IEEE Power & Energy Magazine - May/June 2022 - 26

initially have hundreds of inputs can be reduced to structures
with only a dozen or two relevant regressors. The selection
is " semiautomatic " because LASSO requires the setting of
the tuning hyperparameter that regulates which features are
eliminated. This hyperparameter can be set using cross validation,
a resampling method that uses different portions of
the data to test and train a model.
LASSO-estimated EPF models appeared in the mid2010s
and quickly revolutionized the field. Despite their
relative simplicity and inability to handle nonlinear dependencies,
it is not easy to outperform them, even using much
more complex models. In one of the first EPF applications,
LASSO was used to sparsify 24 regression models, one for
each hour of the day and each with 100+ inputs, as shown
in Figure 3.
A more recent example is the LASSO-estimated autoregressive
(LEAR) model, an open source method that was
proposed in 2021 as one of two challenging benchmarks for
contemporary EPF. The LEAR model is a parameter-rich
autoregressive st ructure withabout 250 explanatory
variables. That is, to predict the price for one hour, the model
utilizes hourly prices from one, two, three, and seven days
ago; hourly DA forecasts of two exogenous variables (e.g.,
the system load and wind power generation) for today, yesterday,
and a week ago; and weekday dummies.
The model structure is visualized in Figure 4 together
with a graphical summary of the importance of selected
inputs for Nord Pool market data. Four years of data (2013-
2016) were used for calibration and two (2017-2018) for testing;
the coefficients (weights) were re-estimated every day.
The gray squares in the middle represent 24-dimensional
vectors of explanatory variables: hourly prices one, two,
three, and seven days ago
( ,,, )-- and
pp pp12 dd-- 37dd and
hourly DA forecasts of two exogenous variables for today,
Model Inputs
pd−1, h
Model Output
Model Inputs
pd−1, h
Hidden Layer
Model Output
pd−2, h
pd−2, h
u1
pd−7, h
pd−7, h
Xd, h
pd, h
Xd, h
u2
.
.
.
DMon
.
.
.
DSun
DMon
un
.
.
.
DSun
pd, h
(a)
(b)
figure 1. The early EPF models: (a) linear regression and (b) a single-output shallow NN. The white squares represent the
inputs, the purple circles are the output variables, and the light blue circles show hidden neurons (or nodes). The arrows indicate
the flow of information (darker/lighter for better visibility). (Source: The human evolution graphic is a modification of the
" Human Evolution Scheme " by José-Manuel Benitos. Licensed under the terms of the GNU Free Documentation License.)
26
ieee power & energy magazine
may/june 2022

IEEE Power & Energy Magazine - May/June 2022

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Contents
IEEE Power & Energy Magazine - May/June 2022 - Cover1
IEEE Power & Energy Magazine - May/June 2022 - Cover2
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