ABSTRACT. A complete understanding of the behavior of an electric arc in air is of great importance when considering insulation distance selection in power ...
IEEE Transactions on Electrical Insulation
VoJ. 27 No. 3, J u n e 1992
45 7
Modeling of Arc Extinction in Air Insulation C. M. Portela, N. H. C. Santiago Universidade Federal, do Rio de Janeiro, Rio de Janeiro, Brasil
0. B. Oliveira Fo, and C. J. D u p o n t Centro de Pesquisas, de Energia Elttrica, Rio de Janeiro, Brasil
ABSTRACT A complete understanding of t h e behavior of an electric arc in air is of great importance when considering insulation distance selection in power systems. Many models have been studied during t h e last decade t o simulate such behavior b u t , u p t o now, these models have not been able t o represent with great accuracy t h e test results. No general agreement on t h e field of application of these models has been achieved yet. The goal of this paper is t o present a reasonably simple, composed model with two thermal time constants which avoid some of t h e inconsistencies of single time constant models currently used. The proposed model is compared with t h e most common models and is shown t o reach more accurate arc simulations. One application example is used t o show the differences between two models and how a model can help in the evaluation of arc self-extinction limits. These limits are important for proper choice of compensation reactors, single-phase successful operation, neutral grounding criteria, protection selection, and insulation coordination.
1. INTRODUCTION power systems, it may be adequate t o accept flashover of air insulation, a t least for small probability overvoltages. As the air insulation is regenerative, it is desirable t h a t any power arc following flashover is interrupted a t a zero current.
I
N
A reasonably accurate definition of arc extinction is importa.nt for a n adequate insulation selection. Therefore, a n accurate knowledge of small current arc behavior is necessary, a s success of arc extinction near zero current depends upon arc-network interaction] including fast phenomena [l]. T h e time constants involved in such interaction are typically in the range of 0.1 t o 100 ps corresponding t o frequencies from 1 kHz t o 1 MHz. T h e experimental work necessary t o study arc behavior presents practical difficulties when related to actual
conditions. To perform a great number of experiments related t o arc behavior] a simplified test circuit was developed which will generate stable electric arcs under low dc current conditions. An impulse current generator was also provided t o perturb t h e electric arc by injection of very small impulse currents.
A systematic test procedure for low current arcs, under static and dynamic conditions, was then carried out, covering a reasonable range of conditions. T h e results of these tests were used t o investigate arc models a n d their suitability for arc simulation.
It was observed t h a t some arc models are not able to represent accurately the actually measured arc currents. A more consistent arc model is proposed a n d confirmed against actual measurements. T h e idea of this model is to consider the electric arc behaving as if it consists of two
0018-9367 $3.00 @ 1992 IEEE
Portela e t al.: Arc Extinction in Air Insulation
458
regions in series, a.nd or in parallel with different cha.ra.cteristics. T h e proposed model showed practical adva.ntages t h a t may be used a s a basis for arc behavior studies and improved definition of arc extinction conditions.
. LV AC / DC
U
Figure 1. Simplified test circuit used to perform the experiments. R, = Charge resistance; D T = Voltage divider; E = Electrode; Rd = Shunt resistance; CCM = Measuring cable; SM = Mercury switching; SC = Manual switching; R, L, C = Components of RLC series circuit.
I Figure
2.
Electrode tip shapes (a) Needle tip. (b) Rounded tip. 5, 10, 15 a n d 20 m m g a p dista.nces a n d currents from 20 t o 350 mA.
2. EXPERIMENTAL WORK In t h e sequence the V - I curves were measured using only the brass electrodes with needle t i p when new, and in a current range from 100 t o 800 mA.
2.1 TESTS SETUP experimental work was performed on a simplified test circuit which provided stable electric arcs under low dc current conditions. An impulse current generator was also included t o perturb the electric arc with the injection of very small impulse currents. T h e main components of this simplified test circuit are show in Figure 1. Much care was taken with the measuring circuit, especially the scale factor determination a n d the adjustment of the dynamic behavior, taking into account the range of signals t o be measured. HE
T
2.2 EXPERIMENTS
2.2.2 MEASUREMENTS O N T H E D Y N A M I C BEHAVIOR OF ARCS
T h e experiments related t o the evaluation of the dynamic behavior of arcs were accomplished by the systematic application of current impulses in the static arc and measuring the resultant arc voltage variation. For 5, 10, 15 a n d 20 m m arc lengths, current impulses were applied with the minimum, or close t o the minimum, feasible amplitude. Current impulses in both polarities and with three different wave shapes, according t o Table 2, were applied.
T h e following experiments were performed t o obtain information a b o u t the static a n d dynamic characteristics of electric arcs.
