Simultaneously optimizing bidding strategy in pay-as-bid-markets and production scheduling

https://doi.org/10.1016/j.compchemeng.2021.107610Get rights and content

Highlights

  • Benders decomposition decouples participation in ancillary service market from day-ahead market.

  • Scheduling problem reformulated without integers for strong duality.

  • Scheduling description with cuts describes lower bound when integrality requirements are relaxed.

  • Branch-and-bound-based algorithm performs superior to explicit enumeration.

Abstract

The volatility of renewable energy sources leads to the development of electricity markets with different time horizons, where flexible consumers can monetize their flexibility to stabilize the electric grid. From an electricity-user perspective, the optimal monetization strategy and choice of markets is difficult to identify. We consider simultaneous participation in an ancillary service market with pay-as-bid mechanism and a day-ahead market. We develop a formulation based on Benders decomposition that decouples the participation in both markets. This allows to optimally distribute flexibility to bids in an ancillary service market and participation in a day-ahead market via scheduling optimizations. In particular, our formulation allows the optimization problem to be solved with general-purpose nonlinear programming solvers. We demonstrate that using the proposed decomposition is computationally more efficient than our previously published enumeration-based approach.

Introduction

Renewable energy sources have the potential to solve the climate crisis (Houghton, 2009), but are fluctuating in time. An established way to help synchronize supply and demand in electricity grids powered by fluctuating renewable energy suppliers is demand-side management (Mitsos, Asprion, Floudas, Bortz, Baldea, Bonvin, Caspari, Schäfer, 2018, Strbac, 2008, Gellings, 1985), which refers to all efforts to utilize consumer flexibility for grid stability.

Flexible electricity users can monetize their flexibility in a variety of markets: For example, Schäfer et al. consider combined participation in a day-ahead market and a primary balancing reserve market (Schäfer et al., 2019b), and extend their approach to also participating in the secondary balancing reserve market (Schäfer et al., 2019a). Otashu and Baldea (2018) aim for participation of a chlor-alkali process in a 15-minute market and Dowling et al. (2017) consider both a hierarchy of ancillary service markets addressing different time scales and a hierarchy of spot markets from day-ahead market to real-time trading. Finally, Zhang et al. (2016) also consider specially negotiated contracts such as discount and penalty contracts. As done in (Dowling et al., 2017), the markets can be categorized into markets for ancillary services and spot markets. Ancillary services, i.e., providing balancing reserve capacity, are often sold in auction-based markets. If a bid is accepted, the electricity user permanently has to reserve sufficient flexibility to serve potential balancing requests within a tight time frame. Alternatively, flexible electricity users can exploit price fluctuations on a spot market to schedule overproduction during times of cheap electricity and reduce consumption when electricity becomes expensive (Ramin, Spinelli, Brusaferri, 2018, Zhang, Grossmann, 2016, Castro, Harjunkoski, Grossmann, 2011, Castro, Harjunkoski, Grossmann, 2009). The question of how much flexibility to monetize in which market is a complex optimization problem (Bohlayer, Fleschutz, Braun, Zöttl, 2018, Klæboe, Fosso, 2013), as answering the question requires simultaneous consideration of an optimal bidding strategy and the influence of that bidding strategy on the ability of the process to reduce its production cost on a spot market.

The markets around the globe, both for ancillary services and spot markets, are evolving (Eid, Codani, Perez, Reneses, Hakvoort, 2016, Hu, Harmsen, Crijns-Graus, Worrell, van den Broek, 2018). The considered time horizons for ancillary service bids, payment mechanisms for accepted bids, qualifications for participation in ancillary service markets and spot markets and several other details are adapted, in part based on research with the goal to harmonize the markets. We follow the German market structure presented in our previous work (Schäfer et al., 2019b): a pay-as-bid balancing reserve market and the day-ahead market. Therein, we developed a method to optimally distribute flexibility between these two markets. Our solution approach in (Schäfer et al., 2019b) relies on explicit enumeration of scenarios of acceptance and rejection of bids on the balancing market. Because of combinatorial explosion, such an algorithm rapidly becomes intractable, even on modern computers. To facilitate computationally more efficient solution algorithms for the simultaneous optimization of bidding strategy and production scheduling, we improve on both the formulation and solution approach presented in our previous work (Schäfer et al., 2019b).

