Mape_Maker: A Scenario Creator
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Mape_Maker: A Scenario Creator Guillaume Goujard1 · Jean‑Paul Watson2 · David L. Woodruff3 Received: 10 October 2019 / Accepted: 19 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We describe algorithms for creating probabilistic scenarios for renewables power production. Our approach allows for tailoring of forecast uncertainty, such that scenarios can be constructed to capture the situation where the underlying forecast methodology is more (or less) accurate than it has been historically. Such scenarios can be used in studies that extend into the future and may need to consider the possibility that forecast technology will improve. Our approach can also be used to generate alternative realizations of renewable energy production that are consistent with historical forecast accuracy, in effect serving as a method for creating families of realistic alternatives—which are often critical in simulation-based analysis methodologies. We illustrate the methods using real data for day-ahead wind forecasts. Nomenclature Observed Variables xt Timeseries of independent input data (e.g. actuals) yt Timeseries of dependent input data (e.g. forecasts) X Set of paired input data (actuals, forecasts) or (forecasts, actuals) xtSID Timeseries of simulation input data XSID Set of Simulation Input Data (SID) upon which the simulation is performed r̃ Target MARE (Mean Absolute Relative Error) Random Variables 𝜀̃ t Random vector of simulated errors ỹ t Random vector of simulated values ũ t Random vector of uniform base process
* David L. Woodruff [email protected] 1
University of California Berkeley, Berkeley, USA
2
Lawrence Livermore National Laboratory, Livermore, USA
3
University of California Davis, Davis, USA
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E Random variable of the error Ẽ Random variable of the simulated error 𝐗 Random variable of the input E, 𝐗) 𝐙 Joint random variable : Z = (E fX Marginal density function of the input data X f𝜀 Marginal density function of the error random variable fE|𝐗=x Conditional density function of the error given the input FE|𝐗=x Cumulative distribution function of the error given the input Estimation a Percent of data used to estimate each conditional distribution Ixa Interval of 2a fraction of data around x in X x̄ (x, a) Center of the interval Ixa cap Capacity b(⋅;𝛼, 𝛽, l, s) Density function of a beta for parameters : 𝛼, 𝛽, l, s Ŝ x Set of estimated beta parameters of the conditional distributions E |𝐗 = x over X m(x) ̂ Expected value of the absolute estimated error given the input m(x, ̃ r̃ , 𝜔) Expected value of the absolute simulated error given the input, a target MARE, and a weight function 𝜔X (⋅) Weight function over X F̂ E|𝐗=x Cumulative distribution function of the estimated error given the input f̂E|𝐗=x Estimated conditional density function of the error given the input in X mmax (x) Maximum value of the expected value of the absolute estimated error, given x rm̂ Expected value of the mean abso
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