  This paper aims to propose a two-step approach for day-ahead hourly
scheduling in a distribution system operation, which contains two operation
costs, the operation cost at substation level and feeder level. In the first
step, the objective is to minimize the electric power purchase from the
day-ahead market with the stochastic optimization. The historical data of
day-ahead hourly electric power consumption is used to provide the forecast
results with the forecasting error, which is presented by a chance constraint
and formulated into a deterministic form by Gaussian mixture model (GMM). In
the second step, the objective is to minimize the system loss. Considering the
nonconvexity of the three-phase balanced AC optimal power flow problem in
distribution systems, the second-order cone program (SOCP) is used to relax the
problem. Then, a distributed optimization approach is built based on the
alternating direction method of multiplier (ADMM). The results shows that the
validity and effectiveness method.
