IEEE Power & Energy Magazine - May/June 2022 - 30

price-the significantly (up to 100 times) higher computational
cost. Is it worth the effort? Does it pay off? Answering
these questions requires a much more thorough analysis,
involving diverse error metrics, trading strategies, realistic
operational costs, and so on.
Outlook for the Future
The methods presented so far yield point forecasts, like the
expected price today at 6 p.m. This knowledge is important
for decision makers, but it does not convey all of the relevant
information. Probabilistic EPF is a possible remedy.
The output of such a model will no longer be a single value,
e.g., the expected price today at 6 p.m., but a distribution of
possible values. For instance, looking at a probabilistic (also
called distributional) forecast, we will be able to conclude
that the price today at 6 p.m. will be between €100 and €110
with 90% probability.
There are multiple approaches to probabilistic forecasting.
However, one that is particularly relevant in our case
uses NNs to output the distributions directly. This can be
achieved by making only a small change in the DNN model
presented earlier. Instead of returning the 24 hourly prices,
the network can return the parameter sets of 24 probability
distribution functions. Assuming that the distribution of
interest is Gaussian, the probabilistic NN will have 48 outputs
with two parameters (i.e., the mean and standard deviation)
for each hour of a day, as illustrated in Figure 7. Compared
to the DNN in Figure 5(b), the so-called distribution
layer in Figure 7 is placed between the last hidden and the
output layer. Nodes of the distribution layer contain estimates
(or predictions) of the parameters of a distribution
(here, Gaussian). The output is a predictive distribution,
f ,h
one for each hour of the day.
The downside is that the distribution itself is a hyperparameter;
i.e., it has to be estimated or set ex ante. A more
flexible distribution can account for skewness and heavy
tails, but this also comes at a price. In general, the more
parameters there are to be estimated, the harder it is to calibrate
the model to a given data set. Nevertheless, probabilistic
NNs may be objects of interest in the future.
The Good, the Bad, and the Ugly
Like the main characters in the epic spaghetti Western film
directed by Sergio Leone, the practices we can observe in
the EPF literature come in all shapes and sizes. They range
from highly undesirable (the bad, which lead to meaningless
results that cannot be compared) and undesirable
(the ugly, which compromise research reproducibility) to
worth recommending (the good). We conclude this article
by summarizing these practices-particularly common in
the ML EPF literature-and providing better alternatives.
The Bad-Avoid at All Costs
New models are rarely compared against established
state-of-the-art models and even less frequently against
open access benchmarks. This leads to unjustified claims
Model Inputs
Hidden Layer 1
pd−1
f1
σd,1
pd−2
...
µd,2
pd−7
u1,2
...
Xd
...
D
σd,24
u1,n
u2,1
...
u2,m
µd,24
f24
f2
σd,2
...
...
u1,1
u2,2
Hidden Layer 2
Distribution Layer
µd,1
Model Output
figure 7. A probabilistic NN architecture for EPF. The output is a predictive distribution, fh, one for each hour of the day.
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