Short-Circuit Design Forces in Power Lines & Substations
Electrical engineering of short-circuits...
SHORT-CIRCUIT DESIGN FORCES IN POWER LINES AND SUBSTATIONS
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.
Power line design load includes severe wind action and in some cases heavy ice loads acting on much larger spans than in substations. Therefore design loads due to short circuits may be of the same order as design wind and ice loads in substations, but much less in transmission lines.
Bundle Conductor Lines For bundle conductor lines, during a fault, the subconductors of the bundle move closer to each other due to strong attraction forces because of the very short distance between subconductors (Figure1). Detailed discussions of this phenomenon were given by Manuzio and Hoshino (Manuzio 1967; Hoshino 1970). From their initial rest position, the subconductors move towards each other, remaining more or less parallel in most of the subspan, except close to the spacer (Figures 1 and 2). After first impact, which for power lines is typically around 40 to 100 ms after fault inception, there is a rapid propagation of the wave in the noncontact zone near the spacers, sequence c-d-e of Figure 2. The inward slope of the subconductors at the spacer results in a component of subconductor tension that tends to compress the spacer. This compressive force, or “pinch,” while it is associated primarily with the change in angle, can be further increased by the rise in tension in the subconductors due to bundle collapse. This jump results from the fact that subconductor length in the collapsed condition is greater than in the normal condition. The pinch is maximum when the wave propagation stops towards the spacer, position e in Figure 2. 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, but with decreasing amplitude. If the short circuit is long enough, the pinch oscillations result in a “permanent” oscillating force, sensibly lower than peak value, typically 50%. During the fault, the spacer is strongly compressed. The compression is related to maximum pinch force in the conductor and the angle between the spacer and the subconductor.
Figure 1 Example of quad bundle before and during short-circuit test at 50 kA, showing distortion of the subconductors. One flexible spacer at mid-span (courtesy Pfisterer/Sefag). The subconductor movements occur at very high acceleration. For example, a 40 kA fault on a twin bundle of 620 mm2 conductor, with a separation of 40 cm, may have acceleration up to several tens of g, depending on the instantaneous current value. Spacers are subjected to compression forces; and these instantaneous compression loads can be very high.
Upward movement of the whole span follows the rapid contraction of the bundle and reduces the conductor tension, but does not reduce the maximum forces on the spacers occurring during initial impact.
Figure 2 Attraction of subconductors of a bundle at a spacer during a short-circuit (Manuzio 1967). Interphase Effects and Distribution Lines The video available on my web site (http://www.tdee.ulg.ac.be/doc-5.html) contains some short-circuit tests on rigid bus, flexible bus and high-voltage overhead lines and distribution lines. Fault currents produce an impulse tending to make the separate phases of a circuit swing away from each other, independently of whether the phases are bundled. The impulse that causes this lasts only as long as the fault, so it is brief relative to the fundamental period of the span. The momentum from the impulse carries the phases outward for a certain distance before their tension arrests and reverses the motion. They then swing inward. This inward swing may be 4
large enough to cause cable contact and even permanent wrap-up at the middle of the span. For double-circuit towers, the circuit subjected to the short circuit could force its phases to come in contact with another circuit, thus causing outages on both circuits. There may also be sag increases, up to several times the initial sag in distribution lines, due to heating effects under short circuit, which may significantly affect the amplitude of movements. Even though the inward swing could be short of interphase contact, if the phase spacing is less than the critical flashover distance, and the inward swing occurs at the time that voltage is restored by automatic reclosure, there will be a second fault. Very large movements may be seen on distribution lines. Figure 3 shows the motion produced during full-scale testing on an actual line. This is from an actual three-phase short-circuit test on a 15-kV distribution line near Liège, Belgium (Lilien and Vercheval 1987). The photo shows an instantaneous position of the conductors taken during the test. The fault current level was 3 kA. The reduction in phase spacing may be particularly dramatic on mediumvoltage lines, even if the short-circuit level is much lower.
