  Chance-constrained programming (CCP) is a promising approach to handle
uncertainties in optimal power flow (OPF). However, conventional CCP usually
assumes that uncertainties follow Gaussian distributions, which may not match
reality. A few papers employed the Gaussian mixture model (GMM) to extend CCP
to cases with non-Gaussian uncertainties, but they are only appropriate for
cases with uncertainties on the right-hand side but not applicable to DC OPF
that containing left-hand side uncertainties. To address this, we develop a
tractable GMM-based chance-constrained DC OPF model. In this model, we not only
leverage GMM to capture the probability characteristics of non-Gaussian
distributed uncertainties, but also develop a linearization technique to
reformulate the chance constraints with non-Gaussian distributed uncertainties
on the left-hand side into tractable forms. A mathematical proof is further
provided to demonstrate that the corresponding reformulation is a safe
approximation of the original problem, which guarantees the feasibility of
solutions.
