Is Mandating 'Smart Meters' Smart?

AuthorLeautier, Thomas-Olivier
  1. INTRODUCTION

    "Smart meters" which allow electric power users to respond to wholesale spot prices, are expected to transform the electric power industry. Consumers will reduce their consumption during peak hours, thus reducing installed capacity requirement and emissions of CO2 and other pollutants. The potential value of these demand management benefits is significant. For example, Faruqui et al. (2009), estimate the annual potential value for all of Europe of reduced capacity cost at [euro] 4.8 billions, and the value from reduced electricity consumption at [euro] 600 millions. Similarly, the Department of Energy and Climate Change (DECC) estimates the Present Value for Britain of energy savings benefits at [pounds sterling] 4,400 millions, carbon savings at [pounds sterling] 1,100 millions, and peak load shifting at [pounds sterling] 800 millions. As a result, full deployment of "smart meters" is underway in many European countries and U.S. states.

    The policy discussion of smart meters appears to be framed as a one-or-zero problem: should we install meters for all users or for none? This is surprising. As all economic problems, it should be cast as an optimal share of deployment problem: which consumer groups should be equipped with smart meters? To answer that question, one should compare the marginal value of equipping a class of consumers against its marginal cost. A key ingredient in the analysis is the marginal value of Real Time Pricing (RTP), i.e., the marginal surplus generated by one customer becoming price responsive. This is precisely what this article estimates.

    This article builds on and complements a rich literature. Reiss and White (2005) and Allcott (2011) estimate individual price elasticity of customers, and use these elasticities to estimate welfare effects. Reiss and White (2005), using data from California households, focus on the non-linearity of the pricing schedule and estimate demand for eight different types of electric appliances, e.g., electric space heating, room air conditioning, etc. They then estimate the welfare impact of a rate structure change proposed in California. Allcott (2011) estimates the demand function from consumers opting for Real Time Pricing in a pilot program in Chicago. He then estimates the annualized short term consumer surplus increase from RTP, assuming wholesale prices and producers profits are constant, at $10 per household.

    Holland and Mansur (2006), Borenstein (2005), Borenstein and Holland (2005), and Allcott (2012) use existing estimates of price elasticity to estimate the welfare impact of RTP. Holland and Mansur (2006) estimate the short-term welfare impact of exposing 33%, 67%, and 100% of demand to RTP in the Pennsylvania-New Jersey-Maryland market (PJM), a large power market in the North East of the United States. The estimated gross welfare gain if 100% of load is exposed to RTP is 0.24% of the total energy bill. Borenstein (2005) estimates the long-term welfare impact, including adjustment to the generation mix, of exposing 33%, 66%, and 99% of demand to RTP in the California market. For example if 33% of demand faces RTP, the estimated gross welfare gain ranges from 1.2% of the total energy bill for low elasticity to 7% for high elasticity. Allcott (2012) estimates the long-term welfare impact of moving 20% of demand to RTP in PJM, taking into account the impact of demand elasticity on producers' market power. He finds a gross welfare increase (excluding infrastructure cost) of 38.90 $ per kW of average demand equipped with smart meters.

    This article follows a different approach, that proposes a closed form expression for the marginal value of RTP, then estimates it using the load duration curve of the French power system1 and previous estimates of demand elasticity. Its contribution is twofold. First, it proposes an analytically tractable approximation of the solution to the optimal investment problem for a power system. The general principles of peak-load pricing have been developed in the late 1940s (Boiteux (1949)), and revisited recently (e.g., Borenstein and Holland (2005), Joskow and Tirole (2007)). However, the approximation developed here is the only one I am aware of that provides (almost) closed form solutions to the problem, while closely matching real data. This approximation may be used to examine other issues pertaining to power markets, but also more general issues of sizing and pricing of facilities when demand is uncertain and multiple technologies are available (e.g., infrastructure, cloud computing, etc.).

    This article's second contribution is an estimate of the marginal increase in net surplus of a customer switching to RTP. Using the load duration curve of the French power system and previous estimates of demand elasticity, this value is estimated at 1 to 4 [euro]/customer per year for a small residential customer, whose peak demand is lower than 6 kVA. As a comparison point, this value is far below the cost of installing smart meters for small customers (residential and non residential), currently estimated around 25 [euro]/meter per year.

