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Optimal storage and transmission investments in a bilevel electricity market model

  • S.I. : Game theory and optimization
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Abstract

This paper analyzes the interplay of transmission and storage investments in a multistage game that we translate into a bilevel market model. In particular, on the first level we assume that a transmission system operator chooses optimal line investments and a corresponding optimal network fee. On the second level we model competitive firms that trade energy on a zonal market with limited transmission capacities and decide on their optimal storage facility investments. To the best of our knowledge, we are the first to analyze interdependent transmission and storage facility investments in a zonal market environment that accounts for the described hierarchical decision structure. As a first best benchmark, we also present an integrated, single-level problem that may be interpreted as a long-run nodal pricing model. Our numerical results show that adequate storage facility investments of firms may in general have the potential to reduce the amount of line investments of the transmission system operator. However, our bilevel zonal pricing model may yield inefficient investments in storages, which may be accompanied by suboptimal network facility extensions as compared to the nodal pricing benchmark. In this context, the chosen zonal configuration of the network will highly influence the equilibrium investment outcomes including the size and location of the newly invested facilities. As zonal pricing is used for instance in Australia or Europe, our models may be seen as valuable tools for evaluating different regulatory policy options in the context of long-run investments in storage and network facilities.

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Notes

  1. In contrast to simple two-period models [see, e.g., Sioshansi (2010) or Sioshansi (2014)] our model is able to capture more than two time periods. Ultimately, this may help to increase the accuracy of the proposed storage model.

  2. Observe that for an infinitely small slope, such an affine investment cost function will converge to a constant investment cost function.

  3. For applications of this zonal pricing formulation, see for instance Bjørndal et al. (2003), Ehrenmann and Smeers (2005), Bjørndal and Jørnsten (2007), Weibelzahl (2017), or Weibelzahl and Märtz (2017).

  4. We note that the time to build new transmission lines will in general be much larger than the time to build (battery) storage facilities. In turn, investments in storage facilities will have a larger time horizon than the market clearing interval. From this point of view, our bilevel model may be (re)interpreted as some kind of trilevel problem. On the first level, again the TSO chooses an optimal line extension plan with a corresponding network fee. The TSO anticipates optimal storage investments of perfectly competitive firms on the second level and competitive market outcomes of a zonal market on the third level. Assuming perfectly competitive firms, the objective functions of the second level and of the third level will be affine-equivalent as described in Grimm et al. (2016a). In particular, the objective of the second level will correspond to the aggregated difference between consumer surplus, variable generation cost, network charges, and storage investment cost. On the opposite, on the third level the spot market welfare objective can be expressed as the difference between consumer surplus, network fees, and variable production cost. From a mathematical point of view, we can equivalently subtract storage investment costs from the objective function of the third level without changing the optimal solution. This implies that the discussed hierarchical trilevel model may be reformulated and solved as the bilevel maximization problem introduced in this section. On the other hand, our proposed bilevel model may be reinterpreted using three levels that correspond to long-term line investment, medium-term storage investment, and short-term market clearing.

  5. An alternative approach would be to use an explicit formulation of the strong duality equality; see, e.g., Garcés et al. (2009b).

  6. Note that for the case of presentation, we neglect supply functions in (20).

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Acknowledgements

We thank Claudia Ehrig, Arie M.C.A. Koster, Katja Kutzer, Paul Schott and Nils Spiekermann for their valuable comments and discussions. In addition, we highly acknowledge the good cooperation with Veronika Grimm, Alexander Martin, Martin Schmidt, Christian Sölch, and Gregor Zöttl at the Friedrich-Alexander-University Erlangen-Nuremberg in the past years.

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Authors and Affiliations

  1. FIM Research Center, Wittelsbacherring 10, 95444, Bayreuth, Germany

    Martin Weibelzahl

  2. University of Bayreuth, Wittelsbacherring 10, 95444, Bayreuth, Germany

    Martin Weibelzahl

  3. Chair of Energy Economics, Institute for Industrial Production (IIP), Karlsruhe Institute of Technology, Hertzstrasse 16, 76187, Karlsruhe, Germany

    Alexandra Märtz

  4. Discrete Optimization, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Alexandra Märtz

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Correspondence to Martin Weibelzahl.

Appendix: Sets, parameters, and variables

Appendix: Sets, parameters, and variables

Tables 4, 5, and 6 summarize the main sets, parameters, and variables used in this paper.

Table 4 Sets
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Table 5 Parameters
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Table 6 Variables and Derived Quantities
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Weibelzahl, M., Märtz, A. Optimal storage and transmission investments in a bilevel electricity market model. Ann Oper Res 287, 911–940 (2020). https://doi.org/10.1007/s10479-018-2815-1

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