Insulated Cables
3.8 Cases Studies Example 3.3
π
s 2
3 A 2
r r (3.50)
3.8 Cases Studies Example 3.3
The procedures outlined above, to prepare input data, will be applied to a 66 kV cable as shown in Figure 3.22. The following data were provided by the manufacturer (see Section 3.7 for nota-tions) [35]:
Core cross-sectional area:
• Ac = 1000 mm2
C
• = 0.24 nF/m
Inner semiconductor Outer semiconductor
Wire screen
Core
Insulation
FIGURE 3.22
Example 3.3: SC XLPE test cable.
R
• DC = 2.9E-5 Ω/m r1 = 19.5 mm
•
Thickness of inner insulation screen: 0.8 mm
•
Thickness of insulation: 14 mm
•
Thickness of outer insulation screen: 0.4 mm
•
Wire screen area:
• As = 50 mm2
This example is aimed at illustrating how to apply the previous recommendations to account for semiconducting screens in CC routines. It also serves to show how to account for variations and uncertainties on manufacturers’ data. Finally, it provides a comparison between measurements and simulations of inrush currents. The comparison shows that it is best to obtain capacitance data from a specimen and that a lower accuracy is obtained by neglecting the semiconducting screens.
a. Data consistency
Insulation screens can be represented as short circuits when calculating the shunt admittance. This is equivalent to a capacitance between two cylindrical shells deduced from Equation 3.20. In this case a = (19.5 + 0.8) mm = 20.3 mm, and b = a + 14 = 34.3 mm. With a relative permittivity of 2.3 for XLPE, this results in a capacitance of 0.244 nF/m, which is in agreement with the capacitance of 0.24 nF/m provided by the manufacturer.
b. Data conversion
The outer radius is calculated using Equation 3.50: r3 = 34.93 mm.
ρs = 1.718E-8 Ω · m (copper).
c. Manufacturer’s data inaccuracy
Relevant cable standards (e.g., IEC 840, IEC 60502) limit the minimum thickness of each cable layer (in relation to the nominal thickness), but not the maximum thickness. Therefore, the manu-facturer is free to use layers thicker than the nominal ones; e.g., to account for dispersity in pro-duction and aging effects. This situation is prevalent for the main insulation, the oversheath, and the semiconducting screens.
After measuring a specimen of the 66 kV cable, it was found that the insulation and, in particu-lar, the semiconducting screens were thicker than stated in the data sheets:
Thickness of inner insulation screen: 1.5 mm.
•
Thickness of insulation: 14.7 mm.
•
Thickness of outer insulation screen: 1.1 mm.
•
Separation between the outer insulation screen and the center of each conductor in wire
•
screen: 1 mm.
This gives the following modifi ed model:
r
d. Sensitivity analysis
At high frequencies, the asymptotic (lossless) propagation velocity and surge impedance are given as
=1/ 0
v L C (3.51)
c 0/
Z = L C (3.52)
where
0 0 ln( / )2 1
L = 2μ r r
π (3.53)
with μ0 = 4πE-7.
Consider the following three cases, which are used to compare the asymptotic propagation characteristics:
Case 1
• : The semiconducting screens are neglected; both capacitance and inductance are calculated using Equations 3.20 and 3.53 with a = r1, b = r2.
Case 2
• : The semiconducting screens are taken into account; capacitance and geometrical data are provided by the manufacturer.
Case 3
• : The semiconducting screens are taken into account; the capacitance is provided by the manufacturer; geometrical data are deduced from cable specimen.
Table 3.5 shows input data for each case, and the values deduced for the velocity and the charac-teristic impedance, using the inductance calculated from Equation 3.53. It is obvious from these results that the cable propagation characteristics are highly sensitive to the representation of the core–sheath layers.
e. Field tests and time-domain simulation
A fi eld test was carried out on a cable of 6.05 km length, see Figure 3.23. One core conductor was charged up to a 5 kV DC voltage and then shorted to ground. Thus, a negative step voltage was in effect applied to the cable end.
