Short-Circuit Design Forces in Power Lines & Substations



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SHORT-CIRCUIT DESIGN FORCES IN POWER LINES AND SUBSTATIONS1 1. INTRODUCTION Short-circuit currents in power lines and substations induce electromagnetic forces acting on the conductors. The forces generated by short-circuit forces are very important for highvoltage bundle conductor lines, medium-voltage distribution lines, and substations, where spacer compression forces and interphase spacings are significantly affected by them. Power Lines and Substations Short-circuit mechanical design loads have been a subject of significant importance for transmission line and substation design for many years, and numerous papers, technical brochures and standards have been published (Manuzio 1967; Hoshino 1970; Havard et al. 1986; CIGRE 1996; CIGRE 2002; IEC 1993 and 1996; Lilien and Papailiou 2000). Under short-circuit forces, there are some similarities and some differences between the behavior of flexible bus and power lines. For both the power lines and substations, the electromagnetic forces are similar in their origin and shapes because they come from short-circuit current (IEC 1988). Nevertheless, as listed below, there are some major differences between short-circuit effects on substation bus systems and power lines:  Power lines are subjected to short-circuit current intensity, which is only a fraction of the level met in substation bus systems. The short-circuit level is dependent on short-circuit location, because longer lengths of lines mean larger impedance and lower short-circuit level. The level also depends on power station location and network configuration.  Power line circuit configuration may not be a horizontal or vertical arrangement, thus inducing other spatial components of the forces than in bus systems, and the movement may be quite different.  Power lines have much longer spans and thus much larger sags than flexible bus and rigid bus. This induces a very low basic swing frequency of the power line span (a fraction of one Hz). Therefore the oscillating components of the force at the network frequency (and its double) have negligible action on power lines.  Power line phase spacings are much larger than those in substations, and this has a dramatic reduction effect on forces between phases.  Bundle conductors in power lines have much larger subspans than in substations, and bundle diameter is often larger, too. Sometimes very large bundle diameter and a large number of subconductors are used compared to bundled substation flexible bus. This has significant effects on the phenomenon because long subspans reduce the effect of bundle collapse upon the tension in the subconductors during short circuit conditions. Fig. 1 demonstrates the distortion of the subconductors of a quad bundle around a flexible spacer during a short-circuit, known as the pinch effect, which causes the tension increase.  Due to differences in structure height and stiffness, power line towers have significantly lower fundamental natural frequencies than substation structures. One result is that the substation structures are more likely to respond dynamically to the sudden increase in tension that results from the pinch effect. 2 the subconductors move towards each other. remaining more or less parallel in most of the subspan. which for power lines is typically around 40 to 100 ms after fault inception. If the short circuit is long enough. and these instantaneous compression loads can be very high. can be further increased by the rise in tension in the subconductors due to bundle collapse. Spacers are subjected to compression forces. a 40 kA fault on a twin bundle of 620 mm2 conductor. The pinch is maximum when the wave propagation stops towards the spacer. Figure 1 Example of quad bundle before and during short-circuit test at 50 kA. After first impact. Detailed discussions of this phenomenon were given by Manuzio and Hoshino (Manuzio 1967. Therefore design loads due to short circuits may be of the same order as design wind and ice loads in substations. 3 . This jump results from the fact that subconductor length in the collapsed condition is greater than in the normal condition. During the fault. From their initial rest position. sequence c-d-e of Figure 2. For example. or “pinch. the pinch oscillations result in a “permanent” oscillating force. depending on the instantaneous current value. the subconductors of the bundle move closer to each other due to strong attraction forces because of the very short distance between subconductors (Figure1). The inward slope of the subconductors at the spacer results in a component of subconductor tension that tends to compress the spacer. typically 50%. showing distortion of the subconductors. Power line design load includes severe wind action and in some cases heavy ice loads acting on much larger spans than in substations. the spacer is strongly compressed. Hoshino 1970). position e in Figure 2. This compressive force. The compression is related to maximum pinch force in the conductor and the angle between the spacer and the subconductor. The triangle of collapse then performs oscillations through positions d-c-d-e-d-c-ed-c and so on as long as electromagnetic force is still on. except close to the spacer (Figures 1 and 