The Optimal Share of Variable Renewables: How the Variability of Wind and Solar Power affects their Welfare-optimal Deployment.

Author:Hirth, Lion

    Many jurisdictions have formulated quantitative targets for energy policy, such as targets for greenhouse gas mitigation, energy efficiency, or deployment of renewable energy sources. For example, the European Union aims at reaching a renewables share in electricity consumption of 35% by 2020 and 60-80% in 2050; (1) similar targets have been set in many regions, countries, states, and provinces around the globe. Implicitly or explicitly, such targets seem to be determined as the welfare-maximal or "optimal share" of renewables, however, it is often unclear how targets are derived. This paper discusses the socially optimal share of wind and solar power in electricity supply. It provides a theoretical analysis that is focused on the variability of these energy sources, a structured methodological literature review, and numerical estimates for Northwestern Europe.

    The optimal amount of wind and solar capacity is determined by the intersection of their marginal benefit and marginal cost curves. Both curves are not trivial to characterize, since they are affected by many drivers. Marginal costs are impacted by technological learning, raw material prices, and the supply curve of the primary energy resource. Marginal benefits are driven by the private and social costs of alternative electricity sources, such as investment costs, fuel prices and environmental and health externalities. They are also affected by the variability of wind and solar power. This paper discusses the impact of variability on solar and wind power's marginal benefit curve and their welfare-optimal quantities.

    Wind and solar power have been labeled variable renewable energy (VRE) sources (also known as intermittent, fluctuating, or non-dispatchable), since their generation possibilities vary with the underlying primary energy source. Specifically, we refer to "variability" as three inherent properties of these technologies: variability over time, limited predictability, and the fact that they are bound to certain locations (cf. Milligan et al., 2011; Sims et al., 2011). These three aspects of variability have implication for welfare, cost-benefit, and competitiveness analyses. For example, the marginal value (or price) of electricity depends on the time it is produced, and hence the marginal benefit of solar generators might be increased by the fact that they produce electricity at times of high demand. For unbiased estimates of the optimal amount of wind and solar capacity, their variability has to be accounted for. This paper explains theoretically why variability matters, how it can be accounted for, and presents an empirical application.

    This study contributes to the literature in four ways. Firstly, we theoretically explain why variability has economic consequences. We present a framework that allows accounting comprehensively and consistently for of all aspects of VRE variability, but is simple enough to allow for quantifications. Secondly, we provide an extensive review of the existing empirical model landscape to explain which kind of modeling approaches are able to capture which driver of marginal costs and benefits, and specifically, which models are able to represent variability. Thirdly, we present new numerical model results. Results are derived from the power market model EMMA that has been developed to capture variability appropriately. Variability is shown to have a large impact on the optimal share of VRE. Finally, we test the impact of price, policy, and technology shocks on the optimal share numerically. We find and explain a number of unexpected results, for example that higher CO2 or fuel prices can reduce the optimal VRE share under certain conditions.

    The paper is structured as follows. Section 2 discusses welfare analysis theoretically. Section 3 reviews the literature. Section 4 introduces the numerical electricity market model EMMA that is used in section 5 to estimate optimal penetration rates of wind and solar power for Northwestern Europe. Section 6 summarizes the numerical results and section 7 concludes.


    This section discusses the economics of variable renewables theoretically. It applies microeconomic theory to electricity markets to derive the welfare-optimal quantity of wind and solar capacity. This paper focuses on different aspects of variability. Other economic issues such as endogenous learning, externalities, or political economy issues of security of supply are important, but beyond the scope of this paper. The theoretical arguments put forward in this section are not restricted to variable renewables, but apply to all generation technologies.

    As common practice in economics, we determine the "optimal amount" of wind and solar power as the welfare-maximizing amount. Elsewhere, the optimal VRE capacity has been determined by minimizing curtailment (Bode 2013), minimizing storage needs (Heide et al. 2010), or optimizing other technical characteristics of the power system. Denny & O'Malley (2007) determine the "critical amount" of wind power, where net benefits become zero.