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). Substation with rigid busbars The behavior of a rigid bus under short-circuit load is very depending of its first natural eigenmode and eigenfrequency. Indeed electromagnetic forces includes pseudo-continuous component combined with a 50 Hz and a 100 Hz component. Some example are shown on the next figure. 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, when high voltage (typically 400 kV) would have long bar length and large tubes. Moreover the busbar is installed on supporting insulators which have their own eigenfrequencies, close to 50 Hz for 150 kV level. So that dynamics of such structures is far from obvious and case dependent.
Fig xx : rigid busbar response to ta given electromagnetic force similar to a two-phase fault with asymmetrical component in the short-circuit current. The transient response is given for different busbar first eigenfrequency between 1.7 Hz and 150 Hz. (extract from CIGRE brochure N° 105, 1996).
Fig xx : a tested rigid bus (all details in CIGRE brochure 105, 1996), Measurement points are located as S2, I2,C3 (constrains). 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.
Fig xx test results. The first eigenfrequency of the whole structure is about 3.3 Hz. There is quasi no effect of the 50 Hz nor of the 100 Hz component of the force. As damping was negligeable, as time to reclosure was particularly dramatic compared to structure oscillation, the second fault induced about twice as much constrains compared to the first fault.
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. The AC component generally is of constant amplitude for the duration of the fault, and although the system through which the fault passes is multimesh, it can usually be assigned a single “global” time constant for the decay of the DC component. In high-voltage lines, and even more in lowvoltage lines, because the ratio X/R, reactance to resistance, is much less at low-voltage level, the global time constant of the system “” is rather low, typically 20 to 80 ms, compared to substations where it is typically 70 to 200 ms.
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
Where Irms is the root-mean-square value of the short-circuit current (A). = 2f is the network pulsation (rad/s) equal to 314 rad/s in Europe and 377 rad/s in the United States. is the network time constant (= L/R) at the location of the fault (s). is an angle depending on the time of fault occurrence in the voltage oscillation (rad). Asymmetry is very dependent on . In the case of a two-phase fault, it is possible to have no asymmetry if = 0 rad.
According to the basic physics of electromagnetism for a three- or a two-phase arrangement, there is always a repulsion force between phases from each other. For a single-phase fault, only one current is involved. In the case of bundle conductors, it is generally considered that the short-circuit current is equally divided among all subconductors. The force acting between subconductors of the same phase is an attractive force, as discussed in Section 3. In the general case of parallel conductors, the force, Fn(t) in N/m, applied on each of the phases can be expressed by:
0 i1 (t ).i2 (t ) i1 (t ).i3 (t ) x 2 a 2a i (t ).i2 (t ) i2 (t ).i3 (t ) F2 (t ) 0 x 1 2 a a i (t ).i3 (t ) i2 (t ).i3 (t ) F3 (t ) 0 x 1 2 2a a F1 (t )
0 is the vacuum magnetic permeability = 410-7 H/m. a is the interphase distance (m). The force, being due to current flow, very much depends on phase shift between currents. It generally includes:
Pseudo-continuous DC component, with a time-constant decay, Continuous dc component, sometimes, and Two oscillating AC components, one at network frequency, with a time-constant decay, and one at the double of the network frequency, which is not damped. In the case of a two-phase fault, the force is proportional to the square of the current. Thus it always has the same direction—that is, a repulsion between the two faulted phases. In the case of a three-phase fault, it is much more complex. In flat-phase configuration, illustrated by the top view of Figure 4, the middle phase has a zero mean value, and at least one of the outer phases has forces similar to those generated by a two-phase fault (Figure 5 left). The same location in a network gives two different values of current for three- or two-phase faults with a ratio 0.866 between them. For example, a 34.8 kA three-phase fault would give a 30.1 kA two-phase fault at the same location. Therefore, a three-phase fault has to be considered for estimation of design forces. Figures 4 (top) and 5 give examples of currents and forces on horizontal, or purely vertical, arrangements. In the case of an equilateral triangular arrangement, Figure 4 (bottom), the forces are similar on all three phases, similar to the force on phase 1 for the horizontal arrangement. 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. This is for a horizontal or vertical arrangement of the circuit. The fault current is 34.8 kA rms with peak currents of 90.4, 79.2, and 61.2 kA. The time constant is 70 ms, and the short-circuit duration is 0.245 seconds. The current frequency is 50 Hz. The loads shown are per unit length for a = 6 m clearance between phases. The repulsion peak load on phase 1 is 228 N/m. (= 1.39 rad). The signs convention is positive in the directions shown in the upper diagram in Figure 4. But the time dependence of the forces is very different on the outer phases compared to middle phase. On the outer phases, the force is unidirectional and has a significant continuous component. On phase 2, the continuous component is zero (except during the asymmetrical part of the wave).