2). but much less in transmission lines. there is a rapid propagation of the wave in the noncontact zone near the spacers. The subconductor movements occur at very high acceleration. with a separation of 40 cm. during a fault.” while it is associated primarily with the change in angle. One flexible spacer at mid-span (courtesy Pfisterer/Sefag). sensibly lower than peak value. but with decreasing amplitude. Bundle Conductor Lines For bundle conductor lines. may have acceleration up to several tens of g. tdee. but does not reduce the maximum forces on the spacers occurring during initial impact. The momentum from the impulse carries the phases outward for a certain distance before their tension arrests and reverses the motion. Interphase Effects and Distribution Lines The video available on my web site (http://www. independently of whether the phases are bundled. Figure 2 Attraction of subconductors of a bundle at a spacer during a short-circuit (Manuzio 1967). They then swing inward.Upward movement of the whole span follows the rapid contraction of the bundle and reduces the conductor tension.ulg. Fault currents produce an impulse tending to make the separate phases of a circuit swing away from each other. The impulse that causes this lasts only as long as the fault.ac.be/doc-5. so it is brief relative to the fundamental period of the span. flexible bus and high-voltage overhead lines and distribution lines.html) contains some short-circuit tests on rigid bus. This inward swing may be 4 . Even though the inward swing could be short of interphase contact. Substation with rigid busbars The behavior of a rigid bus under short-circuit load is very depending of its first natural eigenmode and eigenfrequency. up to several times the initial sag in distribution lines. Figure 3 Instantaneous position of the conductors taken during three-phase short-circuit test on 15-kV distribution line near Liège (Lilien and Vercheval 1987). Indeed electromagnetic forces includes pseudo-continuous component combined with a 50 Hz and a 100 Hz component. This is from an actual three-phase short-circuit test on a 15-kV distribution line near Liège. thus causing outages on both circuits. There may also be sag increases. The transient response is thus very depending on the voltage as low voltage (say 70 kV) would have a short bar length and a reduced size tubular bar. Very large movements may be seen on distribution lines. 5 . For double-circuit towers. So that dynamics of such structures is far from obvious and case dependent. Some example are shown on the next figure. and the inward swing occurs at the time that voltage is restored by automatic reclosure. which may significantly affect the amplitude of movements. if the phase spacing is less than the critical flashover distance. The photo shows an instantaneous position of the conductors taken during the test. Belgium (Lilien and Vercheval 1987). the circuit subjected to the short circuit could force its phases to come in contact with another circuit. Figure 3 shows the motion produced during full-scale testing on an actual line. The fault current level was 3 kA. even if the short-circuit level is much lower. due to heating effects under short circuit.large enough to cause cable contact and even permanent wrap-up at the middle of the span. close to 50 Hz for 150 kV level. there will be a second fault. Moreover the busbar is installed on supporting insulators which have their own eigenfrequencies. when high voltage (typically 400 kV) would have long bar length and large tubes. The reduction in phase spacing may be particularly dramatic on mediumvoltage lines. 1996). I2. Short-circuit of 16 kA during 135 ms with automatic reclosure after 445 ms and a second fault of 305 ms with same amplitude as the first one.7 Hz and 150 Hz.Fig xx : rigid busbar response to ta given electromagnetic force similar to a two-phase fault with asymmetrical component in the short-circuit current. Measurement points are located as S2. (extract from CIGRE brochure N° 105. 1996). The transient response is given for different busbar first eigenfrequency between 1. Fig xx : a tested rigid bus (all details in CIGRE brochure 105.C3 (constrains). 6 . The first eigenfrequency of the whole structure is about 3. the second fault induced about twice as much constrains compared to the first fault. as time to reclosure was particularly dramatic compared to structure oscillation. There is quasi no effect of the 50 Hz nor of the 100 Hz component of the force.3 Hz. 7 .Fig xx test results. As damping was negligeable. only one current is involved. For a single-phase fault.  