IEEE Power & Energy Magazine - May/June 2022 - 19

execute different variants of the process. For example,
some may add a preprocessing step to cleanse the load and
weather history before sending them to the modeling process,
while others may add a postprocessing step at the end
to fine-tune the load forecast. Looking at load forecasting
literature, most papers have focused on the modeling
process by trying various techniques for load forecasting.
For most load forecasting techniques, the modeling processes
are somewhat similar. A forecaster slices the historical
data into three periods. The first is for parameter estimation
(or training). The goodness of fit for this period is called
in-sample fit. An accurate model would result in a good insample
fit, but a good fit may not indicate an accurate model.
Sometimes a model overfits the data by capturing random
noises so that the prediction may be far away from the actual
observation or normal energy consumption level. This is
known as the overfitting issue.
To avoid the overfitting issue, the second period is set for
model selection (or validation). The goodness of fit for this
period is called a postsample fit. A forecaster may train several
models, using each to forecast the second period. The
model with the best postsample fit result can be selected as
the winner for forecasting. In practice, when a large number
of models are trained and fed to the validation period, the
winning model may be the result of overfitting the validation
period.
To add another layer of insurance, the third period
is reserved for an out-of-sample test. A forecaster tests
the winning model from the postsample fit on the third
period, which is completely blind from parameter estimation
and model selection. When the selected model does
not give surprisingly bad results, it can be promoted
for forecasting.
Some variants of the aforementioned process have been
used in many business sectors, including load forecasting.
For example, the process may be simplified by removing the
out-of-sample test. In many case studies, forecasters execute
the training and validation steps multiple times on different
periods of the historical data, known as cross validation. As
load forecasting is a time series forecasting problem, sliding
simulation is often used in place of training and validation,
mentioned previously.
Illusions 1: A Nonlinear Shape, So We
Have to Use Nonlinear Models
The relationship between load and temperature is nonlinear,
as depicted in Figure 5. The shape of that scatter plot
is commonly known as a hockey stick or Nike swoosh. On
the left side, the load increases as the temperature decreases
due to heating needs. On the right, the load increases as the
temperature increases due to cooling needs.
Many papers used the nonlinear relationship as motivation
for nonlinear models. However, a nonlinear relationship
does not require nonlinear models. In many situations,
linear models are better than nonlinear models at modeling
may/june 2022
nonlinear curvatures. The " linear " in linear models means
linearity in parameters.
In other words, as long as the
parameters being estimated are in a set of linear equations,
the model is linear.
The shape in Figure 5 can be modeled by a polynomial
regression model, which is in the family of linear
regression models. Both second- (blue line in Figure 5)
and third-order polynomials (brown line in Figure 5) have
been used for load forecasting models. A piecewise linear
regression model can also model the shape.
Clarification 1
Linear models can be used to model nonlinear relationships.
The business needs designate which family of models
should be considered. The exact model to be used should
be determined based on the outcome of the model selection
process.
Illusion 2: Techniques Are Siloed;
Either AI or Statistics, But Not Both
AI and statistics (or econometrics) are often considered
rivals. Many load forecasters in either camp rarely look at
the work done by the other group. In academic literature,
many AI papers compare proposed load forecasting models
with other AI-based models. Even if comparisons were
made using statistical models, the models are often far less
powerful than state of the art in that model family.
ANNs and regression analysis,
two seemingly different
techniques in AI and statistics, respectively, are connected
in many ways. Both techniques ask for similar input
variables such as weather and calendar information. Both
require the estimation of parameters, which can be formulated
as optimization problems. The parameters of ANNs
can be
estimated through backpropagation, while
the
parameters (or coefficients) for a regression model can be
estimated by minimizing the sum of squared errors. Such
regression analyses are called an ordinary least squares
(OLS) regression.
6,000
5,000
4,000
3,000
2,000
1,000
-10
10
30
50
Temperature (F)
figure 5. Using regression models to capture the load
temperature relationship.
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Demand (MW)
IEEE Power & Energy Magazine - May/June 2022

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