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Risk management of power portfolios and valuation of flexibility

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Abstract

Risk management by applying operational flexibility is becoming a key issue for production companies. This paper discusses how a power portfolio can be hedged through its own production assets. In particular we model operational flexibility of a hydro pump storage plant and show how to dispatch it to hedge against adverse movements in the portfolio. Moreover, we present how volume risk, which is not hedgeable with standard contracts from power exchanges, can be managed by an intelligent dispatch policy. Despite the incompleteness of the market we quantify the value of this operational flexibility in the framework of coherent risk measures.

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Notes

  1. i.e. non-risk-neutral.

  2. Evaluated in this context means to decide on the technical investment or its zero-coupon equivalent. Additionally the optimal level of operations can be determined.

  3. Ramp-up times are within 10 s.

  4. Spot prices are determined for each hour of the next day. This is done on hourly auctions.

  5. Subadditivity is probably the most important property to be a good risk measure for portfolios.

  6. These results have been numerically shown by Acerbi and Tasche (2002) and Frey and McNeil (2002)

  7. See Rockafellar and Uryasev (2002) for the mathematical assumptions.

  8. i.e. we assume that the strategy of a single power generation company will not influence spot markets.

  9. In our case for every scenario j, ω j corresponds to a joint path of the stochastic values, spot price S t , demand D t and inflow I t , over all periods t=1,...,T.

  10. A more rigorous mathematical analysis is presented in Rockafellar and Uryasev (2000).

  11. All marginal production costs exclude costs of electricity and neglect Swiss water taxes.

  12. Monthly futures contracts have the highest liquidity in the EEX market.

  13. Using Monte-Carlo simulation techniques.

  14. The risk constraint is no longer a binding restriction.

  15. Note that ΔV is always negative. A smaller end level of water leads to a higher volume as more water can now be used to produce electricity.

  16. Assuming once again non-degeneracy. For degenerated optimal points directional derivatives have to be applied. This additional step will not change the methodology we suggest.

  17. Any coherent or convex risk measure could have been used.

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Authors and Affiliations

  1. Institute for Operations Research, Department of Mathematics, ETH Zürich, Clausiusstrasse 45, 8092, Zürich, Switzerland

    Jorg Doege, Philippe Schiltknecht & Hans-Jakob Lüthi

Authors
  1. Jorg Doege
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  2. Philippe Schiltknecht
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  3. Hans-Jakob Lüthi
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Correspondence to Hans-Jakob Lüthi.

Additional information

This research project is gratefully supported by the Swiss Innovation Promotion Agency KTI/CTI, Berne (CH).

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Doege, J., Schiltknecht, P. & Lüthi, HJ. Risk management of power portfolios and valuation of flexibility. OR Spectrum 28, 267–287 (2006). https://doi.org/10.1007/s00291-005-0005-4

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