

S.NO

Increasing the length ofthe GIS in between CT

and PT

Transient voltageacross the loadterminals of CT

Transientvoltages

across theload

terminals ofPT

1 One pi-section 0.62 kV 4.08 kV

2 Two pi-sections 0.80 kV 4.54 kV

3 Three pi-sections 1.02 kV 4.20 kV

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