Figure 3.24 shows the measured initial inrush current fl owing into the core conductor in p.u. of the DC-voltage. The initial current corresponds to the surge admittance of the cable core–sheath loop, which is the inverse of the surge impedance.
TABLE 3.5
Example 3.3: Sensitivity of Cable Propagation Characteristics
Case 1 Case 2 Case 3
R1 (mm) 19.5 19.5 19.5
R2 (mm) 33.5 34.7 37.8
εr1 2.300 2.486 2.856
v (m/μs) 197.7 190.1 (−3.8%) 177.4 (−10.3%) Zc (Ω) 21.39 21.91 (+2.4%) 23.49 (+9.8%) Source: Gustavsen, B., IEEE PES Winter Meeting, January
28–February 1, 2001. With permission.
The inrush current was simulated using the so-called Universal Line model (ULM) [5]. The CC routine was applied for the three different cases defi ned above. It is seen that using the cable representation in Case 3 gives a calculated response which is in fairly close agreement with the measured response. The two other representations have a much larger discrepancy.
The spike occurring at about 50 μs resulted because of long leads connecting the two cable sections.
f. Improved modeling of semiconducting screens
Stone and Boggs [33] suggest modeling the admittance between the core and the sheath by means of the circuit shown in Figure 3.25, in which each semiconducting screen is modeled by a conductance in parallel with a capacitor. With component values obtained from measurements, a good agreement between measured attenuation and calculated attenuation can be obtained in the range of 1–125 MHz. The attenuation effect of the semiconducting screens was strong. Weeks
Negative step voltage
+
3.85 km 2.20 km
15 m
V
Core Sheath
FIGURE 3.23
Example 3.3: Cable test setup.
–0.05
0 20
3 2 1
Measured 3
2 1 Measured
40
Time (μs)
60 80 100
–0.045 –0.035 –0.025 –0.015 –0.005
–0.04 –0.03 –0.02 –0.01 0
1/21.39 1/21.91 1/23.49
Current (p.u.)
FIGURE 3.24
Example 3.3: Measured and simulated inrush current. (From Gustavsen, B., IEEE PES Winter Meeting, January 28–February 1, 2001. With permission.)
and Min Diao [34] give a systematic investigation of the effects of semiconducting screens on propagation characteristics.
The conductivity and permittivity of the semiconducting screens depend very much on the amount of carbon added, the structure of the carbon, and the type of base polymer. Very high carbon concentrations are used (e.g., 35%). IEC 840 recommends a resistivity below 1000 Ω · m for the inner screen and below 500 Ω · m for the outer screen. One manufacturer stated that they use a much lower resistivity, typically 0.1–10 Ω · m. The relative permittivity is very high, typically of the order of 1000. The permittivity and conductivity can present a strong frequency dependency.
In order to investigate the possible attenuation effects of the insulation screens of the cable considered in this example, a representation as in Figure 3.25 was employed assuming fre-quency independent conductances and capacitances. The component values were calculated as follows:
1 0 r 2
2 0 r 1
1 2
2 1
0.24 nF/m (from manufacturer) 2 /ln( / )
2 /ln( / ) 2 /ln( / ) 2 /ln( / ) C
C r a
C a r
G r b
G a r
=
= πε ε
= πε ε
= πσ
= πσ
where
a is the outer radius of inner semiconducting screen b is the inner radius of outer semiconducting screen εr is the relative permittivity of semiconducting screens σ is the conductivity of semiconducting screens
Core
C1
C2 G2
G1
C Y
Inner semiconducting screen
Outer semiconducting screen
Sheath
Main insulation
FIGURE 3.25
Example 3.3: Improved model of insulation screens. (From Stone, G.C. and Boggs, S.A., Proceedings of the Conference on Electrical Insulation and Dielectric Phenomena, National Academy of Sciences, Washington, DC, pp.
275–280, October 1982. With permission.)