t  i1 (t )  2 I rms (sin(t   )  e sin( )) t  2 2  i2 (t )  2 I rms (sin(t    )  e sin(  )) 3 3 t  2 2 i3 (t )  2 I rms (sin(t    )  e  sin(  )) 3 3 (Amperes) 1 Where Irms is the root-mean-square value of the short-circuit current (A). and although the system through which the fault passes is multimesh. because the ratio X/R.i3 (t ) i2 (t ). is much less at low-voltage level. = 2f is the network pulsation (rad/s) equal to 314 rad/s in Europe and 377 rad/s in the United States. The force acting between subconductors of the same phase is an attractive force.or a two-phase arrangement. FAULT CURRENTS AND INTERPHASE FORCES A short-circuit current wave shape consists of an AC component and a decaying DC component due to the offset of the current at the instant of the fault. typically 20 to 80 ms. is an angle depending on the time of fault occurrence in the voltage oscillation (rad). and even more in lowvoltage lines. applied on each of the phases can be expressed by: 0  i1 (t ). According to the basic physics of electromagnetism for a three. as discussed in Section 3. it is possible to have no asymmetry if = 0 rad. the global time constant of the system “” is rather low.i2 (t ) i1 (t ). In high-voltage lines. In the case of a two-phase fault. Fn(t) in N/m. In the case of bundle conductors. reactance to resistance.i3 (t ) F2 (t )  0 x  1   2  a a    i (t ).2. the force. compared to substations where it is typically 70 to 200 ms. Asymmetry is very dependent on .i3 (t ) F3 (t )  0 x  1  2  2a a   F1 (t )  (N/m) 2 Where 8 . it is generally considered that the short-circuit current is equally divided among all subconductors.i2 (t ) i2 (t ).i3 (t ) x   2  a 2a     i (t ). there is always a repulsion force between phases from each other.  is the network time constant (= L/R) at the location of the fault (s). it can usually be assigned a single “global” time constant for the decay of the DC component. The AC component generally is of constant amplitude for the duration of the fault. In the general case of parallel conductors. In the case of a three-phase fault. The same location in a network gives two different values of current for three. the force is unidirectional and has a significant continuous component. arrangements. For example. it is much more complex. with a time-constant decay. being due to current flow. and the short-circuit duration is 0. Figures 4 (top) and 5 give examples of currents and forces on horizontal. It generally includes:  Pseudo-continuous DC component.245 seconds. illustrated by the top view of Figure 4.866 between them. which is not damped. In the case of a two-phase fault. very much depends on phase shift between currents. and one at the double of the network frequency. This is for a horizontal or vertical arrangement of the circuit.4. sometimes. The current frequency is 50 Hz.8 kA three-phase fault would give a 30. On phase 2.or two-phase faults with a ratio 0. The force.2 kA. and  Two oscillating AC components. 9 . one at network frequency. Thus it always has the same direction—that is. and at least one of the outer phases has forces similar to those generated by a two-phase fault (Figure 5 left). On the outer phases.39 rad). a is the interphase distance (m). the continuous component is zero (except during the asymmetrical part of the wave). The repulsion peak load on phase 1 is 228 N/m. Figure 5 shows the currents and forces applied to each phase during a three-phase fault with an asymmetry chosen to create the maximum peak force on one outer phase as calculated using Equation 2.  Continuous dc component. or purely vertical.1 kA two-phase fault at the same location. The fault current is 34. (= 1. But the time dependence of the forces is very different on the outer phases compared to middle phase.8 kA rms with peak currents of 90. In the case of an equilateral triangular arrangement. with a time-constant decay. The time constant is 70 ms. In flat-phase configuration. Figure 4 (bottom). 79. the force is proportional to the square of the current. a three-phase fault has to be considered for estimation of design forces. Therefore. The loads shown are per unit length for a = 6 m clearance between phases.2. the middle phase has a zero mean value. The signs convention is positive in the directions shown in the upper diagram in Figure 4.0 is the vacuum magnetic permeability = 410-7 H/m. and 61. similar to the force on phase 1 for the horizontal arrangement. a 34. the forces are similar on all three phases. a repulsion between the two faulted phases. about 200 N/m in Figure 5. But the continuous component is much lower. in the other direction. it is closer to the conductor weight. Under actual shortcircuit levels and clearances. 2. Figure 5 Example of calculated three-phase short-circuit current wave shape and corresponding loads on a horizontal or vertical circuit arrangement. is far greater than the conductor weight and is proportional to the square of the current.Figure 4 Two different geometric arrangements for a three-phase circuit and the electromagnetic force reference directions on each phase corresponding to Equation 2. about 30 N/m in this case. 10 . but acts. It must be noted that the level of the peak force. as shown later. in most cases. and 3 are phase numbers. See upper right panel in Figure 5. The numbers 1. in Figure 5.75  1.  is the network time constant at that location (s). For example. The continuous dc component acting after the short transient during the asymmetrical period of the current is obtained by using t = infinity in Equation 3. may be summarized as: 1.3 N/m 6 11 . because the structural response to these loads has to be taken into account.2 2 I 3 (0.82 x0. the continuous dc component after transient is given by: F 0. 