The Integration of Variable Generation and Storage into Electricity Capacity Markets.

AuthorZachary, Stan
  1. INTRODUCTION

In order to ensure the adequacy of electricity supplies many systems, including those of Great Britain and other European countries and several North American regions, now provide a capacity market--see, e.g., Helm (2017); Newbery (2015); Moye and Meyn (2018); Holmberg and Ritz (2020); National Grid pic (2018a); ISO New England (2020). (Others, e.g. those of Australia and Texas, continue to rely on energy-only markets.) So as to operate such a market both fairly and optimally it is necessary to value appropriately (i.e. mathematically correctly) the contributions of the individual capacity providers, whether they provide conventional generation, variable generation, or storage. Present approaches to capacity market design have primarily been designed with conventional generation in mind, e.g. in GB (National Grid plc, 2018a) and in North America (Bowring, 2013; Moye and Meyn, 2018). Conventional generation is typically approximated as firm capacity, where we define the latter as idealised capacity which is always available to supply energy as needed up to a given constant rate. (To do so nominal generator capacities are usually multiplied by appropriate 'de-rating' factors to acknowledge occasional unavailability--see National Grid plc, 2018a; Bowring, 2013.)

When all capacity is capable of being approximated as if it were firm, an economic theory of capacity markets is straightforward, and may be based on balancing procurement cost against cost of unserved energy (Stoft, 2002; Zhao et al., 2018). Bothwell and Hobbs (2017) consider the impact on societal welfare of the (mathematically) incorrect de-rating of variable generation, but consider neither storage nor the mechanism of running a capacity market. The need to rapidly reduce fossil fuel dependence means that both variable generation--e.g. wind and solar power--and storage now have increasingly important contributions to make to capacity adequacy (Geske and Green, 2020). The present paper shows how current approaches to capacity market design may be extended to give an integrated theory for the inclusion within a capacity market of all types of capacity provision. As at present, the theory is necessarily based on a probabilistic description of the electricity supply-demand balance process. However, storage has a natural energy constraint and thus can supply energy only for a limited period of time before needing to be replenished; subject to this constraint it may be scheduled flexibly. Hence, in order to understand both how to schedule storage and to determine its contribution to capacity adequacy, it is necessary to pay attention to the sequential statistical structure of the supply-demand balance process to which that storage is contributing--see Sections 2 and 3. The present paper extends and generalises theory which was developed by the authors in conjunction with National Grid ESO for the integration of storage into the GB capacity market (National Grid plc, 2018b). However, the theory is applicable wherever capacity contributions of variable generation and storage need to be correctly assessed. This includes the European and North American markets referenced above.

The determination of a volume of capacity-to-be-procured in a capacity market may be achieved either via the satisfaction of an appropriate security-of-supply standard defined in terms of some given system risk metric, or via the minimisation of an appropriate economic cost. (In the latter case the capacity-to-procure may be variable and specified as a function of the clearing price in the capacity auction; this is what currently happens in GB.) These two approaches are closely related--see Section 5. In either case, a key step in the development of an integrated theory is that of the provision of an appropriate definition of the equivalent firm capacity (EFC) of any capacity-providing resource. This EFC is the firm capacity which makes an (appropriately defined) equivalent contribution to the overall supply-demand balance. Hence the EFC is necessarily defined with respect to the pre-existing supply-demand balance process to which this resource is being added (Zachary and Dent, 2011; Dent and Zachary, 2014). When the set of capacity-providing resources contains significant storage, particular care is required in the determination of EFCs. One reason for this is the need to account for the flexibility of scheduling of additional storage added to an existing supply-demand balance process. More subtly, when any further resource--including, for example, firm capacity--is added to an existing set of capacity-providing resources which already contains storage, that pre-existing storage may also be rescheduled so as to enhance the usefulness of the additional contribution. A consequence, as we show formally at the end of Section 3 and demonstrate in the example of Section 6, is that the EFC of further storage added to an existing system is less (than it would otherwise be) in the case where that additional system already contains significant storage.

