Polyhedral Predictive Regions for Power System Applications

Faranak Golestaneh*, Pierre Pinson, Hoay Beng Gooi

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either cost-optimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chance-constrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In the work, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under $L_{1}\ and\ L_\infty$ norms), the parameters of which may be modelled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra.
Original language English I E E E Transactions on Power Systems 34 1 693 - 704 0885-8950 https://doi.org/10.1109/TPWRS.2018.2861705 Published - 2018

Keywords

• Probabilistic forecasting
• Box uncertainty sets
• Polyhedron
• Robust optimization
• Chance-constrained optimization

Cite this

Golestaneh, Faranak ; Pinson, Pierre ; Gooi, Hoay Beng. / Polyhedral Predictive Regions for Power System Applications. In: I E E E Transactions on Power Systems. 2018 ; Vol. 34, No. 1. pp. 693 - 704.
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title = "Polyhedral Predictive Regions for Power System Applications",
abstract = "Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either cost-optimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chance-constrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In the work, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under $L_{1}\ and\ L_\infty$ norms), the parameters of which may be modelled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra.",
keywords = "Probabilistic forecasting, Box uncertainty sets, Polyhedron, Robust optimization, Chance-constrained optimization",
author = "Faranak Golestaneh and Pierre Pinson and Gooi, {Hoay Beng}",
year = "2018",
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language = "English",
volume = "34",
pages = "693 -- 704",
journal = "I E E E Transactions on Power Systems",
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Polyhedral Predictive Regions for Power System Applications. / Golestaneh, Faranak; Pinson, Pierre; Gooi, Hoay Beng.

In: I E E E Transactions on Power Systems, Vol. 34, No. 1, 2018, p. 693 - 704.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Polyhedral Predictive Regions for Power System Applications

AU - Golestaneh, Faranak

AU - Pinson, Pierre

AU - Gooi, Hoay Beng

PY - 2018

Y1 - 2018

N2 - Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either cost-optimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chance-constrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In the work, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under $L_{1}\ and\ L_\infty$ norms), the parameters of which may be modelled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra.

AB - Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either cost-optimal decisions in expectation, or decision with probabilistic guarantees. The representation of uncertainty serves as an interface between forecasting and decision-making problems, with different approaches handling various objects and their parameterization as input. Following substantial developments based on scenario-based stochastic methods, robust and chance-constrained optimization approaches have gained increasing attention. These often rely on polyhedra as a representation of the convex envelope of uncertainty. In the work, we aim to bridge the gap between the probabilistic forecasting literature and such optimization approaches by generating forecasts in the form of polyhedra with probabilistic guarantees. For that, we see polyhedra as parameterized objects under alternative definitions (under $L_{1}\ and\ L_\infty$ norms), the parameters of which may be modelled and predicted. We additionally discuss assessing the predictive skill of such multivariate probabilistic forecasts. An application and related empirical investigation results allow us to verify probabilistic calibration and predictive skills of our polyhedra.

KW - Probabilistic forecasting

KW - Box uncertainty sets

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KW - Robust optimization

KW - Chance-constrained optimization

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