Figure 4 Two different geometric arrangements for a three-phase circuit and the electromagnetic force reference directions on each phase corresponding to Equation 2. The numbers 1, 2, and 3 are phase numbers. It must be noted that the level of the peak force, about 200 N/m in Figure 5, is far greater than the conductor weight and is proportional to the square of the current. But the continuous component is much lower, about 30 N/m in this case, as shown later. Under actual shortcircuit levels and clearances, it is closer to the conductor weight, but acts, in most cases, in the other direction. See upper right panel in Figure 5.
Figure 5 Example of calculated three-phase short-circuit current wave shape and corresponding loads on a horizontal or vertical circuit arrangement.
Thus the interphase effects, for the case of horizontal or purely vertical arrangement only, may be summarized as: 1. 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. Taking into account the fact that only the continuous dc component has to be considered, the force on an outer phase can be approximated by Equation 3. This is the horizontal repulsion force for the horizontal arrangement, or the vertical repulsion force for the vertical arrangement: F
0.2 2 I 3 (0.75 1.616e 2t / ) a
Where a is the interphase distance (m). I3 the rms three-phase fault at that location (kA).
is the network time constant at that location (s). t is time (s). 2. The forces considered above cannot be directly applied to structure design loads, because the structural response to these loads has to be taken into account. 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. For example, in Figure 5, the continuous dc component after transient is given by: F
0.2 34.82 x0.75 30.3 N/m 6
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. Some results from a program of tests at the Veiki substation in Hungary are used here for that purpose (Lilien and Papailiou 2000). The systematic single-phase fault tests on twin conductors were performed in the 1990s on a power line with a double deadended span, with a length of 60 m, with the following characteristics (Figure 6): Span length 60 m Sub conductor type ACSR CONDOR (455 mm², = 27.7 mm, 1.52 kg/m, UTS 125 kN) Spacing 0.457 m Current 35 kA (90 kA peak), Time constant 33 ms Duration 0.17 to 0.2 s Sagging tensions 15, 25, or 35 kN (per subconductor) All cases are single-phase faults; the return path is through the ground Supporting structure: Stiffness: about 8.5 106 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. (Lilien and Papailiou 2000). 60 m
measurement Figure 7 Two test span arrangements for spacer compression tests (Lilien and Papailiou 2000).
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). For the 30-m sub-span, two spacers were installed close to each other so as to receive half the contribution. The installation of measurement is such that actual load for spacers in power lines would be twice the measured value. The following oscillograms were recorded (Figure 8). On the left hand side, the 60-m span length results are presented, and on the right-hand side, the 30-m span length results are presented. It should be noted that the actual “pinch” occurs during the first approximately 0.2 seconds, while the fault current is on, and that the other “spikes” in the records arise from subsequent motion of the bundle. Sagging tension 15 kN - 35/90 kA
Sagging tension 15 kN - 35/90 kA 6000
C om pressiveloads(N )
1000 0 0
-2000 time (s)
subspan length 60 m
time (s) subspan length 30 m
Sagging tension 25 kN - 35/90 kA
Sagging tension 25 kN - 35/90 kA 8000
Compressive load (N)
Compressive loads (N)
subspan length 30 m
subspan length 60 m
Sagging tension 35 kN - 30/90 kA 7000
Sagging tension 35 kN - 30/90 kA
Compressive loads (N)
Compressive loads (N)
3000 2000 1000
2000 1000 0 0
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, at 35 kA on twin-bundle line 2x Condor, with different sagging tensions. Half of the compression is given. 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. (Courtesy Pfisterer/Sefag).
