Why Wind Is Not Coal: On the Economics of Electricity Generation.

• Author: Hirth, Lion

1. INTRODUCTION

   In several parts of the world, it is cheaper to generate electricity from wind than from conventional power sources such as coal-fired plants, and many observers expect wind turbine costs to continue to fall. It is widely believed that this cost advantage by itself implies that wind power is profitable (as a private investment option) or efficient (for society). However, this is not the case.

   Inferring about competitiveness from a cost advantage would only be correct if electricity was a homogenous economic good. If that was the case, one megawatt-hour of electricity generated by wind turbines would be a perfect substitute for one MWh of electricity generated by coal plants, and their output could be compared on a pure cost basis. However, electricity prices vary over time, which makes electricity a heterogeneous good.

   We show how ignoring heterogeneity introduces two biases. First, it favors conventional base-load generators relative to peak-load generators, and second, at high penetration rates, it favors variable renewable energy sources (VRE), such as wind and solar power, relative to dispatchable generators. Tools that are used in practice for policy advice and decision support implicitly assume homogeneity and thus run the risk of biasing results: "levelized costs of electricity" (LCOE), "grid parity", and large numerical economical models.

   LCOE are the discounted lifetime average generation costs per unit of energy ($/MWh). Electricity generation technologies, such as coal-fired power plants and wind turbines, are often compared in terms of LCOE (for references see section 4d). Many readers interpret a cost advantage as a signal of competitiveness. Such reasoning implicitly assumes that the electricity generated by all plant types has the same economic value. This is not, however, the case. The same caveat applies to "grid parity", the point where generation costs drop below the retail electricity price. Many macroeconomic models implicitly assume homogeneity as well. Calibrated macroeconomic multi-sector models such as integrated assessment models (IAM) and computable general equilibrium (CGE) models are heavily used for research and policy advice. Simple versions of such models implicitly assume the output of different power technologies to be perfect substitutes, which makes model results prone to the above-mentioned biases.

   Building on earlier work, (1) this paper applies standard microeconomic methods to the power sector, and shows how these methods have to be adopted to accommodate the peculiar characteristics of electricity as an economic good. It offers a rigorous and general discussion of heterogeneity, arguing that electricity prices vary not only over time, but also across space, and with respect to lead-time between contract and delivery. As a consequence, the economic value of electricity generated by different power plant technologies is not identical. In other words, different power plant types produce different goods. LCOE and grid parity do not account for heterogeneity and hence do not account for value differences, which is why they can be biased. The paper shows that value differences can be interpreted as system-level costs. A new cost metric is proposed as the sum of LCOE and system-level costs of a technology, System LCOE, which allows for economically meaningful cost comparisons. Finally, the paper applies this theoretical framework to wind and solar power. We argue that the difference between "variable" and "dispatchable" generators is quantitative, rather than qualitative.

   This article relates to several branches of the literature: screening curves (Phillips et al. 1969, Stoughton et al. 1980, Green 2005), numerical power market models to optimize the generation mix (Covarrubias 1979, Neuhoff et al. 2008, Lamont 2008, Musgens 2013), marginal value of wind and solar power (Grubb 1991, Borenstein 2008, Mills & Wiser 2012, Schmalensee 2013), integration costs (Sims et al. 2011, Holttinen et al. 2011, Milligan et al. 2011, NEA 2012, Sijm 2014), and integrated assessment modelling (Luderer et al. 2014, Sullivan et al. 2013).

   The paper contributes to these branches of the literature by providing theoretical foundations. It adapts textbook microeconomics to accommodate the peculiarities of electricity generation and discusses the implications in a welfare-economic framework.

   The remainder of this paper is organized as follows. Section 2 discusses heterogeneity and gives a formal definition. Section 3 derives first-order conditions for the optimal power mix. Section 4 suggests an alternative formulation of first-order conditions and shows how neglecting heterogeneity can bias findings. Section 5 proposes a decomposition of system costs. Section 6 discusses the economics of VRE. Section 7 concludes.

