1 the view from the other side: how transformers affect gic d.h. boteler geomagnetic laboratory...
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The View from the Other Side:How Transformers affect GIC
D.H. BotelerGeomagnetic Laboratory
Ottawa
Geomagnetic Disturbance Workshop, Idaho National Laboratory, April 7-8, 2015
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Factors affecting GIC in Power Systems
Geomagnetic Induction Earth Conductivity Rate of change of magnetic field
System Characteristics Network
Configuration Impedances
The higher the sampling rate the larger the dB/dt value
GIC modelling uses resistances only.
What about inductances?
How does system L/R time constant affect GIC?
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Hydro-Quebec HVDC Tests Bolduc et al, 1989
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Hydro-Quebec HVDC Tests
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Hydro-Quebec HVDC Tests
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Later Reports
Dong, 2002
Walling and Khan, 1991
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Calculations of growth of GIC
Bolduc et al (1989b)
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Bolduc’s formula for time to saturation
( . / )A tf K Vi
I A A A
p+
+ + -
0
2 3
1 0 13 2 1
15 27 160
;
( )/
/ //
p
K RA tf
V X Xp=
+
1 23 2 1 2
1 20 2
8
3
//
/
. pX XVt A
f K R
é ù+ê ú= ê úë û
2 31 220
1 2
0 355
Fraction of steady-state current reached after time, t
As a function of parameter
Gives time
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Using Bolduc’s formulas
a) “Backwards” calculation determine T (secs) for specified i/I
b) “Forwards” calculation determine i/I for specified T (secs)
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Effective Inductance seen by GIC
Walling, 2013
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Effective Inductance seen by GIC
satt
Tq=
tsat
T
Lunsaturated
LsaturatedIndu
ctan
ce
time
Fraction of time in saturation,
Fraction of time not in saturation,
satT t
Tq
-- =1
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Effective Inductance seen by GIC
( )
effL L L
q q-= +
1 2
1 1
T
Lunsaturated
Lsaturated
Indu
ctan
ce
dc dc
eff
e i RDi
Dt L
-=
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Relation between θ and GIC
( )( ) cosAI t I ftp= 2
UA mag
S
LI I
L=where
Tq
-2
Tq2
sADC
II in
qp
p
æ ö÷ç= ÷ç ÷çè ø2
2
DC
IdtI
T=
ò
sin DC
A
I
Iq p
p-
æ ö÷ç ÷= ç ÷ç ÷çè ø11
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Incremental Growth of GIC
dc dc
eff
e i Ri t
L
-D = D
1. Initially, i = 0, Leff = Lunsaturated
2. Calculate current increase, Δi for time interval, Δt
3. For new value of i, calculate fraction of time in saturation, θ
4. Calculate new value of effective inductance, Leff
5. Return to Step 2, etc
sin DC
A
I
Iq p
p-
æ ö÷ç ÷= ç ÷ç ÷çè ø11
( )
effL L L
q q-= +
1 2
1 1
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Incremental Growth of GIC
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3-leg 3-phase transformer
Slope L2
Slope L2
Magnetising curve for AC
Magnetising curve for DC
eff saturatedL L=
Inductance is constant
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Transformer with delta tertiary
DC current
Flux offset
Current circulating in delta tertiary
“Delta” phase
“Normal” phase
Walling, 2013
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Slope L2
Slope L2
Magnetising curve for “normal” phase
Magnetising curve for “Delta” phase
Transformer with delta tertiary
eff saturatedL L=“Delta” phase
“Normal” phase( )
effL L L
q q-= +
1 2
1 1
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Questions? Answers?
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References Bolduc, L., Pelletier, P. and Boisclair, J-G., DC current in AC transmission system near the electrode of the HVDC converter
at DES Cantons substation, Proceedings of the EPRI Conference on Geomagnetically Induced Currents, Burlingame, California, November 8-10, 1989.
Bolduc, L. and Kieffer, P., A recipe for fast simulation of the effect of the DC component of magnetizing steady-state currents in transformers using EMTP, Proceedings of the EPRI Conference on Geomagnetically Induced Currents, Burlingame, California, November 8-10, 1989.
Bolduc, L., Formula to approximate the setting time for the DC component of magnetizing currents in transformers, Proceedings of the EPRI Conference on Geomagnetically Induced Currents, Burlingame, California, November 8-10, 1989.
Bolduc, L., A. Gardreau, and A. Dutil, “Saturation time of transformers under dc excitation,” Elect. Power Syst. Res., vol. 56, pp. 95–102, 2000.
Boteler, D.H., Characteristics of time-varying inductance, IEEE Trans. Magnetics, 30, 172-176, 1994.
Dong, X., Study of power transformer abnormalities and IT applications in power systems, PhD Thesis, Virginia Polytechnic Institute, 2002.
Walling, R.A. and Khan, A.H., Characteristics of Transformer Exciting Current During Geomagnetic Disturbances, IEEE Trans. Power Delivery, Vol. 6, No. 4, October 1991.