IUL34KRI3UIRU2332IUJI32IWEQHJHJHJJOP,E9UWEEIOWUWEUHJQWHJWQHHWQJDHJWJKXJASLJXLASSJA SHORT-CIRCUIT DESIGN FORCES IN POWER LINES AND SUBSTATIONS

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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 high-voltage 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

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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-e-d-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.

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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 large enough to cause cable contact and even permanent wrap-up at the middle of the span.

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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 medium-voltage 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.

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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.

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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.

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2. 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 low-voltage 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.

(Amperes) 1

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:

(N/m) 2

Where

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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).

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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 short-circuit 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.

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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.

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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.

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3. 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 tf 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 tpi). 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: Fpi 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

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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 mm2 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 kA2. two-phase fault of 63 kA3. initial wind of 60 km/h followed by a gust at 100 km/h for 5 seconds on a quarter of the

span4. 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).

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