Our novel formulation is based on the idea of Benders decomposition (BD) (Benders, 1962) to separate the production scheduling problem from the optimal bidding problem. BD relies on strong duality of the subproblems of the decomposition. In our case, the subproblem is the scheduling problem, which is often formulated as Mixed-Integer Linear Problem (MILP) (Zhang and Grossmann, 2016) because such models have the capability to model a broad variety of situations and powerful solution algorithms exist for this class of problems. For example, Zhang et al. (2016) model continuous process networks, Kelley et al. (2018) formulate MILP-models to integrate scheduling and control, and Raman and Grossmann (1991) formulate logic constraints as mixed-integer linear constraints. The scheduling problem in (Schäfer et al., 2019b) is also formulated as MILP. Despite all the advantages that come with this problem class, strong duality rarely holds for MILPs. Therefore, it is not enough to reformulate the interaction between scheduling problem and bidding problem. We also reformulate the scheduling problem itself to a continuous linear program (LP), so that strong duality holds.

The key contributions of this work are:

  • We reformulate the scheduling model in a way that strong duality holds.

  • We exploit the property of strong duality to embed optimal scheduling information in a bidding strategy model. As a consequence, explicit enumeration is not required to find an optimal bidding strategy anymore.

  • We reconstruct results from (Schäfer et al., 2019b) and show that our new formulation enables solution algorithms that can be more efficient than explicit enumeration.

Section snippets

Background

Production processes are subject to a variety of constraints to satisfy quality standards, safety requirements, timing of demand and supply, and storage space. Other constraints arise from physics and technical limits. An optimal schedule satisfies all these constraints and chooses the degrees of freedom of the process in a way that optimizes the process aim. Typically, many degrees of freedom of energy-intensive processes can be found in the production profile, i.e. the distribution of

An improved formulation to integrate optimization of bidding strategy and flexible scheduling

In (Schäfer et al., 2019b), we developed a model of an aluminum electrolysis participating in a pay-as-bid balancing market and a day-ahead spot market. We reported that a monolithic formulation, including both the bidding and the scheduling problem, does not allow to compute a global solution with state-of-the-art solvers. Instead, we exploited that the variables which couple bidding and scheduling are the amounts of reserved balancing capacity. Because of market regulations, the offered

Case study

We repeat the case study of an aluminum production process presented in (Schäfer et al., 2019b), which we briefly reviewed in Section 3.1, and simultaneously optimize bidding strategy and production scheduling for this setup. We compare solving the original formulation by an explicit enumeration scheme to solving our reformulation with a general-purpose MINLP solver. Coming from the bidding model and scheduling model presented in (Schäfer et al., 2019b), we replace the parts of the scheduling

Results and discussion

We solved the problem of simultaneous optimization of bidding strategy in pay-as-bid markets and production scheduling with the explicit enumeration strategy from (Schäfer et al., 2019b) and as monolithic MINLP enabled by our reformulation. As convergence criterion, we define a relative optimality gap of 0.1%. Such a tight relative tolerance is desired because the absolute production costs are several hundred thousand euros per week. Thus, even relatively small savings correspond to a

Conclusion

Based on BD, we developed a reformulation of the problem of simultaneous optimization of bidding strategy in pay-as-bid markets and production scheduling that enables the solution with general-purpose MINLP solvers. A case study on the German primary balancing market and the German day-ahead-market of 2018 showed that the reformulation enables reductions of the computational runtimes to find and proof a globally optimal solution, often to a third or less of the time an explicit enumeration

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 333849990/ GRK2379 (IRTG Modern Inverse Problems). The authors gratefully acknowledge the financial support of the Kopernikus project SynErgie by the Federal Ministry of Education and Research (BMBF) and the project supervision by the project management organization Projekttrger Jlich.

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