  Managing uncertainty and variability in power injections has become a major
concern for power system operators due to the increasing levels of fluctuating
renewable energy connected to the grid. This work addresses this uncertainty
via a joint chance-constrained formulation of the DC optimal power flow (OPF)
problem, which satisfies \emph{all} the constraints \emph{jointly} with a
pre-determined probability. The few existing approaches for solving joint
chance-constrained OPF problems are typically either computationally
intractable for large-scale problems or give overly conservative solutions that
satisfy the constraints far more often than required, resulting in excessively
costly operation. This paper proposes an algorithm for solving joint
chance-constrained DC OPF problems by adopting an S$\ell_1$QP-type trust-region
algorithm. This algorithm uses a sample-based approach that avoids making
strong assumptions on the distribution of the uncertainties, scales favorably
to large problems, and can be tuned to obtain less conservative results. We
illustrate the performance of our method using several IEEE test cases. The
results demonstrate the proposed algorithm's advantages in computational times
and limited conservativeness of the solutions relative to other joint
chance-constrained DC OPF algorithms.
