IEEE Power & Energy Magazine - May/June 2022 - 25

E
ELECTRICITY PRICE FORECASTING (EPF) IS A
branch of forecasting at the interface of electrical engineering,
statistics, computer science, and finance that focuses on
predicting prices in wholesale electricity markets for a whole
spectrum of horizons. These range from a few minutes (realtime/intraday
auctions and continuous trading); through days
(day-ahead [DA] auctions); to weeks, months, or even years
(exchange and over-the-counter traded futures and forward
contracts). DA markets are the workhorse of power trading,
particularly in Europe, and a commonly used proxy for " the
electricity price. " The vast majority-up to 90%-of the
EPF literature has focused on predicting DA prices. These
are typically determined around noon during 24 uniformprice
auctions, one for each hour of the next day. This has
direct implications for the way EPF models are built.
Over the last 25 years, various methods and computational
tools have been applied to intraday and DA EPF.
Until the early 2010s, the field was dominated by relatively
small linear regression models and (artificial) neural networks
(NNs), typically with no more than two dozen inputs.
As time passed, more data and more computational power
became available. The models grew larger to the extent
that expert knowledge was no longer enough to manage the
complex structures. This, in turn, led to the introduction of
machine learning (ML) techniques in this rapidly developing
and fascinating area. Here, we provide an overview of
the main trends and EPF models as of 2022. Note that the
article uses EPF as the abbreviation for both " electricity
price forecasting " and " electricity price forecast. " The plural
form, i.e., forecasts, is abbreviated as EPFs.
25 Years of Evolution
The beginnings of EPF can be traced back to the 1990s. The
first attempt to predict electricity price dynamics used linear
regression techniques. Recall that such a model assumes a
linear relationship between the predicted variable (e.g., the
electricity price today at 6 p.m.) and inputs (e.g., past electricity
prices and the load forecast for today). The inputs are
also called features, explanatory variables, regressors, or
predictors. More formally, the predicted variable is represented
as a weighted sum of the inputs.
Early regression models were built on expert knowledge.
The inputs included past prices (typically, those from
one, two, and seven days ago), exogenous variables, and a
seasonal component. Seasonality was captured either by a
sinusoidal function or-more commonly-a set of so-called
dummy variables taking the value of one on a given day of
the week and zero otherwise.
A sample regression EPF model is illustrated in Figure 1(a).
White squares represent individual explanatory variables
(also called regressors, inputs, or features), whereas the
purple circle represents an output variable: p ,dh
and X ,,dh
respectively, stand for the electricity price and an exogenous
variable (e.g., the DA load forecast) for day d and hour h,
while
DD
,,
may/june 2022
MonSunf are the so-called dummy variables,
with DMon = for Monday and zero otherwise, and so on.
1
Arrows indicate the flow of information-there is a coefficient
(or weight) assigned to each arrow. The output is just
a weighted sum of all of the inputs.
The most relevant and, often, only used exogenous variable,
even in more recent models, is the DA load forecast.
Interestingly, the actual load is not a better predictor. The
reason is that the bids in the DA market are placed based
on DA load forecasts instead of the actual loads observed
a day later. Since the electricity price-load relationship is
nonlinear (see Figure 2) forecasters also played around with
(artificial) NNs.
An NN consists of layers of nodes. Each node is a neuron.
Layers are connected by links between neurons, so a neuron
can transmit a signal to another neuron in the subsequent
layer, the structure of which resembles the synapses in a
human brain. Thus, the output of a neuron is a weighted sum
of all of the inputs-as in linear regression-transformed by
the so-called activation function.
The simplest NN with input nodes connected directly to
an output node with a linear activation function is equivalent
to the linear regression model depicted in Figure 1(a). By
using nonlinear activation functions and inserting additional
(so-called hidden) layers of nodes, the relationship between
the inputs (i.e., the predictors) and the output (i.e., the predicted
variable) becomes more complex. The NN models of
the 1990s and 2000s were typically shallow structures with
only one hidden layer, one output neuron (e.g., the electricity
price today at 6 p.m.), and a feedforward architecture
[see Figure 1(b)]. The latter means that the information was
propagated in only one direction-from inputs to the output.
In contrast to linear regression, where the output is just
a weighted sum of all of the inputs, in NN models, additional
nonlinear transformations may be applied to this sum
at each node.
Shrinking Redundant Features
Uncovering the nonlinear relationship between the variables
is a challenge for the linear regression-based approach.
Another difficulty is the handling of a large number of
inputs. Even a few dozens of explanatory variables can lead
to unreliable estimates and predictions when using the classical
regression model and ordinary least squares for minimizing
the sum of squared errors between the forecasted
and observed values. A working remedy provides so-called
regularization algorithms. These shrink (hence, the alternative
name-shrinkage algorithms) coefficients, or weights
of the less important inputs, toward zero by adding a penalty
for large coefficients to the sum of squared errors.
One of the most widely used regularization algorithms
is the least absolute shrinkage and selection operator
(LASSO), popularized by Robert Tibshirani in the mid1990s.
This ML (also called statistical learning) technique
shrinks some coefficients to zero and, thus, performs semiautomatic,
data-driven variable selection. EPF models that
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