New technologies—and new expectations—require taking a fresh look at the institutions and practices that have provided reliable electricity for the past century. Collective action is needed to...
Getting It Right: The Real Cost Impacts of a Renewables Portfolio Standard
Although the analysis can be performed using these kilowatt-hour costs directly, transforming them into measures of return yields more useful graphical results that closely resemble the standard textbook presentation of portfolio theory. Annual return measures an output (yield) divided by an input (cost). A useful return measure for our purposes is kilowatt-hour per $0.01 - the simple inverse of the familiar busbar cost. The resulting portfolio risk measure thus remains essentially one of cash-flow variance.
Figure 3 illustrates the results, using the historic fossil prices and their correlation. The 100 percent coal portfolio (Point B) "yields" 12.5 percent, (1 kWh at $0.08). Adding some gas to the mix helps; it reduces risk while simultaneously raising return (up to Point V; this result is driven by the historic covariance of the fuel prices so that altering the levelized costs for A and B does not change this outcome). As a nation, however, we have pretty much exploited these gains over the past decade by expanding our gas-based generation from its 1990 levels.
The minimum variance of the fossil portfolio (0.21) occurs at V, which represents a coal-gas mix of approximately 80 percent-20 percent. (Each tick mark represents a 5 percent change in mix on the fossil portfolio.) After this point, further gas additions increase both risk and return until a 100 percent gas portfolio is obtained (Figure 3 is truncated at 60 percent gas-40 percent coal for illustration purposes).
As in Figure 2, the straight-line segment in Figure 3 represents portfolios consisting of the mix M combined with a riskless resource. At F (lower left), the portfolio consists of 100 percent riskless renewables. (Each tick mark along the line segment represents a 25 percent addition of the fossil mix M.) Finally, at M, the portfolio consists entirely of the fossil mix. Portfolios along the dashed line above M consist of M plus the riskless (i.e., fixed-price) sale of power at $0.12 per kilowatt-hour, which is directly analogous to the previous section's results using margin borrowing. Such portfolios may have important implications for private power marketers, although their public policy ramifications do not seem clear at this time.
The Optimal Mix:
Coal vs. Gas vs. Renewables
What does portfolio theory teach us about the optimal mix of coal- and gas-fired generation?
The optimal coal-gas mix is entirely analogous to the optimal mix of risky financial assets in the last section. In the presence of the $0.12 per kilowatt-hour riskless renewable, it turns out that the optimal mix is 72 percent coal-28 percent gas (Figure 3, Point M). By comparison, the 1998 U.S. coal-gas generation mix (utility and non-utility power plants) already is at 77 percent coal-23 percent gas (Figure 3, Point U).[Fn.17] The results of Figure 3 therefore clearly imply that we must reconsider our policy of significantly higher gas usage. From a risk-reward perspective, gas usage should be expanded by only 22 percent to reach M (seven percentage points, from 23 percent to 28 percent of the mix).[Fn.18] Further increases push the mix past this optimum into an undesirable region where the risk