After the short circuit, the subconductors separate from each other during a long transient, with wave propagation along each subspan (as can be seen in the video that accompanies this book and in Figure 8). During that transient, significant tensile forces (the opposite of compression) are applied on the spacers, the level of which reach about 50% of the maximum compression load. In spite of their smaller magnitude, the effect of these tension forces on the spacer must be considered separately, because some spacer attachments are not as strong in tension as they are in compression. A particular example is the attachment using an open or “saddle” clamp, with helical rods to capture the subconductor. These loads are repeated with every passage of the wave up and down the span. Note the shorter repetition time in the 30-m span. These loads decay very slowly, so that many repeated such loads have to be taken into account. The graphs in Figure 8 show the effect of gradually increasing initial tension before the fault from 15 kN (12.5% EDS) to 35 kN (28% EDS). The effect on propagation speed can be seen in the after short-circuit peaks, but the influence on maximum pinch is limited in actual range, as predicted by Manuzio (the pinch being proportional to the square root of the tension), and it
is particularly valid for long subspans, as used in power lines and as validated by Manuzio’s test arrangements (Manuzio 1967). In case of spring-type dampers, which could be compressed by the pinch, 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. Depending on the configurations of the spacer and spacer dampers, the short-circuit forces could cause large bending moment in the conductor and the elements of the spacer.
Figure 9 Typical tension oscillogram in one subconductor during and after the fault, for the 60-m span length configuration (15 kN initial). Irms 35 kA (peak 90 kA), 0.18 s courtesy Pfisterer/Sefag).
In these tests, limited to one-phase fault, there is no interphase effect but, due to the increment in tension caused by the pinch, the whole phase jumps up after short-circuit inception and falls down afterwards. This behavior induces some tension changes in the conductors, as can be seen in Figures 9 and 10. It is notable that the pinch effect (the first peak during the fault in the first 0.18 s) in the conductor has a smaller tension rise than that which occurs, at 0.9 seconds, as the phase falls. In both cases, the latter is limited to 1.8 times the initial static sagging tension.
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). Irms 35 kA (peak 90 kA), 0.18 s. (courtesy Pfisterer/Sefag).
Subspan Length Effect Bundle pinch is very much related to subspan length. There exists a critical subspan length under which no contact is possible and over which contact occurs on a significant part of the subspan. Of course, that length depends on short-circuit level and some other parameters. That critical value corresponds to extreme loading (for pinch effect in substations [El Adnani 1987; Lilien and El Adnani 1986]). For the power lines with typical subspan lengths, subconductors experience contact in all cases except in jumpers. Subconductor Separation Effect A closer bundle spacing results in a smaller increment in subconductor tension. In fact, initial electromagnetic force are stronger, but the tension increment is generated by conductor deformation into the triangles of Figure 2 after contact, and most of deformation is located in those triangles. Smaller conductor separation thus leads to less deformation in that area. At the limit, if conductors are in contact all along the span, there is no increment in 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). Both cable tension versus time (Figure11 left) and phase movement in a vertical plane at mid-span (Figure 11 right) are shown. On the cable tension curve, three maxima (and their corresponding time on the abscissa) have been indicated, which is discussed below. On the phase movement curve at mid-span, the curve has been marked by dots every 0.1 s to get an idea of the cable speed, and in particular to show that the short circuit ends before there is significant movement of the phase. 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. Peak design load could occur under the following three conditions: 1. 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, so that a large part is converted in deformation energy—that is, increase of tension. In power lines, tt occurs always after the end of the short circuit (the cable position at the end of the short circuit (0.1 s) is indicated in Figure 11 right). 2. 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. tf always occurs after the end of the short circuit. 3. The pinch effect Fpi (at a very short time after short-circuit inception at t pi). The pinch effect only occurs with bundle conductors, when subconductors come close to each other: tpi always occurs during short circuit.