2. Taking into account the fact that only the continuous dc component has to be considered. for the case of horizontal or purely vertical arrangement only.Thus the interphase effects. or the vertical repulsion force for the vertical arrangement: F 0. t is time (s). the force on an outer phase can be approximated by Equation 3.75  30. This is the horizontal repulsion force for the horizontal arrangement.2 34. The design force on the horizontal or vertical three-phase arrangement is the force due to a three-phase fault considering the outer phase with appropriate asymmetry.616e 2t / ) a (N/m) 3 Where a is the interphase distance (m). The forces considered above cannot be directly applied to structure design loads. I3 the rms three-phase fault at that location (kA). 7 mm. (Lilien and Papailiou 2000).3. with the following characteristics (Figure 6): Span length 60 m Sub conductor type ACSR CONDOR (455 mm². BEHAVIOR OF BUNDLE CONDUCTORS UNDER SHORT CIRCUITS Detailed behavior of bundle conductors under short circuit is most easily illustrated through short-circuit tests in actual bundles.2 s Sagging tensions 15. Time constant 33 ms Duration 0. the return path is through the ground Supporting structure: Stiffness: about 8. The systematic single-phase fault tests on twin conductors were performed in the 1990s on a power line with a double deadended span. 25.17 to 0. UTS 125 kN) Spacing 0. Some results from a program of tests at the Veiki substation in Hungary are used here for that purpose (Lilien and Papailiou 2000).52 kg/m.457 m Current 35 kA (90 kA peak). 60 m measurement 12 .  = 27.5 106 N/m First eigen frequency: about 14 Hz Figure 6 Test arrangement applying short circuits to a 60-m span length with one spacer at mid-span. 1. with a length of 60 m. or 35 kN (per subconductor) All cases are single-phase faults. 4 0.8 1 1. the 60-m span length results are presented.4 0.6 0.2 0. The installation of measurement is such that actual load for spacers in power lines would be twice the measured value.4 -1000 -1000 -2000 -3000 -2000 time (s) subspan length 60 m time (s) subspan length 30 m 13 . and on the right-hand side. and that the other “spikes” in the records arise from subsequent motion of the bundle.35/90 kA 6000 4000 5000 3000 4000 3000 2000 C om pressiveloads(N ) com pressiveload(N) 2000 1000 0 0 0.2 seconds.30 m 30 m measurement Figure 7 Two test span arrangements for spacer compression tests (Lilien and Papailiou 2000). the 30-m span length results are presented. Sagging tension 15 kN . The following oscillograms were recorded (Figure 8).2 1.35/90 kA Sagging tension 15 kN . two spacers were installed close to each other so as to receive half the contribution. On the left hand side. while the fault current is on.8 1000 0 0 1 0.2 0.6 0. It should be noted that the actual “pinch” occurs during the first approximately 0. For the 30-m sub-span. Figure 7 shows installation of rigid spacers and measurement points (bold lines) for the 60-m subspan (Figure 7 top) and 30-m subspan (Figure 7 bottom). 30/90 kA 6000 6000 5000 5000 4000 4000 3000 Compressive loads (N) 7000 Compressive loads (N) 3000 2000 1000 2000 1000 0 0 0 0 0.2 2000 0 0 1. The effect on propagation speed can be seen in the after short-circuit peaks.30/90 kA 7000 Sagging tension 35 kN .8 1 1.4 0. and it 14 . During that transient.2 0. because some spacer attachments are not as strong in tension as they are in compression. the level of which reach about 50% of the maximum compression load.4 0.8 1 1.4 -1000 -1000 -2000 -2000 -3000 -3000 time (s) time(s) subspan length 60 m subspan length 30 m Figure 8 Typical tests results on spacer compression on 60-m and 30-m subspan length.5% EDS) to 35 kN (28% EDS). A particular example is the attachment using an open or “saddle” clamp.35/90 kA Sagging tension 25 kN .2 1.4 0.6 0. with different sagging tensions. with wave propagation along each subspan (as can be seen in the video that accompanies this book and in Figure 8).8 1 1. The drawings are covering short-circuit and significant after short-circuit time to better see the wave propagation effects after the end of the short circuit.2 0. at 35 kA on twin-bundle line 2x Condor.6 0. but the influence on maximum pinch is limited in actual range.35/90 kA 8000 8000 6000 6000 4000 Compressive load (N) Compressive loads (N) 4000 2000 0 0 0. with helical rods to capture the subconductor. The graphs in Figure 8 show the effect of gradually increasing initial tension before the fault from 15 kN (12. Note the shorter repetition time in the 30-m span.2 0. significant tensile forces (the opposite of compression) are applied on the spacers. These loads are repeated with every passage of the wave up and down the span. These loads decay very slowly. Half of the compression is given.4 0.2 1. the effect of these tension forces on the spacer must be considered separately.4 1. so that many repeated such loads have to be taken into account.Sagging tension 25 kN .6 -2000 -2000 -4000 -4000 time (s) time (s) subspan length 30 m subspan length 60 m Sagging tension 35 kN . After the short circuit.6 0.6 0. as predicted by Manuzio (the pinch being proportional to the square root of the tension). (Courtesy Pfisterer/Sefag). the subconductors separate from each other during a long transient. In spite of their smaller magnitude.2 1.4 0.8 1 1.4 0.2 0. as the phase falls. due to the increment in tension caused by the pinch. In these tests. Depending on the configurations of the spacer and spacer dampers. This behavior induces some tension changes in the conductors. 