  The extensive penetration of wind farms (WFs) presents challenges to the
operation of distribution networks (DNs). Building a probability distribution
of the aggregated wind power forecast error is of great value for decision
making. However, as a result of recent government incentives, many WFs are
being newly built with little historical data for training distribution models.
Moreover, WFs with different stakeholders may refuse to submit the raw data to
a data center for model training. To address these problems, a Gaussian mixture
model (GMM) is applied to build the distribution of the aggregated wind power
forecast error; then, the maximum a posteriori (MAP) estimation method is
adopted to overcome the limited training data problem in GMM parameter
estimation. Next, a distributed MAP estimation method is developed based on the
average consensus filter algorithm to address the data privacy issue. The
distribution control center is introduced into the distributed estimation
process to acquire more precise estimation results and better adapt to the DN
control architecture. The effectiveness of the proposed algorithm is
empirically verified using historical data.
