  To capture the stochastic characteristics of renewable energy generation
output, the chance-constrained unit commitment (CCUC) model is widely used.
Conventionally, analytical solution for CCUC is usually based on simplified
probability assumption or neglecting some operational constraints, otherwise
scenar-io-based methods are used to approximate probability with heavy
computation burden. In this paper, Gaussian mixture model (GMM) is employed to
characterize the correlation between wind farms and probability distribution of
their forecast errors. In our model, chance constraints including reserve
sufficiency and branch power flow bounds are ensured to be satisfied with
pre-determined probability. To solve this CCUC problem, we propose a Newton
method based procedure to acquire the quantiles and transform chance
constraints into deterministic constraints. Therefore, the CCUC model is
efficiently solved as a mixed-integer quadratic programming problem. Numerical
tests are performed on several systems to illustrate efficiency and scalability
of the proposed method.
