Increasing or Diversifying Risk? Tail Correlations, Transmission Flows and Prices across Wind Power Areas.

AuthorMauritzen, Johannes

    Before wind power became a mature technology, generation tended to be built out in countries and regions that provided financial support, such as Denmark and Northern Germany in Europe and California in the United States. This often meant that wind power was geographically concentrated. Wind power costs have come down dramatically in the previous decade, and onshore wind power is often competitive with traditional generation in many areas (Trancik, 2015; Campisi et al., 2016; Williams et al, 2017; Wiser et al., 2019, 2020). This has meant that wind power capacity has been built up in many more locales, often in countries or regions adjacent to each other. Given available transmission capacity, such geographic dispersion can act as a form of diversification: Mitigating the risks that stem from wind power's intermittency (Grothe and Schnieders, 2011; Simoes et al., 2017; Novacheck and Johnson, 2017; Katzenstein et al., 2010; Roques et al., 2010; Schmalensee, 2016; Green et al., 2016). When there is less wind power in one place, power can be transferred from a neighboring area where the wind is blowing.

    However, experience from other asset classes-both real and financial-have shown that risks that appear to be diversified away in normal times, may show strong correlations during extreme events (Hartmann et al., 2004; Ye et al., 2017). In the context of electricity markets with high penetrations of wind power, the risk that has been most explored is the systemic risk that may come from periods of low wind power generation highly correlated across a wide geographic area leading to a shortfall of generation relative to load. Yet there is also a risk of too much wind generation. If wind is highly correlated across areas at high production times, then it could have the effect of driving down the price towards the short-run marginal cost of wind power-near zero. This price risk is born by wind power producers, but also owners of other generation assets that face lower-than-expected prices and more price volatility. There is also a risk born by the power system as a whole, as excess generation can lead to increased balancing costs and expensive curtailment. The extra uncertainty around prices and electricity market operations can lead to a higher cost of capital, with adverse effects on further investments in renewable energy generation.

    Analyses of the effect of wind power, and in general intermittent generation on power markets and prices have become important subjects within energy economics. Increasing penetrations of renewable generation sources can fundamentally change the price formation process and risk characteristics of wholesale electricity markets. For example, power prices driven by commodity markets will tend to be random walks, while markets dominated by renewables will tend to display mean reversion and trend stationarity (Gianfreda and Bunn, 2018). Correlations between production from renewable sources and power prices may also increase with higher renewable penetrations (Ernstsen and Boomsma, 2018).

    A related area of research has been devising valuation models of wind power that take into account the special characteristics of the generation technology and its effects on market prices and volatility. Many of these analyses take a real-options approach, where correctly specifying uncertainty becomes a particularly important factor in the investment decision and its timing (Tseng and Barz, 2002; Thompson et al., 2004; Munoz et al., 2011; Ernstsen and Boomsma, 2018).

    Many analyses of wind power's effects on power prices use time series techniques to try to estimate a marginal average effect in electricity markets: Gelabert et al. (2011) for Spain, Ketterer (2014) and Paraschiv et al. (2014) for Germany, and Mulder and Scholtens (2013) for the Netherlands. Wen et al. (2020) takes an explicitly spatial econometric approach to estimating the effects of wind on nodal prices in the New Zealand market, but still relies on average marginal estimates. The results of such statistical models have become important inputs in the models of transmission system operators (TSO), and wind power developers who seek to make accurate valuations of proposed projects.

    But we argue that the inference from such models is incomplete. Point estimates that indicate average marginal effects are most useful when a distribution is approximately normal, with few outliers and with most of the probability mass located near the mean value. But wind power is not well approximated by a normal distribution. Instead, production tends to be better approximated by distributions with right-skewness and "fat tails" where periods of large positive production, far removed from the median value of the distribution, can be expected to happen relatively frequently. Recent analytical analyses of the wind power valuation problem, such as Ernstsen and Boomsma (2018) therefore tend to use fat-tailed and right-skewed distributions like the Weibull distribution to model wind power production. Analyses of the effects of wind power on prices that use more flexible, non-parametric modelling such as Rivard and Yatchew (2016) for Ontario and Jonsson et al. (2010) for Denmark, tend to find non-linear effects in periods of high production. We extend this literature by devising a time-series econometric model that allows the estimates of the effect of wind power on prices to vary by decile of production.

    The right-skewness and fat-tails of wind power distributions and their spatial correlation are important considerations in valuation models of wind power. Gonzalez-Pedraz et al. (2014) show how standard methods used in energy markets that tend to ignore or minimize tail behavior will tend to substantially underestimate the risk of a portfolio of generation technologies. Elberg and Hagspiel (2015) develop a stochastic wind turbine valuation model that takes into account the spatial dependence of a given wind power plant and the aggregate wind power production. They note a pronounced "upper-tail dependence"-that is that correlations increase markedly at periods of especially high production, and that this can lead to adverse effects on revenue. A model with purely linear dependence would as a consequence tend to over-value a wind power farm. The spatial character of wind power can also interact with weaknesses in the electricity market structure. BJ0rndal et al. (2018) note that zonal pricing, as exists in the Nordic markets, fails to include enough locational price signals and can therefore lead to excess transmission flows due to wind power.

    While it has long been acknowledged that electricity from intermittent generation will tend to obtain on average lower prices than electricity from dispatchable generators (Joskow, 2011), Hirth (2013) and Schmalensee (2016) point out that the price of electricity from intermittent generation will also tend to consistently diverge from average electricity prices due to the correlations between production and prices. Hirth (2013) devises a statistic he calls a value factor to estimate this divergence. A value factor of 1 represents a situation where electricity from intermittent generation sells at the same averate rate as the average market price. Schmalensee (2016) finds that solar power in many of the areas of the US have a value factor slightly higher than 1, however wind power tends to have value factors somewhat below 1, indicating that production tends to be correlated with low-price periods. This article contributes to this literature, showing how wind power not only is correlated with low prices, but at high penetrations and during high-production periods, can also cause prices to drop further, potentially leading to even lower value factors.

    In this article we study data from Denmark and Sweden: Two countries with large wind power penetrations, which are connected through both large physical transmission capacity as well as through the common Nordic electricity market. We use hourly data from 2016 and 2017 on wind power production, electricity prices, transmission capacities and flows. We particularly focus on the eastern price area in Denmark, called DK2, consisting of the island of Zealand, where the Copenhagen metropolitan area is located. This price area lies between the western Danish area and the southermost Swedish price area, both of which have high penetrations of wind power.

    We first present some descriptive evidence that suggests that for much of the distribution of wind power generation, geographic dispersion of wind power can have a diversifying effect. Geographic correlations between wind power production-even in in adjacent areas-are relatively weak.

    However, a marked difference appears in the 90th decile of the distribution of wind power production. Wind power production at the highest deciles in a given price area are strongly correlated with wind power production in adjacent areas. This suggests that the pattern of power flow, congestion in the network, and marginal price effects may be substantially different in these tail periods compared to average marginal effects.

    To formally explore the patterns of wind power distribution on prices and flows, we develop a flexible but also simple and robust methodology: A dynamic decile group model. We decompose the price and flow variables that serve as our dependent variables into deterministic and stochastic components. Then, instead of estimating an average marginal effect of wind power, we allow the effect of wind to vary by decile of production.

    Our modeling reveals wind power's nuanced effects on pricing and exchange on the electricity market. Wind power in the Danish areas at low deciles of production tends to have little to no effect on prices in DK.2. Instead, the main effect of wind power in this situation is a linear effect on net exchange towards the Swedish price area, which in turn is connected to the flexible hydro...

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