Underground High Voltage Power Cable Maximum Length Estimator
Underground AC power cables have length limitations due to the effects of reactive power flow. This calculator can be used to estimate the maximum theoretical and practical length of AC underground cables on the basis of their thermal rating. Enter the input data, then press "Check Inputs and Calculate Results". This calculator is for "back of the envelope" estimating and should not be used for engineering design. See disclaimer at end of page.
Input Data Default input data is just an example and can be overwritten.
System Data
System Line-to-Line Voltage [kV]
Power system frequency [Hz]
*Earth resistivity [Ohm-m]
Cable Layer Data
Cable thermal rating [Amps]
Core outer radius [cm]
Sheath inner radius [cm]
Sheath outer radius [cm]
Cable outer radius [cm]
**Insulation dielectric constant, εr
Cu Al Core Metal
Cu Al Sheath Metal
Coordinates of Cable Centers (horizontal | depth) [m]
| Phase A
| Phase B
| Phase C
*Typical soil is 100 Ohm-m
**Typical values for εr :
XLPE ≈ 2.3, EPR ≈ 2.8-3.5, PVC ≈ 3.5-8.0, Oil Impregnated Paper ≈ 3.0-5.0
System Line-to-Line Voltage [kV]
Power system frequency [Hz]
*Earth resistivity [Ohm-m]
Cable Layer Data
Cable thermal rating [Amps]
Core outer radius [cm]
Sheath inner radius [cm]
Sheath outer radius [cm]
Cable outer radius [cm]
**Insulation dielectric constant, εr
Cu Al Core Metal
Cu Al Sheath Metal
Coordinates of Cable Centers (horizontal | depth) [m]
| Phase A
| Phase B
| Phase C
*Typical soil is 100 Ohm-m
**Typical values for εr :
XLPE ≈ 2.3, EPR ≈ 2.8-3.5, PVC ≈ 3.5-8.0, Oil Impregnated Paper ≈ 3.0-5.0
Error/Warning Messages
Note: Calculations execute even if input errors/warnings are present, but results may be invalid.
Results
Approximate positive sequence impedance
Per unit length positive sequence inductance
Per unit length positive sequence capacitance
Surge impedance
Surge impedance loading (SIL)
Rated apparent power
Rated apparent power as a fraction of SIL
Maximum theoretical length when operating at rated current with sources at both ends (both switches closed in Fig. 1. See also Fig. 3 and Fig. 5.)
*Approximate maximum practical Length based on no-load conditions (Switch 1 closed and Switch 2 open in Fig. 1. See also Fig. 4.)
Real power transmitted with the practical length cable operating at rated current (both switches closed in Fig. 1. See also Fig. 3.)
Reactive power exported at each end of the practical length cable operating at rated current (both switches closed in Fig. 1. See also Fig. 3.)
*This result is based on the cable thermal rating limitation, but voltage rise (Ferranti effects) at the remote end of the cable (not calculated here) should also be a consideration. Energizing the cable with shunt reactive compensation at the remote end would extend the length of cable that could be energized without exceeding the cable rating. This would also help with Ferranti rise. Studies should be completed to verify effectiveness of shunt compensation and to verify that no resonance problems are introduced. Another option for estimating practical length is to identify the maximum length that gives the minimum allowable ratio of power flow to rated power flow. This can be done using the plot in Fig. 3.
Per unit length positive sequence inductance
Per unit length positive sequence capacitance
Surge impedance
Surge impedance loading (SIL)
Rated apparent power
Rated apparent power as a fraction of SIL
Maximum theoretical length when operating at rated current with sources at both ends (both switches closed in Fig. 1. See also Fig. 3 and Fig. 5.)
*Approximate maximum practical Length based on no-load conditions (Switch 1 closed and Switch 2 open in Fig. 1. See also Fig. 4.)
Real power transmitted with the practical length cable operating at rated current (both switches closed in Fig. 1. See also Fig. 3.)
Reactive power exported at each end of the practical length cable operating at rated current (both switches closed in Fig. 1. See also Fig. 3.)
*This result is based on the cable thermal rating limitation, but voltage rise (Ferranti effects) at the remote end of the cable (not calculated here) should also be a consideration. Energizing the cable with shunt reactive compensation at the remote end would extend the length of cable that could be energized without exceeding the cable rating. This would also help with Ferranti rise. Studies should be completed to verify effectiveness of shunt compensation and to verify that no resonance problems are introduced. Another option for estimating practical length is to identify the maximum length that gives the minimum allowable ratio of power flow to rated power flow. This can be done using the plot in Fig. 3.
Figure 1. Cable system illustration. Interconnecting AC systems could include shunt reactive compensation.
Figure 2. Cable system geometry as entered by user.
Figure 3. Real and reactive power components of flow.
The plot assumes both ends of the cable are connected to sources and have equivalent shunt compensation.
Figure 4. Steady state condition after cable energization from one end.
The plot assumes the remote end of the cable is open circuited and is not connected to any shunt reactors.
Figure 5.
Dashed line is theoretical and indicates the contour that would exist without the effects of reactive power.
The solid contours include the effects of reactive power (substantial reduction in real power transfer capabilty as length increases).
Contour labels indicate the ratio of rated power to surge impedance loading in percent.
Figure 6.
Dashed lines are theoretical and indicate the contours that would exist without the effects of reactive power.
The solid contours include the effects of reactive power (substantial reduction in real power transfer capabilty as length increases).
Contour labels indicate the ratio of rated power to surge impedance loading in percent.
APPROXIMATIONS / ASSUMPTIONS
1. The calculations use an equivalent cable-to-cable spacing determined as: deq = (d12 x d13 x d23)(1/3).
2. The Wilcox-Wedepohl equation is used for earth self and mutual impedances, see [3],[4].
3. Relative magnetic permeabilities of all components are assumed to be 1.0.
4. Calculations do not support armor, but results will still be a rough approximation for cables with both sheath and armor.
5. Losses are neglected.
6. |V1| = |V2| (see Fig. 1)
REFERENCES
[1] M.D. Brenna, F. Donazzi, A. Mansoldo, Long Length EHV Underground Cable Systesm in the Transmission Network, WG B1-304, CIGRE Session 2004.
[2] G. E. Balog, N. Christl, G. Evenset, F. Rudolfsen, Power Transmission Over Long Distances with Cables, WG B1-306, CIGRE Session 2004.
[3] J. A. Martinez-Velasco, "Power System Transients Parameter Determination", CRC Press, Boca Raton, FL, 2010.
[4] A. Ametani, T. Ohno, N. Nagaoka, "Cable System Transients, Theory, Modeling, and Simulation", IEEE Press / John Wiley & Sons, Singapore, 2015.
[5] T. Noda, Numerical Techniques for Accurate Evalaution of Overhead Line and Underground Cable Constants, IEEJ Transactions on Electrical and Electronic Engineering, August, 2008.
DISCLAIMER
This calculator and accompanying background information are provided "as-is" without warranty of any kind and. Electric Utility Design Tools, LLC does not warrant, guarantee, or make any representations regarding the use, results, or documentation in terms of correctness, accuracy, reliability, currentness, or otherwise. The entire risk as to the results of this calculator is assumed by the user.
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