Optimal bidding of a virtual power plant on the Spanish day-ahead and intraday market for electricity

Highlights

• Bidding on the Spanish spot markets can be planned as Markov decision process.

• The problems solve sufficiently fast for the intended application.

• Using intraday markets offers additional revenue over a pure day-ahead strategy.

• Using complex bidding functions increases the out-of-sample profits.

Abstract

We develop a multi-stage stochastic programming approach to optimize the bidding strategy of a virtual power plant (VPP) operating on the Spanish spot market for electricity. The VPP markets electricity produced in the wind parks it manages on the day-ahead market and on six staggered auction-based intraday markets. Uncertainty enters the problem via stochastic electricity prices as well as uncertain wind energy production. We set up the problem of bidding for one day of operation as a Markov decision process (MDP) that is solved using a variant of the stochastic dual dynamic programming algorithm. We conduct an extensive out-of-sample comparison demonstrating that the optimal policy obtained by the stochastic program clearly outperforms deterministic planning, a pure day-ahead strategy, a benchmark that only uses the day-ahead market and the first intraday market, as well as a proprietary stochastic programming approach developed in the industry. Furthermore, we study the effect of risk aversion as modeled by the nested Conditional Value-at-Risk as well as the impact of changes in various problem parameters.

Introduction

In recent years it has become increasingly obvious that anthropogenic climate change is real, progressing at an accelerating pace, and threatening modern society as we know it (IPCC, 2014). However, after more than two decades of efforts to promote renewable energy, the global share of energy produced from fossil fuels remains at a staggering 81% (International Energy Agency, 2016).

In a renewed effort to forge an international framework to combat global warming, the 2015 UN Climate Change Conference in Paris brought about a broad consensus to mitigate climate change and keep global warming at a minimum (United Nations Framework Convention on Climate Change, 2015). Apart from saving energy by efficient appliances and well insulated buildings, the roadmap to decarbonization involves electrification of heating and transport complemented by a transition to low-carbon electricity systems dominated by renewable generation. Consequently, green electricity is at the heart of future energy systems.

New clean generation capacity is mostly built in the form of decentralized renewable electricity sources (renewables in short) with intermittent production patterns. In the last decade, the expansion of renewables was driven by subsidies in the form of feed-in tariffs that free investors from the complications and risks of selling their production on electricity markets and guarantee fixed sales prices. However, eventually renewable generation capacities will have to be integrated into power markets to send and receive useful coordination signals. Therefore many countries are currently moving away from feed-in tariffs to other forms of subsidy schemes that require owners of renewable capacity to market their production on power markets (Fraunhofer ISI, 2016).

Market integration of small players is complicated by the prohibitively high transaction costs in power markets, which are set up for professional traders and require “24/7” operations. Furthermore, exposure to fluctuating market prices in combination with intermittent production patterns creates a substantial risk for owners of renewables that is currently not very well understood. The transaction costs on electricity markets generate demand for players that act as intermediaries between markets and distributed capacities. Such intermediaries pool distributed renewable generation to provide market access and manage risks arising from uncertainty in prices and quantities. We call such entities virtual power plants (VPPs).

Pudjianto, Ramsay, and Strbac (2007) describe VPPs as the primary vehicle to deliver cost-efficient integration of renewable energy sources and differentiate between technical and commercial VPPs. While a technical VPP manages a local network zone or control area and ensures network stability in the face of intermittent generation, a commercial VPP integrates renewable sources of electricity into existing power markets. In this paper, we consider the problem of a Spanish commercial VPP facing the problem of optimal bidding on short-term electricity markets.

Electricity markets are usually organized as a cascade of nested futures markets that allow participants to trade in different temporal granularity (months, days, hours,…) and with different times to maturity. This design gives market participants the opportunity to start trading early in order to close parts of their open positions and re-balance until close to delivery to adapt their positions as uncertainty unfolds and new information arises. As electricity for the same delivery periods, say a specific hour of a day, is traded in multiple markets, the bidding problems on these markets are naturally interdependent. Furthermore, as the number of delivery periods is high, decision makers are confronted with a large number of decisions that have to be made under uncertainty about future market developments and, in case of variable renewables, about actual production output. In particular, short-term rebalancing on intraday markets is gaining importance due to the intermittency of renewables and the resulting requirement of a frequent correction of bids. There are two dominant forms of intraday trading in Europe: continuous trading as for example in France, Germany, and the Scandinavian countries and auctions such as in Italy, Portugal, or Spain.

Finding good strategies that deal with the multi-settlement system of power markets and take into account the pertaining uncertainties of daily operations requires the solution of a complex optimization problem involving several uncertain quantities. There are various approaches in the literature that deal with the bidding strategies on electricity spot markets. Some papers treat all variables in the resulting optimization problems as deterministic (see, e.g. Hellmers, Zugno, Skajaa, Morales, 2016, Mashhour, Moghaddas-Tafreshi, 2011, Vasirani, Kota, Cavalcante, Ossowski, Jennings, 2013). Other papers explicitly model price or renewable production as stochastic but fail to model the multi-stage nature of the problem (e.g., Baringo, Conejo, 2013, Dabbagh, Sheikh-El-Eslami, 2016, Ding, Pinson, Hu, Song, 2016, Garcia-Gonzalez, de la Muela, Santos, Gonzalez, 2008, Momber, Siddiqui, Román, Söder, 2015, Muñoz, de la Nieta, Agustín, Contreras, Bernal-Agustín, 2009, Pandžić, Kuzle, Capuder, 2013a, Pandžić, Morales, Conejo, Kuzle, 2013b, Peik-Herfeh, Seifi, Sheikh-El-Eslami, 2013, Rahimiyan, Baringo, 2016, Tajeddini, Rahimi-Kian, Soroudi, 2014, Zamani, Zakariazadeh, Jadid, 2016). The typical approach in these papers is to consider one single day of operation where the day-ahead bids are considered as here-and-now decisions and the balancing decisions on the next day are represented as second stage wait-and-see decisions of a two-stage stochastic optimization problem. This implicitly assumes that the decision makers face no uncertainty on the day of operation. Since intraday prices change during the day and the production profile of fluctuating renewables remains uncertain until delivery, this approach does not accurately model the underlying information structure and therefore leads to biased and often over-optimistic decisions.