15 . In both cases.8 times the initial static sagging tension. as used in power lines and as validated by Manuzio’s test arrangements (Manuzio 1967). the whole phase jumps up after short-circuit inception and falls down afterwards.9 seconds. which could be compressed by the pinch.is particularly valid for long subspans. limited to one-phase fault. there is no interphase effect but. as can be seen in Figures 9 and 10. the latter is limited to 1. for the 60-m span length configuration (15 kN initial). the short-circuit forces could cause large bending moment in the conductor and the elements of the spacer.18 s) in the conductor has a smaller tension rise than that which occurs. 0. at 0.18 s courtesy Pfisterer/Sefag). In case of spring-type dampers. Irms 35 kA (peak 90 kA). Figure 9 Typical tension oscillogram in one subconductor during and after the fault. It is notable that the pinch effect (the first peak during the fault in the first 0. there could be a large increase of these tensile loads acting on spacer attachment as the relaxation of energy stored in spring compression during short-circuit is released after the end of the short circuit. Figure 10 Typical tension oscillogram in one subconductor during and after the fault for the 2 x 30-m span length configuration (15 kN initial). Of course. Lilien and El Adnani 1986]). Subconductor Separation Effect A closer bundle spacing results in a smaller increment in subconductor tension. For the power lines with typical subspan lengths. Smaller conductor separation thus leads to less deformation in that area. At the limit. Irms 35 kA (peak 90 kA). 16 . and most of deformation is located in those triangles. that length depends on short-circuit level and some other parameters. There exists a critical subspan length under which no contact is possible and over which contact occurs on a significant part of the subspan. Subspan Length Effect Bundle pinch is very much related to subspan length. initial electromagnetic force are stronger. but the tension increment is generated by conductor deformation into the triangles of Figure 2 after contact. if conductors are in contact all along the span.18 s. 0. That critical value corresponds to extreme loading (for pinch effect in substations [El Adnani 1987. In fact. there is no increment in tension. subconductors experience contact in all cases except in jumpers. (courtesy Pfisterer/Sefag). Maximum swing-out Ft (at time tt in Figure 11left and square 1 in Figure 11 right): very little kinetic energy (cable speed close to zero) and potential energy with reference to gravity. tt occurs always after the end of the short circuit (the cable position at the end of the short circuit (0.4. Three maxima: F pi at time Tpi (so-called pinch effect. 2. Tpi -40 ms. Maximum Ff at the extreme of downward motion (at time t f in Figure 11 left and square 2 in Figure 11 right): generally more critical because of a loss of potential energy of gravity due to the cable position at that moment. 3. Peak design load could occur under the following three conditions: 1. Ft at time Tt (the maximum of the force due to maximum swing of the span represented by circle point 1 on the right figure). Typical maximum loads (Figures 11 and 12) that could influence design appear when total energy (including a large input during short circuit) has to be mainly transformed to deformation energy. In power lines. Figure 11 Left Figure: Tensile force (left) time evolution of a typical twin-bundle span during two-phase short circuit between horizontal phases. so that a large part is converted in deformation energy—that is. and in particular to show that the short circuit ends before there is significant movement of the phase. the curve has been marked by dots every 0.1 s to get an idea of the cable speed. Typically. increase of tension. INTERPHASE EFFECTS UNDER SHORT CIRCUITS Maximum Tensile Loads during Movement of the Phases Figure 11 shows a typical response of a bundle conductor two-phase fault in a horizontal arrangement (CIGRE 1996).1 s) is indicated in Figure 11 right). Both cable tension versus time (Figure11 left) and phase movement in a vertical plane at mid-span (Figure 11 right) are shown. Tt +1. On the phase movement curve at mid-span. On the cable tension curve. due to bundle collapse). The pinch effect Fpi (at a very short time after short-circuit inception at t pi). tf always occurs after the end of the short circuit. and F f at time Tf (the maximum of the force due to cable drop represented by circle 2 in the right figure.2 s and Tf = 4 s 17 . The pinch effect only occurs with bundle conductors. when subconductors come close to each other: tpi always occurs during short circuit. three maxima (and their corresponding time on the abscissa) have been indicated. which is discussed below. 