Level versus Variability Trade-offs in Wind and Solar Generation Investments: The Case of California.

• Author: Wolak, Frank A.

1. INTRODUCTION

   This paper quantifies the total renewable energy output and revenue consequences of different combinations of wind and solar generation investments in California using hourly output and real-time market revenue data for all wind and solar generation units in the California Independent System Operator (ISO) control area from April 1, 2011 to March 31, 2012. This data is used to construct an economic model that provides an estimate of the average annual mean and covariance matrix of the hourly energy production and the average annual mean and covariance matrix of hourly real-time revenues for all existing wind and solar locations in California for any amount of renewable generation capacity at each existing renewable location.

   The economic model is used to compute the shares of statewide wind and solar capacity at existing wind and solar locations in California that yield the highest annual average hourly output for a given value of the annual variability of hourly output, or equivalently the lowest annual variability in hourly output for a given value of the average hourly output. These pairs of annual average hourly output and annual variability in hourly output define the mean output and standard deviation of output efficient frontier for wind and solar investments at existing wind and solar locations in California. Points on this efficient frontier are compared to the actual hourly average output and annual variability in hourly output from actual wind and solar generation units.

   This same exercise is repeated for the annual average hourly revenue and annual variability in hourly revenue for wind and solar generation locations in California. Locational capacity shares at all existing wind and solar locations in California are computed that yield the highest annual average hourly revenues for a given value of the annual variability of hourly revenues, or equivalently the lowest annual variability in hourly revenues for a given value of average hourly revenues. These annual average hourly revenues and annual variability in hourly revenues pairs define the mean hourly revenue and standard deviation of hourly revenue efficient frontier of wind and solar investments at existing wind and solar locations in California. Points on this efficient frontier are compared to the actual hourly average revenue and annual variability in hourly revenue from the actual portfolio of wind and solar generation units.

   Although the renewable generation locations are distributed throughout a state with a geographic area slightly smaller than France and slightly larger than Germany, these two analyses reveal a high degree of contemporaneous correlation between the hourly output of the 13 solar locations and 40 wind locations in California that produced energy throughout the 2011-2012 fiscal year. This result suggests modest opportunities to reduce the variability in the total hourly output and hourly revenue of wind and solar resource owners by optimizing where and how much solar and wind generation capacity is placed at each existing location in California. Nevertheless, the hourly output efficient frontier implies that a 48 percent increase in the annual average hourly output of solar and wind units is possible without increasing the annual standard deviation of hourly output only by changing the state-wide capacity shares of the wind and solar investments at the existing wind and solar locations in California. More modest increases in the average hourly revenue for solar and wind generation units can be obtained by optimizing the locational capacity shares of these investments. The hourly revenue efficient frontier implies that 26 percent increase in the annual average hourly real-time revenue of the solar and wind generation capacity is possible without increasing the annual standard deviation in hourly revenues by changing the state-wide capacity shares of the wind and solar investments at the existing wind and solar locations. This 26 percent increase in the annual average hourly revenue is found to be statistically significantly smaller than the 48 percentage increase in annual average hourly output.

   To assess the extent to which the results described above are robust across hours of the day, separate efficient frontiers are computed for four groups of hours of the day. The largest gains in expected output or reductions in the standard deviation of output as a result of moving from the actual capacity shares of wind and solar investments to the efficient frontier appears to be during the late morning and afternoon hours of the day.

   The capacity shares of wind and solar investments on the annual hourly output efficient frontier and the capacity shares on annual hourly total revenue efficient frontier are similar, but they are both very different from the actual capacity shares. The capacity shares on both efficient frontiers concentrate the statewide capacity of wind and solar investments on a substantially smaller number of locations than actual wind and solar capacity investments.

   Taken together, these empirical results have implications for the design of policies to stimulate the deployment of renewable generation capacity. As the share of annual energy production provided by intermittent generation resources in a region increases, the cost of managing the real-time supply and demand balance increases. (1) For the same annual average hourly output from wind and solar resources, a more variable hourly output from these generation units implies more operating reserves are required to maintain grid reliability standards. Consequently, a substantial amount of the increased hourly renewable energy output variability associated with scaling wind and solar energy production in California could be mitigated by constructing additional wind and solar capacity in the resource areas that minimize the increase in the annual standard deviation of hourly output.

   To demonstrate the empirical content of this statement, the elasticity of annual average hourly output with respect to the annual standard deviation of hourly output for a 1 MW increase in capacity at that location is computed for each existing wind and solar location in California starting from the current statewide locational capacity shares for wind and solar generation capacity. There is substantial heterogeneity in these elasticities across locations. For some locations the elasticity is as much as ten times larger than it is at the majority of wind and solar locations in California, indicating that at these locationsa1MWincrease in wind or solar capacity would have a significantly larger increase in the annual average wind and solar output for the same increase in the annual standard deviation in hourly output from these units. There are even some locations where the elasticity is negative, meaning that a 1 MW increase in wind or solar capacity at that location would increase the annual average hourly output and reduce the annual standard deviation of hourly output. Wind and solar investments at locations with the highest values of these elasticities are likely to minimize the system reliability and operating costs associated with achieving any statewide renewable energy goal.

   The remainder of the paper proceeds as follows. The next section provides a discussion of related research. Section 3 presents a model of output and revenue risk diversification for wind and solar generation investments. Section 4 contains descriptive statistics on the California electricity market and discusses the data used to construct the efficient frontiers. Section 5 discusses the computation of the efficient frontiers and the procedure used to compute the maximum risk-adjusted expected output and expected revenue points on these curves as well as location-specific measures of non-diversifiable wind and solar output and revenue risk. Section 6 presents the empirical results. Section 7 discusses the implications of these results and the design of potential policies to minimize the reliability and operating costs associated with meeting any renewable energy goal. Section 8 concludes.

2. PORTFOLIO-BASED APPROACHES TO NEW GENERATION INVESTMENT DECISIONS

   A number of papers have formulated electricity generation capacity technology mix decisions as portfolio choice problems. Bar-Lev and Katz (1976) first applied expected return and risk (standard deviation of return) portfolio theory to the choice of the mix of fossil fuel generation capacity--coal, natural gas, and oil--used to produce electricity. Awerbuch and Berger (2003) employed mean-variance portfolio theory to derive European Union (EU) generation portfolios that enhance energy securities objectives. They quantified the investment return and risk diversification benefits of increasing the amount of renewable generation capacity in the EU. Roques, Newbery and Nuttal (2008) employ Monte Carlo simulations of natural gas, coal, and nuclear generation unit investment return distributions to solve a mean-variance portfolio choice problem for an optimal mix of these generation technologies for firms in a re-structured wholesale electricity market. Bazilian and Roques (2008) contains a number of papers that extend in a number of directions the application of expected return and risk portfolio theory to electricity supply industry investment decision-making processes.

   Westner and Madlener (2010) apply mean-variance portfolio theory to Monte Carlo simulations of distributions of the net present value (NPV) of individual combined heat and power technologies in the four largest Western European countries to study the potential for regional diversification benefits of investments in these technologies. Westner and Madlener (2011) consider investments in four combined heat and power technologies in Germany and employ Monte Carlo simulations of the joint distribution of the NPVs of each technology, and from this compute the NPV...