Currents in the overhead transmission line lighting wire in case of single-phase short circuit

The algorithms for currents induced in a grounded lightning wire (LW) with single-phase short circuit (SC) calculation are considered. It is shown that the method of short-circuit current and current in LW simultaneous determination gives more correct results for the assessment of LW thermal resistance


Introduction
At the present time overhead transmission lines (OTL) are equipped with lighting wires (LW) containing fiberoptic communication channels (FOLW). FOLW technologically are grounded through even OTL tower by grounding device. In case of single phase short circuit (SPhSC) the damaged OTL phase current magnetic field induces the current in FOLW. This current magnitude should not be more than permissible thermal resistance. 220 кВ OTL with 46.956 km length and 326.75 m span length is made without transpositions. Network resistance from substation 1 (S1) side is Z S1 =0.932+j8.455 Оm, and from S2 side is Z S2 =0.841+j5.796 Оm.
Electromotive force Wk E , induced in LW wire to the span length l sp (km) by 220 kV OTL k phase k I current magnetic field is calculated by expression [2]: 3 220 kV OTL operating in the no-load operation mode SPhSC currents SC leed to the arc emission between OTL damaged phase and the earth (grounded object), with R A arc resistance. R A value for 220 kV OTL under 15 kA SC current is determined by lines in [3] and is: R A = 0.42 Ohm.
Consider the option when OTL operationg mode is no-load operation (NLO) with the connection of one side to the busbar source, and on the other -with the disconnection of all phases from the busbar. There were calculated SPhSC currents at different distances from S1 and S2 by use computer program «EMPVL», «OTL EMF» [4] computer program later modification. In case of equal distances from S1 with Z S1 and S2 with Z S2 the modules of the SPhSC current values powered by S2 are higher than modules powered by S1 because Z S1 >Z S2 . When calculating the currents induced in LW should focus on high SPhSC currents, i.e. the currents powered by S2. Figure 2 shows the lines of phase C2 (nearest to LW phase) SPhSC current module distribution along to 220 kV OTL for SPhSC distances 0.5, 5, 10 and 30 km from S2. SPhSC current module decrease with SC place distance from S2.   In case of SPhSC distance l SC2 = 0.5 km from S2 SPhSC current SCC2 I affect to the first two spans of LW, grounded on each tower i by means of grounding device (GD) resistance R GDi . The rest spans are a sequence of passive double-poles, rolling the input resistance of which from the end of the OTL to the end of its second span, we obtain the resulting resistance Z NE . We write a system of equations by the method of contour currents for scheme shown in Fiure 3:

Currents induced in LW for case of 220 kV OTL SPhSC in the no-load mode
; .
Resistansce Z NE value calculate. At fig. 4 The second packaging of input resistance etc. until the end of 2 nd span. After 50 packaging (16.34 km from S1 and 30.32 km from S2) resistance N-i Z ceases to change in thousandths of the real and imaginary parts, as both for GDN R = 0.5 Оhm, and for GDN R = 10 Оhm, and Z NE = N-50 Z = 1.245 + j0.809 Оhm. Initial data for the equations of system (4) Currents induced for chosen FOLW types are carried out under phase C2 SPhSC at l SC2 = 0.5, 5 and 10 km distance from S2. For example, consider phase C2 220 kV OTL SPhSC with FOLW-sh-1-24(G.652)-18.7/93 following at l SC2 = 5 km distance (see Figure 5).  . e e e e Z Z R R R The data for system of equations (5) Оhm; GDS R = 0.5 Оhm; GD R = 10 Оhm.
Solving the system (5), we obtain the values of induced in LW currents: There were carried out the calculations of the highest currents Wmax I under C2 phase SPhSC at l SC2 = 0.5, 1, 2, 3, 4, 5, 7.842 and 10 km distances from S2 for FOLWsh-1-24(G.652)-18.7/93 and FOLW-c-1-24(G.652)-12/94 (with the greatest differences in nominal radii r wLW and resistivities R LW0 ). Table 2 given distances l SC2 of SC points, number of spans Р КЗ , exposed by SC current magnetic field (MF), the values of C2 phase SC current SCC2 I as well as electromotive force WC2 E , induced in FOLW span by current SCC2 I MF. Current module histograms Wmax I shown in Figure 6.  On one side, as the distance l SC2 increase the number of LW span exposed to SCC2 I SC current rise, each of which adds FOLW longitudinal resistance, GD cross-resistance and longitudinal electromotive force WC2 E , which leads to current module Wmax I elevation.
But on another side l SC2 distance increase leads to SC current module SCC2 I decrease, induced by current electromotive force WC2 E reduce as well as Wmax I current value decrease. For considered 220 kV OTL the process of W max I current value increase prevails for distfances from SC point l SC2 < 5 km, and for distances l SC2 > 5 km process of SCC2 I , current value decrease as well as current decrease prevails. Thus when l SC2 = 5 km W max I current reaches its greatest value W max I = 5480 А for FOLW -sh-1-24(G.652)-18.7/93 and T max I = 3100 А for FOLW -c-1-24(G.652)-12/94.

