Mape_Maker: A Scenario Creator

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.

Putting It All Together

In this section we summarize the process to deliver a simulation with correct targets.

1.1 Procedures for Estimation

First, as shown in Algorithm 1, we preprocess the data and estimate the conditional distributions using the methods explained in Sect. 2.3. This results in a set of beta distribution parameters for each input from the whole dataset, called $\hat{{\mathcal {S}}}$. To estimate the parameters we recall that the user should specify a data fraction for the sampling (e.g., 0.05). (The software provides an option to produce a curve for the scores described in Sect. 2.4.)

Next, as shown in Algorithm 2, we estimate the partitioning of the mean absolute percent errors according to the input and we encode this information in the weight function. An important feature of this procedure is the computation of $r_{{\hat{m}}}$ which is the expected mean absolute relative error from the conditional distributions (which may be close in value to, but is different from, ${\hat{r}}$.) This procedure is explained in Sect. 3.3.

The next phase, shown in Algorithm 3, is estimation of the underlying base_process that generates autocorrelation in the time series of the errors. This is done by using the CDF B of the beta distribution whose parameters have been inferred in step 1. Then we operate a grid search over the p and q parameters to select the order of the model that minimizes the BIC criterion. We save the coefficients. Recalling that we want the marginal of Z to follow a standard normal, we set the variance of the errors of the base process so that $Var[{\mathbf {Z}}_t] = 1$. This procedure is explained in Sect. 4.

1.2 Procedures to Deliver the Target MARE

First, as shown in Algorithm 4, given a target MARE ${\tilde{r}}$, and a ${\mathcal {X}}_{SID}$ we verify that ${\tilde{r}}$ is feasible. If it is, we aim at targeting a mean absolute error for each conditional distribution with input in the ${\mathcal {X}}_{SID}$. For this, we compute a target function using the estimated weight function (see Sect. 3.4).

Second, as shown in Algorithm 5, according to a target function ${\tilde{m}}$, we assign adjusted parameters for each conditional distribution whose input is in the ${\mathcal {X}}_{SID}$. We adjust the location parameters from the estimated values while keeping the shape parameters. See Sect. 3.2.

1.3 Procedure to Simulate the Output

Using methods summarized in Algorithm 6, we simulate a base process sample of length $|{\mathcal {X}}_{SID}|$ and use the simulated conditional distributions to obtain conditioned errors. We directly get the simulation by summing the errors and the input data. Finally, if the user asks for it, we optimize the curvature a posteriori, see Sect. 5.