Figure 3.26 shows the attenuation per km, for a few combinations of σ and εr. The curves defi ne to which peak value a sinusoidal voltage of 1 p.u. peak value decays over a distance of 1 km. (The signal decays exponentially as function of length.) The model predicts a signifi cant contribution from the semiconducting screens for a low value of both the relative permittivity (10, 100) and the conductivity (0.001). With the high permittivity (1000), the capacitance tends to short out the conductance, and no appreciable increase of the attenuation is seen. The lowest value for the permittivity (10) is probably unrealistic.
Example 3.4
Consider the three 145 kV SC cable system shown in Figure 3.27. The cable design uses a cop-per core and XLPE insulation, the core radius and insulation thicknesses being those shown in Table 3.6. Semiconductor layers are taken into account by using Equation 3.49.
Using the ULM [5], the voltage caused by a step voltage excitation is calculated at the receiv-ing end of a 5 km cable, see Figure 3.28. All sheaths are treated as continuously grounded. This example has the purpose of showing the effect of sheath resistances and of insulation losses on the transient response of cables. It also shows the effects of the semiconducting screens on the speed of transient waves.
1. Sensitivity to sheath resistance
The resulting step voltage is calculated for the following cable sheaths: 1 mm Pb; 2 mm Pb; 3 mm Pb; 0.215 mm Cu (which represents a 50 mm2 wire screen).
The receiving end voltages are shown in Figure 3.29, assuming 1 mm semiconducting layers. It can be seen that reducing the thickness of the lead sheath from 2 mm to 1 mm leads to a strong increase in the attenuation, whereas a reduction from 3 mm to 2 mm has little effect. This can be understood by considering that the dominant frequency component of the transient is about
0.8
0 1 2 3 4 5
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1
Frequency (MHz)
Attenuation per km
Neglecting semiconducting screens σ=0.001 S/m, εr=10
σ=0.001 S/m, εr=100 σ=0.001 S/m, εr=1000 σ=0.01 S/m, εr=1000
FIGURE 3.26
Example 3.3: Effect of semiconducting screens on attenuation. (From Gustavsen, B., IEEE PES Winter Meeting, January 28–February 1, 2001. With permission.)
10 kHz. At this frequency, the penetration depth in lead is 2.6 mm, according to Equation 3.43.
Thus, increasing the thickness of the lead sheath beyond 2.6 mm will not lead to a signifi cant change in the response.
2. Sensitivity to semiconductor thickness
Assuming a 0.215 mm Cu sheath, the step response is calculated for different thicknesses of the semiconductor layers: 0; 1; 2; 3 mm.
The responses in Figure 3.30 show that the semiconductors lead to a decrease in the propaga-tion speed, as previously explained in Secpropaga-tion 3.7.
1 2 3
ρsoil=100 Ω.m
1.0 m
0.5 m
FIGURE 3.27
Example 3.4: Cable confi guration.
Unit step
voltage 5 km
+ V
FIGURE 3.28
Example 3.4: Step voltage excitation.
TABLE 3.6
Example 3.4: Test Cable Parameters
Radius (m) Thickness (m) r (Ω · m) er
Core 20E-3 1.72E-8
Main insulation 15E-3 2.3
Outer insulation 5E-3 2.3
Source: Gustavsen, B. et al., IEEE Trans. Power Deliv., 20(3), 2045, 2005.
With permission.
3. Sensitivity to insulation losses
In this new calculation the XLPE main insulation is replaced by a paper–oil insulation. It is further assumed that the cable has a 2 mm lead sheath and no semiconducting screens. The open end voltage is calculated by applying a 2 μs and a 10 μs width square voltage pulse. The simulation is performed with the following representations of the main insulation:
0 100 200 300 400 500
0 1 2
Time (μs)
Voltage (V)
1 mm Pb 0.215 mm Cu
2 mm Pb 3 mm Pb
FIGURE 3.29
Example 3.4: Effect of sheath design on overvoltage. (From Gustavsen, B. et al., IEEE Trans. Power Deliv., 20, 2045, 2005. With permission.)