14001
1200
E 1OOOC
2.2.1 MEASUREMENT OF T H E STATIC BEHAVIOR OF ARCS
800
T h e experiments related t o the determination of static characteristics of arcs were developed in two steps. In the preliminary step, the static characteristics ( V - I curves) were measured for arcs generated between electrodes with two different t i p shapes and two different materials. T h e electrode t i p shapes are presented in Figure 2 a n d the materials used were brass a n d tungsten. T h e voltage vs. current ( V - I ) curves were measured for arc lengths of
m
2
4001
2oot
I
:
;
30
60
; 90 ARC
;
;
;
;
;
;
1 2 0 1 5 0 180 210 2 4 0 2 7 0 CURRENT ( m A )
Figure 3.
Preliminary results obtained for V - I curves.
; 300
,
~
459
Vol. 27 No. 3, June I992
IEEE Transactions on Electrical Insulation
2.3 RESULTS 12
2.3.1 STATIC BEHAVIOR
T h e preliminary results of V - I curves presented a discontinuity region as can be seen in Figure 3. Such discontinuity occurred similarly for all arc lengths (La), in a current range dependent upon L a . When performing measurements with the arc instability, a fa.st motion of the points of arc formation o n the electrode surfaces, both anode a n d cathode, was observed.
do
0;s
t 'k.
ALEb
900 +'\ 800
"t
+LAO
0TB-a
80
110
180 210 260 CURRENT (mA)
310
220mA
;5
I00 125 150 ARC LENGTH ( m m )
1;s
20.0
'
Figure 6
I
Arc voltage V, as a function of arc lengths Ri for some currents.
OLAb
I
-10
=
360
T h e V - I curves for all arc lengths (5, 10, 15 and 20 m m ) similar t o those of Figure 4 were then digitalized in order t o determine the arc voltage per unit length I/; a n d the anode-cathode voltage Vac,as well as the arc resistance per unit of length a n d the anode-cathode resistance Rat. T h e procedure used, shown on Figure 5, was based on a linear regression for the arc voltage Va as a function of L a = \?La (1)
va
+ vac
+
R a = RlLa R a c Figure 4. (2) V - I curves for arcs between brass electrodes with T h e variation of Va with La was linear a s shown by the rounded tip (LB), brass with needle tip (LA), experimental results in Figure 6. tungsten with rounded tip (TB) and tungsten with needle tip (TA). LAa, LBa, TAa and T B a belong to the upper part of the V - I curves; LAb, - - ? O O.€ ' LBb, TAb and T B b belong to the lower part of +.. \ the V - I curves. La = 5 mm.
'.
1.0 r
0.1 :
h '
I
TAa
""
Lo
20
QTBa 1
100
400
CURRENT (mA)
Figure 5. Procedure used to calculate K and Vac
Figure 7.
T h e V - I curves for arcs between electrodes made of brass a n d tungsten, with shapes shown in Figure 2 , d o not present any significant influence of the varied parameters (material a n d shape of electrodes) on the discontinuity region. One set of these results is shown in Figure 4.
n
Arc resistance Rt per unit of length
T h e values of RI a n d Raccalculated according t o Equation 2 with the experimental results are shown in Figures 7 and 8. It can be seen t h a t only the anode-cathode regions are affected by the phenomenon which produces the discontinuities in V - I curves.
Portela et al.: A r c Extinction in A i r Insulation
460
riiC
f
I
r X r b
>
,:x3
\
-BO
4 -70
5
5c
233
100
20
100
4OO
303
603
-0
700
CLRRENT (mA)
400
C U R R E M (mA)
Figure 10. r/; and
Figure 8. Anode-cathode resistance R,,
Vaccalculated according to Figure 5 from
results of Figure 9.
lomlFmI
combination of Equations 1, 3 a n d 4 are also shown in Figure 9 as solid lines. Table 1. Parameters values of Equations 3 and 4 Kange o f
('rrrrerits
Pd r a m e t e r s
- 0 . h36
0 040
01 0
100
L
ZOO
300
M30
400
I
600
I
700
I
1
1
7
1
70.9
97.6
800
CURRENT (mA)
Figure 9. I curves for arc lengths of 5, 10, 1 5 and 20 mm, brass electrodes with needle tip (dotted lines = measured, solid lines = calculated)
V
When the anode-cathode voltage can be neglected, i.e. for longer arcs, the arc power P = V a l , can be expressed a s function of the arc conductance g = I,/Va
-
In order to avoid possible complications caused by these discontinuities in the later analysis of the results on the arc dynamics, a new set of measurements was performed over a wider current range, from 100 t o 800 mA. T h e results are shown in Figure 9. T h e arc voltage per unit length V, a n d the anode-cathode voltage Vac were calculated from these results a n d are shown in Figure 10.
(5)
p=with
x and X
1SX 1-X
a s in in Equation ( 3 ) .
By using curve fitting techniques, the following equations were derived from Figure 10. __
v, = XI;
(3)
Range of '1 i n i e Wave S h a p c
F r o 11t t
n
vac
=y+
(4)
I, where I , = arc current, A, VI = arc voltage per unit of length, V / m , Vac = anode-cathode voltage, V, and x, A, y a n d q are shown in Table 1. T h e results from the
Fast
i IIIC'
0..5 t o 2 . 0 :,.I1
SI ow
I O
~~
IO.0
f'arameters
.- ..
