|Fig. 1: Transmission in Oregon, United States, roughly one mil south of Celilo Converter Station. One the left is a 230 kV AC line. On the right is the Pacific DC Intertie, the largest HVDC project in the United States. (Source: Wikimedia Commons)|
Ultra-High Voltage (UHV) cabling has been proposed in conjunction with other smart grid technologies to make electrical cabling systems more amenable to renewable energy sources.  In particular, since hydro, solar, and wind power generation all produce direct current (DC) electricity, long-distance, DC renewable energy transmission lines are desirable for the supply of renewables in regions where they are scarce or highly intermittent.  Any list of proposed HVDC lines, at least in the United States, is long and mostly unrealized, however. As a result, it is important to understand, even in a pixelated manner, the economics of these interconnects and their prospects in the current energy marketplace.
Standard power supply is accomplished with alternating current (AC) transmission in which the direction of charge transport in an electrical line changes periodically as a sinusoidal wave. Renewable energy often generates unidirectional, DC electricity, however.  Use of DC electricity in most American cities (and other electrical grids in developed countries) would require new investment in large scale conversion of DC to AC current at the local level, which until recently was far more expensive than the AC-to-DC conversion accomplished by rectifiers in outlets. 
Furthermore, transformers capable of voltage up- and down-conversion operate using the induced current from an AC source to produce a magnetic field.  Without oscillations in the current, no magnetic field is induced, so rectification is needed to convert AC to DC current for subsequent voltage down-conversion on a local grid. This process requires expensive high-voltage inverters that must be repaired every few years and replaced more frequently than transmission lines, dis-incentivizing the use of high-voltage direct current (HVDC) transmission over short distances. 
Ohmic, or resistive, losses represent the largest portion of losses in power transmission.  Ohmic losses in AC and DC wires are comparable depend only upon constants such as wire thickness, wire separation, and rated voltage in the line.  For economic reasons, these thicknesses tend to be similar in both AC and DC high-voltage lines, meaning that losses due to resistance in the wire are roughly the same in practice. 
Additionally, while it is true that the skin effect, a phenomenon in which current in an AC line pools around the edges of the wire, leads to additional losses, these can be minimized by engineering to contribute to only very slightly lower losses from DC transmission up to 1000 km over land. [8,9] The preference for DC over long distances can be explained more simply by the electrical length of a transmission line, given by l = c/f, where c is the speed of light and f is the frequency. For f = 60 Hz, l ~ 5000 km. 
At about 5,000 km, the wire is one electrical length, meaning that the phase has been shifted by a single cycle.  This represents a potential signaling instability. AC connections t hus need to be electrically short, preferably less than 10% of this length.  The result is that, for distances greater than 500 km, and certainly after the 800 km often cited as an economic break-even distance, it is advantageous to use DC interconnects because the current in a DC line has no phases and thus no phase shifts. [2,11] In fact, the phasing issue is so cumbersome to overcome that utilities often choose to convert to HVDC for lengthy transmission between networks, rather than synchronizing phase between AC networks. 
A consequence of this electrical length argument is that the lion's share of the long, renewable energy-carrying interconnects envisioned by smart grid advocates will be DC. Transporting wind power from the Great Plains to the East, hydropower from the Northeast to California, or solar from the Mojave to any major urban regions outside of Los Angeles and Las Vegas will require connections over the 500 km limit of electrical shortness and involve DC power sources. The same phase-related limitations also apply to electrical grids in China, hence the adoption of HVDC lines to move electricity upwards of 1000 km from the west of the country to its more populous east. Since renewable energy sources are scattered geographically and hydro, solar, and wind power all produce DC, an understanding of whether HVDC interconnects are cost-competitive is fundamental to assessing the compatibility of renewable energy sources with the electrical grid.
Large investments in China are often cited as reason for optimism about HVDC technology.  The Chinese government built 9 HVDC lines between 2009 and 2017, connecting energy sources in its northwest (wind farms, in particular) with population centers in the east.  China's State Grid invested $57 billion in high-voltage projects between 2009 and 2018. The country is widely considered the global leader in HV transmission deployment, with approximately 60% of the worlds capacity. [14,15]
Because the Chinese government is relatively free of economic constraints, stagnation in smart grid developments in the United States is perhaps the better lens through which to assess HVDCs prospects globally. In spite of numerous propositions, perhaps most notably a 4 GW Plains and Eastern Clean Line from wind farms in the Oklahoma Panhandle to the Memphis area, HVDC projects in America have been few and far between since 1970, when the Pacific Intertie was commissioned. [16,17] (See Fig. 1.)