Figure 11 Left Figure: Tensile force (left) time evolution of a typical twin-bundle span during two-phase short circuit between horizontal phases. Three maxima: F pi at time Tpi (so-called pinch effect, due to bundle collapse), 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), and F f at time Tf (the maximum of the force due to cable drop represented by circle 2 in the right figure. Typically, Tpi -40 ms, Tt +1.2 s and Tf = 4 s
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, perpendicular to the cable. Z is vertical, -10 m is the initial point showing sag, and X is horizontal and transverse to the cable). Such movement has been calculated for a two-phase fault of 63 kA (duration 0.1 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 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. Figure 12 shows cable tension versus time in different dynamic loading conditions, as explained in the legend. It can be seen that cable tensions due to short-circuit currents are significantly smaller than other causes such as ice shedding.
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, R, and S in Figure 13) for loading conditions (Lilien and Dal Maso 1990): 1. three-phase fault of 72.3 kA 2. two-phase fault of 63 kA 3. initial wind of 60 km/h followed by a gust at 100 km/h for 5 seconds on a quarter of the span 4. shedding of ice sleeve of 6 kg/m Reduction in Phase Spacing After the initial outward swing, the phases move towards each other. For the case illustrated in Figure 11, this inward movement exceeds 4 m per phase. That means a phase-spacing reduction of more than 8 m. 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. 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. That would induce a second fault with the dramatic consequence of a lock-out circuit breaker operation, with all its consequences (power outage).
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, S, and T are their phase locations in still conditions) (Lilien and Dal Maso 1990): 1. two-phase short-circuit 63 kA either RT, RS, or TS 2. three-phase short-circuit 72.3 kA 3. 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.
Figure 14 Calculated envelope of phase-conductor movements for two-phase faults of different rms amplitude (Lilien and Dal Maso 1990). Distribution Lines As mentioned earlier, very large movements may be seen on distribution lines (Figure 3). Figure 15 shows a case of two circuits on the tower, where the faulted circuit forces some of its phases to get in contact with the second (healthy) circuit, inducing a fault in the other circuit so that both circuits trip out. How to estimate the required interphase spacing is discussed further in Section 5 (Equation 8)
Figure 15 Three-phase short-circuit on 15-kV line (left circuit), with autoreclosure. a = fault inception, b = 0.1 s, end of the first fault, c =0.4 s, time of reclosing, and d = 1.4 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, conductor 93.3 mm2 AAAC (Lilien and Vercheval 1987).
ESTIMATION OF DESIGN LOADS
The most critical effects on power lines are: 1. For bundle conductors: spacer compression (Equation 4). 2. For power lines in general, but particularly for distribution lines: reduction in phase spacing (Equation 8 for high-voltage line). 3. To a much lesser extent, 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). The loads under no. 3 above due to short circuits should be considered by line designers by including them in the loading schedule for structures. Since there are three ways to have one phase fault, three to have a two-phase fault, and one to have a three-phase fault, there may be seven different loading conditions. They must, of course, be taken separately, since these events cannot occur simultaneously. Advanced calculation methods (Lilien 1983, El Adnani 1987, Wendt et al 1996, Declercq 1998, Stein et al 2000) may be used for any situation. Bundle Conductors in Transmission Lines Manuzio developed a simple method for spacer compression effect in bundle conductors (Manuzio 1967).