(11s)
'IaiI 1. i we 10 t o 30
_____
- .~
;jo t < , (ill
3 0 0 t o ,500
____~__~
~
1
461
Vol. 2 7 N o . 3, J u n e 1982
IEEE Transactions on Electrical Insulation
Table 3 . Peak values of currents and voltages, medium waveshape, positive polarity for different arc length (La) and different operating points (vo, I o ) . I,, 130
51H
6 5 . fj
i
_ .
a
I
’
I
I
1
I
1
2.3.2 DYNAMIC BEHAVIOR
T h e waveshapes of the impulse currents injected in the arc were classified in three types (see Table 2):
--
1. Fast: currents with significant variations A I within lo-’ t o 1 ps. time intervals At of 2. Medium: within At of 10 ps. 3. Slow: within At of 10’ ps.
-
T h e peak values of impulse currents injected in the arc a n d their respective pea.k voltages are presented in Table 3 in the case of medium waveshape a n d positive polarity. T h e slope variations of dynamic V - I curves with the operating point (VO,Io) a t which the impulse current is injected are shown in Figures l l ( a ) a n d ( b ) . These slope variations refer t o the straight line, defined by the origin a n d the point Vo, Io.
3. ARC MODELING R O M results of already performed tests [2], it was no-
F
ticed t h a t t o have a correct representation of transient arcs, different physical mechanisms with a t least two different orders of magnitudes of ‘time constants’ are involved because: Different local conditions, a s is the case of anodecathode regions a n d regions far from anode and cathode in arc column, or different conditions, e.g. due t o air
ill
b
Figure 11. Dynamic V - 1 curves for arc with La = 5 mm and medium current waveshape. - - - Reference straight line defined by the origin and the point (Vo, l o ) , . . . static characteristic. macroscopic turbulence; and different rapid changes in what concerns global trical arc properties, as a consequence sion in the radial direction a n d electric axial direction.
relative effects of thermal and elecof heat transmisconduction in the
W i t h some physical consistency criteria, namely arc parameters independent of particular shape of small amplitude disturbances, though dependent on the arc operating point, a n d static characteristic satisfying a dynamic model, a rea.sonably simple model was found t h a t would avoid some inconsistencies of the single time constant models. It was found t h a t a model with two time constants, each of them associated t o a n equivalent sub-arc region, with the two sub-arcs in series or in parallel, allowed a reason-
Portela et al.: Arc Extinction in Air Insulation
4 62
ably accurate arc simulation t h a t satisfied all consistency criteria.
characterize the arc. Naturally, according t o the previous interpretation given t o J , the several parameters are not independent.
Two simple a n d , t o some extent, dual forms of t,he proposed model with two time constants correspond t o two fictitious arcs either in series or in parallel, with conductances g1 a n d gz, t o which electric power pl a n d pz are supplied.
4. CONSIDERATIONS FOR ARC
EXTINCTION CONDITIONS
T
following hypothesis can be considered related t o the parameters of t h e two time constants arc model:
HE
el = c , e2 =
cl
p0 = c l = c l J =
were the element J In(g:/gl) is related t o the interaction between the two fictitious arcs. T h e Mayr model may be interpreted in a simple and approximate way. For instance, considering PO is the power supplied by the arc t o t h e surroundings, a n d supposing the arc region is characterized by a heat capacity a n d a thermal conductivity related t o the surroundings and supposing a n electrical conductivity is a n approximate exponential function of the absolute temperature. In the two time constant model the same interpretation can be considered, supposing the total power supplied to the surroundings separated in two parts, (Po and (1 - ( ) P O and , supposing the heat transmission between the two regions is the parameter J .
where c is a constant. T h e approximate analytical determination of the arc extinction conditions, using the two time constant model, would be naturally more laborious than in the case with only one time constant [3]. However, for hypothesis ( l o ) , considered above, and for a circuit in parallel with the arc acting incrementally a s a n impedance 2 , in parallel with a current source a s in the Norton equivalent circuit, the limit condition of arc extinction is approximately similar t o t h a t for a one time constant model. In this case, the a a n d 0 values are the same for the two type models with a n equivalent time constant Be or A* equivalent t o A ; and with a n equivalent arc power Po,, or B equivalent B e .
For the sake of simplicity, the element J In(gz/gl) of Equations 6 a n d 7 may be replaced by J In(&gz/gl) with For instance, in the case of two time constants, with different values of J a n d E . In this form, the given parameters are interpreted a s sub-arcs in series E = (1 - ( ) / I , 0 2 >> 81 a n d ,5 a n d (1 - I ) not t o much ess than 1, the series model gives and sub-arcs in parallel E = [ / ( l - I ) . If E = 1, = 0.5, both formulations are obviously identical. For arc current i, arc voltage V I P = V/i a n d g = 2/17, then, for sub-arcs in series
J > O _1 - _1 9
p=V2 1 +-=r=r1+r2
91
Po ;
;
$e
E
ee 'Y (el
01
if
+ ( I