Throughout the present paper we treat the process of electricity demand as given. However, demand response may also be used to assist in balancing systems. Demand response has many of the characteristics of storage, typically making a similarly flexible contribution. Its contribution to electricity capacity, and its integration into capacity markets, may be analysed analogously. However, in present day markets it is often treated as demand which may be effectively foregone--see Lopes and Algarvio (2018) for a review, and also National Grid plc (2018b).

Sections 2 and 3 of the paper study respectively risk metrics and EFC. The latter is necessarily defined in terms of some risk metric and is essential to the understanding of both capacity adequacy and the operation of a capacity market. The studied properties are implicit in the theory of present markets for what is mostly conventional generation. However, so as to understand how to incorporate into such markets both variable generation and time-limited but flexible resources such as storage, it is necessary to make these properties explicit. It is further necessary to make explicit assumptions of continuity and smoothness as available capacity-providing resource is varied. We argue that these assumptions, which are often implicit in other work, e.g. Bothwell and Hobbs (2017), are usually sufficiently satisfied in practice. The smoothness assumption yields an important local additivity property for EFCs; this is essential for the optimal operation of markets--even in the case where all resource is provided by firm capacity. In Section 3 we also show how to determine the EFCs of marginal contributions of both variable generation and storage, notably when the objective is the minimisation of expected energy unserved (EEU). For storage this requires consideration of how it may be optimally scheduled.

Section 4 studies the operation of capacity markets when the objective is that of obtaining at minimum cost sufficient capacity to meet a given security-of-supply standard defined in terms of a risk metric. Section 5 studies the operation of such markets when the objective is that of the minimisation of an overall economic cost. The present economic theory of such markets requires substantial modification in the presence of variable generation and, especially, storage.

The flexibility of storage scheduling has important consequences for the way in which a capacity market operates, and these are illustrated in the detailed example of Section 6. This example shows the application of nearly all the above theory, and is chosen to be realistic in the context of a country such as GB. It further demonstrates the practical reasonableness of the assumptions required for a tractable theory.

(2.) RISK METRICS

In the analysis of capacity adequacy, the length of time over which system risk is assessed--typically a year or a peak season--is usually divided into n time periods, each typically of an hour or a half-hour in length (Billinton and Allan, 1996; National Grid plc, 2018b). Let random variables [D.sub.t] and [X.sub.t] denote respectively the total energy demand and total energy supply in time period t. Then the supply-demand balance in the time period t is given by the random variable [Z.sub.t]=[X.sub.t]-[D.sub.t]. Values of [Z.sub.t] less than zero correspond to an energy shortfall or loss-of-load at time t. The depth of shortfall at that time is given by the random variable max(-[Z.sub.t],0).

Any risk metric p is a function of the entire process ([Z.sub.t],t = 1,...,n). Risk metrics may either be used directly in the setting of reliability standards--as in the case of the present GB LOLE-based standard (National Grid plc, 2018b)--or may arise naturally in economic approaches to determining security-of-supply (see Section 5).

LOLE and EEU. The two most commonly used risk metrics are loss-of-load expectation (LOLE) and expected energy unserved (EEU), given respectively by

[Please download the PDF to view the mathematical expression] (1)

[Please download the PDF to view the mathematical expression] (2)

where P denotes probability and E denotes expectation (Billinton and Allan, 1996; Keane et al., 2011; Zachary and Dent, 2011). It follows from the additivity of expectations that, in discrete time, LOLE is the expected number of periods of shortfall during the season under study, while EEU is the expectation of the sum of the depths of shortfall during such periods, i.e. the expectation of the total unserved energy.

The use of EEU as a measure of economic cost corresponds to a uniform valuation of unserved energy, regardless of the overall depth of energy shortfall at any given time and also of the overall duration of the energy shortfall periods. The present paper mainly considers such a uniform valuation. However, often modest depths or durations of shortfall may be managed...

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