Currents in LW under no-loaded mode OTL two self-titled phases SPhSC
Concider the rare but possible case when in 220 kV OTL at l SC2 = 5 km from S2 there are simultanious SC selftitle phases С1 and С2 on the earth (see Figure 7). The greatest value of induced in LW current module is at the 6th span, where W6 I = 6.296 kА, аnd according to table 1, FOLW-sh-1-24(G.652)-18.7/93 1 s withstand the 18.7 kА short-circuit current, i.e can operate with more than a double margin for thermal resistance.
6 Currents induced in LW by magnetic field of 220 kV OTL, operating in the connected mode, but without power transfer SPhSC Figure 8 shows the scheme of calculation the currents in case of 220 kV double-circuit OTL, operating in the connected mode, but without power transfer, C2 phase SPhSC. SC point is located at 5 km distance from S2. Fig. 8. The scheme of calculation the currents in case of 220 kV double-circuit OTL, operating in the connected mode, but without power transfer, C2 phase SPhSC С2 phase l = 46.956 km length consists of 142 spans and is diveded into two parts: l 1 = 5 km from S2 to SC point contains 15 spans, and l 2 = 41.956 km from SC point to S1 contains 127 spans. Since the capacitive resistances between phase and SC arc earth of C2 phase both parts are shunted by resistance R D = 0.42 Оhm, currents in capacitive resistances (tens of kOhm) are neglected. C1 phase is represented by T-shaped replacement circuit. I 3 and I 4 currents are oppositily directed, I 7 and I 8 currents are in the same direction, but opposite I 3 current.  Figure 9 shows the diagram of the phases C1 and C2 with SC currents, combined with the circuit grounded at the ends of wire W spans.   Figure 9, by the method of contour currents we obtain: Resistance values: Z W + Z e + R GDS + R GD = 10.580 + j0.2375 Оhm; Z W + Z e + 2R GD = 20.080 + j0.2375 Оhm; Z W + Z e + R GD + Z NE = 11.334 + j1.0465 Оhm; Z NE = 1.245 + j0.809 Оhm; R GDS = 0.5 Оhm; R GD = 10 Оhm.
Solving the system of equations (6), we obtain the currents in LW I Wi = J i . Current I Wi modules distribution along OTL is shown in Figure 10. 220 kV OTL operating in the connected mode at both ends, but without power transfer SPhSC at 5 km distance from S2 leads to induce in LW current with maximal module value I Wma x = 5,152 А in 5th span, but it is less than I Wma x = 5,480 А under SPhSC in the same OTL in no-load mode.

Simultaneous determination of SC currents and induced in LW currents
The considered methods for calculating the currents induced in LW by SPhSC current MF do not take into account SC current itself passage in LW from SC point to the phase electromotive force (voltage) in the line beginning, for example C2 E . Figure 11 shows the scheme of simultaneous SC current at 5 km from S2 distance and currents in LW determination for 220 kV OTL in noloaded mode. Figure 11: R С2 + jX LС 2 -phase C2 wire in single span resistance-inductive reactance; R W + jX L W -wire LW in single span resistance-inductive reactance; Z e -resistance to reverse current in the ground for a single span; Z WC 2 -mutual inductive reactance C2 phase and LW in span, obtained by equation (2); R S 2 + jX LS 2 -network resistance for S2; Z NE -resulting resistance after wire passive two-terminal network folding withрезультирующее сопротивление после сворачивания пассивных двухполюсников троса with step l sp = 0.33 km; R GDS = 0.5 Оhm -S GD resistance; R GD = 10 Оhm -OTL tower GD resistance; R D = 0.42 Оhm -SC arc resistance; C2 E = 127,017∠120° V -C2 phase electromotive force. Let us formulate a system of equations by the method of contour currents: