IEEE Power & Energy Magazine - May/June 2022 - 39

A recently introduced method, however, bypasses all
these barriers as it eliminates the need to evaluate discrete
test samples. The trained neural network is reformulated to a
set of linear equations with continuous and binary variables
to set up an optimization problem. Inside the optimization
problem, we also include the physical power system modeling
equations. In essence, these act as a representation of
the ground truth. Note that this procedure is applied only
to extract worst-case guarantees. As soon as the user (e.g.,
power system operator, trader, and so on) is satisfied with the
neural network performance, the trained neural network can
be deployed for real application.
The goal of this method is to find the maximum constraint
violation, which can now run across the whole continuous
input region [Figure 5(b)]. If we find that the maximum
constraint violation is zero, we can then certify that for
the entire input region, the neural network predictions will
never violate the constraints. If the maximum constraint
violation is not zero, we then obtain worst-case guarantees,
i.e., we determine the maximum violation that the neural
network prediction can result in for any possible input it
can receive. This then becomes a powerful tool that can
build the trust lacking from grid operators. When considered
from a risk assessment perspective, these metrics can
decide whether the network's performance is good enough
or whether further training and evaluation are required to
reach an acceptable performance.
Physics-Informed Neural Networks
The previous sections focused on how to provide guarantees
about the performance of a trained neural network, building
the trust of system operators and other users. In this section,
we discuss how neural networks can take advantage of the
decades-long development of physical power system models.
Including this knowledge in neural network training yields
significantly better performance with much fewer data.
These are so-called physics-informed networks.
First let us look at a concrete example. Assume we want
to determine the evolution of power system frequency under
a disturbance. The models that describe this evolution often
use differential equations that express how the system
changes from one instance to the next (the simplest of which
is a " swing equation " that many power engineers learn during
their studies). To solve a system of differential equations,
we usually employ computer software and numerical solvers
which, in most cases, means that we track in small steps
how the system state (e.g., the frequency) changes over time.
The resulting trajectory can become a very complex function,
possibly requiring significant computational resources.
And the rapidly increasing integration of power electronic
Conventional Performance Assessment (Statistical Evaluation)
Possible Power System Operating Scenarios
Sample-Based Estimation of Worst-Case Performance
Trained
Neural Network
Dispatch Prediction by Neural Network
Obtaining Performance Guarantees
Possible Power System Operating Region
Worst-Case Performance Guarantees for Entire Region
Physical Ground Truth
Trained
Neural Network
Dispatch Prediction by Neural Network
Physical Ground Truth
figure 5. A comparison of the (a) standard evaluation of neural network performance using a test set with (b) the
proposed methodology for obtaining guarantees of neural network behavior. The proposed method can determine the
largest deviation of the neural network prediction from the physical ground truth across the entire region (and not only for
random discrete samples): this offers a rigorous, worst-case guarantee.
may/june 2022
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IEEE Power & Energy Magazine - May/June 2022

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