1 s end of short circuit being noted on the figure) on a 2 X 570 mm 2 ASTER on a 400-m span length (sag 10 m) (Lilien and Dal Maso 1990). It can be seen that cable tensions due to short-circuit currents are significantly smaller than other causes such as ice shedding. Z is vertical. Figure 12 shows cable tension versus time in different dynamic loading conditions. Other cases are shown in Figures 13 and 14 (only the rectangular envelope of the movement is given) for different configurations and short-circuit level. with all its consequences (power outage). R. That would induce a second fault with the dramatic consequence of a lock-out circuit breaker operation. and X is horizontal and transverse to the cable). Such movement has been calculated for a two-phase fault of 63 kA (duration 0. The timing of this inward swing may be such that the phase spacing is less than the critical flashover distance at the time that voltage is restored by automatic reclosure. three-phase fault of 72. as explained in the legend. It is interesting to compare the level of these loads with typical overhead line design loads related to wind or ice problem (Electra 1991). Figure 11 shows results of such a case calculated by simulation on a typical 400-kV overhead line configuration. and S in Figure 13) for loading conditions (Lilien and Dal Maso 1990): 1. the phases move towards each other. For the case illustrated in Figure 11. two-phase fault of 63 kA 3. That means a phase-spacing reduction of more than 8 m. initial wind of 60 km/h followed by a gust at 100 km/h for 5 seconds on a quarter of the span 4.3 kA 2. perpendicular to the cable. this inward movement exceeds 4 m per phase. Figure 12 Simulated longitudinal loads applied on attachment point on a cross arm on a “Beaubourg” tower (the circuit configuration is shown by points T. shedding of ice sleeve of 6 kg/m Reduction in Phase Spacing After the initial outward swing. -10 m is the initial point showing sag. 18 .Right figure: Movement of one phase (right) in a vertical plane at mid-span (X and Z are the two orthogonal axes taken in the vertical plane at mid-span. S. or TS 2. Figure 15 shows a case of two circuits on the tower. How to estimate the required interphase spacing is discussed further in Section 5 (Equation 8) 19 . inducing a fault in the other circuit so that both circuits trip out. where the faulted circuit forces some of its phases to get in contact with the second (healthy) circuit. and T are their phase locations in still conditions) (Lilien and Dal Maso 1990): 1. initial wind speed of 60 km/h followed by a wind gust at 100 km/h during 5 s on a quarter of the span.3 kA 3. Distribution Lines As mentioned earlier. two-phase short-circuit 63 kA either RT.Figure 13 Calculated envelopes of phase-conductor movements for three types of loading conditions on a “Beaubourg” tower (the figure is drawn in a vertical plane located at midspan: R. RS. three-phase short-circuit 72. Figure 14 Calculated envelope of phase-conductor movements for two-phase faults of different rms amplitude (Lilien and Dal Maso 1990). very large movements may be seen on distribution lines (Figure 3). 20 . conductor 93.4 s.1 s.Figure 15 Three-phase short-circuit on 15-kV line (left circuit). b = 0. with autoreclosure.4 s end of the second fault and definitive removal of the voltage on the line. Short-circuit of 2700 A on a 165-m span length. a = fault inception. time of reclosing. and d = 1. c =0. end of the first fault.3 mm2 AAAC (Lilien and Vercheval 1987). I is the rms short-circuit value/phase (kA). The loads under no. For power lines in general. Fc  kI Fst log10 ( s / s ) (N) 4 Where: Fst is initial sagging tension for each subconductor (N). Stein et al 2000) may be used for any situation. since these events cannot occur simultaneously. be taken separately. related to subconductor separation “as” by the formula (n = number as of subconductors): s  (m) 5 sin(180 / n) s is the subconductor diameter (m). there may be seven different loading conditions.57. but particularly for distribution lines: reduction in phase spacing (Equation 8 for high-voltage line). kquad = 1. Since there are three ways to have one phase fault. 3 above due to short circuits should be considered by line designers by including them in the loading schedule for structures.27. of course. Wendt et al 1996. Bundle Conductors in Transmission Lines Manuzio developed a simple method for spacer compression effect in bundle conductors (Manuzio 1967). and generally having negligible effect compared to other kind of loading: tension increase generating longitudinal and transverse loads (Equation 7 for longitudinal load due to interphase effect). ktripple= 1. El Adnani 1987. s is the bundle diameter. and one to have a three-phase fault. For bundle conductors: spacer compression (Equation 4). Example: 21 . They must. To a much lesser extent.44. Advanced calculation methods (Lilien 1983. ktwin = 1. 2. 3. Declercq 1998. k is a correction factor depending on the number of subconductors.5. ESTIMATION OF DESIGN LOADS The most critical effects on power lines are: 1. three to have a two-phase fault. and conductor separation is increased compared to a spacered bundle. 