|Fig. 1: Illustration of the model.|
As was demonstrated in the class, current lengths of power lines and their placement is largely determined by the economics. In order to reduce costs it is possible to use Monopolar High Voltage Direct Current cables. Use of one cable instead of 3, less stringent isolation requirements and comparable power carrying capacity make them a viable alternative to long AC power lines. Unlike AC power lines Monopolar HVDC transmits power through one cable using ground instead of second cable. Efficiency of such line is by large determined by resistance of the "ground line" since intrinsic resistance of copper wire can be ignored. In order to estimate required resistance of ground connection let's consider a 500kV, 1GW power line, and shoot for 5% ohmic losses:
This seems to be unrealistically small value of resistance for hundreds of miles of soil which has very high specific resistivity (1010 times more than copper), however we also need to consider that thickness of the ground is much higher than that of a typical copper cable.
In order to keep derivation simple let's assume following setup: two metallic spheres of radius r are placed deep underground, ground specific resistance is ρ (Fig 1.), copper wire with zero resistance connects power source and user's load.
Ohm's law for spheres:
Voltage drop in the ground:
Ground resistance is thus:
It is also interesting to note that converges very fast therefore we should be only concerned with specific resistivity of the ground immediately close to the spheres and can neglect long range dependence.
Transmission line performance in limited by size of electrodes as well as soil resistivity :
|Soil||Average resistivity (ohm-cm)|
|Ashes, cinders, brine, waste||2370|
|Clay, shale, gumbo, load||4060|
|Same, with varying proportion of sand and gravel||15,800|
|Gravel, sand, stones with little clay or loam||94,000|
As was shown before, we are limited by resistivity immediately near the connections therefore we can choose to place electrodes in the region of lowest ground resistance. Let's assume that we used clay of California shore with specific resistance of 5000 ohm-cm, in this case 70 cm electrodes would be enough to achieve projected 12.5 Ω, and save abou 50% of the building and maintenance cost by using two times less material for the wires.
It is not always possible to use Monopolar HVDC - for example in areas with high resistance or frozen soil. These lines also carry sufficient health hazard large stray voltages in the soil and should be avoided in densely populated areas. Both of these problems are solved for long distance over the sea power cables, for example Basslink in Australia that delivers over 500MW through a single wire from mainland to George Town. 
© Dmitry Pushkarev. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 P. Gill, Electrical Power Equipment Maintenance and Testing, 2nd Edition (CRC Press, 2009), p. 684.
 M. Carter et al., "Basslink - Project Design Considerations," in Distribution 2003: 7th International Energy Transmission and Distribution Conference and Exibition (Waldron Smith Management, 2003).