Electricity market clearing with improved scheduling of stochastic production

Highlights

• Day-ahead markets should not be cleared with the expected stochastic production.

• The stochastic dispatch maximizes market efficiency, but producers may incur losses.

• The conventional dispatch is revenue adequate per scenario.

• A bilevel program determines the optimal stochastic production schedule.

• The optimal schedule makes the conventional dispatch closer to the stochastic ideal.

Abstract

In this paper, we consider an electricity market that consists of a day-ahead and a balancing settlement, and includes a number of stochastic producers. We first introduce two reference procedures for scheduling and pricing energy in the day-ahead market: on the one hand, a conventional network-constrained auction purely based on the least-cost merit order, where stochastic generation enters with its expected production and a low marginal cost; on the other, a counterfactual auction that also accounts for the projected balancing costs using stochastic programming. Although the stochastic clearing procedure attains higher market efficiency in expectation than the conventional day-ahead auction, it suffers from fundamental drawbacks with a view to its practical implementation. In particular, it requires flexible producers (those that make up for the lack or surplus of stochastic generation) to accept losses in some scenarios. Using a bilevel programming framework, we then show that the conventional auction, if combined with a suitable day-ahead dispatch of stochastic producers (generally different from their expected production), can substantially increase market efficiency and emulate the advantageous features of the stochastic optimization ideal, while avoiding its major pitfalls.

A two-node power system serves as both an illustrative example and a proof of concept. Finally, a more realistic case study highlights the main advantages of a smart day-ahead dispatch of stochastic producers.

Introduction

The penetration of stochastic production in electric energy systems is notably increasing worldwide, primarily owing to a booming wind power industry. There is a broad consensus in the research community that today’s electricity market designs are to be revisited so that stochastic producers can enter the competition in a fair and efficient manner.

In its most basic form, an electricity market consists of a forward (typically day-ahead) market and a balancing market. On the one hand, the day-ahead market is required to accommodate the generation from the inflexible power plants, i.e., from those generating units that need advance planning in order to efficiently and reliably set their production levels. On the other, the balancing market clears the energy deployed to maintain the constant balance of supply and demand over periods of time with finer resolution, commonly spanning from minutes to one hour. Being cleared shortly before real time, balancing markets allow the trade of energy between flexible firms, which can adjust their output quickly, and stochastic producers, whose generation is predictable only with limited accuracy at the day-ahead stage.

Conventionally the day-ahead and the balancing markets are settled independently. Furthermore, with respect to the participation of stochastic producers, the day-ahead market is typically cleared considering their expected production at a very low marginal cost (e.g., zero). The eventual energy adjustments needed to cope with the associated forecast errors are left then to the flexible units participating in the balancing market. Consequently, if this market is not provided with enough flexible capacity, balancing costs may escalate dramatically. It is expected that this problem becomes exacerbated as the penetration of stochastic production increases (Holttinen, 2005, Doherty and O’Malley, 2005, Helman et al., 2010).

To face this challenge, two main solution strategies have been considered, namely:

• To establish reserve markets, where flexible capacity is procured sufficiently in advance of energy delivery and then made available to the balancing market, where it is dispatched if needed. The reserve demand in these markets is exogenously specified by the Transmission System Operator, which opens up a number of different ad hoc criteria, see e.g. Ela, Milligan, and Kirby (2011).

• To clear the forward market using stochastic programming (Birge & Louveaux, 2011), which allows modeling future balancing needs and costs in a probabilistic framework, thus yielding the day-ahead energy dispatch that minimizes the expected system operating costs. One of the major advantages of this approach is that it endogenously solves for the optimal amount of reserve capacity to be left to the balancing market, weighing the expected costs and benefits of such capacity (Galiana et al., 2005, Bouffard and Galiana, 2008, Morales et al., 2009, Papavasiliou et al., 2011).

Ideally, the stochastic solution method attains maximum market efficiency (as it minimizes the expected system operating cost) and therefore, it is used here as a reference in this respect. For its practical application within a market environment, though, it must be first complemented with a set of prices and payments that make market participants satisfied with the resulting day-ahead dispatch. In this vein, Galiana et al. (2005) and Wong and Fuller (2007) define prices for both energy and reserve capacity. However, determining who should pay for such reserve and to which extent is still a major source of conflict and debate (Hogan, 2005).

In this paper, we follow the approach of Pritchard, Zakeri, and Philpott (2010) and Morales, Conejo, Liu, and Zhong (2012), where the stochastic dispatch is supported by energy prices only. However, this approach is not without its problems either. Indeed, Morales et al. (2012) illustrate that the energy-only market settlement associated with the stochastic dispatch requires flexible producers to accept losses for some realizations of the stochastic production, which also raises concerns on its practical applicability.

Starting from this point, the objective of this paper is to show that, if cleared with an appropriate value of stochastic production, generally different from the expected value, the conventional settlement of the day-ahead market can notably approach the behavior of the ideal stochastic dispatch, while sidestepping its theoretical drawbacks. For this purpose, we construct a bilevel programming formulation that determines the optimal value of stochastic production that should be used to clear the day-ahead market under the conventional settlement.

The rest of this paper is organized as follows. Section 2 presents the conventional and stochastic dispatch models that we use as references in our work, and provides the mathematical insight to calculate the optimal day-ahead schedule of stochastic production under the conventional market settlement. Section 3 discusses results from a small example and a case study. More specifically, the example serves to illustrate the different dispatch models, which are subsequently compared and tested using a more realistic setup in the case study. Lastly, Section 4 concludes the paper.