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Stochastic Optimization of Power Generation and Storage Management in a Market Environment

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Handbook of Risk Management in Energy Production and Trading

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 199))

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Abstract

This chapter provides an overview of practically applying mathematical optimization techniques to short-term and medium-term planning of a power generation system in a market environment. The considered power generating system may contain thermal plants (gas or coal fired), hydro power plants, new renewables, as well as dedicated energy storages (e.g., gas storages, hydro reservoirs). We argue that stochastic optimization is an appropriate modeling framework in order to take into account the uncertainty of input data (such as natural hydrologic inflows and energy market prices), market decision structures, as well as the optional character of power generating units and energy storages.

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Notes

  1. 1.

    This financial settlement is such that, if the holder of a future buys the energy for all the delivery hours on the day-ahead market, the resulting net costs in the end are the same as for the holder of a forward for the same delivery period; however, the intermediate payments before the end of the delivery period can be very different.

  2. 2.

    If there is a liquid gas spot market, a gas fired plant (e.g., a CCGT) can also be understood as a bundle of call options on the clean spark spread, i.e., on the difference between hourly power price minus appropriately scaled gas and CO2 prices.

  3. 3.

    In this chapter we do not consider nodal pricing systems which are applied, e.g., in the USA [28].

  4. 4.

    With regard to (7.1), process with infinitely many possible outcomes can in many cases be suitably approximated by finite ones, e.g., by Monte Carlo sampling and clustering on the basis of stability theory (cf., e.g., [16, 17, 25]) or via other (Quasi) Monte Carlo methods. Thereby, the discrete approximation of the stochastic process is separated from the solution process; however, there is also work on integrated sampling and solution algorithms. Note that, without any sampling, (7.1) would have to be solved analytically and that is possible only in very special cases.

  5. 5.

    Note that price elasticity, if it is approximated in a piecewise linear way, can easily be incorporated into (7.1) without inducing additional integer variables.

  6. 6.

    Alternatively, it is possible to include a risk constraint of the form \(\rho (c_{1} \cdot x_{1},\ldots,c_{T} \cdot x_{T}) \leq \beta\) into (7.1) with some fixed real number β.

  7. 7.

    For the risk-averse problem (7.2) such a decomposition is also possible but only for special risk functional such as recursive [34] or polyhedral ones [7].

  8. 8.

    For certain data processes d 1, …, d T , it can be shown that \(C_{t}(x_{t-1},d_{t-1})\) is also convex with respect to the right-hand sides h t−1 (e.g., hydrologic inflows) and this can be used to save further computation time by calculating cutting planes jointly for both arguments x t−1 and h t−1; cf. [24]. We here restrict the presentation to the more general case.

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Author information

Authors and Affiliations

  1. VERBUND Trading AG, Am Hof 6a, 1010, Vienna, Austria

    Andreas Eichhorn

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  1. Andreas Eichhorn
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Correspondence to Andreas Eichhorn .

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Editors and Affiliations

  1. Department of Statistics & OR, University of Vienna, Wien, Austria

    Raimund M. Kovacevic

  2. Department of Statistics & OR, University of Vienna, Wien, Austria

    Georg Ch. Pflug

  3. Department of IT & Mathematical Methods, University of Bergamo, Dalmine, Bergamo, Italy

    Maria Teresa Vespucci

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Eichhorn, A. (2013). Stochastic Optimization of Power Generation and Storage Management in a Market Environment. In: Kovacevic, R., Pflug, G., Vespucci, M. (eds) Handbook of Risk Management in Energy Production and Trading. International Series in Operations Research & Management Science, vol 199. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9035-7_7

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