Selling Wind.

• Author: Kakhbod, Ali

1. INTRODUCTION

   The market share and total production of renewable electricity is growing rapidly. In 2018, wind energy was responsible for 6.5% of U.S. electricity generation, nearly doubling its market share and total production from five years prior. Renewable electricity is a critical component of global efforts to reduce carbon dioxide emissions, and its cost is rapidly declining.

   Prominent sources of renewable electricity--wind and solar energy--have stochastic resource availability: it is not possible to perfectly predict the quantity of wind or solar power available at any given point in time. The associated spatial and temporal variability of renewable energy resources has a significant impact on their value to society (Joskow, 2006; Hirth, 2013; Hirth et al., 2016). Furthermore, since wind production reduces local prices due to the merit order effect, highly correlated local wind energy availability reduces the average value of wind energy produced (Woo et al., 2011; Ketterer, 2014).

   Existing literature focuses on strategic behavior in electricity markets without substantial amounts of renewable energy. Research on market power in the electricity sector (Joskow et al., 1988) provided important insight for electricity system deregulation. Electricity system market power research does not traditionally focus on stochasticity because fossil-fuel generators do not have significant resource uncertainty. Instead, it focuses on other key features of the electricity sector that impact market power, like transmission constraints (Cardell et al., 1997), financial transmission rights (Joskow and Tirole, 2000), and market price caps (Joskow and Tirole, 2007). Acemoglu et al. (2017) establish that diverse ownership portfolios of renewable and thermal generation by strategic firms may be welfare reducing, because they can reduce (or even neutralize) the merit order effect. Butner (2018) provides empirical evidence of these effects. Since we model an extreme case of competition with only wind producers, our firms strategically withhold wind energy. In practice, when firms own diverse generation portfolios, they will prefer to withhold output from resources with high marginal costs (Acemoglu et al., 2017). Our model explains how information about production availability influences strategy; it can be combined with the existing literature to help explain producer strategy in systems with diverse ownership portfolios and stochastic, correlated, production constraints for renewable energy. Our model also helps show how public information sharing can improve welfare in systems with strategic behavior and stochastic renewable energy production.

   We are interested in how a particular characteristic of renewable energy resources--the stochastic dependence of resource availability across firms-impacts strategic behavior, market power, and welfare. The link between stochastic heterogeneity (1) of resource availability and welfare is an important area for research because various policies impact the investment strategies of wind producers and therefore the stochastic characteristics of the wind energy portfolio in a given region (Kok et al., 2016; Schneider and Roozbehani, 2017b). Common subsidy forms for renewable energy, like the production tax credit (PTC) and state-level renewable portfolio standards (RPS), impact renewable energy investments (Fischer, 2010). Figure 1 shows probability distributions for two different wind farms in the MISO region, conditional on the output of a third wind farm i in the MISO region. The nature of stochastic dependence is very different for each pair of wind farms. Wind farm i 's output is highly correlated with the output of the wind farm displayed on the right, and essentially uncorrelated with the output of the wind farm displayed on the left. (2)

   Clearly, policy changes can impact investment strategies for renewable energy and the characteristics of system-wide resource uncertainty. This begs the questions: Is it important to encourage policies that increase the heterogeneity of stochastic resources? Will investment in wind energy naturally lead to the level of resource heterogeneity that maximizes social welfare? Just as policy makers seek to limit market concentration in certain industries, they might support policies to increase stochastic heterogeneity of renewable resources in the electric power industry. These efforts have growing import because existing strategies for market power monitoring in electricity markets will be challenged by an influx of renewable generation. Regulators have imperfect information regarding resource availability and risk preferences for firms that own stochastic generation. Regulators also have imperfect information regarding opportunity costs for storage facilities that are proposed to mitigate the variability of renewable resources. (3)

   We study strategic firms participating in a Bayesian Game, where firms have private information regarding their realized energy availability, or "state." This energy availability is equivalent to a production constraint, because it limits the extent of production by the firm in any given period. Since the resource availability of wind energy is uncertain, from an individual firm's perspective its competitors' production constraints are stochastic. However, the resource availability of wind energy has a high degree of stochastic dependence; firms can gain important information about their competitors' production constraints from the realization of their own resource availability. As such, the extent of stochastic dependence regarding firms' resource availability becomes an important factor that impacts strategic behavior, market power, and welfare. For clarity, we focus on wind energy, but the insights can be extended directly to solar energy or any other resource with stochastic availability and negligible marginal costs. Since solar and wind resources are not highly correlated, a market with a mix of solar and wind generation probably has greater stochastic heterogeneity than a market with only wind energy and no solar energy. Similarly, a market with a mix of onshore and offshore wind resources probably has greater stochastic heterogeneity than a market with only onshore or offshore wind resources.

   We model producer competition as an incomplete information Cournot game with correlated types, where the type refers to the stochastic resource availability (production constraint) that is private information for each individual producer. The base model uses a Cournot duopoly market. We utilize a parameter d to represent the level of heterogeneity amongst wind producers; throughout, we refer to d as the level of dispersion. Intuitively, we can think of dispersion as being similar to geographic distance; research has shown that correlation in wind availability across pairs of wind producers is generally decreasing in geographic distance (Sinden, 2007). This is a useful intuition but not a general rule; distance is only one feature among many (e.g. geography, climate, turbine orientation) that could impact the level of stochastic dispersion across wind farms.

   The results provide clear insight to explain how stochastic resource heterogeneity can impact welfare in imperfect electricity markets. Increasing heterogeneity in wind resource availability is beneficial for two distinct reasons: it increases the diversification of resources, and it also reduces strategic withholding because it changes the information that a producer's own energy availability provides about the likely energy availability of the other firms in the market. The results of our model imply that imperfect competition in energy markets can affect investment in renewable energy, resulting in a system with sub-optimal levels of resource heterogeneity. (4)

   Next, we investigate the effects of public sharing of high-quality weather forecasts, using the limiting case where the true realized energy availability of firms is monitored and shared. Information sharing through improved forecasting is socially beneficial, but it does not always improve producer profits. As such, it will not necessarily be undertaken by producers acting in their own best interest. This result is conceptually similar to the information sharing literature; we show that it is upheld in our model where production constraints are stochastic and correlated across wind farms. Since producers have stochastic availability, high quality weather forecasting can be undertaken publicly in order to maximize social welfare.

   Finally, the model is utilized to examine the effects of heterogeneity on collusion and on policies to prevent collusion. If they do not face potential penalties for collusion, firms with stochastic availability will always choose to collude because they benefit from sharing information and from sharing monopolistic profits. Increasing heterogeneity of wind production has a range of impacts on collusion, impacting its value to producers, the costs of collusion on social welfare, and the level of enforcement required to prevent collusion.

   These results provide a framework for evaluating policies that impact investment and information-provision in imperfectly competitive markets where firms have stochastic production constraints, like electricity markets with a high penetration of renewable resources. The results can help us understand how policies that impact the dispersion of renewable energy resources, and thus the characteristics of stochastic energy availability, ultimately impact welfare in imperfectly competitive electricity markets.

   1.1 Literature Review

   Literature on wind diversification has focused on the impacts of resource heterogeneity on average electricity prices and the cost of wind integration. Increased heterogeneity of wind resources has at least three impacts on social welfare and the cost of electricity:

1. Balancing costs for managing wind production...