IEEE Power & Energy Magazine - November/December 2017 - 46

correlations, i.e., each ensemble member ensures a consistent
behavior for each plant in the grid area and for each point in
time over the prediction horizon.

Terminology and Methodology
Regarding Forecast Uncertainty
Where does uncertainty in the forecast of RES generation
originate? To answer this question, we must separate weather
forecast uncertainty and the energy- or power-generation forecast uncertainty of RES. Weather forecast uncertainty stems
in large part from 1) observational limitations and 2) scientific limitations. The first category results from insufficient
data, inconsistencies among instruments, or simply incorrect
measurements. These types of limitations lead to uncertainty
in the initial or boundary conditions, which are propagated
into the future. The second category is a mixture of limitations caused by an incomplete understanding of complex
physical, chemical, and dynamic processes and the need for
approximations to model these complex atmospheric processes. In practice, it is a combination of both limitations that
causes overall weather forecast uncertainty.
RES forecast uncertainty adds another dimension to the
problem: uncertainty in measurements and calibration of the
power-generating units that are unrelated to weather. Even
though a physical description of the power output from wind
turbines (or solar panels) exists, there are differences in the
hardware that cause uncertainty of the power output. The
conversion to wind/solar power is not well defined and is
governed by nonlinear equations. Before discussing in more
detail how forecast uncertainty can be produced, we need to
establish a standard terminology.

NWP
Determinstic
Model

It is important to make a distinction between the concepts
of forecast interval and confidence interval as well as forecast error and forecast uncertainty. The confidence interval
provides an interval of values and a respective confidence
level that is likely to contain the population parameter of
interest. Conversely, the forecast interval provides an interval of values and respective probability that is likely to contain the real value of the forecast parameter. Forecast error
is the actual deviation between the forecast and measured
value at one point in time, while forecast uncertainty refers
to a range of possible values in the future; forecast error can
also refer to an error measure, e.g., mean absolute error. The
uncertainty forecast should be conditional based on a set
of explanatory variables (flow dependent), such as forecast
wind speed, expected value of generation levels, weather
ensembles dispersion, and so forth. The simple construction
of empirical distributions from historical forecast error is not
a true forecast uncertainty.
Forecast uncertainty can be estimated with three standard processes (Figure 6):
1) statistical algorithms
2) physically based ensemble forecasts
3) statistically based ensemble forecasts.
In the first process, a statistical learning algorithm (e.g.,
machine learning) with an adequate loss function is fit to
historical-point NWP and power data and generates uncertainty forecasts from an operational NWP. Other methods
such as the analog ensemble algorithm search through historical forecasts for those past forecasts most analogous to
the current forecast. Those observations form the probability
distribution of the forecast uncertainty.

Marginal/Spacial
Probability
Distribution

Statistical Learning
Algorithm
(a)

Multiple
NWP Model
Parameterizations
Initial/Boundary
Condition Perturbations

Postprocessing

Power
Conversion
Model

Calibration

Physical
Ensembles
Inclusive Extremes

(b)
NWP
Determinstic
Model

Statistical
Dependence
Structure

Statistical
Learning Algorithm

Spatiotemporal
Scenarios

(c)

figure 6. The standard procedures to generate uncertainty forecasts for renewable energy sources. The black arrows indicate where the generation of the so-called ensemble members takes place.
46

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