Fc kI Fst log10 ( s / s ) (N)
Where: Fst is initial sagging tension for each subconductor (N). k is a correction factor depending on the number of subconductors. ktwin = 1.57. ktripple= 1.44. kquad = 1.27. I is the rms short-circuit value/phase (kA). s is the bundle diameter, 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). Example: 21
Consider a case of a short circuit of 35 kA (rms/phase) acting on a twin ACSR Condor (27.7 mm diameter) conductor with 0.457 m conductor separation, tensioned at 25 kN/subconductor. Equation 4 gives a spacer compression force of: Fc 1.57 x35 25000 x log10 (0.457 / 0.0277) 9586 N However, in the analysis by Manuzio (Manuzio 1967), short-circuit current asymmetry was neglected. That has been taken into account in IEC 60865 for evaluating the maximum tension in the conductor during fault. But IEC 60865 gives no recommendation for spacer compression. Other methods to estimate spacer compression forces have been proposed (Hoshino 1970; Pon et al. 1993; Lilien and Papailiou 2000). Some tests performed in Canada (Pon et al. 1993) on spacer dampers for power-line-estimated spacer-compression design load up to 20 kN for typical configurations and anticipated short-circuit levels. Manuzio’s method can be safely applied to faults with maximum asymmetry through a correction factor of 25% (multiply all k factors by 1.25). In fact, Manuzio’s method is very simple to apply compared to other methods. It may not be accurate enough for use with respect to substation flexible bus. Alternatively, if we define Fpi (as shown in Figure 11) as the maximum tensile load in one subconductor during the bundle pinch, another best fit would be to use Manuzio method (without correction factor), but using Fpi pinch value instead of initial static pull. F pi can be evaluated by IEC 60685 method. Fpi increases linearly (and not with the square) with short-circuit current. That is because a stronger short-circuit current will increase contact length, thus reducing acting parts of the conductors.
Note: In the use of IEC method 60865 to evaluate Fpi, there is a need to introduce the socalled “ supporting structure stiffness.” In this application, that stiffness is not simply the static stiffness of supporting structure, 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, from short-circuit inception up to the maximum pinch value, after about 40 to 90 ms. 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. Despacering as a Means to Limit Pinch Effect Despacering (removal of spacers) is an antigalloping measure (see Section 4.5) for some power lines. It has been used up to the 245-kV level for twin bundles of limited diameter. In such cases, the bundle is turned in vertical or slightly oblique position, and conductor separation is increased compared to a spacered bundle. Moreover, it has been recommended to use larger subconductor spacing at the middle of the span (compared to end of the span)— for example, 0.6 m at ends and 0.8 m at mid-span. Such configurations may suffer from the “kissing” phenomenon under high electrical load, because electromagnetic forces also act under load current. At such current levels, nevertheless, the electrostatic repulsion (due to voltage) cannot be neglected. It can be shown 22
that, at surge impedance loading (SIL), equilibrium exists between attraction and repulsion forces. Power flows are often several times (up to four times) the SIL, so that attraction forces are generally stronger than repulsion. One of the major problems of such configurations is linked to possible sticking of the subconductors following a perturbation. As electromagnetic forces depend on distances, there exists a distance under which the subconductors always come together and stick together, and it is very difficult to separate them without opening the circuit. Sticking induces large permanent noise and increase in corona. To avoid such problems, line designers have developed several proposals like the “hoop” spacer (see Section 4.5). Under short circuit, these configurations result in clashing between subconductors and, as “subspan” length (= span length in this case) is very large, there is little increment in tension. But, in the case of hoop spacers or similar, the conductor clashing destroys these light spacers beyond a certain level of short-circuit current.
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). Only one span is considered. a = interphase distance (m). m = mass per unit of length of one phase (kg/m). Irms = root mean square of the three phase short-circuit current/phase (kA). = time constant of the short-circuit asymmetric component decay (s). tcc = duration of the fault (= time of first fault + time of second fault if auto-reclosing) (s). L = span length (m). Tst = phase conductor static tension before the fault condition (N). EA/L = conductor extensional stiffness (product of Young modulus times cross section divided by span length) (N/m). K = tower stiffness (N/m) (order of amplitude 105 N/m). f = initial sag (m). R = maximum displacement (m).