0 100 200 300 400 500
0 1 2
Time (μs)
Voltage (V)
0 mm 1 mm 2 mm 3 mm
FIGURE 3.30
Example 3.4: Effect of semiconductor thickness on overvoltage. (From Gustavsen, B. et al., IEEE Trans. on Power Deliv., 20, 2045, 2005. With permission.)
a. Lossless insulation, εr = 3.44; i.e., DC-value in Equation 3.4.
b. Lossy insulation by Equation 3.4.
Figure 3.31 shows an expanded view of the initial transient (receiving) end. It can be seen that the lossy insulation gives a much stronger reduction of the peak value for the narrow pulse (2 μs) than that for the lossless insulation. This reduction is an effect of both attenuation and frequency-dependent velocity. It is further seen that the travel time of the lossy insulation is smaller than that of the lossless insulation, which is caused by the reduction in permittivity at high frequencies, according to Equation 3.4.
Example 3.5
In this example an armor of 5 mm steel wires and a 5 mm outer insulation are incorporated into the cable design. It is further assumed XLPE main insulation, a 2 mm lead sheath, and 1 mm semi-conducting screens. Only one cable is considered.
The resulting voltage of the open-circuit step response is calculated for different values of the armor permeability: μr = 1, 10, 100, being the cable length 50 km, see Figure 3.32. It is seen that increasing the permeability strongly increases the effective attenuation of the voltage. The reason is that a permeability increase reduces the penetration depth in the armor, thus increasing the resistance of the inner armor surface impedance. For a 5 km cable length, the signifi cance of the armor was found to be small as the magnetic fi eld would not appreciably penetrate the sheath conductor, due to the increased frequency of the transient.
Example 3.6
This example shows the differences that one can obtain when predicting the transient response of an underground cable system as various approximations are used to evaluate ground-return
20 25 30 35 40 45 50
−0.5 0 0.5 1 1.5 2
Time (μs)
Voltage (V)
Lossless Lossy
T = 10 μs
T = 2 μs
FIGURE 3.31
Example 3.4: Effect of insulation losses on overvoltage. (From Gustavsen, B. et al., IEEE Trans. Power Deliv., 20, 2045, 2005. With permission.)
impedances. Consider the system depicted by Figure 3.33a and b. The fi rst fi gure provides the transversal geometry, as well as the ground resistivity. All the permitivities and permeabilities are considered equal to those of vacuum. The second fi gure provides the longitudinal geometry and the system confi guration. The cable is energized by injecting a 1 p.u. step at the core of cable 1
0 1 2 3 4 5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (ms)
Voltage (V)
μr = 100 μr = 10 μr = 1
FIGURE 3.32
Example 3.5: Effect of armor permeability on overvoltage. (From Gustavsen, B. et al., IEEE Trans. Power Deliv., 20, 2045, 2005. With permission.)
x = 15.24 cm (a)
Air Soil h = 76.2 cm
ρcu ρpb ε2=3.3 ε1=3.3
rnirnersirse
rni= 1.27 cm rne= 2.82 cm rsi= 2.93 cm rse= 3.45 cm Cable radii μ2, ε2, ρ2=10 Ω.m
μ1, ε1, σ1=0
(b)
Cable 1
VL V0
Cable 2
Cable 3
ℓ = 1000 m
Core 1 Sheath 1
Sheath 2
Sheath 3 Core 2
Core 3
u(t)
FIGURE 3.33
Example 3.6: Underground transmission system. (a) Transversal confi guration; (b) longitudinal confi guration.
by an ideal voltage source. Note in Figure 3.33b that unenergized cores and sheaths are solidly grounded at the source end and opened at the load-end. Note also in Figure 3.33a that semicon-ducting screens are not included. The transient response of the system is now obtained by using the numerical Laplace transform (NLT) technique [37], and by applying four different methods for calculating Zg. These methods are: (1) Carson approximation (Equation 3.24), (2) SGG formula (Equation 3.25), (3) WW formula (Equation 3.26), and (4) Infi nite Earth Model formulas (Equations 3.27 and 3.28).