    As for all other goods, the welfare-optimal quantity of wind or solar capacity is characterized by the intersection of its long-term marginal costs and marginal value (benefit). However, deriving wind power's marginal cost and marginal benefit is not trivial. Economic cost-benefit analyses of electricity generation technologies require careful assessment and appropriate tools, because electricity as an economic good features some peculiar characteristics that make it distinct from other goods. In this section, we identify those peculiarities (2.1), derive the marginal cost (2.2) and marginal value (2.3) of VRE, and determine its optimal quantity (2.4). Throughout the paper, we expressed VRE quantities as share of total electricity consumption.

    2.1 Electricity is a Peculiar Commodity

    Electricity, being a perfectly homogeneous good, is the archetype of a commodity. Like other commodities, trade of electricity often takes place via standardized contracts on exchanges. In that sense, it seems straightforward to apply simple textbook microeconomics to wholesale power markets. However, the physical laws of electromagnetism impose crucial constraints, with important economic implications: i) storing electricity is costly and subject to losses; ii) transmitting electricity is costly and subject to losses; iii) supply and demand of electricity need to be balanced at every moment in time to guarantee frequency stability. These three aspects require an appropriate treatment of the good "electricity" in economic analysis (Hirth et al. 2014).

    As an immediate consequence of these constraints, the equilibrium wholesale spot electricity price varies over time, across space, and over lead-time between contract and delivery:

    i) Since inventories cannot be used to smooth supply and demand shocks, the equilibrium electricity price varies dramatically over time. Wholesale prices can vary by two orders of magnitudes within one day, a degree of price variation that is hardly observed for other goods.

    ii) Similarly, transmission constraints limit the amount of electricity that can be transported geographically, leading to sometimes significant price spreads between quite close locations.

    iii) Because demand and supply has to be balanced at every instant, but fast adjustment of power plant output is costly, the price of electricity supplied at short notice can be very different from the price contracted with more lead-time. Hence, there is a cost to uncertainty.

    Across all three dimensions, price spreads occur both randomly and with predictable patterns. While the economic literature has emphasized temporal heterogeneity (Bessiere 1970, Stoughton et al. 1980, Bessembinder & Lemmon 2002, Lamont 2008, Joskow 2011), the other two dimensions have not received similar attention.

    In other words, electricity indeed is a perfectly homogenous good and the law of one price applies, but this is true only for a given point in time at a given location for a given lead-time. Along these three dimensions, electricity is a heterogeneous good and electricity prices vary. Figure 1 visualizes the three dimensions of heterogeneity by displaying the array of wholesale spot prices in one power system in one year.

    This fundamental economic property of electricity is approximated in real-world power market design: at European power exchanges, a different clearing price is determined for each hour and for each geographic bidding area. U.S. markets typically feature an even finer resolution, clearing the market every five minutes for each of several thousand transmission nodes. In addition, there is a set of power markets with different lead-times: in most European markets, there is a day-ahead market (12-36 hours before delivery), an intra-day market (few hours before delivery), and a balancing power market (close to real-time). As a consequence, there is not one electricity price per market and year, but 26,000 prices (in Germany) or three billion prices (in Texas). (2) Hence, it is not possible to say what "the" electricity price in Germany or Texas was in 2012.

    The heterogeneity of electricity is not only reflected in market design, but also in technology. For homogenous goods, one production technology is efficient. In electricity generation, this is not the case: there exists a set of generation technologies that are efficiently used simultaneously in the same geographic market. There are nuclear and coal-fired so-called "base load", natural gas-fired "mid load" combined cycle gas turbines, and gas- and oil-fired "peak load" open cycle gas turbines. These technologies can be distinguished by their fixed-to-variable costs ratio: Base load have high capital costs but low variable costs. They are the most economical supply option for the share of electricity demand that is constant. Peak load plants have low fixed...

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