Two exceptions from this pattern are Morales, Conejo, and Pérez-Ruiz (2010) and Heredia, Cuadrado, and Corchero (2018). Morales et al. (2010) propose a three stage stochastic optimization problem for the Spanish short-term electricity market, where the first stage models bidding on the day-ahead market, the second stage models bidding on one intraday market, while the third stage models the random balancing market. The stochastic optimization model in Heredia et al. (2018) also considers the day-ahead market, one intraday market, and the balancing market. Both authors propose three stage optimization problems. However, both papers do not model the full complexity of the Spanish spot markets consisting of a day-ahead market and six staggered intraday markets.

In this paper, we consider the stochastic optimization problem of a VPP that markets electricity produced by wind power plants (WPPs) on the Spanish spot market for electricity. We assume that the VPP’s main business model is to market renewable (intermittent) production for the owners of the respective assets. The VPP thus provides expertise about the electricity markets and the infrastructure to implement complex trading strategies, including the required technical equipment and a well staffed trading floor.

To the best of our knowledge, we are the first to treat the problem of bidding on the day-ahead market and all the intraday markets in an integrated multistage stochastic optimization model that allows the decision maker to explicitly take into account the dependency of the decisions on these markets as well as the flow of information during the course of the whole time period between opening of the day-ahead market and the delivery of electricity. We parametrize the problem using data from our industry partner, the VPP psaier.energies.

The contribution of the paper is thus threefold: Firstly, we propose a computationally tractable stochastic optimization formulation for bidding on all available spot markets for electricity in Spain. Bids are submitted in the form of bidding functions, encapsulating the full complexity of the bidding process in the Spanish spot market. The resulting models are quite involved, due to the high dimensionality and the intricate nature of the intraday market with its changing number of traded hours. We formulate the problem as Markov decision process (MDP), which we solve using approximate dual dynamic programming (ADDP, Löhndorf, Shapiro, 2019, Löhndorf, Wozabal, Minner, 2013). As opposed to classical tree-based stochastic programming, we use scenario lattices to discretize the underlying randomness. This enables us to solve the resulting high-dimensional stochastic optimization problems and at the same time use sufficiently fine discrete representations of the uncertainty to achieve good out-of-sample performance.

Secondly, we carefully calibrate econometric models for electricity prices and wind energy production to describe the stochastic processes in the ensuing stochastic optimization problem. We use LASSO regression and feature selection based on cross validation to estimate models that capture deterministic trends of prices and show that the residuals from these regressions can be modeled as Markov processes. We test different distributional models including normal distributions, normal inverse Gaussian distribution, and resampling to describe the innovations of the Markov models.

Thirdly, we benchmark our solution against a policy that sells all the production on the spot markets, an expectation planner benchmark, a policy resulting from a proprietary stochastic programming software employed by our industry partner, and a reduced three stage version of our model that only bids on the day-ahead market and the first intraday market. To this end, we set up an an extensive out-of-sample study and are able to demonstrate that all benchmark strategies generate clearly less revenues out of sample than the solutions found by ADDP. The improvement in revenues over the strategy that only trades on the spot markets and the benchmark that trades only on one intraday market are driven by the potential for statistical arbitrage between the six intraday markets. These possibilities are exploited by the ADDP solution but cannot be captured by simpler models that do not model all markets. We further study the effect of different risk preferences described by the nested Conditional Value-at-Risk as well as changes in some algorithmic parameters on computational effort and the quality of the solution. We show that the proposed solution approach is able to handle the high dimensional bidding problems and generate a substantial added value. Furthermore, the study shows large revenue potentials of updated and improved wind production forecasts as well as the use of non-trivial bidding functions. The latter yield greatly improved results as compared to the simple flat bids that have been considered up till now in the literature. Lastly, our study shows that computation times, which range from several seconds to several minutes depending on the chosen algorithmic settings, are acceptable for the intended application as a decision support system for trading on intraday auction markets such as the Spanish spot markets for electricity.

The paper is structured as follows: In Section 2, we describe the Spanish market, our assumptions, and the formulation of the multi-stage stochastic optimization problem. Section 3 is devoted to the description of the stochastic models describing the random variables in our stochastic optimization framework, in particular, spot prices for electricity and production of the wind park. In Section 4, we briefly review the main ideas of the ADDP algorithm, i.e., how we discretize the stochastic processes and use stochastic dual dynamic programming (SDDP) to numerically solve the MDPs formulated in Section 2. Section 5 discusses the results of an out-of-sample study for the year 2015 comparing the bidding strategies found by ADDP to the benchmarks. Section 6 concludes the paper and discusses possible extensions and avenues for further research.