1993) on spacer dampers for power-line-estimated spacer-compression design load up to 20 kN for typical configurations and anticipated short-circuit levels. but must take into account insulator chain movement during the first tens of milliseconds of the fault to arrive at an equivalent stiffness (which in fact would permit evaluation of span end movement.57 x35 25000 x log10 (0. Moreover.Consider a case of a short circuit of 35 kA (rms/phase) acting on a twin ACSR Condor (27. Lilien and Papailiou 2000). Alternatively. from short-circuit inception up to the maximum pinch value. Other methods to estimate spacer compression forces have been proposed (Hoshino 1970. At such current levels. But IEC 60865 gives no recommendation for spacer compression. It has been used up to the 245-kV level for twin bundles of limited diameter. Equation 4 gives a spacer compression force of: Fc  1. but using Fpi pinch value instead of initial static pull.” In this application. tensioned at 25 kN/subconductor.0277)  9586 N However. It may not be accurate enough for use with respect to substation flexible bus. there is a need to introduce the socalled “ supporting structure stiffness. if we define Fpi (as shown in Figure 11) as the maximum tensile load in one subconductor during the bundle pinch. nevertheless. thus reducing acting parts of the conductors.457 / 0. after about 40 to 90 ms. Such configurations may suffer from the “kissing” phenomenon under high electrical load. It can be shown 22 . F pi can be evaluated by IEC 60685 method. Note: In the use of IEC method 60865 to evaluate Fpi. Manuzio’s method can be safely applied to faults with maximum asymmetry through a correction factor of 25% (multiply all k factors by 1. Manuzio’s method is very simple to apply compared to other methods. Despacering as a Means to Limit Pinch Effect Despacering (removal of spacers) is an antigalloping measure (see Section 4. 0. short-circuit current asymmetry was neglected.7 mm diameter) conductor with 0. That has been taken into account in IEC 60865 for evaluating the maximum tension in the conductor during fault. Pon et al. 1993.457 m conductor separation.8 m at mid-span. Fpi increases linearly (and not with the square) with short-circuit current. the bundle is turned in vertical or slightly oblique position. the electrostatic repulsion (due to voltage) cannot be neglected. Some tests performed in Canada (Pon et al. In fact. In such cases. because electromagnetic forces also act under load current. that stiffness is not simply the static stiffness of supporting structure. An heuristic evaluation indicates that a good estimate for such equivalent stiffness may be to consider in most of the practical cases a value of 105 N/m. it has been recommended to use larger subconductor spacing at the middle of the span (compared to end of the span)— for example.6 m at ends and 0.5) for some power lines. in the analysis by Manuzio (Manuzio 1967). That is because a stronger short-circuit current will increase contact length.25). another best fit would be to use Manuzio method (without correction factor). One of the major problems of such configurations is linked to possible sticking of the subconductors following a perturbation.that. Under short circuit. f = initial sag (m). L = span length (m). The energy imparted to the conductor is given by: 23 . and it is very difficult to separate them without opening the circuit. Interphase Effects: Estimation of Tension Increase and Reduction in Phase Spacing The following discussion pertains to the case of horizontal/vertical configuration and neglects temperature heating effects (Lilien and Dal Maso 1990). the conductor clashing destroys these light spacers beyond a certain level of short-circuit current. at surge impedance loading (SIL). so that attraction forces are generally stronger than repulsion. Irms = root mean square of the three phase short-circuit current/phase (kA). line designers have developed several proposals like the “hoop” spacer (see Section 4. Tst = phase conductor static tension before the fault condition (N).5). equilibrium exists between attraction and repulsion forces. EA/L = conductor extensional stiffness (product of Young modulus times cross section divided by span length) (N/m). R = maximum displacement (m). these configurations result in clashing between subconductors and. tcc = duration of the fault (= time of first fault + time of second fault if auto-reclosing) (s). there exists a distance under which the subconductors always come together and stick together.  = time constant of the short-circuit asymmetric component decay (s). a = interphase distance (m). Sticking induces large permanent noise and increase in corona. To avoid such problems. there is little increment in tension. Power flows are often several times (up to four times) the SIL. K = tower stiffness (N/m) (order of amplitude 105 N/m). m = mass per unit of length of one phase (kg/m). in the case of hoop spacers or similar. 1. Only one span is considered. As electromagnetic forces depend on distances. But. as “subspan” length (= span length in this case) is very large. But phase spacings can be critical when the phases move back towards each other.6 R. 3L (Joules) 4 6 2. The maximum displacement of one phase (zero to peak):   2  E0  2 R2   f   f 2  mgL  3   8 That maximum may be observed in the case when the conductors are moving away from each other. 80% of the separation movement). 24 .2 I rms E0  m   2  a. The maximum tension in the conductor during movements: Tmax  Tst2  2 E0 L 2  EA K 7 3. In this case. the clearances may be reduced (the most dramatic case being a two-phase fault) by 2 x 0.m  2 . in which case there is generally lower displacement (say.2 (tcc   ) 1  0.8 x R or 1. 