2. ELECTRICITY IS A HETEROGENEOUS GOOD

   Electricity is a paradoxical economic good, being at the same time homogeneous and heterogeneous. In the one hand, it is a homogenous (undifferentiated) commodity, possibly more so than most other commodities. On the other hand, it is also heterogeneous (differentiated) in the sense that its price can vary dramatically between different moments in time (Boiteux 1949, Bessembinder & Lemmon 2002, and Joskow 2011). This section argues that electricity is not only heterogeneous over time, but along two further dimensions: space, and lead-time between contract and delivery. Figure 1 illustrates how wholesale electricity prices vary along these three dimensions, using observed price data from Germany and Texas.

   2.1 Homogeneity of Electricity

   Electricity can be seen as the archetype of a perfectly homogenous commodity: consumers cannot distinguish electricity produced by different power sources, such as wind turbines or coal-fired plants. (2) In other words, electricity from one source is a perfect substitute for electricity from another source, both in production functions and utility functions. The law of one price applies: electricity from wind has the same economic value as electricity from coal.

   This perfect substitutability is reflected in the real-world market structure, where bilateral contracts are not fulfilled physically in the sense that electrons are delivered from one party to another, but via an "electricity pool": generators inject energy to the grid and the consumer feed out the same quantity. In liberalized markets, electricity is traded under standardized contracts on power exchanges. Wholesale markets for electricity, both spot and future markets, share many similarities with markets for other homogenous commodities such as crude oil, hard coal, natural gas, metals, or agricultural bulk products.

   However, homogeneity applies only at a certain point in time. Since storing electricity is (very) costly, the price of electricity varies over time. More precisely, its price is subject to large predictable and random fluctuations on time scales as short as days, hours, and minutes. Before we discuss this and the other two dimensions of heterogeneity, we formally define "homogeneity" and "heterogeneity".

   2.2 A Formal Definition of Heterogeneity

   We classify a good as heterogeneous if its marginal economic value is variable. More formally, we define a good q to be heterogeneous along a certain dimension (e.g., time) if its marginal economic values varies significantly between different points p (e.g., hours) within a certain range P (e.g., one year).

   We define the "instantaneous" marginal economic value [v'.sub.p] at a point p [member of]P as the derivative of welfare W with respect to an increase of consumption of q at point p.

   [v'.sub.p]:=[partial derivative]W ([d.sub.p],*)/[[partial derivative]q.sub.p] [for all]p[member of]P (1)

   We define a good to be homogeneous along a dimension if

   [v'.sub.p] [congruent to] [v'.sub.p] [for all]p,q[member of]P (2)

   Otherwise, the good is heterogeneous along that dimension. (3)

   For example, a good is heterogeneous in time if its marginal value differs significantly between two moments during one year; a good is heterogeneous in space if its marginal value differs significantly between two locations in one country. Examples of heterogeneous goods include hotel rooms (which are more expensive during the holiday season or during trade fairs than otherwise), airplane travel (which is more expensive on Fridays and Mondays than the rest of the week), and many personal services.

   Heterogeneity requires three conditions. The most fundamental condition for heterogeneity is the absence of arbitrage possibilities. For example, storable goods feature little price fluctuations over time, because inventories allow for inter-temporal arbitrage, (4) and, in the same way, transportable goods feature little price fluctuation across space.

   Constrained arbitrage is a necessary condition of heterogeneity, but it is not sufficient. Demand and/or supply conditions also need to differ between points along the dimension. Take the example of time: if supply and demand functions are unchanged over time, the absence of electricity storage would not lead to price fluctuations. In addition, both demand and supply need to be less than perfectly price-elastic. For example, if the supply curve was horizontal, despite demand fluctuations and lack of storability, the price would remain unchanged.

   Summing up, there are three conditions that are individually necessary and jointly sufficient to make a heterogeneous good: 1. constrained arbitrage; 2. differences in demand and/or supply conditions; 3. non-horizontal demand and supply curves.

   2.3 The Three Dimensional Heterogeneity of Electricity

   We now come back to the three dimensions of the heterogeneity of electricity. The physics of electricity imposes three arbitrage constraints, along the dimensions time, space, and lead-time:

   * Electricity is electromagnetic energy. It can be stored directly in inductors and capacitors, or indirectly in the form of chemical energy...