    This article is structured as follows. The model used in this article is the one developed by Borenstein and Holland (2005) and Joskow and Tirole (2007), building on the earlier work by Boiteux (1949). For convenience, Section 2 summarizes its main features and results. The reader familiar with the model can proceed to Section 3, that presents the impact of a marginal switch to RTP, the main analytical result of the article. Section 4 discusses the development of numerical simulations for the French market, and presents the main empirical results. Section 5 concludes, that proposes avenues of future work. Technical proofs are gathered in the Appendix, available from the author upon request.

  2. THE MODEL

    2.1 Model Structure

    Uncertainty Uncertainty is an essential feature of power markets. In this work, only demand uncertainty is explicitly modeled, since including production uncertainty does not modify the economic insights, although, as discussed in Section 5, it raises the value of RTP. The number of possible states of the world is infinite, and these are indexed by t [member of] [0, + [infinity]]. f(t) and F(t) are respectively the ex ante probability and cumulative density functions of state t.

    Demand

    Assumption 1 All customers have the same underlying demand D(p;t) in state t, where p is the electric power price, up to a scaling factor.

    Assumption 1 greatly simplifies the derivations, while preserving the main economics insights. Inverse demand is P(q;t) defined by D(P(q;t);t) = q, and gross consumers surplus is [mathematical expression not reproducible] is downward sloping: [P.sub.q](q;t)

    Two categories of consumers exist: a fraction [alpha] of consumers faces and react to wholesale Real Time Prices (RTP consumers), and a fraction (1 - [alpha]) of consumers faces a constant two-part pricing scheme ("constant price" consumers), with price [p.sup.R] per MWh, constant across all states of the world, and connection charge A per year.

    Since all consumers have the same load profile up to a scaling factor by Assumption 1, [alpha] is constant across states of the world.

    Supply Different generation technologies are available, indexed by n = 1,..., N. [c.sub.n] is the marginal cost, and [r.sup.n] is the hourly investment cost (i.e., annual investment cost expressed in [euro]/MW/year divided by 8,760 hours per year) of technology n, both expressed in [euro]/MWh. Generation technologies are ordered by increasing marginal cost: [c.sub.n] > [c.sub.m] [for all] n [greater than or equal to] m. There is a trade-off between investment and marginal costs: if a technology produces at higher variable cost, it then requires lower investment cost, i.e., [r.sub.n]

    Sufficient conditions on the costs [{[c.sub.n], [r.sub.n]}.sub.n], presented later in the text, ensure that technologies 1 to N are used at the optimum.

    Rationing and Value of Lost Load As shown for example by Joskow and Tirole (2007), in some states of the world, it may be optimal to curtail constant price customers.

    Assumption 2 The SO has the technical ability to curtail "constant price" customers while not curtailing RTP customers.

    Assumption 2 is unrealistic today, as the SO can only organize curtailment by zone, and cannot differentiate by type of customer. However, it will be met when "smart meters" are being rolled out, which is precisely the situation considered.

    Denote [gamma] [member of] [0,1] the serving ratio: [gamma] = 0 means full curtailment, while [gamma] = 1 means no curtailment. For state t, D(p,[gamma],t) is the demand for price p and serving ratio [gamma], and S(p,[gamma],t) is the gross consumer surplus. By construction, D(p,1,t) [equivalent to] D(p,t) and S(p,1,t) [equivalent to] S(p,t).

    Since curtailed customers are homogeneous, the SO has no basis to discriminate. Thus, curtailment proceeds by geographic zones, and

    D([p.sup.R],[gamma],t) = [gamma]D([p.sup.R],t).

    S([p.sup.R],[gamma],t) depends on the customers' information structure. Suppose first rationing is perfectly anticipated, e.g., the SO announces the day before the exact duration and location of the curtailment. The fraction [gamma] of customers that will not be curtailed consumes normally, hence receives surplus S ([p.sup.R],t) per customers. The fraction (1 - [gamma]) of customers that will be curtailed does not attempt to consume, hence receives no surplus. At the aggregate level, it is reasonable to assume

    S([p.sup.R],[gamma];t) = [gamma]S ([p.sup.R];t).

    If rationing is not perfectly anticipated, customers that end up not being curtailed may refrain from consuming, hence receive no surplus. Conversely, consumers that end up being curtailed may engage in electricity consuming activity (e.g., step in an elevator), hence derive a negative surplus when power is cut. Joskow and Tirole (2007) illustrate on a simple example how the net surplus...

To continue reading

Request your trial

VLEX uses login cookies to provide you with a better browsing experience. If you click on 'Accept' or continue browsing this site we consider that you accept our cookie policy. ACCEPT