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Peak-load pricing with different types of dispatchability

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Abstract

We extend the theory of peak-load pricing by considering that the production with different technologies can be adjusted within their capacity at different speeds. In the established analysis, all production decisions can be made after the random variables realize. In our setting, in contrast, some decisions are made before, others after. This is important, e.g., when increasing capacities of renewables are integrated in electricity systems worldwide. We consider fixed load and three types of capacities: partially dispatchable capacity (e.g., nuclear power-plants) needs to be scheduled ahead of actual production, non-dispatchable capacity (e.g., wind turbines) produces randomly, and highly-dispatchable capacity (e.g., gas turbines) can instantly adjust. If capacities differ in their dispatchability, some standard results of peak-load pricing break down. For example, less capacity types will be employed. Either a system with partially dispatchable technologies only, or a system dominated by non-dispatchable technologies and supplemented by highly-dispatchables occurs. Non- and highly dispatchable technologies can be substitutes or complements. The probability of outage does not rise if non-dispatchable capacity becomes cheaper. In a system with non-dispatchables, capacity decisions cannot be decentralized by conventional markets because cost recovery is not possible. Thus, the integration of renewable electricity generators requires alternative market designs.

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Notes

  1. In the simple case where only partially dispatchable capacity is employed, we have \(k_{P}=D\). Only the parameters \(b_{P},c_{P}\) are relevant. Marginal utility is equal to LRMC of partially dispatchable technologies, demand decreases in \(b_{P},c_{P}\), and \(\frac{\partial k_{P}}{\partial b_{P}},\frac{\partial k_{P}}{\partial c_{P}}<0\).

  2. Such a specification better reflects characteristics of renewable generators. Wind turbines and PV power stations can easily turn off production in case of excess supply.

  3. We can also combine downward-dispatchability with multiple periods, as in Proposition 4. Results do not differ qualitatively for both stochastically independent and perfectly correlated marginal generating units.

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Acknowledgements

We are indebted to Carsten Helm, Sebastian Schwenen, and an anonymous referee for helpful comments. Additionally, we thank several colleagues at the Department for Economics and Statistics, University of Oldenburg, for their feedback. Substantial parts of this paper were developed there. We finally thank for feedback obtained on various conferences and research seminars.

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  1. Resource Economics Group, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Klaus Eisenack

  2. Center for Energy, Climate and Resources, ifo Institute, Poschingerstr. 5, 81679, Munich, Germany

    Mathias Mier

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Part of this work was supported by the German Ministry of Education and Research (Grant No. 03EK3523) and Volkswagen Foundation (Grant No. VWZN3045).

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Eisenack, K., Mier, M. Peak-load pricing with different types of dispatchability. J Regul Econ 56, 105–124 (2019). https://doi.org/10.1007/s11149-019-09394-9

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