  The increasing penetration of distributed energy resources (DERs) will
decrease the rotational inertia of the power system and further degrade the
system frequency stability. To address the above issues, this paper leverages
the advanced neural network (NN) to learn the frequency dynamics and
incorporates NN to facilitate system reliable operation. This paper proposes
the conservative sparse neural network (CSNN) embedded frequency-constrained
unit commitment (FCUC) with converter-based DERs, including the learning and
optimization stages. In the learning stage, it samples the inertia parameters,
calculates the corresponding frequency, and characterizes the stability region
of the sampled parameters using the convex hulls to ensure stability and avoid
extrapolation. For conservativeness, the positive prediction error penalty is
added to the loss function to prevent possible frequency requirement violation.
For the sparsity, the NN topology pruning is employed to eliminate unnecessary
connections for solving acceleration. In the optimization stage, the trained
CSNN is transformed into mixed-integer linear constraints using the big-M
method and then incorporated to establish the data-enhanced model. The case
study verifies 1) the effectiveness of the proposed model in terms of high
accuracy, fewer parameters, and significant solving acceleration; 2) the stable
system operation against frequency violation under contingency.