2 = 8.32 m.2 m Thus the reduction in phase spacing is 2 x 0. Example: For example.2 x 632 (0.6 x 1010 N/m2 and tower stiffness of K= 5 x 105 N/m.5 .81x 400   3 3     2  9. for example.m  2  0.3 = 0. consider the following: Short-circuit current at 63 kA during 100 ms (with time constant 60 ms) on a twin ASTER 570 mm2 (m = 2 x 1.8.1x9.1   4 2  8. the results are: E0 = 2812 Joules Tmax = 66270 N 25 .100  0. because full-scale tests on power lines have not been conducted. span length of 400 m and initial sagging tension of 2 x 31000 = 62000 N: Energy imparted to the conductor using Equation 6: 2 (tcc   ) 1  0.2 I rms E0  m   2  a.610 x57010 Assuming an initial sag of 9.5 m. There is very limited experimental validation of these formulas.1 kg/m) with interphase distance a = 8.82  27.060) 3L 1 . the maximum displacement of one phase is :   2     E0  10803  R2   f   f 2  9.88 means R = 5. For the same case at 45 kA.2 m.8 x 5.8 m. It must be noted that advanced methods (finite elements) can be used to evaluate these effects (details are given in CIGRE brochure 214-2002).5 x3.8    2 2    mgL 3.55 = 3. the maximum conductor tension is calculated as: Tmax  620002  2 x10803  77127 400 2  Newtons    10 6 5 510   2 x5. It means that the remaining clearance is 8.  3.The combined values of Tmax and R result in a transverse load on the suspension tower in the case of a horizontal arrangement.1  2 . It is estimated that these formulas give results with 20% precision on the conservative side. 3 x 400  10803 Joule 4 s With conductor Young modulus = 5. jumpers are used to connect the adjacent spans. 26 . Such effects may easily be limited by installation of appropriate hold-down weights. In case of bundle configuration. subspan length in the jumper cannot be large. Interphase spacers may be subjected to bending stresses induced by conductor movements.Remaining clearance = 4.3 m It can be noted that that energy varies as the fourth power of the short-circuit current. Thus. and energy in the system varies with the square of that speed. Experience has shown that appropriate installation of such devices may effectively maintain appropriate clearances since conductor movement is restricted at some location in the span. A major challenge is defining the design load on these interphase spacers. This is due to the fact that short-circuit forces vary with the square of the current. Tests can be performed. the pinch effect may cause the jumpers to bound upward toward the tower cross arms. Advanced calculation methods may also help to define these loads. Interphase Spacers as a Mean to Limit Clearances Problem Linked with Short Circuit Interphase spacers have been proposed to solve the phase-clearance problem during short circuits (Declercq 1998). Reference (CIGRE 1996) explains how to choose short subspans to avoid conductor clashing. Their use in substations may be of interest in that connection. The Case of Jumpers At deadend structures. and some are available on the video accompanying this book. Use of short subspans in jumpers may be recommended to avoid clashing. so the speed of the conductor at the end of the short-circuit also varies with the square of the current. These jumpers also react during short circuit: Interphase forces may cause jumper swing with possible drastic reduction of clearance with tower legs or cross arms. IEEE Trans on Power Apparatus and Systems. pp 100-111 H. 1987.. Transmission Section. 86. S.Demoulin 1992 . D.Gaudry.. Y. Y. 1988 Loading and strength of overhead transmission lines. Short-circuit current calculation in three-phase a.1983. Behaviour of dead-end suspension double-conductor bus during shortcircuit. A. N°11. 1993. N°112. Pon. Hoshino. line hardware subsection. Proceedings . J. Serizawa. PhD 1983. Lilien.L 1983. Collections des publications de la Faculté des Sciences Appliquées de l’Université de Liège. CIRED 1987. Collections des publications de la Faculté des Sciences Appliquées de l’Université de Liège. c.L. N°2. IEEE Trans. N°87 Tsanakas. pp 492-501 El Adnani. Goel.. Geneva: IEC. 1986. pp 1475-1484 Lilien. Lilien. 1991 (published by WG 06 of SC 22). Problems linked to changes in the arrangement of double circuit line conductors. El Adnani M. session 3 (cable and overhead lines).04 (6 pages). Vol. Québec. Montréal. Efforts électrodynamiques dans les liaisons à haute tension constituées de faisceaux de conducteurs. 1967. Compressive loads on spacer-dampers due to short-circuit currents. Krishnasamy. 1967. 102 (1983). 89. The Journal of the Institute of Electrical Engineers of Japan. 1970. PhD 1987. J. IEEE Trans.L. Estimate of forces exerted against spacers when faulty condition occurs. P. Contraintes et conséquences électromécaniques liées au passage du courant dans les structures en cables. REFERENCES Manuzio C. Vercheval. An investigation of forces on bundle conductor spacers under fault conditions.. M. M.Maugain 1992. CEA report. M. Syst. Faisceaux de conducteurs et efforts électrodynamiques. 27 . IEC 60909 1988. Nov 1967. Proceedings of the 5th International symposium on shortcircuit currents in power system C. H. 1987. Grad. Pp 79-84 J. Vol. Influence of the wind on the mechanical design of transmission structures against short-circuits. pp166-185. Proceedings of IEEE Montech’86 Conference on AC Power Systems.6. 1993. Influence of short-circuit duration on dynamic stresses in substations. Power App. Vol 87. March 30. L. Vers une approche numérique fiable. On Power Apparatus and Systems. systems. Papadias. report d. N°7. 1967. International Conference on Electricity Distribution.Bulot. 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