1. The energy imparted to the conductor is given by:
2 (tcc ) 1 0.2 I rms E0 m 2 a.m
3L (Joules) 4
2. The maximum tension in the conductor during movements: Tmax Tst2
2 E0 L 2 EA K
3. The maximum displacement of one phase (zero to peak):
E0 2 R2 f f 2 mgL 3
That maximum may be observed in the case when the conductors are moving away from each other. But phase spacings can be critical when the phases move back towards each other, in which case there is generally lower displacement (say, 80% of the separation movement). In this case, the clearances may be reduced (the most dramatic case being a two-phase fault) by 2 x 0.8 x R or 1.6 R.
The combined values of Tmax and R result in a transverse load on the suspension tower in the case of a horizontal arrangement, for example. There is very limited experimental validation of these formulas, because full-scale tests on power lines have not been conducted. It must be noted that advanced methods (finite elements) can be used to evaluate these effects (details are given in CIGRE brochure 214-2002). It is estimated that these formulas give results with 20% precision on the conservative side. Example: For example, 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 1.55 = 3.1 kg/m) with interphase distance a = 8.5 m, 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.m
0.2 x 632 (0.100 0.060) 3L 1 . 3.1 4 2 8.5 x3.1
3 x 400 10803 Joule 4
s With conductor Young modulus = 5.6 x 1010 N/m2 and tower stiffness of K= 5 x 105 N/m, the maximum conductor tension is calculated as: Tmax 620002
2 x10803 77127 400 2 Newtons 10 6 5 510 2 x5.610 x57010
Assuming an initial sag of 9.8 m, the maximum displacement of one phase is :
E0 10803 R2 f f 2 9.8 2 2 mgL 3.1x9.81x 400 3 3
9.82 27.88 means R = 5.2 m
Thus the reduction in phase spacing is 2 x 0.8 x 5.2 = 8.32 m. It means that the remaining clearance is 8.5 - 8.3 = 0.2 m. For the same case at 45 kA, the results are: E0 = 2812 Joules Tmax = 66270 N
Remaining clearance = 4.3 m It can be noted that that energy varies as the fourth power of the short-circuit current. This is due to the fact that short-circuit forces vary with the square of the current, so the speed of the conductor at the end of the short-circuit also varies with the square of the current, and energy in the system varies with the square of that speed. The Case of Jumpers At deadend structures, jumpers are used to connect the adjacent spans. 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. 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. Thus, the pinch effect may cause the jumpers to bound upward toward the tower cross arms. Use of short subspans in jumpers may be recommended to avoid clashing. Their use in substations may be of interest in that connection. Reference (CIGRE 1996) explains how to choose short subspans to avoid conductor clashing.
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). 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. Tests can be performed, and some are available on the video accompanying this book. Advanced calculation methods may also help to define these loads. Interphase spacers may be subjected to bending stresses induced by conductor movements.