Figure 3.34a shows the four waveforms obtained at the load-end of the energized core. Since the differences among these plots are diffi cult to detect by eye, Figure 3.34b provides their percent differences taking as reference the one obtained with the SGG formula. Note that the differences are negligible.
Figure 3.35a shows the waveforms of voltage induced at the load-end of core 3 as obtained with the four methods for evaluating Zg. Now the differences among the four results are more noticeable than those in Figure 3.34a. Figure 3.35b provides the percent differences by taking the SGG results as reference. It can be observed from this last fi gure that the error at approximating Zg has a larger effect on the calculation of induced voltages as the distance between the cables is increased. This observation can be of particular relevance when analyzing transient inductions that are caused by underground cables on pipeline systems.
00 0.1 0.2
Example 3.6: Transient response of energized core. (a) Voltage waveforms as obtained with four different methods to estimate Zg; (b) percent relative differences taking SGG results as reference.
0 0.1 0.2
Example 3.6: Induced transient. (a) Voltage waveforms as obtained with four different methods to estimate Zg; (b) percent relative differences taking SGG results as reference.
3.9 Conclusions
This chapter has presented conversion procedures aimed at preparing available cable data for application of CC routines and considered cable data for simulating transients on phase conductors of SC cables, three-phase cables, and pipe-type cables. The main conclusions can be summarized as follows:
1. CC routines do not directly apply to SC cables with semiconducting screens, so a conversion procedure is needed before entering the cable data. This chapter describes the needed conversions and also describes the conversions needed for handling the core stranding and wire screens.
2. The nominal thickness of the various insulation and semiconducting cable screens, as stated by manufacturers, can be smaller than those found in actual cables. This can result in a signifi cant error for the propagation characteristics of the cable model.
3. CC routines do not take into account any additional attenuation at very high fre-quencies resulting from the semiconducting screens.
The chapter has focused also on the importance of a correct modeling of semiconducting screens of SC coaxial-type cables. It is shown that a careless modeling can produce a model with too low surge impedance and a too high propagation velocity. The importance of accurate modeling is strongly dependent on the type of transient study. If the cable is part of a resonant overvoltage phenomenon, an accurate representation of the surge impedance and the propagation velocity is crucial. The conclusions derived from the study on input data can be summarized as follows:
a. It is always necessary to accurately specify the geometry and material properties of the core conductor, the main insulation, and the sheath conductor. It is also important to take the semiconducting layers into account. A simple procedure for achieving the latter is shown in Section 3.4.
b. Lossy effects of paper–oil insulation lead to a strong attenuation and dispersion of narrow pulses. At present, none of the existing CC routines can take this into account.
c. The representation of insulating layers external to the sheath conductors is not very important when the sheaths are grounded at both ends.
d. The representation of metallic conductors external to the sheath conductors is important at low frequencies where the penetration depth exceeds the sheath thickness.
e. Transient voltages can be strongly sensitive to the permeability of any steel armor-ing when the magnetic fi eld penetrates the sheaths.
f. Ground-return impedance is a more infl uential parameter in arrays of parallel coaxial cables than in three-phase self-contained cables or in pipe-type cables. For the latter ones, the ground-return currents could even be ignored.
g. Error maps provided in Figures 3.9 and 3.10 can be used on a case by case basis for an assessment of two methods of ground-return impedance estimation.
h. Ground-return impedance presents a low sensitivity to changes in burial depth of cables. Ground-return resistance has a low sensitivity to changes in transversal
distances and in ground resistivity, whereas ground-return inductance presents a higher sensitivity to these two physical parameters. Nevertheless, variations either in cable distances or in ground resistivity produce changes one order of magnitude lower on ground-return inductances.
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