A cost calculation using the Plains and Eastern Clean Line can help us understand why this might be the case. While we will not include inflation and upkeep costs, the fact that natural gas is often cheaper than coal, or underestimation of costs with regard to transmission line projects, we can get a rough economic picture by comparing the proposed HVDC project's price tag to the daily cost of shipping coal to Memphis and seeing where in the future a break-even point occurs. For a large transmission line to be economically competitive (i.e. not reliant on government financing for installation), the break-even point should be roughly at or below the lifespan of the cable.
The Plains and Eastern Clean Line would be a 4GW project, so the amount of power it carries in a day is [16,17]
An average coal car in a train has a bed capacity of about 112.5 tons when cost is minimized.  The average energy content of bituminous coal (though this varies by coal source) is 2.74 × 1010 Joules per ton.  Multiplying gives a minimum of 3.08 × 1012 Joules per train car. Dividing 2.68 × 1014 by this value indicates that a train carrying coal would have to deliver 87 cars carrying 112.5 tons of coal apiece to provide as much energy as the transmission line in a day. Coal cost per ton-mile (the price of shipping one ton of coal one mile by railroad, estimated using the surrogate figure of revenue per ton-mile) was about 2.17 cents in 2018, or $0.0217.  Multiplying by 87 cars carrying 112.5 tons apiece yields a cost of $212.25 to ship the Plains and Eastern Clean Lines 1 day equivalent in coal one mile.
The proposed HVDC project's length was 720 miles, a factor that greatly affects its $2.5 billion price tag.  Since transmission cables generally follow straight lines, it is easy to fall into the trap of assuming that travel the shortest path between energy source and energy sink. This erroneous assumption, applied here, would give a cost of $212.25 per day-mile multiplied by 720 miles, or about $153,000 per day. Dividing $2.5 billion by this value yields a timeframe of 16359 days or roughly 44.8 years after which the costs associated with the HVDC project are lower than those from shipping coal to local power plants. Since HV transmission lines have stated lifespan of about 40 years, such a calculation explains enthusiasm over their economic competitiveness. 
As it turns out, however, there are plenty of coal sources less than 720 miles from Memphis, including substantial ones in Illinois and Kentucky (even much of West Virginia is less than 720 miles away). Let us, for the sake of argument, assume that the coal comes from Kentucky's Muhlenberg County (once the state's largest in terms of coal production), about 250 miles from Memphis.  Then
In other words, the Plains and Eastern Clean Line would take three times its projected lifespan to pay off, even without accounting for maintenance and DC-to-AC converter replacements, which occur every 20 years . It is clear, then, that coal is cheaper for Memphis. Without massive government investments, an HVDC project makes little economic sense compared to coal trains except in specialized circumstances, such as transporting wind or hydroelectric power to places where coal sources are quite distant. Since government support seems to be, in most cases, a prerequisite for overcoming this cost calculus, it appears that the development of a high-voltage smart grid capable of transporting renewable energy across America is highly dependent on political will.
It is difficult to locate comparable figures for use assessing the economic situation in China. Sources for coal costs per ton are poorly documented, and locating costs per ton-mile (or ton-km) is more difficult still. There is reason to believe that the economic incentives for HVDC projects are even weaker in China, though. The deregulation of railroads in the United States in 1980 led to increased coal prices because, as a commodity, coal is heavy, bulky, and cheap and therefore cannot at present deliver large profits to the railroad companies shipping it. [20,23] Since China is the world's largest coal consumer and its railroads are state-owned, it stands to reason that the cost issue with long-distance HVDC lines in America would be more pronounced there. [24,25]
Government-sponsored HVDC projects in China, then, would not appear to have any more an economic basis than those in America. The key difference seems not to be economics but rather the government's willingness to sponsor massive engineering programs. While that is the case, investments large enough to shift the energy landscape in favor of renewables will prove difficult. Even in China, HVDC projects had an installed capacity of 119.7 GW in 2018, compared with a forecasted energy demand above 1200 GW, meaning that HVDC lines carry less than 10% of the country's electricity.  Dreams of HV transit routes for solar energy produced in deserts and wind energy in plains, in the United States and China alike, will require an order of magnitude greater investment than the $57 billion invested by China and the $60 billion proposed for smart grid strategies in the U.S. as part of Hillary Clinton's 2016 environmental platform. [14,26] Since these investments do not pass muster economically, they are, at present, a bitter pill to swallow and a major barrier to large-scale renewable energy deployment.
© Caravaggio Caniglia. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. 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.
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