Manuzio C. 1967. An investigation of forces on bundle conductor spacers under fault conditions. IEEE Trans. On Power Apparatus and Systems, Vol. 86, N°2, 1967, pp166-185. Serizawa, 1967. Y. Behaviour of dead-end suspension double-conductor bus during shortcircuit. The Journal of the Institute of Electrical Engineers of Japan, Vol 87, N°11, Nov 1967, pp 100-111 H. Hoshino, 1970. Estimate of forces exerted against spacers when faulty condition occurs. IEEE Trans on Power Apparatus and Systems, Vol. 89, N°7, pp 1475-1484 Lilien, J.L 1983., Contraintes et conséquences électromécaniques liées au passage du courant dans les structures en cables. PhD 1983. Collections des publications de la Faculté des Sciences Appliquées de l’Université de Liège, N°87 Tsanakas, D.; Papadias, B.1983. Influence of short-circuit duration on dynamic stresses in substations. IEEE Trans. Power App. Syst. 102 (1983), pp 492-501 El Adnani, M. 1987. Efforts électrodynamiques dans les liaisons à haute tension constituées de faisceaux de conducteurs. PhD 1987. Collections des publications de la Faculté des Sciences Appliquées de l’Université de Liège, N°112. Lilien, J.L., El Adnani M., 1986. Faisceaux de conducteurs et efforts électrodynamiques. Vers une approche numérique fiable. Proceedings of IEEE Montech’86 Conference on AC Power Systems. Pp 79-84 J.L. Lilien, P. Vercheval. 1987. Problems linked to changes in the arrangement of double circuit line conductors. International Conference on Electricity Distribution. CIRED 1987, session 3 (cable and overhead lines). Proceedings , report d.04 (6 pages). IEC 60909 1988. Short-circuit current calculation in three-phase a. c. systems. Geneva: IEC, 1988 Loading and strength of overhead transmission lines. ELECTRA n°137. 1991 (published by WG 06 of SC 22). M.Bulot, L.Demoulin 1992 . Contribution of Reliability analyses to the study of the effects of short-circuit, Proceedings of the 5th International symposium on short-circuit currents in power system. M.Gaudry, Y.Maugain 1992. Influence of the wind on the mechanical design of transmission structures against short-circuits, Proceedings of the 5th International symposium on shortcircuit currents in power system C. Pon, A. Goel, S. Krishnasamy, H. Grad. 1993. Compressive loads on spacer-dampers due to short-circuit currents. CEA report. Transmission Section, line hardware subsection, March 30, 1993, Montréal, Québec.
IEC 60865-1 1993. Short-circuit currents - Calculation of effects. Part 1: Definitions and calculation method, Geneva: IEC, 1993 EN 60865-1 1993. Short-circuit currents - Calculation of effects. Part 1: Definitions and calculation method. Brussels: CENELEC, 1993 IEC 60865-2 1994. Short-circuit currents - Calculation of effects. Part 2: Examples of calculation. Genève: IEC, 1994. G. de Wendt, T. Tietz, A:M. Miri, R. Ahlers, N. Stein 1996 Dynamic and Static Case Stress Analysis of a HV Substation with Stranded Conductors (Test-Results- Calculation). Proceedings of the 7th Int. Symposium on short-circuit currents in Power Systems, 1996. CIGRE-105 1996. The mechanical effects of short-circuit currents in open-air substations (Rigid and flexible bus-bars). Paris: CIGRÉ, technical brochure N°105. 2 volumes (180 pages). Declercq, G.1998. Tests with droppers and interphase spacers. Proceedings of the 8th International Symposium on Short-Circuit Currents in Power Systems, Brussels (Belgium), 810 October 1998, Proceedings pp. 143-148 Stein, N.; Meyer, W.; Miri, A.M. 2000. Tests and Calculation of Short-Circuit Forces and Displacements in High Voltage Substations with Strained Conductors and Droppers. ETEP 10 (2000) No. 3 , pp 131–138 J.L. Lilien, E. Hansenne, K.O. Papailiou. J. Kempf.2000. Spacer Compression for a tripple conductor arrangement. IEEE Trans. On Power Delivery, Vol. 15, N°1, pp 236-241, January 2000. J.L. Lilien, K.O. Papailiou. 2000. Calculation of Spacer Compression for Bundle Lines under Short-Circuit . IEEE Trans. On Power Delivery, Vol 15, N°2, pp839-845. CIGRE-214 2002. The mechanical effects of short-circuit currents in open-air substations (Rigid and flexible bus-bars) (Part II) CIGRÉ, technical brochure N°214. 2 volumes (200 pages). J.L. Lilien and F. Dal Maso, 1990. Contribution to Line Design by Accurate Predetermination of Severe but Occasional Stresses. CIGRE Plenary session, 1990, Paris, Report 22-103. D.G. Havard, C.J.Pon, H.A.Ewing,G.D.Dumol and A.C. Wong, 1986, Probabilistic Short – Circuit uprating of Station Bus System-Mechanical Aspects, IEEE PES